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Engineering Mechanics & Mechanics of Materials(35)Vibrations & Machine Design(10)

Engineering Mechanics & Mechanics of Materials

35 Questions

GATE→2026→Applied Mechanics and Structures→Engineering Mechanics & Mechanics of Materials

Q1

MCQ[1 Mark]

The state of plane stress in an element is shown in the figure. The maximum shear stress in the element is N/mm^2.

(A)

0

(B)

5

(C)

10

(D)

25

Explanation

GATE→2026→Applied Mechanics and Structures→Engineering Mechanics & Mechanics of Materials

Q2

MCQ[1 Mark]

The virtual work principle states that

(A)

external virtual work is equal to internal virtual work

(B)

there is equilibrium of external and internal forces

(C)

virtual work is inversely proportional to virtual displacement

(D)

the potential energy of the system is equal to its kinetic energy

Explanation

GATE→2026→Applied Mechanics and Structures→Engineering Mechanics & Mechanics of Materials

Q3

MSQ[1 Mark]

Which ONE or MORE of the following welds can be performed through resistance welding method?

(A)

Seam

(B)

Spot

(C)

Fillet

(D)

Groove

Explanation

GATE→2026→Applied Mechanics and Structures→Engineering Mechanics & Mechanics of Materials

Q4

NAT[1 Mark]

A solid beam with a rectangular cross-section of breadth 0.5 m and depth 0.12 m, experiences a vertical shear force of 50 kN at a section. The maximum shear stress in that section is MPa (answer in two decimal places).

Explanation

GATE→2026→Applied Mechanics and Structures→Engineering Mechanics & Mechanics of Materials

Q5

MCQ[2 Marks]

For the truss shown in the figure, the magnitude of force in the member PR is kN.

(A)

10

(B)

0

(C)

$\frac{20}{\sqrt{3}}$

(D)

$10\sqrt{3}$

Explanation

GATE→2026→Applied Mechanics and Structures→Engineering Mechanics & Mechanics of Materials

Q6

MCQ[2 Marks]

Choose the CORRECT bending moment diagram for the simply supported beam shown in the figure with a concentric moment M at mid span. Consider hogging as positive and sagging as negative. Figures not to scale

(A)

Diagram A

(B)

Diagram B

(C)

Diagram C

(D)

Diagram D

Explanation

GATE→2026→Applied Mechanics and Structures→Engineering Mechanics & Mechanics of Materials

Q7

MCQ[2 Marks]

The stresses in a shaft are: i. Shear stress due to torsion ii. Normal stress due to bending moments iii. Axial stress Which ONE of the following options lists the stresses that are considered while designing a circular propeller shaft?

(A)

(i) and (ii) only

(B)

(ii) and (iii) only

(C)

(i) and (iii) only

(D)

(i), (ii) and (iii)

Explanation

GATE→2026→Applied Mechanics and Structures→Engineering Mechanics & Mechanics of Materials

Q8

NAT[2 Marks]

The critical buckling load of a 6 m long, 10 cm diameter axially loaded solid steel column with hinged support at both ends is KN (rounded off to nearest integer). Assume Young's modulus of steel as $2 \times 10^5\text{ N/mm}^2$.

Explanation

GATE→2026→Applied Mechanics and Structures→Engineering Mechanics & Mechanics of Materials

Q9

NAT[2 Marks]

A steel girder of length 10 m has one end rigidly attached to a ship's bulkhead and the other end free. It is subjected to a torsional moment of 30 kNm about its longitudinal axis at the free end. The shear modulus of steel is 80 GPa and the polar moment of inertia of the section is $6 \times 10^{-4}\text{ m}^4$. The total twist at the free end is $\times 10^{-4}$ rad (rounded off to one decimal place).

Explanation

GATE→2025→Applied Mechanics and Structures→Engineering Mechanics & Mechanics of Materials

Q10

MCQ[1 Mark]

In the stress-strain curve of mild steel, plastic deformation starts at the

(A)

proportional limit

(B)

elastic limit

(C)

upper yield point

(D)

lower yield point

Explanation

GATE→2025→Applied Mechanics and Structures→Engineering Mechanics & Mechanics of Materials

Q11

MCQ[2 Marks]

A square shaped body is subjected to only direct tensile stresses $\sigma_x$ and $\sigma_y$ as shown in the figure. If $\sigma_x > \sigma_y$, then the value of normal stress $(\sigma_{\theta})$ and shear stress $(\tau_{\theta})$ respectively on the principal/reference planes are given by options.

