Max Shear Stress in a Rectangular Beam
Mediumshear stress
A rectangular beam 200 mm wide × 300 mm deep carries a shear force of 60 kN. What is the maximum transverse shear stress?
- A1.5 MPa
- B1.0 MPa
- C3.0 MPa
- D0.75 MPa
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Answer: A. 1.5 MPa
For a rectangle the shear stress is parabolic with τmax = 1.5 V / A at the neutral axis. A = 200 · 300 = 60000 mm², so τmax = 1.5 · 60000 N / 60000 mm² = 1.5 MPa. 1.0 MPa is the average V/A, which underestimates the peak by a third.
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