Calculating Force on an Aluminum Beam with Temp Change

In summary, an aluminum beam with a length of 79 m and cross-sectional area of 0.095 m2 is clamped rigidly at both ends and used as part of a bridge. The magnitude of the extra force exerted by the beam on one of its supports when the temperature is increased by 29°C is 4.46x10^7. To calculate this, the change in length of the beam must be taken into account by using the equation delta L = alpha of alum (a constant) * L * delta T. When attempting part (b) of the problem, the same equation can be used, except with a temperature decrease of 43°C.
  • #1
theskyisgreen
8
0

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?
 
Physics news on Phys.org
  • #2


Check your first equation; it should include the change in temperature.
 
  • #3


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


theskyisgreen said:
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?
 

1. How does temperature change affect the force on an aluminum beam?

Temperature change can cause the aluminum beam to expand or contract, which can lead to changes in its dimensions and ultimately affect the force applied on it.

2. How do you calculate the force on an aluminum beam with temperature change?

The force on an aluminum beam with temperature change can be calculated using the equation F = αEΔT, where F is the force, α is the coefficient of thermal expansion, E is the Young's modulus of aluminum, and ΔT is the change in temperature.

3. What is the coefficient of thermal expansion for aluminum?

The coefficient of thermal expansion for aluminum is 23.6 x 10^-6 m/mK. This means that for every 1 degree Celsius increase in temperature, the aluminum beam will expand by 23.6 micrometers per meter in length.

4. How does the Young's modulus of aluminum affect the force calculation?

The Young's modulus of aluminum is a measure of its stiffness and it affects the force calculation by determining how much the beam will bend or deform under a given force. A higher Young's modulus means the beam will be stiffer and require more force to bend.

5. Can temperature change cause failure in an aluminum beam?

Yes, temperature change can cause failure in an aluminum beam if the force applied exceeds the beam's strength. This is because temperature change can alter the beam's dimensions and lead to additional stress, which can result in failure if it exceeds the beam's ultimate strength.

Similar threads

  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
906
  • Introductory Physics Homework Help
Replies
10
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
2K
  • Introductory Physics Homework Help
Replies
6
Views
9K
  • Introductory Physics Homework Help
Replies
4
Views
11K
  • Introductory Physics Homework Help
Replies
1
Views
5K
  • Introductory Physics Homework Help
Replies
5
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
2K
Back
Top