Question

A bar of cross section A is subjected to equal and opposite tensile forces F at its ends. Consider a plane through the bar making an angle `theta` with a plane at right angles to the bar as shown in figure.

The tensile stress at this plane in terms of F, A and `theta` is
A. What is the tensile stress at this plane in terms of `F, A` and `theta` ?
B. What is the sherating stress at the plane, in terms of `F, A` and `theta` ?
C. For what value of `theta` is the tensile stress a maximum ?
D. For what valule of `theta` is shearing stress a maximum?

Answer 1

Correct Answer - A::B::C::D
(a) tensile stress `= (Fcostheta)/(A//costheta) = (Fcos^(2)theta)/(A)`
(b) shearing stress `= (Fsintheta)/(A//costheta) = (F)/(A) sinthetacostheta`
for max. tensile stress
`theta = 0^(@)`
(d) for max. shering stress
`theta = 45^(@)`