Chapter 3 Composite floor with steel profiled sheeting组合楼板

By Professor Shiming Chen Lecture Notes for Presentation

2015

• OBJECTIVE/SCOPE• To describe the design of composite slabs,

formed using profiled steel sheeting and a concrete topping, including consideration of the ultimate and serviceability limit state.

• Steel profiled sheeting(deck)、types of deck• Composite floor• Application in construction• Design method• Detailing requirement

3.1 Introduction• 压型钢板-混凝土组合楼板-压型钢板与混凝土通过某种构造措施组成整体共同受力构件。

• Composite flooring system consists of a cold-formed, profiled steel sheet which acts, not only as the permanent formwork for an in-situ cast concrete slab, but also as the tensile reinforcement

• Essential composite action between the steel deck and the concrete slab is provided by some form of interlocking device, capable of resisting horizontal shear and preventing vertical separation at the steel/concrete interface.

Composite slab with profiled steel sheet

it provides a working platform for construction.it acts as formwork for the concrete slab.it constitutes bottom reinforcement for the slab.

Profiled Steel sheeting(a pattern of ‘embossments’)

Construction stage: place the profiled steel sheeting over the support beams

Construction stage: weld studs through the steel sheeting with portable welding gun

Construction stage: place the light steel reinforcement/ steel mesh

Construction stage: cast concrete

Types of Profiled Sheet压型钢板类型

Re-entrant types闭口型

Trapezoidal types 开口型

Advantages identified:The steel deck acts as permanent shuttering for

the in-situ cast concrete slab, with a consequentsaving in time and labor.It once in position, immediately provides a

platform to support construction loads and a safe,sturdy working surface.It acts as the tensile reinforcement.The steel deck geometry can result in a reduction

of labor about 30% in the amount of concrete fillrequired for the floor, significant reduction indead weight loads .

3.2. DESIGN PRINCIPLES

Design Situations（设计工况）

Two distinct structural states must be checked: • firstly, the temporary state of execution, when

only the sheeting resists the applied loads（construction stage 施工阶段）;

• secondly, the permanent state, after the concrete is bonded to the steel giving composite action（composite stage 正常使用阶段）.

Relevant limit states and load cases are considered for both design situations.

a) Construction stage ( Steel deck shuttering)

Verifications at the ultimate limit and serviceabilitylimit states are required, with respect to the safety and serviceability of the steel deck acting as formwork for the wet concrete. The effects of any temporary props used during execution, must be taken into account in this design situation.

b)Composite stage (composite slabs)

Verifications at the ultimate limit and serviceability limit states are required, with respect to the safety and the serviceability of the composite slab after composite behaviour has commenced and any props have been removed.

Major aspects for consideration during thedesign of a composite flooring deck:

o The steel deck itself must be sufficiently strong andrigid to support the weight of wet concrete duringcasting-construction stage.

o The steel deck acting compositely with the hardenedconcrete, and spanning between the supporting steelbeams, must support the imposed live loading--composite slab action.

o The steel beams, acting compositely with thehardened concrete through the stud shear connectorsmust support the imposed live loading--compositebeam action.

Criteria for the design of composite floors

• In design, it is necessary to ensure that the strength and deflections both during construction and in service (when composite action has been achieved) are satisfactory.

• Construction stage:• Profiled steel deck as shuttering, withstands the

weight of wet concrete, workman and equipment, has to have adequate bending strength and stiffness.

• The deck behaves as a folded plate structure and, for low load levels, the behavior is similar to simple beam behavior.

• At higher load levels, buckling of the component plates may occur. The prediction of bucklingstresses on the component plates can be achieved using classical or energy methods.

• The section properties of steel deck can be computed based on the analytical methods provided by design codes.

• Manufacturers prefer to carry out load tests on their products to assess full capacity and provide load-span tables appropriate to each steel profile.

• Propping can dramatically reduce deflections.

Composite slab stage:• The hardened concrete slab, acting compositely with

the profiled steel sheet, spans between the supporting beams and carries the imposed live loads

• The steel deck acts as tensile reinforcement to the slab and the development of composite action depends entirely upon adequate transference of horizontal shear forces at the steel/concrete interface.

• To evaluate the shear bond resistance at the interface between the concrete and the profiled deck, Porter and Ekberg (1976) proposed a testing program (shear-bond test) now worldwide adopted in determination of the shear bond resistance for composite slabs.

3.3 BEHAVIOR AND ANALYSIS

Steel deck alone（混凝土结硬前：压型钢板）

• During execution when the concrete is wet, the steel deck alone resists the exterior loads. Its behavior is then comparable to that of profiles used for roof decking.

• The steel deck is subjected mainly to bending and shear; compression due to bending may arise in either the flanges or the web; shear occurs essentially near the supports.

• Composite action: Once the concrete has hardened the steel deck and concrete combine to form a single structural unit, the composite slab.

• Behavior of a composite slab is analogous to that of a conventional reinforced concrete slab.

• The bond between the steel deck and concrete may not be fully effective and longitudinal slip may occur before the steel deck yields.

