Plastic Analysis MCQ with answer and solution

Concept

Shape factor is the ratio of plastic section modulus to elastic section modulus of a beam section.

Formula

Shape Factor (S) = Z_p / Z_e

Step-by-step solution

1. For a rectangular section of width b and depth d, the elastic section modulus is Z_e = (b × d²) / 6. 2. The plastic section modulus is Z_p = (b × d²) / 4. 3. Divide Z_p by Z_e to find the shape factor: S = ((b × d²) / 4) / ((b × d²) / 6) = 6 / 4 = 1.5. Answer: (B) 1.5

Explanation

Shape factor shows the reserve strength of a section after yield stress is reached. For a solid rectangular section, the shape factor is always 1.5.

Why the other options are wrong

A: 1.0 is the minimum theoretical limit for a section with material placed far from the neutral axis. C: 1.7 is the shape factor for a solid circular section. D: 2.0 is the shape factor for a diamond or square section with diagonal parallel to neutral axis.

Shortcut

Remember standard shape factors: Rectangular = 1.5, Triangular = 2.34, Circular = 1.7, Diamond = 2.0.

Common mistake

Confusing the shape factor of a rectangular section (1.5) with a circular section (1.7) or diamond section (2.0).