Economical Beams

The following consideration is made to determine the most economical dimensions of a Beam for a required section Modulus. Let Z = I/Y = the required section modulus.

A = total cross section area of Beam

Aw = area of web

Af = area of flanges

h = depth between centres of gravity of flanges

t = minimum thickness capable of being rolled

tw = thickness web

tf = thickness of each flange

then Aw = twh + twxtf/2 X 2 = twh (approx,)

Af = A-Aw

    = A-twh-twxtf = A-twh (approx.).