In plastic analysis, what is the shape factor (M_p / M_y) for a solid circular cross-section?

Introduction / Context:The shape factor f = M_p / M_y indicates the reserve plastic strength beyond first yield and depends only on the cross-section's geometry. For a solid circle, f is higher than for a rectangle because more material lies away from the neutral axis and can contribute under plastic redistribution.

Given Data / Assumptions:

• Elastic–perfectly plastic bending model.
• Solid circular cross-section.
• Plane sections remain plane; no shear yield limitation.

Concept / Approach:Yield moment M_y is based on the elastic section modulus; plastic moment M_p is computed from equal-area compression and tension blocks at yield stress. For a circle, the resulting ratio is approximately 1.70 (commonly rounded to 1.7) and is a standard handbook value used in plastic design.

Step-by-Step Solution:Step 1: Recognize f = M_p / M_y is geometric.Step 2: Use the known result for a solid circle: f ≈ 1.698 → 1.7.Step 3: Select 1.7 from the options.

Verification / Alternative check:Reference tables list f_rect = 1.5, f_circle ≈ 1.7, f_triangle ≈ 2.34, validating the chosen value.

Why Other Options Are Wrong:

• 1.5: For a rectangle.
• 1.6, 1.75: Near but not equal to the standard circular value.

Common Pitfalls:Assuming the same shape factor across different section shapes; mixing up rectangle and circle values.

Final Answer:1.7