Answer to Question #239517 in Mechanical Engineering for Vicky

Question

Determine the variation in stress in fully restrianed steel members resulting from change in ambient temperature.
Coefficient of linear expansion for steel, = 11×10^-6/

Answer 1

Linear expansion due to change in temperature can be expressed as

$d_l = α l_o dt$                   (1)

where 

dl = elongation (m, in)

α = temperature expansion coefficient (m/mK, in/in ^oF)

l_o = initial length (m, in)

dt = temperature difference (^oC, ^oF) 

The strain - or deformation - for an unrestricted expansion can be expressed as

$ε = d_l / l_o$                         (2)

where

ε = strain - deformation 

The Elastic modulus (Young's Modulus) can be expressed as

E = σ / ε                (3)

where 

$E = Young's Modulus (Pa (N/m2), psi)$

$σ = stress (Pa (N/m2), psi)$

Stress

When restricted expansion is "converted" to stress - then (1), (2) and (3) can be combined to

$σdt = E ε \space = E d_l / l_o \space = E α l_o d_t / l_o = E α dt$