F. K. Kong MA, MSc, PhD, CEng, FICE, FIStructE, R. H. Evans CBE, DSc, D ès Sc, DTech, PhD, CEng, FICE, FIMechE, FIStructE (auth.)-Reinforced and Prestressed Concrete-Springer US (1987)

Torsioll ill plaill cOllcrete beal1ls 227
~-5"----<J}m
1· hmolt----t .. 1
(a) Plan
(b) End view
Fig.6.8-2 Sand heap for reetangular section
2T
VI = ') (6.8-8)
h~lin[hOlax - hOlin/3]
Marshall [40] has analysed the test results of many investigators and
shown that a reasonable estimate of the cracking torque T could be
obtained from eqn (6.8-8) by using the splitting cylinder strengthfl for VI;
this confirms similar conclusions drawn by others [33, 34]. It might appear
surprising that eqn (6.8-8), which is based on a plastic stress distribution,
should give better agreement with test results than does a strictly elastic
analysis based on direct application of eqns (6.8-1) and (6.8-2). The
reason is not quite understood, though it is possible that by the time the
diagonal cracks become visible, the stress distribution has already been
somewhat affected by microcracking. In this connection, it is appropriate
to mention the authors' experience with modulus of rupture tests on plain
concrete specimens: collapse, which occurs simultaneously with visible
cracking, is always preceded by microcracking, and the microcracking load
is only about 65% of the visible-cracking load [41].
The sand-heap analogy, being based on eqns (6.8-1) and (6.8-2), is
applicable to a cross-section of arbitrary shape. For simple flanged
sections, the sand heaps are approximately as shown in Fig. 6.8-3.
Consider, for example, the T-section. Since the quantity vlhp (where 1/J
is the slope of the faces of the sand heap) is the same for both the flange
and the web, we have
~ _ Tr _ Tw
1/J - 2 x volume of flange heap - 2 x volume of web heap
(a) (b) (e)
Fig. 6.8-3 Approximate sand heaps for simple ftanged sections