Civil Engineering Reference
In-Depth Information
Chapter
11
/ Torsion of Beams
Torsion in beams arises generally from the action of shear loads whose points of appli-
cation do not coincide with the shear centre of the beam section. Examples of practical
situations where this occurs are shown in Fig. 11.1 where, in Fig. 11.1(a), a concrete
encased I-section steel beam supports an offset masonry wall and in Fig. 11.1(b) a
floor slab, cast integrally with its supporting reinforced concrete beams, causes torsion
of the beams as it deflects under load. Codes of Practice either imply or demand that
torsional stresses and deflections be checked and provided for in design.
Reinforced concrete
beam
F
IGURE
11.1
Causes of torsion in
beams
(a)
(b)
The solution of torsion problems is complex particularly in the case of beams of solid
section and arbitrary shape for which exact solutions do not exist. Use is then made
of empirical formulae which are conveniently expressed in terms of correction factors
based on the geometry of a particular shape of cross section. The simplest case involv-
ing the torsion of solid section beams (as opposed to hollow cellular sections) is that of
a circular section shaft or bar. Therefore, this case forms an instructive introduction
to the more complex cases of the torsion of solid section, thin-walled open section and
closed section beams.
11.1 T
ORSION OF
S
OLID AND
H
OLLOW
C
IRCULAR
S
ECTION
B
ARS
Initially, as in the cases of bending and shear, we shall examine the physical aspects of
torsion.
Suppose that the circular section bar shown in Fig. 11.2(a) is cut at some point along
its length and that the two parts of the bar are threaded onto a spindle along its axis.
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