Ufa State Petroleum Technological University

Manual on Building EngineeringPart II

Арсланова Айгуль Ринатовна

Федеральное агентство по образованиюГосударственное образовательное учреждение высшего

профессионального образования«УФИМСКИЙ ГОСУДАРСТВЕННЫЙ НЕФТЯНОЙ

ТЕХНИЧЕСКИЙ УНИВЕРСИТЕТ»

Кафедра иностранных языков

УЧЕБНО-МЕТОДИЧЕСКОЕ ПОСОБИЕдля внеаудиторного чтения по английскому языку

специальности БПГ

Уфа 2013

4

Учебно-методическое пособие для внеаудиторного чтения поанглийскому языку для специальности БПГ издаётся с целью обучениячтению и переводу иностранной литературы во внеаудиторное время.

Тексты имеют адаптированный характер: лексические трудностиснимаются благодаря подробному словарю, представленному в концеучебно-методического пособия, а также примечаний после каждого текста,комментирующих содержание значений отдельных терминов и сокращений,и заданий к тексту в виде вопросов, на которые должны быть даны ответы сцелью выяснения степени понимания текста.

Составитель Арсланова А.Р., преподаватель

© Уфимский государственный нефтяной технический университет, 2012

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Text 3 for written translation (5 т. зн.)

1. Translate the text paying attention to the following points:

1. The types of construction projects should be considered.

2. Construction processes.

3. What do we mean by the term “Authority having jurisdiction”.

4. Construction careers you would prefer.

Types of construction projects

Each type of construction project requires a unique team to plan, design, construct,

and maintain the project1. In general, there are three types of construction:

1. Building construction

2. Heavy/civil construction

3. Industrial construction

Building construction

In the fields of architecture and civil engineering, construction is a process that

consists of the building or assembling of infrastructure.

Building construction for several apartment blocks.

The blue material is insulation cladding, which will

be covered later.

Far from being a single activity, large scale

construction is a feat of multitasking2.

Normally the job is managed by the project

manager and supervised by the construction

manager, design engineer, construction engineer or project architect. For the

1 «содержать проект»

2 «мастерство выполнять множество различных задач»6

successful execution of a project, effective planning is essential. Those involved

with the design and execution of the infrastructure in question must consider the

environmental impact of the job, the successful scheduling, budgeting, site safety,

availability of materials, logistics, inconvenience to the public caused by

construction delays, preparing tender documents, etc.

Building construction is the process of adding structure to real property. The vast

majority of building construction projects are small renovations, such as addition

of a room, or renovation of a bathroom.

A large unfinished building

Often, the owner of the property acts as

labourer, paymaster, and design team for the

entire project. However, all building

construction projects include some elements in

common – design, financial, and legal

considerations. Many projects of varying sizes

reach undesirable end results, such as structural collapse, cost overruns, and/or

litigation reason, those with experience in the field3 make detailed plans and

maintain careful oversight during the project to ensure a positive outcome.

Building construction is procured privately or publicly utilizing various delivery

methodologies, including hard bid, negotiated price, traditional, management

contracting, construction management-at-risk, design & build and design-build

bridging.

Trump International Hotel and Tower (Chicago4)

3 field experience – производственный опыт; производственная практика

4 [ʃɪ'kɑ:gəu]7

May, 23, 2006

Residential construction practices, technologies, and resources must conform to

local building authority regulations and codes of practice. Materials readily

available in the area generally dictate the construction materials used (e.g. brick

versus stone, versus timber). Cost of construction on a per square metre5 (or per

square foot) basis for houses can vary dramatically based on site conditions, local

regulations, economies of scale (custom designed homes are always more

expensive to build) and the availability of skilled tradespeople.

As residential (as well as all other types of construction) can generate a lot of

waste, careful planning again is needed here.

September 14, 2007

The most popular method of residential construction in

the United States is wood framed construction6. As

efficiency codes have come into effect in recent years,

new construction technologies and methods have

emerged. University Construction Management

departments are on the cutting edge of the newest

methods of construction intended to improve efficiency,

performance and reduce construction waste.

Industrial construction

Construction of the Havelock City Project in Sri

Lanka.

Industrial construction, though a relatively

small part of the entire construction industry, is

5 on a per square metre – за (один) квадратный метр

6 6 деревянная фахверковая конструкция (фахверк – деревянный брусчатый остов малоэтажного здания, см.также framework, half-timbering, trelliswork)

8

a very important component. Owners of these projects are usually large, for-profit,

industrial corporations. These corporations can be found in such industries as

medicine, petroleum, chemical, power generation, manufacturing, etc. Processes

in these industries require highly specialized expertise in planning, design, and

construction. As in building and heavy/highway construction, this type of

construction requires a team of individuals to ensure a successful project.

Construction processes

Design team

In the modern industrialized world, construction usually involves the translation of

paper or computer based designs7 into reality.

