5.5 Design of Individual Members Exposed to Fire
5.6.6 Axial Restraint
5.6.6.1 Effect of Restraint on Heated Members
Figure 5.18 shows a simply supported concrete beam, located between rigid supports which permit rotation but no elongation at the ends. As the bottom of the beam heats up, it tries to expand, but is unable to do so because of the rigid supports. An axial thrust T develops in the beam, contributing to its strength. The thrust may be thought of as external prestressing.
Figure 5.18 shows a situation where the elevated temperature moment capacity Mf can drop to less than the applied moment M*fire without collapse because the flexural resistance is enhanced by the moment Te, where e is the eccentricity between the line of action of the thermal thrust and the centroid of the compression block near the top of the beam. The total flexural resis- tance Rfire Mf Te is then greater than the applied moment M*fire. The Te line is curved as shown because of the deflection of the beam.
In some situations, where the surrounding structure has sufficient stiffness, the moment capacity Mf at elevated temperature can drop to zero without failure, with all of the moment being resisted by the Te couple. This explains the large difference between the listed ‘restrained’
and ‘unrestrained’ ratings for some assemblies which have been tested under both conditions (e.g. UL, 2012).
Figure 5.19 shows a free body diagram of a reinforced concrete beam subjected to a com- pressive axial restraint force T. The compression stress block must now develop a force C equal to the sum of the axial restraint force T plus the tensile force in the reinforcing Ty.
w
A B C
2θ
θ
θ
δ
δ δ'
Figure 5.17 Plastic failure mechanisms for an indeterminate beam
Axial restraint does not always have a beneficial effect on fire resistance. Restraint can have a negative effect if mid‐span deflections become excessive, or if the axial thrust develops near the top of the cross section. In order to utilize the beneficial effects of axial restraint, it is essential that the line of thermally induced thrust is below the centroid of the compression region of the beam or slab, so that the eccentricity e shown in Figure 5.17 and Figure 5.18 has a positive value. It can sometimes be difficult to calculate the axial restraint because the posi- tion of the axial thrust can change from being positive to negative and vice versa as deforma- tions and rotations occur during fire exposure. Figure 5.20 (Carlson et al., 1965) shows how the location of the axial restraint force depends on the support conditions of the beam or slab.
An axial restraint force near the top of the beam as shown in Figure 5.20(a) would lead to
Bending moment Rfire
Mfire
Mcold Rcold 6
8 10 12
T.e
Figure 5.18 Effect of axial restraint force on bending moment diagram
e C Δ
d
Midspan Ty R
R T
dT
Figure 5.19 Free body diagram of reinforced concrete beam with axial restraint
premature failure of the floor system. This can be a problem with double‐tee precast pre- stressed concrete floor panels if the webs are cut away at the ends and all the support is provided at the level of the top flange, as shown in Chapter 7. For the sliding connection in Figure 5.20(b), the axial thrust is below the centroidal axis, resulting in a positive value of eccentricity. Figure 5.20(c) also shows a positive eccentricity, due to the lower location of the axial thrust force. For built‐in construction where the line of action of the restraint force is not known [Figure 5.20(d)] the thrust will usually be near the bottom where most of the heating and thermal expansion occurs.
This discussion has been based on the assumption that the restrained slab or beam does not buckle due to lateral instability under high axial loads, which is usually a good assumption for reinforced concrete structures. Rotter et al. (1999) have shown that fire‐exposed steel beams with composite concrete slabs may buckle as a result of the large axial forces induced when they try to expand axially against a stiff and strong surrounding structure. This buckling results in large downwards deflections of the beam and slab which can be beneficial because the large deflections reduce the horizontal restraint forces on the surrounding structure. There is a com- plex interaction between the axial forces, downwards deflections and stiffness of the structure.
Once buckling occurs, resulting in large deformations, the analysis presented above for single members does not apply. Later in the fire, the slab or slab‐beam assembly may lose flexural strength and deform into a catenary. The slab will then develop internal tensile forces which pull inwards on the surrounding structure with tensile membrane action. This behaviour is described with reference to the Cardington tests in Chapter 6.
Welded plates
(a) (b)
(c) (d)
T
T T
T Centroidal
axis
Centroidal axis
Centroidal axis
Centroidal axis Sliding connection
Sliding bearing
Position varies (see text) Shim
Figure 5.20 Location of axial thrust for several support conditions. Reproduced from Carlson et al.
(1965) by permission of Portland Cement Association
vide the necessary resistance to the axial restraint forces.
A negative effect of axial restraint may be serious damage to the surrounding structure, caused by large forces resulting from the thermal expansion. Such damage is more likely in concrete or masonry buildings rather than in ductile steel buildings, because of the inability of a stiff and brittle surrounding structure to absorb the imposed thermal forces or deformations.