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A square plate of dimension L × L is subjected to a uniform pressure load p = 250 MPa on its edges as shown in the figure. Assume plane stress conditions. The Young's modulus E= 200 GPa.
The deformed shape is a square of dimension L – 2δ. If L = 2 m and δ = 0.001 m, the Poisson's ratio of the piate material is ________.
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- 0.2
- 7
- 9
- 0.8
Correct Option: A
| = | (1 − v) | ||
| V | E |
εv = εx + εy εz
| εv = |  | − |  | + | | − | | − | |||||
| E | E | E | E | E |
Due to plane stress condition εz = 0
| εv = | × 2 × (1 − μ) | |
| E |
| = − | × 2(1 − μ) | ||
| 22 | E |
| − 2 × 10−3 = | × 2 × (1 − μ) | |
| 200 × 103 |
| = 1 − μ | |
| 200 |
0.8 = 1 − μ
∴ μ = 0.2