Shasta Dam under construction

The design usually consists of drawings

and specifications, usually prepared by a

design team including the client

architects8, interior designers, surveyors,

civil engineers, cost engineers (or quantity

surveyors), mechanical engineers, electrical engineers, structural engineers, and

fire protection engineers. The design team is most commonly employed by (i.e. in

contract with) the property owner. Under this system, once the design is completed

by the design team, a number of construction companies or construction

management companies may then be asked to make a bid for the work, either

based directly on the design, or on the basis of drawings and a bill of quantities

7 компьютерная система проектирования (система программ, позволяющая осуществлять большую часть проектирования в электронном режиме) (cf: CAD (Computer-Aided Design)система автоматизированного проектирования, САПР)

8 архитектор, работающий с клиентами (сотрудник компании, отвечающий заиндивидуальную работу с клиентами; находится в постоянном контакте с клиентом,отвечает на его вопросы или консультирует по проблемам, связанным с проектированием)

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provided by a quantity surveyor. Following evaluation of bids, the owner will

typically award a contract to the lowest responsible bidder. The modern trend in

design is toward integration of previously separated specialties, especially among

large firms. In the past, architects, interior designers, engineers, developers,

construction managers, and general contractors were more likely to be entirely

separate companies, even in the larger firms.

Apartment is under construction in Daegu, South Korea.

Presently, a firm that is nominally an "architecture" or "construction management"

firm may have experts from all related fields as employees, or to have an

associated company that provides each necessary skill. Thus, each such firm may

offer itself as "one-stop shopping" for a construction project, from beginning to

end. This is designated as a "design Build9" contract where the contractor is given

a performance specification, and must

undertake the project from design to

construction, while adhering to the

performance specifications.

Construction of a prefabricated house

Several project structures can

assist the owner in this

integration, including design-

build, partnering, and

construction management. In

general, each of these project structures allows the owner to integrate the services

of architects, interior designers, engineers, and constructors throughout design and

construction. In response, many companies are growing beyond traditional

9 «от проекта до строительства»10

offerings of design or construction services alone, and are placing more emphasis

on establishing relationships with other necessary participants through the design-

build process.

The increasing complexity of construction projects creates the need for design

professionals trained in all phases of the project's life-cycle and develop an

appreciation of the building as an advanced technological system requiring close

integration of many sub-systems and their individual components, including

sustainability. Building engineering is an emerging discipline that attempts to meet

this new challenge.

Construction on a building in Kansas City

During the planning of a building, thezoning and planning boards of thegovernmental agency or sub-agencywhich regulates the construction processwill review the overall compliance of theproposed building with the municipalGeneral Plan and zoning regulations.Once the proposed building has been

approved, detailed civil, architectural, and structural plans must be submitted to themunicipal building department (and sometimes the public works department) todetermine compliance with the building code and sometimes for fit with existinginfrastructure. Often, the municipal fire department will review the plans forcompliance with fire-safety ordinances and regulations.

Before the foundation can be dug, contractors are typically required to notifyutility companies, either directly or through a company such as Dig Safe to ensurethat underground utility lines can be marked. This lessens the likelihood of damageto the existing electrical, water, sewage, phone, and cable facilities, which couldcause outages and potentially hazardous situations. During the construction of abuilding, the municipal building inspector inspects the building periodically toensure that the construction adheres to the approved plans and the local buildingcode. Once construction is complete and a final inspection has been passed, anoccupancy permit may be issued. Changes made to a building that affect safety,

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including its use, expansion, structural integrity, and fire protection items, usuallyrequire approval of the AHJ for review concerning the building code.

Construction careers

Ironworkers erecting the steel frame of a new building,

at the Massachusetts General Hospital, USA

There are many routes to the different careerswithin the construction industry which vary bycountry. However, there are three main tiers ofcareers based on educational background whichare common internationally:

Unskilled and Semi-Skilled – General sitelabour with little or no constructionqualifications.

Skilled On-site managers whom possess extensive knowledge and experience in their craft or profession.

Technical and Management – Personnel with the greatest educationalqualifications, usually graduate degree10s, trained to design, manage andinstruct the construction process.

Skilled occupations in the UK require Further Education qualifications, often invocational subject areas. These qualifications are either obtained directly after thecompletion of compulsory education or through "on the job" apprenticeshiptraining. In the UK, 8500 construction-related apprenticeships were commenced in2007.

Technical and specialised occupations require more training as a greater technicalknowledge is required. These professions also hold more legal responsibility. Ashort list of the main careers with an outline of the educational requirements aregiven below:

Architect – Typically holds at least a 4-year degree in architecture. To usethe title "architect" the individual must hold chartered status with the RoyalInstitute of British Architects and be on the Architects Registration Board.