(A)

$\frac{\sigma_x-\sigma_y}{2}$ and $\frac{\sigma_x+\sigma_y}{2}$

(B)

$\frac{\sigma_x+\sigma_y}{2}$ and $\frac{\sigma_x-\sigma_y}{2}$

(C)

$\frac{\sigma_x+\sigma_y}{2}$ and $\frac{\sigma_x+\sigma_y}{2}$

(D)

$\frac{\sigma_x-\sigma_y}{2}$ and $\frac{\sigma_x-\sigma_y}{2}$

Explanation

GATE→2025→Applied Mechanics and Structures→Engineering Mechanics & Mechanics of Materials

Q12

MCQ[2 Marks]

The beam PQRS is subjected to a vertical point load of 10 kN at point S as shown in the figure.\nThe magnitude of fixed end moment at P is kN-m.

(A)

50

(B)

10

(C)

30

(D)

40

Explanation

GATE→2025→Applied Mechanics and Structures→Engineering Mechanics & Mechanics of Materials

Q13

MCQ[2 Marks]

For a butt weld joint of two plates, which one of the following loading scenarios has the least permissible stress?

(A)

Tensile

(B)

Bending

(C)

Bearing

(D)

Shear

Explanation

GATE→2025→Applied Mechanics and Structures→Engineering Mechanics & Mechanics of Materials

Q14

NAT[2 Marks]

A simply supported solid beam is subjected to a vertical point load of 10 N at the middle. The length of the beam is 4 m, and the cross section is $0.5\text{ m} \times 0.5\text{ m}$.\nThe magnitude of maximum tensile stress in the beam is $N/m^2$ (answer in integer).

Explanation

GATE→2025→Applied Mechanics and Structures→Engineering Mechanics & Mechanics of Materials

Q15

NAT[2 Marks]

The displacement field of a body is given by $\vec{u} = yx\hat{i} + yz\hat{j} + (z + x^2)\hat{k}$.\nThe shear strain $\gamma_{xy}$ at $(2, 1, 5)$ is (answer in integer).

Explanation

GATE→2024→Applied Mechanics and Structures→Engineering Mechanics & Mechanics of Materials

Q16

MCQ[1 Mark]

Consider an initially perfectly straight elastic column with pinned supports at both ends. If E is the Young's modulus of the material, L is the length of the column between the supports, and I is the least moment of inertia of the constant cross-sectional area of the column, then the Euler load is given by

(A)

$\frac{\pi^{2}EI}{L^{2}}$

(B)

$\frac{\pi^{2}EI}{4L^{2}}$

(C)

$\frac{\pi^{2}EI}{\sqrt{2}L^{2}}$

(D)

$\frac{2\pi^{2}EI}{L^{2}}$

Explanation

GATE→2024→Applied Mechanics and Structures→Engineering Mechanics & Mechanics of Materials

Q17

MCQ[1 Mark]

For a plane stress condition in elasticity, normal stress $\sigma_z$ is zero, and...

(A)

Option A

(B)

normal strain $\epsilon_z$ is zero

(C)

Option C

(D)

Option D

Explanation

GATE→2024→Applied Mechanics and Structures→Engineering Mechanics & Mechanics of Materials

Q18

MCQ[1 Mark]

How many independent material constants in solids are required to define isotropic materials?

(A)

2

(B)

3

(C)

9

(D)

21

Explanation

GATE→2024→Applied Mechanics and Structures→Engineering Mechanics & Mechanics of Materials

Q19

MCQ[2 Marks]

A simply supported beam is subjected to a concentrated moment M at the mid span as shown in the figure. The magnitude of the bending moment at a distance of $L/4$ from the left support A is equal to

(A)

M

(B)

$\frac{ML}{4}$

(C)

$\frac{M}{4}$

(D)

$\frac{M}{2}$

Explanation

GATE→2024→Applied Mechanics and Structures→Engineering Mechanics & Mechanics of Materials

Q20

MCQ[2 Marks]

A steel deck plate of a tanker is supported by two longitudinal stiffeners as shown in the figure. The width of the plate is a and its length is 5 times the width. Assume that the long edge is simply supported, and the short edge is free. The plate is loaded by a distributed pressure, $p = p_{0}\sin\left(\frac{\pi y}{a}\right)$ where $p_0$ is the pressure at $y=a/2$. The flexural rigidity of the plate is D. The plate equation is given by

