1

Membrane Action of Composite Floor Slabs in Fire Condition

Guo-Qiang Li * Nasi Zhang **

* Tongji University, China

** State University of New York at Buffalo Abstract A new method to predict the membrane action for simply supported steel-concrete composite floor slab is presented in this paper. In the analysis model, the slab is divided into one elliptical paraboloid reinforcement tensile mesh in the center and four concrete rigid plates at the boundary of the slab which will form a compressive concrete ring to provided anchorage for the reinforcement. According to force and bending moment equilibrium equation, the load capacity offered by membrane action is obtained. 4 full-scale composite floor slab test are performed at Tongji University, for the purpose to observe the membrane action and to verify the validity of the new method. Comparison of the tests’ result and the prediction by the method proposed is presented and analyzed. Keywords: Composite floor slab, fire-resistance, membrane action, analysis method, full-scale test

1. Introduction Tests’ results and real fire disasters show that the load bearing capacity of composite floor slab without protecting the deck and secondary beams in fire condition is much higher than that predicted by using traditional yield line method (bending method) without considering membrane action. From 1995 to 1996, six localized fire tests were performed in a full-scale, eight-storey, steel frame building at Building Research Establishment Laboratory at Cardington. The tests showed that the composite floor slabs can maintained their load bearing capacity, although the temperature of the unprotected beam was higher than 1000 ℃because of membrane action (Huang, 2003). Since 1990s, many researchers including C.G. Bailey, A.S. Usmani and Guo-qiang Li conducted studies on membrane action. Bailey developed a method to predict the membrane bearing capacity based on yield line method (Bailey, 2000, 2001, 2004). Usmani analyzed the membrane action by solving the equilibrium equation and compatibility equation for isotropic flat slab (Usmani, 2001, 2004). Li presented a simplified model to estimate the load bearing capacity of composite floor slab in fire condition with considering membrane action (Li, 2007). In this paper, a new method to estimate the membrane action developed by Guo-Qiang Li and Na-Si Zhang is

presented. In order to observe the phenomena of membrane action and to verify the validity of the new method, 4 full-scaled slab tests were performed in ISO-834 standard fire at Tongji University under the sponsoring from National Natural Science Foundation of China. 2. Theoretical analysis 2.1. Development of membrane action in floor slab When the composite slab is exposed to fire, the strength and stiffness of the steel and concrete will continuously decrease with the temperature elevation. In consequence, the load capacity provided by bending mechanism will not be enough to carry the applied load, and will be displaced by membrane action. Fig.1 shows the development of membrane action (Li, 2007): 1) at the beginning of the fire, when the temperature is not very high, the load on the slab is almost carried by the bending mechanism; 2) as the temperature becomes higher, the yield lines will be form due to the decrease of the strength and stiffness of the steel and concrete (Fig.1(a)-(b)); 3) with further increase of the temperature, the yield lines will be completely developed, the load capacity offered by the bending mechanism will not be enough, and then the membrane action will take place to bear the applied load(Fig.1(c)-

2

(e)); 4) finally, most of the load will be carried by membrane action with the reinforcement acting as a mesh, and being anchored in a concrete compression ring formed in the peripheral part of the slab (Fig. 1(f)).

(a) Initialization

of yield line (b) Forming of

yield lines (c) Yield lines

completed

(d) Appearance of membrane

action

(e) Development of Membrane

action

(f) Membrane action at the limit state

Fig.1 The development of membrane action

in a floor slab 2.2. Assumption of modeling membrane action The following assumptions are adopted to model membrane action: 1) The slab is rectangular, and the ratio between length

and width should not be greater than 2; 2) The support-beams bellow the edges of the slab are

protected and are strong enough to support the load coming from the slab in fire;

3) The boundaries of the slab are vertically restrained but no horizontal and rotational restraints are considered;

4) The reinforcement in the slab is continuous, and arranged in two orthogonal directions to assure the formation of reinforcement mesh. The strain hardening of the reinforcement is ignored;

5) At the limit state, the deformation of the slab is like Fig.1-(f). The slab can be divided into five parts as shown in Fig.2, where (x0, y0) is the intersecting point of the bending yield line and the ellipse; α is the separation angle between yield line and long edge of the slab. Plates 1 through 4 are assumed to be rigid, therefore they only have rigid rotational deformation. In the center of the slab, the concrete is cracked and its effect can be ignored. So the central reinforced concrete slab can be simplified as a reinforcement mesh. According to investigation of experiment and real fire disasters, the deformation of central part can be assumed as elliptic paraboloid, governed by Eq.(1)