Civil Engineer – Typically holds a degree in a related subject. TheChartered Engineer qualification is controlled by the Institution of CivilEngineers. A new university graduate must hold a masters degree to

10 степень выпускника учебного заведения12

become chartered, persons with bachelors degrees may become anIncorporated Engineer.

Building Services Engineer – Often referred to as an "M&E Engineer"typically holds a degree in mechanical or electrical engineering. CharteredEngineer status is governed by the Chartered Institution of Building ServicesEngineers.

Project Manager – Typically holds a 2-year or greater higher educationqualification, but are often also qualified in another field such as quantitysurveying or civil engineering.

Quantity Surveyor – Typically holds a masters degree in quantity surveying. Chartered status is gained from the Royal Institute of Chartered Surveyors.

Structural Engineer – Typically holds a bachelors or masters degree instructural engineering, new university graduates must hold a masters degreeto gain chartered status from the Institution of Structural Engineers.

The construction industry in the United States provides employment to millionswith all types and levels of education. Construction contributes 14% of the UnitedStates Gross National Product. Construction engineering provides much of thedesign aspect used both in the construction office and in the field on project sites.To complete projects construction engineers rely on plans and specificationscreated by architects, engineers and other constructors. During most of the 20thcentury structures have been first designed then engineering staff ensure it is builtto plans and specifications by testing and overseeing the construction. Previous tothe 20th century and more commonly since the start of the 21st century structuresare designed and built in combination, allowing for site considerations andconstruction methods to influence the design process.

Construction engineers have a wide range of responsibilities. Typically entry levelconstruction engineers analyze reports and estimate project costs both in the officeand in the field. Other tasks may include: analyzing maps, drawings, blueprints,aerial photography and other topographical information. Construction engineersalso have to use computer software to design hydraulic systems and structureswhile following construction codes. Keeping a workplace safe is key to having asuccessful construction company. It is the construction engineer's job to makesure11 that everything is conducted correctly. In addition to safety, the constructionengineer has to make sure that the site stays clean and sanitary. They have to makesure that there are no impediments in the way of the structure's planned locationand must move any that exist. Finally, more seasoned construction engineers will

11 «именно работой инженера-строителя является убедиться, что…»13

assume the role of project management on a construction site and are involvedheavily with the construction schedule and document control as well as budget andcost control. Their role on site is to provide construction information, includingrepairs, requests for information, change orders and payment applications to themanagers and/or the owner's representatives.

Construction engineers should have strong understanding for math and science, butmany other skills are required, including critical thinking, listening, learning,problem solving, monitoring and decision making. Construction engineers have tobe able to think about all aspects of a problem and listen to other’s ideas so thatthey can learn everything about a project before it begins. During projectconstruction they must solve the problems that they encounter using math andscience. Construction Engineers must maintain project control of labor andequipment for safety, to ensure the project is on schedule and monitor qualitycontrol. When a problem occurs it is the construction engineer who will create andenact a solution.

Construction engineers need different abilities to do their job. They must have theability to reason, convey instructions to others, comprehend multi variables,anticipate problems, comprehend verbal, written and graphic instructions, organizedata sets, speak clearly, visualize in 4D time-space and understand Virtual Designand Construction methods.

Text 4 (20 т.зн.)

1. Read the text and answer the questions:

1. What is a structural engineer? 2. Which structural elements are usually used in construction? 3. What does the structural engineering theory perceives? 4. What are common building materials?

1. Structural engineer

Structural engineers are responsible for engineering design and analysis. Entry-level structural engineers may design the individual structural elements of astructure, for example the beams, columns, and floors of a building. Moreexperienced engineers would be responsible for the structural design and integrityof an entire system, such as a building. Structural engineers often specialise inparticular fields, such as bridge engineering, building engineering, pipelineengineering, industrial structures or special structures such as vehicles or aircraft.

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Structural engineering has existed since humans first started to construct their ownstructures. It became a more defined and formalised profession with the emergenceof the architecture profession as distinct from the engineering profession during theindustrial revolution in the late 19th Century. Until then, the architect and thestructural engineer were often one and the same – the master builder. Only with theunderstanding of structural theories that emerged during the 19th and 20th centurydid the professional structural engineer come into existence. The role of astructural engineer today involves a significant understanding of both static anddynamic loading, and the structures that are available to resist them. Thecomplexity of modern structures often requires a great deal of creativity from theengineer in order to ensure the structures support and resist the loads they aresubjected to. A structural engineer will typically have a four or five yearundergraduate degree, followed by a minimum of three years of professionalpractice before being considered fully qualified. Structural engineers are licensedor accredited by different learned societies and regulatory bodies around the world(for example, the Institution of Structural Engineers in the UK). Depending on thedegree course they have studied and/or the jurisdiction they are seeking licensurein, they may be accredited (or licensed) as just structural engineers, or as civilengineers, or as both civil and structural engineers.

