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Strength of Materials(29)Flight Vehicle Structures(9)Structural Dynamics(11)Theory of Elasticity(3)

Strength of Materials

29 Questions

GATE→2026→Structures→Strength of Materials

Q1

MSQ[1 Mark]

The state of stress at a point in a 2-D body, in the x-y Cartesian coordinate system, is represented in matrix form as [σ]. The transformation matrix [Q] rotates the coordinate system to a new x'-y' Cartesian coordinate system. Select the CORRECT option(s) that represent(s) the state of stress in the new coordinate system.

(A)

[Q] [σ] [Q]T

(B)

[Q] [σ] [Q]–1

(C)

([Q]–1)T [σ] [Q]T

(D)

[Q]–1 [σ] [Q]

Explanation

GATE→2026→Structures→Strength of Materials

Q2

MCQ[2 Marks]

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.

(A)

biaxial deformation

(B)

pure shear

(C)

pure bending

(D)

rigid body rotation

Explanation

GATE→2026→Structures→Strength of Materials

Q3

NAT[2 Marks]

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).

Explanation

GATE→2026→Structures→Strength of Materials

Q4

NAT[2 Marks]

A stepped cantilever beam, made of a material having Young’s modulus E = 200 GPa, is shown in the figure below. The length and the moment of inertia of the beam from point A to B are L1 = 100 mm and I1 = 100 mm4, respectively. The length and the moment of inertia of the beam from point B to C are L2 = 100 mm and I2 = 700 mm4, respectively. A shear force P = 30 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).

Explanation

GATE→2025→Structures→Strength of Materials

Q5

MCQ[1 Mark]

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

(A)

𝐺= 2𝐸(1 + 𝜈)

(B)

2𝐺= 𝐸(1 + 𝜈)

(C)

𝐸= 2𝐺(1 + 𝜈)

(D)

2𝐸= 𝐺(1 + 𝜈)

Explanation

GATE→2025→Structures→Strength of Materials

Q6

MCQ[1 Mark]

In the given figure, plate ABCD in its undeformed configuration (solid line) is a rhombus with all the internal angles being 90o. 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 𝛾𝑥𝑦 is equal to ____.

(A)

0

(B)

0.002

(C)

0.004

(D)

-0.004

Explanation

GATE→2025→Structures→Strength of Materials

Q7

MCQ[2 Marks]

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? Properties Material α Material β Material  Material  Density (kg/m3) 2700 4500 7800 9000 Young’s modulus (GPa) 70 115 200 130 Yield Strength (MPa) 270 900 520 540

(A)

Material α

(B)

Material β

(C)

Material 

(D)

Material 

Explanation

GATE→2025→Structures→Strength of Materials

Q8

NAT[2 Marks]

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).

Explanation

GATE→2025→Structures→Strength of Materials

Q9

NAT[2 Marks]

A prismatic vertical column of cross-section 𝑎× 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 ( 𝑙 𝑎) is _____(rounded off to one decimal place).

Explanation

GATE→2025→Structures→Strength of Materials

Q10

NAT[2 Marks]

A thin flat plate is subjected to the following stresses: 𝜎𝑥𝑥= 160 MPa; 𝜎𝑦𝑦= 40 MPa; 𝜏𝑥𝑦= 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).

Explanation

GATE→2024→Structures→Strength of Materials

Q11

NAT[1 Mark]

A material has Poisson’s ratio 𝜈= 0.5 and Young’s modulus E=2500 MPa. The percentage change in its volume when subjected to a hydrostatic stress of magnitude 10 MPa is ______ (answer in integer).

Explanation

GATE→2024→Structures→Strength of Materials

Q12

NAT[2 Marks]

Consider the plane strain field given by 𝜀𝑥𝑥= 10 𝑥𝑦2, 𝜀𝑦𝑦= −5 𝑥2𝑦 and 𝛾𝑥𝑦= 𝐴 𝑥𝑦 (2𝑥−𝑦) where, A is a constant and 𝛾𝑥𝑦 is the engineering shear strain. The value of the constant A for the strain field to be compatible is _____________ (rounded off to 1 decimal place).

