For rectangular beams it is usually sufficiently accurate to take the
shear area for deflection as where is the breadth
and the depth of the section. The corresponding maximum shear stress
is . It should be noted however that for wide
beams the maximum shear stress is underestimated by this formula: for a
beam with an aspect ratio of 1 the maximum stress is 12.6% higher. (For
a beam with an aspect ratio of 50 (for example a slab) the maximum
stress is about 2000% higher but, as this is a Poisson’s ratio effect,
it is difficult to believe that this has any practical
significance!)

For circular sections the shear area for deflections is

where is Poisson’s ratio and the radius. The expression is very
insensitive to the value of . The maximum shear stress is given by

which varies from

to

with

This item was written by John Blanchard and Ian Feltham for Feedback
Notes [an Ove Arup & Partners internal publication] (1992 NST/21)
originally published in October 1992. Incorporates 1996NST/10 and is
reproduced here with permission.

Timoshenko, S.P. and Goodier, J.N. Theory of elasticity. 3rd edition. McGraw-Hill, 1970.