Thermal Stresses In Stepped Bars:

In this, we will discuss the determination of thermal stresses in bars whose cross- sectional area changes in steps over the length.

Fully Restrained Stepped Bar

Assume a bar of length L which contains a uniform cross-sectional area A₁ over length L₁ while in the rest of the length L₂ the cross-sectional area is A₂. Assume the Young's Modulus and the coefficient of linear expansion for the two parts is E₁, α₁ and E₂, α₂, respectively.

The ends of the bar are completely restrained. The bar is illustrated in Figure. Let the temperature of the bar be grown up by ΔT.