Civil engineering structures

The Millau Viaduct in France, designed by Michel

Virlogeux with Foster & Partners

Civil structural engineering includes all structural engineering related to the built environment. It includes:

Bridges Dams

Earthworks Foundations

Offshore structures

Pipelines

Power stations Railways

Retaining structures and walls Roads

Tunnels

Waterways

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The structural engineer is the lead designer on these structures, and often the soledesigner. In the design of structures such as these, structural safety is of paramountimportance (in the UK, designs for dams, nuclear power stations and bridges mustbe signed off by a chartered engineer).

Civil engineering structures are often subjected to very extreme forces, such aslarge variations in temperature, dynamic loads such as waves or traffic, or highpressures from water or compressed gases. They are also often constructed incorrosive environments, such as at sea, in industrial facilities or below ground.

An Airbus A380, the world's largest passenger

airliner

The design of static structures assumes theyalways have the same geometry (in fact, so-called static structures can movesignificantly, and structural engineering

design must take this into account where necessary), but the design of moveable ormoving structures must account for fatigue, variation in the method in which loadis resisted and significant deflections of structures.

The forces which parts of a machine are subjected to can vary significantly, andcan do so at a great rate. The forces which a boat or aircraft are subjected to varyenormously and will do so thousands of times over the structure's lifetime. Thestructural design must ensure that such structures are able to endure such loadingfor their entire design life without failing.

These works can require mechanical structural engineering:

Airframes and fuselages Boilers and pressure vessels Coachworks and carriages Cranes Elevators Escalators Marine vessels and hulls

2. Structural elements

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A statically

determinate simply

supported beam,

bending under an

evenly distributed

load.

Anystructure is essentially made up of only a smallnumber of different types of elements:

Columns Beams Plates Arches Shells Catenaries

Many of these elements can be classified according to form (straight, plane / curve)and dimensionality (one-dimensional / two-dimensional):

One-dimensional Two-dimensional

straight curve plane curve

(predominantly) bending beamcontinuous

archplate, concrete

slablamina,dome

(predominant) tensilestress

rope Catenary shell

(predominant)compression

pier, column Load-bearing wall

Columns

Columns are elements that carry only axial force – either tension or compression –or both axial force and bending (which is technically called a beam-column butpractically, just a column). The design of a column must check the axial capacityof the element, and the buckling capacity. The buckling capacity is the capacity ofthe element to withstand the propensity to buckle. Its capacity depends upon itsgeometry, material, and the effective length of the column, which depends uponthe restraint conditions at the top and bottom of the column. The effective length isK * l *where K is the real length of the column/. The capacity of a column to carry

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axial load depends on the degree of bending it is subjected to, and vice versa. Thisis represented on an interaction chart and is a complex non-linear relationship.

Beams

A beam may be:

cantilevered (supported at one end only with a fixed connection) simply supported (supported vertically at each end; horizontally on only oneto withstand friction, and able to rotate at the supports) continuous (supported by three or more supports) a combination of the above (ex. supported at one end and in the middle)

Beams are elements which carry pure bending only. Bending causes one section ofa beam (divided along its length) to go into compression and the other section intotension. The compression section must be designed to resist buckling and crushing,while the tension section must be able to adequately resist the tension.

Struts and ties

Little Belt: a truss bridge in Denmark

A truss is a structure comprising two types ofstructural element, ie struts and ties. A strut is arelatively lightweight column and a tie is aslender element designed to withstand tensionforces. In a pin-jointed truss (where all jointsare essentially hinges), the individual elements

of a truss theoretically carry only axial load. From experiments it can be shownthat even trusses with rigid joints will behave as though the joints arepinned.Trusses are usually utilised to span large distances, where it would beuneconomical and unattractive to use solid beams.

The McDonnell Planetarium by Gyo Obata in St

Louis, Missouri, USA, a concrete shell structure

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A masonry arch

1. Keystone

2. Voussoir

3. Extrados

4. Impost

5. Intrados

6. Rise

7. Clear span

8. Abutment

Plates

Plates carry bending in two directions. A concrete flat slab is an example of a plate.Plates are understood by using continuum mechanics, but due to the complexityinvolved they are most often designed using a codified empirical approach, orcomputer analysis. They can also be designed with yield line theory, where anassumed collapse mechanism is analysed to give an upper bound on the collapseload (see Plasticity). This is rarely used in practice.

Shells

Shells derive their strength from their form, and carry forces in compression in twodirections. A dome is an example of a shell. They can be designed by making ahanging-chain model, which will act as a catenary in pure tension, and invertingthe form to achieve pure compression.

Arches

Arches carry forces in compression in one direction only, which is why it isappropriate to build arches out of masonry. They are designed by ensuring that theline of thrust of the force remains within the depth of the arch.

