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ESDEP Lecture 10COMPOSITE CONSTRUCTIONhttp://www.fgg.uni-lj.si/kmk/esdep/master/wg10/toc.htm

10.1 Composite Construction General; excluding sections: 3.3, 3.5 and 5

10.2 The Behaviour of Beams; excluding section 4

10.3 Single Span Beams

10.5.1 Design for Serviceability I; excluding section 3

10.6.1 Shear Connection I

10.6.2 Shear Connection II

10.7 Composite Slabs

10.8.1 Columns I

10.8.2 Columns II; excluding section 8

10.1 Composite Construction General

Eurocode 4: Design of Composite Steel and Concrete Structures: EN 1994-1-1: Part 1.1: General rules and rules for buildings

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CONCLUDING SUMMARY

Composite construction, particularly that using profiled steel sheeting, allows rapid construction.

The weight of steelwork required in composite construction is significantly less than if the materials were used independently.

There is no need for expensive formwork because the steel beam is able to sustain the self weight of steel and concrete. Timber formwork can be replaced by precast concrete elements or profiled steel sheeting.

The aforementioned advantages present a very strong argument for the use of composite beams in buildings. They are more significant, however, for medium to long spans than for short spans.

The main disadvantage of composite construction is the need to provide connectors at the steel-concrete interface.

Another minor drawback is that it is somewhat more complicated than other methods to design and construct.

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10.2 The Behaviour of Beams

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Dead load on composite beam Dead load on steel beam

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CONCLUDING SUMMARY

Composite beams, subject to sagging moments, fail by yielding of the steel section, crushing of the concrete slab or shear of the connectors.

Unpropped composite beams need the steel section to be strong and stiff enough to carry the weight of wet concrete.

Partially connected composite beams may be used to ensure economy of shear connection.

10.3 Single Span Beams

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Eurocode 4

beff = L/4

Beam spacing

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Resistance of concrete flange : Rc = beff hc 0.85 fck /cResistance of steel flange : Rf = b tf fy /aResistance of shear connection : Rq = N Q

Resistance of steel beam : Rs = A fy / aResistance of clear web depth : Rv = d tw fy / aResistance of overall web depth : Rw = Rs - 2 Rf

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a

x = (Afy /a) / (beff kfck /c) = (Rs/Rc ).hcMpl.Rd = Rc.z = Rc (h/2 + hp + hc - Rs.hc/2Rc)

Rconcrete > Rsteel beam

Mpl.Rd = Rs.h/2 + Rc (hc/2 + hp) - (Rs - Rc)2.tf / 4Rf

Rsteel beam > Rconcrete > Rweb

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d = clear height of web between fillets

Rv = dtwfy

Mpl.Rd = Rc.(h + 2 hp + hc)/2 + Mpl.a.Rd - (Rc2/Rv)(d/4)

Rs > Rc < Rweb

=

Mpl,V-red.Rd = {1 - (1 - do/d).A/(2A - Av)}.Mpl.RdAv = shear area of steel section = 1.04htw

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CONCLUDING SUMMARY

Plastic analysis of the cross-section is used to determine the positive bending moment resistance of composite beams.

Eurocode 4 gives simple formulae for the effective width of concrete slab acting compositely with the steel; this "concrete flange" must be detailed to avoid longitudinal shear and splitting.

Design of composite beams involves ensuring that the forces and moments due to factored loads are less than the corresponding design resistance.

Various expressions for the design of the positive moment of resistance can be derived; these depend on the position of the neutral axis.

Eurocode 4 gives simplified rules governing the design of the shear resistance of simply supported composite beams, with full shear connection.

Where high shear and moment are coincident part of the steel web is reserved to carry shear, resulting in a decrease in moment resistance.

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10.5.1 Design for Serviceability - I

ac

aa

I = Ia + (Ac/n) . (hc2/12) + (Ac/n) . ac2 + As . (ac + as)2

NAc

NAcomposite

NAsteel beam

n = Es/Ec

a

fsteel = Mz/I fconcrete = Mz/nI

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Owing to a variety of factors, the deflections of composite elements deviate from the values which would be predicted by a simple elastic model. These factors include: the continuous variation in member stiffness arising from cracking and from

variations in the areas of reinforcing steel. the effects of tension stiffening in the cracked regions of reinforced concrete. the variation with time of Young's Modulus for concrete. shrinkage and creep of the concrete. yielding of the steel member, as may happen at supports in continuous beams. slip at the steel-concrete interface. shear lag. temperature.

