# Consider a long steel bar under a tensile stress due to forces F acting at the edges along the length of the bar. Consider a plane making an angle  with the length. What are the tensile and shearing stresses on this planet?a) for what angle is the tensile stress a maximum?b) for what angle is the shearing stress a maximum?

a) Tensile stress = normal forces to the surface of plane F/ area

A = area of cross-section which is perpendicular to the bar

A’ = the area of plane cut along aa’ of the cross section

The force perpendicular component along A or

Tensile stress =

For max value, sin θ should be equal to 1. Hence,

b)  Shearing stress = forces along the plane F/ area =

for shearing stress to be maximum,

which gives us

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