Catenaries

Catenaries derive their strength from their form, and carry transverse forces inpure tension by deflecting (just as a tightrope will sag when someone walks on it).They are almost always cable or fabric structures. A fabric structure acts as acatenary in two directions.

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3. Structural engineering theory

Figure of a bolt in shear. Top figure illustrates single shear,

bottom figure illustrates double shear.

Structural engineering depends upon a detailedknowledge of loads, physics and materials tounderstand and predict how structures support andresist self-weight and imposed loads. To apply theknowledge successfully a structural engineer willneed a detailed knowledge of mathematics and ofrelevant empirical and theoretical design codes. He

will also need to know about the corrosion resistance of the materials andstructures, especially when those structures are exposed to the externalenvironment. The criteria which govern the design of a structure are eitherserviceability (criteria which define whether the structure is able to adequatelyfulfill its function) or strength (criteria which define whether a structure is able tosafely support and resist its design loads). A structural engineer designs a structureto have sufficient strength and stiffness to meet these criteria.

Loads imposed on structures are supported by means of forces transmitted throughstructural elements. These forces can manifest themselves as:

tension (axial force) compression (axial force) shear bending, or flexure (a bending moment is a force multiplied by a distance, orlever arm, hence producing a turning effect or torque)

Loads

Some Structural loads on structures can be classified as live (imposed) loads, deadloads, earthquake (seismic) loads, wind loads, soil pressure loads, fluid pressureloads, impact loads, and vibratory loads. Live loads are transitory or temporaryloads, and are relatively unpredictable in magnitude. They may include the weightof a building's occupants and furniture, and temporary loads the structure issubjected to during construction. Dead loads are permanent, and may include theweight of the structure itself and all major permanent components. Dead load mayalso include the weight of the structure itself supported in a way it wouldn'tnormally be supported, for example during construction.

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Strength

Strength depends upon material properties. The strength of a material depends onits capacity to withstand axial stress, shear stress, bending, and torsion. Thestrength of a material is measured in force per unit area (newtons per squaremillimetre or N/mm², or the equivalent megapascals or MPa in the SI system andoften pounds per square inch psi in the United States Customary Units system).

A structure fails the strength criterion when the stress (force divided by area of material) induced by the loading is greater than the capacity of the structural material to resist the load without breaking, or when the strain (percentage extension) is so great that the element no longer fulfills its function (yield).

Stiffness

Stiffness depends upon material properties and geometry. The stiffness of astructural element of a given material is the product of the material's Young'smodulus and the element's second moment of area. Stiffness is measured in forceper unit length (newtons per millimetre or N/mm), and is equivalent to the 'forceconstant' in Hooke's Law. The deflection of a structure under loading is dependenton its stiffness. The dynamic response of a structure to dynamic loads (the naturalfrequency of a structure) is also dependent on its stiffness. In a structure made upof multiple structural elements where the surface distributing the forces to theelements is rigid, the elements will carry loads in proportion to their relativestiffness - the stiffer an element, the more load it will attract. In a structure wherethe surface distributing the forces to the elements is flexible (like a wood framedstructure), the elements will carry loads in proportion to their relative tributaryareas. A structure is considered to fail the chosen serviceability criteria if it isinsufficiently stiff to have acceptably small deflection or dynamic response underloading. The inverse of stiffness is the flexibility.

Safety factors

The safe design of structures requires a design approach which takes account of thestatistical likelihood of the failure of the structure. Structural design codes arebased upon the assumption that both the loads and the material strengths vary witha normal distribution. The job of the structural engineer is to ensure that the chanceof overlap between the distribution of loads on a structure and the distribution ofmaterial strength of a structure is acceptably small (it is impossible to reduce thatchance to zero). It is normal to apply a partial safety factor to the loads and to the

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material strengths, to design using 95th percentiles (two standard deviations fromthe mean). The safety factor applied to the load will typically ensure that in 95% oftimes the actual load will be smaller than the design load, while the factor appliedto the strength ensures that 95% of times the actual strength will be higher than thedesign strength. The safety factors for material strength vary depending on thematerial and the use it is being put to and on the design codes applicable in thecountry or region.

Load cases

A load case is a combination of different types of loads with safety factors appliedto them. A structure is checked for strength and serviceability against all the loadcases it is likely to experience during its lifetime.

Typical load cases for design for strength (ultimate load cases; ULS) are:

1.4 x Dead Load + 1.6 x Live Load 1.2 x Dead Load + 1.2 x Live Load + 1.2 x Wind Load

A typical load case for design for serviceability (characteristic load cases; SLS) is:

1.0 x Dead Load + 1.0 x Live Load

Different load cases would be used for different loading conditions. For example,in the case of design for fire a load case of 1.0 x Dead Load + 0.8 x Live Load maybe used, as it is reasonable to assume everyone has left the building if there is afire. In multi-story buildings it is normal to reduce the total live load depending onthe number of stories being supported, as the probability of maximum load beingapplied to all floors simultaneously is negligibly small. It is not uncommon forlarge buildings to require hundreds of different load cases to be considered in thedesign.