The time-dependence of certain of these factors means that the actual sequence of loading will have a bearing on the final deflections, and may invalidate simple calculation procedures based on the superposition of effects. Additionally, material properties (Young's Modulus, creep factor, etc.) which are used in analysis will depend on factors such as the actual concrete mix used, and on temperature and humidity levels during the early life of the structure.

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CONCLUDING SUMMARY

The serviceability limit state must be checked when designing simply supported and continuous composite beams. The main points to consider are:

The main design criteria are, deflection, control of crack width and limitation of stresses.

For elastic calculations in positive moment regions, an uncracked section, with or without reinforcement, can be assumed.

In negative moment regions, cracked sections must be assumed.

The influence of shrinkage, creep and temperature must be included.

10.6.1 Shear Connection - I

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Increased connector force near plastic hinge at beam center

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The design shear resistance of a stud is given by the smaller of:

stud shear resistance:

PRd = 0.8 fu (d2/4) / vwhere the shear resistance of the connector is related to the tensile strength of the steel fu, using a factor of 0.8

concrete resistance:

PRd = 0.29 d2 (fckEcm)1/2 / vwhere d is the diameter of the shank of the stud, fu is the specified ultimate tensile strength of the stud material ( 500N/mm2), fck is the characteristic cylinder strength of concrete, Ecm is the mean value of the secant modulus of concrete, = 0.2 [(h/d) + 1] if 3 h/d 4 where h is the overall height of the stud and for h/d > 4 = 1.0.The partial safety factor v is normally taken as 1.25.

including strain hardening

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bo

hph

Reduction in shear resistance of studs

Ribs transverse to beam

kt = 0.7(bo/hp)(h/hp-1) / Nr1/2

kt 1.0 for Nr = 1 and kt 0.8 for Nr = 2

Ribs parallel to beam

kt = 0.6(bo/hp)(h/hp-1) 1.0

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CONCLUDING SUMMARY

The shear connectors between the slab and steel section in a composite beam are required to resist shear, bending and tensile forces.

The stiffness, resistance and amount of confining concrete around each connector affects the performance of the connection.

Welded shear studs are the most common form of connector.

Connector resistances may be determined using empirical formulae or "push-out" tests.

The design resistance of a connector is normally assumed to be 0.8 times the ultimate resistance.

Studs may normally be uniformly spaced along the beam.

Slabs formed with profiled steel sheeting may be used with composite beams as long as the concrete in the troughs is ignored when calculating section properties.

10.6.2 Shear Connection - II

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"critical cross-section" is the cross-section of maximum bending moment.

"critical length" is the length between two adjacent critical cross-sections: AB and BC

The longitudinal shear force Vlf is equal to the lesser plastic axial resistance of either the steel member or the concrete slab in the critical cross-section concerned

Vlf = lesser value of (Aa fy/a or 0.85Ac fck/c)

The required number of connectors to obtain full shear connection for the critical length is Nf = Vlf / PRd

If the number N of shear connectors within the critical length is less than Nf: N < Nf then the critical length is in partial shear connection and its degree of connection is defined by the ratio N/Nf.

Fu(r) = NPRd = V

Obtain location of plastic neutral axis from equilibrium, i.e. Fcompression = Ftension

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The position of neutral axis ya and the ultimate moment Mu(r) are:

For ya t1 (neutral axis in top steel flange)ya = [As(fy/a) Fu(r)] / [2b1(fy/a)] Mu(r) = Fu(r)(hc + da- yc/2) + 2b1ya(fy/a)(da - ya/2)

For t1 ya da (neutral axis in steel web)ya = {(Aa + 2t1tw - 2b1t1)(fy/a) - Fu(r)} / [2tw(fy/a)]Mu(r) = Fu(r)(hc+ da- yc/2) + 2b1t1(fy/a)(da- t1/2) + tw(ya- t1)(fy/a)(2da- ya- t1)

Mu(r) = Muapl + (N/Nf)(Mu - Muapl)

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For steel sections with equal flanges:

(N/Nf)B = 0.4 where L 5 m (N/Nf)B = 0.25 + 0.03L 1 where L > 5 m For steel sections having a bottom flange with an area not exceeding 3 times the area of the upper flange:(N/Nf)B = 0.4 + 0.03L 1 In the case of slabs cast on profiled steel sheeting it is reasonable to consider an increase in the ductility of the connectors and, therefore:

0.4 (N/Nf)B = 0.04L 1 for steel sections with equal or unequal flanges.

