Question

A bar of cross-section A is subjected to two equal and opposite tensile forces at its ends. Consider a plane section of the bar whose normal makes an angle θ with the axis of the bar.

·What is the tensile stress on this plane?

·What is the shearing stress on this plane?

• A. $\frac{F}{A}co{s}^2\theta ,\frac{Fsin\theta cos\theta }{A}$
• B. $\frac{F}{A}si{n}^2\theta ,\frac{F}{A}co{s}^2\theta$
• C. $\frac{F}{A}si{n}^2\theta ,\frac{Fsin\theta cos\theta }{A}$
• D. $\frac{F}{A}co{s}^2\theta ,\frac{F}{A}si{n}^2\theta$

Answer 1

The correct option is A

$\frac{F}{A}co{s}^2\theta ,\frac{Fsin\theta cos\theta }{A}$

$A^1$=$\frac{A}{cos\theta }$
$\therefore$ Tensile stress =$\frac{Fcos\theta }{A}=\frac{F}{A}co{s}^2\theta$
shear stress=$\frac{Fsin\theta }{A^1}=\frac{Fsin\theta cos\theta }{A}$