( ) ( )zw

KBw

y

KLw

x−=

⋅+

⋅ 2

2

2

2

11 (1)

where L is the length of the slab; B is the width of the slab; w is the maximum deflection of the elliptic part of the slab; K is the ratio of half length of the long or short axis of the ellipse to the corresponding length of the long

or short edge of the slab, which satisfies 0<K<0.5;

Fig.2 Division and coordinates of the slab at the limit state

6) At the limit state, the force distribution is assumed

as Fig.3, where C is the compression force between rigid plates; S is the shear force in the XY coordinate plane between rigid plates; Txh and Tyh represent the in-plane components tension force of the reinforcement in X direction and Y direction respectively; ○× and □× represent the vertical components force of the reinforcement in X direction and Y direction respectively;

Fig.3 Force distribution in slab at the limit state 7) At the limit state, the finial deflection of the slab is

supposed as shown in Fig.4, where θx, θy are the rotation of the rigid plates about Y and X axis respectively. The maximum of the deflection can be divided into two parts: dr and w, where dr is the deflection caused by the rotation of rigid plates and w is the deflection of elliptic part.

8) The failure criterion of the slab is the fracture of central reinforcement mesh or the crushing of the concrete in the rigid plates.

3

Fig.4 Deflection of slab at limited state 2.3. Parameter determination The main parameters in the new method proposed here are the angle between yield line and long edge of the slab, α; the intersecting point of the yield line and the ellipse, (x0, y0); the deflection of elliptic part, w; the deflection caused by the rotation of the rigid plates, dr; and the rotations of the rigid plates, θx and θy. The determinations of these parameters are presented below. 1) α can be determined by the traditional yield line

theory, since the ultimate deflection of the slab at the limit state is developed from yield line mechanism.

2) (x0, y0) can be obtained by geometrical relationship given by Eq. (2) and (3)

( )αααααα

222

2242242334222422

0 2442)(

tgLBtgBLKLBKtgBLBLtgBLLtgLtgB

x⋅+

⋅++⋅+−⋅−+⋅⋅−⋅−=

(2)

2200BtgLxy +⋅⎟

⎠⎞

⎜⎝⎛ −= α

(3)

3) In order to determine w, it is assumed that the reinforcement is going to reach its mechanical strain limit at the ultimate state. In this way, the maximum deflection of the elliptic part can be determined by the limited elongation ratio of the reinforced bars along short span, because at the same level of deflection in the middle of the slab, the average strain in the reinforcement along the short span is larger than that along the long span. Based on the assumption 5) and 7) in section 2.2, the total deflection of the slab can be obtained by the summation of deflection caused by the elongation of the reinforcement and the deflection caused by the rotation of rigid plates by using Eq. (4) (Li, 2007).

( )[ ] ⎟⎠⎞

⎜⎝⎛ −⋅+−⋅+=+= KBBTTKBdww xsukrtotal 28

32 0 θαε (4)

where εuk is the characteristic limited elongation of reinforcement, recommended to be 2.5% for the diameter of the reinforcement less than or equal to 12mm, or 5% for the diameter of the reinforcement greater than 16mm (European Code 2, 1992); αs is the average coefficient of thermal expansion for the reinforcement, taken as 1.4*10-5; θx is the rotation of the rigid plates 1 and 2 (in Fig.2); T0 is the room temperature which is 20℃, and T is the temperature of the reinforcement after t minutes in ISO 834 standard fire exposure, which can be estimated

by the simulating formula, Eq (5) (Li, 1999).

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

+⋅⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡+

−⋅=

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛−+

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟

⎠⎞

⎜⎝⎛−+−

811.06.0

22

4

220

005.020

0145.0007.020

005.020

135.005.0

0

ttdtt

ww

eTdH

eT

(5) where t (unit: min) is the heating-up time; T0 (unit: ℃) is the room temperature; d (unit: m) is the distance between reinforcement and the bottom of the slab; H (unit: m) is the thickness of the slab; and w2 and w4 are the dimension of steel deck for the slab, which are shown in Fig.5.

Fig.5 Dimension of the slab

4) To determine θx and θy, it is supposed that the rigid

plate 1, 2 and the tangent of the elliptic paraboloid are continuous on the boundaries. Therefore θx is equal to the gradient of the elliptic paraboloid at point (0, KB). Taking partial derivative of Eq. (1) about y at point (0, KB), θx can be obtained by Eq. (6).

