Max Bending Stress in a Rectangular Beam
Mediumbending stressflexure formula
A rectangular beam 200 mm wide and 400 mm deep carries a bending moment of 50 kN·m. What is the maximum bending stress?
- A9.4 MPa
- B4.7 MPa
- C18.8 MPa
- D37.5 MPa
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Answer: A. 9.4 MPa
I = b h3 / 12 = 200 · 4003 / 12 = 1.067 × 109 mm4, and c = h/2 = 200 mm. σ = M c / I = (50 × 106 N·mm)(200) / 1.067 × 109 = 9.375 ≈ 9.4 MPa. Equivalently σ = M / S with S = b h2 / 6 = 5.33 × 106 mm3. 4.7 MPa uses c = h/4; 18.8 uses c = h.
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