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Influence of partial connections on beam deflections

For propped beams:

= f + 0.5 (1 - N/Nf) (a - f)For unpropped beams:

= f + 0.3 (1 - N/Nf) (a - f)

CONCLUDING SUMMARY

Partial shear connection is an important option for the economic use of composite beams in buildings.

When non-ductile shear connectors are used, the simplest design method uses elastic beam theory to calculate the longitudinal shear force per unit length.

When ductile shear connectors are used, the design method is based on plastic resistance of cross-sections using the stress block method.

Attention is drawn to the requirement for a minimum degree of connection depending on the beam span.

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10.7 Composite Slabs

provides a working platform for construction acts as formwork for the concrete slabconstitutes bottom reinforcement for the slab

Steel grade 280 : fyb = 280 N/mm2Steel grade 350 : fyb = 350 N/mm2

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Bond by friction:

(a) and (b).

Embossments: (c).

End anchorages:

(d), (e) and (f)

For the situation where the profiled sheeting acts as formwork, the following loads should be considered:

self-weight of the profiled sheetingweight of the wet concreteconstruction loadstemporary storage load

The construction loads represent the weight of the operatives, any loads due to placing the concrete, and also take into account any impact or vibration likely to occur during execution. Eurocode 4: use 1.5kN/m2 distributed on an area 3m x 3m and 0.75kN/m2 on the remaining formwork surface.

For the situation where the steel and the concrete act compositely, the loads acting on the slab should comply with Eurocode 1:

self-weight of the slab (profiled sheeting and concrete) weight of floor finishes imposed loads

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a) Analysis for the ultimate limit statesIn most cases analysis of composite slabs, continuous over several spans, is performed according to the elastic method, for a slab of unit width (1m), comparable to a beam of constant inertia. The assumed inertia is that of the uncracked section.

It is possible to take concrete cracking into account in several ways: Arbitrarily reduce the moment at the supports and increase the span moments Neglect reinforcement over the supports and consider the slab as a series of simply supported beams Consider that the slab is a beam with variable inertia, depending on the reinforcement. The assumed inertia is that of the cracked section.

Critical sections which to be verified: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.

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The ultimate moment of resistance of a section, Mpc, may be determined by assuming a plastic distribution of stresses. The position of the plastic neutral axis is

x = [Aap.fyap/ap] / [b.0.85fck/c]The neutral axis is in the concrete zone if

Aapfyap/ap 0.85bfck/cThen

Mp,Rd = Aap.fyap[ds - x/2]/ap

ds

Neglecting the concrete in the troughs

Mp,Rd = Ncz + Mpa,r

z = ht - hc/2 - ep + (ep - e)Nc/[Aap.fyap/ap]Nc = hc0.85fck/cMpa,r = 1.25Mpa [1 - Nc/(Aap.fyap/ap)] Mpa

ep

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Nc = bcx 0.85fck/c = As.fys/s= Ntx = [As.fys/s][bc0.85fck/c]z = ds - x/2

Mp,Rd = As.fysz / s

Shear and Punching shear

Vv,Rd = bods cc = Rd k1 k2k1 = 1.6 - ds 1.0 (ds in m)k2 = 1.2 + 40 oo = As/bo ds < 0.02As is the area of reinforcement in tension. In positive bending regions, As is to be replaced by Aap.Rd basic shear strength: 0.30N/mm2

The punching shear resistance of a composite slab at a concentrated load isVp,Rd = Cp hc c

dp

dp

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V,Rd = bds[(mAsp/bs) + k] / vsds or dp = distance from outermost concrete fiber to N.A. of steel s the shear spanvs partial safety factor for longitudinal shear only

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b) Analysis for the serviceability limit states

An analysis of the composite slab, for calculating deflection, may be made with the following assumptions:

The slab is comparable to a continuous beam of constant inertia, equal in value to the average inertia of the cracked and uncracked section.

Long-term loading effects on the concrete are taken into account using a variation in the modular ratio Ea/Ec. For simplification, Eurocode 4 recommends an average value of Ea/Ec for both long and short term effects.

