CP 63.13330.2012

RUSSIAN FEDERATION MINISTRY OF REGIONAL DEVELOPMENT

CODE OF PRACTICE SP 63.13330.2012

CONCRETE AND REINFORCED CONCRETE STRUCTURES GENERAL

Updated edition

SNiP 52-01-2003

Official Publication

Moscow, 2012

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CP 63.13330.2012

Foreword

The objectives and principles for standardization in the Russian Federation were established by the Federal Law of December 27, 2002 No. 184-FZ “Technical Regulation”, while the regulations were established by the Russian Federation Government resolution “Procedure for Development and Approval of Summaries of Regulations” dated November 19, 2008.

Information on this Code of Practice

1 AUTHORS: A.A. Gvozdev Research Institute of Reinforced Concrete, NITs Construction OJSC

2 SUBMITTED by Technical Committee for Standardization TK 465, "Construction".

3 PREPARED for approval by the Department of Architecture, Construction, and Urban Development Policies.

4 APPROVED by Russian Federation Ministry of Regional Development (Minregion of Russia) on December 29,

2011 No. 635/8 and effective as of January 1, 2013.

5 REGISTERED with the Federal Agency for Technical Regulation and Metrology (Rosstandart). Review of SP

63.13330.2011 “SNiP 52-01-2003 Concrete and Reinforced Concrete Structures. Basic provisions.

Information about amendments to this Code of Practice will be summarized in the annual Index of National Standards. The text of these amendments and revisions will be published in the appropriate monthly Indices of National Standards. In case this Code of Practice is amended, superseded or cancelled, a notice to that effect will be published in the appropriate monthly Index of National Standards. Relevant information, notices, and text will also be available to the general public at the official Internet website of the originator (the Ministry of Regional Development of the Russian Federation).

© Minregion of Russia, 2011

This regulation may not be reproduced, copied or distributed in whole or in part as an official publication in Russian Federation territory without the permission of Minregion of Russia.

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Contents

1 Scope.................................................................................................................................................................22 Regulatory References......................................................................................................................................23 Terms and Definitions.......................................................................................................................................24 General Requirements for Concrete and Reinforced Concrete Structures.......................................................25 Requirements for Analysis of Concrete and Reinforced Concrete Structures..................................................2

5.1 General.......................................................................................................................................................25.2 Requirements for strength analysis of concrete and reinforced concrete elements...................................25.3 Requirements for analysis of reinforced concrete elements according to crack formation.......................25.4 Requirements for crack spread analysis of reinforced concrete elements.................................................25.5 Requirements for deformation analysis of reinforced concrete elements..................................................2

6 Materials for concrete and reinforced concrete structural elements.................................................................26.1 Concrete.....................................................................................................................................................26.2 Reinforcement............................................................................................................................................2

7 Concrete structures............................................................................................................................................27.1 Strength Analysis of Concrete Members...................................................................................................2

8 Concrete and reinforced concrete structures without rebar prestressing..........................................................28.1 Limit state analysis of members of reinforced concrete structures............................................................28.2. Analysis of Members of Reinforced Concrete Structures for Group 2 Limit States................................2

9. Prestressed Reinforced Concrete Structures....................................................................................................29.1. Prestress in Reinforcements......................................................................................................................29.2. Analysis of Members of Prestressed Reinforced Concrete Structures for Group 1 Limit States.............29.3. Analysis of Prestressed Members of Reinforced Concrete Structures for Group 2 Limit States.............2

10 Structural Requirements..................................................................................................................................210.1 General.....................................................................................................................................................210.2 Requirements for Geometric Dimensions................................................................................................210.3 Requirements for Reinforcement.............................................................................................................210.4 Engineering the main reinforced concrete load-bearing structures.........................................................2

11 Requirements for Fabrication, Erection, and Service of Concrete and Reinforced Concrete Structures.......211.1 Concrete...................................................................................................................................................211.2 Reinforcement..........................................................................................................................................211.3 Formwork.................................................................................................................................................211.4 Concrete and reinforced concrete structures............................................................................................211.5 Quality control.........................................................................................................................................2

12 Requirements for Restoring and Strengthening Reinforced Concrete Structures...........................................212.1 General.....................................................................................................................................................212.2 Onsite Surveys of Structures....................................................................................................................212.3 Verification Calculations for Structures..................................................................................................212.4 Strengthening of Reinforced Concrete Structures...................................................................................2

13 Fatigue analysis of reinforced concrete structures.......................................................................................2

Appendix A (reference) Basic Alphanumeric Codes...........................................................................................2Appendix B (for reference) Design of Embedded Parts.....................................................................................2Appendix C (B) (reference) Analysis of structural systems................................................................................2Appendix E (reference) Analysis of Columns with Round and Annular Sections..............................................2Appendix F (reference) Analysis of Concrete Keys............................................................................................2Appendix G (reference) Analysis of Short Cantilevers.......................................................................................2Appendix H (reference) Analysis of Prefabricated/Cast-in-place (Composite) Structures.................................2

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Annex K (reference) Factoring in Confinement Reinforcement in Analysis of Eccentrically Compressed Members Based on the Nonlinear Strain Model..................................................................................................2References............................................................................................................................................................2

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CP 63.13330.2012

Introduction

This summary of regulations was developed subject to the mandatory requirements established in the Federal Laws of December 27, 2002 No. 184-FZ “Technical Regulation” and of December 30, 2009 No. 384-FZ “Technical Regulation on the Safety of Buildings and Structures” and contains the requirements for analysis and design of concrete and reinforced concrete structures for factory/industrial and public occupancies and structures.

This summary of regulations was developed by a team of authors at the A.A. Gvozdev Scientific Research Institute of Reinforced Concrete OAO NITs Construction (project manager doctor in technical sciences T. A. Mukhamediev, doctors in technical sciences A.S. Zalesov, A. I. Zvezdov, E.A. Chistyakov, candidate in technical sciences S.A. Zenin) with the participation of the Russian Academy of Architectural and Construction Sciences (doctors in technical sciences V.M. Bondarenko, N.I. Karpenko and V.I. Travush) and OAO TsNIIpromzdaniy (doctors in technical sciences E.N. Kodysh, N.N. Trekin, engineer I.K. Nikitin).

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CP 63.13330.2012

CODE OF PRACTICE

CONCRETE AND REINFORCED CONCRETE STRUCTURES GENERAL

Concrete and won concrete constructionDesign requirements

Effective date 01.01.2013

1 Scope

This summary of regulations applies to the design of concrete and reinforced concrete structural elements of buildings and structures operated under the climate conditions of Russia (where systematically exposed to temperatures not exceeding 50 °С and not lower than minus 70 °С), in a nonaggressive medium.

This summary of regulations establishes the requirements for the design of concrete and reinforced concrete structures made of heavyweight, fine-grained, lightweight, cellular and self-stressing.

The requirements of this summary of regulations shall not apply to the design of composite reinforced concrete structures, fiber reinforced concrete structures, precast and cast-in-place structures, concrete and reinforced concrete structural components of hydraulic structures, bridges, road pavements and other special structures, as well as for structures made of concretes with medium density of less than 500 and more than 2500 kg/m3, polymer concretes, concretes on limestone, slag and mixed binders (except cellular concrete used in them), concretes on gypsum and special binders, and porous concrete.

This summary of regulations does not contain the requirements for the design of specific structural elements (hollow slabs, structural elements with notches, caps, etc.).

2 Regulatory References

This Code of Practice makes reference to the following normative (regulatory) documents:SP 14.13330.2011, SNiP II-7-81*, Construction in Seismic RegionsSP 16.13330.2011, SNiP II-23-81* Structural SteelSP 20.13330.2011, SNiP 2.01.07-85* Loads and EffectsSP 22.13330.2011, SNiP 2.02.01-83*, Building and Structure FoundationsSP 28.13330.2012, SNiP 2.03.11-85, Corrosion Protection of Building StructuresSP 48.13330.2011, SNiP 12-01-2004 Construction ManagementSP 50.13330.2012, SNiP 23-02-2003 Thermal Performance of BuildingsSP 70.13330.2012, SNiP 3.03.01-87: Supporting and Enclosing Structures

Official Publication

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SP 122.13330.2012, SNiP 32-04-97 Railroad and Motor Road TunnelsSP130.13330.2012, SNiP 3.09.01-85. The Manufacture of Precast Reinforced Concrete Structures and

ProductsSP 131.13330.2012 SNiP 23-01-99 Construction ClimatologyGOST R 52085-2003 Formwork. General SpecificationsGOST R 52086-2003 Formwork. Terms and DefinitionsGOST R 52544-2006 ”Weldable Deformed Reinforcing Rolled Products of Classes A500C and

B500C for Reinforcement of Reinforced Concrete Structures"GOST R 53231-2008 Concretes. Regulations on Strength Control and AssessmentGOST R 54257-2010 “Reliability of Building Structures and Foundations”. Basic Provisions and

Requirements.GOST 4.212-80 System of Design Documents for Construction. Construction. Concretes.

Nomenclature of parametersGOST 535-2005 Section and Shape Rolled Stock Made From Ordinary Quality Carbon Steel. General

Specifications.GOST 5781-82 Hot-Rolled Steel for Reinforcement of Reinforced Concrete Structures. Technical

Specifications.GOST 7473-94 Concrete Mixes. Technical Specifications.GOST 8267-93 Crushed Stone and Gravel From Dense Rock for Construction Work. Technical

Specifications.GOST 8736-93 Sand for Construction Work. Technical Specifications. GOST 8829-94 Precast Reinforced Concrete and Concrete Construction Products. Methods of Load

Testing. Rules for Assessing Strength, Rigidity, and Crack ResistanceGOST 10060.0-95 Concretes. Methods of Determining Frost Resistance. Basic RequirementsGOST 10180-90 Concretes. Methods of Determining Strength Using Control SpecimensGOST 10181-2000 Concrete Mixes. Testing Methods.GOST 10884-94 Thermo-Mechanically Treated Steel Bars for Reinforced Concrete Structures.

Technical Specifications.GOST 10922-90 Welded Reinforcement and Embedded Units, Weld Splices for Reinforcement and

Embedded Units in Reinforced Concrete Structures. General Specifications.GOST 12730.0-78 Concretes. General Requirements for Methods of Determining Density, Moisture

Content, Water Absorption Capacity, Porosity, and Water Impermeability GOST 12730.1-78 Concretes. Methods for Determining Density GOST 12730.5-84 Concretes. Methods for Determining Water Impermeability GOST 13015-2003 Reinforced Concrete and Concrete Products for Construction. General Technical

Requirements. Requirements for Acceptance, Labeling, Transportation and Storage.GOST 14098-91 Weld Splices for Reinforcement and Embedded Units in Reinforced Concrete

Structures. Types, Design, and DimensionsGOST 17624-87 Concretes. Ultrasonic Method of Strength Testing GOST 22690-88 Concretes. Strength Evaluation by Mechanical Nondestructive Testing MethodsGOST 23732-79 Water for concretes and mortars. Technical Specifications.GOST 23858 79 Butt and T-Welds for Reinforcement

Reinforced concrete structures. Ultrasound methods of quality control. Rules of acceptanceGOST 24211-91 Concrete admixtures. General Technical Requirements.

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GOST 25192-82 Concretes. Classification and general technical requirementsGOST 25781-83 Steel forms for fabricating reinforced concrete structures. Technical Specifications.GOST 26633-91 Heavy and fine-aggregate concretes. Technical Specifications.GOST 27005-86 Lightweight and foam concretes. Rules for measuring average densityGOST 27006-86 Concretes. Rules for selecting compositionsGOST 28570-90 Concretes. Methods for determining strength from specimens taken from structuresGOST 30515-97 Cements. General SpecificationsN o t e : When using this code, it is advisable to verify that the standards referenced herein are still in effect by using

the public information system on the official website of the national standardization authority of the Russian Federation or the annual information directory National Standards, which is published as of January 1 of the current year, and the applicable monthly information directories published in the current year. If a reference document has been replaced or revised, the replacement / revised version of the document should be followed when using this Standard. If a referenced document has been revoked without having been superseded, then the provision that cites this reference shall remain applicable to the extent not involving said reference.

3 Terms and Definitions

This Standard uses the following terms and definitions:3.1 Reinforcement anchorage: enablement of the reinforcement to take up the forces acting on it by

taking it to a certain length beyond the design cross section or arranging special anchors at the ends.3.2 Structural reinforcement: reinforcement embedded without analysis out of structural

considerations.3.3 Prestressed reinforcement: reinforcement in which initial (preliminary) stresses have been

induced during fabrication before external loads are applied during the service stage.3.4 Working reinforcement: reinforcement embedded according to analysis.3.5 Concrete cover layer: the thickness of the layer of concrete from the side of a member to the

nearest surface of the reinforcing bar.3.6 Concrete structures: structures made of concrete without reinforcement or with reinforcement

that is embedded out of structural considerations and is not taken into account during analysis; design forces from all impacts in concrete structures should be taken up by the concrete.

3.7 Structures dispersed reinforced (fiber reinforced concrete, ferrocement): Reinforced concrete structures that include dispersed fibers or narrow mesh made of fine steel wire.

3.8 Reinforced concrete structures Structural elements made of concrete with working and structural reinforcement (reinforced concrete structural elements): the design forces from all effects in reinforced concrete structural components shall be borne by the concrete and the working reinforcement.

3.9 Composite steel/reinforced concrete structures reinforced concrete structures that include steel members other than reinforcement steel that work in unison with the reinforced concrete members.

3.10 Reinforcement ratio of reinforced concrete, μ: The ratio of the cross-sectional area of the reinforcement to the working cross-sectional area of the concrete, expressed in percent.

3.11 Concrete impermeability grade, W The permeability index of the concrete, characterized by the maximum water pressure at which water will not penetrate through a concrete specimen under standard test conditions.

3.12 Concrete grade based on its frost resistance, F The minimum number (specified by the standards) of freezing and thawing cycles of specimens of concrete tested under standard conditions at which they will retain their initial physical mechanical properties within the specified limits.

3.13 Self-stress grade of Sp: The pre-stress specified by the standards and created in the concrete (MPa) as a result of its expansion at a longitudinal reinforcement ratio, μ = 0.01.

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3.14 Average density grade of concrete, D: The density of concretes (in kg/m3) specified by the standards to which the requirements for thermal insulation apply.

3.15 Massive structural element: Structural elements for which the ratio of the surface exposed to drying (m2) to the total volume (m3) is equal to or less than 2.

3.16 Concrete frost-resistance The capacity of concrete to retain its physical mechanical properties under repeated alternating freezing and thawing, regulated by the freeze resistance grade, F.

3.17 Normal cross section: The cross section of an element by the plane perpendicular to its longitudinal axis.

3.18 Oblique cross section: The cross section of an element by the plane inclined to its longitudinal axis and perpendicular to the vertical plan passing through the element.

3.19 Density of Concrete A characteristic of concrete equal to the ratio of its mass to volume, regulated by the average density grade, D.

3.20 Ultimate force the greatest force that can be taken up by a member, by its cross section, for the assumed material characteristics.

3.21 Permeability of concrete: The capacity of concrete to pas gases or fluids through it in the presence of a pressure differential (regulated by the water impermeability grade W) or to support diffusive permeability of substances dissolved in water in the absence of a pressure differential (regulated by the specified current density and electrical potential).

3.22 Working section height distance from the compressed side of a member to the center of gravity of tensile longitudinal reinforcement.

3.23 Self-stressing of concrete: A stress state occurring in concrete structural elements when hardened as a result of expansion of the cement under conditions that limit this expansion, regulated by the self-stressing grade, Sp.

3.24 Reinforcement lap splices joining the reinforcing bars lengthwise without welding by overlapping the ends of reinforcing bars.

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4 General Requirements for Concrete and Reinforced Concrete Structures

4.1 Concrete and reinforced concrete structures of all types must meet requirements with regard to:Safety;Suitability for service;Longevity;Durability, and any additional requirements that are given in design specifications.4.2 In order to meet safety requirements, structures should have initial characteristics that, with a due

degree of reliability, preclude various design impacts during the construction and service of buildings and facilities from causing any kinds of failures or unserviceability that occasion damage to human life and/or health, to property or the environment.

4.3 To meet serviceability requirements, structures should have initial characteristics that, with a due degree of reliability, preclude various design impacts from causing cracks to form or become excessive in size, or from causing excessive movements, vibrations or other damage that impedes normal service (failure to meet requirements for external appearance of the structure, process requirements for the normal operation of equipment, structural requirements for members to work in unison, and any other requirements prescribed during the design).

Where required, structures should have characteristics meeting requirements for thermal insulation, sound insulation, biological protection, etc.

Requirements for absence of cracks apply to reinforced concrete structures that, with their cross section in full tension, must remain impermeable (to pressurized liquids or gases, radiation impact, etc.), unique structures with elevated durability requirements, and structures exposed to severely corrosive environments, as specified in SP 28.13330.

In other reinforced concrete structures the formation of cracks is permissible, and the requirements placed on them are for limitation of crack width.

4.4 In order to meet durability requirements, structures should have initial characteristics such that for a prescribed lengthy period of time they meet safety and serviceability requirements while exposed to various design impacts on their geometric characteristics and the mechanical properties of their materials (long-term load effects, adverse climatic, process, temperature, and moisture impacts, alternate freeze-thaw, corrosive impacts, etc.).

4.5 The safety, serviceability, and durability of concrete and reinforced concrete structures, together with other requirements laid down in the design specifications, should be guaranteed by satisfying the:

Requirements for the concrete and its components;Requirements for reinforcement;Requirements for analysis of the structures;Structural requirements;Process and operating requirements.The requirements for loads and effects, fire resistance rating, impermeability, freeze-thaw resistance,

limit indicators or deformations (sag, displacement, amplitude of oscillations), the design values of the outdoor air temperature and humidity, on protection of structural elements against aggressive media, etc. are specified by the applicable regulations (SP 20.13330, SP 14.13330, SP 28.13330, SP 22.13330, SP 131.13330, SP 122.13330).

4.6 For designing concrete and reinforced concrete structures, the reliability of the structures should be defined in accordance with GOST R 54257 by the semi-probabilistic method, using the design loads and

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impacts and design characteristics of the concrete and reinforcement (or structural steel) that are calculated by applying respective partial reliability factors to the standard values of those characteristics as appropriate to the criticality level of the buildings or facilities.

The specified values of the loads and effects, load safety margin, structural function safety margin, and the division of the loads into dead and live loads (sustained and short-term) are specified by the applicable regulations for structural elements (SP 20.13330).

The design loads and impacts should be defined depending on the type of design limiting state and the design situation.

The reliability of the design material characteristics should be defined depending on the design situation and the danger of achieving the corresponding limiting state, and should be adjusted using the reliability factors for the concrete and reinforcement (or structural steel).

Analysis of concrete and reinforced concrete structures can be performed for a specified reliability value based on a full probabilistic analysis if sufficient data is available on the variability of the basic factors included in the analysis relationships.

5 Requirements for Analysis of Concrete and Reinforced Concrete Structures

5.1 General

5.1.1 Analysis of concrete and reinforced concrete structures should be performed in accordance with GOST 27751 by the method of limiting states, including:

group 1 limiting states leading to the complete unserviceability of the structures;group 2 limiting states that impede normal service of the structures or reduce the durability of

buildings and facilities compared with their planned service life.Analysis should ensure the reliability of buildings or facilities for their entire service life, as well as

during the performance of any work, in accordance with the requirements placed on them.Analysis for group 1 limiting states should include: Strength analysisShape stability analysis (for thin-walled structures)Position stability analysis (overturning, sliding, floating) Strength analyses for concrete and reinforced

concrete structures should be based on the condition that the forces, stresses, and strains in the structures due to various impacts, taking into account the initial stressed state (prestressing, thermal and other impacts) do not exceed the corresponding values defined by standards.

Shape stability analyses for a structure, and also position stability analyses (taking account of the combined operation of the structure and foundation, their strain properties, shear resistance along the contact with the foundation, and other aspects) should conform to regulatory instructions for individual types of structures.

Where required, depending on the type and purpose of the structure, analyses should be made for limiting states involving events that make it necessary to take the structure out of service (excessive strains, shifts in joints, and other events).

Analysis for group 2 limiting states should include:Crack formation analysisCrack width analysisStrain analysisCrack formation analyses for concrete and reinforced concrete structures should be such that the

forces, stresses, and strains in the structures due to various impacts do not exceed their respective ultimate values that are absorbed by the structure on the formation of cracks.

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Crack width analyses for reinforced concrete structures should be such that the crack width in the structure due to various impacts does not exceed the maximum permissible values defined depending on the requirements placed on the structure, its service conditions, environmental impacts, and the material characteristics, including corrosion behavior of the reinforcement.

Strain analysis of concrete and reinforced concrete structures should be such that flexures, rotation angles, displacements, and vibration amplitudes of the structures caused by various impacts do not exceed the respective maximum permissible values.

For structures in which there must be no crack formation, requirements should be laid down for an absence of cracks. In this case, a crack opening analysis is not performed.

For other structures in which crack formation is permissible, a crack formation analysis should be performed to determine the need for a crack width analysis and to take account of cracks in the strain analysis.

5.1.2 Analysis of concrete and reinforced concrete structural elements (linear, planar, three-dimensional and massive) for limit states of the first and second groups is performed for the stresses, forces, deformations and movements calculated from the external effects on the structural elements and the systems of buildings and structures formed by them with allowance for physical nonlinearity (inelastic deformations of concrete and reinforcement), possible formation of cracks and, in the necessary cases, anisotropy, accumulation of damage and geometrical nonlinearity (the influence of deformations on the change in the forces in structural elements). Physical anisotropy and nonlinearity must be considered in the defining relationships between the stresses and deformations (or forces and movements), as well as in the requirements for the strength and crack resistance of the material.

In statically indeterminate structures, account should be taken of the redistribution of forces in system members due to crack formation and the development of inelastic strains in the concrete and reinforcement right up to the appearance of a limiting state in the member. Where analysis methods that account for the inelastic properties of reinforced are not available, and for preliminary analyses with consideration of the inelastic properties of reinforced concrete, it shall be permitted to determine the forces and stresses in statically indeterminate structural elements and systems under the assumption of elastic operation of the reinforced concrete elements. In this case it is recommended that physical nonlinearity be accounted for by adjusting the results of a linear analysis based on empirical research data, nonlinear modeling, analysis results for similar facilities, and expert assessments.

In analyzing structures for strength, strains, and the formation and widening of cracks based on the finite element method, the conditions of strength and crack resistance for all the finite elements comprising the structure, and the conditions of appearance of excessive displacements of the structure, should be checked. For assessing the strength limit state, individual finite elements may be assumed to have failed, unless this results in progressive collapse of the building or facility and if, after the given load ceases to act, the serviceability of the building or facility is retained or can be restored.

Ultimate forces and strains in concrete and reinforced concrete structures should be determined based on analytical models that match as closely as possible the actual physical nature of the structures' operation and materials in the given limit state.

The bearing capacity of reinforced concrete structures capable of withstanding sufficient plastic strains (particularly when reinforcement with an elastic limit is used) may be determined by the ultimate equilibrium method.

5.1.3 In analyses of concrete and reinforced concrete structural elements according to limit states, it is necessary to consider various design situations in compliance with GOST R 54257, including the fabrication, transportation and erection stages, emergencies and fires.

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5.1.4 Analyses of concrete and reinforced concrete structures should be performed for all types of loads matching the functional purpose of the buildings and facilities, taking account of environmental effects (climatic impacts and water, for structures that are surrounded by water) and, where required, taking account of fire impact, process temperature and moisture impacts, and impacts by corrosive chemical environments.

5.1.5 Concrete and reinforced concrete structures should be analyzed for bending moments, longitudinal forces, transverse forces, torsion moments, and local loads.

5.1.6 In the analyses of precast structural elements for the effect of the forces occurring during hoisting, transporting and installation, the load from the weight of the elements should be considered with a dynamic factor equal to:

1.60 for transportation,1.40 for hoisting and installation.It shall be permitted to assume lower, duly justified dynamic factors, but not less than 1.25.5.1.7 Analyses of concrete and reinforced concrete structures should take account of the particular

properties of various types of concrete and reinforcement, the effect on them of the nature of the load and the environment, methods of reinforcement, the combined operation of reinforcement and concrete (in the presence and absence of bonding between the reinforcement and concrete), and the procedure for fabricating structural types of reinforced concrete members for buildings and facilities.

5.1.8 Analysis of prestressed structures should take account of the initial (preliminary) stresses and strains in the reinforcement and concrete, prestressing losses, and aspects of the transfer of prestressing to the concrete.

5.1.9 For cast-in-place structures, strength should be ensured taking account of construction joints.5.1.10 Analysis of precast structures should ensure the strength of assembly and butt joints of

precast elements made by joining the steel embedded parts and starter bars and embedding them in concrete.5.1.11 Analysis of planar and spatial structures subjected to force impacts in two mutually

perpendicular directions should examine individual planar or spatial small, typical members singled out from the structure with forces acting along the sides of the member. Where there are cracks, these forces should be determined taking account of the crack locations, axial and tangential stiffness of the reinforcement, stiffness of the concrete (between the cracks and in the cracks), and other aspects. Where there are no cracks, the forces should be determined as for a solid body.

Where cracks are present, the forces may be determined assuming the behavior of the reinforced concrete member to be elastic.

Analysis of members should be performed on the most hazardous cross sections located at an angle to the direction of the forces acting on the member, based on analysis models that take account of the behavior of reinforcement in tension in a crack and the behavior of the concrete between the cracks in a plane stressed state.

5.1.12 Planar and spatial structures may be analyzed for the structure as a whole based on the ultimate equilibrium method, including taking account of the state of strain at the moment of failure, and also using simplified analysis models.

5.1.13 Analysis of massive structures subjected to force impacts in three mutually perpendicular directions should examine individual small, typical members singled out from the structure with forces acting along the edges of the member. Here the forces should be determined based on assumptions similar to those used for planar members (see 5.1.11).

Analysis of members should be performed on the most hazardous cross sections located at an angle to the direction of the forces acting on the member, based on analysis models that take account of the behavior of the concrete and reinforcement in a three-dimensional state of stress.

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5.1.14 For structures with a complex configuration (e.g. spatial), in additional to mathematical methods for predicting bearing capacity, crack resistance, and deformability, the test results from physical models may also be used.

5.2 Requirements for strength analysis of concrete and reinforced concrete elements

5.2.1 Strength analysis of concrete and reinforced concrete members should be performed:Over normal cross sections (under the effects of bending moments and longitudinal forces) – using a

nonlinear deformation model. For simple types of reinforced concrete structural elements (rectangular, with I-shaped and H-shaped cross sections with reinforcement located at the upper and lower edges of the cross section), it shall be permitted to perform the analysis according to limit forces;

Over inclined cross sections (under the effects of transverse forces), on three-dimensional cross sections (under the effects of torsional moments), for the local action of a load (local compression, punching shear) – using ultimate forces.

Strength analysis of short reinforced concrete members (short cantilevers, etc.) should be based on a shell and rod model.

5.2.2 Strength analysis of concrete and reinforced concrete members for ultimate forces should be such that the force F from external loads and impacts in the given cross section does not exceed the ultimate force Fult that can be taken up by the member in that cross section

F≤ Fult. (5-1)

Strength analysis of concrete members

5.2.3 Depending on the conditions under which they function and the requirements placed on them, concrete members should be analyzed in normal cross sections for ultimate forces without taking account (5.2.4) or taking account (5.2.5) of the concrete resistance in the zone under tension.

5.2.4 Without taking account of the concrete resistance in the tension zone, analysis of eccentrically compressed concrete members should be made for values of eccentricity of the longitudinal force not exceeding 90% of the distance from the center of gravity of the cross section to the most compressed fiber. The ultimate force that can be taken up by a member should be determined from the design resistances of the concrete to compression Rb that are evenly distributed along the arbitrary compressed zone of the cross section with a center of gravity that coincides with the point of application of the longitudinal force.

For massive concrete structures a triangular diagram of stresses that do not exceed the design value of concrete resistance to compression Rb should be assumed in the compressed zone. Here the eccentricity of the longitudinal force relative to the center of gravity of the cross section should not exceed 65% of the distance from the center of gravity to the most compressed fiber of the concrete.

5.2.5 Taking into account the concrete resistance in the tension zone, analysis should be made of eccentrically compressed concrete elements with a longitudinal force eccentricity greater than that in 5.2.4, flexural concrete members (those that are permitted to be used), and eccentrically compressed members with the same longitudinal force eccentricity as described in 5.2.4, but in which crack formation is not permissible under service conditions. The ultimate force that can be taken up by the cross section of a member should be determined as for an elastic body under maximum tensile stresses equal to the design value of the concrete resistance to tension Rbt.

5.2.6 Analysis of eccentrically compressed concrete members should take account of the effect of longitudinal flexure and random eccentricities.

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Analysis of reinforced concrete members for strength of normal cross sections

5.2.7 Analysis of reinforced concrete members for ultimate forces should determine the ultimate forces that can be taken up by the concrete and reinforcement in a normal cross section based on the following assumptions:

Concrete resistance to tension is assumed to be equal to zero.Concrete resistance to compression is represented as the stresses that are equal to the design concrete

resistance to compression and are evenly distributed along the concrete compressed zone.Tensile and compressive stresses in the reinforcement are assumed to be no greater than the design

resistance to tension and compression respectively.5.2.8 Analysis of reinforced concrete members according to a nonlinear strain model should be based

on stress-strain curves of the concrete and reinforcement proceeding from the plane section hypothesis. The strength criterion of normal cross sections is the achievement of ultimate relative strains in the concrete or reinforcement.

5.2.9 Analysis of eccentrically compressed members should take account of random eccentricity and the effect of longitudinal flexure.

Analysis of reinforced concrete members for strength of inclined cross sections

5.2.10 Analysis of reinforced concrete members for strength of inclined cross sections over an inclined cross section for the effect of a transverse force, over an inclined cross section for the effect of bending moment, and over a strip between inclined cross sections for the effect of a transverse force.

5.2.11 In the analysis of a reinforced concrete member for strength of an inclined cross section under the action of transverse force, the ultimate transverse force that can be taken up by the member in the inclined cross section should be defined as the sum of the ultimate transverse forces taken up by the concrete in the inclined cross section and by the transverse reinforcement that intersects the inclined cross section.

5.2.12 In the analysis of a reinforced concrete member for strength of an inclined cross section under the action of bending moment, the ultimate moment that can be taken up by the member in the inclined cross section should be defined as the sum of the ultimate moments taken up by the longitudinal and transverse reinforcement intersecting the inclined cross section relative to the axis passing through the point of application of the resultant forces in the compressed zone.

5.2.13 In the analysis of a reinforced concrete member along a strip between inclined cross sections for the action of transverse force, the ultimate transverse force that can be taken up by the member should be defined based on the strength of the inclined concrete strip that is exposed to compressive forces along the strip and the tensile forces from the transverse reinforcement intersecting the inclined strip.

Analysis of reinforced concrete members for strength of three-dimensional cross sections

5.2.14 In the analysis of reinforced concrete members for strength of three-dimensional cross sections, the ultimate torsional moment that can be taken up by the member should be defined as the sum of the ultimate torsional moments taken up by the longitudinal and transverse reinforcement located on each side of the member and intersecting the three-dimensional cross section. In addition, analysis should be performed for the strength of a reinforced concrete member along the concrete strip that is located between the three-dimensional cross sections and is exposed to compressive forces along the strip and tensile forces from the transverse reinforcement intersecting the strip.

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CP 63.13330.2012

Analysis of reinforced concrete members for local load action

5.2.15 In the analysis of reinforced concrete members for local compression, the ultimate compressive force that can be taken up by a member should be determined based on the concrete resistance in a three-dimensionally stressed state created by the surrounding concrete and lateral reinforcement, if any.