Newton's laws of motion

The most important natural laws for structural engineering are Newton's Laws ofMotion. Newton's first law states that every body perseveres in its state of being atrest or of moving uniformly straight forward, except insofar as it is compelled tochange its state by force impressed. Newton's second law states that the rate ofchange of momentum of a body is proportional to the resultant force acting on the

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body and is in the same direction. Mathematically, F=ma (force = mass xacceleration). Newton's third law states that all forces occur in pairs, and these twoforces are equal in magnitude and opposite in direction. With these laws it ispossible to understand the forces on a structure and how that structure will resistthem. The Third Law requires that for a structure to be stable all the internal andexternal forces must be in equilibrium. This means that the sum of all internal andexternal forces on a free-body diagram must be zero:

: the vectorial sum of the forces acting on the body equals zero.This translates to

Σ H = 0: the sum of the horizontal components of the forces equals zero;

Σ V = 0: the sum of the vertical components of forces equals zero;

: the sum of the moments (about an arbitrary point) of all forcesequals zero.

Statical determinacy

A structural engineer must understand the internal and external forces of astructural system consisting of structural elements and nodes at their intersections.A statically determinate structure can be fully analysed using only consideration ofequilibrium, from Newton's Laws of Motion. A statically indeterminate structurehas more unknowns than equilibrium considerations can supply equations for (seesimultaneous equations). Such a system can be solved using consideration ofequations of compatibility between geometry and deflections in addition toequilibrium equations, or by using virtual work. If a system is made up of b bars, jpin joints and r support reactions, then it cannot be statically determinate if thefollowing relationship does not hold:

r + b = 2j

It should be noted that even if this relationship does hold, a structure can bearranged in such a way as to be statically indeterminate.

Elasticity

Much engineering design is based on the assumption that materials behaveelastically. For most materials this assumption is incorrect, but empirical evidence

23

has shown that design using this assumption can be safe. Materials that are elasticobey Hooke's Law, and plasticity does not occur.

For systems that obey Hooke's Law, the extension produced is directlyproportional to the load:

where

x is the distance that the spring has been stretched or compressed away from theequilibrium position, which is the position where the spring would naturally cometo rest [usually in meters],

F is the restoring force exerted by the material [usually in newtons], and

k is the force constant (or spring constant). This is the stiffness of the spring. Theconstant has units of force per unit length (usually in newtons per metre)

Plasticity

Comparison of Tresca and Von Mises Criteria

Some design is based on the assumption thatmaterials will behave plastically.[27] A plasticmaterial is one which does not obey Hooke'sLaw, and therefore deformation is notproportional to the applied load. Plasticmaterials are ductile materials. Plasticity theorycan be used for some reinforced concretestructures assuming they are underreinforced,meaning that the steel reinforcement fails before

the concrete does. Plasticity theory states that the point at which a structurecollapses (reaches yield) lies between an upper and a lower bound on the load,defined as follows:

If, for a given external load, it is possible to find a distribution of momentsthat satisfies equilibrium requirements, with the moment not exceeding theyield moment at any location, and if the boundary conditions are satisfied,then the given load is a lower bound on the collapse load.

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If, for a small increment of displacement, the internal work done by thestructure, assuming that the moment at every plastic hinge is equal to theyield moment and that the boundary conditions are satisfied, is equal to theexternal work done by the given load for that same small increment ofdisplacement, then that load is an upper bound on the collapse load.

If the correct collapse load is found, the two methods will give the same result forthe collapse load.

Plasticity theory depends upon a correct understanding of when yield will occur. Anumber of different models for stress distribution and approximations to the yield surface of plastic materials exist

Mohr's circle Von Mises yield criterion Henri Tresca

The Euler-Bernoulli beam equation

The Euler-Bernoulli beam equation defines the behaviour of a beam element (seebelow). It is based on five assumptions:

(1) continuum mechanics is valid for a bending beam(2) the stress at a cross section varies linearly in the direction of bending, and is zero at the centroid of every cross section.(3) the bending moment at a particular cross section varies linearly with the secondderivative of the deflected shape at that location.(4) the beam is composed of an isotropic material(5) the applied load is orthogonal to the beam's neutral axis and acts in a unique plane.

A simplified version of Euler-Bernoulli beam equation is:

Here u is the deflection and w(x) is a load per unit length. E is the elastic modulusand I is the second moment of area, the product of these giving the stiffness of thebeam.

This equation is very common in engineering practice: it describes the deflectionof a uniform, static beam.

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Successive derivatives of u have important meaning:

is the deflection.

is the slope of the beam.

is the bending moment in the beam.

is the shear force in the beam.

