Question:
A bar of cross section A is subjected to equal and opposite tensile force F at its ends. Consider a plane through a bar making an angle (Theta) with a plane at right angles to the bar length. A.) What is the tensile stress at this plane in terms of F, A and (theta). B.) What is the shearing stress at this plane, in terms of F,A and (theta)
Answer:
FN = Normal force = F cos θ
AN = Area = A / cos θ
Tensile stress = Normal force / Area = F cos θ / (A / cos θ) = F cos2θ / A
Shearing stress = Tangential force / Area = F sin θ / A cos θ = F sin 2θ / 2A
The shearing stress is maximum if sin 2θ = 1 or 2θ = 900 or θ = 450
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