KBw

yz

KByx

2=

∂∂

==

θ (6)

According to the deformation compatibility of rigid plates 1, 2 and 3, 4 at the points of (x0, y0), (x0, -y0), (-x0, y0), (-x0, -y0), the rotation of plates 3, 4 can be determined by Eq. (7).

0

0

2arctan tan2y x

B yL x

θ θ⎛ ⎞−

= ⋅⎜ ⎟−⎝ ⎠ (7)

2.4. Force and bending moment equilibrium

equations Reduced strength of reinforcement and concrete (CECS200:2006) were used based on the temperature predicted in Eq. (5). For simplification, the effective tensile force per unit width of reinforcement at T ℃ in X and Y direction were denoted by fxT and fyT respectively. The force, exerted from reinforcement, on the rigid plates at the boundary of the elliptic paraboloid is shown in Fig.6.

Fig.6 Force of the reinforcement at the boundary of the

elliptic paraboloid In Y direction, tanφy is the gradient at the intersection of the elliptic part and rigid plate, and can be determined by Eq. (8).

4

2

0

2tan 1yz

z w xy KB KL

ϕ=

∂ ⎛ ⎞= = −⎜ ⎟∂ ⎝ ⎠ (8)

So the horizontal and vertical component forces of reinforcement in Y direction are obtained by Eq. (9) and Eq. (10).

( )

( )⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−+

⋅=2

22 14KLxwKB

KBTT yuxyh

(9)

( )

( )⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−+

⎟⎠⎞

⎜⎝⎛−

⋅=2

22

2

14

12

KLxwKB

KLxw

TT yuxyv

(10)

In the same way, for the reinforcement in X direction, the horizontal and vertical component forces of reinforcement are given by Eq. (11) and Eq. (12)

( )

( )⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−+

⋅=2

22 14KBywKL

KLTT xuyxh

(11)

( )

( )⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−+

⎟⎠⎞

⎜⎝⎛−

⋅=2

22

2

14

12

KBywKL

KByw

TT xuyxv

(12)

At the limit state, the membrane forces in each rigid plate of the slab are shown in Fig.7. The force equilibrium in X and Y direction can be expressed as

( )

( )⎪⎩

⎪⎨⎧

+⋅=⋅

=⋅+⋅

∫∫

0

0

0

0

2cos2sin2

2sin2cos2y

yxh

x

xyh

dyTSC

dxTSC

αα

αα (13)

which leads to

( ) ( )

( )⎪⎪

⎩

⎪⎪

⎨

⎧

⋅−=

⋅−⋅=

∫

∫∫

α

α

αα

cos2

sin222

2cos2sin

0

00

0

00

SdxTC

dyTdxTS

x

xyh

y

yxh

x

xyh (14)

Fig.7 Membrane forces in rigid plates 1 and 3

At the limit state, the force on each rigid plate are shown in Fig.8, where q12 is the loading capacity of plates 1 and 2, and q34 is the loading capacity of plates 3 and 4.The bending moment equilibriums equations about O’ and O axis can be expressed as

⎪⎪⎪⎪⎪

⎩

⎪⎪⎪⎪⎪

⎨

⎧

=−⎥⎦

⎤⎢⎣

⎡⋅⎟⎠⎞

⎜⎝⎛ −−⋅⋅

+⎥⎦

⎤⎢⎣

⎡⋅⎟⎠⎞

⎜⎝⎛ −−⋅⋅−++

=−⎥⎦

⎤⎢⎣

⎡⋅⎟⎠⎞

⎜⎝⎛ −−⋅⋅

−⎥⎦

⎤⎢⎣

⎡⋅⎟⎠⎞

⎜⎝⎛ −−⋅⋅−++

022

1cos2

231sin2

022

1sin2

231cos2

00

0034

00

0012

yuyy

yyThyTvyq

xuxx

xxThxTvxq

MxLhS

xLhCMMM

MyBhS

yBhCMMM

θα

θα

θα

θα (15)

where M12 and M34 are the bending moments induced by q12 and q34 respectively; MThx and MTvx are the bending moments induced by horizontal and vertical component forces of reinforcement in plates 1 and 2 respectively; MThy and MTvy are the bending moments induced by horizontal and vertical component forces of reinforcement in plates 3 and 4 respectively; and Mux and Muy are the bending resistance of the slab about the yield line respectively. M12, MThx, MTvx, M34, MThy, MTvy, Mux and Muy can be determined by Eq. (16) and Eq. (17).

