If 'α' is coefficient of thermal expansion, 'ΔT' is magnitude of change in temperature and 'E' is modulus of elasticity, then the expression for thermal stress induced in a rod of length 'l' that is fixed between two rigid ends is given as-

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RRB JE ME CBT 2 Previous Paper 2: Held on 31 Aug 2019

Answer 1

Concept:

If Rod is free to expand,

Free elongation ΔL = LαΔT

∴ ΔL/L = αΔT

Here rod is fixed at both ends so strain will be zero but due to restriction given by fixed ends, there will be reaction force at the end.

That reaction force per unit area is known as thermal stress.

It is given by-

\(\sigma = E\epsilon\)

or, σ = E(ΔL/L) = Eα(ΔT)

Since rod is fixed at both ends, so thermal strain will be zero but there will be thermal stress.