Explanation

GATE→2023→Structures→Strength of Materials

Q13

MSQ[1 Mark]

Which of the following statement(s) is/are true about the state of stress in a plane?

(A)

Maximum or major principal stress is algebraically the largest direct stress at a point.

(B)

The magnitude of minor principal stress cannot be greater than the magnitude of major principal stress.

(C)

The planes of maximum shear stress are inclined at 90 degrees to the principal axes.

(D)

The normal stresses along the planes of maximum shear stress are equal. Aerospace Engineering (AE)

Explanation

GATE→2023→Structures→Strength of Materials

Q14

MSQ[2 Marks]

Which of the following statement(s) about the elastic flexural buckling load of columns is/are correct?

(A)

The buckling load increases with increase in flexural rigidity of the column.

(B)

The buckling load increases with increase in the length of the column.

(C)

The boundary conditions of the column affect the buckling load.

(D)

The buckling load is NOT directly dependent on the density of the material used for the column.

Explanation

GATE→2023→Structures→Strength of Materials

Q15

NAT[2 Marks]

The thickness of a uniform hollow circular shaft is equal to the difference between the outer radius and the inner radius. The ratio of the inner diameter to outer diameter of the shaft is 0.5. For the shaft reacting to an applied torque, the ratio of the maximum shear stress  to the maximum shear stress thin − wall obtained using the thin-wall approximation is . (round off to one decimal place) Aerospace Engineering (AE)

Explanation

GATE→2023→Structures→Strength of Materials

Q16

NAT[2 Marks]

A rigid bar AB is subjected to a uniformly distributed load of 100 N/m as shown in the figure. The bar is supported by rod CD, with A, C, and D as pin joints. The rod CD has axial stiffness of 40 N/mm. The vertical deflection at point D is __________ mm. (round off to nearest integer)

Explanation

GATE→2023→Structures→Strength of Materials

Q17

NAT[2 Marks]

A cantilever beam of length 2a is loaded at the tip with force F as shown in the figure. The beam is supported in the middle by a roller with a pin. The magnitude of moment reaction at the built-in end of the beam is αFa, where αis ______ . (round off to one decimal place)

Explanation

GATE→2023→Structures→Strength of Materials

Q18

NAT[2 Marks]

Consider a thin-walled cylindrical pressure vessel made of an alloy with yield strength of 300 MPa. The vessel has end caps to contain the pressure. The ratio of radius of the vessel to its wall thickness is 100. As per the von Mises yield criterion, the internal pressure that would cause the failure of the vessel is _____ MPa. (round off to two decimal places)

Explanation

GATE→2022→Structures→Strength of Materials

Q19

MCQ[1 Mark]

A beam with a symmetrical T-shaped cross-section is subjected to pure bending. The maximum magnitude of the normal stress is realised:

(A)

only at the top fibres of the cross-section

(B)

only at the bottom fibres of the cross-section

(C)

both at the top and bottom fibres of the cross-section

(D)

only at the centroidal fibres of the cross-section

Explanation

GATE→2022→Structures→Strength of Materials

Q20

MCQ[1 Mark]

A three-member truss is simply supported at Q and R, and loaded at P by a horizontal force F as shown. The force in QR is

(A)

0

(B)

F (tensile)

(C)

F / sqrt(2) (compressive)

(D)

sqrt(2) F (tensile)

Explanation

GATE→2022→Structures→Strength of Materials

Q21

MSQ[1 Mark]

Let $\sigma$ and $\tau$ represent normal stress and shear stress on a plane, respectively. The Mohr circle(s) that may possibly represent the state of stress at points in a beam of rectangular cross-section under pure bending is/are:

(A)

A

(B)

B

(C)

C

(D)

D

Explanation

GATE→2022→Structures→Strength of Materials

Q22

MSQ[1 Mark]

An isotropic linear elastic material point under plane strain condition in the x-y plane always obeys:

(A)

out-of-plane normal strain, epsilon_zz = 0

(B)

out-of-plane normal stress, sigma_zz = 0

(C)

out-of-plane shear stress, tau_xz = 0

(D)

out-of-plane shear strain, gamma_xz = 0

Explanation

GATE→2022→Structures→Strength of Materials

Q23

NAT[1 Mark]

The two-dimensional plane-stress state at a point is: $\sigma_{xx} = 110$ MPa; $\sigma_{yy} = 30$ MPa; $\tau_{xy} = 40$ MPa. The normal stress, $\sigma_n$, on a plane inclined $45^{\circ}$ is ______ (round off to the nearest integer).

Explanation

GATE→2022→Structures→Strength of Materials

Q24

MCQ[2 Marks]

A horizontal load $F$ is applied at point R on a two-member truss, as shown in the figure. Both members are prismatic with cross-sectional area $A_0$ and Young's modulus $E$. The horizontal displacement of point R is:

(A)

0

(B)

Fl / (EA_0)

(C)

sqrt(2) Fl / (EA_0)

(D)

2 Fl / (EA_0)

Explanation

GATE→2022→Structures→Strength of Materials

Q25

NAT[2 Marks]

A cantilever PQ of rectangular cross-section is subjected to transverse load $F$ at its mid-point. Case I: Q is free. Case II: Q is simply supported. The ratio of the magnitude of maximum bending stress at P in Case I to that in Case II is ______ (round off to one decimal place).

Explanation

GATE→2022→Structures→Strength of Materials

Q26

NAT[2 Marks]

A simply supported Aluminium column of length $1\text{ m}$ and rectangular cross-section $w \times t$ with $t \le w$, is subjected to axial compressive loading. Young's modulus is $70\text{ GPa}$, yield stress $120\text{ MPa}$. The value of $t$ at which failure load for yielding and buckling coincide is ______ mm.

Explanation

GATE→2022→Structures→Strength of Materials

Q27

NAT[2 Marks]

A $0.5\text{-m}$ long thin-walled circular shaft of radius $2\text{ cm}$ is designed for axial load $7.4\text{ kN}$ and torque $148\text{ Nm}$. Allowable stress under uniaxial tension is $100\text{ MPa}$. Using maximum principal stress criterion, minimum thickness $t$ is ______ mm (round off to nearest integer).

Explanation

GATE→2022→Structures→Strength of Materials

Q28

NAT[2 Marks]

A $10\text{ kN}$ axial load is applied eccentrically on a rod of square cross-section ($1\text{ cm} \times 1\text{ cm}$). Strains measured by two strain gages are $\epsilon_1 = 0.0016$ and $\epsilon_2 = 0.0004$. The eccentricity in loading, $e$, is ______ mm.

Explanation

GATE→2022→Structures→Strength of Materials

Q29

NAT[2 Marks]

For a thin-walled I section, flange width and web height are $2b = 20\text{ mm}$, thickness $0.6\text{ mm}$. Second moment of area about horizontal centroidal axis is ______ $\text{mm}^4$.

Explanation

Flight Vehicle Structures

9 Questions

GATE→2026→Structures→Flight Vehicle Structures

Q30

MCQ[1 Mark]

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

Explanation

GATE→2025→Structures→Flight Vehicle Structures

Q31

MCQ[1 Mark]

A simply supported horizontal beam is subjected to a distributed transverse load varying linearly from 𝑞0 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.

Explanation

GATE→2025→Structures→Flight Vehicle Structures

Q32

MCQ[1 Mark]

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)

𝑃2𝐿3 6EI

(B)

𝑃𝐿3 3EI

(C)

𝑃𝐿3 6EI

(D)

𝑃2𝐿3 3EI

Explanation

GATE→2025→Structures→Flight Vehicle Structures

Q33

NAT[2 Marks]

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).

Explanation

GATE→2025→Structures→Flight Vehicle Structures

Q34

NAT[2 Marks]

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).

