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A thin cylinder of 100 mm internal diameter and 5 mm thickness is subjected to an internal pressure of 10 MPa and a torque of 2000 Nm. Calculate the magnitudes of the principal stresses.
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- 109.75 & 40.25 MPa
- 19.75 & 40.25 MPa
- 101.75 & 41.25 MPa
- 19.75 & 44.25 MPa
- None of these
Correct Option: A
di = o.1 m, do = di + 2t
t = 0.005 m, do = 0.11 m
T = 2000 Nm
P = 10 MPa
| σc = | = | = 50 MPa | ||
| 4t | 4 × 0.005 |
| σc = | = | = 100 MPa | ||
| 2t | 2 × 0.005 |
| = | ||||
| J | r |
| τ = | ||
| J |
| = | 200 × | ||
| 2 | |||
| (0.114 - 0.14) | |||
| 32 | |||
| σ1 , 2 = | ± √ |  |  |  | ² | + τ²xy |  | ||
| 2 | 2 |
| = | ± √ | | | | ² | + 24.142 | | ||
| 2 | 2 |
= 75 ± 34.75
= 109.75 & 40.25 MPa
