Unit 23: Shear Stress & Strain
Practice Problems
Note: problem difficulty is ranked using a star system.
(*) One-star problems are fundamental to the unit, and can be done relatively quickly. Use these problems to introduce yourself to the material.
(**) Two-star problems are more difficult, and require an understanding of one or two key concepts. Use these problems to test your understanding of the material.
(***) Three-star problems are the most difficult, and require some creative thinking in addition to a deep familiarity with multiple key concepts. Use these problems to challenge yourself; if you can complete one of these, you’re on your way to mastering the material.
*Q23.1) A cube of jello (sidelength 10cm and shear modulus 200 kPa) rests on a table with its bottom face fixed in place. If you push on the top surface with a force of 50 N, by how much would the top surface be laterally displaced relative to the bottom surface?
**Q23.2) A hollow steel cylinder (shear modulus 79.3 GPa) has an inner radius of of 2cm, an outer radius of 3cm, and a length of 30cm.
a) What shear force would cause a shear strain of 5%?
b) What lateral displacement of the top surface relative to the bottom surface corresponds to a shear strain of 5%?
***Q23.3) Two hollow cylinders made of the same material are subjected to shear stresses. Both cylinders have thicknesses equal to the inner radius of the smaller cylinder, and the larger cylinder has twice the inner radius of the smaller. If both cylinders are to experience the same strain, what’s the ratio of the shear force experienced by the larger cylinder to that experienced by the smaller one?