Consider an I-beam made from structural steel used to support a highway overpass
ID: 3896359 • Letter: C
Question
Consider an I-beam made from structural steel used to support a highway overpass. The beam is
10.0 m long when its temperature is 20.00 C and is free to expand due to expansion joints. The
cross sectional area of the beam is 0.100 m2
.
a. What is the length of the beam during a cold winter night when the temperature of the
steel drops to -15.0 C?
b. What is the length of the beam during a hot summer afternoon when the temperature
of the steel rises to 35.0 C?
c. How much stress would build in this beam if it was not allowed to expand, installed at
20.00 C and then increased in temperature to 35.0 C?
d. How much internal force would build in part (c)?
e. How much internal force would build in part (c) if the beam was made out of invar
instead of structural steel?
Explanation / Answer
a)
Change in length = L*alpha*temp. difference.....where alpha = coeff. of thermal expansion = 13*10^-6 /deg C
= 10*(13*10^-6)*(20 - (-15))
= 0.00455 m
New length = 10 - 0.00455 = 9.99545 m
b)
Change in length = L*alpha*temp. difference.....where alpha = coeff. of thermal expansion = 13*10^-6 /deg C
= 10*(13*10^-6)*(35 - 20)
= 0.00195 m
New length = 10 + 0.00455 = 10.00195 m
c)
Stress = E*strain.........where E = Young's modulus = 200 GPa for steel
Stress = 200*(0.00195 / 10)
= 0.039 GPa
= 39 MPa
d)
Force = stress*area
= 39*0.1
= 3.9 MN
= 3900 kN
e)