Strain and stress related to young modulus

  • Thread starter songoku
  • Start date
  • #1
1,833
180

Homework Statement


A three-legged stool has one leg of aluminium (E = 7 x 1010 Pa), one copper (E = 11 x 1010 Pa) and one of steel (E = 20 x 1010) Pa. The legs have the same dimensions. If the load on the stool is at the exact center,
a. Which leg is under the greatest stress? Explain why
b. Which leg experience the greatest strain? Explain why


Homework Equations


stress = force / area
strain = extension / original length
young modulus = stress /strain
force = (E.A.extension) / original length


The Attempt at a Solution


a. All the legs have same dimensions means that the area are the same, so the stress is directly proportional to the force. Assuming they all have the same extension, then the force is directly proportional to young modulus. So the steel is under the greatest stress

b. Because all the legs have same extension and original length, the strain experienced is the same for all


Am I correct? I am really not sure, especially about the assumption that the extension is the same for all.

Thanks
 

Answers and Replies

  • #2
21,627
4,911

Homework Statement


A three-legged stool has one leg of aluminium (E = 7 x 1010 Pa), one copper (E = 11 x 1010 Pa) and one of steel (E = 20 x 1010) Pa. The legs have the same dimensions. If the load on the stool is at the exact center,
a. Which leg is under the greatest stress? Explain why
b. Which leg experience the greatest strain? Explain why


Homework Equations


stress = force / area
strain = extension / original length
young modulus = stress /strain
force = (E.A.extension) / original length


The Attempt at a Solution


a. All the legs have same dimensions means that the area are the same, so the stress is directly proportional to the force. Assuming they all have the same extension, then the force is directly proportional to young modulus. So the steel is under the greatest stress

b. Because all the legs have same extension and original length, the strain experienced is the same for all


Am I correct? I am really not sure, especially about the assumption that the extension is the same for all.

Thanks

What fraction of the load is carried by each leg? (This is a statics problem)
How do the stresses in the three legs compare?
 
  • #3
1,833
180
What fraction of the load is carried by each leg? (This is a statics problem)
How do the stresses in the three legs compare?

The leg each carries 1/3 of the load. I don't know how to relate that information to answer the question
 
  • #4
21,627
4,911
The leg each carries 1/3 of the load. I don't know how to relate that information to answer the question

If each leg carries the same load (force), and if stress is force per unit area (and the cross sectional areas of the legs are the same), what does this tell you about how the compressive stresses in the legs compare?
 
  • #5
1,833
180
If each leg carries the same load (force), and if stress is force per unit area (and the cross sectional areas of the legs are the same), what does this tell you about how the compressive stresses in the legs compare?

Oh I see. So the stress should be the same for all. Because the stress is the same, I can use formula of young modulus to compare the strain.

Thanks for the help
 

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