5.2.16 Analysis for punching shear should be made for planar reinforced concrete members (slabs) under the action of concentrated force and moment in the punching zone. The ultimate force that can be taken up by a reinforced concrete member during punching should be defined as the sum of the ultimate forces taken up by the concrete and the lateral reinforcement in the punching zone.

5.3 Requirements for analysis of reinforced concrete elements according to crack formation

5.3.1 Analysis of reinforced concrete members for crack formation should be performed using ultimate forces or a nonlinear strain model. Analysis for the formation of inclined cracks should be performed using ultimate forces.

5.3.2 Crack formation analysis of reinforced concrete members using ultimate forces should be such that the force F from external loads and impacts in the given cross section does not exceed the ultimate force Fcrc that can be taken up by the reinforced concrete member when cracks are formed

F≤ Fcrc,ult. (5-2)

5.3.3 The ultimate force taken up by a reinforced concrete member when normal cracks are formed should be defined based on analysis of the reinforced concrete member as a solid body taking account of elastic strains in the reinforcement and inelastic strains in the tensile and compressed concrete under maximum normal tensile stresses in the concrete equal to the design values of the concrete tensile resistance Rbt.

5.3.4 Analysis of reinforced concrete members for the formation of normal cracks using a nonlinear strain model should be based on stress-strain curves of the reinforcement and tensile and compressed concrete, and the plane section hypothesis. The criterion of crack formation is the achievement of ultimate relative strains in the tensile concrete.

5.3.5 The ultimate force that can be taken up by a reinforced concrete member when inclined cracks form should be determined based on an analysis of the reinforced concrete member as a solid elastic body and the criterion of concrete strength in a plane compression-tension state of stress.

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CP 63.13330.2012

5.4 Requirements for crack spread analysis of reinforced concrete elements

5.4.1 An analysis of reinforced concrete members for the width of various types of cracks should be performed in those cases where an analysis check for the formation of cracks has shown that cracks are formed.

5.4.2 Crack width analysis should be such that the crack width due to an external load acrc does not exceed the maximum permissible value of crack width acrc,ult.

асrс≤ асrс,ult. ( 5 - 3 )

5.4.3 The width of normal cracks is calculated as the product of the average relative strains of the reinforcement in the segment between the cracks and the length of that segment. The average relative strains of the reinforcement between the cracks should be calculated taking account of the behavior of the tensile concrete between the cracks. The relative strains of reinforcement in the crack should be calculated by a conventional elastic analysis of the reinforced concrete member with cracks using an adjusted strain modulus of the compressed concrete that is determined taking account of the effect of inelastic strains of the concrete in the compression zone, or else by a non-linear strain model. The distance between the cracks should be defined so that the force difference in the longitudinal reinforcement in the cross section with the crack and between the cracks is absorbed by the bonding forces of the reinforcement with the concrete over the length of that segment.

The width of normal cracks should be defined taking account of the nature of the load action (recurrence, duration, etc.) and the type of reinforcement profile.

5.4.4 Maximum permissible crack width should be defined based on aesthetic considerations, the existence of requirements for permeability of the structures, and depending on the duration of the load action, the type of reinforcement steel, and whether it is prone to corrosion in the crack.

5.5 Requirements for deformation analysis of reinforced concrete elements

5.5.1 Strain analysis of reinforced concrete members should be such that deflections or displacements of the structures f due to the action of an external load do not exceed the maximum permissible values of deflections or displacements fult.

f≤ fult (5.4)

5.5.2 Deflections or displacements of reinforced concrete structures should be defined according to the general rules of structural analysis depending on the bending, shear, and axial strain (stiffness) characteristics of the reinforced concrete member in the cross sections along its length (flexure, shear angles, etc.).

5.5.3 In cases where deflections of the reinforced concrete members basically depend on bending strains, the deflection values should be defined according to the stiffness or flexure of the members.

The flexure of a reinforced concrete member should be defined as the quotient after division of the bending moment by the flexural stiffness of the reinforced concrete cross section.

The rigidity of the cross section of the reinforced concrete element examined is determined using the general laws of resistance of materials; for a cross section without cracks - as for a conditionally elastic element, while for a cross section with cracks - as for a conditionally elastic element with cracks (assuming a linear dependence between the stresses and deformations). The effect of concrete inelastic strains should be taken into account by means of an adjusted concrete strain modulus, and the effect of the operation of the tensile concrete between cracks by means of an adjusted reinforcement strain modulus.

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CP 63.13330.2012

Strain analysis of reinforced concrete members taking account of cracks should be performed in cases where an analysis check for the formation of cracks has shown that cracks are formed. Otherwise, a strain analysis should be made as for a reinforced concrete member without cracks.

The flexure and longitudinal strains of a reinforced concrete member should also be defined using a nonlinear strain model based on equilibrium equations for the external and internal forces acting in a normal cross section of the member, the plane section hypothesis, stress-strain curves of the concrete and reinforcement, and the average strains in the reinforcement between the cracks.

5.5.4 Strain analysis of reinforced concrete members should take account of the duration of loads specified in the relevant regulatory documents.

When calculating the flexure, the rigidity of sections of an element shall be determined with consideration of the presence or absence of cracks perpendicular to the longitudinal axis of the element in the extended zone of their cross section.

5.5.5 The maximum allowable deformations shall be selected according to the instructions in 8.2.20. Under the action of dead loads and continuous and short-term live loads, the deflection of reinforced concrete members in all cases should not exceed 1/150 of the span and 1/75 of the cantilever overhang.

6 Materials for concrete and reinforced concrete structural elements

6.1 Concrete

6.1.1 Concrete and reinforced concrete structures designed according to the present Instructions should utilize the following structural modified concretes:

Heavyweight, medium density from 2200 to 2500 kg/m3 inclusively;Fine-grained, medium density from 1800 to 2200 kg/m3;Lightweight;Cellular;Self-stressing.6.1.2 When designing concrete and reinforced concrete facilities in accordance with the

requirements prescribed for specific structures, the type of concrete and its standard and controlled quality parameters must be defined (GOST 25192, GOST 4.212).

6.1.3 The basic standardized and controlled quality parameters for concrete are:class according to compressive strength (B)class according to axial tension strength (Bt)grade of frost resistance (F)grade of water impermeability (W)grade of average density (D)Self-stress grade SР.The compressive strength class В of the concrete corresponds to the cubic strength of the concrete in

compression (MPa) with a 0.95 confidence interval (the specified cubic strength).The axial tension strength class В of the concrete corresponds to the cubic strength of the concrete in

axial tension (MPa) with a 0.95 confidence interval (the specified strength of the concrete).A different probability value of concrete compressive strength and axial tension strength may be used

where specified in the regulatory requirements for certain special types of facilities.The freeze-thaw resistance grade of the concrete F corresponds to the minimum number of freezing

and thawing cycles that the specimen withstands in standard testing.

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CP 63.13330.2012

The water impermeability grade W of the concrete corresponds to the maximum water pressure (in MPa-10"1), that a concrete specimen withstands in tests.

The average density grade D of the concrete corresponds to the weight by volume of the concrete (kg/m3).

The self-stress grade of self-stressing concrete is the pre-stress in the concrete (MPa) created as a result of its expansion at a longitudinal reinforcement ratio μ = 0.01.

Where required, additional concrete quality parameters should be defined for thermal conductance, thermal resistance, fire resistance, corrosion resistance (both for the concrete itself and its reinforcement), biological protection, and other requirements placed on the structure (SNiP 50.13330-02, SNiP 2.03.11).

The specified quality indicators of the concrete shall be ensured by proper design of the composition of the concrete mix (on the basis of the specifications for the materials for the concrete and the requirements for the concrete), the technology for preparing the concrete mix and performing the concrete work when fabricating (constructing) concrete and reinforced concrete items and structural elements. The specified quality indicators of the concrete shall be monitored both during work and directly when fabricating the structural elements.

The required concrete parameters should be defined during the design of concrete and reinforced concrete structures according to analysis and the service conditions, factoring in the various environmental impacts and the protective properties of the concrete with respect to the chosen type of reinforcement.

The compressive strength class В of the concrete shall be specified for all types of concrete and structural elements.

A concrete axial tension strength class Bt should be designated in cases where this characteristic is of prime importance and is controlled during fabrication.

A concrete frost resistance grade F should be designated for structures that are exposed to alternate freezing and thawing.

A concrete water permeability grade W should be designated for structures that are required to have limited water permeability.

The self-stress grade of the concrete must be specified for self-stressing structural elements when this characteristic is considered in the analysis and monitored during work.

6.1.4 Concretes of the following classes and grades indicated in Tables 6.1-6.6 shall be provided for concrete and reinforced concrete structural elements.

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CP 63.13330.2012

T a b l e 6 . 1Concrete Compressive Strength Classes

Heavy Concrete B3.5; B5; B7.5; B10; B12.5; B15; B20; B25; B30; B35; B40; B45; B50; B55; B60; B70; B80; B90; B100

Self-stressing concrete B20; B25; B30; B35; B40; B45; B50; B55; B60; B70Fine-grained concrete of groups:А – natural curing or subjected to heat treatment at atmospheric pressure

В3.5; В5; В7.5; В10; В12.5; В15; В20; В25; В30; В35; В40

B- autoclaved В15; В20; В25; В30; В35; В40; В45; В50; В55; В60Lightweight concrete with average density grades:D800, D900 В2.5; В3.5; В5; В7.501000,01100 В2.5; В3.5; В5; В7.5; В10; В 12.501200,01300 В2.5; В3.5; В5; В7.5; В10; В12.5; В15; В2001400,01500 В3.5; В5; В7.5; В10; В12.5; В15; В20; В25; В3001600, 01700 В7.5; В10; В12.5; В15; В20; В25; В30; В35; В4001800, 01900 В15; В20; В25; В30; В35; В4002000 В25; В30; В35; В40Cellular concrete with average density grades:

Autoclaved Non-autoclaved

0500 В1.5;В2; В2.5 -

0600 В1.5; В2; В2.5; В3.5 В1.5; В20700 В2;В2.5;ВЗ.5;В5 В1.5; В2; В2.5D800 В2.5; В3.5; В5; В7.5 В2; В2.5; В3.50900 В3.5; В5; В7.5; В10 В2.5; В3.5; В5D1000 В7,5; В10; В12,5 В5;В7.501100 В10; В12.5; В15; В17.5 В7,5; В1001200 В12.5; В15; В17.5; В20 В10; В12.5

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CP 63.13330.2012

End of Table 6.1

Porous concrete at average density grades:0800, 0900,01000 В2.5; В3.5; В501100,01200,01300 В7.501400 В3.5;В5;В7.5

N o t e – In this summary of regulations, the terms “lightweight concrete and “porous concrete” are used, respectively, to designate lightweight concrete with a dense structure and lightweight concrete with a porous structure (with porosity exceeding 6%).

Table 6.2 – Axial tensile strength classes of concrete

Concrete Axial tension strength classesHeavyweight, self-stressing and fine-grained concretes

В.0.8; В.1.2; В.1.6; В.2.0; 8.2.4; В.2.8; В.3.2; В.3.6; В.4.0

Lightweight Concrete В.0.8; В.1.2; В.1.6; В.2.0; В.2.4; В.2.8; В.3.2

Table 6.3 – Freeze-thaw resistance grades of concrete

Concrete Freeze-thaw resistance gradeHeavyweight, self-stressing and fine-grained concretes

F50; F75; F100; F150; F200; F300; F400; F500;F600; F700; F800; F1000

Lightweight Concrete F25; F35; F50; F75; F100; F150; F200; F300; F400; F500

Cellular and porous concretes F15; F25; F35; F50; F75; F100

Table 6.4 – Water impermeability grades of concrete

Concrete Water impermeability gradesHeavyweight and fine-grained concretes

W2; W4; W6; W8; W10; W12; W14; W16; W18; W20

Lightweight Concrete W2; W4; W6; W8; W10; W12N o t e - For self-stressing concrete, the water impermeability grades shall be not lower than

W12 and may not be indicated in the plans.

Table 6.5 – Average density grades of concrete

Concrete Average density gradesLightweight Concrete 0800; 0900; 01000; 100; 01200; 01300; 01400; 01500;

01600; 01700; 01800; 01900; 02000Cellular concrete D500; D600; D700; D800; D900; D1000; D1100; D1200Porous concrete D800; D900; D1000; D1100; D1200; D1300; D1400

Table 6.6 Self-stress grades of concrete

Concrete Self-stress gradesSelf-stressing concrete 8,0,6; 8,0,8; 8,1; 8,, 1,2; 8,1,5; 8,2; 8,3; 8,4.

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CP 63.13330.2012

6.1.5 The design age of the concrete, i.e., the age at which the concrete must acquire all of the quality indicators shall be specified in the design according to the possible actual schedules for loading of structural elements with design loads, with allowance for the methods for construction of structures and the concrete curing conditions. If this data is unavailable, the concrete class should be defined with a design age of 28 days.

The specified delivery and transfer strength of the concrete in precast structural elements shall be specified in conformity with GOST 13015 and the standards for the specific types of structural elements.

6.1.6 A compressive strength class of concrete of at least B15 shall be used for reinforced concrete structural elements.

The compressive strength class of the concrete for prestressed reinforced concrete structural elements shall be selected according to the type and class of the stressed reinforcement, but not lower than В20.

The transfer strength of the concrete Kbр (the strength of the concrete at the time it is compressed, monitored like the compressive strength class) shall be at least 15 MPa and not less than 50% of the selected compressive strength class of the concrete.

6.1.7 It shall not be permitted to use fine-grained concrete for reinforced concrete structural elements subjected to multiple repeated loadings, or for prestressed structural elements with a span of more than 12 m with reinforcing wire of classes В, Вр and K without special experimental justification.

The compressive strength class of fine-grained concrete used for corrosion protection and to ensure adhesion of the stressed reinforcement with the concrete located in the grooves and on the surface of structural elements shall be not less than В20, and not less than B25 for concrete injected into channels.

6.1.8 The freeze-thaw resistance grade of the concrete shall be selected according to the requirements for the structural elements, the operating conditions and the environmental conditions according to SP 28.13330.

For structural elements above ground exposed to atmospheric environmental effects at a design outdoor air temperature below freezing during the winter from -5 °С to -40 °С, the freeze-thaw resistance grade of the concrete shall be no lower than F75. At a design outdoor air temperature above -5 °С, the freeze-thaw resistance grade of the concrete shall not be specified for structural elements above ground.

6.1.9 The water impermeability grade of the concrete shall be selected according to the requirements for the structural elements, the operating conditions and the environmental conditions according to SP 28.13330.

For structural elements above ground exposed to atmospheric environmental effects at a design outdoor air temperature below freezing but above -40 °С, as well as for exterior walls of heated buildings, the freeze-thaw resistance grade of the concrete shall not be specified.

6.1.10 The basic strength characteristics of concrete are the standard values of:concrete resistance to axial compression Rb,n

concrete resistance to axial tension Rbt,n

Specified axial compressive strength (prism strength) and axial tensile strength of concrete (at assigning concrete compressive strength) are assigned based on the compressive strength (B) of concrete, according to Table 6.7.

When determining the axial tensile strength class of concrete Bt, the standard resistance of the concrete to axial tension shall be assumed equal to the numerical designation for the axial tensile strength class of the concrete.

6.1.11. The values calculated for the resistance of the concrete to axial compression and axial tension Rbt shall be determined using the following equations:

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CP 63.13330.2012

(6.1)

(6.1)

where the factors of safety for the concrete in compression, γb, are assumed to be equal to:For Group 1 limit state design:1.3 for heavy, fine-grained, pre-stressed, and light concretes;1.5 for cellular concrete;For Group 2 limit state design: 1,0.where the factors of safety for the concrete in tension γbt, are assumed to be equal to:For Group 1 limit state design when determining the compressive strength class for concrete:1.5 for heavy, fine-grained, pre-stressed, and light concretes;2.3 for cellular concrete;For Group 1 limit state design when determining the tensile strength class for concrete:1.3 for heavy, fine-grained, pre-stressed, and light concretes;For Group 2 limit state design: 1,0.The calculated strength values Rb, Rbt, Rb,ser, Rbt.ser (rounded off) for the concrete as a function of

compressive strength class and axial tensile strength class are given in: For Group 1 limit states, in Tables 6.8 and 6.9; for Group 2 limit states, in Table 6.7.

6.1.12 Where necessary, the calculated strength characteristics of the concrete shall be multiplied by the following service factors γb1 which take into account the functional characteristics of the concrete in the structure (nature of the load, environmental conditions, etc.):

a) γb1 - For concrete and reinforced-concrete structures erected with calculated strength values Rb and Rbt and taking into account the duration of action by the static load:

γb1=1.0 for a short-acting (short-duration) load;γb1 =0.9 for a long-acting (long-term) load; For cellular and aerated concretes, γb1 = 0.85;b) γb2 - For concrete and reinforced-concrete structures erected with calculated strength values Rb and

taking into account the nature of failure in such structures, γb2 = 0.9;c) γb3 – for concrete and reinforced-concrete structures cast in the vertical direction in which concrete

is placed to a thickness greater than 1.5 m, erected with a calculated concrete strength value Rb, γb3 = 0.85 [possible typo in Russian fixed].

d) γb4 - For cellular concrete erected with calculated strength values Rb:γb4= 1.00 for cellular concrete water content 10% or less; γb4= 0.85 for cellular concrete water content greater than 25%; by interpolation for cellular concrete water content greater than or equal to 10% and less than 25%.

The effect of freeze-thaw cycles and temperatures below freezing are taken into account using a service factor γb5 < 1.0. For above-ground structures exposed to ambient atmospheric effects for design-basis cold-season outdoor air temperatures of minus 40 °C or more, γb5 = 1.0 shall be assumed. In all other cases, the factor shall be determined based on the purpose of the structure and ambient conditions as described in special instructions.

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CP 63.13330.2012

Type ConcreteSpecified strengths Rb,n, Rbt,n (MPa) and design strengths of concrete for limit states of the second group Rb,ser, Rbt,ser (MPa) at a compressive strength class

of the concreteВ1.5 В2 В2,5 В3,5 В5 В7.5 В10 В 12.5 В15 В20 В25 В30 В35 В40 В45 В50 В55 В60 В 70 В8 0 В 90 В100

CompressionAxial(prism strength)

Rb,n and Rb, ser

Heavyweight, fine- grained and self-stressing

- - - 2,7 3,5 5,5 7,5 9,5 1 1 15 18,5 22 25,5 29 32 36 39,5 43 50 57 64 71

Lightweight - - 1,9 2.7 3,5 5,5 7,5 9,5 11 15 ?8,5 22 25,5 29Cellular 1,4 1,9 2,4 3,3 4,6 6,9 9,0 10,5 11,5 -

Axial tension Rbt, n and Rbt,

ser

Heavyweight, fine-and self-stressing

- - - 0,39 0,55 0,70 0,85 1,00 1,10 1,35 1,55 1,75 1,95 2,10 2,25 2,45 2,60 2,75 3,00 3.30 3,60 3,80

Lightweight - - 0,29 0,39 0,55 0,70 0,85 1,00 1,10 1,35 1,55 1,75 1,95 2,10Cellular 0,22 0,26 0.31 0,41 0,55 0,63 0,89 1,00 1,05 -

N o t e s1 The strength values are given for cellular concrete with average water content of 10%.2 For fine-grained sand concrete with a fineness modulus of 2.0 or less, and also for lightweight concrete with fine porous filler, the design strengths Rbi shall be multiplied times a

factor of 0.8.3 For porous concrete, and also for expanded clay aggregate concrete, the design strengths Rbt,n, Rbt,ser shall be those for lightweight concrete, multiplied times a factor of 0.7.4 For self-stressing concrete, the values of Rbt,n, Rbt,ser shall be multiplied times a factor of 1.2.

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CP 63.13330.2012

Type Concrete Design strengths of concrete Rb,n, Rbt,n (MPa) for limit states of the first group for a compressive strength class of the concrete

concreteВ 1.5

В2 В2,5 В3,5 В5 В7.5 В10 В 12.5

В15 В20 В25 В30 В35 В40 В45 В50 В55 В60 В 70 В8 0 В90 В100

Compression Axial (prism and strength)Rb

Heavyweight, - - - 2,1 2,8 4,5 6,0 7,5 8,5 11,5 14,5 17,0 19,5 22,0 25,0 27,5 30,0 33,0 37,0 41,0 44,0 47,5fine-grained andSelf-stressing Lightweight - - 1,5 2,1 2,8 4,5 6,0 7,5 8,5 11,5 14,5 17.0 19,5 22,0Cellular 0,95 1,3 1,6 2,2 4,6 6,0 7,0 7,7

Axial tension Rbt

Heavyweight, - - - 0,26 0,37 0,48 0,56 0,66 0,75 0,90 1,05 1,15 1,30 1,40 1,50 1,60 1,70 1,80 1,90 2,10 2,15 2,20fine-and self-stressing Lightweight - - 0,20 0,26 0,37 0,48 0,56 0,66 0,75 0,90 1,05 1,15 1,30 1,40Cellular 0,09 0,12 0,14 0,18 0,24 0.28 0,39 0,44 0,46

N o t e s1The strength values are given for cellular concrete with average water content of 10%.2 For fine-aggregate sand concrete with a fineness modulus of 2.0 or less, as well as for lightweight concrete with fine porous aggregate, the

design resistance values Rbt should be multiplied by a factor of 0.8.3For aerated concrete, as well as for perlite concrete with expanded perlitic sand, the design resistance values Rbt should be assumed as the

values for lightweight concrete multiplied by a factor of 0.7.4For self-stressing concrete, the values of Rbt should be multiplied by a factor of 1.2.5 For class B70-B100 heavyweight concretes, the design values of resistance to axial compression Rb, and resistance to axial tension Rbt, must

include an additional reduction factor γb,br, which accounts for the increased brittleness of high-strength concretes due to reduced creep deformations

and is equal where B is the compressive strength class

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CP 63.13330.2012

Type of resistance Concrete The design values of concrete resistance at ultimate limit stresses Rbt (MPa), with an axial tension strength class of:

В, 0.8 В, 1,2 В, 1,6 В, 2,0 В, 2,4 В, 2,8 В, 3,2Axial tension Rbt Heavyweight, fine-

aggregate, self-stressing and lightweight

0,62 0,93 1,25 1,55 1,85 2,15 2,45

6.1.13 The basic strain characteristics of concrete are the standard values of the:the concrete's ultimate relative axial compression and tension strains (with the concrete in a

homogenous state of stress) b0 and bt0;

Initial modulus of elasticity Eb;

Shear modulus G;

Creep coefficient (curve) φb,cr;Concrete lateral strain coefficient (Poisson's ratio) νb,P;

Concrete linear temperature strain coefficient αbt.6.1.14 The values of the ultimate relative strains of heavyweight, fine-aggregate, and self-

stressing concretes are taken to be equal to:for a short-term load effect:b0 = 0.002 under axial compression;bt0 = 0.0001 under axial tension;under a short-term load effect - per table 6.10, depending the relative ambient air humidity.

T a b l e 6 . 1 0Ambient air humidity, % Relative strains of heavyweight, fine-aggregate, self-stressing concrete under a long-

term load effectunder compression under tension

bo*103 b2*103 bl, red*103 Ebl0*103 Ebl2*103 bl, red*103

Over 75 3,0 4,2 2,4 0,21 0,27 0,1940-75 3,4 4,8 2,8 0,24 0,31 0,22Below 40 4,0 5,6 3,4 0,28 0,36 0,26

N o t e s1 The relative ambient air humidity is specified per SP 131.13330 as the average monthly relative humidity of the

warmest month for the construction area.2 For high-strength concretes, the values of the relative strains Eb2 should be multiplied by the ratio (270—В)/210.

The values of the ultimate relative strains for lightweight, foam, and aerated concretes should be assigned in accordance with special instructions.

It is permitted to take the values of the ultimate relative strains of lightweight concretes under a long-term load effect per table 6.4 with a reduction coefficient [(0.4 + 0.6 р / 2200) > 0.7] (here р - density of concrete.)

6.1.15 The values of the concrete's initial modulus of elasticity upon compression and tension are taken as a function of the concrete's class according to compressive strength В per Table 6.11. The values of the concrete's shear modulus are assumed as equal to 0.4Еb.

Under a long-term load effect, the values of the concrete's strain modulus are determined using the formula

(6.3)

where is the concrete's creep coefficient, which is taken per 6.1.16.

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CP 63.13330.2012

6.1.16 The values of the concrete's creep coefficient - are taken in accordance with the environmental conditions (relative air humidity) and class of the concrete. The values of the creep coefficients of heavyweight, fine-aggregate, and self-stressing concretes are presented in table 6.12.

The values of the creep coefficient of lightweight, foam, and aerated concretes should be assigned in accordance with special instructions.

It is permitted to assign the values of the creep coefficient of lightweight concretes per table 6.12 with a reduction coefficient (ρ / 2200)2.

6.1.17 The value of the concrete's lateral strain coefficient may be taken as

= 0,2.

6.1.18 The value of the concrete's linear temperature strain coefficient given a temperature change from minus 40 °С to plus 50 °С is taken as:

- for heavyweight, fine-aggregate, and self-stressing concretes, and lightweight

concrete with fine, dense aggregate;

- for lightweight concrete with fine, porous aggregate;

- for foam and aerated concretes.

22

Table 6.11Concrete The values of the concrete's initial modulus of elasticity under compression and tension Eb, MPa-10"1, with the following concrete

compressive strength class:В1.5 В2 В2,5 В3.5 В5 В7.5 В10 В 12.5 В15 В20 В25 В30 В35 В40 В45 В50 В55 В60 В70 В80 В90 B100

Heavyweight - - - 9,5 13.0 16,0 19.0 21,5 24,0 27,5 30,0 32,5 34.5 36,0 37,0 38.0 39,0 39,5 41,0 42,0 42,5 43Fine-aggregategroup:А — natural

- - - 7,0 10 13,5 15,5 17,5 19.5 22,0 24,0 26,0 27,5 28,5

curingB - autoclave - - - - - - - - 16,5 18,0 19,5 21,0 22,0 23,0 23,5 24,0 24,5 25,0 — — — —curingLightweight andporouswith average density: D800 ____ ___ 4,0 4,5 5.0 5,5D1000 - - 5,0 5,5 6,3 7,2 8,0 8,4D1200 - - 6,0 6,7 7.6 8,7 9,5 10,0 10,5D1400 - - 7,0 7,8 8,8 10,0 11,0 11.7 12,5 13,5 14,5 15,5 — — — — — — — — _ ___D1600 - - - 9,0 10.0 11,5 12,5 13,2 14,0 15,5 16.5 17.5 18,0D1800 - - - - 11,2 13,0 14,0 14,7 15,5 17,0 18.5 19,5 20,5 21.0 —D2000 - - - - - 14,5 16,0 17,0 18,0 19,5 21,0 22,0 23,0 23,5Foam autoclavecuring,medium density D500 1.4D600 1,7 1,8 2,1D700 1,9 2,2 2,5 2,9D800 - - 2,9 3,4 4.0D900 - - - 3,8 4,5 5,5D1000 - - - - 5,0 6,0 7,0D1100 - - - - - 6,8 7.9 8,3 8,6D1200 - - - - - - 8,4 8,8 9,3

N o t e s1 For group A fine-aggregate concrete that has undergone heat treatment, or at atmospheric pressure, the values of the concrete's initial modulus of

elasticity should be assigned using a coefficient of 0.89.2For lightweight, porous, and aerated concretes with intermediate densities, the initial modulus of elasticity values are taken using linear

interpolation.3For porous concrete with non-autoclave curing, the values of Еr are taken as for autoclave-curing concrete multiplied by a coefficient of 0.8.4 For self-stressing concrete, the values of Еr are taken as for heavyweight concrete multiplied by a coefficient of α = 0.56 + 0.006 В.

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CP 63.13330.2012

T a b l e 6.12

Ambient air humidity, %

Values of the concrete's creep coefficient φb,cr with a heavyweight concrete compressive class of:

CompressionВ10 В15 В20 В25 В30 В35 В40 В45 В50 В55 В60-В100

Over 75 2,8 2,4 2,0 1,8 1,6 1,5 1,4 1,3 1,2 1,1 1,040-75 3,9 3,4 2,8 2,5 2,3 2,1 1,9 1,8 1,6 1,5 1,4Below 40 5,6 4,8 4,0 3,6 3,2 3,0 2,8 2,6 2,4 2,2 2,0

N o t e – The relative ambient air humidity is taken per SP 131.13330 as the average monthly relative humidity of the warmest month for the construction area.

6.1.19 Concrete stress-strain diagrams are used when analyzing reinforced concrete members using a non-linear deformation model.

Any type of concrete diagrams may be used as stress-strain analysis diagrams, which define the link between stresses and relative strains: curvilinear, including those with a descending branch (Attachment А), piecewise linear (two-line and three-line), which reflect the behavior of the concrete. The main parametric points of the diagrams must also be designated (maximum stresses and corresponding strains, limit values, etc.).

Simplified three-line and two-line diagrams (figures 6.1, а, b) similar to Prandial diagrams are used as working stress-strain diagrams for heavyweight, fine-aggregate, and self-stressing concrete, which define the link between stresses and strains.

6.1.20 In a three-line diagram (figure 6.1 а), the concrete's compressive stresses σ b, depending on the relative compressional strains , are determined using the formulas:If

(6.4)

If

(6.5)

If

(6.6)

The values of the stresses σbl are taken as

while the values of the relative strains are taken as

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C P 63.13330.2012

b

а - Three-line stress-strain diagram for compressed concrete; b - Two-line stress-strain diagram for compressed concrete

Figure 6.1 – Compressed concrete stress-strain diagrams

The values of the relative strains εb2 for heavyweight, fine-aggregate, and self-stressing concretes are

taken as:

for a short-term load effect: for concretes with a compression strength class of В60 and below, εb2 = 0,0035; for high-strength concretes with a compression strength class of В70-В100, εb2 is taken in a linear manner, from 0.0033 for В70 to 0.0028 for В100; under a long-term load effect - per table 6.10, the values of Rь, Еь and εb0 are taken per 6.1.11, 6.1.12, 6.1.14, and 6.1.15. 6.1.21 In a two-line diagram (figure 6.1, b) the concrete's compressive stresses σb, depending on the relative strains εb, are determined using the formulas:

If

(6.7)

If

The reduced (normalized) value of the modulus of deformation Eb,red, it is assumed to be:

(6-9)The values of the relative strains Ebl,red are taken as:

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CP 63.13330.2012

for heavyweight concrete under a short-term load effect Ebl,red=0.0015;for lightweight concrete under a short-term load effect Ebl,red=0.0022;for heavyweight concrete under a long-term load effect - per table 6.10.The values of Rb, Eb2 are taken as in 6.1.20.6.1.22 The concrete's tensile stresses depending on of the relative strains Ebl, are determined

using the diagrams presented in 6.1.20 and 6.1.21. In this case, the design values of the concrete's resistance to compression Rb are replaced by the design values of the concrete's resistance to tension Rb per 6.1.11 and 6.1.12, the values of the initial modulus of elasticity Еbl are determined per 6.1.15, the values of the relative strain Еbl2 are taken per 6.1.12, and the values of the relative strain Еbl2 for heavyweight, fine-aggregate, and self-stressing concretes are taken as: under a short-term load effect –Ebt2= 0.00015, under a long-term load effect - per table 6.10. For a two-line diagram, we assume Ebt1,red= 0.00008 under a short-term load effect, and under a long-term load effect - per table 6.10; the values of Ebt,red are determined using the formula (6.10), substituting Rbt and Ebt1,red.

