Present Research and Objectives• Understanding tensile membrane action at elevated temperatures

• Ascertaining the effects of thermal gradients, thermal stresses and slab edge support boundary conditions

• Quantifying the effects of reinforcement bond strength on composite slab capacity in fire

• Developing failure criteria for composite slabs in fire

Background• Accidental fires and full-scale fire tests have identified the significant contribution tensile membrane action has on composite slabs in fire

• Effective use of this mechanism in the design of steel-framed buildings introduces economy, as a large number of floor beams can be left unprotected

• A current design method predicts composite floor capacities by calculating enhancements tensile membrane action provides in addition to the yield-line load of the slab

• The method, developed from ambient-temperature observations, ignores certain critical issues that experimental evidence has highlighted

• The present research, therefore, is re-examining the development of the tensile membrane mechanism with more emphasis on elevated-temperature behaviour

The Mechanics of Tensile Membrane Action in Composite Slabs The Mechanics of Tensile Membrane Action in Composite Slabs

at High Temperaturesat High TemperaturesA.K. Abu, I.W. Burgess & R.J. PlankA.K. Abu, I.W. Burgess & R.J. Plank

Department of Civil & Structural Engineering, University of ShefDepartment of Civil & Structural Engineering, University of Sheffieldfield

Preliminary Studies

Rayleigh-Ritz Study

To observe the difference in development of the mechanism at elevated temperatures, an analytical study of the effects of thermal gradients (acting alone) was performed with the Rayleigh-Ritz approach.

...,3,2,1,,coscos1 1

== ∑∑∞

=

∞

=

nmb

yn

a

xmA

m nmnx

ππε

...,3,2,1,,coscos1 1

== ∑∑∞

=

∞

=

nma

xn

b

ymB

m nmny

ππε

...,5,3,1,,coscos1 1

== ∑∑∞

=

∞

=

nmb

yn

a

xmWw

m nmn

ππ

Mechanical strains at any point :

Tx

wz

x

w

x

ux ∆−

∂

∂−

∂

∂+

∂

∂= αε

2

22

2

1

yxw

zyw

xw

xv

yu

xy ∂∂∂

−∂∂

∂∂

+∂∂

+∂∂

=

22γ

Ty

wz

y

w

y

vy ∆−

∂

∂−

∂

∂+

∂

∂= αε

2

22

2

1

Vertical deflection w defined as:

b a

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Vertical Displacement Bottom Layer StressesMembrane Tractions

The study was conducted at ambient and elevated temperatures

Rayleigh-Ritz

Vulcan

Axial & Rotational Restraints and Thermal Stresses

Further studies were conducted with finite element software (Vulcan). The effects of a range of thermal gradients on the mechanical stress development through the depth of the slab were investigated, with reference to the degree of axial restraint, rotational restraint and the thermal stress distribution

2a2

b

mmC01

mmC0

4

mmC05

mmC0

6

mmC0

7

mmC03

mmC0

2

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ess (

N/m

m2 )

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ess (

N/m

m2)

Membrane Tractions Top Layer StressesBottom Layer Stresses

Total membrane strains εx and εy :

Restraints aid membrane action. These induce compressive stresses in the slab. However, higher thermal gradients overcome these stresses, generating the

required slab deflection profile required for membrane action

Experimental Investigation

The test models the behaviour of composite slabs in fire. The investigation focuses on the influences of thermal gradients, the tensile strength of concrete, reinforcement ratios and the bond strength between concrete and reinforcement on tensile membrane action.

Description

Uniform area loading is simulated by 12 point loads. The edges of the thin slabs are supported on rollers on a support frame and placed over the test furnace. The slab is clamped at its corners. The transient tests are performed on slabs prepared with varying ratios of reinforcement area of either smooth or deformed bars.

Setup

Span/4Span/4Span/4 Span/8Span/8

Span/6

Span/3

Span/3

Span/6

Results

Two types of failure modes were observed:

1. Fracture of reinforcement across the short span with lower reinforcement ratios, accompanied by distinct yield-lines

2. Compressive crushing of concrete at the corners with higher reinforcement ratios, with distributed cracks following the trajectory of yield-lines

Membrane action is enhanced by ductile reinforcement and bond-slip. For the same reinforcement ratio, the smooth reinforcement (pink) produced larger displacements and survived longer under the same conditions.

