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Civil Engineering QUESTION #2124
Question 1
The plastic moment capacity \(M_p\) of a steel section in plastic analysis is related to the elastic moment capacity \(M_y\) by the shape factor \(f\). For a rectangular cross-section, the shape factor is:
  • 1.0
  • 1.12
  • 1.5✔️
  • 2.0
Correct Answer Explanation
Shape factor \(f = \dfrac{M_p}{M_y} = \dfrac{Z_p}{Z_e}\), where \(Z_p\) = plastic section modulus and \(Z_e\) = elastic section modulus. For a rectangle: \(Z_p = \dfrac{bd^2}{4}\) and \(Z_e = \dfrac{bd^2}{6}\). Therefore \(f = \dfrac{bd^2/4}{bd^2/6} = \dfrac{6}{4} = 1.5\). For I-sections, \(f \approx 1.12\). The shape factor quantifies the reserve strength beyond first yield — the basis of plastic design.