A bent circular bar has AB=0.55 m along x, BC=0.5 m along y and radius 0.01 m. An out-of-plane force F acts at C as shown. Yield strength is 280 MPa. Using von Mises yield theory, find the largest F in N such that AB remains elastic (nearest integer).
The critical section at A has bending moment 0.55F and torque 0.5F. For a solid circular section, $\sigma_b=4(0.55F)/(\pi r^3)$ and $\tau=2(0.5F)/(\pi r^3)$. Set $\sqrt{\sigma_b^2+3\tau^2}=280\times10^6$ Pa. Substitution with r=0.01 m gives F≈314 N. Both bending and torsion must be included.
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