Thermal Stresses in Tapered Bars:

In this section, we will study the problem of thermal stresses in slowly tapering bars. Because the cross-sectional area is differing along the length of the bar, so does the stress. Herein, we will derive expression for thermal stress in bars along circular cross-section. For other cross-sections, as square etc., expressions for stresses may be derived in a similar fashion.

Fully Restrained Tapered Bar

Let the bar shown in given fig, which is circular in cross-section but tapering from a diameter d₂ to d₁ over the length L. The bar is totally restrained at its ends. Now, Assume the temperature of the bar enhanced by ΔT.