6.1.23 When analyzing the strength of reinforced concrete members using a non-linear deformation model, the stress-strain diagrams for compressed concrete presented in 6.1.20 and 6.1.21 are used to determine the stress-strain state of the compression zone of the concrete, with the strain characteristics reflecting a short-acting load. A two-line diagram is used in this case as the simplest option.

6.1.24 When analyzing crack formation in reinforced concrete structures using a non-linear deformation model, the three-line stress-strain diagram presented in 6.1.20 and 6.1.22 are used to determine the stress-strain state of compressed and tensioned concrete, with the strain characteristics reflecting a short-term load. The two-line diagram (6.1.21), since it is the most simple, is used to determine the stress-strain state of tensioned concrete for the elastic behavior of compressed concrete.

6.1.25 When analyzing the deformations of reinforced concrete members using a non-linear deformation model in the absence of cracks, a three-line stress-strain diagram accounting for a short-term and long-term load is used to evaluate the stress-strain state in compressed and tensioned concrete. Aside from the diagram indicated above, a two-line diagram (as the most simple) that accounts for a short-term and long-term load is used to evaluate the stress-strain state of compressed concrete if cracks are present.

6.1.26 When analyzing crack opening using a non-linear deformation model, the stress-strain diagrams presented in 6.1.20 and 6.1.21, taking into account a short-term load, are used to evaluate the stress-strain state in compressed concrete. A two-line diagram is used in this case as the simplest option.

6.1.27 The effect of alternating freezing and thawing and subzero temperatures on the concrete's strain characteristics are accounted for by a service factor γbt≤1.0. For aboveground structures subjected to atmospheric environmental effects at a design external air temperature during the cold season of minus 40 °С and above, a factor of γbt =1.0 is used. Otherwise the values of the factor γbt are taken in accordance with the purpose of the structures and the environmental conditions.

6.1.28 The strength characteristics of concrete in a plane (biaxially) stressed state or a three-dimensional (triaxially) stressed state should be determined, depending on the concrete type and class, from the criterion expressing the link between the ultimate stresses acting in two or three mutually perpendicular directions.

Concrete strains should be determined based on the plane or three-dimensional state of stress.6.1.29 The characteristics of a concrete matrix in structures with dispersed reinforcement should be

taken as for both concrete and reinforced concrete structures.The characteristics of fiber concrete in fiber concrete structures should be defined depending on the

concrete characteristics, the relative content, shape, size, and location of the fibers in the concrete, the fiber bond with concrete and its physical and mechanical properties, and also depending on the dimensions of the member or structure.

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C P 63.13330.2012

6.2 Reinforcement

6.2.1 In designing reinforced concrete buildings and facilities according to the requirements for concrete and reinforced concrete structures, the type of reinforcement and its standard and controlled quality parameters should be defined.

6.2.2 Reinforcement of the following types that meet the requirements of the applicable standards or duly approved technical specifications should be used for reinforcing reinforced concrete structures:

6-50 mm hot-rolled smooth and ribbed bar with a constant or variable rib height (round and crescent-shaped bar, respectively);

6–50 mm thermomechanically treated ribbed bar;3-16 mm cold-worked ribbed bar;6–15 mm reinforcing cables;6.2.3 The main quality indicator of reinforcement to be specified during design is the tensile

strength class, which is designated as follows:A – for hot rolled and thermomechanically hardened rebarB, Bp - for cold formed rebarK – for reinforcing cables.Reinforcing cables are divided into:K7, made from round smooth wire;K7Т, made from ribbed wire;K7O, plastically constricted, made from smooth wire.The tensile strength classes of reinforcement shall meet the guaranteed yield point value, physical or

conventional (equal to the value of the stresses corresponding to residual relative elongation of 0.1 % or 0.2 %), with a probability of at least 0.95, which is determined by the relevant standards.

In addition, requirements on the following additional quality indicators shall be imposed when necessary: weldability, plasticity, cold resistance, corrosion resistance, concrete-bonding characteristics, etc.

6.2.4 For reinforced concrete structures without pre-stressing of reinforcement, ribbed rebar of classes А400, А500, and А600, as well as class B500 and Bp500 in welded mesh and mats, should be used as reinforcement to be specified by calculation. It is permitted to use higher-class reinforcement if the economic efficiency is substantiated.

For transverse and confinement reinforcement, should primarily be used class A240 rebar made of steel grades St3sp and St3ps (with regulated parameter categories no lower than 2 per GOST 535), as well as ribbed rebar of classes А400, А500, V500, and Bp500.

The following should be specified for pre-stressed reinforced concrete structures:as pre-stressed reinforcement:hot-rolled and thermomechanically-hardened ribbed rebar of classes А600, А800, and А1000;cold-worked ribbed reinforcement of classes ranging from Bp1200 to Bp1600; 7-wire (K7) cable reinforcement of classes K1400, K1500, K1600, K1700; as non-prestressed reinforcement: hot-rolled smooth reinforcement of class А240;hot-rolled, thermomechanically-hardened, and cold-worked ribbed reinforcement of classes А400,

А500, А600, B500, and Bp5006.2.5 When selecting the type and grades of steel for design-specified reinforcement, as well as rolled

steels for concrete inserts, the operating temperature conditions of the structures and the nature of their stressing should be taken into account.

In structures working under a static (or quasistatic) load in heated buildings, as well as in the open air or in heated buildings with a design temperature of minus 40 °С and above, reinforcement of all the classes mentioned above may be used, with the exception of class А400 reinforcement made of grade 35GS steel or

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CP 63.13330.2012

class А240 reinforcement made of grade St3kp steel, which are used at a design temperature of minus 30 °С and above.

With a design temperature below minus 55 °С, it is recommended that reinforcement of class Ac500S per [1] and class А600 made of grade 20G2SFBA steel be used.

Under other operating conditions, the reinforcement class and steel grade are specified in accordance with special instructions.

the type of surface of the reinforcement should be taken into account (GOST R 52544, [3]) when designing the pre-stressing area, the anchoring of the reinforcement in the concrete, and the overlapping joints of the reinforcement (without welding).

When designing welded joints of reinforcement, the reinforcement fabrication method should be taken into account (GOST 14098, [2]).

6.2.6 Hot-rolled reinforcing steel of class А240, grades St3sp and St3ps (with regulated parameter categories no lower than 2 per GOST 535), should be used for assembly (lifting) lugs of precast reinforced concrete members and concrete structures.

If the structures could possibly be installed in a design winter temperature below minus 40 °С, it is not permitted to use grade St3ps steel for the assembly lugs.

6.2.7 The main strength characteristic of reinforcement is the standard value of the resistance to tension, which is specified in accordance with the class of the reinforcement per table 6.13.

6.2.8 The design values of the reinforcement's resistance to tension Rs are determined using the formula

„ (6-9)

where γs - safety factor for the reinforcement, assumed as 1.15 for the ultimate limit states and 1.0 - for the service limit states.The design values of the reinforcement's resistance to tension Rs are presented (with rounding) for

the ultimate limit states in table 6.14, and for the service limit states - in table 6.13. In this case, the values Rs,n for the ultimate limit states are taken as the lowest regulated values per the relevant standards.

T a b l e 6.13Reinforcement class Nominal bar size

(mm)Standard values of resistance to tension Rs,n and design values of

resistance to tension for the service limit states Rs,ser (MPa)А240 6-40 240А400 6-40 400А500 10-40 500А600 10-40 600А800 10-32 800А1000 10-32 1000В500 3-16 500Вр500 3-5 500Вр1200 8 1200ВР1300 7 1300Вр1400 4; 5; 6 1400ВР1500 3 1500Вр1600 3-5 1600К1400 15 1400К1500 6-18 1500К1600 6; 9; 11; 12; 15 1600К1700 6-9 1700

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C P 63.13330.2012

The values of the reinforcement's design resistance to compression R sс are taken to be equal to the reinforcement's design values of resistance to tension Rs, but shall not exceed the values corresponding to shortening deformations of the concrete surrounding the compressed reinforcement: for a short-term load effect - no more than 400 MPa, for a long-term load effect - no more than 500 MPa.

For class V500 and А600 reinforcement, the limit values of the resistance to compression are specified with a reduction coefficient for the operating conditions. The design values of R sс are presented in table 6.14.

Table 6.14Reinforcement class The values of the design resistance of reinforcement for the ultimate limit states

(MPa)

to tension Rs to compression Rsс.А240 210 210А400 350 350А500 435 435(400)А600 520 470(400)А800 695 500(400)А1000 870 500(400)В500 435 415(380)Вр500 415 390(360)Вр1200 1050 500(400)ВР1300 1130 500(400)ВР1400 1215 500(400)Bp 1500 1300 500(400)Вр1600 1390 500(400)К1400 1215 500(400)К1500 1300 500(400)К1600 1390 500(400)К1700 1475 500(400)

N o t e – the values of Rsс given in parentheses are only used when calculating for a short-term load effect.

6.2.9 When necessary, the design values of the reinforcement's strength characteristics are multiplied by service factor уsi, which accounts for the specific operating conditions of the reinforcement in the structure.

The design values of Rsw, for reinforcement of classes А240 - А500, B500 are presented in table 6.15.For transverse reinforcement of all classes, the design values of the resistance R sw should be taken as

no more than 300 MPa.Table 6.15

Reinforcement class The design resistance values of transverse reinforcement (stirrups and bent rods) to tension for the ultimate limit states, MPa

А240 170А400 280А500 300В500 300

6.2.10 The basic strain characteristics of reinforcement are the standard values of the:of the relative tensile strains of the reinforcement Es0 when the stresses reach the design resistance Rsof the reinforcement's modulus of elasticity Еs.6.2.11 The values of the relative strains of the reinforcement Es0 are taken to be equal to:

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CP 63.13330.2012

for reinforcement with a physical yield point of

(6.11)for reinforcement with a conventional yield point of

. (6.12)6.2.12 The values of the reinforcement's modulus of elasticity Е3 are taken as identical under both

tension and compression and are equal to:Es = 1.95-105 MPa - for cable reinforcement (K);Es = 2.0-105 MPa - for other types of reinforcement (А and B).6.2.13 Stress-strain diagrams of reinforcement are used when analyzing reinforced concrete members

using a non-linear deformation model.When analyzing reinforced concrete members using a non-linear deformation model, simplified

diagrams similar to Prandtl diagrams are used as follows as stress-strain diagrams for the reinforcement,

which establish the link between stresses and relative strains Es: two-line diagrams are used for class А240 - А500 and B500 reinforcement with a physical yield point (Figure 6.2, а), while three-line diagrams (Figure 6.2, b), without accouting for hardening beyond the yield point, are used for class А600 - А1000, Bp1200 - Bp1500, K1400, K1500 and K1600 reinforcement with a conventional yield point.

Stress-strain diagrams of reinforcement under tension and compression are taken as identical, taking into account the reinforcement's specified design resistances to tension and compression.

For stress-strain diagrams for the reinforcement, it is permitted to use curvilinear analysis diagrams that approximate the reinforcement's actual deformation diagrams.

6.2.14 Stresses in the reinforcement , according to a two-line stress-strain diagram for the reinforcement, are determined in accordance with the relative strains εS using the formulas:

If

(6.13)

If

(6.14)The values of εs0, Еs and Rs are taken per 6.2.11, 6.2.12 and 6.2.8. The values of the relative strain εs2

are taken to be equal to 0.025.With the appropriate justification, it is permitted to specify the value of the relative strain εs2 as less

than or greater than 0.025, depending on the grade of the steel, the type of reinforcement, the structure's reliability criterion, and other factors.

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C P 63.13330.2012

а - two-line diagram; b - three-line diagram Figure 6.2 - Stress-strain diagrams for tensioned reinforcement

6.2.15 Stresses in the reinforcement σS, according to a three-line stress-strain diagram for the reinforcement, are determined in accordance with the relative strains εS using the formulas:

If

(6.15)

If

(6.16)

The values of εs0, Еs and Rs are taken per 6.2.11, 6.2.12 and 6.2.8.The values of the stresses are taken to be equal to 0.9RS, while the stresses are taken as 1.1Rs

The values of the relative strains εs1are taken to be equal to , while the strains εs2 are taken as 0.015.

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CP 63.13330.2012

7 Concrete structures

Structures are considered to be concrete if their strength is only provided by concrete.Concrete members are used:а) primarily in compression when the longitudinal compressive force is located within the member's

cross section;b) in some cases, in structures working in compression with the longitudinal compressive force

located outside of the member's cross section, as well as in bending structures, when their collapse does not pose a direct threat to human life or the integrity of equipment.

Structures with reinforcement whose cross sectional area is less than minimally permissible per the design requirements of 10.3 shall be treated as concrete structures.

7.1 Strength Analysis of Concrete Members

7.1.1 Concrete members are analyzed for their strength against longitudinal compressive forces, bending moments, and lateral forces, as well as local compression.

7.1.2 Strength analysis of concrete members under a longitudinal compressive force (eccentric compression) and bending moment should be performed for cross sections perpendicular to their longitudinal axis.

Concrete members area analyzed using a non-linear deformation model per 8.1.20-8.1.30, assuming a reinforcement area of zero in the calculations. It is permitted to analyze T-shaped and rectangular concrete members under forces in the plane of symmetry of the normal cross section using the limit forces per 7.1.7-7.1.12.

7.1.3 Depending on the conditions under which they function and the requirements placed on them, concrete members should be analyzed in normal cross sections for ultimate forces without taking account or taking account of the concrete resistance in the zone under tension.

With accounting for the concrete resistance in the zone under tension (figure 7.1), the eccentric compressed members shall be analyzed with the longitudinal compressive force located within the member's cross section, assuming that reaching the limit state is characterized by the failure of the compressed concrete.

In limit state design, the concrete's resistance to compression shall be conventionally represented by stresses equal to Rb, which are uniformly distributed through part of the compression zone (conventional compression zone) with a center of gravity coinciding with the center of the longitudinal force (7.1.9).Taking into account resistance of the concrete in the zone under tension (figure 7.2), the analysis shall be performed for the members working in compression with the longitudinal compressive force located outside of the member's cross section, the bending members, and the members in which cracks are not permitted due to the structures' operating conditions. In this case, when performing limit state design, it is assumed that the limit state is characterized by the attainment of the ultimate forces in the concrete in the zone under tension, which are determined on the assumption of the concrete's elastic operation (7.1.9, 7.1.10, 7.1.12).

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C P 63.13330.2012

Figure 7.1 – Diagram of forces and the stress envelope in a cross section perpendicular to the longitudinal axis of an eccentric compressed concrete member analyzed for strength without accounting for the resistance of the

concrete in the zone under tension

Figure 7.2 - Diagram of forces and the stress envelope in a cross section perpendicular to the longitudinal axis of a bending (eccentrically compressed) concrete member analyzed for strength with account for the resistance of the concrete in the zone under tension

7.1.4 Concrete members under lateral forces shall undergo strength analysis based on the condition that the sum of the ratios of the principal tensile

stress to the concrete's design resistance to axial tension and of the principal compressive stress to the

concrete's design resistance to axial compression must not exceed 1.0. 7.1.5 Strength analysis of concrete members for the effect of a local load (local compression) shall be

performed per the instructions in 8.1.43 - 8.1.45.7.1.6 Structural reinforcement must be provided in concrete members in the instances specified in

10.3.7.Limit state analysis of eccentrically compressed concrete members

7.1.7 When analyzing eccentrically compressed concrete members for strength against a longitudinal compressive force, random eccentricity ег, should be taken into account, which should be assumed as no less than:

1/600 of the length of the member or of the distance between its fixed cross sections;1/30 of the height of the cross section;

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CP 63.13330.2012

10 mm.For members of statically indeterminate structures, the value of the eccentricity of the longitudinal

force relative to the center of gravity of the transformed section е0 is taken as equal to the value of the eccentricity obtained from a static calculation, but shall be no less than еа.

For members of statically determinate structures, eccentricity е0 is assumed as equal to the sum of the eccentricities – from a static calculation of the structures and the random eccentricity.

7.1.8 For flexible members , the impact of deflections on their bearing capacity must be accounted for by multiplying the values of е0 by factor n, which is determined per 7.1.11.

7.1.9 The analysis of eccentrically compressed concrete members with a longitudinal compressive force located within the member's cross section shall be performed based on the condition

(7.1)where N — design longitudinal force;Аh – area of the concrete's compression zone, which is determined based on the condition that its

center of gravity coincides with the center of longitudinal force N (taking into account deflection).For members with a rectangular cross section:

(7.2)

It is permitted to analyze eccentrically compressed members with a rectangular cross section, with

eccentricity of the longitudinal force , based on the condition

(7.3)

where А - cross-sectional area of member;φ – factor used when there is a long-term load effect per table 7.1

depending on the flexibility of the member, with a short-term load effectНthe values of φ are determined in a linear manner, assuming φ = 0.9 if

= 10 and φ = 0.85 if =20;lo - design length of member, which is determined the same as for reinforced concrete members.

T a b l e 7.16 10 15 20

φ 0,92 0,9 0,8 0,6

Eccentrically compressed concrete members, in which cracks are not permitted due to the operating conditions, regardless of the calculated based on the condition (7.1), must be verified taking into account the resistance of the concrete in the tension zone, based on the condition

(7.4)

For members with a rectangular cross section, the condition (7.4) is given by

(7.5)

In the formulas (7.4) and (7.5): А – cross-sectional area of concrete member;

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C P 63.13330.2012

I - moment of inertia of the concrete member's cross section relative to its center of gravity; yt - distance from the center of gravity of the member's cross section to the most tensioned fiber; η – factor determined in accordance with 7.1.11.

7.1.10 The analysis of eccentrically compressed concrete members with a longitudinal compressive force located outside the member's cross section is performed based on the conditions (7.4) and (7.5).

7.1.11 The value of factor n, which accounts for the effect of deflection on the eccentricity of the longitudinal force ео, is determined using the formula

where N nominal critical load, which is determined using the formula

where D - stiffness of member in the ultimate limit state, which is determined the same as for reinforced concrete members, but without accounting for reinforcement, per 8.1.15.

Limit state analysis of bending concrete members

7.1.12 Analysis of bending concrete members should be performed based on the conditionМ≤Мult (7.8)

where М - bending moment from external load;Мult - ultimate bending moment that can be supported by the member's cross section.

The value of Мult is determined using the formulaМult=Rbt*W, (7.9)

where W- moment of resistance of member's cross section for most remote fiber. For members with a rectangular cross section:

(7.10)

8 Concrete and reinforced concrete structures without rebar prestressing.

8.1 Limit state analysis of members of reinforced concrete structures

Strength analysis of concrete members

Reinforced concrete members are analyzed for strength against the effect of bending moments, longitudinal forces, lateral forces, torque, and the local effect of a load (local compression, bursting).

Strength analysis of reinforced concrete members against the effect of bending moments and longitudinal forces

General8.1.1 Strength analysis of reinforced concrete members against the effect of bending moments and

longitudinal forces (eccentric compression or tension) should be performed for cross sections perpendicular to their longitudinal axis.

Strength analysis of normal cross sections of reinforced concrete members should be performed using a non-linear deformation model per 8.1.20-8.1.30.

It is permitted to perform the analysis based on ultimate forces: of reinforced concrete members of rectangular, T-shaped, and H-shaped cross sections with reinforcement located in the perpendicular bending planes of the face of the member,

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CP 63.13330.2012

under forces in the plane of symmetry of normal cross sections - per 8.1.4-8.1.16;of eccentrically compressed members with round and circular cross sections – per the instructions in

Attachment D.8.1.2 When analyzing eccentrically compressed members, the effect of deflection on their bearing

capacity should be accounted for, generally through analyzing the structures using the strain method.It is permitted to analyze structures using non-strain method,

in which, given flexibility of , the effect of the member's deflection on its strength should be accounted for by multiplying initial eccentricity е0 by the factor , which is determined per the instructions in 8.1.15.

8.1.3 For reinforced concrete members whose limit stress turns out to be less than the ultimate crack-forming stress (sections 8.2.8 - 8.2.14.), the cross-sectional area of the longitudinal tension reinforcement must be increased by at least 15% relative to the value required from the strength analysis, or it must be determined from a strength analysis for the effect of the ultimate crack-forming stress.

Limit state analysis of normal cross sections 8.1.4 The ultimate forces in a cross section perpendicular to the longitudinal axis of member should

be determined proceeding from the following based on the following presuppositions:the concrete's resistance to tension is assumed as equal to zero; the concrete's resistance to

compression is represented by stresses equal to Rb and uniformly distributed through the compression zone of the concrete;

the strains (stresses) in the reinforcement are determined in accordance with the height of the concrete's compression zone;

the tensile stresses in the reinforcement are taken as no more than the design resistance to tension Rs;the compressive stresses in the reinforcement are taken as no more than the design resistance to

compression Rsc.8.1.5 Strength analysis of normal cross sections should be performed in accordance with the ratio

between the value of the relative height of the compression zone

of the concrete , as determined based on the corresponding equilibrium conditions, and the limit

value of the relative height of the compression zone at which the limit state of the member occurs at the same time that the stresses in the tension reinforcement become equal to the design resistance Rs.

8.1.6 The value of ξR is determined using the formula

(8.1)

where is the relative strain of the tension reinforcement under stresses equal to Rs.

(8.2)

b2- relative strain of compressed concrete under stresses equal to Kь, which is assumed in accordance with 6.1.20.

For heavyweight concrete of classes В70 - В100 and for fine-aggregate concrete, 0.7 should be used

in the numerator of the formula (8.1) instead of 0.8.

8.1.7 When analyzing eccentrically compressed reinforced concrete members, random eccentricity еа, which should be taken as no less than the following, should be accounted for in the initial eccentricity of the application of longitudinal force e0:

1/600 of the length of the member or of the distance between its fixed cross sections;1/30 of the height of the cross section;

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C P 63.13330.2012

10 mm.For members of statically indeterminate structures, the value of the eccentricity of the longitudinal

force relative to the center of gravity of the transformed section е0 is taken as equal to the value of the eccentricity obtained from a static calculation, but shall be no less than еа.

For members of statically determinate structures, eccentricity е0 is assumed as equal to the sum of the eccentricities from a static calculation of the structures and the random eccentricity.

Analysis of flexural members

8.1.8 Strength analysis of the cross sections of bending members is performed based on the conditionМ ≤ М u l t (8.3)

where М - bending moment from external load:

Мult - ultimate bending moment that can be supported by the cross section of the member.8.1.9 The value of Мult for bending members with a rectangular cross section (figure 8.1) for

is determined using the formula

(8.4)In this case the concrete compression side height is determined from the following formula:

(8.5)

8.1.10 The value of Мult for bending members with a flange in the compression zone (T-shaped and

H-shaped cross sections), if , is determined depending on the location of the compression zone boundary:

а) if the boundary goes into the flange (figure 8.2, а), i.e., the condition

(8.6)is met, then the value of Мult is determined per 8.1.9 the same as for a rectangular cross section with width b’f,

b) if the boundary goes into the web (figure 8.2, b), i.e., the condition (8.6) is not met, then the value of Мult , is determined using the formula

(8. 7)

In this case the concrete compression side height is determined from the following formula:

(8.8)

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CP 63.13330.2012

RbAs

Ah

RscAsRhAh

RsAs

M

h

h0

Asb

Figure 8.1 – Diagram of forces and the stress envelope in a cross section perpendicular to the longitudinal axis of a bending reinforced concrete member during strength analysis

u Ashj

As

As

bh

As

hj

hj

u

h0h0

a

x

hj

x

a a

Figure 8.2 – Location of compression zone boundary in the cross section of a bending reinforced concrete member

8.1.11 The value of to be entered into the calculation is taken based on the condition that the width of the overhang of the flange in each direction from the web must be no more than 1/6 the span of the member and no more than:

а) if there are cross members, or if – 1/2 the distance in the clear between the longitudinal members;

b) if there are no cross members (or if the distances between them are greater than the distances

between the longitudinal members) and c) if the flange has cantilever overhangs:

If

If

if - the overhangs are not considered.8.1.12 When analyzing the strength of bending members, it is recommended that the condition

is met.If due to design considerations or based on a service limit state analysis, the area of the tension

reinforcement is taken as greater than is required to meet the condition , it is permitted to

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C P 63.13330.2012

determine the ultimate bending moment Мult using the formulas (8.4) or (8.7), using the values of the

compression zone height

8.1.13 If symmetrical reinforcement is used, when , then the value of Мult, is determined using the formula

(8.9)If the height of the compression zone calculated without accounting for compression reinforcement (Аs =0) is

х<2а', then the value x/2 is used in the formula (8.9) in place of а' 2'

Analysis of eccentrically compressed members8.1.14 Strength analysis of the rectangular cross sections of eccentrically compressed members is

performed based on the condition

(8.10)where N- longitudinal force from external load;

е – the distance from the center of longitudinal force N to the center of gravity of the cross section of the tension reinforcement or least compressive reinforcement (if the member cross section is completely compressed), which is equal to

(8.11)

Here – a factor accounting for the effect of the longitudinal bending (deflection) of the member on its bearing capacity and which is determined per 8.1.15 e0 – per 8.1.7The height of the compression zone х is determined:

а) if (figure 8.3) using the formula

(8. 12)

b) if using the formula

(8. 13)

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CP 63.13330.2012

Figure 8.3 – Diagram of forces and the stress envelope in a cross section perpendicular to the longitudinal axis of an eccentrically compressed concrete member during strength analysis

8.1.15 When analyzing structures using non-strain method, the value of factor is determined using the equation

(8. 14)

where N- longitudinal force from external load;Ncr is the assumed critical load determined from

(8. 15)

Here D is the stiffness of the reinforced concrete member in the ultimate strength stage, determined according to the instructions for strain analysis;

l0 is the design length of the member, determined according to 8.1.17. The value of О may be determined from

where are the modulus of elasticity for the concrete and the reinforcement respectively;- are the moments of inertia of the cross sections of the concrete and the entire longitudinal

reinforcement respectively, relative to the axis passing through the center of gravity of the cross section of

the member;

- is a factor taking into account the effect of the duration of the load action

, but is not more than 2. Here are the moments relative to the center of the bar under the greatest tension or least

compression (where a section is compressed in its entirety) respectively when exposed to full load and to dead and long-term loads;

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C P 63.13330.2012

- is the relative value of the eccentricity of the longitudinal force — ,assumed to be not less than 0.15 and not more than 1.5. The value of the factor may be reduced,

taking into account the distribution of the bending moments along the length of the member, the nature of its strain, and the effect of deflections on the value of the bending moment in the design section, by analyzing the structure as an elastic system.

8.1.16 Strength analysis of rectangular cross sections of eccentrically compressed members with reinforcement located on opposite sides in the plane of bending of the section, where the eccentricity of the

longitudinal force and the flexibility may be based on the condition thatN ≤ N u l t (8.16)

where Nult is the ultimate value of the longitudinal force that can be taken up by a member, determined from

(8. 15)

Here А is the area of the concrete section;Аstot is the area of all the longitudinal reinforcement in the cross section of a member;F is a factor assumed in the case of a long-term load action according to Table 8.1 depending on the

flexibility of the member; in the case of a short-term load action the values of F are determined linearly, assuming

when and when Concrete Class when value

6 10 15 20

В20-В55 0,92 0,9 0,83 0,7

В60 0,91 0,89 0,80 0,65

В80 0,90 0,88 0,79 0,64

8.1.17 The design length l0 of an eccentrically compressed member is determined in the same way as for frame structure members, taking account of the state of strain if the load is in the most unfavorable location for the member in question, and allowing for inelastic strains in materials and the presence of cracks.

The design length l0 of members with a constant cross section along their length l exposed to longitudinal force may be assumed to be:

а) for members with a hinged support at two ends - 1,0/;b) for members with rigid embedding (preventing the bearing cross section from rotating) at one end

and the other end free (cantilever) - 2,0/;c) for members with a hinged restrained support at end, and at the other end:rigid (non-rotating) embedding - 0,7/;yielding (allowing limited rotation) embedding - 2,0/;d) for members with a yielding hinged support (limited movement of the support) at one end and at

the other end: -1,5/;with rigid (non-rotating) embedding with yielding (with limited rotation) embeddinge) for members with restrained embedding at both ends: -0,5/;rigid (non-rotating) yielding (with limited rotation) -0,8/;f) for members with embedding with limited movement at both ends: rigid (non-rotating) -0,5/;

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CP 63.13330.2012

yielding (with limited rotation) -1,2/;Analysis of members under axial tension

(8.18)8.1.18 Strength analysis of sections of members under axial tension should be based on the condition

where N is the longitudinal tensile force from external loads; Nult is the ultimate value of the longitudinal force that can be taken up by the member. The value of force Nult is determined from

(8.19)where As,tot is the area of the cross section of all the longitudinal reinforcement.

Analysis of members under eccentric tension

8.1.19 Strength analysis of rectangular sections of members under eccentric tension should be performed depending on the position of the longitudinal force

а) if the longitudinal force N is applied between the resultant forces in the reinforcement S and S’ (Figure 8.4, a) – based on conditions

; (8.20)

(8.21)

where are the forces from external loads;

are the ultimate forces that can be taken up by the section

The forces are determined from

(8.22)

(8.23)

b) if the longitudinal force N is applied outside the distance between the resultant forces in the

reinforcement S and S' (Figure 8.4, b) based on (8.20), by determining the ultimate moment using

(8.24)In this case the concrete compression side height is determined from the following formula:

(8.25)

If the value obtained from the calculation made using (8.25) is substituted in (8.24) х

= , where ^ is determined according to the instructions in 8.1.6.

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C P 63.13330.2012

a – between the resultant forces in reinforcement S and S';

b – outside the distances between the resultant forces in the reinforcement S and S'Figure 8.4 – Force and stress-strain diagrams for a section normal to the longitudinal axis of a reinforced

concrete member under eccentric tension, during a strength analysis with longitudinal force N applied

Strength analysis of normal sections based on a non-linear deformation model

8.1.20 During a strength analysis the forces and strains in a section normal to the longitudinal axis of a member are determined based on a nonlinear deformation model, which uses equilibrium equations for the external and internal forces acting in the section of the member, and also based on the following assumptions:

The concrete and reinforcement unit strain distribution by the member cross section height is assumed to follow the linear law.

The relation between the axial stresses and the relative strains in the concrete and reinforcement is assumed to follow the stress-strain curves of the concrete and reinforcement.

The resistance of the concrete in the tensile zone does not have to be taken into account, assuming

where stresses . In individual cases (for example, flexural 43

CP 63.13330.2012

concrete structures and those under eccentric compression in which cracks are not permitted) the strength analysis takes the behavior of the concrete under tension into account.

8.1.21 It is recommended that the transition from the concrete stress diagram to the generalized internal forces be performed with the help of the method of numerical integration in the normal cross section. To do this, the normal section is nominally broken down into small parts: where there is oblique eccentric compression (tension) and skew bending – along the height and width of the section; where there is eccentric compression (tension) and bending in the plane of the axis of symmetry of the cross section of the member – only along the height of the section. The stresses within each of the small areas are assumed to be evenly distributed (averaged).

8.1.22 When analyzing members using a strain model the following are assumed:the values of the compressive longitudinal force, and of the compressive stresses and strains which

shorten the concrete and reinforcement, with a “minus” sign;the values of the tensile longitudinal force, and of the tensile stresses and strains which elongate the

concrete and reinforcement, with a “plus” sign.The signs for the coordinates of the centers of gravity of the reinforcing bars and of the areas of

concrete singled out, and the points of application of longitudinal force, are assumed in accordance with the specified XOY coordinate system. The starting point for the coordinates in this system (point 0 in Figure 8.5) is generally located at a random point within the cross section of the member.

