Thermal Stresses

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Whenever there is some increase or decrease in the temperature of a body, it causes the body toĀ expand or contract. A little consideration will show that if the body is allowed to expand or contractĀ freely, with the rise or fall of the temperature, no stresses are induced in the body. But, if the deformationĀ of the body is prevented, some stresses are induced in the body. Such stresses are known as thermalĀ stresses.

The definition of the compound bar is a bar made āāof two or more materials with both mountedrigidly applied so that the burden can be shared and experienced the same extension @shortening. Bars compound can be categorized into two types, series and parallel bars.

Let l = Original length of the body,
t = Rise or fall of temperature,

andĀ Ī± = Coefficient of thermal expansion,

ā“ Increase or decrease in length,
Ī“l = l. Ī±.t

If the ends of the body are fixed to rigid supports, so that its expansion is prevented, thenĀ compressive strain induced in the body,

Īµc =Ī“/l=l.Ī±.t/=Ī±.t
ā“ Thermal stress, Ļth = Īµc.E = Ī±.t.E

Notes :

1. When a body is composed of two or different materials having different coefficient of thermalĀ expansions, then due to the rise in temperature, the material with higher coefficient of thermal expansion will beĀ subjected to compressive stress whereas the material with low coefficient of expansion will be subjected toĀ tensile stress.
2. When a thin tyre is shrunk on to a wheel of diameter D, its internal diameter d is a little less than theĀ wheel diameter. When the tyre is heated, its circumferance Ļ d will increase to Ļ D. In this condition, it isĀ slipped on to the wheel. When it cools, it wants to return to its original circumference Ļ d, but the wheel if it isĀ assumed to be rigid, prevents it from doing so.

ā“ Strain, Īµ =(ĻD-Ļd)/Ļd=(D-d)/d

This strain is known as circumferential or hoop strain.
ā“ Circumferential or hoop stress,

Ļ = E.Īµ =E(D-d)/d

Reference

A textbook of Machine Design by R.S.Khurmi and J.K.Gupta

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