For standard rolled I-beam (rolled steel beam) sections used in practice, the plastic shape factor (Mp/My) generally lies within which range?

Introduction / Context:The plastic shape factor S = Mp/My measures the reserve bending capacity beyond first yield. For rolled I-beams (compact proportions without local buckling), S is only modestly above 1.0 because flanges carry much of the plasticity while the web contributes less than in a rectangular section.

Given Data / Assumptions:

• Standard rolled I-beam shapes with usual proportions.
• Elastic–perfectly plastic idealization; no premature local buckling.

Concept / Approach:Typical tabulated values show S ≈ 1.10–1.20 for common I-sections, compared to S = 1.50 for rectangles. The exact value depends on flange and web dimensions, but remains within this narrow band for standard sections.

Step-by-Step Solution:1) Define S = Z_p / Z (plastic to elastic section modulus).2) Recognize I-beams have flanges far from the neutral axis (efficient elastically), but plastic neutral axis movement does not raise capacity as much as in rectangles.3) Thus, S clusters around 1.1–1.2 in common tables.

Verification / Alternative check:Design manuals (steel codes) consistently list S in this range for rolled I-sections; values beyond 1.3 are atypical for standard rolled beams.

Why Other Options Are Wrong:

• 1.20–1.30, 1.30–1.40, 1.40–1.50: Too high for standard rolled I-beams; such factors correspond to other shapes or special proportions.

Common Pitfalls:

• Misapplying the rectangular section value (1.5) to I-beams.
• Ignoring slenderness/local buckling, which can reduce plastic capacity.

Final Answer:1.10 to 1.20.