Civil Engineering Reference
In-Depth Information
15
Torsion
15.1
INTRODUCTION
The average designer probably does not worry about torsion very much. He or she thinks
almost exclusively of axial forces, shears, and bending moments, and yet most rein-
forced concrete structures are subject to some degree of torsion. Until recent years the
safety factors required by codes for the design of reinforced concrete members for shear,
moment, and so forth were so large that the effects of torsion could be safely neglected
in all but the most extreme cases. Today, however, overall safety factors are less than
they used to be and members are smaller, with the result that torsion is a more common
problem.
Appreciable torsion does occur in many structures, such as in the main girders of
bridges, which are twisted by transverse beams or slabs. It occurs in buildings where
the edge of a floor slab and its beams are supported by a spandrel beam running be-
tween the exterior columns. This situation is illustrated in Figure 15.1, where the floor
beams tend to twist the spandrel beam laterally. Earthquakes can cause dangerous tor-
sional forces in all buildings. This is particularly true in asymmetrical structures
where the centers of mass and rigidity do not coincide. Other cases where torsion may
be significant are in curved bridge girders, spiral stairways, balcony girders, and
whenever large loads are applied to any beam “off center.” An off-center case where
torsional stress can be very large is illustrated in Figure 15.2. It should be realized
that if the supporting member is able to rotate, the resulting torsional stresses will be
fairly small. If, however, the member is restrained, the torsional stresses can be quite
large.
Should a plain concrete member be subjected to pure torsion, it will crack and fail
along 45
spiral lines due to the diagonal tension corresponding to the torsional stresses.
For a very effective demonstration of this type of failure, you can take a piece of chalk in
your hands and twist it until it breaks. Although the diagonal tension stresses produced by
twisting are very similar to those caused by shear, they will occur on all faces of a mem-
ber. As a result, they add to the stresses caused by shear on one side and subtract from
them on the other.
1
1
White, R. N., Gergely, P., and Sexsmith, R. G., 1974,
Structural Engineering
, vol. 3 (New York: John Wiley &
Sons), pp. 423-424.
475
