# # Solid Sections

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.