Answer to Question #239517 in Mechanical Engineering for Vicky

Question #239517
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/
1
Expert's answer
2021-09-22T00:24:46-0400

Linear expansion due to change in temperature can be expressed as

"d_l = \u03b1 l_o dt"                   (1)

where 

dl = elongation (m, in)

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

lo = initial length (m, in)

dt = temperature difference (oC, oF) 

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

"\u03b5 = 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)"

"\u03c3 = stress (Pa (N\/m2), psi)"


Stress

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

"\u03c3dt = E \u03b5 \n\\space = E d_l \/ l_o \n \\space = E \u03b1 l_o d_t \/ l_o\n = E \u03b1 dt"



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