L'Figure 8.5 – Design diagram of a normal section of a reinforced concrete member

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C P 63.13330.2012

8.1.23 A strength analysis of normal sections is generally performed using (see Figure 8.5):equilibrium equations for the external and internal forces acting in the normal section of a member:

(8-26)

(8.27)

(8.28)Equations that determine the deformation distribution in the member cross section:

(8-29)

(8.30)

And relationships that couple stresses and unit strains in concrete and reinforcement:

(8.31)

(8.32)In equations (8.26) - (8.32):

are the bending moments from the external load relative to the coordinate axes selected and located within the cross section of the member (acting in planes XOZ and YOZ or parallel to them respectively), determined from:

(8.33)

(8.34)

here are the bending moments in the corresponding planes from the external load, determined from a static analysis of the structure; N is the longitudinal force from the external load;x, y are the distances from the point of application of longitudinal force N to the corresponding selected axes;

- the area, the coordinates of the center of gravity of the i-th concrete section and the stress at the level of its center of gravity;

is the area, the coordinates of the center of gravity of the j-th reinforcing bar and the stress in it;

-is the relative strain in a fiber located at the point of intersection of the selected axes (at point 0);

is the flexure of the longitudinal axis in the given cross section of the member in bending moment

Мх and Му planes

-concrete elastic modulus;

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CP 63.13330.2012

-is the modulus of elasticity of the j-th reinforcing bar;

Vhi is the elasticity ratio of the concrete in the j-th area;

Vsi is the elasticity ratio of the j-th reinforcing bar.

Ratios Vbi and Vsj are taken from the corresponding stress-strain curves of the concrete and the

reinforcement shown in 6.1.19, 6.2.13.

The values of ratios Vbi and Vsj are determined as the ratio of the values of the stresses and strains for the given points on the corresponding concrete and reinforcement stress-strain curves, assumed in the analysis, divided by the modulus of elasticity for the concrete Eb and reinforcement Es (in case of a two-line

concrete stress-strain curve – by the adjusted strain modulus for compressed concrete ). In this case the “stress – strain” relationships (6.5)—(6.9), (6.14) and (6.15) on the given sections of the diagrams are used.

(8.35)

(8.36)

8.1.24 The strength of normal reinforced concrete member cross section is analyzed on the basis of the following conditions:

(8.37)

(8.38)

where is the relative strain of the most compressed concrete fiber in the normal section of the member

due to external load;

-is the relative strain of the reinforcing bar under the greatest tension in the normal section of the

member due to external load;

is the ultimate value of the relative strain of the concrete under compression,

assumed in accordance with the instructions in 8.1.30;

-is the ultimate value of the relative strain lengthening the reinforcement, assumed in accordance

with 8.1.30.

8.1.25 For reinforced concrete members exposed to bending moments in two directions and

longitudinal force (Figure 8.5), the concrete and reinforcement strains in a normal section of

random shape are determined by solving simultaneous equations (8.39) (8.41) using equations (8.29) and

(8.30)

(8.39)

(8.40)

(8.41)

The stiffness (i,j-1,2,3) in the simultaneous equations (8.39)-(8.41) is determined from

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C P 63.13330.2012

(8.42)

(8.43)

(8.44)

(8.45)

(8.46)

(8.47)

For a key to the above, see 8.1.23.8.1.26 For reinforced concrete members only exposed to bending moments in two directions Мx and

Мy (skew bending), in equation (8.41) it is assumed that N=0.8.1.27 For reinforced concrete members under eccentric compression in the cross section plane of

symmetry and the location of the X axis in this plane, it is assumed that Mу=0 and D 12=D22=D23 =0. In this case the equilibrium equations look like this:

(8.48)

(8.49)

8.1.28 For reinforced concrete members bending in the plane of symmetry of the cross section and the location of the X axis in this plane, it is assumed that N=0, My, D12=D22=D23=0. In this case the equilibrium equations look like this:

(8.50)

(8.51)

8.1.29 A strength analysis of the normal sections of concrete members under eccentric compression where the longitudinal compressive force is located within the cross section of the member is performed on the basis of (8.37) in accordance with the instructions in 8.1.24 - 8.1.28, in the formulae in 8.1.25 to determine D11, assuming the area of the reinforcement Asi = 0.

For flexural concrete members and concrete members under eccentric compression, in which cracks are not permitted, the strength analysis takes the behavior of the concrete under tension into account

(8.52)

Where is the relative strain of the concrete fiber under the greatest tension in the normal section of

the member from the action of the external load, determined in accordance with 8.1.25-8.1.28;

-is the ultimate value of the relative strain of concrete under tension, assumed in accordance

with the instructions in 8.1.3047

CP 63.13330.2012

8.1.30 The ultimate values of the relative strains of concrete are assumed, in the

case of a two-value strain diagram (compression and tension) in the cross section of the concrete in a

member (flexing, eccentric compression or tension with significant eccentricity), to be

Where members are under eccentric compression or tension and where strains of only one value are distributed in the cross section of the concrete in the member, the ultimate values of the relative concrete

strains are determined depending on the ratio between the concrete strains on opposite sides

of the section of the member from:

(8.53)

(8.52)

where are the strain parameters in the design stress-strain curves for the concrete (6.1.14, 6.1.20, 6.1.22).

The ultimate values of the relative strain in the reinforcement are assumed to be:0.025 – for reinforcement with a yield point;0.015 – for reinforcement with an offset yield point.

Strength analysis for reinforced concrete members under the action of transverse forces

General

8.1.31 A strength analysis for reinforced concrete members under the action of transverse forces is performed on the basis of an oblique cross section model.

In calculations with the help of the model, the oblique cross sections have to be supported by the strength of their members under the effect of shearing forces along the strip between the oblique cross sections and in the oblique cross section itself, as well as the strength under the effect of moment along the oblique cross section.

The strength over the inclined strip is described by the maximum value of the transverse force that can be taken up by an inclined strip that is exposed to compressive forces along the strip and tensile forces from the transverse reinforcement that intersects the inclined strip. The strength of the concrete is determined in terms of the resistance of the concrete to axial compression, taking into account the effect of the complex stressed state in the inclined strip.

The analysis in terms of the strength of the oblique cross section under the action of transverse forces is performed on the basis of an equilibrium equation of the external and internal transverse forces acting in an oblique cross section with projection length C onto the longitudinal axis of the member. Internal transverse forces include the transverse force taken up by the concrete in the oblique cross section, and the transverse force taken up by the transverse reinforcement that intersects the inclined section. The transverse forces taken up by the concrete and by the transverse reinforcement are determined in terms of the resistance of the concrete and the transverse reinforcement to tension, taking into account the length of projection C on the inclined section.

The analysis in terms of the strength of the oblique cross section under the action of moment is performed on the basis of an equilibrium equation of the moments from external and internal forces acting in the oblique cross section with projection length C onto the longitudinal axis of the member. The moments from internal forces include the moment taken up by the longitudinal tensile reinforcement intersecting the oblique cross section, and the moment taken up by the transverse reinforcement intersecting the oblique cross section. The moments taken up by the longitudinal and transverse reinforcement are determined in

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C P 63.13330.2012

terms of the resistance of the longitudinal and transverse reinforcement to tension, taking account of projection C on the inclined section.

Analysis of reinforced concrete members on a strip between oblique cross sections

8.1.32 The analysis of bended reinforced concrete member in the strip between the oblique cross sections is performed on the basis of the condition:

(8.55)

where the transverse is force in the normal section of the member, and is the factor assumed to be 0.3.

Analysis of reinforced concrete members on inclined sections for the action of transverse forces

8.1.33 The analysis of flexural members on an inclined section (Figure 8.6) is performed on the

basis of:

(8.56)

where is the transverse force in the oblique cross section with length C projected onto the longitudinal axis of the member, determined from all the external forces on one side of the given oblique cross section; the most dangerous loading within the oblique cross section is taken into account;

-is the transverse force taken up by the concrete in the oblique cross section;

-is the transverse force taken up by the transverse reinforcement in the oblique cross section.

The transverse force is determined from (8.57)

but is assumed to be not more than and not less than

-is a coefficient assumed to be 1.5;

Figure 8.6 – Diagram of forces for an analysis of reinforced concrete members on an inclined cross section for the action of transverse forces

The force for the transverse reinforcement, normal to the longitudinal axis of the member, is determined from

, (8.58)

where is a coefficient assumed to be 0.75;

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CP 63.13330.2012

- is the force in the transverse reinforcement per unit of length of the member, equal to

, (8.59)

The analysis is performed for a series of oblique cross sections located along the length of the member, with the most dangerous length of the projection of the oblique cross section С. The length of

projection С in the formula (8.58) is assumed to be not less than 1.0 and not more than 2.0 The analysis may be performed for the oblique cross sections without considering the inclined sections

when determining the transverse force from an external load, based on

, (8.60)

where is the transverse force in a normal section from an external load;

, (8.61)

, (8.62)

If a normal section in which a transverse force is taken into account is located near a support at distance а less than 2.5 the analysis based on (8.60) is performed by multiplying the values determined

from formula (8.61), by a factor equal to but the value is assumed to be not more than

If a normal section in which a transverse force is taken into account is located at distance а less

than the analysis based on (8.60) is performed by multiplying the value determined from formula

(8.62), by a factor equal to Transverse (crosswise) reinforcement is taken into account in the analysis if the following condition is

met:

.The transverse reinforcement may also be taken into account if that condition is not met, if in (8.56) it

is assumed

The spacing in the reinforcement taken into account in the analysis must not be greater than

the value of

If there is no transverse reinforcement or if the requirements indicated above, and those contained in 10.3 of the structural requirements, are not met, the analysis is performed based on (8.56) or (8.60),

assuming that the forces or equal zero.The transverse reinforcement must meet the structural requirements contained in 10.3.8.1.34 An analysis for the strip between oblique cross sections and for the inclined sections

themselves should take into account the effect of compressive and tensile stresses, using factor φn which is multiplied by the right-hand side of conditions (8.55), (8.56) or (8.60).

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C P 63.13330.2012

The values of are assumed as: If

1,25 If

If

If

where -is the average compressive stress in the concrete from the effect of longitudinal forces, assumed

to be positive. The value of is taken as the average stress in the cross section of the member

taking the reinforcement into account,

- the average tensile stress in the concrete from the effect of longitudinal forces, assumed to be

positive.

The values of and are taken as the average stresses in the cross sections of members.

The values and a may be determined without taking the reinforcement into account if the

content of longitudinal reinforcement is not more than 3 %.

Analysis of reinforced concrete members for inclined sections for the action of moments

8.1.35 Analysis of reinforced concrete members for inclined sections for the action of moments (Figure 8.7) is performed on the basis of

(8.63)

where М is the moment in the oblique cross section with projection length C onto the longitudinal axis of the member, determined from all the external forces on one side from a given inclined section, relative to the end of the inclined section (point 0), opposite to the end where the longitudinal reinforcement being tested is situated, that takes the tension from the moment in the oblique cross section; the most dangerous loading within the oblique cross section is taken into account; Мs is the moment taken up by the longitudinal reinforcement that intersects the oblique cross section, relative to the opposite end of the oblique cross section (point 0);Msw is the moment taken up by the transverse reinforcement that intersects the oblique cross section in relation to the opposite end of the oblique cross section (point 0).

The moment Мsw is determined from

(8.64)

where Ns is the force in the longitudinal tensile reinforcement, assumed to be , and in the anchorage zone determined in accordance with 10.3.21-10.3.28;

-is the arm of internal couple; it may be assumed to be The moment Мsw for the longitudinal reinforcement normal to the longitudinal axis of the member, is determined from

(8.65)

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CP 63.13330.2012

where – is the force in the transverse reinforcement assumed to be equal to С;

-is determined from (8.59), and C is assumed to be between and The analysis is performed for oblique cross sections located along the length of the member in its end

areas and in places where the longitudinal reinforcement breaks off, with the most dangerous length of the projection of the oblique cross section C taken to be within the limits indicated above. The analysis of oblique cross sections may be performed assuming in (8.63) moment М in the oblique cross section with length of projection C onto the longitudinal axis of the member,

Strength analysis of reinforced concrete members under the effect of torsion moments

General

8.1.36 A strength analysis of reinforced concrete members of rectangular cross section under the effect of torsional moments is performed on the basis of a three-dimensional section model.

An analysis using a three-dimensional section model examines the sections formed by inclined straight line segments following the three sides of the member that are under tensions and ending in a straight line segment along the fourth compressed side of the member.

An analysis of reinforced concrete members for the action of torsional moments is performed in terms of the strength of the members between the three-dimensional sections and the strength of the three-dimensional sections.

For concrete the strength between the three-dimensional sections is denoted by the maximum value of the torsional moment, determined from the resistance of the concrete to axial compression, taking into account the stressed state in the concrete between the three-dimensional sections.

The analysis for the three-dimensional sections is performed on the basis of equilibrium equations of all the internal and external forces relative to the axis located in the center of the compressed zone of the three-dimensional section of the member. The internal moments include the moment taken up by the reinforcement going along the axis of the member, and the reinforcement going across the axis of the member, intersecting the three-dimensional section and located in the tensile zone of the three-dimensional section and on the edge of the member which is under tension opposite to the compressed zone of the three-dimensional section. The forces taken up by the reinforcement are determined from the design values of the resistance to tension of the longitudinal and transverse reinforcement.

The analysis examines all the positions of the three-dimensional section, taking the compressed zone of the three-dimensional section near the lower, side and upper edges of the member.

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C P 63.13330.2012

The analysis for the combined effect of torsion and bending moments, and torsional moments and transverse forces, is performed based on equations of the interaction between the corresponding force factors.

Analysis for the effect of torsional moment8.1.37 The strength analysis of a member between three-dimensional sections is performed based on

(8.66)

where Т is the torsional moment from external loads in the normal cross section of the member; b and h are the lesser and greater dimensions respectively of the cross section of the member.

8.1.38 The strength analysis of three-dimensional sections is performed on the basis of (Figure 8.8)

(8.67)

where T is the torsional moment in the three-dimensional section, determined from all the external forces located on one side of the three-dimensional section;

is the torsional moment taken up by the reinforcement of the three-dimensional section located in the direction transverse to the axis of the member;Тs is the torsional moment taken up by the reinforcement of the three-dimensional section located in the longitudinal direction.

Figure 8.8 - 3D cross section load diagrams when calculating action of Rotary torque

The value of the ratio between loads in transverse and longitudinal reinforcement taken into account in the condition (8.67) is presented below.

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CP 63.13330.2012

Rotary torque Tsw. is calculated using the formula

(8.68)

and rotary torque Тs is calculated using the formula

(8.69)

Where is the force in the transverse reinforcement; for reinforcement normal to the member’s longitudinal axis, the force is found using the formula

(8.70)

-Force in this reinforcement per unit of member length,

(8.71)

Cross section area of the transverse reinforcement;

The spacing of this reinforcement; The projected length of the tensioned side of the cross section onto the member’s longitudinal axis

(8.72)

5 – the factor taking into account the ratio of the cross section dimensions

(8.73)

С – the projected length of the compressed side of the cross section onto the member’s longitudinal axis;Ns – the force in the longitudinal reinforcement at the given face of the member

(8.74)

- The cross section area of the longitudinal reinforcement at the given side of the member;Z1 and Z2 – the length of the side of the cross section of the given tensioned face of the member and the

length of the other side of the cross section of the member.

The ratio is used from 0.5 to 1.5. Only to the Extent that

the value of is outside the specified range, then the calculation takes into consideration the quantity

of reinforcement (longitudinal or lateral) at which the value of remains within the specified range.The calculation is performed for a series of spatial sections located along the member, for the most

hazardous length of projection of section C on the member longitudinal axis. In this case, the value of С

shall be taken to be no more than and no more than .It is admissible to perform analysis for the effect of the torsional moment—without regard for the

three-dimensional sections when determining the torsional moment from external loads—based on the following condition:

(8.75)

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C P 63.13330.2012

where is the torsional moment in the normal section of the member;

- the torsional moment taken by the reinforcement located along the analyzed side of the member in the transverse direction, and determined from the formula

(8.76)the torsional moment taken by the longitudinal reinforcement located along the analyzed side of the

member, and determined from the formula

(8.77)

The ratio shall be adopted within the aforementioned range.

Analysis shall be performed for a series of normal sections located along the length of a member, and for reinforcements located along each analyzed side of the member.

The design requirements given in 10.3 shall be complied with for members subjected to torsional moments.

Analysis for the Combined Effect of Torsion and Bending Moments

8.1.39 Strength analysis of a member between three-dimensional sections shall be performed according to 8.1.36.

8.1.40 Strength analysis for a three-dimensional section shall be performed based on the following condition:

(8.78)

where T – the torsional moment from an external load in the three-dimensional section;T0 – the ultimate torsional moment taken by the three-dimensional section;

M – the bending moment from an external load in the normal section;M0 – the ultimate bending moment taken by the normal section.

Analysis for the combined effect of torsion and bending moments shall examine the three-dimensional section with a tensile reinforcement located along the side subjected to tension from the bending moment, i.e. along the side that is normal relative to the plane in which the bending moment is acting.

The torsional moment T from an external load shall be determined in the normal section located at the midpoint of the length of projection C onto the longitudinal axis of the member. The bending moment M from the external load shall be also determined in this normal section.

The ultimate torsional moment shall be determined according to 8.1.37 and taken to equal the right part of condition (8.67) (which equals Тт+Тs) for the analyzed three-dimensional section.

The ultimate bending moment M0 shall be determined according to 8.1.9.It is admissible to use condition (8.75) for determining torsional moments. In this case, the torsional

moment Т-Т1 and the bending moment М shall be determined in normal sections along the length of the member. In the analyzed normal section, the ultimate torsional moment shall be taken to equal the right part

of condition (8.75)

The ultimate bending moment shall be determined for the same normal section in the manner described above.

In the case of a combined effect of torsion and bending moments, the design and structural requirements given in 10.3 and 8.1.38 shall be complied with.

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CP 63.13330.2012

Analysis for the Combined Effect of the Torsional moment and the Transverse Force

8.1.41 The strength analysis of a member between three-dimensional sections is performed based on

(8.79)

where T – the torsional moment from an external load in the normal section;Т0 – the ultimate torsional moment taken by the member between three-dimensional sections, and taken

to equal the right part of condition (8.66);- the transverse force from an external load in the same normal section;

- the ultimate transverse force taken by the concrete between the oblique sections, and taken to equal the right part of condition (8.55).

8.1.42 Strength analysis of the three-dimensional section shall be performed according to condition (8.79) in which the following values shall be adopted:T – the torsional moment from an external load in the three-dimensional section;T0 – the ultimate torsional moment taken by the three-dimensional section;

the transverse force in the oblique section;

– the ultimate transverse force taken by the oblique section.Analysis for the combined effect of the torsional moment and the transverse force shall examine the

three-dimensional section with a tensile reinforcement located along one of the sides subjected to tension from the transverse force, i.e. along the side that is parallel to the plane in which the transverse force is acting.

The torsional moment T from the external load shall be determined in the normal section located at

the midpoint of the length C along the longitudinal axis of the member. The transverse force from the external load shall be determined in the same normal section.

The ultimate torsional moment shall be determined according to 8.1.38 and taken to equal the right part of condition (8.67) (which equals Тsw+Тs) for the analyzed three-dimensional section.

The ultimate transverse force shall be determined according to 8.1.33 and taken to equal the right part of condition (8.56). In this case, the midpoint of the length of the projection of the oblique section onto the longitudinal axis of the member shall be positioned in the normal section passing through the midpoint of the length of the projection of the three-dimensional section onto the longitudinal axis of the member.

It is admissible to use condition (8.75) for determining torsional moments, and condition (8.60) for

determining transverse forces. In this case, the torsional moment Т=Т1 and the transverse force from an external load shall be determined in normal sections along the length of the member. In the analyzed

normal section, the ultimate torsional moment shall be taken to equal the right part of condition (8.75)

(which equals ), and the ultimate transverse force in the same normal section shall be taken to

equal the right part of condition (8.60) (which equals ).In the case of a combined effect of torsional moments and transverse forces, one shall comply with

the design and structural requirements indicated in 10.3.Analysis of Reinforced Concrete Members for Local Compression8.1.43 Reinforced concrete members shall be analyzed for local compression (bearing stress) when

they are subjected to a compressive force that is applied on a limited area normally to the surface of a

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reinforced concrete member. In this case, one shall factor in the increased compressive strength of concrete within the load transfer area (bearing stress area) owing to the three-dimensional state of stress of concrete under the bearing stress area, which strength depends on the location of the bearing stress area on the surface of the member.

If confinement reinforcements are present in the local compression area, one shall additionally factor in the increased compressive strength of concrete under the bearing stress area owing to the added strength of the confinement reinforcements.

Members shall be analyzed for local compression according to 8.1.44 in the absence of confinement reinforcements, or 8.1.45 in the presence of confinement reinforcements.

8.1.44 Members shall be analyzed for local compression in the absence of confinement reinforcements (Fig. 8.9) in accordance with the condition:

(8.80)

where N – the local compressive force from an external load;

- the area of application of the compressive force (bearing stress area);

-the design strength of concrete under compression when subjected to the local effect of the compressive force;

ψ – a factor taken to equal 1.0 in the case of uniform distribution of the local load over the bearing stress area, or 0.75 in the case of irregular distribution.

The value of shall be determined from the formula:

(8.81)

where is a factor determined from the formula:

(8.82)but taken to equal no more than 2.5 and no less than 1.0 in any case. In formula (8.82):

- the maximum design area established according to the following rules: the centers of gravity of

the areas and match;

the boundaries of the design area are separated from each side of the area by a distance equivalent to the respective dimensions of such sides (Fig. 8.9).

8.1.45 Members shall be analyzed for local compression in the presence of confinement reinforcements in the form of a welded mesh in accordance with the condition:

(8.83)

where – the design strength of concrete under compression, reduced to account for the presence of confinement reinforcements and calculated from the formula:

(8.84)

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CP 63.13330.2012

a – away from edges of the member; b – across the entire width of the member; c – by the edge (butt) of the member along its entire width; d – at the corner of the member; e – by one edge of the member; f – near one edge of the member; 1 – the

member subjected to the local load; 2 – the bearing stress area ; 3 – the maximum design area Ab.max; 4 – the center of

gravity of the areas and Ab.max; 5 – the minimum zone of reinforcement with welded meshes whereby confinement reinforcement is factored into the analysis.

Fig. 8.9: Schematics for Analysis of Members for Local Compression for Different Positions of the Local Load

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Here – a factor determined from the formula:

(8.85)

– the area confined within the outline of meshes of confinement reinforcement, traced along the

outer-most bars of the meshes, and taken to be no more than in formula (8.85).design tensile strength of confinement reinforcements;

factor of confinement reinforcement determined from the formula:

(8.86)

– number of bars, cross-sectional area and length of the mesh bar, along the axes

of outer-most bars in the X direction; – ditto in the Y direction;s – pitch of meshes of confinement reinforcements.

The values of and N shall be taken according to 8.1.44.The value of the local compressive force taken by a member with confinement reinforcement (the

right part of condition (8.83)) shall be taken as no more than double the value of the local compressive force applied to a member without confinement reinforcement (the right part of condition (8.80)).

Confinement reinforcement shall meet the structural requirements indicated in 10.3.

Analysis of Reinforced Concrete Members for Punching Shear

General

8.1.46. Analysis for punching shear shall be performed for flat reinforced concrete members (slabs) subjected to local concentrated stress (normally to the member plane) – concentrated force and concentrated bending moment.

Analysis for punching shear shall examine the design cross-section located around the zone of

transfer of stress to the member at a distance of normally to its longitudinal axis, the surface of which member is subjected to tangential stresses from the concentrated force and concentrated bending moment (Fig. 8.10).

The tangential stresses acting on the area of the design cross-section shall be taken by the concrete

having axial compression strength and by the transverse reinforcements at a distance of no more than

and no less than from the load transfer area, with tensile strength of .When a concentrated force is applied, the tangential stresses taken by concrete and reinforcements

shall be assumed to be uniformly distributed throughout the entire area of the design cross-section. When a bending moment is applied, the tangential stresses taken by the concrete and reinforcements shall be assumed to be linearly varying along the length of the design cross-section in the direction of the moment with the maximum tangential stresses having the opposite sign by the edges of the design cross-section in this direction.

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Figure 8.10: Provisional Model for Analysis for Punching Shear

Analysis for punching shear under the effect of a concentrated force and in the absence of transverse reinforcements shall be performed according to 8.1.47; under the effect of a concentrated force and in the presence of transverse reinforcements – according to 8.1.48; under the effect of a concentrated force and a concentrated bending moment and in the absence of transverse reinforcements – according to 8.1.49; and under the effect of a concentrated force and a concentrated bending moment and in the presence of transverse reinforcements – according to 8.1.50.

The design outline of the cross-section shall be taken to be: if the load transfer area is located inside a flat member – enclosed and located around the load transfer area (Fig. 8.11, a, d); if the load transfer area is located by the edge or corner of a flat member – as one of the two options: enclosed and located around the load transfer area, and unenclosed and traced from the edges of the flat member (Fig. 8.11, b, c), in which case analysis shall factor in the smallest bearing capacity between the two options of the location of the design outline of the cross-section.

If a hole in a slab is located at a distance of less than 6h from the corner or edge of the load transfer area to the corner or edge of the hole, the segment of the design outline located between the two lines that are tangent to the hole and drawn from the center of gravity of the load transfer area shall not be disregarded during analysis.

When the moment acts at the point of concentrated load application, one half of this moment shall be taken into consideration during analysis for punching shear, and the other half – during analysis for normal sections along the section width that includes the width of the load transfer area and the height of the section of the flat member on both sides of the load transfer area.

When the concentrated moments and force act under strength conditions, the ratio between the acting

concentrated moments M taken into account in analysis for punching shear and the ultimate shall be

taken to be no more than one half of the ratio between the acting concentrated force F and the ultimate .

When the concentrated force is applied eccentrically relative to the center of gravity of the outline of the design cross-section, the values of concentrated bending moments from an external load shall be determined taking into account the additional moment from the eccentric application of the concentrated force relative to the center of gravity of the outline of the design cross-section with a positive or negative sign relative to moments in the column.

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1 – area of load application; 2 – design outline of the cross-section; 2' – second option of the design outline location; 3 – center of gravity of the design outline (the point of intersection of the axes Х1 and Y1); 4 – center of gravity of the area of load application (the

point of intersection of the axes X and Y); 5 – transverse reinforcement; 6 – outline of the design cross-section excluded from analysis of the transverse reinforcement; 7 – boundary (edge) of the flat member

Figure 8.11: Schematic of Design Outlines of the Cross-Section During Punching Shear

Analysis of Members for Punching Shear under the Effect of a Concentrated Force8.1.47. Members without transverse reinforcements shall be analyzed for punching shear under the

effect of a concentrated force based on the condition:

(8.87)where F – the concentrated force from an external load;Fb.ult – the ultimate stress taken by concrete. The stress Fb.ult shall be determined from the formula:

(8.88)where Ab – the area of the design cross-section located at a distance of 0.5 h 0 from the boundary of the area

of application of the concentrated force F with the section working height h0 (Fig. 8.12).

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1 –

design cross-section; 2 – outline of the design cross-section; 3 – outline of the area of load application.

Figure 8.12: Schematic for Analysis of Reinforced Concrete Members Without Transverse Reinforcements for Punching Shear

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The area Ab shall be determined from the formula:

(8.89)where u is the perimeter of the outline of the design cross-section;

h0 – reduced working height of the section.here h0x and h0у – working height of the section for longitudinal reinforcements located in the direction of the

X and Y axes.8.1.48. Members with transverse reinforcements shall be analyzed for punching shear under the effect of a concentrated force (Fig. 8.13) based on the condition:

(8.90)

where – ultimate stress taken by the transverse reinforcement during punching shear;Fb,ult – ultimate stress taken by concrete, determined according to 8.1.47.

The stress taken by the transverse reinforcement that is normal relative to the longitudinal axis of the member and located uniformly along the outline of the design cross-section shall be determined from the formula:

(8.91)where qsw is the stress in transverse reinforcements per unit of length of the design cross-section outline

located within the boundaries of the distance 0.5h0 on both sides of the outline of the design section.

(8.92)Аsw – sectional area of the transverse reinforcements with a pitch of sw, located within the boundaries of the distance h0 on both sides of the outline of the design cross-section along the perimeter of the outline of the design cross-section;и – perimeter of the outline of the design cross-section determined according to 8.1.47.When the transverse reinforcement is positioned in an irregular pattern along the outline of the design

cross-section and in a concentrated pattern along the axes of the load transfer area (crosswise pattern of transverse reinforcements), the outline perimeter u for transverse reinforcements shall be taken to equal the

actual lengths of the transverse reinforcement sections and positioned along the design outline of punching shear (Fig. 8.11, d).

The value of shall be taken to be no more than . Transverse reinforcements

shall be factored into analysis when is no less than 0.25 .Outside the boundaries of transverse reinforcements, analysis for punching shear shall be performed

according to 8.1.47, with the outline of the design cross-section positioned at a distance of 0.5h0 from the boundary of transverse reinforcements (Fig. 8.13). When transverse reinforcements are positioned in a concentrated pattern along the axes of the load transfer area, the design outline of the concrete cross-section shall be additionally adopted along the diagonal lines traced from the edge of the transverse reinforcements (Fig. 8.11, d).

Transverse reinforcements shall meet the structural requirements indicated in 10.3. When the structural requirements of 10.3 are not met, analysis for punching shear shall factor in only transverse reinforcements crossing the punching shear pyramid, provided that the anchoring requirements for such transverse reinforcements are complied with.

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1 – design cross-section; 2 – outline of the design cross-section; 3 – boundaries of the zone within which transverse reinforcements are factored into analysis; 4 – outline of the design cross-section without transverse reinforcements factored

into analysis; 5 – outline of the load application area.

Fig 8.13: Schematic for Analyzing Reinforced Concrete Slabs with Vertical Regularly Distributed Transverse Reinforcements for Punching Shear

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Analysis of Members for Punching Shear under the Effect of a Concentrated Force and a

Concentrated Bending Moment

8.1.49. Members without transverse reinforcements shall be analyzed for punching shear under the combined effect of a concentrated force and a concentrated bending moment (Fig. 8.12) based on the condition:

(8.93)

where F – the concentrated force from an external load;М – concentrated bending moment from an external load, which is factored into analysis for

punching shear (8.1.46);

and – ultimate concentrated force and concentrated bending moment that can be taken by concrete in the design cross-section while they are acting separately.

In a reinforced concrete frame of buildings with flat floor / ceiling assemblies, the concentrated

bending moment equals the total bending moment in the sections of the top and bottom columns adjoining the floor / ceiling assembly in the relevant joint.

The ultimate force shall be determined according to 8.1.47.

The ultimate bending moment shall be determined from the formula:

(8.94)

where is the moment of resistance of the design cross-section determined according to 8.1.51.When bending moments act in two mutually perpendicular planes, analysis shall be performed based

on the condition:

(8.95)

where F, Мх and Му – concentrated force and concentrated bending moments in the directions of the X and Y axes, which are factored into analysis for punching shear (8.1.46), from an external load;

- the ultimate concentrated force and concentrated bending moments in the directions of the X and Y axes, which can be taken by concrete in the design cross-section while they act separately.

