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Question

A metallic bar of diameter 20 mm is shown in figure.


Modulus of elasticity of bar is 2×105 MPa, coefficient of thermal expansions is 12×106/C. The temperature of metallic bar is increased by 100C, then what is the reaction generated at right support if the right supports yields by 0.1 mm is ___ kN
  1. 12.56

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Solution

The correct option is A 12.56
Increase in length due to temperature increment = LαΔT
=200×12×106×100=0.24 mm Deformation prevented = 0.24 - gap length - yielding
=0.240.10.1 =0.04 mm
Let R be the reaction generated at right support.
RLAE=0.04
R=0.04×π4×(20)2×2×105200=12566.3 N
R=12.56 kN

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