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Published online by Cambridge University Press: 28 July 2016
At a section of a cantilever distant x from its tip, let the depth of section be h and the bending moment M. Then if all the resistance to bending is concentrated in the flanges the loads in the flanges are ±M/h. If the flanges are inclined at a small angle α these flange loads have a component transverse to the cantilever axis of magnitude Mα/h. Now α=dh/dx and the shear load at section x is dM/dx. Therefore the shear load on the web of the cantilever is dM/dx-(M/h)dh/dx, and, if h/M is constant, the web is not sheared at all.
page 760 note * The figure quoted is an upper limit; rather thinner webs might suffice.
Page 761 note * The concavity of the tension flange results in a cross tension in the web, and this tension combined with the thrust from the compression flange sets up a secondary system of shear stress in the web. The actual stress system is rather complex; but the general conclusion that progressive taper results in heavier stresses in the web is justified.