GATE AE 2025 • Q55 NAT • 2 Marks Aerospace Structures

Aerospace Structures

Strength of Materials & Elasticity

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

Question Statement:

A 1 m long rod of 1 cm × 1 cm cross section is subjected to an axial tensile force of 35 kN. The Young's modulus of the material is 70 GPa. The cross-section of the deformed rod is 0.998 cm × 0.998 cm. The Poisson's ratio of the material is ________ (rounded off to one decimal place).

Official Answer Key:

0.4

Step-by-Step Solution & Explanation

### **Detailed Step-by-Step Solution (GATE AE 2025 Q.55)** **1. Intuitive Physical Setup & Given Parameters**: - Tensile bar: length $L = 1\text{ m}$. - Initial square cross-section: $b_0 = 1\text{ cm} = 0.01\text{ m}$, $A_0 = 1\text{ cm}^2 = 10^{-4}\text{ m}^2$. - Axial tensile force: $P = 35\text{ kN} = 35,000\text{ N}$. - Young's modulus: $E = 70\text{ GPa} = 70 \times 10^9\text{ N/m}^2$. - Deformed cross-section: $b = 0.998\text{ cm}$. We need to determine Poisson's ratio $\nu$ (rounded off to one decimal place). **2. Step-by-Step Mechanics of Materials Derivation**: 1. **Longitudinal (Axial) Strain ($\varepsilon_{\text{long}}$)**: Axial tensile stress: \sigma = \frac{P}{A_0} = \frac{35,000\text{ N}}{10^{-4}\text{ m}^2} = 350 \times 10^6\text{ Pa} = 350\text{ MPa} By Hooke's law: \varepsilon_{\text{long}} = \frac{\sigma}{E} = \frac{350 \times 10^6\text{ Pa}}{70 \times 10^9\text{ Pa}} = 5 \times 10^{-3} = 0.005 2. **Lateral Strain ($\varepsilon_{\text{lat}}$)**: \Delta b = b - b_0 = 0.998\text{ cm} - 1.000\text{ cm} = -0.002\text{ cm} \varepsilon_{\text{lat}} = \frac{\Delta b}{b_0} = \frac{-0.002}{1.000} = -0.002 3. **Definition of Poisson's Ratio ($\nu$)**: \nu = -\frac{\varepsilon_{\text{lat}}}{\varepsilon_{\text{long}}} = -\frac{-0.002}{0.005} = \frac{2}{5} = 0.4 **3. Comprehensive Options & Distractor Analysis**: - **Evaluation Criteria**: Numerical Answer Type (NAT). - **Exact Analytical Result**: $\nu = 0.4$. - **Rounding Requirement**: One decimal place $\implies \mathbf{0.4}$. **4. Official Master Key & Exam Takeaway**: - **Official Answer Key**: **0.4** (Acceptable Range: **0.4 to 0.4**) - **Exam Takeaway**: $\nu = |\varepsilon_{\text{lat}}| / \varepsilon_{\text{long}} = \frac{|\Delta b / b_0|}{\sigma / E} = \frac{0.002}{0.005} = 0.4$.
← Previous (Q54) All 2025 Questions Next (Q56) →

Related Strength of Materials & Elasticity Solved Questions

View All Strength of Materials & Elasticity PYQs →
GATE AE 2026 Q12 MCQ • 1M

The Fourier series representation of a square wave is shown in the figure below. The fluctuations seen near x = ±1 are named after which one of the following scientists?
GATE AE 2026 Q40 MCQ • 2M

Consider a unit square body as shown in the figure below. The body is subjected to the deformation field u = -ay and v = ax, where 'a' is a constant. Due to the application of this deformation field, the body undergoes _______ in the x-y plane.
GATE AE 2026 Q45 MSQ • 2M

The deformation of an open-section bar subjected to pure torsion can be solved by choosing an appropriate Prandtl stress function. Which of the following statements is/are true about the Prandtl stress function?
GATE AE 2026 Q57 NAT • 2M

WA and WB are the respective maximum take-off weights of an aircraft for two ambient air conditions given below. Condition A: p = 1 bar, T = 50 oC; Condition B: p = 0.66 bar, T = -30 oC If all other parameters relevant for take-off are kept the same in these two conditions, the ratio WB/WA is ________ (rounded off to 3 decimal places).

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