Strength of Materials

Cover Strength of Materials
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176.
Digitized by Google 342 STRENGTH OF MATERIALS.
[CH. XIl.
ring as a straight beam, as in Art. 77, where ^ is an element of length equal to KdO, smce X =^ gr "^^ bendmg per unit length, — •/ V •^ Substituting the value of M from (i) and dividing by g^j — V and therefore from (i)- M = Wr(^ - J sin ^) .
and at the section AB where ^ = o— WR Mo = or P-3I8WR.
(3) (4) The bending moment vanishes for sin tf = - and its values at all sections are shown in Fig. 177 plotted radially from the central
...line SLTK.
Additional Direct and Shearing Farces, — In addition to the bending stress there is on every section such as XX the direct W force — sin 0^ giving an additional cir- cumferential stress of intensity — Wsing 2A W and a shearing force — cos 6 across the radial sections, which will produce shear- ing stress distributed more or less as indicated in Art. 71. The greatest shearing force — at ^ = o will produce W an average shear stress of intensity -v* Taking the circular section, for example, the maximum intensity would be about | of this amount.


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