Consider a long steel bar under tensile stress due to vector forces F⃗ applied at the ends along the bar. For a plane making angle θ with the bar, find the tensile and shear stresses on that plane. (a) At what angle is tensile stress maximum? (b) At what angle is shear stress maximum?
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Question

Consider a long steel bar under tensile stress due to vector forces F⃗ applied at the ends along the bar. For a plane making angle θ with the bar, find the tensile and shear stresses on that plane. (a) At what angle is tensile stress maximum? (b) At what angle is shear stress maximum?

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G1 Physics · Accepted Answer

Use stress σ=F/A, strain ε=ΔL/L and Young's modulus Y=σ/ε. For a uniform segment, ΔL=FL/(AY); for thermal restraint, thermal strain αΔT produces stress YαΔT. Evaluating the given data/statements gives θ(t)=π/2; θₛ=π/4. Therefore the correct answer is A.