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Finding the force exerted on a beam when the temp of the aluminum beam is increased

  • #1

Homework Statement


An aluminum beam 79 m long and with a cross-sectional area of 0.095 m2 is used as part of a bridge. The beam is clamped rigidly at both ends.

(a) If the temperature of the beam is increased by 29°C, what is magnitude of the extra force exerted by the beam on one of its supports?

(b) What is the magnitude of the force if the temperature of the beam is decreased by 43°C?


Homework Equations


delta L = alpha of alum (a constant) * L * temp
Force = Young's Modulus of alum * area * delta L / L

The Attempt at a Solution



For a)
delta L = (22.2x10^-6)*(79m)*(302 K) = .53m

F= (7.0x10^10)*(.095m^2)*(.53m)/(79m) = 4.46x10^7

Unfortunately, that was incorrect.

Because I couldn't get the first part correct, I haven't been able to attempt b, but I'm assuming you do the same thing but change the temp in the first equation.

Any help?
 

Answers and Replies

  • #2
Mapes
Science Advisor
Homework Helper
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17


Check your first equation; it should include the change in temperature.
 
  • #3
rl.bhat
Homework Helper
4,433
5


delta L = (22.2x10^-6)*(79m)*(302 K) = .53m
ΔT = 29 degrees, not 302 K
 
  • #4


I thought I did that..
Although I did convert the celsius to Kelvin, but 29+273 = 302 K.
Am I not supposed to convert it to K?
 
  • #5
Mapes
Science Advisor
Homework Helper
Gold Member
2,593
17


I thought I did that..
Although I did convert the celsius to Kelvin, but 29+273 = 302 K.
Am I not supposed to convert it to K?
A temperature of 29°C is a temperature of 302 K, but a temperature change of 29°C is a temperature change of 29 K. A degree Celsius is equivalent to a Kelvin, but their reference points, their zeros, are different. Does this make sense?
 

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