( )

0

0

0

12 12 12

0 00

2

0

0

22

2 1 22 2

0.59 2

q

x

Thx yh x x

x KB

Tvx yv xvy

yTux sx yT cx sx

cT

M q A dy

BM T h y dx

B x BM T KB dx T y dyKL

fM A f h A L x

f

θ

= ⋅ ⋅⎧⎪

⎡ ⎤⎛ ⎞⎪ = ⋅ − − ⋅ ⋅⎜ ⎟⎢ ⎥⎪ ⎝ ⎠⎣ ⎦⎪⎪ ⎡ ⎤⎛ ⎞ ⎛ ⎞⎨ ⎢ ⎥= ⋅ − − ⋅ + ⋅ − ⋅⎜ ⎟ ⎜ ⎟⎪ ⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦⎪⎪ ⎛ ⎞⎪ = − ⋅ −⎜ ⎟⎪ ⎝ ⎠⎩

∫

∫ ∫

(16)

( )

0

0

0

34 34 34

0 00

2

0

0

22

2 1 22 2

0.59 2

q

y

Thy xh y y

y KL

Tvy xv xvx

yTuy sy yT cy sy

cT

M q A dx

LM T h x dy

L y LM T KL dy T x dxKB

fM A f h A B y

f

θ

= ⋅ ⋅⎧⎪

⎡ ⎤⎛ ⎞⎪ = ⋅ − − ⋅ ⋅⎜ ⎟⎢ ⎥⎪ ⎝ ⎠⎣ ⎦⎪⎪ ⎡ ⎤⎛ ⎞ ⎛ ⎞⎨ ⎢ ⎥= ⋅ − − ⋅ + ⋅ − ⋅⎜ ⎟ ⎜ ⎟⎪ ⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦⎪⎪ ⎛ ⎞⎪ = − ⋅ −⎜ ⎟⎪ ⎝ ⎠⎩

∫

∫ ∫

(17) where A12 and A34 are the area of the rigid plates 1 or 2 and plate 3 or 4 respectively; dy and dx are the distances between gravity center of rigid plate 1 or 2 and axis O’ and between plate 3 or 4 and axis O respectively; hcx and hcy are the distances between reinforcement and the upper side of the slab in Y and X direction respectively.

Fig.8 Forces on rigid plate 1 and 3 2.5. Ultimate load capacity of the slab The load capacity of the elliptic part is contributed by the vertical component force of reinforcement in the elliptic paraboloid, which can be obtained by Eq. (18).

( ) ( )

( ) ( )KBKL

dyTdxTq

KB

yxv

KL

xyv

e ⋅⋅⎥⎦⎤

⎢⎣⎡ ⋅+⋅

=∫∫

π00

4 (18)

The ultimate load capacity of the slab can be obtained by

5

averaging the load capacity of the rigid plates and that of the central elliptical part by using Eq. (19).

( ) ( )

LB

dyTdxTAqAqq

KB

yxv

KL

xyv ⎥⎦⎤

⎢⎣⎡ ⋅+⋅+⋅+⋅

=∫∫ 0034341212 422 (19)

2.6. Check the strength of the concrete compression

ring The concrete compression ring might crush prior to the fracture of the reinforcement due to large load capacity of the elliptical reinforcement mesh. Therefore the compression strength in the rigid plates should be check to insure the membrane action works. At the limit state, the compressive stress of concrete will be reached at the cross section A-A and B-B as shown in Fig.9. So, the force equilibrium in the concrete compression ring can be expressed as Eq. (20) and Eq. (21) in X and Y direction respectively.

( ) cTcx

BK

yxh fhBKdyTx ⋅⋅⋅⎟⎠⎞

⎜⎝⎛ −=⋅∫ 2

10

(20)

( ) cTcy

LK

xyh fhLKdxTy ⋅⋅⋅⎟⎠⎞

⎜⎝⎛ −=⋅∫ 2

10

(21)

Kx and Ky can be obtained by solving Eq. (20) and Eq. (21). If Kx or Ky is smaller than K, the concrete compression ring will be crushed earlier than the

reinforcement. Taking the smaller one of Kx, Ky and K and substitute into the equations (15), (18) and (19), the revised ultimate load capacity of the slab can be obtained.

