A bar of cross-sectional area A is subjected to equal and opposite tensile forces at its ends. Consider a plane section (PS) of the bar, whose normal makes an angle ϕwith the axis (axis is along the length) of the bar.Match the given columns and select the correct option from the codes given below.Codes
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a
i-r, ii-p, iii-q, iv-t
b
i-p, ii-q, iii-r, iv-s
c
i-q, ii-r, iii-s, iv-p
d
i-p, ii-r, iii--q, iv-t
answer is A.
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Detailed Solution
Tangential force is Ft = F sin ϕ Area of section considered isA' = L(Lcos ϕ) = L2cos ϕ=Acos ϕShearing stress = FtA' = F sin ϕAcos ϕ = FAsinϕcosϕ--------------(i)Normal force on plane section considered as.'. Tensile stress = FNA' = F cos ϕAcos ϕ = FAcos2ϕ--------------(ii)Shearing stress is maximum whenϕ = 45°Tensile stress is maximum whenϕ = 0° [From equation (ii)]