Composite slab failure mode types• Failure type I : (flexural failure)：• Failure type II : (longitudinal shear failure, shear-

bond failure.)：• Failure type III : (vertical shear failure)

Load deflection response of brittle and ductile slabs

• The brittle or ductile mode of failure depends on the characteristics of the steel-concrete interface.

Shear bond failure

• Brittle behavior in which slip causes a sudden decrease in load carrying capacity as the surface bond is broken. The extent to which the load reduces is dependent on the effectiveness of the mechanical embossments.

• Ductile behavior in which case the mechanical shear connection is capable of transferring the shear force until failure occurs. This may be flexural or by longitudinal shear.

Behavior of Composite Slabs

Longitudinal shear in composite slabsThree types of shear connection between a profiled steel sheet and a concrete slab:(1) natural bond between the two, known as ‘frictional interlock’(2) ‘mechanical interlock’ provided by pressing dimples or ribs into the sheet(3) end anchorage provided by means of shot-fired pins, or by welding studs through the sheeting to the steel flange.

Determination of the longitudinal shear strengthThe m-k or shear-bond test

Mode 1 brittle (or non-ductile) behaviorMode 2 ductile behavior

Empirical method for evaluating longitudinal shear resistance

• The merits of using profiled steel deck composite floors: its efficiencies in construction and its higher load carrying capacity over the traditional steel deck as shuttering.

• The shear-bond resistance is essential to the interaction between steel sheeting and concrete at the sheet-concrete interface, and governs the composite slab design.

• Shear-bond tests must be carried out to calibrate different types of steel decks.

• Normally, slabs are tested with no shear connectors.

Partial connection method• The partial connection method can also be used for the

verification of the resistance to longitudinal shear. (slabs with ductile behavior).

The verification procedure is illustrated in the Figure abovefor two slabs with different types of loading and span.Resistant moment diagrams and design bending momentdiagrams are plotted against Lx on the same axis system. Forany cross-section of the span, the design bending momentMSd cannot be higher than the design resistance MRd.

Partial connection method (another expression)

The partial connection method can also be used for the verification of the resistance to longitudinal shear.

• The partial-interaction design method requires that the mean ultimate shear stress is determined.

RdLl VV .≤

Vl — design longitudinal shear force of the composite slab

VL,RD — shear bond resistance determined by tests

Shear-bond strength requirement

Analysis of Composite Slabs

• Linear elastic; linear elastic with moment redistribution.

• Plastic according to the theory of plastic hinges.

3.4 RESISTANCES OF SECTIONS• Section I: ultimate moment of resistance failure for

positive bending.• Section II: ultimate moment of resistance failure for

negative bending.• Section III-IV: ultimate resistance to vertical shear failure.• Section V: ultimate resistance to longitudinal shear failure.

Verification of composite slab at the ultimate limit state (ULS)

• Sagging bending resistance. That failure mode is reached if the steel sheeting

yields in tension or if concrete attains its resistance in compression.• Case 1 – Plastic neutral axis above the sheeting

• Case 2 – Plastic neutral axis in steel sheeting

Case 1 – Plastic neutral axis above the sheeting

Case 2 – Plastic neutral axis in steel sheeting

Verification of the hogging bending resistance

At composite slab stage

• Bending resistance, diagonal shear resistance and shear bond resistance should be checkedIf sufficient shear bond is provided at the

interface between concrete and steel sheeting, its bending resistance normal to strong bending direction as the following: Positive bending :

,sd ps RdM M≤

• When a composite slab spans continuously over supporting beams, with negative reinforcement over the internal support region, the negative moment resistance of the slab can be calculated. Negative bending:

• The bending resistance normal to weak bending direction is treated as reinforced concrete slab.

,hd ph RdM M≤

Vertical shear verification

pt dbf.V 070≤

Punch shear resistance

• Punch shear resistance is checked as

Longitudinal shear bond resistance

• To enable a composite slab, the longitudinal shear bondresistance at the interface between the concrete and theprofiled deck should be sufficient.

Diagonal shear resistance （斜截面抗剪）

)163(, −≤ RdLl VV

)183(7.0 0 −≤ bhfV t

Deflections (serviceability limit state)• The slab is comparable to a continuous beam of

constant inertia, equal in value to the average inertia of the cracked and uncracked section

• For deflection under short term load, the area of concrete section is divided by α E (α E = E s/E c);

• Long-term loading effects: using a variation for deflection under long term load, divided by 2α E.

• Deflection of the steel deck must satisfy the deflection requirement as:

limδ δ<

At construction stage• Bending resistance and deflectionbending resistance of the steel deck is checked as

the following:

Deflection of the steel deck must satisfy the deflection requirement as:

M ≤

limδ δ<

3.5 Some detailing requirements• Detailing is to ensure that the full strength of

components can be developed under the most adverse conditions

• The effects of corrosion on steel sheets about 1 mm thick are more severe than on thicker sections, so the materials are usually galvanized.

• The overall depth of a composite slab should not be less than 90 mm, while the distance between the top surface of concrete and the top of the steel ribs should not be less than 50 mm.

• The concrete grade is better over C20.