Fig.9 Force distribution over concrete compression ring

at limit state 2.7. Verification The method of modeling membrane action for fire-resistance of slab presented in this paper can be verified by previous tests performed by other researchers (Bailey, 2004; Huang, 2003; Jiang, 2004). The details of the slabs tested in fire are given in Table 1. The maximum deflection of the slabs measured in the tests and that predicted by various methods are compared in Table 2; and the test load and the load capacity predicted are compared in Table 3.

Table 1 The details of test slabs

Test No. Reference Slab size

(m)

Effective thickness

(mm)

Reinft dia.

(mm)

Reinft spacing(mm)

Steel yield strength fy (N/mm2)

Max deflection recorded in the

test (mm)

Test load (kN/m2)

1 1.6*1.1 26 3 30 263 127 45.13 2

Sawczuk 2.0*1.0 26 3 60 263 76 17.14

3 1.829*1.829 43.6 4.8 76.2 376 81 42.9 4 1.829*1.829 37.3 4.8 63.5 376 98 39.03 5

Taylor etal 1.829*1.829 69 4.8 122 376 84 38.13

6 2.745*1.829 68.2 6.36 120 450 106 45.5 7

Ghoneim& MacGregor 1.829*1.829 67.8 6.35 120 450 100 75

8 Cardington 9.98*7.57 6 200 460 390 5.48

9 Guoqiang Li 3*2 U76-305-610 4 150 300 90 10

Table 2 Comparison of maximum deflections between measured and predicted

Test No.

Maximum deflection measured wtest (mm)

Predicted by Bailey et al wBailey (mm)

Predicted by Guoqiang Li wG.Q Li (mm)

Predicted by the method proposed

wnew (mm) test

Bailey

ww

test

G.Q Li

ww

test

new

ww

1 127 25 43 58.6 0.356 0.339 0.4612 76 31 36 55 0.187 0.474 0.7243 81 33.5 72 95.9 0.435 0.889 1.1844 98 33.5 72 92.8 0.409 0.735 0.9475 84 33.5 72 103.8 0.372 0.857 1.2366 106 95.1 0.8977 100 93.6 0.9368 390 450.2 1.154

6

9 90 127 1.4

Table 3 Comparison of test load and predicted

Test No.

Test load qtest

(mm)

Predicted by Bailey et al

qBailey (kN/m2)

Predicted by Guo-Qiang Li

qG.Q Li (kN/m2)

Predicted by the method proposed

qnew (kN/m2) test

Bailey

qq

test

G.Q Li

qq

test

new

qq

1 45.13 45.24 44.18 34.4 1.002 0.979 0.7622 17.14 14.21 14.63 17.85 0.829 0.854 1.0413 42.9 35.27 33.60 41.18 0.822 0.783 0.9604 39.03 40.03 35.51 48.75 1.026 0.910 1.2495 38.13 31.22 31.22 31.18 0.819 0.819 0.8186 45.5 41.89 0.8977 75 58.3 0.7358 5.48 5.318 0.9709 10 7.13 0.713

Tests 1-7 were performed at ambient temperature, and Test 8, 9 were performed at high temperatures. The limit elongation is reduced by 30% for test 1-7 because the limit elongation of the reinforcement at ambient temperature is less than that at high temperature based on statistical regression analysis. The comparisons shown that the method proposed in this paper can well predict to the maximum deflection and load-bearing capacity of slabs exposed to fire. 3. Experimental study on full-scaled test 4 full-scaled composite slab tests were performed in ISO 834 standard fire at Tongji University to observe the membrane action and verify the presented method. 3.1. General information of the tests The test specimens were 4 pieces of 5.232m*3.72m composite floor slabs numbered from S-1 to S-4 with the secondary beam and steel decks unprotected. The slabs were contributed with the profiled steel sheet YX76-344-688 which is commonly used in China. The thickness of the deck was 1mm, and its strength was larger than 270N/mm2 (270 N/mm2 was considered in the calculation, GB/T 2518-2004). The decks were fixed on the primary beams and secondary beams (if existed) by shear connector with a diameter of 16mm and a height of 125mm.Total depth of the slabs was 146mm and the thickness of the concrete on the top of the decks was

