Answer to Question #175544 in Civil and Environmental Engineering for Sandhiya

Question

A steel rod 15m long is at a temperature 15°c. Find the free expansion of the length when the temperature is raised to 65°c. Find the temperature stress produced when

1. The expansion of the rod is prevented

2. The rod is permitted to expand by 6mm.

Take: Elastic modulus = 200GN/m^2 and temperature coefficient = 12 × 10^-6°c

Answer 1

Linear thermal expansion is ΔL = αLΔT, where ΔL is the change in length L, ΔT is the change in temperature, and α is the coefficient of linear expansion, which varies slightly with temperature. The change in area due to thermal expansion is ΔA = 2αAΔT, where ΔA is the change in area.

ΔL = αLΔT

Coefficient of linear expansion= 12 × 10– ⁶

Change in temperature = 65º C˗ 15ºC =50º C

                                   (12 × 10– ⁶ ) (15m) (50ºC) =

                                       Cº

(12 × 10ˉˉ⁶ ) (15m) (50ºC) = Cº

=0.3

^1.       The formula of thermal stress is Y (α ΔT) / L₀, where Y is Young's modulus of the given material, ΔT is the change in temperature, α is the coefficient of linear thermal expansion of the given material and L₀ is the original length of the material before the expansion.

Y (α ΔT) / L₀

200GN/m^2 (12 × 10– ⁶ (50ºC) /65m

3.0769ºC

 

2.     Y (α ΔT) / L₀

(200GN/m^2 (12 × 10– ⁶ (50ºC) /65m) 6mm

3.0769 × 6

18.461ºC