A bending moment manifests itself as a tension and a compression force, acting asa couple in a beam. The stresses caused by these forces can be represented by:

where σ is the stress, M is the bending moment, y is the distance from the neutralaxis of the beam to the point under consideration and I is the second moment ofarea. Often the equation is simplified to the moment divided by the sectionmodulus (S), which is I/y. This equation allows a structural engineer to assess thestress in a structural element when subjected to a bending moment.

Buckling

A column under a centric axial load exhibiting the characteristic

deformation of buckling.

When subjected to compressive forces it is possible for structural elements to deform significantly due to the destabilising effect of that load. The effect can be initiated or exacerbated by possible inaccuracies in manufacture or construction.

Lateral-torsional buckling of an aluminium alloy plate girder

designed and built by students at Imperial College London.

The Euler buckling formula defines the axial compression force which will cause a strut (or column) to fail in buckling.

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where

F = maximum or critical force (vertical load on column),

E = modulus of elasticity,

I = area moment of inertia, or second moment of area

l = unsupported length of column,

K = column effective length factor, whose value depends on the conditions of end support of the column, as follows.

For both ends pinned (hinged, free to rotate), K = 1.0.

For both ends fixed, K = 0.50.

For one end fixed and the other end pinned, 0.70.

For one end fixed and the other end free to move laterally, K = 2.0. This value is sometimes expressed for design purposes as a critical buckling stress.

where

σ = maximum or critical stress

r = the least radius of gyration of the cross section

Other forms of buckling include lateral torsional buckling, where the compressionflange of a beam in bending will buckle, and buckling of plate elements in plate

girders due to compression in the plane of the plate.

4. Materials

Stress-strain curve for low-

carbon steel. Hooke's law

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(see above) is only valid for the portion of the curve between

the origin and the yield point.

1. Ultimate strength2. Yield strength-corresponds to yield point.

3. Rupture4. Strain hardening region

5. Necking region.

A: Apparent stress (F/A0)B: Actual stress (F/A)

Structural engineering depends on the knowledge of materials and their properties,in order to understand how different materials support and resist loads.

Common structural materials are:

Wrought iron

Wrought iron is the simplest form of iron, and is almost pure iron (typically lessthan 0.15% carbon). It usually contains some slag. Its uses are almost entirelyobsolete, and it is no longer commercially produced. Wrought iron is very poor infires. It is ductile, malleable and tough. It does not corrode as easily as steel.

Cast iron

Cast iron is a brittle form of iron which is weaker in tension than in compression. Ithas a relatively low melting point, good fluidity, castability, excellentmachinability and wear resistance. Though almost entirely replaced by steel inbuilding structures, cast irons have become an engineering material with a widerange of applications, including pipes, machine and car parts. Cast iron retains highstrength in fires, despite its low melting point. It is usually around 95% iron, withbetween 2.1-4% carbon and between 1-3% silicon. It does not corrode as easily as

steel.

Steel

The 630 foot (192 m) high, stainless-clad (type 304) Gateway Arch

in Saint Louis, Missouri

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Steel is a iron alloy with between 0.2 and 1.7% carbon. Steel is used extremelywidely in all types of structures, due to its relatively low cost, high strength toweight ratio and speed of construction. Steel is a ductile material, which willbehave elastically until it reaches yield (point 2 on the stress-strain curve), when itbecomes plastic and will fail in a ductile manner (large strains, or extensions,before fracture at point 3 on the curve). Steel is equally strong in tension andcompression.

Steel is weak in fires, and must be protected in most buildings. Because of its highstrength to weight ratio, steel buildings typically have low thermal mass, andrequire more energy to heat (or cool) than similar concrete buildings. The elasticmodulus of steel is approximately 205 GPa. Steel is very prone to corrosion (rust).

Stainless steel

Stainless steel is an iron-carbon alloy with a minimum of 10.5% chromiumcontent. There are different types of stainless steel, containing different proportionsof iron, carbon, molybdenum, nickel. It has similar structural properties to steel,although its strength varies significantly.

It is rarely used for primary structure, and more for architectural finishes andbuilding cladding.

It is highly resistant to corrosion and staining.

Concrete

The interior of the Sagrada Familia, constructed of

reinforced concrete to a design by Gaudi

Concrete is used extremely widely inbuilding and civil engineering structures,due to its low cost, flexibility, durability,and high strength. It also has high

resistance to fire.

A "cage" of reinforcing steel

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Concrete is a brittle material and it is strong in compression and very weak intension. It behaves non-linearly at all times. Because it has essentially zero strengthin tension, it is almost always used as reinforced concrete, a composite material. Itis a mixture of sand, aggregate, cement and water. It is placed in a mould, or form,as a liquid, and then it sets (goes off), due to a chemical reaction between the waterand cement. The hardening of the concrete is called curing. The reaction isexothermic (gives off heat).

