Max In-Plane Shear Stress at a Point
MediumMohr's circlemaximum shear
At a point, σx = 80 MPa, σy = 20 MPa and τxy = 30 MPa. The maximum in-plane shear stress is most nearly:
- A30.0 MPa
- B37.5 MPa
- C42.4 MPa
- D50.0 MPa
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Answer: C. 42.4 MPa
Equation: the maximum in-plane shear stress is the radius of Mohr's circle, τmax = R = √[((σx − σy)/2)² + τxy²]. Values: σx = 80 MPa and σy = 20 MPa are positive because the arrows point outward (tension). τxy = +30 MPa is positive because on the right (+x) face it points up (+y). Step 1: half the difference of normal stresses, (80 − 20)/2 = 30 MPa. Step 2: τmax = √(30² + 30²) = √1800 = 42.4 MPa. 30 MPa is just the applied τxy, and 50 MPa is the circle's centre, not its radius.
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