The deflection of a composite slab is calculated using elastic theory.

a) Cracked sectionIvc = [bx3/3n] + Aap(ds - x)2 + Iap

where x is the position of the elastic neutral axis:x = [nAap/b]{[1 + (2bds/nAap)] - 1}

Iap is the unreduced second moment of area of the sheet

b) Uncracked sectionThe second moment of area Ibu of the uncracked section can be obtained from:

Ibu =

bc is the total average rib width over a slab width of 1 m.xu is the position of the elastic neutral axis:

xu =

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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 composite performance of the steel and hardened concrete under the imposed floor loading.

In 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 adequate shear resistance.

10.8.1 Columns I

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The plastic resistance of the cross-section of a composite column is given by the sum of its component resistances:

Npl.Rd = Aa fyd + Ac fcd + As fsd is 1.0 for concrete filled cross-sections and 0.85 in all other cases

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The relative slenderness, , for the determination of the load-bearing resistance of a column under axial load is given by:

Npl.R is the cross-section resistance a = c = s = 1.0Ncr is the elastic buckling load of the column

Ncr = (EI)e2/e2

(EI)e is the effective bending stiffness.e is the buckling length of the column.

The effective bending stiffness is determined by adding up the individual components:

(EI)e = EaIa + 0.8 EcdIc + EsIs

0.8 EcdIc is the effective bending stiffness of the concrete part and Ecd = Ecm / cEcm is the secant modulus of the concrete and c can be reduced to 1.35

When assessing the importance of creep and shrinkage using Table below

= Aafyd / NplRdThis represents the contribution of the structural steel to the normal force resistance.

Braced andnon-sway systems

Unbraced andsway systems

Concrete encased sections 0.8 0.5

Concrete filled sections 0.8 / (1-) 0.5 / (1-)

For slenderness less than values given in Table, creep and shrinkage can be ignored

The influence of creep and shrinkage can be taken into account by modification of the modulus of elasticity of the concrete

Ec = Ecd

NSd is the design normal force.NG.Sd is the permanently acting part of it

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For each of the principal bending axes of the column it must be shown that:

NSd Npl.RdNpl.Rd is the cross-section resistance for axial load is the reduction factor from the appropriate buckling curvecurve a for concrete filled hollow steel sections

curve b for partially and completely concrete encased I-sections with bending about the strong axis of the steel cross-section

curve c for partially and completely concrete encased I-sections with bending about the weak axis of the steel cross-section

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CONCLUDING SUMMARY

Composite columns can be either partly or totally encased open sections, or alternatively, they may be concrete filled tubes.

Eurocode 4 [1] gives limiting ratios for exposed steel parts of composite columns, to ensure that local buckling does not occur. For fully encased sections local buckling is not a problem.

Eurocode 4 gives simplified rules (European Buckling Curves, etc.), for calculating the resistance of a composite column to axial load.

10.8.2. Columns II

= 0.66 + 0.44 r 0.44

Design bending moment

MSd = Mmax / (1 NSd/Ncr)

MmaxMmin

Bending moment diagram

r = Mmin / Mmax-1.0 r 1.0

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represents maximum buckling load on column, i.e. no bendingk = moment due to imperfection decreases linearly to zero for n = 0.25(1 - r)For design d = NSd / Npl.Rd , represents the remaining moment resistance

M-N Interaction curve

Strength only

MSd 0.9 Mpl.Rd

Design procedure for compression and uniaxial bending

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C

D

At D: Mmax.Rd = Wpa fyd + 0.5 Wpc fcd + Wps fsd

For the example of the concrete filled rectangular hollow section:

hn =

Mn.Rd = Wpanfyd + 0.5 Wpcnfcd + (Wpsnfsd)Wpan, Wpcn and Wpsn plastic moments of resistance of the areas in the region of 2hn

At B the moment resistance Mpl.Rd = Mmax.Rd - Mn.Rd

Nc.Rd = fcd.2hn.b - fcd.hn.2t + 2fyd.2hn.2tb

Now Nc,Rd/2

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My.Sd/(y Mply.Rd) 0.9Mz.Sd/(z Mplz.Rd) 0.9

My.Sd/(yMply.Rd) + Mz.Sd/(zMplz.Rd) 1.0

CONCLUDING SUMMARY

The influence of second order effects must be taken into account for slender columns under significant axial load.

Combined bending and axial load can be checked using interaction diagrams which also form the basis of the approach adopted in Annex D of Eurocode 4 .

Shear forces are taken into account by reducing the effective area resisting bending; the cross-section interaction curve can then be determined using the reduced section.