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Elasticity: Tensile stress - normal, tangential; shear stress

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See attached diagram.

A bar with cross sectional area A is subjected to equal and opposite tensile forces F at its ends. Consider a plan through the bar making an angle ? with a plane at right angles to the bar.

a.) What is the tensile (normal) stress at this plane in terms of F, A, and ? ?

b.) What is the shear (tangential) stress at the plane in terms of F, A, and ? ?

c.) For what value of ? is the shear stress a maximum?

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