Using strength of materials theory (see Appendix D), the bending stress sq for curved beams is given

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Using strength of materials theory (see Appendix D), the bending stress sq for curved beams is given by σθ =–M(r– B)/[rA(R– B)], where A = b –a, B = (b– a)/log(b/a), R = (a + b)/2. For the problem shown in Fig. 8.30, compare and plot the strength of materials and elasticity predictions for the cases of b/a = 2 and 4. Follow the nondimensional plotting scheme used in Fig. 8.31.

Fig 8.30

M = r M

Fig 8.31

Dimensionless Stress, a/M 1.2 1 0.8 0.6 0.4+ 0.2+ of -0.2 -0.4+ -0.6 1 1.5 b/a = 4 Theory of Elasticity


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