Question

3 3. (25 pts.) A system of bars consists of a steel bar (AB) and an aluminum bar (BC). Bar AB has a cross-section of 2 inches by 0.75 inches and has a modulus of elasticity of 29000 ksi and a coefficient of thermal expansion of 6.5x10-6 /F. Bar BC has a cross-section of 3 inches by 0.75 inches and has a modulus of elasticity of 10600 ksi and a coefficient of thermal expansion of 12.8x106/F. A gap of 0.03 inches exists between the left wall and point A when the bars are at a temperature of 70 degrees F. Both bars are then subjected to a temperature increase of the same magnitude. Determine: a) the temperature at which the stress in bar AB will be equal to 25 ksi. Gap = 0.03 inches. b) the change in length of both the aluminum and steel bar. 02:55:40 The temperature in the system of bars is The change in length of the aluminum bar is The change in length of the steel bar is (in.) (in.) B C A 2 in. 3 in. 32 in. 44 in. Gap

Answer 1

Thermal stress x2

0 = a Τ.Ε

Thermal expansion in Area= x2

Aa.AT

a) Thermal stress $\varepsi \sigma$ _AB= $\alpha$ _steel .$\Delta$T .E x 2

25=2x(6.5x10^-6-6)(T₂ -T₁)x29x10³

25=2x(6.5x10^-6)(T₂-70)x29x10³

T₂ = 136.3⁰F

b) (  $\Delta A$)_AB = A .$\alpha$_steelx2

VI

(2×0.75)×2 x 6.5×10^-6 ×66.3=1.3×10^-3 in²

($\Delta A$)_BC= A .$\alpha$_aluminiumx 2

VI

( $\Delta A$ )_BC = (3×0.75)×2 x 12.8×10^-6 × =3.82×10^-3 in²