The stress Fb.ult shall be determined according to 8.1.47.The stresses Mbx.ult and Mby.ult shall be determined according to the foregoing instructions, when

the moment is acting in the plane of the X and Y axes, respectively.8.1.50. Strength analysis of members with transverse reinforcements for punching shear under the

effect of a concentrated force and concentrated bending moments in two mutually perpendicular planes shall be performed based on the condition:

(8.96)

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and – the ultimate concentrated force and concentrated bending moments in the directions of the X and Y axes, which can be taken by the concrete in the design cross-section while they act separately;

and – the ultimate concentrated force and concentrated bending moments in the directions of the X and Y axes, which can be taken by the transverse reinforcements while they act separately.

The stresses , , , and shall be determined according to guidelines

presented in 8.1.48 and 8.1.49. The stresses and taken by the transverse reinforcement that is normal relative to the longitudinal axis of the member and located uniformly along the outline of the design section shall be determined—under the effect of a bending moment in the directions of the X and Y axes, respectively—from the formula:

(8.97)

where and shall be determined according to 8.1.48 and 8.1.51.

The values of in condition (8.96) shall

be taken to be no more than , respectively.The transverse reinforcement must meet the structural requirements contained in 10.3. When the

structural requirements of section 10.3 are not met, analysis for punching shear shall factor in only transverse reinforcements crossing the punching shear pyramid, provided that the anchoring requirements for such transverse reinforcements are complied with.

8.1.51. As a general rule, the values of the moment of resistance of the design outline of concrete

subjected to punching shear in the directions of the mutually perpendicular axes X and Y shall be determined from the formula:

( 8 . 9 8 )

where – the moment of inertia of the design outline relative to the Y1 and Х1 axes passing through its center of gravity (Fig. 8.11);

- the maximum distance from the design outline to its center of gravity;The value of the moment of inertia Ibх(у) shall be determined as the sum of the moments of inertia Ibх(у)i

of individual segments of the design outline of the cross-section relative to central axes passing through the center of gravity of the design outline, with the width of each segment provisionally taken to equal 1.

The position of the center of gravity of the design outline relative to the chosen axis shall be determined from the formula:

( 8 . 9 9 )

where Li is the length of an individual segment of the design outline;

- the distance from the centers of gravity of individual segments of the design outline to the chosen axes.

Analysis shall use the smallest values of the moments of resistance and . The moment of resistance of the design outline of concrete for columns with a circular section shall be determined from the formula:

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where D is the column diameter.8.1.52. The values of the moments of resistance of transverse reinforcements subjected to punching

shear , when the transverse reinforcements are located in a regular pattern along the design outline of

punching shear within a zone whose boundaries are located at a distance of on each side of the outline of punching shear of the concrete

(see Fig. 8.13), shall be taken to equal the corresponding values of and .When transverse reinforcements are located inside a flat member in a concentrated pattern along the

axes of the load transfer area (for example, along the axis of columns — crosswise pattern of transverse reinforcements within the span), the moment of resistance of the transverse reinforcements shall be determined according to the same rules that apply to the moments of resistance of concrete, with the corresponding actual length of the confined zone where transverse reinforcements are located to be adopted

from the design outline of punching shear and (Fig. 8.11, d).

Strength Analysis of Planar Reinforced Concrete Members of Slabs and Walls

8.1.53. Strength analysis of flat slabs for floors/ceilings, roofs, and basements shall be performed identically to analysis of isolated flat members for the combined effect of bending moments in the direction of mutually perpendicular axes and the bending moments applied to the lateral sides of the isolated flat member, as well as for the effect of longitudinal and transverse forces applied to the lateral sides of the flat member (Fig. 8.14).

In addition, when flat slabs are resting on columns, slab analysis for punching shear under the effect of concentrated normal forces and moments shall be performed according to 8.1.46 - 8.1.52.

Figure 8.14: Schematic of Stresses Acting on the Isolated Flat Wall Member of Unit Width

8.1.54. As a general rule, it is recommended to perform strength analysis of flat slabs by dividing the flat member into separate layers of compressed concrete and tensile reinforcements, and analyzing each layer separately for the effect of normal and shearing forces in this layer resulting from the effects of bending and torsional moments and normal forces (Fig. 8.15).

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Figure 8.15: Schematic of Stresses Acting in the Concrete and Reinforcement Layers of the Isolated Flat Member of a Slab (Stresses Acting on the Opposite Sides are not Shown Provisionally)

Flat members of slabs can be also analyzed—without dividing the concrete and tensile reinforcements into layers—for the combined effect of bending and torsional moments according to the conditions based on the generalized equations of limit equilibrium:

(8.100)

(8.101)

(8.102)

(8.103)

where – the bending and torsional moments acting on the isolated flat member;

- ultimate bending and torsional moments taken by the isolated flat member.

The values of the ultimate bending moments and shall be determined from analysis of normal sections (perpendicular to the X and Y axes) of the isolated flat member with longitudinal reinforcements parallel to the X and Y axes as prescribed in 8.1.1.-8.1.13.

The values of ultimate torsional moments shall be determined for concrete and for tensile

longitudinal reinforcements from the formulas:

(8.104)where b and h are the smaller and greater dimensions of the isolated flat member, respectively;

(8.105)

where Аsx and Аsy are the sectional areas of longitudinal reinforcements in the direction of the X and Y axes; h0 is the working height of the slab cross-section. It is also admissible to use other methods of strength analysis of the isolated flat member, which are based on the equilibrium of external stresses acting on the lateral sides of the isolated member and internal stresses in the diagonal section of the isolated flat member.

When the flat member of slabs is also subjected to the longitudinal force, analysis shall be performed identically to the isolated flat member of walls according to 8.1.57.

8.1.55 Analysis of an isolated flat member for the effect of transverse forces shall be performed on the basis of the following condition:

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(8.106)

where and – transverse forces acting on the lateral sides of the isolatedflat member;

and – ultimate transverse forces taken by the isolated flat member.The values of ultimate transverse forces shall be determined from the formula:

(8.107)

where and – ultimate transverse forces taken by the concrete and transverse reinforcement, respectively, which are determined from the formulas:

(8.108)

(8.109)

where – power of transverse reinforcement determined from formula (8.59).8.1.56 As a general rule, strength analysis of walls shall be performed identically to isolated flat

members for the combined effect of normal forces, bending moments, torsional moments, shearing forces, and transverse forces applied to the lateral sides of the isolated flat member (Fig. 8.16).

8.1.57 As a general rule, it is recommended to perform analysis of walls by dividing the flat member into separate layers of compressed concrete and tensile reinforcements, and analyzing each layer separately for the effect of normal and shearing forces in this layer resulting from the effects of bending and torsional moments, and combined normal and shearing forces.

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CP 63.13330.2012

Figure 8.16: Schematic of Stresses Acting on the Isolated Flat Wall Member of Unit Width (Stresses Acting on the Opposite Sides are not Shown Provisionally)

It is admissible to perform analysis (without isolating separate layers of concrete and tensile reinforcements from the plane of the wall) for the combined effect of bending moments, torsional moments, and normal forces, and within the plane of the wall – for the combined effect of normal and shearing forces.

It is recommended to perform wall analysis within its plane according to conditions based on the generalized equations of limit equilibrium:

(8.110)

(8.111)

(8.112)

(8.113)

where , and – normal and shearing forces acting on the lateral sides of an isolated flat member;

ultimate normal and shearing forces taken by the isolated flat member;

The values of the ultimate normal forces and shall be determined based on analysis of normal sections (perpendicular to the X and Y axes) of the isolated flat member with vertical and horizontal reinforcements that are parallel to the X and Y axes, as prescribed in 8.1.14 - 8.1.19.

The values of ultimate shearing forces shall be determined for concrete and for

reinforcements from the formulas:

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(8.114)

where Ab – the working cross-sectional area of concrete of the isolated member.

(8.115)

where Аsx and Аsу – the sectional area of reinforcements in the directions of the X and Y axes in the isolated

member.

Analysis within the wall plane shall be performed identically to analysis of the flat slabs of floor/ceiling assemblies, with the values of ultimate bending moments determined taking into account the effect of normal forces.

It is also admissible to use other methods of strength analysis of the isolated flat member, which are based on the equilibrium of external stresses acting on the lateral sides of the isolated member and internal stresses in the diagonal section of the isolated member.

8.1.58 Strength analysis of isolated flat members of walls for the effect of transverse forces shall be performed identically to analysis of slabs, but also taking into account the effect of longitudinal forces.

8.1.59 Analysis of crack resistance of slabs (in terms of the formation and opening of cracks that are normal relative to the longitudinal axis of the member) shall be performed for the effect of bending moments (without taking into account torsional moments) as prescribed in 8.2.

8.2. Analysis of Members of Reinforced Concrete Structures for Group 2 Limit States

General

8.2.1 Analysis for group 2 limiting states should include:Crack formation analysisCrack width analysisStrain analysis8.2.2 Crack formation analysis shall be performed when it is necessary to ensure the absence of

cracks (see 4.3). It shall be also performed to support crack opening analysis and strain analysis.8.2.3 During crack formation analysis performed to prevent crack formation, the load safety factor

shall be taken to be (identically to strength analysis). During crack opening analysis and strain

analysis (including supporting crack formation analysis), the load safety factor shall be taken to be .

Crack Formation Analysis of Reinforced Concrete Members

8.2.4 Crack formation analysis of reinforced concrete members shall be performed based on the following condition:

(8.116)where M – the bending moment from an external load relative to an axis that is normal to the plane of

the moment and passes through the center of gravity of the reduced cross-section of the member;Мcrc – the bending moment taken by the normal section of a member during crack formation,

which is determined from formula (8.121). In the case of centrally tensile members, crack formation shall be determined based on the

following condition:

(8.117)where N – longitudinal tensile stress from an external load;

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- longitudinal tensile stress taken by the member during crack formation, which is determined according to 8.2.13.

8.2.5 When condition (8.116) or (8.117) is satisfied, crack opening calculation shall be performed. Reinforced concrete members shall be performed for intermittent and continuous crack opening.

Intermittent crack opening shall be determined from the combined action of permanent and temporary (continuous and intermittent) loads. Continuous crack opening shall be determined from permanent and temporary continuous loads only (4.6).(8.118),

8.2.6 Crack opening analysis shall be performed based on the following condition:

(8.118)

where – width of crack opening under the effect of an external load, determined according to 8.2.7, 8.2.15 - 8.2.17.

-maximum permissible width of crack opening.

The values of shall be taken to equal: (а) from the condition of continued safety of class А240...А600, В500 reinforcements:

0.3 mm – for continuous crack opening0.4 mm – for intermittent crack opening; class А800, А1000, Вр1200-Вр1400, K1400, K1500

(K-19), and K1500 (K-7), K1600 reinforcements

12 mm in diameter:0,2 mm – for continuous crack opening0.4 mm – for intermittent crack opening

class Вp1500, K1500 (K-7), K1600 reinforcements 6 and 9 mm in diameter:0,1 mm – for continuous crack opening0.2 mm – for intermittent crack opening

b) from the limit of permeability of the structures:0,2 mm – for continuous crack opening0.3 mm – for intermittent crack opening8.2.7 Crack width analysis of reinforced concrete members should be performed for continuous and

intermittent opening of normal and inclined cracks.The width of continuous cracks is determined by the formula

(8.119)

and the width of intermittent cracks by the formula

(8.120)

where is the width of cracks due to the continuous action of dead loads and live long-term loads;

- width of crack opening from intermittent effects of dead and live (continuous and

intermittent) loads;

- width of crack opening from intermittent effects of dead and temporary continuous

loads.

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Determining the Moment of Formation of Cracks that Are Normal Relative to the Longitudinal Axis member

8.2.8 As a general rule, the bending moment during crack formation shall be determined from the strain model according to 8.2.14.

In the case of members with rectangular, T-bar, or double-T bar sections and reinforcements located near the top and bottom sides, it is admissible to determine the moment of crack formation taking into account non-elastic strain of tensile concrete as prescribed in 8.2.10 - 8.2.12.

8.2.9 It is admissible to determine the moment of crack formation without taking into account non-

elastic strain of tensile concrete as prescribed in 8.2.11, by adopting in formula (8.121). If condition (8.118) or condition (8.139) is not satisfied in this case, the moment of crack formation shall be determined taking into account non-elastic strain of tensile concrete.

8.2.10 The moment of crack formation taking into account non-elastic strain of tensile concrete shall be determined in accordance with the following provisions:

sections remain flat after being subjected to strain;the diagram of stresses in the compressive region of concrete shall be adopted with a triangular shape,

just like for an elastic body (Fig. 8.17);the diagram of stresses in the tensile region of concrete shall be adopted with a trapezoid shape with

stresses that do not exceed the values of the design tensile strength of concrete.relative strain of the outermost tensile fiber of concrete shall be taken to equal its previous value

under the intermittent effect of a load (8.1.30); in the case of a double-digit strain diagram in the

member section: .

stresses in reinforcements shall be adopted depending on relative strain just like for an elastic body.8.2.11 The moment of crack formation taking into account non-elastic strain of tensile concrete

shall be determined from the formula:

(8.121)

where – elasto-plastic moment of resistance of the section for the outermost tensile concrete fiber, determined taking into account the provisions of 8.2.10;

ех – distance from the point of application of the longitudinal force N (located at the center of gravity of the reduced section of the member) to the core point that is farthermost from the tensile region whose crack formation is being analyzed.

In formula (8.121), the plus sign shall be adopted in the case of the compressive longitudinal force N, and the minus sign – in the case of a tensile force.

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l – Level of the center of gravity of the reduced cross-section

Figure 8.17: Schematic of the Stress-Strain State of the Member Section During Analysis of Crack Formation under the Effect of the Bending Moment (a), Bending Moment and Longitudinal Force (b)

In the case of rectangular sections and T-bar sections with a flange located in the compressive region, the value of Wpl under the effect of the moment acting in the plane of the axis of symmetry may be taken to equal:

(8.122)

where – elastic moment of resistance of the reduced section over the tensile region of the section, which is determined in accordance with 8.2.12.

8.2.12. The moment of resistance Wred and the distance ех shall be determined from the formulas:

(8.123)

(8.124)where Ired – the moment of inertia of the reduced section of the member relative to its center of gravity

(8.125)

- area moments of inertia of concrete, tensile reinforcements, and compressed reinforcements, respectively;

Ared – area of the reduced cross-section of the member, which is determined from the formula:

(8.126)α – factor of reinforcement reduction to concrete

– cross-sectional areas of concrete, tensile and compressed reinforcements, respectively;

уt – distance from the concrete fiber subjected to the most tension to the center of gravity of the reduced cross-section of the member

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here is the static moment of the reduced cross-sectional area of the member relative to the concrete fiber subjected to the most tension.

It is admissible to determine the moment of resistance while disregarding the reinforcements.

8.2.13 The stress during crack formation in centrally tensile members shall be determined from the formula:

(8.127)

8.2.14 The moment of crack formation shall be determined on the basis of the nonlinear strain model in accordance with the general provisions given in 6.1.24 and 8.1.20 - 8.1.30, but also taking into account the behavior of concrete in the tensile region of the normal section, which shall be determined from the tensile concrete state diagram according to 6.1.22. The design characteristics of materials shall be adopted for Group 2 limit states.

The value of Мcrc shall be determined from the solution of the system of equations given in 8.1.20-

8.1.30, while taking the relative strain of concrete along the side of the member subjected to tension

from an external load to equal the ultimate relative strain of concrete subjected to tension , which shall be determined as prescribed in 8.1.30.

Analysis of the Width of Opening of Cracks that Are Normal Relative to the Longitudinal Axis of the Member

8.2.15 The opening width of normal cracks shall be determined from the formula:

(8.128)

where – stress in the longitudinal tensile reinforcement in the normal section with a crack caused by the relevant external load, to be determined according to 8.2.16;

-basic distance (without regard for the effect from the type of surface of the reinforcement) between adjacent normal cracks, to be determined according to 8.2.17;

-a factor accounting for irregular distribution of relative strains of tensile reinforcements between

cracks; it is admissible to take the factor to equal 1; if condition (8.118) is not satisfied, the value of shall be determined from formula (8.138);

- a factor accounting for the duration of effect from a load, which is taken to equal:1.0 – for intermittent loads;1.4 – for continuous loads;

- a factor accounting for the profile of longitudinal reinforcements, which is taken to equal:0.5 – for reinforcements with a semicontinuous profile and cable reinforcements;0.8 – for smooth reinforcements;

- a factor accounting for the nature of the load, which is taken to equal:1.0 – for flexural members and eccentrically compressed members;1.2 – for tensile members.

8.2.16. The values of stress in tensile reinforcements of flexural members shall be determined from the formula:

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CP 63.13330.2012

(8.129)

where – the moment of inertia and the height of the compressive region of the reduced cross-section of the member, which are determined taking into account the sectional area of the compressive region of concrete only, the sectional areas of the tensile and compressed reinforcements according to 8.2.27, with the

values of the factor of reduction of reinforcements to concrete taken to be in the relevant formulas.

In the case of flexural members (Fig. 8.18), where х – height of the compressive region of concrete, which shall be determined according to 8.2.28 at .

The value of the factor of reinforcement reduction to concrete αs1 shall be determined from the formula:

(8.130)

where – reduced modulus of strain of compressed concrete, which factors in non-elastic strain of compressed concrete and is determined from the formula:

(8.131)

The relative strain of concrete shall be taken to equal 0.0015. It is admissible to determine stress from the formula:

(8.132)

where – the distance from the center of gravity of the tensile reinforcement to the point of application of the resultant of the stresses in the compressive region of the member.

I – Level of the center of gravity of the reduced cross-section

Figure 8.18: Schematic of the Stress-Strain State of the Member with Cracks under the Effect of the Bending Moment (a, b), Bending Moment and Longitudinal Force (c)

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In the case of members with a rectangular cross-section in the absence of (or without regard for)

compressed reinforcements, the value of shall be determined from the formula:

(8.133)In the case of members with a rectangular, T-bar (with a flange in the compressive region), and double-

T-bar cross-section, it is admissible to take the value of to equal 0.8 .

Under the effect of the bending moment M and longitudinal force N, the stress intensile reinforcements shall be determined from the formula:

(8.134)

where – reduced cross-sectional area of the member and distance from the most-compressed concrete fiber to the center of gravity of the reduced section, which shall be determined according to the general rules for calculating the geometric characteristics of sections of elastic members, taking into account the sectional area of the compressive region of concrete only, and the sectional areas of tensile and compressed reinforcements according to 8.2.28, while taking the factor of reinforcement reduction to concrete to equal

.

It is admissible to determine stress from the formula:

(8.135)where еs – the distance from the center of gravity of the tensile reinforcement to the point of application of

the longitudinal force N, taking into account the eccentricity that equals .In the case of members with a rectangular section in the absence of (or without regard for) compressed

reinforcements, it is admissible to determine the value of from formula (8.133) in which:хт – the height of the compressive region of concrete, taking into account the effect of the longitudinal force

determined according to 8.2.28, with the factor of reinforcement reduction to concrete taken to be .In the case of members with a rectangular, T-bar (with a flange in the compressive region), and double-T-bar

cross-section, it is admissible to take the value of to equal .In formulas (8.134) and (8.135), the plus sign shall be used in the case of a tensile force and the minus sign in the case of a compressive longitudinal force.

The stresses σs shall not exceed .8.2.17 The values of the basic distance between cracks ls shall be determined from the formula:

(8.136)

and taken to be no less than 10 ds and 10 cm and no more than 40 ds and 40 cm.Here Abt is the sectional area of tensile concrete;Аs is the sectional area of tensile reinforcements;ds is the nominal diameter of reinforcements. The values of Abt shall be determined based on the height of the tensile region of concrete xt,

according to the rules for analyzing the moment of crack formation as prescribed in 8.2.8 – 8.2.14.In any case, the value of Abt shall be taken to equal the sectional area when its height is within the

range of no less than 2a and no more than 0.5h.77

CP 63.13330.2012

8.2.18 The factor shall be determined from the formula:

(8.137)

where – stress in the longitudinal tensile reinforcement in the section with a crack immediately after the formation of normal cracks, which shall be determined according to 8.2.16, with the value

incorporated into the relevant formulas. - ditto, under the effect of the analyzed load.

In the case of flexural members, it is admissible to determine the value of the factor from the formula:

(8.138)

where shall be determined from formula (8.121).

Strain Analysis of Reinforced Concrete Members8.2.19 Strain analysis of members in reinforced concrete structures shall be performed taking into

account the operating requirements for the structures. Strain analysis shall be performed for effects of:permanent, temporary continuous and intermittent loads (see 4.6), when strain is limited by process or

structural requirements;permanent and temporary continuous loads, when strain is limited by aesthetic requirements.8.2.20 The values of maximum permissible strain of members shall be taken from SP 20.13330 and

regulatory documents applicable to individual types of structures.

Deflection Analysis of Reinforced Concrete Members

8.2.21 Deflection analysis of reinforced concrete members shall be performed based on the following condition:

(8.139)

where – deflection of a reinforced concrete member under the effect of an external load;

- value of the maximum permissible deflection of a reinforced concrete member.Deflections or displacements of reinforced concrete structures should be defined according to the

general rules of structural analysis depending on the bending, shear, and axial strain (stiffness) characteristics of the reinforced concrete member in the cross sections along its length (flexure, shear angles, etc.).

In cases where deflections of the reinforced concrete members basically depend on bending strains, the deflection values should be defined according to the stiffness or flexure of the members.

8.2.22 In the case of flexural members with a constant section along the length of the member and free from cracks, deflections shall be determined according to the general rules of structural mechanics, with the use of the stiffness of cross-sections determined from formula (8.143).

Determining the Curvature of Reinforced Concrete Members

8.2.23 For purposes of determining the deflection of members, the curvature of flexural, eccentrically compressed and eccentrically tensile members shall be determined:

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а) in the case of members or areas of members whose tensile region is free from cracks normal to the longitudinal axis – according to 8.2.24, 8.2.26;

b) in the case of members or areas of members whose tensile region contains cracks – according to 8.2.24, 8.2.25, and 8.2.27.

Members or areas of members shall be analyzed without cracks if no cracks form [i.e., condition (8.116) is not satisfied] under the effect of the total load that includes permanent, temporary continuous and intermittent loads.

The curvature of reinforced concrete members with and without cracks can be also determined from the strain model as prescribed in 8.2.32.

8.2.24 The total curvature of flexural, eccentrically compressed and eccentrically tensile members shall be determined from the formulas:

0

in the case of member areas without cracks in the tensile region:

(8.140)in the case of member areas with cracks in the tensile region:

(8.141)

In formula (8.140):

curvatures from short-term effects of intermittent loads and from long-term effects of permanent and temporary continuous loads, respectively.

In formula (8.141):

curvature from the short-term effect of the total load for which strain analysis is performed;

flexure of the member due to the non-continuous action of dead loads and live long-term loads;

flexure of the member due to the non-continuous action of dead loads and live long-term loads.

The curvatures and shall be determined as prescribed in 8.2.25.

8.2.25 The curvature of reinforced concrete members under the effect of the relevant loads (8.2.24) shall be determined from the formula:

(8.142)where М - is the bending moment from an external load (taking into account the moment from the

longitudinal force N) relative to the axis that is normal to the plane of the bending moment and passes through the center of gravity of the reduced cross-sectional of the member;

D – is the member’s reduced bending cross section stiffness which is determined by the following formula:

(8.143)

where is the modulus of strain of compressed concrete, which is determined depending on the duration of effect from the load and taking into account the presence or absence of cracks;

- the moment of inertia of the reduced cross-section relative to its center of gravity, which is determined taking into account the presence or absence of cracks.

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The values of the modulus of strain of concrete and the moment of inertia of the reduced section for members without cracks in the tensile region and for members with cracks shall be determined as prescribed in 8.2.26 and 8.2.27, respectively.

Stiffness of a Reinforced Concrete Member in an Area without Tensile Region Cracks

8.2.26 The stiffness D of a reinforced concrete member in an area free from cracks shall be determined from formula (8.143).

The member’s reduced transverse cross section moment of inertia relative to its center of gravity is determined as if it were a solid body using the general rules of elastic member strength analysis with reference to the entire concrete cross section area and the reinforcement cross section areas with the reinforcement-to-concrete modular ratios:

(8.144)

where I is the moment of inertia of the concrete section relative to the center of gravity of the reduced cross-section of the member;

- The moments of inertia of the tensile and compressed reinforcement cross section relative to the center of gravity of the reduced transverse cross section of the element are equal to:

α is the factor of reinforcement reduction to concrete;

(8.145)

The value of I shall be determined according to the general rules for analyzing the geometric parameters of sections of elastic members.

It is permissible to determine the moment of inertia without taking reinforcement into account. The values of the modulus of concrete strain in formulas (8.143) and (8.145) shall be taken to equal:for intermittent loads;

(8.146)for continuous loads;

(8.147)

where shall be taken from Table 6.12.

Stiffness of a Reinforced Concrete Member in an Area with Tensile Region Cracks

8.2.27 In determining the stiffness of a reinforced concrete member with a crack in the tensile zone the following provisions are taken into account:

sections remain flat after being subjected to strain;Stresses in the concrete’s compression side are defined as for elastic concrete;The behavior of tensile concrete in the cross section with a normal crack is ignored; and The behavior

of tensile concrete in the area between adjacent normal cracks is taken into account by incorporating the

factor .The reinforced concrete member stiffness D in areas with cracks shall be determined from formula

(8.143) and taken to be no more than the stiffness of areas without cracks.

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The values of the modulus of strain of compressed concrete shall be taken to equal the values of

the reduced modulus of strain , which shall be determined from formula (6.9) with the design

resistance of concrete for the relevant loads (intermittent and continuous loads).

The moment of inertia of the reduced cross-section of the member relative to its center of gravity shall be determined according to the general rules of resistance of elastic members, taking into account the sectional area of concrete in the compressive region only, the sectional areas of compressed reinforcements with the factor of reinforcement reduction to concrete, and the tensile reinforcements with the factor of

reinforcement reduction to concrete .

(8.148)

where – the moments of inertia of the sectional areas of the compressive region of concrete, the tensile and compressed reinforcements, respectively, relative to the center of gravity that has been reduced without taking into account the concrete in the tensile reinforcements of the cross-section.

The values of and shall be determined according to the general rules of resistance of materials, while adopting the distance from the most compressed concrete fiber to the center of gravity of the

reduced cross-section (with the factors of reduction and ) without taking into account the concrete in the tensile region (Fig. 8.19); in the case of flexural members:

where хт – the average height of the compressive region of concrete, which factors in the behavior of tensile concrete between the cracks, determined according to 8.2.28 (Fig. 8.19).

The values of and уcm shall be determined according to the general rules for analyzing geometric parameters of sections of elastic members.

The values of the factors of reinforcement reduction to concrete αs1 and αs2 shall be determined according to 8.2.30.8.2.28 In the case of flexural members, the position of the neutral axis (the average height of the compressive region of concrete) shall be determined from the equation:

(8.149)

where – static moments of the compressive region of concrete, tensile and compressed reinforcements, respectively, relative to the neutral axis. In the case of rectangular sections with tensile reinforcements only, the height of the compressive region shall be determined from the formula:

(8.150)

where In the case of rectangular sections with tensile and compressed reinforcements, the height of the

compressive region shall be determined from the formula:

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CP 63.13330.2012

(8.151)

where

In the case of T-bar (with a flange in the compressive region) and double-T-bar sections, the height of

the compressive region shall be determined from the formula:

(8.152)

where

A'f – sectional area of overhangs of a compressed flange.

I – level of the center of gravity reduced without taking into account the tensile region of the concrete cross-section

Figure 8.19: Reduced Cross-Section (а) and Schematic of the Stress-Strain State of a Member with Cracks (b) for Purposes of Analyzing the Member for Strain under the Effect of the

Bending Moment

In the case of eccentrically compressed and eccentrically tensile members, the position of the neutral axis (height of the compressive region) shall be determined from the equation:

(8.153)

yN – distance from the neutral axis to the point of application of the longitudinal force N, which is

separated from the center of gravity of the complete section (without taking into account the cracks) by a

distance of .

-the moments of inertia and static moments of the compressive region of concrete, the tensile and compressed reinforcements, respectively, relative to the neutral axis.

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In the case of member with a rectangular section, it is admissible to determine the height of the compressive region subjected to the bending moments M and the longitudinal force N from the formula:

(8.154)where хм – the height of the compressive region of the flexural member determined from formulas (8.149)—

(8. 1.52);

- the moment of inertia and the area of the reduced cross-section, which shall be determined for the complete section (without taking into account the cracks).

The values of geometric parameters of a member's section shall be determined according to the general rules for analyzing the section of elastic members.

In formula (8.154), the plus sign shall be used in the case of a compressive force and the minus sign in the case of a tensile longitudinal force.

8.2.29 It is admissible to determine the stiffness of flexural reinforced concrete members from the formula:

(8.155)where z – the distance from the center of gravity of the tensile reinforcement to the point of application of

the resultant of forces in the compressive region. In the case of members with a rectangular section in the absence of (or without regard for) compressed

reinforcements, the value of z shall be determined from the formula:

(8.156)In the case of members with a rectangular, T-bar (with a flange in the compressive region), and

double-T-bar cross-section, it is admissible to take the value of z to equal 0.8 .8.2.30 The values of the factors of reinforcementreduction to concrete shall be taken to equal:

For compressed reinforcement:

(8.157)For tensile reinforcement

(8.158)

where – reduced modulus of strain of compressed concrete, determined from formula (6.9) in the

case of intermittent and continuous loads, with substituted with .

- the reduced modulus of strain of tensile reinforcements, determined taking into account the behavior of tensile concrete between cracks from the formula:

(8.159)

The values of the factor shall be determined from formula (8.138).

It is admissible to take and, accordingly, . In this case, if condition (8.139) is not satisfied, analysis shall be performed taking into account the factor determined from formula (8.138).

8.2.31 Deflections of reinforced concrete members can be determined according to the general rules of structural mechanics by means of the direct flexural stiffness characteristics D instead of curvature

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by substituting the elastic flexural characteristics EI in the analysis relationships with the specified characteristics D calculated from the formulas given in 8.2.25 and 8.2.29.

In the case of the combined effect from intermittent and continuous loads, the total deflection of members without cracks and with cracks in the tensile region shall be determined by summing up the deflections from the relevant loads similarly to the summation of curvature according to 8.2.24, while adopting the stiffness characteristics D depending on the adopted duration of effect from the analyzed load that is mentioned in the same clause.

When determining the stiffness characteristics D of member with cracks in the tensile region, it is

admissible to adopt the factor . In this case, during the combined effect from intermittent and continuous loads, the total deflection of members with cracks shall be determined by summing up the deflections from the short-term effect of an intermittent load and from a long-term effect of a continuous load, taking into account the relevant values of the stiffness characteristics D, i.e. similarly to how this is done for members without cracks.

Determining the Curvature of Reinforced Concrete Members Based on a Non-linear Strain Model

8.2.32 Total curvature of reinforced concrete members in areas without cracks in the tensile region of the section shall be determined from formula (8.140), and in areas with cracks in the tensile region of the section – from formula (8.141).

The curvature values included in formulas (8.140) and (8.141) shall be determined from the solution of the system of equations (8.26) - (8.30). If there are cracks in the members’ tensile region, stresses in reinforcement intersecting the crack are determined from the following formula:

(8.160)where

(8.161)

Here – relative strain of the tensile reinforcement in the section with a crack immediately after the formation of normal cracks;

-weighted average relative strain of the tensile reinforcement that intersects cracks at the current stage of analysis.

When determining curvatures from an intermittent load, analysis shall use the diagrams of short-term strain in compressed and tensile concrete. When determining curvatures from a continuous load, analysis shall use the diagrams of long-term strain in concrete with design characteristics for Group 2 limit states.

