A bimetallic bar (or composite bar) of square cross section with dimensions 2b 2b is constructed of two different metals having moduli of elasticity E1 and E2 (see figure). The two parts of the bar...

A bimetallic bar (or composite bar) of square cross section with dimensions 2b

2b is constructed of two different metals having moduli of elasticity E₁
and E₂
(see figure). The two parts of the bar have the same cross-sectional dimensions. The bar is compressed by forces P acting through rigid end plates. The line of action of the loads has an eccentricity e of such magnitude that each part of the bar is stressed uniformly in compression.

(a) Determine the axial forces P₁
and P₂
in the two parts of the bar.

(b) Determine the eccentricity e of the loads.

(c) Determine the ratio

₁/
₂
of the stresses in the two parts of the bar.