First slide

Stress and strain

Question

A rod AB of uniform cross-sectional area is subjected to an axial tensile force F. If the maximum normal force induced in the rod is 8 KN/cm², the maximum shear stress induced in the rod will be

Moderate

A

6 $KN / {cm}^{2}$
B

3 $KN / {cm}^{2}$
C

zero
D

4 $KN / {cm}^{2}$

Solution

If S be the cross sectional area of the rod,
Then $σ_{\max} = \frac{F}{S}$
Now area of cross section $MN = S / sinθ$
Component of applied force along $MN = Fcosθ$
$∴$ Shear stress on the section $MN = τ = \frac{Fcosθ}{s / sinθ} = \frac{F}{2 S} \sin 2 θ$
When $θ = 45^{o}, τ = τ_{\max} = \frac{F}{2 S} = \frac{σ}{2} = \frac{8}{2} \frac{KN}{{cm}^{2}} = 4 \frac{KN}{{cm}^{2}}$

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