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Questions  

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 

a
6 KN/cm2
b
3 KN/cm2
c
zero
d
4 KN/cm2

detailed solution

Correct option is D

If S be the cross sectional area of the rod, Then  σmax=FSNow area of cross section MN=S/sinθComponent of applied force along MN=Fcosθ∴ Shear stress on the section MN=τ=Fcosθs/sinθ=F2Ssin2θWhen θ=45o, τ=τmax=F2S=σ2=82KNcm2=4 KNcm2

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