• The required bearing overlaps of composite slabs over the different

• When shear studs are welded through steelprofiles to the top flange of a steel beam, thediameter of the studs should be 13 to 16 mm if l<3m, and 16 to 19 mm if 3 m < l< 6 m.

• Distributing steel mesh is used to compensateshrinkage and thermal stress in concrete.

• The minimum steel reinforcement ratio in the twoindividual directions is 0.002 (ρs = As/ bhc).

• Negative steel reinforcement ratio not less than 0.002 for crack width control is required in the top layer of concrete slab at the supports of a simply supported slab.

3.6 Design example – floor slab

• A one way composite floor with profiled steel sheeting, the slab span is 2.2 m. Steel grade Q235, t = 1mm, As=1700 m2 /m (weight 0.149 kN/m2);

• I s = 0.96×106mm4/m. • The depth of concrete above the top ribs is 80 mm,

Concrete grade C20, • dead load : g k1 = 0.29 kN/m2, • live load: qk = 2 kN/m2. • Check bending strength, diagonal shear strength and

deflection of the slab

Solution:Calculations of load and internal forces

Take the unit width b =1m.Dead load (the mean depth of the concrete slab 101 mm)

gk = 0.101×25+0.149+0.29 = 2.964 kN/m g = 1.2×2.964 = 3.56 kN/m

Live load qk = 2×1 = 2kN/m q = 1.4×2 = 2.8 kN/m

M = ( g + q )l02 /8= ( 3.56+2.8 )×2.22/8 = 3.85 kN·m

V = ( g + q ) l0 /2= (3.56+2.8) ×2.2/2 = 7.0 kNCalculation of moment resistance fsy = 205 N/mm2, Es = 2.06×105 N/mm2

fc = 9.6 N/mm2, h0 = 150 – 70/2 =115 mm

mm

= 0.8×1700×205×(115 – 36.3/2) = 27.0 kN·m > M

3.3610006.9

2051700=

××

==bffA

xc

sys

)2/(8.0 0 xhfAM sysu −=

Diagonal shear strengthTake one wave length (200 mm) as a checking unit,subjected to shear force as:

V1 = V×200/1000 = 7.0 × 200/1000 = 1.4 kN f t = 1.10 N/mm2 (C20) 0.7 f t bbm h0 = 0.7×1.10×(70+50)/2×115 = 5.31 kN > V1

Calculation of deflection Take one wave length (200 mm) as a checking unit.

Elastic modulus of concrete: Ec = 2.55×104 N/mm2

αE = E s/E c = 2.06×105/2.55×104 = 8.08Deflection under short term loading

Equivalent width of concrete slab: mm75.2408.8

200200==

αE

Equivalent width of rib:

second moment of area of the transformed section of one wave length of composite slab

mm3.708.8

5959==

αE

mm7.872.01700693.78075.24

2/702.01700)12/69(693.7)2/8070(8075.24=

×+×+×××++××++××

=y

44

262

23/

mm10475)2/707.87(2.017001096.02.0)2/6917.87(693.7

6933.7121)2/803.62(8075.248075.24

121

×=

−××+××+−−××+

××+−××+××=skI

second moment of area per meter of slab: Isk = 5 Isk’ =5×475×104 = 0.238 ×108 mm 4

pk = gk + qk = 2.954 +2 = 4.964 kN / m

Deflection under long term loading

mm31.010238.01006.2

2200964.4384

5384

585

440 =

××××

×==sks

kk IE

lpf

488 10119.02/10238.02/ mmII sksq ×=×==

kN/m754.324.095.2 =×+=ψ+= kqkq qgp

3604697mm47.0

10119.01006.22200754.3

3845

3845 00

85

440 ll

IElp

fsks

qq <==

××××

×==

3.7 Advanced composite floor systemsTrends in modern construction have led to the

development of more advanced composite construction• Fabricated beams with tapped webs

• Haunched beams

Composite trusses

Stub girders

Parallel beam grillage system

Beam with single web openings

• Beams with web openings

• Cellular and castellated beams

• Slim floor system

3.8 CONCLUDING SUMMARY• The design of a composite slab must consider the

performance of the profiled steel sheeting, when it acts as shuttering for the wet concrete during execution, as well as the performance of the steel and hardened concrete at the composite slab stage.

• At the execution stage, the profiled steel sheeting acts as a thin-walled member. Its design must take into account the possibility of local buckling.

• The design of the composite slab must consider the resistance to positive and negative moments and also to vertical and longitudinal shear.

• The resistance to longitudinal shear at the steel/concrete interface is largely derived from embossments in the steel sheet or from connectors placed at the ends of the spans. Empirical methods are used to ensure the adequate shear resistance.

• Shallow floor systems, which combine the floor and slab in the same vertical space, offer a competitive alternative to concrete flat slab construction.

• In seeking an economic design, consideration should be given to overall project costs and flexibility for future changes in building use and services.

• Review points:• What is the longitudinal shear?• Which are governing factors in design of a composite

slab?• Determination of the longitudinal shear by shear bond

tests and defects of the m-k method.• Describe the likely failures of composite slabs

occurring in the construction stage and in the composite slab stage.

• Further reading of design methods for resistance to fire