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Thermal expansion

Two rods of different materials having coefficients of thermal expansion α1,α2  and Young’s modulli Y1, Y2 respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of the rods. If  α1:α2  = 2 : 3, the thermal stresses developed in the two rods are equal provided Y1 : Y2 is equal to : 


Thermal stress  Y1α1Δt=Y2α2Δt

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