Strength of materials - Structures - Aerospace Engineering Previous Year Questions

1

2025 · Aerospace Engineering · Structures · Strength of materials

Aerospace Engineering (AE) 2025

For a homogeneous, isotropic material, the relation between the shear modulus (\(G\)), Young's modulus (\(E\)), and Poisson's ratio (\(\nu\)) is ____.

A

\(G = 2E(1 + \nu)\)

B

\(2G = E(1 + \nu)\)

C

\(E = 2G(1 + \nu)\)

D

\(2E = G(1 + \nu)\)

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2

2025 · Aerospace Engineering · Structures · Strength of materials

Aerospace Engineering (AE) 2025

A simply supported horizontal beam is subjected to a distributed transverse load varying linearly from \(q_0\) at A to zero at B, as shown in the figure. Which one of the following options is correct?

A

The magnitude of the vertical reaction force at A is larger than that at B.

B

The magnitude of the vertical reaction force at B is larger than that at A.

C

The magnitudes of the vertical reaction forces at A and B are equal.

D

The reactions at points A and B are indeterminate.

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3

2025 · Aerospace Engineering · Structures · Strength of materials

Aerospace Engineering (AE) 2025

A stress field is given by \(\sigma_{xx} = \sigma_{zz} = C_1 y\), \(\sigma_{yy} = C_2 y\), \(\tau_{xy} = \tau_{yz} = \tau_{zx} = 0\), where \(C_1\) and \(C_2\) are non-zero constants. If the stress field satisfies equilibrium, which one of the following options is correct?

A

There is no body force per unit volume.

B

There is a constant body force per unit volume in the y-direction.

C

The body force per unit volume varies linearly in the y-direction.

D

The direction of the body force per unit volume depends on the value of \(C_1\).

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4

2025 · Aerospace Engineering · Structures · Strength of materials

Aerospace Engineering (AE) 2025

A uniform symmetric cross-section cantilever beam of length \(L\) is subjected to a transverse force \(P\) at the free end, as shown in the figure. The Young's modulus of the material is E and the moment of inertia is I. Ignoring the contributions due to transverse shear, the strain energy stored in the beam is ____.

A

\(\frac{P^2 L^3}{6EI}\)

B

\(\frac{P L^3}{3EI}\)

C

\(\frac{P L^3}{6EI}\)

D

\(\frac{P^2 L^3}{3EI}\)

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5

2025 · Aerospace Engineering · Structures · Strength of materials

Aerospace Engineering (AE) 2025

In the given figure, plate ABCD in its undeformed configuration (solid line) is a rhombus with all the internal angles being 90°. The lengths of the undeformed diagonals are 20 cm. ABCD deforms as shown by the dotted lines. Upon deformation, diagonal AC reduces to 19.96 cm and BD increases to 20.04 cm. In the given x-y coordinate system, the engineering shear strain \(\gamma_{xy}\) is equal to ____.

A

0

B

0.002

C

0.004

D

-0.004

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6

2025 · Aerospace Engineering · Structures · Strength of materials

Aerospace Engineering (AE) 2025

A 1 m long rod is to be designed to support an axial tensile load P (P >> weight of the rod). The material for the rod is to be chosen from one of the four provided in the table. Using strength-based failure criterion for design, which material results in the lowest weight of the rod?

A

Material α

B

Material β

C

Material γ

D

Material δ

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7

2025 · Aerospace Engineering · Structures · Strength of materials

Aerospace Engineering (AE) 2025

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).

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8

2025 · Aerospace Engineering · Structures · Strength of materials

Aerospace Engineering (AE) 2025

For a three-bar truss loaded as shown in the figure, the magnitude of the force in the horizontal member AB is ________ N (answer in integer).

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9

2025 · Aerospace Engineering · Structures · Strength of materials

Aerospace Engineering (AE) 2025

A prismatic vertical column of cross-section \(a \times 0.5a\) and length \(l\) is rigidly fixed at the bottom and free at the top. A compressive force \(P\) is applied along the centroidal axis at the top surface. The Young’s modulus of the material is 200 GPa and the uniaxial yield stress is 400 MPa. If the critical value of \(P\) for yielding and for buckling of the column are equal, the value of \(\left(\frac{l}{a}\right)\) is ________ (rounded off to one decimal place).

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10

2025 · Aerospace Engineering · Structures · Strength of materials

Aerospace Engineering (AE) 2025

A thin flat plate is subjected to the following stresses: \(\sigma_{xx} = 160\) MPa; \(\sigma_{yy} = 40\) MPa; \(\tau_{xy} = 80\) MPa. Factor of safety is defined as the ratio of the yield stress to the applied stress. The yield stress of the material under uniaxial tensile load is 250 MPa. The factor of safety for the plate assuming that material failure is governed by the von Mises criterion is ________ (rounded off to two decimal places).

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11

2025 · Aerospace Engineering · Structures · Strength of materials

Aerospace Engineering (AE) 2025

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).

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12

2026 · Aerospace Engineering · Structures · Strength of materials

Aerospace Engineering (AE) 2026

The number of independent elastic constants that a fully anisotropic linear elastic material can have is ______.

A

36

B

21

C

10

D

2

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13

2026 · Aerospace Engineering · Structures · Strength of materials

Aerospace Engineering (AE) 2026

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?

A

The beam undergoes only torsion

B

The beam undergoes only bending

C

The beam undergoes both torsion and bending

D

The beam undergoes neither torsion nor bending

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14

2026 · Aerospace Engineering · Structures · Strength of materials

Aerospace Engineering (AE) 2026

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).

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15

2026 · Aerospace Engineering · Structures · Strength of materials

Aerospace Engineering (AE) 2026

A stepped cantilever beam, made of a material having Young's modulus \(E = 200 \text{ GPa}\), is shown in the figure below. The length and the moment of inertia of the beam from point A to B are \(L_1 = 100 \text{ mm}\) and \(I_1 = 100 \text{ mm}^4\), respectively. The length and the moment of inertia of the beam from point B to C are \(L_2 = 100 \text{ mm}\) and \(I_2 = 700 \text{ mm}^4\), respectively. A shear force \(P = 30 \text{ N}\) is applied at point A of the beam. The magnitude of the deflection of the beam at point A is __________ mm (rounded off to 1 decimal place).

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