In the particular cases of effects from an external load (bending in two planes, bending in the plane of the axis of symmetry of the cross-section of a member, etc.), the curvatures included in formulas (8.140) and (8.141) shall be determined from the solution of the system of equations indicated in 8.1.26 - 8.1.28.

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9. Prestressed Reinforced Concrete Structures

9.1. Prestress in Reinforcements

9.1.1 Prestress in reinforcements shall be taken to be no more than 0.9 for hot-rolled,

temperature and mechanically strengthened reinforcements, and no more than 0.8 for cold-worked reinforcements and reinforcement cables.

9.1.2 When analyzing prestressed structures, one shall take account of the reduction in prestress due to prestress losses – before the strain forces are passed to the concrete (early losses) and after the strain forces have been passed to the concrete (late losses).

In the case of the reinforcement prestressing with jacks (Hoyer method of prestressing), the following shall be taken into account:

early losses – from the relaxation of prestress in reinforcements, the temperature differential during thermal treatment of structures, and deformation of anchorages and molds (jacks);

late losses – from concrete shrinkage and creep. In the case of the reinforcement prestressing in concrete, the following shall be taken into account:early losses – from deformation of anchorages, friction between reinforcements and channel walls or structure surface;late losses – from the relaxation of prestress in reinforcements, concrete shrinkage and creep.

9.1.3 Losses from the relaxation of prestress in reinforcements shall be determined from the formulas:for class А600 - А1000 reinforcements depending on the prestressing method:

mechanical – (9.1)

electro-thermal – (9.2)for class Вр1200 - Вр1500, K1400, K1500, K1600 reinforcements depending on the prestressing method:

mechanical – (9.3)

electro-thermal – (9.4)

Here shall be adopted without losses in megapascals.

When the values of are negative, shall be adopted.If more accurate data on reinforcement relaxation is available, it is admissible to adopt other values of

losses from relaxation.

9.1.4 The losses from the temperature differential , which is defined as the difference between the temperature of the tensile reinforcement in the heating zone and the temperature of the device that takes the tensile force when the concrete is heated up, shall be taken to equal:

(9.5)

In the absence of accurate data on the temperature differential, it is admissible to adopt .If more accurate data on temperature treatment of the structure is available, it is admissible to adopt

other values of losses from the temperature differential.

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9.1.5 Losses from deformation of the steel mold (jacks) during non-simultaneous stressing of reinforcements in the mold shall be determined from the formula:

(9.6)where n is the number of bars (groups of bars) that are stressed non-simultaneously;

- convergence of jacks along the line of action of the reinforcement stressing force, which shall be determined based on analysis of mold deformation;

the distance between the outer edges of jacks.In the absence of data on mold design and manufacturing technology, it is admissible to adopt

.In the case of the electro-mechanic method of reinforcement prestressing, losses from mold

deformation shall be disregarded.9.1.6 Losses from deformation of anchorages of prestressing devices Δσsp4 during reinforcement

prestressing on jacks shall be determined from the formula:

(9.7)

where – crimping of anchorages or displacement of the reinforcement bar in the clamps of anchorages;the distance between the outer edges of jacks.

In the absence of data, it is admissible to adopt .In the case of the electro-thermal method of reinforcement prestressing, losses from anchorage shall

be disregarded.9.1.7 When reinforcements are prestressed in concrete, losses from deformation of anchorages of

prestressing devices shall be determined from formula (9.7) in which shall be adopted, while losses from friction against channel walls or surface structure shall be determined from the formula:

e – base of the natural logarithm;

factors determined from Table 9.1;х – length of the segment from the prestressing device to the design section (m);

total angle of axial rotation of the reinforcement (rad);σsp – adopted without losses.

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Table 9.1Channel or surface Factors for determining losses from reinforcement friction

ω δ for reinforcements in the form of

bundles, cables bars with a semicontinuous profile

1. Channel:

with a metal surface 0,0030 0,35 0,40

with a concrete surface 0 0,55 0,65

formed by a rigid

channeling tool

ditto, flexible 0,0015 0,55 0,65

channeling tool

2. Concrete surface 0 0,55 0,65

9.1.8 Losses from concrete shrinkage Δσsp5 during reinforcement prestressing on jacks shall be determined from the formula:

(9.8)

where – deformations from concrete shrinkage, whose values can be taken approximately(depending on the class of concrete) to equal: 0.0002 – for concrete class В35 or lower;0.00025 – for concrete class В40;0.0003 – for concrete class В45 or higher.

In the case of concrete subjected to thermal treatment, losses from concrete shrinkage shall be calculated from formula (9.8) with the result multiplied by a factor of 0.85.

Losses from concrete shrinkage during reinforcement prestressing in concrete shall be determined from formula (9.8) with the result multiplied by a factor of 0.75 irrespective of the concrete hardening conditions.

It is admissible to determine losses from concrete shrinkage using methods that are more accurate.

9.1.9 Losses from concrete creep shall be determined from the formula:

(9.9)

where – factor of concrete creep determined according to 6.1.16;

– stress in the concrete at the level of the center of gravity of the analyzed j-th group of bars of the stressed reinforcement;

– the distance between sectional centers of gravity of the analyzed group of bars of the stressed reinforcement and the reduced cross-section of the member;

– area of the reduced section of the member and its moment of inertia relative to the center of gravity of the reduced section;

– the reinforcement factor, which equals , where А and Аspj are areas of the cross-section of the member and the analyzed group of bars of the stressed reinforcement, respectively.

In the case of concrete subjected to thermal treatment, losses shall be calculated from formula (9.9) with the result multiplied by a factor of 0.85.It is admissible to determine losses from concrete creep using methods that are more accurate.

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Stress shall be determined according to the rules for analyzing elastic materials,while adopting the reduced section of the member, which includes the sectional area of concrete and the sectional area of the entire longitudinal reinforcement (stressed and unstressed) with the factor of

reinforcement reduction to concrete determined according to 9.1.10.

When , analysis shall adopt and .9.1.10. The total values of early losses during reinforcement prestressing (under 9.1.3 - 9.1.6) shall be

determined from the formula:

(9.10)where i is the ordinal number of prestressing losses.

The force of concrete pre-compression, taking into account early losses, equals:

(9.11)

where and – sectional area of the -th group of bars of the stressed reinforcement in the member section and prestress in the group, taking into account early losses.

Here – the initial prestressing of the analyzed group of reinforcement bars.The total values of early losses and late losses during reinforcement prestressing (under 9.1.3 - 9.1.8)

shall be determined from the formula:

(9.12)The force in the stressed reinforcement, taking into account early losses, equals:

(9.13)

In structure designs, the total combined losses for reinforcements located in the tensile region of the member section during the member's operation (the primary working reinforcement) shall be taken to be at least 100 MPa.

When determining the force of concrete pre-compression P, taking into account total losses of stress, one shall take into account the compressing stress in unstressed reinforcements, which are numerically equivalent to the sum of losses from concrete creep and shrinkage at the level of such reinforcements.

When determining the forces of compression, taking into account unstressed reinforcements at the

level of unstressed reinforcements, losses from creep at this level shall be taken to equal , where

– losses from creep for bars of stressed reinforcements closest to the analyzed unstressed

reinforcement; – stresses in concrete at the level of the analyzed unstressed and stressed reinforcements, respectively.

9.1.11 Prestress in concrete during the transfer of the force of pre-compression , which is determined taking into account the early losses, shall not exceed:

if stresses decrease or do not change under the effect of external loads – 0.9Rbр,

if stresses increase under the effect of external loads – .

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Stresses in concrete shall be determined from the formula:

(9.14)

where – force of concrete pre-compression, taking into account early losses;М – bending moment from an external load acting at the compression stage

(self-weight of the member);y – distance from the sectional center of gravity to the analyzed fiber;

– eccentricity of the force relative to the center of gravity of the reducedcross-section of the member;

9.1.12 The length of the zone of transfer of prestress to concrete for reinforcements without additional anchorage devices shall be determine from the formula:

(9.15)

but in any case shall be no less than and 200 mm, and in the case of reinforcement cables also no less than 300 mm. In formula (9.15):

-prestress in the stressed reinforcement taking into account early losses;

- bond resistance of the stressed reinforcement with concrete, which corresponds to the transfer strength of concrete and is determined according to 10.3.24;

Аs, иs – area and perimeter of the reinforcement bar.It is recommended to transfer prestress from reinforcements to concrete gradually.

9.2. Analysis of Members of Prestressed Reinforced Concrete Structures for Group 1 Limit States

Strength Analysis of Prestressed Reinforced Concrete MembersGeneral

9.2.1 Prestressed members shall be analyzed for the operating stage for the effect of bending moments and transverse forces from external loads and for the pre-compression stage for the effect of forces from prestressing of reinforcements and forces from external loads acting at the compression stage.

9.2.2 Strength analysis of prestressed members under the effect of bending moments shall be performed for sections that are normal to their longitudinal axis.

As a general rule, strength analysis of normal sections shall be performed on the basis of a nonlinear strain model according to 9.2.13 - 9.2.15.

It is admissible to analyze reinforced concrete members with rectangular, T-bar, and double-T-bar cross-sections with reinforcements located by the perpendicular bending plane of the member sides, under the effect of forces in the plane of symmetry of normal sections, in accordance with 9.2.7 - 9.2.12.

9.2.3 In the case of reinforced concrete members in which the ultimate strength force turns out to be smaller than the ultimate crack formation force, the sectional area of longitudinal tensile reinforcements shall be increased by at least 15% in comparison with the area required according to the strength analysis, or shall correspond to the results of strength analysis for the moment of crack formation.

9.2.4 Prestressed members at the compression stage shall be analyzed similarly to members subjected to eccentric compression by the pre-compression force in the limit state according to 9.2.10 - 9.2.12,

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9.2.5 Strength analysis of prestressed members under the effect of transverse forces (analysis for oblique sections) and a locally acting load (bearing stress and punching shear analysis) shall be performed as prescribed in 8.1.

9.2.6 Strength analysis of prestressed members shall factor in possible deviations in prestress, which

is determined according to 9.1.9, by multiplying the values of (or the compression force ) for the

analyzed j-th bar or group of bars of stressed reinforcements by the factor of .

The reliability factor values are taken to be equal to:0.9 – if prestress has a favorable effect;1.1 – if prestress has an adverse effect.

Analysis of Prestressed Members for the Effect of Bending Moments at the Operating Stage Based on Ultimate Forces9.2.7 Strength analysis of normal sections shall be performed as prescribed in section 8.1, taking into

account the additional instructions of 9.2.8 - 9.2.9. Also, in the formulas of section 8.1, the designations of sectional areas Аs and А's shall be applied to both stressed and unstressed reinforcements.

For tensile reinforcements with a conventional yield strength, it is admissible to adopt stresses higher

than Rs, but in any case no higher than 1.1 Rs depending on the correlation between and (9.2.8).9.2.8 During calculations of the value of the ultimate height of the compressive region of concrete

, the values of relative strain of reinforcements in the tensile region shall be determined from the formulas:

for reinforcement with a conventional yield point of

(9.16)

where – prestress in reinforcements taking into account all losses and = 0.9; 400 - in MPa.in the case of unstressed reinforcements with a physical yield strength

9.2.9 In the case of unstressed reinforcements located in the compressive region, the design strength

under compression Rsс shall be substituted with stress that equals:

- when the factor of service conditions of concrete is taken into account (para. 6.1.12);

at уb1 = 1.0.

Here - in MPa.

The value of shall be determined with the factor = 1.1.

In all cases, stress shall be taken to be no more than .Analysis of Prestressed Members at the Pre-compression Stage9.2.10 During analysis of a member at the stage of pre-compression, the force in the stressed

reinforcement shall be introduced into analysis as an external longitudinal force equal to:

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(9.17)where А'sр and Аsр – sectional areas of stressed reinforcements located in the most compressed and in the

tensile (less compressed) regions of the section;

and – prestresses taking into account early losses and the factor in the reinforcement with the sectional area of А'sр and Аsр.

9.2.11. Strength analysis of members with a rectangular section at the pre-compression stage shall be performed based on the condition:

(9.18)where ер – distance from the point of application of the longitudinal force Np, taking into account the effect

of the bending moment М from an external load acting at the stage of manufacturing (self-weight of the member), to the sectional center of gravity of unstressed reinforcements that are subjected to tension or the least compression (with the member section completely compressed) from such forces (Fig. 9.1), which is determined from the formula:

(9.19)

– distance from the point of application of the force Nр to the sectional center of gravity of the member;

- the design strength of concrete under compression, which is adopted based on a linear interpolation (Table 6.8) as for the compression strength class that is numerically equivalent to the transfer strength of

concrete ;

- the design strength of reinforcements under compression, which is taken to be no more than 330 MPa at the pre-compression stage;

- the sectional area of unstressed reinforcement located in the most compressed region of the member's section.

The height of the compressive region of concrete shall be determined depending on the value ,

which shall be determined from formula (8.1) with the incorporation of the value , where the

design strength of the tensile unstressed reinforcement Аs, and = 0.003:

а) if (figure 9.1) using the formula

(9.20)

(b) at (where х – see item a in Fig. 9.1) from the formula:

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(9.21)

Figure 9.1: Schematic of Forces and Diagram of Stresses in the Section that is Normal to the Longitudinal Axis of the Flexural Prestressed Member During Strength Analysis of this Member at

the Compression Stage9.2.12. Strength analysis of members with a T-bar and double-T-bar section at the pre-compression

stage shall be performed depending on the location of the compressive region boundary:(a) if the boundary of the compressive region passes through the flange (Fig. 8.2, а), i.e. the following

condition is satisfied

(9.22)

analysis shall be performed identically to a rectangular section with a width of according to 9.2.11;(b) if the boundary of the compressive region passes through the rib (Fig. 8.2, b), i.e. condition (9.22)

is not satisfied, analysis shall be performed based on the condition:

(9.23)

where – see 9.2.11.zs – distance from the sectional center of gravity of the member to the tensile (least compressed)

unstressed reinforcement. The height of the compressive region shall be determined from the formulas:

а) when - see 9.2.11)

(9.24)

(b) when

(9.25)

Strength analysis of normal sections based on a non-linear deformation model

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9.2.13 During strength analysis based on the nonlinear strain model, the forces and strains in the section that is normal to the longitudinal axis of the member shall be determined according to the primary provisions given in 8.1.20 - 8.1.22.

9.2.14 As a general rule, the following shall be used when performing strength analysis of normal sections (Fig. 9.2):

equations of equilibrium between external forces and internal forces in the normal section of the member

(9.26)

(9.27)

(9.28)

equations describing the distribution of strains from an external load across the section of the member

(9.29)

(9.30)

(9.31)

And relationships that couple stresses and unit strains in concrete and reinforcement: Concrete

(9.32)Unstressed reinforcement

(9.33)Stressed reinforcement

(9.34)

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Figure 9.2: Schematic of Analysis of the Normal Section of a Prestressed Reinforced Concrete Member

In equations (9.26) - (9.34):- area, coordinates of the center of gravity of the i-th bar of stressed reinforcement and stress inside it;- relative strain of the i-th bar of stressed reinforcement under the effect of an external load;

- relative strain from prestressing of the reinforcement taking into account the relative strains of prestress losses corresponding to the current analysis stage;- modulus of elasticity of the i-th bar of stressed reinforcement;- factor of elasticity of the i-th bar of unstressed reinforcement; for other parameters see 8.1.23.

The values of factors and shall be determined as prescribed in 8.1.23, and the values of factors – from the formula:

(9.35)

9.2.15. Strength analysis of normal sections of reinforced concrete members shall be performed according to the conditions given in 8.1.24.

9.3. Analysis of Prestressed Members of Reinforced Concrete Structures for Group 2 Limit States

General

9.3.1 Analysis for group 2 limiting states should include: Crack formation analysis crack opening analysis; strain analysis9.3.2 Crack formation analysis shall be performed when it is necessary to ensure the absence of

cracks. It shall be also performed to support analysis of crack opening and strain analysis.Requirements for absence of cracks apply to reinforced concrete structures that, with their cross

section in full tension, must remain impermeable (to pressurized liquids or gases, radiation impact, etc.), unique structures with elevated durability requirements, and structures exposed to severely corrosive environments.

9.3.3 During crack formation analysis performed to prevent crack formation, the load safety factor

shall be taken to be (identically to strength analysis). During crack opening analysis and strain

analysis (including supporting crack formation analysis), the load safety factor shall be taken to be .9.3.4 Analysis of prestressed flexural members for Group 2 limit states shall be performed, just like

in the case of eccentric compression, for the combined effect of forces from the external load M and the longitudinal force Np, which equals the force of pre-compression P.

Analysis of Prestressed Reinforced Concrete Members for Crack Formation and Crack Opening

9.3.5 Prestressed reinforced concrete members shall be analyzed for crack opening based on the general provisions given in section 8.2, subject to the instructions given in 9.3.6 - 9.3.10.

Determining the Moment of Formation of Cracks that Are Normal Relative to the Longitudinal Axis of the Member

9.3.6 As a general rule, the bending moment Мсrс during crack formation shall be determined from the strain model according to 9.3.10. In the case of simple sections (rectangular or T-bar sections with

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reinforcements located near the top and bottom sides of the section, with the flange in the compressive region), it is admissible to determine the moment of crack formation according to 9.3.7.

9.3.7 The moment of crack formation shall be determined taking into account non-elastic strain of tensile concrete according to 9.3.8.

It is admissible to determine the moment of crack formation without taking into account non-elastic

strain of tensile concrete, by adopting in formula (9.36). If conditions (8.118) and (8.139) are not satisfied in this case, the moment of crack formation shall be determined taking into account non-elastic strain of tensile concrete.

9.3.8 The moment of crack formation in prestressed flexural members taking into account non-elastic strain of tensile concrete shall be determined from the formula:

(9.36)

where – the moment of resistance of the reduced section for the outermost tensile fiber, determined

taking into account the provisions of 8.2.10;

еяр = еор + r – the distance from the point of application of the pre-compression force

Р to the core point that is farthermost from the tensile region whose crack formation is being analyzed;

еор – ditto, to the center of gravity of the reduced section;r – the distance from the center of gravity of the reduced section to the core point;

(9.37)

In formula (9.36), the plus sign shall be adopted when the rotational directions of the moments and the external bending moment М are opposite; the minus sign – when the directions match.

The values of and shall be determined as prescribed by 8.2.In the case of rectangular sections and T-bar sections with a flange located in the compressive region,

the value of under the effect of the moment acting in the plane of the axis of symmetry may be determined from formula (8.122).

9.3.9 The force during crack formation in centrally tensile members shall be determined from formula (8.131) 8.2.

9.3.10 The moment of crack formation shall be determined on the basis of the nonlinear strain model in accordance with the general provisions given in 6.1.24 and 9.2.13 - 9.2.15, but also taking into account the behavior of concrete in the tensile region of the normal section, which shall be determined from the tensile concrete state diagram according to 6.1.22. The design characteristics of materials shall be adopted for Group 2 limit states.

The value of Мcrc shall be determined from the solution of the system of equations given in 9.2.13 -

9.2.15, while taking the relative strain of concrete at the side of the member subjected to tension from an external load to equal the ultimate relative strain of concrete subject to tension εbt.ult, which shall be determined as prescribed in 8.1.30.

Analysis of the Width of Opening of Cracks that Are Normal Relative to the Longitudinal Axis of the Member

9.3.11 The width of opening of normal cracks shall be determined from formula (8.128), in which the value of stresses σs in the tensile reinforcements of prestressed flexural members from an external load shall be determined form the formula:

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(9.38)

where – the moment of inertia, the area of the reduced cross-section of the member, and the distance from the most-compressed concrete fiber to the center of gravity of the reduced section, which shall be determined taking into account the sectional area of the compressive region of concrete only, the sectional areas of tensile and compressed reinforcements according to 8.2.28, while taking the factor of

reinforcement reduction to concrete to equal in the relevant formulas.Nр – force of pre-compression (9.3.4);Мр – bending moment from an external load and the force of pre-compression,

determined from the formula:

(9.39)where еор – the distance from the point of application of the force of pre-compression Nр to the

center of gravity of the reduced section. The minus sign shall be adopted in formula (9.39) when the rotational directions of the moments

М and are opposite; the plus sign – when they match.It is admissible to determine stress σs from the formula:

(9.40)where z – the distance from the center of gravity of the reinforcement located in the tensile region of the

section to the point of application of the resultant of forces in the compressive region of the member;

еsр – the distance from the center of gravity of the same reinforcement to the point of application of the force Nр.

In the case of members with a rectangular cross-section in the absence of (or without regard for) compressed reinforcements, the value of z shall be determined from the formula:

(9.41)

where – the height of the compressive region determined according to 8.2.28, taking into account the

effect of the force of pre-compression .In the case of members with a rectangular, T-bar (with a flange in the compressive region), and

double-T-bar cross-section, it is admissible to take the value of z to equal .

Stresses determined from formulas (9.38) and (9.40) shall not exceed .Strain Analysis of Prestressed Reinforced Concrete Members9.3.12 Strain analysis of prestressed reinforced concrete members shall be performed as prescribed in

8.2.19 - 8.2.32, taking into account the additional instructions of 9.3.13 - 9.3.15.9.3.13 For purposes of determining the deflection of members, the total curvature of prestressed flexural

members shall be determined as prescribed in 8.2.24, with the values of curvature and in formulas (8.140) and (8.141) to be determined as prescribed in 9.3.14, taking into account the force of pre-compression.

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When determining the curvature, it is admissible to take into account the effect from strain caused by concrete shrinkage and creep at the pre-compression stage.

9.3.14. The curvature of prestressed flexural members under the effect of the relevant loads shall be determined from the formula:

(9.42)where М – bending moment from an external load;Nр and еор – force of pre-compression and its eccentricity relative to the center of gravity of the reduced cross-section of the member;

D – flexural stiffness of the reduced cross-section of the member, determined as prescribed in 8.2 identically to a member that has been eccentrically compressed by the force of pre-compression, taking into account the bending moment from the external load (Fig. 9.3).

I – level of the center of gravity reduced without taking into account the tensile region of the concrete cross-section

Figure 9.3: Reduced Cross-Section (а) and Schematic of the Stress-Strain State of the Prestressed Flexural Member with Cracks (b) During strain analysis

9.3.15. It is admissible to determine the curvature of prestressed flexural members from the formula:

(9.43)where zр – the distance from the point of application of the force of pre-compression to the point of application of the resultant of forces in the compressive region;z – the distance from the center of gravity of the tensile reinforcement to the point of application of the resultant of forces in the compressive region;

the height of the compressive region taking into account the effect from pre-compression.The height of the compressive region shall be determined identically to flexural members without

prestressing according to 8.2.28, with the value of multiplied by the value of .It is admissible to determine the values of zр and z by taking the distance from the point of application

of the resultant of forces in the compressive region to the most-compressed fiber in the section to be equal to

.Determining the Curvature of Prestressed Members from the Nonlinear Strain Model9.3.16. Total curvature of prestressed flexural members in areas without cracks in the tensile region of

the section shall be determined from formula (8.140), and in areas with cracks in the tensile region of the section – from formula (8.141).

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The curvature values included in formulas (8.140) and (8.141) shall be determined from the solution of the system of equations (9.26) - (9.34), taking into account the instructions given in 9.2.13. If there are normal cracks in the members’ tensile region, stresses in reinforcement intersecting the crack are determined from the following formula:

(9.44) and in unstressed reinforcements

(9.45)

where (9.46)

Here – relative strain of the tensile reinforcement in the section with a crack under the effect of an external load immediately after crack formation;

-weighted average relative strains in the tensile reinforcement intersecting cracks at the stage under examination;

εspi – relative strain from prestressing of reinforcement.When determining curvature from an intermittent load, analysis shall use the diagrams of short-term

strain in compressed and tensile concrete. When determining curvature from a continuous load, analysis shall use the diagrams of long-term strain in concrete with design characteristics for Group 2 limit states.

10 Structural Requirements

10.1 General

10.1.1 To ensure the safety and serviceability of concrete and reinforced concrete structures, besides analysis requirements, structural requirements should also be met for geometric dimensions and reinforcement.

Structural requirements should be established in cases when: it is not possible by analysis to guarantee with sufficient accuracy and absolute certainty the resistance of the structure to external loads and impacts;

structural requirements define the boundary conditions within which the adopted analysis principles may be applied;

structural requirements provide a procedure for fabricating the concrete and reinforced concrete structures.

10.2 Requirements for Geometric Dimensions

10.2.1 The geometric dimensions of concrete and reinforced concrete structures should be no less than the magnitudes that:

allow the reinforcement and its anchoring to be placed, and enable it to operate in unison with the concrete, given the requirements in 10.3;

limit the flexibility of compressed members;provide the required concrete quality parameters in the structure (GOST 13015).10.2.2 The recommended cross-sectional dimensions of eccentrically compressed members that will

ensure their stiffness are those that provide a maximum flexibility in any direction of:

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200 - for reinforced concrete members;120 – for columns that are members of buildings;90 - for concrete members.10.2.3 Building and edifice structures shall be segregated by permanent and temporary contraction

joints, the spacing between which shall be determined by climatic conditions, structural features of the building or edifice, construction sequence, etc.

If there is uneven settling of the foundations, the structures should be segregated by settlement joints.

10.3 Requirements for Reinforcement

Concrete cover layer10.3.1 The concrete cover should: ensure that the reinforcing bars work in unison with the concrete anchor the rebar in the concrete and allow for splicing of the rebar elements protect the rebar against environmental impacts (including corrosive impacts)10.3.2 The thickness of the concrete cover should be selected based on the requirements of this

section, taking account of the role played by the rebar in the structures (working or structural), the type of structure (columns, slabs, beams, foundation members, walls, etc.), and the diameter and type of rebar.

The minimum thickness values of a concrete layer made using working reinforcement (including a layer with reinforcement placed along the inside edges of an annular or box-like hollow-core construction) should be taken from Table 10.1.

For precast elements the Table 10.1 minimum thickness values of a concrete cover layer made using working reinforcement shall be reduced by 5 mm.

For structural reinforcement the minimum thickness values of the concrete cover layer shall be 5 mm less than what is required for working reinforcement.

In all cases the thickness of the concrete cover layer shall be no less than the diameter of the reinforcing bar and no less than 10 mm.

In single-layer structures made from lightweight and expanded concrete of classes В7.5 and below, the thickness of the concrete cover layer must be at least 20 mm, and at least 25 mm for exterior wall panels (without a textured finish layer). In single-layer structures made from foam concrete, the thickness of the concrete cover layer must in all cases be at least 25 mm.T a b l e 10.1

Item No.

Operating conditions of enclosing structures Min. thickness of the concrete cover layer (mm)

1 In enclosed spaces with normal or below-normal humidity levels 20

2 In enclosed spaces with above-normal humidity levels (assuming no supplemental protective measures)

25

3 Outdoors (assuming no supplemental protective measures) 30

4 In the ground (assuming no supplemental protective measures) or in foundations if there is a foundation mat

40

10.3.3 Over the development length (see 9.1.11), the thickness of the concrete cover layer at the ends of prestressed members must be at least 3d, and at least 40 mm for a reinforcing bar and at least 20 mm for reinforcing cables.At its base, the concrete cover layer for prestressed reinforcement, whether with or without anchors, is allowed to have the same cross-section as in a span for prestressed members where the transfer of supporting forces is concentrated onto a steel carrier with lateral reinforcement (spot-welded fabric mat or stirrups spanning the longitudinal reinforcement) installed according to the instructions in Paragraph 10.3.20.10.3.4. In members with prestressed longitudinal post-tensioning reinforcement laid in ducts, the distance from the surface of the member to the surface of the duct should be at least 40 mm and at least the width (diameter) of

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the duct, and to the side edges – at least half the height (diameter) of the duct. When placing prestressed reinforcement in grooves or outside a member’s cross-section, the thickness of the concrete cover layer that is subsequently created by shotcreting or some other method shall be at least 20 mm.

Minimum spacing of reinforcing bars10.3.5 The minimum clear spacing between reinforcing bars shall be sufficient to ensure that the

reinforcement works in unison with the concrete and that the structures are of quality construction owing to how the concrete mixture is poured and compacted, but be no less than the greatest diameter of a reinforcing bar, and also no less than:

25 mm – if the bars are in a horizontal or inclined position for concreting – for bottom reinforcement laid in one or two rows; 30 mm – same as above, for top reinforcement;

50 mm – same as above, for bottom reinforcement laid in more than two rows (except bars in the bottom two rows), and also for bars placed vertically for concreting.

In confined conditions, the reinforcing bars may be arranged in bundled groups (with no gap between the bars). In this case the clear spacing between the bundles must also be at least the equivalent diameter of a bar having a cross-sectional area equivalent to that of the reinforcement bundle, assumed to be

where is the diameter of a single bar in the bundle, n is the number of bars in the bundle.

Longitudinal reinforcement10.3.6 In reinforced concrete members the cross-sectional area of the longitudinal tensile

reinforcement, or longitudinal compressed reinforcement (if required by analysis), as a percentage of the cross-sectional area of the concrete (derived from multiplying the width of the rectangular cross-section, or the width

of the T-shaped (H-shaped) rib, by the effective depth of the cross-section), shall be at least:

0.1 % - in bended, eccentrically tensile members and eccentrically compressed members of flexibility

(for rectangular cross-sections );

0.25 % - in eccentrically compressed members with flexibility (for rectangular cross-sections

);for intermediate values of members’ flexibility the value μs, shall be interpolated.In members with longitudinal reinforcement arranged evenly along the outline of the cross-section, or

in axially tensile members, the minimum cross-sectional area of the entire longitudinal reinforcement shall be two times greater than the values given above and should be based on the full cross-sectional area of the concrete.

10.3.7 Structural reinforcement shall be provided in concrete structures as follows:in locations where the cross-sectional dimensions of members change abruptly; in concrete walls below and above openings;in eccentrically compressed members whose design strength does not account for the effect of the

tensile concrete – at the edges, where tensile stresses arise; in this case the reinforcement ratio μs must be at least 0.025 %.

10.3.8 In reinforced concrete line structures and slabs, the maximum spacing between the axes of longitudinal reinforcing bars that will ensure the concrete is effectively engaged, that stresses and strains are evenly distributed, and that the width of cracks between reinforcing bars is limited, shall be:

in reinforced concrete beams and slabs:

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200 mm – if the cross-section height is h< 150 mm;1.5 k and 400 mm - if the cross-section height h > 150 mm;in reinforced concrete columns:400 mm – in the direction perpendicular to the bending plane;500 mm - in the direction of the bending plane.In reinforced concrete walls the maximum spacing between the vertical reinforcing bars shall not

exceed 2t and 400 mm (t is wall thickness), and between horizontal reinforcing bars – no more than 400 mm.10.3.9 In beams and ribs more than 150 mm wide, there must be at least two longitudinal working

tensile bars in the cross-section. If a member is 150 mm wide or less, one longitudinal bar installed in the cross-section is sufficient.

10.3.10 In beams there shall be at least two longitudinal working reinforcing bars that reach the support, with a cross-sectional area of at least 1/2 the cross-sectional area of the bars in the span.

In slabs the longitudinal working reinforcing bars that reach the support shall have a cross-sectional area of at least 1/3 the cross-sectional area of the bars in the span for every 1 m of spanning slab width.

Transverse reinforcement

10.3.11 Transverse reinforcement shall be installed, based on an analysis of how forces are taken up, in order to limit the spread of cracks, to maintain longitudinal bars in their design position, and to fortify them against lateral buckling in any direction.

Transverse reinforcement shall be installed along all surfaces of reinforced concrete members having longitudinal reinforcement installed nearby.

10.3.12 The diameter of transverse reinforcement (stirrups) in the tied reinforcing mats of eccentrically compressed members shall be at least 0.25 times the maximum diameter of the longitudinal reinforcement and at least 6 mm.

