Identify the property that changes as a function of the geometrical dimensions of a section in structural materials:
Try it first: pick an option, then read the explanation.
Asked in SSC JE 23/03/2021 (Morning)
Detailed Explanation
Properties used in structural calculations fall into two groups: material properties, fixed by what the member is made of, and section (geometric) properties, fixed by its size and shape.
\[ I_{xx} = \int y^2\,dA \qquad I_{yy} = \int x^2\,dA \]
For a rectangle, \(I = \dfrac{bd^3}{12}\) — doubling the depth makes I eight times larger.
Why “Moment of inertia” Is Correct
Moment of inertia is calculated from the areas and distances that make up the section, so it changes with the section's dimensions. Density, Poisson's ratio and modulus of elasticity are the same for a small or a large piece of the same material.
| Section | Axis | Moment of inertia |
|---|---|---|
| Rectangle b × d | Centroidal, parallel to b | bd³/12 |
| Rectangle b × d | Base | bd³/3 |
| Triangle b × h | Centroidal, parallel to base | bh³/36 |
| Triangle b × h | Base | bh³/12 |
| Circle, diameter D | Diameter | πD⁴/64 |
| Circle, diameter D | Polar (centre) | πD⁴/32 |
| Semicircle, radius R | Diameter, or axis of symmetry | πR⁴/8 = πD⁴/128 |
| Semicircle, radius R | Centroidal, parallel to diameter | ≈ 0.1098R⁴ |
Why the Other Options Are Wrong
- A. Mass density: Density is a material property; it does not depend on section size.
- C. Poisson's ratio: Poisson's ratio is a material property.
- D. Modulus of elasticity: Modulus of elasticity is a material property.
Key Point
Section properties (A, I, Z, r) depend on geometry; E, μ, ρ depend on material.
Key Concepts for Students
- Section modulus Z = I/y_max.
- Flexural rigidity EI combines a material and a section property.
- Deep sections are efficient because I grows with depth cubed.
Practice more: this is question 7 in Moment MCQs – Part 1. Try the whole set and check every answer instantly.