70mm. The reinforcing mesh of the slabs was made by smooth reinforcement bar with the gird size of 150mm*150mm. The diameter of the reinforcement bar was 8mm, and the steel grade was Q235. The thickness of the protective layer of reinforcement was 21mm for S-1 and 30mm for S-2 to S-4. S-1 and S-2 had an unprotected secondary beam supporting the slabs in the middle, while S-3 and S-4 did not have. The cross section of the secondary beam was I25b, and the grade of steel was Q235. The slabs, the primary beams and secondary beams were designed in according with the Chinese Code GB50017-2003 and YB 9238-92. The general information of the specimens was shown in Table 4. The arrangement of the specimens and the cross section of the composite slab are shown in the Fig.10 and Fig.11 respectively. The grade of the reinforcement was Q235 and the grade of the concrete was C25. The material property of reinforcement and concrete are shown in Table 5 and Table 6 respectively (Where fy, fu and δ are the yield strength, ultimate strength and the ultimate elongation of the reinforcement respectively. fcu is the cubic compressive strength of concrete). The reinforcement in the test was not anchored at the boundary of the slab, but exceeded the edge of the slab for 150mm, because the reinforcement would fracture at the boundary of the slab according to the phenomena of Cardington test. The anchorage condition of the reinforcement is shown in Fig.12.

Table 4 Constructional information of test slabs (mm)

No. Specim

-ens size

Total depth

Thickness on the top of decks

Arrangementof the

reinforcement

Thickness of the protective layer of reinforcement

Direction of the rib Secondary beam

S-1 5232* 3720 146 70 φ8@150 21 Along the

long edge In the middle of the long

edge, unprotected

S-2 5232* 3720 146 70 φ8@150 30 Along the

long edge In the middle of the long

edge, unprotected S-3 5232* 146 70 φ8@150 30 Along the No secondary beam

7

3720 short edge

S-4 5232* 3720 146 70 φ8@150 30 Along the

short edge No secondary beam

Table 5 Properties of reinforcement bar

at ambient temperature

No. S-1 S-2 S-3、S-4 fy(N/mm2) 579.06 531.84 557.04 fu(N/mm2) 632.05 604.85 661.35 δ(%) 33.3 36 31.33 fy/fu 0.92 0.88 0.84

Table 6 Cubic compressive strength

of concrete

No. S-1 S-2 S-3 S-4 fcu(N/mm2) 26.1 21.0 22.37 22.87

(a) specimens S-1 and S-2

(b) specimens S-3 and S-4

Fig.10 Arrangement of the specimens

Fig.11 Cross section of the slabs

Fig.12 Anchorage of the reinforcement at the boundary of the slabs

The slabs were loaded at 24 points to stimulate uniform load (as shown in Fig.13 and Fig.14) with the load ratio of 60%~65% over the design load capacity of the slabs at the room temperature. ISO834 standard fire is used in the tests. The deflection of slabs, the temperature at the surface and bottom of the slabs, the temperature and strain of the reinforcements in the slabs, as well as the strain of concrete were measured in the tests. The arrangements of the measuring points are shown in Fig.15 to Fig.18.

Fig.13 The planform of loading system

Fig.14 Loading system

8

Fig.15 Arrangement of thermal couples

Fig.16 Arrangement of displacement meters

YX

Fig.17 Arrangement of strain gauges for the reinforcement

Fig.18Arrangement of strain gauges for the concrete

3.2. Test phenomena Statics load was applied on the slab in 10 steps. No crack and failure were found in this stage. Until the load and deformation of the slab were stable, the furnace started to fire. The test load and duration for the 4 tests were shown in Table 7.

Table 7 Test load and duration for 4 tests

No.Ultimate bearing

capacity of design value (kN/m2)

Test load

(kN/m2)

Loadratio (%)

Duration(min)

