MecMovies 4.0 : M5.13: Rod and Post with Temperature Change

The figure shows a post B C labeled 2 of height 200 millimeters attached to a rigid support at C. A cylindrical rod A B labeled 1 of height 400 millimeters is fixed to the post by a flange at B. The rod is fixed to a rigid support at A.

An aluminum rod $(1)$ is attached to a steel post $(2)$ at rigid flange $B$ . Rod $(1)$ and post $(2)$ are initially stress-free when they are connected to the flange at a temperature of $20^{\circ} C$ .

The aluminum rod $(1)$ has a cross-sectional area of $A_{1} = 200 {mm}^{2}$ , a modulus of elasticity of $E_{1} = 70 GPa$ , and a coefficient of thermal expansion of $α_{1} = 23.6 \times 10^{- 6} /^{\circ} C$ .

The steel post $(2)$ has properties of $A_{2} = 450 {mm}^{2}$ , $E_{2} = 200 GPa$ , and $α_{2} = 12.0 \times 10^{- 6} /^{\circ} C$ .

Determine the normal stresses in members $(1)$ and $(2)$ and the deflection at flange $B$ after the temperature rises to $75^{\circ} C$ .