A body is loaded elastically so that strain in y-direction (ey) = 0 and σz = 0. Take σx and σy as finite. What is the value of strain in z-direction (ez) in terms of stress in x-direction (σx), Young's Modulus (E), and Poisson's ratio (ν)?
- Aez = σx ν(1 + 2ν) / E
- Bez = σx ν(1 - 4ν) / E
- Cez = σx (1 + ν) / E
- Dez = -σx ν(1 + ν) / ECorrect
Solution
Concept
Use Hooke's law in 3D. Put ey = 0 to find σy, then find ez.
Formula
ex = [σx - ν(σy + σz)]/E; ey = [σy - ν(σz + σx)]/E; ez = [σz - ν(σx + σy)]/E
Step-by-step solution
1. ey = [σy - ν(σz + σx)]/E = 0 and σz = 0. 2. So σy - νσx = 0, which gives σy = νσx. 3. ez = [σz - ν(σx + σ
Correct answer: D) e_z = -σ_x ν(1 + ν) / E