S-1 30.64 18.38 60 75 S-2 29.51 17.71 60 90 S-3 14.57 8.75 60 100 S-4 14.57 9.47 65 100 * Terminated without fail. In S-1 and S-2, cracks developed beside secondary beam due to the negative moment which was caused by the decrease of the strength and stiffness of the slabs. For S-3 and S-4, in which no secondary beam was provided, the crack started at the boundary of the slab. Significant cracks were found along the long edge of the slabs because of negative moment induced by the large deflection in the center of the slabs (shown in Fig.19). Meanwhile, some cracks occurred along the short edge of the slabs and extended to the side face of the slabs (shown in Fig.20). After the test, significant concrete crush at the yield lines were founded at the corner of the slabs (shown in Fig.21). All of the 4 specimens had large deflection after the test. The deformation of the slabs presented as an elliptic parabolic which validate assumption 5) and provided effective support to the load on the slabs (shown in Fig.22). Fig.23 and Fig.24 show the distribution of the cracks on S-2 and S-4 after the test, where cracks caused by the membrane action can be found both at the center and at corner of the slabs. The deformation of the unprotected secondary beam is shown in Fig.25. It can be seen that although the deflection of the beam is huge, no failure and buckle were found. Fig.26 shows the condition of steel deck after test, in which the profiled decks did not melt down in the high temperature. These indicate that the secondary beam and steel deck still can help to maintain the entirety of the slab system after 90 min fire exposure. No collapse occurred in these 4 tests. The development of membrane action carried the applied load on the slabs and kept the stability of the floor system.

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Fig.19 Cracks along the long edge

Fig.20 Cracks along the short side face

Fig.21 The crush of concrete at the yield line

Fig.22 The deformation of the slab after the test

Fig.23 The cracks on the S-2 after the test

Fig.24 The cracks on S-4 after the test

Fig.25 The deformation of the secondary beam

Fig.26 The steel deck after the test

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3.3. Test result and analysis 1. Temperature ISO 834 standard fire was used in the test. According to the inspection of the temperature in the furnace, the furnace temperature coincided well with the ISO834 fire curve. Fig.27 shows the bottom temperature curve in the middle of the slabs. It can be seen that at the beginning of the test, the temperature of the slab at the bottom was low, and then it increased along with time. At the time of 75 minutes, the temperature can reach to 700 or 800℃. At the time of 90 minutes to 100 minutes, the bottom of the slab can be heated up to around 800℃ or 900℃. Fig.28 is surface temperature curve in the middle of the slabs. It shows that surface temperature of the slab is about 100℃ at 90 minutes, which is much lower than that of bottom. Fig.29 is the average temperature curves of the reinforcement. It can be found that the distance between the reinforcement and the bottom of the slab has a great impact to the temperature of the reinforcement.

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Fig.27 Bottom temperature in the middle of the slabs

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Fig.28 Surface temperature in the middle of the slabs

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Fig.29 Average temperature of the reinforcement of S-1 to S-4

2. The strains of reinforcement and concrete Fig.30 and Fig.31 show the strains of the reinforcement along the short edge and long edge respectively. Since the effective working temperature of the strain gauges is less than 60℃, the data when the temperature was higher than 60 ℃ are taken off in the figures. Since the reinforcement located at the compression zone in the cross section of the slabs, according to the yield line theory, the reinforcement should be under compression. However, the data show that the reinforcement was under tension during most of the test except for the beginning. This phenomenon proves the occurrence of tensile membrane action in the test. Fig.32 is the strains curve of the concrete at the boundary of S-4. It can be found that the concrete in the middle of the boundary was under compression. It validates the existence of the concrete compressive ring which can provide the anchorage for the reinforcement.

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Stra

in (με)

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#1 #2 #3#4 #5 #6#7 #8 #9

Fig.30 The strains of the reinforcement along short edge in S-1

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＃10 ＃11＃12 ＃13＃14 ＃15＃16 ＃17

Fig.31 The strains of the reinforcement along long edge in S-1

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#44 #45 #46#47 #48 #49#50

Fig.32 The strains of the concrete at the boundary of S-4 3. Deflection in the middle of the slabs Fig.33 and Fig.34 show the deflections in the middle of the slabs. It is found that after 90min fire exposure the deflection of slabs can arrive at 1/25 of the short edge of the slabs. Therefore, it is reasonable to deduce that the load-bearing mechanism of the slabs has been changed from bending mechanism to membrane action under such large deflection in the tests.

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Fig.33 The deflection of S-1 and S-2

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Fig.34 The deflection of S-3 and S-4 4. Verification Table 8 shows comparison of the deflection at the center of the slab predicted by the method proposed in section 2 and measured in the tests in section 3. Table 8 Comparison of deflection of tests and prediction

Prediction #1* Prediction #2* Test #

Deflection in tests Defl. % Defl. %

S-1 171 161 -5.85 192 12.28S-2 141 178 26.24 212 50.35S-3 133 192 44.36 212 59.40S-4 148 198 33.78 213 43.92

*The average temperature of reinforcement measured in the test was used in prediction #1, and the reinforcement temperature obtained by Eq. (5) was used in prediction #2. From Table 8, it can be seen that the deflection predicted by the new method presented in this paper is higher than that in tests yielding the following reason. 1) The thermal elongation of the reinforcement was

over predicted by Eq. (4) because the confinement effect of concrete is ignored. In fact, most of the concrete in the center of slab did not crack in the test, which can provide good confinement and resist the elongation of the reinforcement.

