First slide
Elastic behaviour of solids
Question

The bar shown in the figure is made of a single piece of material. It is fixed at one end. It consists of two segments of equal length L/2 each but different cross-sectional area A and 2A.Find the ratio of total elongation in the bar to the elongation produced in thicker segment under the action of an axial force F. Consider the shape of joint to remain circular. (Given: Y is Young's modulus).

Moderate
Solution

ΔL1=F(L/2)AY=FL2AYΔL2=F(L/2)2AY=FL4AYRequired ratio =ΔL1+ΔL2ΔL2=ΔL1ΔL2+1=2+1=3

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