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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Tra
ctio
n (
N/m
m)
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mbra
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m)
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ess (
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m2)
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ess (
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m2)
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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mbra
ne
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ctio
n (
N/m
m)
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Str
ess (
N/m
m2 )
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Distance along span (mm)
Str
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
[email protected] [email protected]
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