Question

Match List - I with List - II.

Choose the correct answer from the options given below :

• A. A-I, B-III, C-IV, D-II
• B. A-II, B-I, C-II, D-IV
• C. A-IV, B-II, C-III, D-I
• D. A-II, B-IV, C-I, D-III

Hint:

The shape factor depends only on the geometry of the cross-section. For an I-section, it typically ranges between 1.12 and 1.15, indicating less reserve strength compared to solid sections.

Answer 1

The Correct Option is D

Concept: The shape factor ($S$) of a cross-section is the ratio of the plastic moment ($M_p$) to the yield moment ($M_y$). It represents the reserve strength of a section beyond its elastic limit. The formula is $S = Z_p / Z_e$, where $Z_p$ is the plastic section modulus and $Z_e$ is the elastic section modulus.

Step 1: Evaluate shape factors for standard geometries.

• Rectangle (A): For a rectangular section, $Z_p = bd^2/4$ and $Z_e = bd^2/6$. Thus, $S = 1.5$. Matches with II.
• Circular (B): For a solid circular section, $Z_p = d^3/6$ and $Z_e = \pi d^3/32$. Thus, $S = 16/(3\pi) \approx 1.7$. Matches with IV.
• Triangular (C): For a solid triangle (with base parallel to the axis), the shape factor is $2.34$. Matches with I.
• Diamond (D): For a diamond section (square with diagonal vertical), the shape factor is $2.0$. Matches with III.

Step 2: Final Matching.
The correct sequence is A-II, B-IV, C-I, D-III.