The diameter of transverse reinforcement in the tied reinforcing mats of flexural elements shall be at least 6 mm.

In welded reinforcing mats the diameter of transverse reinforcement shall be at least the diameter specified for welding using the maximum diameter of the longitudinal reinforcement.

10.3.13 In reinforced concrete members in which analysis shows that the transverse force cannot be

taken up solely by the concrete, transverse reinforcement shall be installed, spaced no more than and no more than 300 mm apart.

In solid slabs, and also in multi-ribbed slabs less than 300 mm tall and in beams (ribs) less than 150 mm tall, along sections of a member where the transverse force, according to analysis, is taken up solely by the concrete, transverse reinforcement need not be installed.

In beams and ribs 150 mm tall or greater, and also in multi-ribbed slabs 300 mm tall or greater, along sections of a member where the transverse force, according to analysis, is taken up solely by the concrete,

transverse reinforcement shall be installed, spaced no more than 0.75 and no more than 500 mm apart.10.3.14 In eccentrically compressed line members, and also in flexural members, assuming the

presence of longitudinal compressed reinforcement required by analysis to prevent buckling of the longitudinal reinforcement, transverse reinforcement shall be installed, spaced no more than 15d and no more than 500 mm apart - the diameter of the longitudinal compressed reinforcement).

If the cross-sectional area of the longitudinal compressed reinforcement installed along one of the edges of the member is greater than 1.5 %, transverse reinforcement shall be installed, spaced no more than 10d and no more than 300 mm apart.

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10.3.15 Stirrups (transverse bars) in eccentrically compressed line members must be designed such that the longitudinal bars (at least every other one) fall at the stirrup bends, and these bends are spaced no more than 400 mm apart along the end width. If the end width is 400 mm or less and there are four or fewer longitudinal bars in profile along this edge, all the longitudinal bars may be spanned by a single stirrup.

10.3.16 In members acted upon by torsional moments, the transverse reinforcement (stirrups) must form a closed loop.

10.3.17 Transverse reinforcement in slabs – in the punching zone, in the direction perpendicular to the sides of the design edge – shall be spaced no more than and no more than 300 mm apart. The bars

closest to the edge of the loading area shall be located no closer than and no farther than from this edge. In addition, the width of the transverse reinforcement installation area (from the edge of the loading area) must be at least 1.5h0. Spacing of the transverse reinforcement may be increased to 1/2h0. Furthermore, the punching pyramid should be put in the worst possible position and only those reinforcing bars intersecting the punching pyramid should be factored into the analysis.

The spacing between transverse reinforcing bars in the direction parallel to the sides of the design edge shall not exceed 1/4 the length of the corresponding side of the design edge.

10.3.18 The design transverse reinforcement, in the form of lateral reinforcement mats for local compression (bearing stress), shall be placed within the design area Аь,тах (8.1.43). If the loading area is situated at the end of a member, the lateral reinforcement mats shall extend across an area whose dimensions in every direction are at least the sum of the two mutually perpendicular sides of the loading area (Figure 8.9).

In terms of depth, the mats shall be placedif the member thickness is more than twice the larger dimension of the loading area – within twice the

loading area dimension;if the member thickness is less than twice the larger dimension of the loading area – within the

member thickness;10.3.19 The transverse reinforcement provided to take up the transverse forces and torsional

moments must be reliably anchored at its ends by the longitudinal reinforcement that is welded to it or otherwise spans it. This anchoring ensures that the joints and transverse reinforcement are of uniform strength,

10.3.20 Additional transverse or lateral reinforcement (welded mats spanning all the longitudinal reinforcing bars, stirrups, etc., spaced 5-10 cm apart) must be installed at the ends of prestressed members along a section length that is at least 0.6 times the length of the prestressing transmission zone Ip, while in members made from lightweight concrete of classes В7.5-В12.5 the spacing shall be 5 cm along a section length that is at least Ip and at least 20 cm for members with anchorless reinforcement; if there are anchoring devices, then the section length shall be twice the length of these devices. Anchors must be installed at the ends of post-tensioning steel and of prestressed steel if the steel (plain wire or stranded wire rope) is insufficiently bonded to the concrete; in this case the anchoring devices must ensure that the reinforcement is reliably embedded in the concrete throughout its entire service life.

When the prestressed working reinforcement used is deformed high-strength reinforcement wire, single-lay reinforcing cables, or hot-rolled and thermally hardened deformed and prestressed reinforcing bar, anchors generally need not be installed at the ends of the prestressed bars.

Reinforcement anchorage

10.3.21 One or more of the following means shall serve as reinforcement anchorage:in the form of a straight bar end (straight embedment of anchorage);

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with a bend at the end in the form of a hook, offset bend (claw) or loop (only for non-prestressed reinforcement);

with transverse bars welded on or installed (only for non-prestressed reinforcement);using special anchoring devices at the end of the bar.10.3.22 Straight embedment of anchorage and anchoring with claws may be used only for deformed

reinforcement. For tensile plain bars hooks, loops, welded-on transverse bars, or special anchoring devices may be used.

Claws, hooks, and loops are not recommended to be used for anchorage of compressed reinforcement, except for plain bars, which may experience tension under certain potential load combinations.

10.3.23 In calculating the length of the reinforcement anchorage, consideration should be given to the means of anchoring, the reinforcement class and reinforcement profile, the reinforcement diameter, the strength of the concrete and its stress state in the anchorage zone, and the structural design of the member in the anchorage zone (the presence of transverse reinforcement, the position of the bars in the member cross-

section, etc.).10.3.24 The basic length of the anchorage required to transfer to the concrete the force in the

reinforcement with total design resistance Rs is calculated from the formula

(10.1)

where Аs and us, respectively, are the cross-sectional area of the anchored reinforcing bar and the perimeter of its cross-section, determined from the nominal diameter of the bar;

Rbond is the reinforcement’s design resistance to bonding with the concrete, assumed to be evenly distributed along the length of the anchorage and determined from the formula

(10.2)

here Rbt is the concrete’s design resistance to axial tension;

- a multiplier that takes into account the influence of the type of reinforcement surface and is taken to be: for non-prestressed reinforcement: 1,5 – for smooth reinforcements;2.0 - for cold-worked, deformed reinforcement;2.5 - for hot-rolled and thermomechanically treated, deformed reinforcement;for prestressed reinforcement:1.7- for cold-worked, deformed reinforcement of class Вр1500, 3 mm in diameter, and

reinforcing cables of class K1500, 6 mm in diameter;1.8- for cold-worked reinforcement of class Вр, 4 mm in diameter or greater;2.2 - for reinforcing cables of class K, 9 mm in diameter or greater;2.4 - for reinforcing cables of class K7Т, 9 mm in diameter or greater,

made from deformed wire;2.5- for hot-rolled and thermomechanically treated reinforcement of class А.

-a multiplier that takes into account the influence of the size of the reinforcement diameter, taken to be:for non-prestressed reinforcement:

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=1.0 for a reinforcement diameter

= 0.9 for a reinforcement diameter of 36 and 40 mm;for prestressed reinforcement:

for all types of prestressed reinforcement. 10.3.25 The required design length of the reinforcement anchorage, taking into account the structural

design of the member in the anchorage zone, is determined from the formula

(10.3)

where is the basic length of the anchorage, determined from the formula (10.1);

- are, respectively, the cross-sectional areas of the reinforcement required by the analysis and actually installed;a is a multiplier that takes into account how anchorage length is influenced by the stress state of the concrete and reinforcement and by the structural design of the member in the anchorage zone.

For non-prestressed reinforcement used in the anchorage of deformed bars with straight ends (straight embedment of anchorage) or of plain bars with hooks or loops without additional anchoring devices, α = 1.0 is assumed for tensile bars, α = 0.75 for compressed bars, and α =1.0 for prestressed reinforcement.

The anchorage length of non-prestressed reinforcing bars may be reduced, depending on the transverse reinforcement quantity and diameter, the type of anchoring devices (welded-on transverse reinforcement, bending the ends of deformed bars), and the magnitude of transverse contraction of the concrete in the anchorage zone (e.g. due to reaction of the support), but by no more than 30%.

In any event, the actual anchorage length shall be at least and 200 mm, or at least for non-prestressed bars

For members made from Group A fine-aggregate concrete, the required anchorage design length must

be increased by for tensile concrete and by for compressed concrete.10.3.26 The force taken up by the anchored reinforcing bar Ns is determined from the formula

(10.4)where lan is the anchor length determined according to 10.3.25, assuming the ratio

ls is the distance from the end of the anchored bar to the given member cross-section.10.3.27 The length to which tensile non-prestressed reinforcing bars are driven into the free end

supports of members, beyond the inner edge of the free support, subject to the condition (see 8.1.31-

8.1.35) must be at least If this condition is not met, the length to which the reinforcement is driven beyond the edge of the support is determined from 10.3.25.

10.3.28 When installing special anchors at the ends of the bars in the form of plates, washers, nuts, angle iron, button-heads, etc., the anchor’s area of contact with the concrete must satisfy the concrete’s bearing strength requirement. Furthermore, in designing welded-on anchors, the weldability characteristics of the metal must be taken into account, as well as the welding methods and conditions.

Non-prestressed reinforcement couplings

10.3.29 One of the following types of splices is used for non-prestressed reinforcement coupling:а) unwelded lap splices:with straight ends on deformed bars;with straight ends on bars having transverse bars welded onto or installed on the lap of the splice;

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with bends at the ends (hooks, claws, loops); only hooks and loops are used for plain bars.b) welded butt splices and mechanical couplings:with welding of the reinforcement;using special mechanical devices (couplings with pressed-on sleeves, threaded sleeves, etc.).10.3.30 Reinforcement lap splices (without welding) are used to couple bars having a maximum working

reinforcement diameter of 40 mm.The instructions in 10.3.22 apply to reinforcement lap splices.

Tensile or compressed reinforcement splices must have a lap length that is at least the length , determined from the formula

(10.5)

where is the basic length of the anchorage, determined from the formula (10.1);

see 10.3.25;а is a multiplier that takes into account the influence of the stressed state of the reinforcement, the

structural design of the member in the bars’ splice zone, the quantity of reinforcement pieces to be spliced in a given cross-section relative to the total number of reinforcement pieces in that section, and the distance between the reinforcement pieces to be spliced.

When splicing deformed reinforcement with straight ends, as well as plain bars with hooks or loops, without additional anchoring devices, the multiplier а shall be 1.2 for tensile reinforcement and 0.9 for compressed reinforcement. Here the following conditions must be met:

the relative quantity of tensile deformed working reinforcement to be spliced in the given design section of the member must be no more than 50%, and no more than 25% for a plain bar (with hooks or loops);

the force taken up by all the transverse reinforcement placed within the splice must be at least half the force taken up by the tensile working reinforcement to be spliced in the given design section of the member;

the distance between the working reinforcing bars to be spliced must not exceed the distance between neighboring lap splices (along the width of the reinforced concrete member)

must be at least and at least 30 mm.

The member segment extending the length of the reinforcement to be spliced shall be used as one of the member design sections to be examined for determining the relative number of reinforcement pieces to be spliced in a given section. Reinforcement splices are considered to be in the same design section if the centers of these splices are within the length of that segment.

The relative number of tensile working reinforcement pieces to be spliced in a given member design section may be raised to 100% if the multiplier a is taken to be 2.0. If the relative number of deformed reinforcement pieces to be spliced in a given design section exceeds 50% (or exceeds 25% for plain bars), the value of the multiplier a shall be determined through linear interpolation.

If there are additional anchoring devices at the ends of the bars to be spliced (welded-on transverse reinforcement, bending the ends of deformed bars to be spliced, etc.), the lap length of the bars to be spliced may be reduced, but by no more than 30%.

In any event, the actual lap length must be at least at least 20 and at least 250 mm.

10.3.31 When weld-splicing reinforcement pieces, the type of weld splice and the welding method shall be chosen based on the structure’s operating conditions, the weldability of the steel, and fabrication method requirements according to GOST 14098.

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10.3.32 When using mechanical devices in the form of sleeves (threaded sleeves, pressed-on sleeves, etc.) for the reinforcement couplings, the bearing capacity of the sleeve joint must be the same as for bars that are to be spliced (under tension or compression, respectively). The ends of the bars to be spliced shall be drawn the required length into the sleeve, which is determined by calculation or through trial and error.

When using threaded sleeves, the threads must grip the required amount to eliminate free-play in the threading.

Bent bars

10.3.33 When using bent reinforcement (offset bends, bends of the ends of the bars) the minimum diameter of the bend in a single bar must be sufficient to preclude the concrete from fracturing or cleaving within the bend of the reinforcing bar or disintegrating at the bend location.

Depending on the bar diameter , the minimum mandrel diameter for the reinforcement shall be at least:

for plain bars

if ;

If

for deformed barsdon = 5 If

If The mandrel diameter may also be determined from the specifications for the specific type of

reinforcement.

10.4 Engineering the main reinforced concrete load-bearing structures

10.4.1 In engineering the main load-bearing elements of the structural system (columns, walls, slabs, floor slabs and roof slabs, foundation slabs), the general requirements of 10.2 and 10.3 regarding the engineering of reinforced concrete structures shall apply, as do the instructions in this subsection.

10.4.2 Columns are reinforced with longitudinal and usually symmetrical reinforcement placed around the perimeter of the cross-section and, when necessary, inside the cross-section, and with transverse reinforcement up the height of the column that spans all the longitudinal bars and is placed around the perimeter of and inside the cross-section.

The design of the transverse reinforcement within the cross-section and the maximum vertical spacing between stirrups and ties going up the column shall ensure that the compressed longitudinal bars do not buckle and that transverse forces are evenly absorbed across the height of the column.

10.4.3 Walls should generally be reinforced with vertical and horizontal reinforcement arranged symmetrically along the faces of the wall, and with transverse bracing linking the vertical and horizontal reinforcement running along opposite faces of the wall.

The maximum spacing between vertical and horizontal bars, and also the maximum spacing between the transverse bracing, must preclude buckling of the vertical compressed bars and must ensure that the forces acting within the wall are taken up evenly.

10.4.4 Transverse reinforcement in the form of П-shaped or closed stirrups shall be used along the full height of the wall ends. These stirrups create the necessary anchorage of the ends of the horizontal bars and prevent buckling of the compressed vertical bars running along the wall ends.

10.4.5 Where walls meet, if the walls’ horizontal reinforcement cannot continue on through the wall assembly joint, then those joints shall be reinforced along the walls’ entire height using overlapping П-shaped stirrups. These stirrups ensure that the concentrated horizontal forces in the wall assembly joints are taken up, prevent buckling of the compressed vertical bars in the assembly joints, and anchor the ends of the horizontal bars.

а а

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a – slab end, b – wall end, c - Т-junction, d – corner junction

Figure 10.1 - Anchorage using П-shaped hardware

10.4.6 Pillars, which in their geometrical characteristics are somewhere in between walls and columns, are reinforced either as columns or as walls, depending on the relative length and width of the pillars’ cross-section.

10.4.7 The quantity of vertical and horizontal reinforcement in a wall shall be determined by the forces acting within the wall. Such reinforcement should be evenly distributed across the wall area, with increased reinforcement at the wall ends and around wall openings.

10.4.8 Flat slabs shall be reinforced with longitudinal reinforcement running along the bottom and top edges of the slab in two directions, and, if necessary, also with transverse reinforcement placed (according to analysis) around columns and walls and across the slab area.

10.4.9 The ends of flat slabs require transverse reinforcement in the form of П-shaped stirrups running along the edge of the slab. These stirrups ensure that torsional moments along the edge of the slab are taken up and that the ends of the longitudinal reinforcement are anchored as required.10.4.10 The quantity of top and bottom longitudinal reinforcement in a ceiling (floor) slab shall be determined based on the applied forces. To simplify the reinforcement in irregular structural systems, it is recommended that: the bottom reinforcement be installed according to the maximum forces acting within the slab span and be identical across the entire area of the given structure; the principal reinforcement in the top be the same as in the bottom, and that around columns and walls additional top reinforcement be installed that, in conjunction with the principal reinforcement, can take up the supporting forces in the slab. For regular structural systems, the longitudinal reinforcement in areas above or between columns should be installed in two mutually perpendicular directions, according to the forces acting in these areas.

A portion of the slab reinforcement may be in the form of continuous welded reinforcing mats installed in two directions in the slab areas above columns (as concealed beams). In this case the mats must pass through the body of the columns.

To conserve reinforcement materials, the minimum percentage of bottom and top reinforcement may be installed across the entire slab area, and in areas where the acting forces exceed the forces that can be taken up by this reinforcement, additional reinforcement shall be installed that, in conjunction with the aforementioned reinforcement, can take up the forces acting in these areas. This approach results in more complicated floor and ceiling reinforcement that requires stricter control of the reinforcing work.

Foundation slabs shall be reinforced in a similar fashion.10.4.11 Beam/column assembly joints shall be engineered in accordance with Figure 10.2. This

requires that transverse reinforcement be provided in the form of closed stirrups or П-shaped hardware in the anchorage zone of the beam’s working reinforcement.

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a – if the tensile zone runs along the top edge of the beam,b - if the tensile zone runs along the bottom edge of the beam

Figure 10.2 – Beam/column assembly joints

Figure 10.3 – Placement of support reinforcement at the intersection of two beams

10.4.12 Additional transverse reinforcement shall be installed at beam intersections to take up the

reaction from the secondary girder. Such reinforcement shall be installed in the main beam across a width

b+2h, where b and h are the width and height of the secondary girder, and in the secondary girder – across a

width of h/3. The reinforcement installed shall take the form of stirrups spanning the longitudinal

reinforcement, in addition to the reinforcement required by analysis of inclined or three-dimensions cross-

sections.

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11 Requirements for Fabrication, Erection, and Service of Concrete and Reinforced Concrete Structures

11.1 Concrete

11.1.1 The composition of a concrete mix should be selected with a view to obtaining a concrete in the structures that matches the technical parameters prescribed in section 6 and those specified in the design.

The basis for selecting the concrete composition should be the defining concrete parameter for the given type of concrete and purpose of the structure. Other, project-specific concrete quality parameters must also be assured.

The composition of a concrete mix of the required strength shall be engineered and selected as per GOST 27006 and GOST 26633.

The composition of a concrete mix should be selected to meet the required quality parameters (workability, conservation quality, non-lamination, air content, etc.).

The properties of the selected concrete mix should match the concreting work procedures, including concrete curing times and conditions, the methods and conditions for preparing and transporting the concrete mix, and other aspects of the fabrication process (GOST 7473, GOST 10181).

The composition of the concrete mix should be selected based on the characteristics of the materials used to make it, including the binders, aggregate, water, and effective admixtures (modifiers) (GOST 30515, GOST 23732, GOST 8267, GOST 8736, and GOST 24211).

The materials selected for a concrete mix should be considered environmentally safe (limited content of radionuclides, radon, toxicity, etc.).

Analysis of the basic parameters of the composition of a concrete mix should be performed using empirically established relationships.

The composition of fiber concrete should be selected to meet the above requirements taking account of the type and properties of the reinforcement fibers.

11.1.2 A concrete mix should be prepared with the required accuracy of metering its components and the sequence in which they are added (SP 70.13330).

Mixing of the concrete mix should ensure the even distribution of the components throughout the whole volume of the mix. Mixing duration should be in accordance with the concrete mixer manufacturer's instructions or should be established experimentally.

11.1.3 Transportation of the concrete mix should employ methods and facilities that ensure the retention of its properties and preclude its segregation or contamination with foreign material. Individual quality parameters of the concrete mix may be restored at the pouring site by applying chemical admixtures or using process procedures provided that all the other required quality parameters have been retained.

11.1.4 Concrete should be poured and compacted so as to provide concrete uniformity and density in the structures sufficient to match the requirements for the given building structure (SP 70.13330).

The casting methods and conditions should provide the specified density and uniformity, and should be defined based on the quality parameters of the concrete mix, the type of structure and article, and the specific geotechnical and process conditions.

The concreting procedure should be defined specifying the location of construction joints to suit the methods of erection of the facility and its structural features. Care must be taken to ensure the required contact strength of the concrete surfaces in the construction joint and also the strength of the structure given the presence of construction joints.

When a concrete mix is poured at low or freezing temperatures, or at elevated temperatures, special measured should be provided to ensure the required concrete quality.

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11.1.5 Concrete should harden with or without using accelerating procedures (by means of heat and moisture treatment at normal or elevated pressures).

The design temperature and moisture conditions must be maintained in the concrete during the curing process. Where conditions must be created to develop concrete strength and mitigate shrinking, special protective measures should be taken. During the process of heat treatment of articles, measures should be taken to reduce temperature differences and reciprocal movements between the formwork and concrete.

In massive cast-in-place structures, steps should be taken to reduce the effect of heat and moisture stress fields associated with curing exothermy on the functioning of the structures.

11.2 Reinforcement

11.2.1 Reinforcement used to reinforce structures should meet project requirements and the requirements of the relevant standards. Reinforcement must have marking and the corresponding certificates attesting to its quality.

Reinforcement storage and transportation conditions should preclude mechanical damage or plastic deformations, contamination that would weaken its bond with the concrete, and corrosion damage.

11.2.2 Tied reinforcement should be installed in formwork in accordance with project requirements. The reinforcing bars should be reliably held in place by means of special measures to ensure that it will not shift during the installation and concreting.

11.2.3 Deviations from the design position of the reinforcement during its installation should not exceed the permissible values laid down by SP 70.13330.

11.2.4 Welded reinforcement (mesh, cages) should be fabricated by spot welding or other methods that ensure the required weld strength and preclude any reduction in strength of the spliced reinforcement elements (GOST 14098, GOST 10922).

Welded reinforcement should be installed in formwork in accordance with project requirements. The reinforcement should be reliably held in place by means of special measures to prevent it from shifting during installation and concreting.

Deviations from the design position of the reinforcement during its installation should not exceed the permissible values laid down by SP 70.13330.

11.2.5 Reinforcing bars should be bent using special mandrels that provide the required radius of curvature.

11.2.6 Reinforcement welds should be made by contact, arc, or molten pool welding. The welding method should ensure the required weld strength and the strength and deformability of the segments of reinforcing bars adjacent to the weld.

11.2.7 Mechanical reinforcement splices (couplings) should be made using pressed-on and threaded sleeves. The strength of a mechanical coupling for tensile reinforcement should be the same as that of the spliced bars.

11.2.8 Pre-tensioning or post-tensioning of reinforcement should result in the project-specified controlled pre-tension within the range of permissible deviations specified in regulatory documents or special requirements.

De-stressing the reinforcement should result in the smooth transfer of prestressing to the concrete.

11.3 Formwork

11.3.1 Formwork should fulfill the following basic functions: giving the design shape of the structure to the concrete, giving the outer surface of the concrete its required appearance, supporting the structure until it gains the strength to permit form striking, and, where required, acting as an anchor during rebar tensioning.

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Forms used in the fabrication of structures can be standard or custom-made, resettable or moving (GOST 52085, GOST 52086, GOST 25781).

Formwork and its fastenings should be designed and fabricated to absorb the loads arising during the work process, enable the structures to freely deform, and maintain the tolerances within the limits specified for the given structure or facility.

Formwork and fastenings should conform to the adopted methods of pouring and compacting the concrete mix, and to the specifications for prestressing, curing, and heat treatment.

Removable formwork should be designed and fabricated so that it can be removed from the structure without damaging the concrete.

Formwork should be removed from structures after the concrete has reached striking strength.Stay-in-place formwork shall be designed as an integral part of the structure.

11.4 Concrete and reinforced concrete structures

11.4.1 The fabrication of concrete and reinforced concrete structures includes construction of formwork, installation of reinforcement, and concreting, which should be performed according to the instructions in subsections 11.1, 11.2 and 11.3.

Finished structures must meet project requirements and the requirements of GOST 13015. Geometry deviations should be within the tolerances specified for the given structure.

11.4.2 By the time that concrete and reinforced concrete structures go into service, the actual concrete strength must be no less than the required concrete strength specified in the project.

Precast concrete and reinforced concrete structures must have the project-specified delivery strength of concrete (concrete strength when the structure is delivered to the client), and for prestressed structures, the project-specified transfer strength (concrete strength when the reinforcement is destressed).

In cast-in-place structures, the striking strength of the concrete should be achieved at the project-specified age (when the support forms are removed).

11.4.3 Structures should be hoisted using special devices (lifting eyes and other devices) specified in the project. The hoisting conditions should preclude any damage, loss of stability, overturning, swaying, or rotation of the structure.

11.4.4 Transportation, warehousing, and storage conditions should conform with project-specified instructions. Integrity of the structure, the concrete surfaces, protruding bars, and lifting eyes must be maintained.

11.4.5 The erection of buildings and facilities using precast members should be carried out in accordance with the work plan, which should specify the sequence of installing the structures and the steps taken to ensure the required installation accuracy, the spatial rigidity of the structures during the process of pre-assembly and installation in the design position, stability of the structures and parts of the building or facility during the process of erection, and safe working conditions.

For the erection of buildings and facilities using cast-in-place concrete there must be a specified sequence of concrete pouring and form removal/resetting to provide strength, crack resistance, and rigidity to the structures during the erection process. In addition, measures should be provided (structural, procedural, and, where required, performance of analysis) to limit the formation and development of construction cracks.

Deviations of the structures from design position should not exceed the permissible values prescribed for the relevant structures (columns, beams, slabs) in buildings and facilities (SP 70.13330).

11.4.6 Structures should be maintained in such a way that they fulfill their project-specified purpose for the entire service life of the building or facility. The service conditions to which concrete and reinforced concrete structures in buildings and facilities are exposed should preclude any reduction in their bearing

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capacity, serviceability or durability due to gross deviations from the standard service conditions (overloading the structures, failure to perform regular maintenance, increasing the corrosiveness of the environment, etc.). If damage to a structure that could reduce its safety or impede its normal functioning is found during the service period, action must be taken as specified in section 12.

11.5 Quality control

11.5.1 Quality control of structures should establish that the technical parameters of the structures (geometric dimensions, strength parameters of the concrete and reinforcement, and the strength, crack resistance, and deformability of the structure) during their fabrication, erection, and service, as well as the production process parameters correspond to those specified in the project, regulatory documents, and the process documentation (SP 48.1330, GOST 13015).

The means of quality control (control regulations, testing methods) are regulated by the relevant standards and specifications.

11.5.2 In order to satisfy the requirements placed on concrete and reinforced concrete structures, there should be product quality control, which includes incoming inspection, in-process inspection, acceptance testing, and in-service inspection.

11.5.3 Concrete strength shall be verified by testing reference specimens that generally are specially fabricated or selected from the structure, as per GOST 10180 and GOST 28570 or using non-destructive testing methods (GOST 22690, GOST 17624).

For cast-in-place structures, concrete strength should also be tested on reference specimens fabricated where the concrete mix was poured and kept in conditions identical to curing in the structure, or by nondestructive methods (GOST 53213, GOST 22690, and GOST 17624).

For cast-in-place structures, concrete strength shall be tested using non-destructive methods. In exceptional circumstances (if the structures cannot be accessed) the concrete strength may be tested using specimens fabricated at the location where the concrete mixture is poured and stored under conditions identical to the concrete setting conditions for the structure.

Concrete strength shall be assessed using statistical methods based on the characteristics of the concrete’s actual strength uniformity. In testing concrete strength using non-destructive methods, the margin of error of the applied NDT methods shall be factored into the determination of the concrete’s strength uniformity characteristics.

Non-statistical testing methods may be used if the number of structures to be tested is limited or during early production, if non-destructive testing of concrete strength is performed using corrected universal relationships rather than plotting the calibration relationships, or, in exceptional circumstances, if the concrete strength of cast-in-place structures is being tested using reference specimens fabricated at the construction site (GOST R 53231).

11.5.4 Concrete frost resistance, water impermeability, and density should be tested according to the requirements in GOST 10060.0, GOST 12730.5, GOST 12730.1, GOST 12730.0, and GOST 27005.

11.5.5 Reinforcement quality (incoming inspection) should be checked according to the requirements given in reinforcement standards and the standards for completing quality assessment reports for reinforced concrete articles.

Weld quality control should be done according to SP 70.13330, GOST 10922, and GOST 23858.11.5.6 Assessment of the suitability of structures according to strength, crack resistance, and

deformability (serviceability) should be performed according to the instructions in GOST 8829 by test loading of structures or by selective destructive loading of individual precast articles taken from a batch of same-type structures. Structure serviceability can also be assessed based on the results of checking a set of individual parameters (for precast and cast-in-place structures) characterizing concrete strength, thickness of concrete cover, geometrical dimensions of cross sections and structures, arrangement of reinforcement and

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weld strength, diameter and mechanical properties of the reinforcement, basic dimensions of reinforcement articles, and reinforcement tension that are obtained during the incoming inspection, in-process inspection, and acceptance testing.

11.5.7 Acceptance of concrete and reinforced concrete structures after their erection should be carried out by establishing that the structure as built conforms with the design (SP 70.13330).

Precast concrete and reinforced concrete structures items and structures shall be accepted according to SP 130.13330 and GOST 13015.

12 Requirements for Restoring and Strengthening Reinforced Concrete Structures

12.1 General

Reinforced structures should be restored and strengthened based on the results of on-site surveys, verification calculations, and analysis and design of the structures to be strengthened.

12.2 Onsite Surveys of Structures

Onsite surveys, depending on their specific goal, should establish: the condition of the structure, geometric dimensions of structures, reinforcement of structures, concrete strength, the type and class of reinforcement and its condition, deflections in the structures, crack widths, lengths and locations, the dimensions and nature of defects and damage, loads, and the static layout of the structures.

12.3 Verification Calculations for Structures

12.3.1 Verification calculations shall be performed for existing structures if the loads acting on them, their operating conditions, or space-planning decisions are changed, and also if serious structural defects or damages are uncovered. Based on the verification calculations, it is determined whether the structures are serviceable, need to be strengthened, require a service load, or are completely unserviceable.

12.3.2 Verification calculations should be made based on the design materials, data on fabrication and erection of the structures, and the results of onsite surveys.

Analytical models used in verification calculations should take account of actual measured geometric dimensions, the actual joints and interactions of the structures and structural members, and any assembly deviations found.

12.3.3 Verification calculations should be made for bearing capacity, deformations, and crack resistance. Verification calculations need not be made for serviceability if displacements and crack widths in existing structures under maximum actual loads do not exceed permissible values, and if the forces in member cross sections due to potential loads do not exceed the forces from actual acting loads.

12.3.4 The design values of concrete characteristics should be selected depending on the concrete class specified in the project, or the assumed concrete class determined by means of conversion factors that provide equivalent strength according to the actual average concrete density obtained from concrete testing by nondestructive methods or testing of specimens taken from the structure.

12.3.5 The design values of reinforcement characteristics should be selected depending on the reinforcement class specified in the project, or the assumed reinforcement class determined by means of conversion factors that provide equivalent strength according to the actual average reinforcement strength obtained from the results of testing reinforcement specimens taken from the structures being investigated.

Where no project data is available and specimens cannot be taken, the reinforcement class may be defined according to the type of profile of the reinforcement, and the design resistances may be 20% below the corresponding values given in the current regulatory documents applying to the given class.

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12.3.6 Verification calculations should take account of any defects or damage in the structure that are found during onsite surveys: reduced strength, local damage or failure of the concrete; rupture in reinforcement, reinforcement corrosion, failed anchorage or reinforcement bonding with concrete; hazardous cracks/crack widths; and/or structural deviations from the project in individual members of the structure and their couplings.

12.3.7 Structures that do not meet the requirements of verification calculations for bearing capacity and serviceability are subject to strengthening or the service load on them should be reduced.

