Project ForgeStrength of Materials
Stress & Strain
GATE 2007
Medium
For the same machine frame (normal stress 67.9 MPa, shear stress 56.6 MPa at point P), the maximum principal stress in MPa and the orientation of the corresponding principal plane in degrees are respectively
- A−32.0 and −29.52
- B100.0 and 60.48
- C−32.0 and 60.48
- 100.0 and −29.52
Explanation
σ1,2 = σ/2 ± √[(σ/2)²+τ²] = 33.95 ± √(1152.6+3203.6) = 33.95±66.0, giving σmax≈100.0 MPa (and σmin≈−32.1 MPa). The corresponding principal-plane orientation for the maximum-stress plane is −29.52° (with the orthogonal plane, containing σmin, at 60.48°).
Source: GATE ME 2007 (2007)
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