Test furnace Loading frameLoad points

Distinct yield-lines (0.2%) Distributed cracks (0.4%)

Current Work• Current predictions for failure of concrete slabs in fire (after cracking) is assumed to be dependent on the

attainment of a pre-defined tensile strain

• This research is therefore looking at predicting tensile failure using a fracture energy criterion

• Depending on the crack width, an estimation of the failure strain can then be determined

• The prediction also depends on finite element size and type, and these will be considered

Further Work• The fracture energy failure criterion for concrete will be incorporated into a new slab model

• The model will allow the simulation of bond-slip and bond-strength characteristics

• An ideal failure criterion, based on the true mechanism of tensile membrane action at elevated temperatures

can then be developed

• The final model will therefore aid accurate predictions of composite slab capacities in fire

cip04aka@sheffield.ac.uk Ian.Burgess@sheffield.ac.uk

Numerical Modelling

A number of assumptions of the Bailey Method were investigated with Vulcan. Vulcan is a 3D finite element frame analysis program. It models beams with 3-noded beam-column elements, while reinforced concrete slabs are modelled with 9-noded layered slab elements. The program includes geometric and material nonlinearities.

The analyses reported here were conducted on a 9m x 7.5m slab panel, with 2 internal unprotected beams spanning in the shorter direction, for comparison with the Bailey Method.

Slab panel vertical support

Slab panel vertical support is lost when beams reach about 550°C, although they are designed for critical temperatures of about 630°C

This loss of stiffness initiates a single-curvature bending mechanism, which may cause failure

Analyses

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Tensile Strength of Concrete

The tensile strength of concrete helps to reduce the total deflections required for tensile membrane action.

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Rotational Restraint

The support provided by adjacent slabs helps to maintain vertical panel support. However, the loss of strength and stiffness of the protected beams at about 550°C requires the use of thicker sections or more protection

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Slab panel with corner

support

Slab panel with edge

support

Relative displacement of

protected secondary beam

Relative displacement of

protected primary beam

Slab panel with edge

support, and including tensile strength of concrete

Slab panel with edge support,

excluding the tensile strength of

concrete

TSLAB failure criterion

BRE required vertical

displacement, A193 mesh

Slab panel with corner

support, rotational restraint

along 4 edges

Slab panel with corner

support, rotational restraint

along 2 edges

Slab panel with corner support,

1X protection thickness

Slab panel with corner support, 2X protection thickness

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Temperature (°C)

0.2% deformed reinforcement

0.2% smooth reinforcement

Tensile membrane action is a mechanism producing increased load-bearing capacity in thin slabs undergoing large vertical displacements, in which stretched central areas of the slab induce an equilibrating peripheral ring of compression

The mechanism relies on two-way bending and the availability of vertical support along the slab’s boundaries

Tensile membrane action occurs irrespective of the horizontal anchorage available along the edges of the slab

The method is based on rigid-plastic theory with large change of geometry. The method divides a floor slab into rectangular slab panels, composed of unprotected beams in the interior, supported on edges that resist vertical deflection.

Slab panels are analysed independently as simply-supported slabs undergoing large vertical displacements through the loss of strength of the internal unprotected beams, as the fire develops.

Bailey – BRE MethodTensile Membrane ActionAssumptions

1. Mechanism at ambient temperature is maintained at elevated temperatures

2. Slabs are supported on edges that effectively resist vertical deflection

3. Tensile strength of concrete is ignored

4. Method predicts higher capacities with increasing reinforcement mesh area

Assumptions & Issues

Increasing vertical deflection

In Practice

1. Thermal bowing of the slab induces membrane action, and failure by a yield-line mechanism is observed in the late stages of the fire

2. Slab panel support is realised by protecting the beams on the perimeter, and these experience vertical deflection

3. The tensile strength of concrete helps to reduce the required vertical displacements for the mobilization of membrane action

4. Experiments show capacity is not linearly proportional to mesh area

φ

T1

T2

S

T2

C

S

CnL

L

l