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A long steel bar of cross-sectional area A is subjected to a tensile force F applied at its ends along its length. Consider a plane inside the bar that makes an angle theta with the bar's length. What are the tensile (normal) and shearing (tangential) stresses on this plane?

1. Tensile stress = (F/A) cos²(theta), Shearing stress = (F/A) sin(theta) cos(theta)
2. Tensile stress = (F/A) sin²(theta), Shearing stress = (F/A) sin(theta) cos(theta)
3. Tensile stress = (F/A) cos(theta), Shearing stress = (F/A) sin(theta)
4. Tensile stress = F/A, Shearing stress = 0

Correct answer: Tensile stress = (F/A) cos²(theta), Shearing stress = (F/A) sin(theta) cos(theta)

Solution

Resolving F across the oblique plane gives tensile stress (F/A)cos²(theta) and shear stress (F/A)sin(theta)cos(theta); the tensile stress is maximum at theta = 0 and the shear stress is maximum at theta = 45 deg.

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