Explanation

GATE→2023→Structures→Flight Vehicle Structures

Q35

MCQ[1 Mark]

Consider the four basic symmetrical flight loading conditions corresponding to the corners of a typical V-n diagram. For one of these flight loading conditions, it is observed that (i) the compressive bending stresses have a maximum value in the bottom aft region (see figure) of the wing cross-section; and (ii) the tensile bending stresses are maximum in the upper forward region (see figure) of the wing cross-section. For the preceding observations, select the corresponding flight loading condition from the options given.

(A)

Positive high angle of attack

(B)

Positive low angle of attack

(C)

Negative high angle of attack

(D)

Negative low angle of attack Aerospace Engineering (AE)

Explanation

GATE→2023→Structures→Flight Vehicle Structures

Q36

MSQ[1 Mark]

Which of the following statement(s) is/are true about the ribs of an airplane wing with semi-monocoque construction?

(A)

For a rectangular planform wing, the dimensions of the ribs DO NOT depend on their spanwise position in the wing.

(B)

Ribs increase the column buckling stress of longitudinal stiffeners connected to them.

(C)

Ribs increase plate buckling stress of the skin panels.

(D)

Ribs help in maintaining aerodynamic shape of the wing.

Explanation

GATE→2023→Structures→Flight Vehicle Structures

Q37

NAT[2 Marks]

The shear flow distribution in a single cell, thin-walled beam under the action of an arbitrary shear load ys applied at the shear centre S is shown in the figure. The cell has horizontal symmetry with booms marked by 1 to 4 that carry direct stresses. The shear modulus G is the same for all the walls, and the area of the cell is 135000 mm2. With respect to the point O marked in the figure, the distance to the shear centre S is ______ mm. (round off to the nearest integer)

Explanation

GATE→2022→Structures→Flight Vehicle Structures

Q38

MCQ[1 Mark]

The closed thin-walled rectangular channel shown in figure (i) is opened by introducing a sharp cut at the center of the bottom edge, as shown in figure (ii). Which one of the following statements is correct?

(A)

Centroids of (i) and (ii) coincide while shear centers do not

(B)

Shear centers of (i) and (ii) coincide while centroids do not

(C)

Both centroids and shear centers of (i) and (ii) coincide

(D)

Neither centroids nor shear centers of (i) and (ii) coincide

Explanation

Structural Dynamics

11 Questions

GATE→2026→Structures→Structural Dynamics

Q39

NAT[1 Mark]

The response 𝑥(𝑡) of a freely vibrating single degree of freedom underdamped system is given below. In the equation, 𝐴 and 𝜙 are constants. The damping ratio of the system is ________ (rounded off to 3 decimal places). 𝑥(𝑡) = 𝐴e−5𝑡 sin(10𝑡 + 𝜙)

Explanation

GATE→2026→Structures→Structural Dynamics

Q40

NAT[2 Marks]

A system comprising a bar, spring and mass is shown in the figure below. The bar, having negligible mass, is made of a material having Young’s modulus E = 200 GPa, cross-sectional area A = 100 mm2, and length L = 100 mm. The spring stiffness k = 200 kN/mm and the mass M = 100 kg. The natural frequency of free vibration of the system is ________ rad/s (rounded off to the nearest integer).

Explanation

GATE→2025→Structures→Structural Dynamics

Q41

NAT[2 Marks]

A uniform rigid bar of mass 3 kg is hinged at point F, and supported by a spring of stiffness k=100 N/m, as shown in the figure. The natural frequency of free vibration of the system is ____rad/s (answer in integer).

Explanation

GATE→2024→Structures→Structural Dynamics

Q42

MCQ[1 Mark]

For a single degree of freedom spring-mass-damper system subjected to harmonic forcing, the part of the motion (response) that decays due to damping is known as:

(A)

transient response

(B)

steady-state response

(C)

harmonic response

(D)

non-transient response

Explanation

GATE→2024→Structures→Structural Dynamics

Q43

NAT[2 Marks]

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 = 0.001 m, the magnitude of maximum normal stress in the cross section is _________N/m2 (answer in integer).