For structures that do not satisfy the requirements of verification calculations for serviceability, reinforcement or load reduction need not be called for if the actual deflections exceed permissible values but do not impede normal operation, or if actual crack widths exceed permissible values but do not create any danger of failure.

12.4 Strengthening of Reinforced Concrete Structures

12.4.1 Reinforced concrete structures should be strengthened by means of steel members, concrete, reinforced concrete, reinforcement, and polymer materials.

12.4.2 In strengthening reinforced concrete structures, account should be taken of the bearing capacity of both the strengthening members and the structure that is being strengthened. For this, the strengthening members must become involved in the operation and operate in unison with the structure that is being strengthened. For drastically damaged structures (50% or more of the concrete cross-section or 50% or more of the working reinforcement cross-sectional area is destroyed), the strengthening members shall be designed for the full acting load, and the bearing capacity of the structure being strengthened shall be ignored in the analysis.

When sealing cracks whose width is greater than permissible and other concrete flaws, the restored areas of the structure should be equal in strength to the basic concrete.

12.4.3 The design characteristics of strengthening materials should be as specified in current regulatory documents.

The design characteristics of materials of the structure being strengthened should be based on project data taking account of the survey results according to the rules used in the verification calculations.

12.4.4 Analysis of a reinforced concrete structure that is to be strengthened should be performed according to the general rules for analysis of reinforced concrete structures taking account of the stress-deformed state of the structure that it acquired before strengthening.

13 Fatigue analysis of reinforced concrete structures

13.1 Fatigue analysis of reinforced concrete structures shall be performed through repeated (regular) stress testing. During the fatigue analysis, fatigue resistance shall be checked separately for the concrete and the reinforcement.

An elastic stage with cracks shall be the context for the fatigue analysis. The work of the tensile concrete and compressed reinforcement shall be disregarded and their fatigue strength shall not be factored in.

13.2 The conditions for performing the fatigue analysis must be those under which the maximum stresses in the compressed concrete and tensile reinforcement from the repeated loading do not exceed the design compressive and tensile fatigue strengths of the concrete and reinforcement, respectively.

13.3 Generally speaking, the design fatigue strengths of the concrete and reinforcement are determined taking into account the asymmetry of the fatigue cycles and the classes of the concrete and reinforcement (for compressive and tensile strength, respectively) for a number of cycles equaling N=2x10 6, using a dependent curvilinear relation obtained experimentally.

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In determining the design fatigue strength of the concrete, consideration shall be given to the type of concrete (heavy or lightweight) and its moisture content. In determining the design fatigue strength of the reinforcement, the presence of weld joints shall be taken into account.

Asymmetry of the fatigue cycles is characterized by the ratio of minimum and maximum stresses in the concrete and reinforcement within the load fluctuation cycle.

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Appendix A(reference)

Basic Alphanumeric Codes

Forces from external loads and impacts in the member cross-section

M - is the bending moment;Мр - is the bending moment that takes account of the prestressing moment, relative to the center

of gravity of the given cross-section;N - is the longitudinal force;

- the transverse force;Т - is the torsional moment.

Material Specifications

is the design axial compressive strength of concrete;are the design axial compressive strengths of concrete for group 1 and 2 limiting states, respectively;-design axial tensile strength of concrete;are the design axial tensile strengths of concrete for group 1 and 2 limiting states, respectively;-the design bearing resistance of concrete;

- the transfer strength of concrete;

- the reinforcement’s design resistance to bonding with the concrete;

are the design tensile strengths of the reinforcement for group 1 and 2 limiting states, respectively;

- the design tensile strength of the transverse reinforcement;

- the design compressive strength of the reinforcement for group 1 limiting states;

- Initial modulus of elasticity in compression and tension

- normalized modulus of deformation of the compressed concrete;

- modulus of elasticity of the reinforcement;

- is the normalized modulus of deformation of the reinforcement in the tensile zone of the member with cracks;

the maximum relative deformations of the concrete under even axial compression and axial tension, respectively;- the relative deformations of the reinforcement under a stress of Rs;

- relative concrete shrinkage strains;

- coefficient of concrete creep; - the ratio of the corresponding moduli of elasticity of the reinforcement Еs and of the

concrete Еb.

Charactistics of the position of the longitudinal reinforcement in the member cross-section

S - is the designation of longitudinal reinforcement:a) when compressive and tensile zones are present in the cross-section due to an external load – placed in the tensile zone;

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b) when the cross-section is fully compressed due to an external load – placed along the less compressed edge of the cross-section;

c) when the cross-section is in full tension due to an external load: for eccentrically tensile members – placed along the edge of the cross-section under greater tension;

for axially tensile members – entirely in the member cross-section;

-the designation of longitudinal reinforcement:а) when compressive and tensile zones are present in the cross-section due to an external load – placed

in the compression zone;b) when the cross-section is in full compression due to an external load – placed along the edge of the

cross-section under greater compression;c) when the cross-section of eccentrically tensile members is in full tension due to an external load –

placed along the edge of the cross-section under less tension;Geometric characteristics

-width of a rectangular cross-section;width of a T-shaped and H-shaped rib;

-width of T-shaped and H-shaped flanges, respectively, in the tensile and compression zones;

-height of the rectangular, T-shaped, and H-shaped cross-sections;

-height of a T-shaped and H-shaped flange, respectively, inthe tensile and compression zones;

- Geometric characteristics a, a'  Distance from the resultant of forces in reinforcement S and S'  to the nearest cross section face;

the working height of the cross-section, equal to and , respectively

-the height of the concrete compression zone;

- the relative height of the concrete compression zone, equal to

- the spacing between stirrups, measured along the member length;

- the eccentricity of normal force N relative to the center of gravity of the normalized cross-section, determined according to the instructions of 7.1.7 and 8.1.7;

- the distances from the point of application of normal force N to the force resultant in the reinforcement are 5 and 5", respectively;

- the eccentricity of the prestressing force relative to the center of gravity of the normalized cross-section;

- the distance from the neutral axis to the point of application of the prestressing force, factoring in the bending moment due to the external load;

- the distance from the point of application of the prestressing force , factoring in the bending moment due to the external load, to the center of gravity of the tensile or least compressed reinforcement;

- member span;

- length of the anchorage zone;

- is the length of the reinforcement’s zone of prestressing transmission to the concrete;117

CP 63.13330.2012

- the design length of the member acted upon by the compressive longitudinal force;

- the radius of inertia of the member cross-section relative to the center of gravity of the cross-section;

- the nominal diameter of the longitudinal and transverse reinforcing bars, respectively;

- the cross-sectional areas of the reinforcement (5 and 8, respectively) - is the cross-sectional area of the stirrups lying in a single plain that is perpendicular to the

member’s longitudinal axis and intersects the oblique cross-section;

- coefficient of reinforcement, defined as the ratio of the cross-sectional area of the

reinforcement S to the area of the member cross-section , disregarding compression and tension flange cantilevers;

А - is the area of all the concrete in cross-section;Аb - is the cross-sectional area of the compression zone concrete;Аbt - is the cross-sectional area of the tensile zone concrete;Аred - is the area of the member’s normalized cross-section;Аloc - is the area of the concrete’s bearing stress;I - is the moment of inertia of the cross-section of all the concrete relative to the center of

gravity of the member’s cross-section;Ired - is the moment of inertia of the member’s normalized cross-section relative to its center of

gravity;W - is the member’s sectional modulus of resistance for the most tensile fiber.

Prestressed member characteristics

- , is the prestressing force, taking into account prestressing losses in the reinforcement corresponding to the given member work stage;

- the force in the prestressed reinforcement, taking into account initial and total prestressing losses, respectively;

- prestressing in the reinforcement being prestressed, taking into account prestressing losses in the reinforcement corresponding to the given member work stage;

- Prestress Loss in Reinforcement

-are the compressive stresses in the concrete during prestressing, taking into account prestressing losses in the reinforcement.

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Appendix B (for reference)

Design of Embedded Parts

B.1 The following condition shall govern the design of normal anchors welded as tee-joints onto the planar members of steel embedded units to counteract the static load’s bending moments and normal and shear forces that are in the same plane of mirror symmetry as the embedded unit:

(B.1)

where - is the maximum tensile force in a single row of anchors, equal to:

(B.2)

- the shear force acting on a single row of anchors, equal to:

(B.3)

- the maximum compressive force in a single row of anchors, determined from the formula

(B.4)

Figure B.1 – Diagram of forces acting on the embedded unit

- is the shear force taken up by the anchors, determined from the formula

(B.5)

where is the coefficient equal to 1.65;

- the maximum tensile force taken up by a single row of anchors, determined from the formula

(B.6)In formulas (B. 1) - (B.6):

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М, N, Q _ the moment and normal and shear forces acting on the embedded unit, respectively; the moment is determined relative to the axis that is in the plane of the plate’s outside edge and passes through the center of gravity of all the anchors;

пап - is the number of rows of anchors in the direction of the shear force; if the shear force is not transmitted evenly to all rows of anchors, then no more than four rows are considered when

determining the shear force ;z - is the distance between the anchor end rows;

- the total cross-sectional area of the anchors in the most stressed row;The cross-sectional area of the anchors in all other rows must equal the cross-sectional area of the

anchors in the most stressed row.In formulas (2) and (4) the normal force N is positive if it points away from the embedded unit (see

Figure B.1) and negative if it points toward it. In instances when has a negative value, then is used in formula (B.3).

When the embedded unit is placed on the top (for concreting) surface of the product, the value is assumed to be zero.

A.B.2 In an embedded unit with anchors lap-welded at an angle of 15 to 30, the inclined anchors are

designed to withstand the shear force (assuming 0, > N1 where N is the tearing force) using the formula

(B.7)

where is the total cross-sectional area of the inclined anchors;

- see. 8.1.1.

This requires the installation of normal anchors, calculated from formula (B.1) and for values equal to 0.1 times the shear force, determined from formula (B.3).

B.3 The design of welded embedded units having welded onto them members that transfer the load to the embedded units must ensure that the anchor bars are engaged as per the adopted design model. The outer members of embedded units and their weld joints shall be designed according to SP 16.13330. In designing plates and shape rolled stock for a tearing force, it is assumed that they are pivotally connected with normal anchor bars.

In addition, the thickness of plate I of the design embedded unit to which the anchors are tee-joint welded, must be verified as meeting the condition:

(B.8)

where is the anchor bar diameter required by analysis;

- is the steel’s design shear resistance taken from SP 16.13330. For types of weld joints that, when the situation calls for it, provide a large zone of plate engagement

when the anchor bar is pulled out from it, condition (B.8) may be adjusted to reduce plate thickness.The plate thickness must also conform to the welding procedural requirements.

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Appendix C (B)(reference)

Analysis of structural systems

C.1 Analysis of structural systems must include:determining the forces in members of the structural system (columns, floor and ceiling slabs,

foundation slabs, walls, cores) and the forces acting on the foundation bases;determining shifts of the structural system overall and of its individual members, as well as

accelerations of floor/ceiling vibrations on the upper floors;structural system stability analysis (shape and position stability);estimate of the bearing capacity and deformation of the foundation base;and in certain instances also an assessment of the structural system’s resistance to progressive

collapse.C.2 The load-bearing structural system, including the above-ground and below-ground structures and

foundation, shall be designed for the service stage. If any design assumptions should change signifcantly during construction, the load-bearing structural system shall be designed for all subsequent construction stages, using analytical models that correspond to the given stages.

C.3 Generally speaking, in terms of spatial arrangement, the load-bearing structural system shall be designed to account for the joint operation of above-ground and below-ground structures, the foundation, and the base beneath it.

C.4 In designing load-bearing structural systems made up of precast elements, the yielding of their joints must be taken into account.

C.5 Load-bearing structural systems shall be designed based on the linear and non-linear strain (stiffness) characteristics of the reinforced concrete members.

The linear strain characteristics of the reinforced concrete members shall be determined for a solid elastic body.

The non-linear strain characteristics of reinforced concrete members with defined reinforcement shall be determined based on the possible formation of cracks in the cross-sections, and based on the development of inelastic strains in the concrete and reinforcement that correspond to the action of transient and sustained loads.

C.6 Analysis of the load-bearing structural system must result in establishing: in columns – the values of the longitudinal and transverse forces and bending moments; in flat floor/ceiling/foundation slabs – the values of the bending moments, torsional moments, and transverse and longitudinal forces; in walls – the values of longitudinal and shear forces, bending moments, torsional moments and transverse forces.

The forces in members of the structural system shall be determined based on the action of the constant, sustained, and transient specified loads.

C.7 Analysis of the load-bearing structural system must result in establishing the vertical displacement (deflection) values of floors and ceilings, the horizontal displacements of the structural system, and for taller buildings – the acceleration of floor/ceiling vibrations on upper stories. The magnitude of the displacements and vibrational acceleration must not exceed the permissible values established in the relevant normative documents.

Horizontal displacements of the structural system shall be determined based on the action of the specified (for Group 2 limiting states) constant, sustained, and transient horizontal and vertical loads.

Vertical displacements (deflections) of floors and ceilings shall be determined based on the action of unfactored constant and sustained vertical loads.

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The stiffness of structural system members shall be determined based on the reinforcement and the presence of cracks and inelastic strains in the concrete and reinforcement, according to the instructions in 8.2.26 and 8.2.27.

Accelerations of floor/ceiling vibrations on the upper stories of a building shall be determined based on the action of the pulsation component of the wind load.

C.8 In analyzing structural system stability, the structural system’s shape stability and position stability (against overturning or sliding) shall be verified.

C.9 Structural system stability shall be analyzed based on the action of specified constant, sustained, and transient vertical and horizontal loads.

In analyzing the shape stability of the structural system, the stiffness of structural system members shall be determined based on the reinforcement and the presence of cracks and inelastic strains in the concrete and reinforcement.

In analyzing the position stability, the structural systems shall be viewed as a rigid, unstrained body.In the overturning analysis, the resisting moment from the vertical load must exceed the overturn

moment from the horizontal load with a safety margin of 1.5.In the sliding analysis, the resisting horizontal force must exceed the acting shear force with a safety

margin of 1.2. Here the least favorable values of the load reliability factors should be applied.C. 10 Analysis of stability against progressive collapse must ensure the strength and stability of the

structural system overall, should any one member of the structural system (column, wall section, floor/ceiling section) fail, potentially causing nearby members then to collapse. In addition, where warranted, a design situation shall be analyzed in which a portion of the foundation base fails (e.g., in the case of a sinkhole forming).

C.11 Stability against progressive collapse shall be analyzed based on the action of unfactored vertical loads with standard resistance values of the concrete and reinforcement.

C.12 The bearing capacity and deformations of the foundation shall be assessed according to the relevant normative documents, assuming that forces act on the foundation as indicated in the structural system analysis of the building.

Design methods

C.13 Structural analysis methods shall be used to design the structural systems. Here, generally speaking, the finite elements method should be used.

C.14 Calculation using the ultimate equilibrium method may be used to estimate the bearing capacity of floors and ceilings.

C.15 Using the finite elements method, the structural system shall be analyzed as a 3D, statically indeterminate system.

C.16 The structural systems shall be modeled using shell, bar, and (if required) solid finite elements.C.17 In creating a 3D model of the structural system, how the bar, shell, and solid finite elements

function together should be taken into account, which has to do with the varying degrees of freedom that each of these elements has.

C.18 The non-rigid properties of the foundation base should be accounted for by using commonly accepted analytical models of the foundation base, applying different types of finite elements or edge conditions with a specified yielding, and modeling the entire soil body beneath the building using solid finite elements, or by using all the aforementioned methods in an integrated manner.

C.19 During the first stage of structural system analysis, the deformability of the foundation base may be accounted for using a modulus of subgrade reaction derived from averaged soil characteristics.

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C.20 When using pile or pile-slab foundations, the piles shall be modelled as reinforced concrete structures, or how they function with the soil shall be accounted for collectively by viewing the foundation base as a whole, with normalized moduli of subgrade reaction.

C.21 In constructing the finite-elements analytical model, the dimensions and configuration of the finite elements shall be specified based on the capabilities of the particular analysis programs being used, and shall be sufficient to ensure the required accuracy in determining the forces along the length of the columns and across the area of floor/ceiling slabs, foundations, and walls.

C.22 The stiffness of finite elements during the initial structural system analysis phase, when the structures’ reinforcement is not yet known, shall be determined from linear strain characteristics.

C.23 After the reinforcement in floor/ceiling slabs has been defined, an additional analysis shall be performed of the deflections in these structures, using updated values of the stiffness of the slabs with the bi-directional reinforcement accounted for.

C.24 An additional structural system analysis should also be performed to produce a more precise estimate of the bending moments in floor, ceiling, and foundation slab members, as well as of the longitudinal forces in walls and columns, taking account of the non-linear stiffness of the finite elements.

C.25 Structural systems shall be analyzed using the finite-elements method and computer programs that have been specially certified in Russia.

C.26 Floor/ceiling bearing capacity shall be analyzed by the ultimate equilibrium method, using the equal work of external loads and internal forces in displacements as a criterion in the ultimate equilibrium of a floor/ceiling slab breaking in the most hazardous manner, resulting in its collapse.

C.27 The structural systems of unique buildings and structures, and of Tier 1 criticality facilities per GOST R 54257, should be analyzed with scientific and technical oversight from outside organizations.

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Appendix D (for reference).

Concrete deformation diagrams

D.1 The analytical relationship between the curvilinear diagrams of concrete strain shall be adopted as follows:

(D.1)

where – relative strains, stresses, and initial moduli of elasticity (d – differential sign), respectively;

т – index of the material (for concrete, т =b,bt; for reinforcements, т =s);νm – the factor of variation of the secant modulus, determined from the

formula:

(D.2)

here – the value of the factor at the vertex of the diagram (at );ν0 – the initial factor of variation of the secant modulus (at the beginning of the diagram or at the

beginning of its curvilinear segment);

- factors describing the completeness of the diagram of the material,

- the level of stress increment, which shall be determined as the ratio

(D.3)

σm,el – stresses corresponding to the elastic strength of the material;

- the factor of variation of the tangent modulus, which is associated with the factor of variation of the secant modulus through the following relationship:

(D.4)In formulas (D.2) and (D.4), the plus sign shall be adopted for the reinforcement strain diagram and

for the ascending branch of the concrete strain diagram, and the minus sign – for the descending branch of the concrete strain diagram.

The descending branch of the diagram may be used up to the stress level (subject to the additional requirements of D.2).

for both branches of the diagram

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(D.5)for the ascending branch

(D.6)for the descending branch

(D.7)

Figure D.1: Curvilinear Concrete Strain Diagrams

The X coordinate of the vertex of the diagram of axial compression of concrete shall be determined from the formula:

(D.8)where B – concrete class in terms of compressive strength;

- a dimensionless factor depending on the type of concrete, taken to equal: for heavy and fine-

grained concrete = 1;

for light medium-density concrete

for porous concrete .In the case of uniaxial and uniform compression of concrete, the reference concrete strain diagram

shall be described by relationships (D.1) - (D.3), which shall adopt:

(D.9)

here – a factor taken to equal 1 in the case of central tension;for flexural members

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, (D. 10)

here cm – a certain reference height of the section,h – height of the section in centimeters,

МPa.

The parameters shall be determined from formulas (D.6) and (D.7) with the substitution

of with

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Appendix E(reference)

Analysis of Columns with Round and Annular Sections

E.1. Strength analysis of annular sections of columns (Fig. E.1), with a ratio of inside to outside radii of r1/r2≥0.5 and with reinforcements uniformly distributed throughout the circle (with a minimum of seven longitudinal bars), shall be performed depending on the relative area of the compressive region of concrete:

, (E.1)

а) at – from the condition

, (E.2)

b) at ≤ 0.15 – from the condition

, (E.3)c) at – from the condition

, (E.4)where

, (E.5)In formulas (E.1) - (E.5):

– the sectional area of the entire longitudinal reinforcement;

- radius of a circle passing through the centers of gravity of bars of longitudinal reinforcements;

Figure E. 1: Schematic Used in Analyzing the Annular Section of a Compressed Member

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The moment M shall be determined taking into account the deflection of the member. E.2. Strength analysis of the round sections of columns (Fig. E.2) with reinforcements uniformly distributed throughout the circle (with a minimum of seven longitudinal bars), with the reinforcement class no higher than A400, shall be verified according to the condition:

, (E.6)where rт and rs — see E.1;

-relative area of the compressive region of concrete, determined as follows: when the following condition is satisfied:

, (E.7)from the solution of the equation:

, (E.8)when the condition (D.7) is not satisfied – from the solution of the equation:

, (E.9)ϕ – the factor accounting for the behavior of tensile reinforcements, which is taken to equal: when the

condition is satisfied, but in any case no more than 1.0; when the condition

(E.7) is not satisfied, ϕ = 0;

- the sectional area of the entire longitudinal reinforcement;

- radius of a circle passing through the centers of gravity of bars of longitudinal reinforcements.The moment M shall be determined taking into account the deflection of the member.

Figure E.2: Schematic Used When Analyzing the Annular Section of an Eccentrically Compressed Member

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Appendix F(reference)

Analysis of Concrete Keys

F.1. It is recommended to determine the dimensions of concrete keys that transfer the shearing forces between a prefabricated member and additionally laid concrete or mortar from the following formulas:

, (F.1)

, (F.2)

where – the shearing force transferred through concrete keys;

– depth, height, and length of a concrete key;

- number of keys introduced into analysis and taken to be no more than 3.0

1 – prefabricated member; 2 – cast-in-place concrete

Figure F.1: Schematic for Analyzing Concrete Keys that Transfer Shearing Forces from a

Prefabricated Member to Cast-in-Place Concrete

In the presence of a compressive force N, it is admissible to determine the height of keys from the formula:

, (F.3)

and may be lesser compared to the height determined from formula (F.2) by no more than twofold.When members of the roof deck are joined by means of concrete keys, the key length introduced into

analysis shall be no more than one half of the member span, and the value of Ǫ shall be taken to equal the sum of shearing forces along the entire length of the member.

Conditions (F.1) to (F.3) shall be used to analyze concrete keys in a prefabricated member and keys

fashioned from additionally laid concrete, with the design strength of the concrete of the keys and adopted identically as for concrete structures. When performing analysis for extraction of the tensile member of a two-member column from the socket of the foundation, it is admissible to factor in the behavior of five keys (Figure F.1).

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Appendix G(reference)

Analysis of Short Cantilevers

G.1. For purposes of ensuring strength along an inclined compressed strip between the load and the

base, analysis of short cantilevers of columns at (Figure G.1) for the effect of the transverse force shall be performed based on the condition:

, (G.1)

in which the right part shall be taken to be no more than and no less than . In condition (G.1):

the length of the load supporting platform along the cantilever overhang;

- the angle of inclination of the design compressed strip relative to the horizontal

-the factor of reinforcement with clamps located at the height of the cantilever;

here – the distance between clamps measured along the normal to them.Analysis shall factor in horizontal clamps and inclined clamps at an angle of no more than 45° to the

horizontal.Compressive stress at the points of load transfer to the cantilever shall not exceed the design crushing

strength of concrete .In the case of short cantilevers that are part of a rigid assembly with a framed design and an embedded

joint, the value of in condition (G.1) shall be taken to equal the cantilever overhang if conditions

and are satisfied (where М and Q – the moment tensioning the top side of the joist and the transverse force in the normal section of the joist along the edge of the cantilever, respectively).

In this case, the right part of condition (G.1) shall be taken to be no more than

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Figure G.1: Analysis Schematic for a Short Cantilever Subjected to a Transverse Force

When a short cantilever provides hinge support for a beam running along the cantilever overhang in the absence of special protruding embedded parts that hold the supporting platform in place (Fig. G.2), the value of lsup in condition (G.1) shall be taken to equal two-thirds of the length of the actual supporting platform.

Transverse reinforcement of short cantilevers shall meet the design requirements.

Figure G.2: Analysis Schematic for a Short Cantilever Providing Hinge Support for a Prefabricated Beam Running Along the Cantilever Overhang

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G.2. When the column cantilever provides hinge support for a beam, longitudinal reinforcements of the cantilever shall be analyzed based on the following condition:

(G.2)

where – see Figure G.1.In this case, longitudinal reinforcements of the cantilever shall pass all the way through to the free end

of the cantilever and shall have proper anchorage.In the case of a rigid connection between the joist and the column with the embedment of the joint and

the welding of the bottom reinforcement of the joist to the cantilever reinforcement through embedded parts, cantilever reinforcement shall be analyzed based on the condition:

(G.3)where – the overhang and the working height of a short cantilever, respectively;

- the horizontal force acting on the top of the cantilever from the joist, which equals:

(G.4)

and taken to be no more than (where and – the height and length of the fillet

weld joining the embedded parts of the joist and the cantilever; – design shearing strength of fillet welds depending on weld metal, determined according to SP 16.13330, with electrodes MPa; 0.3 –

steel-on-steel friction coefficient), and no more than (where and – design strength and sectional area of the top reinforcement of the joist, respectively).

In formulas (G.3) and (G.4):

– bending moment and transverse force, respectively, in the normal section of the joist along the edge of the cantilever; if the moment M is tensioning the bottom side of the joist, the value of M shall be introduced into formula (G.4) with the minus sign;

– the actual length of the load supporting platform along the cantilever overhang;

- working height of the joist.

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Appendix H(reference)

Analysis of Prefabricated/Cast-in-place (Composite) Structures

H.1. Prefabricated/cast-in-place (composite) structures consist of prefabricated reinforced concrete members, cast-in-place concrete, and reinforcements.

Both custom-design and standard reinforced concrete members, either prestressed or non-prestressed, are used as prefabricated members of prefabricated structures.

H.2. Prefabricated/cast-in-place (composite) reinforced concrete structures shall meet the requirements of analysis for bearing capacity (Group 1 limit states) and for normal serviceability (Group 2 limit states).

Prefabricated/cast-in-place (composite) structures shall be analyzed for strength, crack formation and opening, and strain for the following two stages of structure behavior:

until the cast-in-place concrete has attained its design strength – for the effects of the self-weight of such concrete and other loads acting at the current stage of structure construction;

after the cast-in-place concrete has attained its design strength – for loads acting at the current stage of structure construction and operation.

Analysis of prefabricated/cast-in-place (composite) structures after the cast-in-place concrete has attained its design strength shall be performed taking into account the initial stresses and strains that manifested themselves in the prefabricated members before the cast-in-place concrete attained its design strength.

H.3. It is recommended to reliably connect the cast-in-place concrete with the concrete of prefabricated members by means of reinforcements protruding out of the prefabricated members, by fitting concrete keys or using rough surfaces, longitudinal protrusions, or using other reliable proven methods.

Strength analysis of contact joints under the effect of shearing, tensile, and compressive forces between the prefabricated member and cast-in-place concrete shall be performed according to H.4 - H.8.

H.4. It is recommended to perform analysis of contact joints for tension based on the condition:

(H.1)

where – a factor taken to equal 0.25 for treated joints, or 0 for untreated joints.It is recommended to perform analysis of reinforced contact joints for tension based on the condition:

(H.2)H.5. It is recommended to perform analysis of contact joints for shear based on the condition:

(H.3)

where – a factor taken to equal 0.5 for untreated joints, or 1.0 for treated joints;It is recommended to perform analysis of reinforced contact joints for shear based on the condition:

(H.4)

but in any case no more than

where factor taken to equal the factor adopted in condition (H.3);

- factor taken to equal 133

CP 63.13330.2012

– factor taken to equal 2.0.H.6. Analysis of contact joints for the combined effect of shearing and tensile forces shall be

performed based on the condition:

, (H.5)

where the force is taken to equal the right part in conditions (H.1) and (H.2), and the force

- is taken to equal the right part in conditions (H.З) and (H.4).H.7. It is recommended to perform analysis of contact joints for compression based on the condition:

, (H.6)It is recommended to perform analysis of reinforced contact joints for compression based on the

condition:

, (H.7)H.8. Analysis of contact joints for the combined effect of shearing and compressive forces shall be

performed based on the following conditions:

, (H.8)

If

, (H.9)

If

, (H.10)

If

where the force Nj.0 is taken to equal the right part of conditions (H.6) and (H.7), the force b.j.0 is taken to equal the right part of conditions (H.З) and (H.4), and the factor γjw shall be taken to equal 1.0, and in special cases requiring experimental substantiation – based on the data of direct experimental tests.

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Annex K (reference)Factoring in Confinement Reinforcement in Analysis of Eccentrically Compressed Members Based on

the Nonlinear Strain Model

K.1. Analysis of eccentrically compressed rod-type members made from heavy or fine-grained concrete with confinement reinforcement shall be performed on the basis of the nonlinear strain model as prescribed by 8.1.20 - 8.1.30 and taking into account the additional instructions of K.2 - K.4.

K.2. The stiffness characteristics Dij (i,j - 1,2,3) in equations (8.39) - (8.41) for determining concrete and reinforcement strain in the normal section of members with confinement reinforcement shall be determined from the formulas:

(К.1)

(K.2)

(К.З)

(K.1)

(K.5)

(K.6)where:Abk, Zbxk, Zbyk – area, coordinates of the center of gravity of the k-th compressed segment of concrete with confinement reinforcement and stress at the level of its center of gravity;Vbk – factor of elasticity of concrete with confinement reinforcement of the k-th segment; for other symbols, see

It is admissible to adopt Аbi = 0 in formulas (K.1) - (K.6).K.3. Values of the factor νbk shall be determined from the strain diagram for concrete with

confinement reinforcement under axial compression.When bilinear or trilineral diagrams are used, the values of the factor νbk shall be determined from

relationships (6.5) – (6.9) in which the concrete characteristics Rb, εb0, and εb2 shall be substituted with the characteristics of concrete with confinement reinforcement

(К-7)

(К.8)

(К.9)where Rs,xy is the design strength of reinforcements in confinement reinforcement meshes;

(K.10)

here Nx, Asx,lx – the number of bars, the cross-sectional area, and length of the mesh, respectively (along the axes of outer-most bars) in one direction; Ny, Asy, ly – ditto, in the opposite direction;

(K.11)

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(K.12)K.4. When curvilinear strain diagrams are used, the values of the factor Vbk shall be determined using

relationships (K.2) - (K.8) in whichconcrete characteristics σb and εb shall be substituted with the characteristics of concrete with confinement reinforcement Rb,red and εb0,red, and the value of the parameter v0 for the ascending branch of the diagram of axial compression of concrete shall be taken to equal the value calculated using the formula:

(К.13)

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References [1] TU 14-1-5543-2006. Class Ac500C thermo-mechanically strengthened rolled bars with improved

cold resistance for reinforcement of reinforced concrete structures.[2] Procedural guidelines for welding and quality control of reinforcement joints with embedded parts

in reinforced concrete structures[3] TU 14-1-5526-2006. Class A500SP rolled reinforcement bars with an effective semicontinuous

profile.

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Keywords: concrete and reinforced concrete structures, design values, strength and strain properties of concrete, requirements for reinforcements, strength analysis, cracking analysis, strain analysis, protection of structures against adverse impacts.

138

Universal Decimal Classification (UDC) code: 624.012.3/4(083.13)

National Classification for Standards (OKS) number: 91.080.40

Official Publication.

Code of Practice

SP 63.13330.2012.

Concrete and reinforced concrete structures general

Updated edition

SNiP 52-01-2003.

Prepared for Publication by the Federal Center for Regulation, Standardization, and Technical

Assessment of Compliance in Construction (495) 930-64-69; (495) 930-96-11; (495) 930-09-14

Format: 60x84 1/8. Press run: 150 copies. Order No. 1373/12.

Printed by Analitik LLC, Moscow, 18 Leningradskoye Shosse