2) The strength decline of the reinforcement and concrete cannot be exactly obtained in the test.

3) Strain hardening of the reinforcement was not considered in the prediction.

4) Although the catenary effort of secondary beam and the membrane action of steel deck is small, ignoring these efforts made the prediction conservative.

5) The average of top and bottom temperature of concrete was used in prediction. However the real temperature of the concrete should be lower because the temperature gradient in concrete is significant large.

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5. Conclusion Membrane action will take place to remain the load capacity in fire condition. A new method to model the membrane action for simply supported composite floor slab with continuous reinforcement in two directions was presented in this paper. For the slabs, with that potential horizontal restraint on the boundaries, this method is also applicable with conservation. Full-scale test were performed on 4 steel-concrete composite floor slabs. It shows that: 1) Membrane action will occur to carry the applied

load instead of bending mechanism due to large deflection when the composite floor slabs are subjected to fire. This membrane action can help to keep the load capacity of the slabs and maintain the stability of the floor system under fire condition.

2) The reinforcement in the slabs will be under tensile and form an elliptical paraboloid tensile mesh which can bear the load on the slabs. A concrete compressive ring will be formed at the boundary of the slabs to provide anchorage for the reinforcement.

3) Due to the membrane action, the existence of secondary beams to support the slab is not necessary in fire condition, which can save the fire protection for secondary beams.

A comparison of the deflection measured in the tests and that predicted by the new method was presented in this paper. The reasons for this difference between the deflection obtained by the new method and that measured in the test were analyzed. More research should be conducted on the thermal elongation of the reinforcement, the bond condition between the reinforcement and concrete. 6. Acknowledgement The work reported in this paper was financially supported by the National Natural Science Foundation of China under contract 50621062, 50738005 and 50728805. The support is gratefully acknowledged. References Bailey C.G. and Moore D.B. (2000) The structural

behaviour of steel frames with composite floor slabs subjected to fire: Part 1: Theory, The Structural Engineer 2000, Vol. 78(11), pp.19-27.

Bailey C.G. (2001) Membrane action of unrestrained lightly reinforced concrete slabs at large displacements, Engineering Structure 23(2001), pp. 470-483.

Bailey C.G. (2004) Membrane action of slab/beam composite floor systems in fire, Engineering Structure 26(2004), pp.1691-1703.

Code for design of steel structures. GB50017-2003, China.

Continuously Hot-Dip Zinc-Coated Steel Sheet and Strip. GB/T 2518-2004, China.

Eurocode 2: Design of concrete structures. Technical Report ENV 1992-1-1, Brussels, European Committee for Standardisation, 1992.

Huang Z.H., Burgess I.W. and Plank R.J. (2003) Modeling Membrane Action of Concrete Slabs in composite Building in Fire. II: Validations, Journal of Structural Engineering, (ASCE), Vol.129, No.8, 2003, pp. 1103-1112.

Jiang S.C, Li G.Q., Zhou H.Y. and Wang Q. (2004) Experimental study of behavior of steel-concrete composite slabs subjected to fire, Journal of Building Structure, Vol. 25, No.3, June 2004: pp45-50.

Lamont S., Usmani A.S. and Drysdale D.D. (2001) Heat transfer analysis of the composite slab in the Cardington frame fire tests, Fire Safety Journal 36(2001), pp. 815-839.

Li G.Q., Yin Y.Z. and Jiang S.C. (1999) Analysis of the temperature distribution in composite slabs subjected to fires”. Industrial Construction, No. 12, Vol.29, 1999.

Li G.Q., Guo S.X, and Zhou H.S. (2007) Modeling of membrane action in floor slabs subjected to fire, Engineering Structures 29(2007), pp. 880-887.

Specification for design and construction of steel-concrete composite floor system, YB 9238-92, China

Technical Code for Fire Safety of Steel Structure in Buildings. CECS 200:2006.

Usmani A.S. and Cameron N.J.K. (2004) Limit capacity of laterally restrained reinforced concrete floor slabs, Cement & Concrete Composites 26(2004), pp. 127-140