Explanation

GATE→2024→Structures→Structural Dynamics

Q44

NAT[2 Marks]

The equations of motion for a two degrees of freedom undamped spring-mass system are: 𝑚𝑥̈1 + 2𝑘𝑥1 −𝑘𝑥2 = 0 𝑚𝑥̈2 −𝑘𝑥1 + 2𝑘𝑥2 = 0 where m and k represent mass and stiffness respectively, in corresponding SI units, and 𝑥1 and 𝑥2 are the degrees of freedom. The larger of the two natural frequencies is given by: 𝜔= 𝛼√𝑘 𝑚 rad/s. The value of 𝛼 is ________ (rounded off to 2 decimal places).

Explanation

GATE→2023→Structures→Structural Dynamics

Q45

MSQ[1 Mark]

Which of the following statement(s) is/are true about harmonically excited forced vibration of a single degree-of-freedom linear spring-mass-damper system?

(A)

The total response of the mass is a combination of free vibration transient and steady-state response.

(B)

The free vibration transient dies out with time for each of the three possible conditions of damping (under-damped, critically damped, and over-damped).

(C)

The steady-state periodic response is dependent on the initial conditions at the time of application of external forcing.

(D)

The rate of decay of free vibration transient response depends on the mass, spring stiffness and damping constant.

Explanation

GATE→2023→Structures→Structural Dynamics

Q46

NAT[1 Mark]

For studying wing vibrations, a wing of mass M and finite dimensions has been idealized by assuming it to be supported using a linear spring of equivalent as shown in the figure. stiffness k and a torsional spring of equivalent stiffness kθ The centre of gravity (CG) of the wing idealized as an airfoil is marked in the figure. The number of degree(s) of freedom for this idealized wing vibration model is _________. (Answer in integer) Aerospace Engineering (AE)

Explanation

GATE→2023→Structures→Structural Dynamics

Q47

NAT[2 Marks]

A single degree-of-freedom spring-mass-damper system has viscous damping ratio of 0.1. The mass is given an initial displacement of 10 cm without imparting any velocity. After exactly two complete cycles of oscillation (i.e., after time 2 dT , where dT is the period of the damped vibration), the amplitude of the displacement is ______ cm. (round off to two decimal place) Aerospace Engineering (AE)

Explanation

GATE→2022→Structures→Structural Dynamics

Q48

NAT[2 Marks]

A damper with damping coefficient $c$ is attached to mass $5\text{ kg}$ and spring stiffness $5\text{ kN/m}$. Ratio of 3rd to 4th amplitude is $1.5$. Value of $c$ is ______ Ns/m (round off to nearest integer).

Explanation

GATE→2022→Structures→Structural Dynamics

Q49

NAT[2 Marks]

A uniform rigid prismatic bar of total mass $m$ is suspended from a ceiling by two identical springs. Let $\omega_1$ and $\omega_2$ be natural frequencies of mode I and II. The ratio $\omega_2 / \omega_1$ is ______ (round off to one decimal place).

Explanation

Theory of Elasticity

3 Questions

GATE→2026→Structures→Theory of Elasticity

Q50

MCQ[1 Mark]

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

(A)

36

(B)

21

(C)

10

(D)

2

Explanation

GATE→2026→Structures→Theory of Elasticity

Q51

MSQ[2 Marks]

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?

(A)

It satisfies the equilibrium equation

(B)

It is zero on the lateral surfaces of the bar

(C)

It satisfies the compatibility equation

(D)

It does not satisfy the equilibrium equation

Explanation

GATE→2025→Structures→Theory of Elasticity

Q52

MCQ[1 Mark]

A stress field is given by 𝜎𝑥𝑥= 𝜎𝑧𝑧= 𝐶1𝑦; 𝜎𝑦𝑦= 𝐶2𝑦; 𝜏𝑥𝑦= 𝜏𝑦𝑧= 𝜏𝑧𝑥= 0, where 𝐶1 and 𝐶2 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 𝐶1.

Explanation