Concrete increases in strength continually from the day it is cast. Assuming it isnot cast under water or in constantly 100% relative humididy, it shrinks over timeas it dries out, and it deforms over time due to a phenomenon called creep. Itsstrength depends highly on how it is mixed, poured, cast, compacted, cured (keptwet while setting), and whether or not any admixtures were used in the mix. It canbe cast into any shape that a form can be made for. Its colour, quality, and finishdepend upon the complexity of the structure, the material used for the form, andthe skill of the worker.

Concrete is a non-linear, non-elastic material, and will fail suddenly, with a brittlefailure, unless adequate reinforced with steel. An "under-reinforced" concreteelement will fail with a ductile manner, as the steel will fail before the concrete. An"over-reinforced" element will fail suddenly, as the concrete will fail first.Reinforced concrete elements should be designed to be under-reinforced so usersof the structure will receive warning of impending collapse. This is a technicalterm. Reinforced concrete can be designed without enough reinforcing. A betterterm would be properly reinforced where the member can resist all the design loadsadequately and it is not over-reinforced. The elastic modulus of concrete can varywidely and depends on the concrete mix, age, and quality, as well as on the typeand duration of loading applied to it. It is usually taken as approximately 25 GPafor long-term loads once it has attained its full strength (usually considered to be at28 days after casting). It is taken as approximately 38 GPa for very short-termloading, such as footfalls. Concrete has very favourable properties in fire - it is notadversely affected by fire until it reaches very high temperatures. It also has veryhigh mass, so it is good for providing sound insulation and heat retention (leading

to lower energy requirements for the heatingof concrete buildings). This is offset by thefact that producing and transporting concreteis very energy intensive.

Aluminium

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Stress vs. Strain curve typical of aluminum

1. Ultimate strength2. Yield strength3. Proportional Limit Stress4. Rupture5. Offset strain (typically 0.002).

Aluminium is a soft, lightweight, malleable metal. The yield strength of purealuminium is 7–11 MPa, while aluminium alloys have yield strengths ranging from200 MPa to 600 MPa. Aluminium has about one-third the density and stiffness ofsteel. It is ductile, and easily machined, cast, and extruded. Corrosion resistance isexcellent due to a thin surface layer of aluminium oxide that forms when the metalis exposed to air, effectively preventing further oxidation. The strongest aluminiumalloys are less corrosion resistant due to galvanic reactions with alloyed copper.Aluminium is used in some building structures (mainly in facades) and very widelyin aircraft engineering because of its good strength to weight ratio. It is a relativelyexpensive material.

In aircraft it is gradually being replaced by carbon composite materials.

Composites

Light composite aircraft

Composite materials are usedincreasingly in vehicles and aircraftstructures, and to some extent in otherstructures. They are increasingly usedin bridges, especially for conservationof old structures such as Coalport castiron bridge built in 1818. Compositesare often anisotropic (they have

different material properties in different directions) as they can be laminarmaterials. They most often behave non-linearly and will fail in a brittle mannerwhen overloaded. They provide extremely good strength to weight ratios, but arealso very expensive. The manufacturing processes, which are often extrusion, donot currently provide the economical flexibility that concrete or steel provide. Themost commonly used in structural applications are glass-reinforced plastics.

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Masonry

A brick wall built using Flemish Bond

Masonry has been used in structuresfor hundreds of years, and can takethe form of stone, brick orblockwork. Masonry is very strongin compression but cannot carrytension (because the mortar betweenbricks or blocks is unable to carry

tension). Because it cannot carry structural tension, it also cannot carry bending, somasonry walls become unstable at relatively small heights. High masonrystructures require stabilisation against lateral loads from buttresses (as with theflying buttresses seen in many European medieval churches) or from windposts.

Historically masonry was constructed with no mortar or with lime mortar. Inmodern times cement based mortars are used. The mortar glues the blockstogether, and also smoothes out the interface between the blocks, avoidinglocalised point loads that might have led to cracking.

Since the widespread use of concrete, stone is rarely used as a primary structural material, often only appearing as a cladding, because of its cost and the high skills needed to produce it. Brick and concrete blockwork have taken its place.

Masonry, like concrete, has good sound insulation properties and high thermalmass, but is generally less energy intensive to produce. It is just as energy intensiveas concrete to transport.

Timber

The reconstructed Globe Theatre, London,

by Buro Happold

Timber is the oldest of structuralmaterials, and though mainlysupplanted by steel, masonry andconcrete, it is still used in asignificant number of buildings. Theproperties of timber are non-linearand very variable, depending on the

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quality, treatment of wood, and type of wood supplied. The design of woodenstructures is based strongly on empirical evidence. Wood is strong in tension andcompression, but can be weak in bending due to its fibrous structure. Wood isrelatively good in fire as it chars, which provides the wood in the centre of theelement with some protection and allows the structure to retain some strength for areasonable length of time.

Bamboo scaffolding can reach great heights.

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