GATE AE 2017 • Q53 NAT • 2 Marks Aerospace Structures

Aerospace Structures

Thin-Walled Structures

Subtopic: Bending of Unsymmetrical Thin-Walled Sections

Question Statement:

The maximum normal stress in MN/m$^2$ for the thin-walled beam of square cross-section (side $b = 100$ mm, thickness $t = 2$ mm) under an applied bending moment of $M = 2$ kN-m is _________ (round off to the nearest integer).

Official Answer Key:

75.0

Step-by-Step Solution & Explanation

### **Detailed Step-by-Step Solution (GATE AE 2017 Q.53)** **1. Intuitive Physical Setup & Given Parameters**: - Square box section: outer dimension $b = 100\text{ mm} = 0.1\text{ m}$. - Wall thickness: $t = 2\text{ mm} = 0.002\text{ m}$. - Applied bending moment: $M = 2\text{ kN m} = 2000\text{ N m}$. **2. Step-by-Step Structural Derivation**: 1. **Area Moment of Inertia of Thin-Walled Square Tube**: I = \frac{2}{3} b^3 t = \frac{2}{3} (0.1)^3 (0.002) = \frac{2}{3} \times 10^{-3} \times 0.002 = \frac{4}{3} \times 10^{-6}\text{ m}^4 \approx 1.333 \times 10^{-6}\text{ m}^4 2. **Maximum Bending Stress**: \sigma_{\max} = \frac{M y_{\max}}{I} = \frac{M (b/2)}{I} \sigma_{\max} = \frac{2000 \times 0.05}{\frac{4}{3} \times 10^{-6}} = \frac{100}{1.333 \times 10^{-6}} = 75 \times 10^6\text{ N/m}^2 = 75.0\text{ MN/m}^2 The maximum normal stress is exactly **75 MN/m$^2$**. **3. Comprehensive Options & Distractor Analysis**: - **Question Type**: Numerical Answer Type (NAT). - **Exact Analytical Result**: **75.0 MN/m$^2$** (Acceptable Range: [73, 77]). **4. Official Master Key & Exam Takeaway**: - **Official Answer**: **75.0** - **Key Formula**: $\sigma = \frac{M y}{I}$ with $I = \frac{2}{3} b^3 t$ for thin square tube.
← Previous (Q52) All 2017 Questions Next (Q54) →

Related Thin-Walled Structures Solved Questions

View All Thin-Walled Structures PYQs →
GATE AE 2026 Q17 MCQ • 1M

A cantilever beam with an unsymmetric cross-section is subjected to a transverse shear force (P) at its free end. P acts at the shear center of the beam cross-section. Which one of the following statements is TRUE about the deformation of this beam?
GATE AE 2026 Q58 NAT • 2M

A thin-walled circular tube is made of a material whose magnitude of the ultimate strength, both in tension and compression, is 200 MPa. The mean radius of the tube is 0.2 m and the wall thickness is 0.004 m. Based on the maximum stress criteria, the maximum torque that the tube can sustain is ________ kN-m (round off to the nearest integer).
GATE AE 2025 Q60 NAT • 2M

Two designs A and B, shown in the figure, are proposed for a thin-walled closed section that is expected to carry only torque. Both A and B have a semi-circular nose, and are made of the same material with a wall thickness of 1 mm. With strength as the only criterion for failure, the ratio of maximum torque that B can support to the maximum torque that A can support is__ (rounded off to two decimal places).
GATE AE 2024 Q54 NAT • 2M

The cross section of a thin-walled beam with uniform wall thickness t, shown in the figure, is subjected to a bending moment Mx = 10 Nm. If h = 1 m and t = 0.00 1 m, the magnitude of maximum normal stress in the cross section is _________N/m^2 (answer in integer).

Practice This in Real CBT Exam Interface

Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.

Launch CBT Mock Test