(A)

$\frac{\partial^{4}w}{\partial y^{4}}=\frac{p_{0}}{D}\sin\left(\frac{\pi y}{a}\right)$

(B)

$\frac{\partial^{2}w}{\partial x^{2}}=\frac{p_{0}}{D}\sin\left(\frac{\pi y}{a}\right)$

(C)

$\frac{\partial^{2}w}{\partial y^{2}}=\frac{p_{0}}{D}\sin\left(\frac{\pi y}{a}\right)$

(D)

$\frac{\partial^{4}w}{\partial x^{4}}=\frac{p_{0}}{D}\sin\left(\frac{\pi y}{a}\right)$

Explanation

GATE→2024→Applied Mechanics and Structures→Engineering Mechanics & Mechanics of Materials

Q21

MCQ[2 Marks]

In the solution of statically indeterminate problems, Castigliano's second theorem employs the

(A)

principle of virtual work

(B)

virtual displacement method

(C)

virtual force method

(D)

principle of least work

Explanation

GATE→2024→Applied Mechanics and Structures→Engineering Mechanics & Mechanics of Materials

Q22

NAT[2 Marks]

Structural mechanics or thermodynamics calculation task.

Explanation

GATE→2024→Applied Mechanics and Structures→Engineering Mechanics & Mechanics of Materials

Q23

NAT[2 Marks]

Consider a thin-walled closed cylindrical steel vessel with an internal pressure of $2\text{ N/mm}^2$. The inner diameter is 1 m, and the thickness of the wall is 10 mm. The hoop stress is $N/mm^2$ (rounded off to one decimal place).

Explanation

GATE→2024→Applied Mechanics and Structures→Engineering Mechanics & Mechanics of Materials

Q24

NAT[2 Marks]

Consider a rectangular plate with in-plane loads. The state of the stress at an arbitrary angle $\theta$ is defined by $\sigma_{x}$, $\sigma_{y}$ and $\tau_{xy}$ as shown in the figure. If the principal plane is at $\theta=45^{\circ}$ and the principal stresses are $\sigma_1 = 8\text{ N/mm}^2$ and $\sigma_2 = 3\text{ N/mm}^2$, then the corresponding $\tau_{xy} =$ N/mm².

Explanation

GATE→2023→Applied Mechanics and Structures→Engineering Mechanics & Mechanics of Materials

Q25

MCQ[1 Mark]

Which method among the following is based on the strain energy principle?

(A)

Conjugate beam method

(B)

Castigliano's method

(C)

Slope-deflection method

(D)

Moment distribution method

Explanation

GATE→2023→Applied Mechanics and Structures→Engineering Mechanics & Mechanics of Materials

Q26

MSQ[1 Mark]

The failure modes that may be observed in a riveted joint to fasten two plate members, subjected to shear load are

(A)

bending of the rivet

(B)

shearing of the rivet

(C)

tensile failure of a plate member

(D)

tensile failure of the rivet

Explanation

GATE→2023→Applied Mechanics and Structures→Engineering Mechanics & Mechanics of Materials

Q27

NAT[1 Mark]

A solid cantilever shaft of diameter 0.1 m and length 2 m is subjected to a torque of 10 kN-m at the free end (shear modulus is 82 GPa).\nThe maximum induced shear stress is $N/mm^2$ (round off to the nearest integer).

Explanation

GATE→2023→Applied Mechanics and Structures→Engineering Mechanics & Mechanics of Materials

Q28

MCQ[2 Marks]

A simply supported beam with an overhang has experienced the bending moment as shown below. The corresponding concentrated load is

(A)

5 kN at mid span of PR

(B)

10 kN at Q

(C)

10 kN at mid span of RS

(D)

5 kN at S

Explanation

GATE→2023→Applied Mechanics and Structures→Engineering Mechanics & Mechanics of Materials

Q29

MSQ[2 Marks]

The stress field given would satisfy the strain compatibility condition if

(A)

both $\sigma_x$ and $\sigma_y$ are multiplied by $\frac{1}{2}$

(B)

both $\sigma_x$ and $\sigma_y$ are multiplied by 2

(C)

$\tau_{xy}$ is multiplied by $\frac{1}{2}$

(D)

$\tau_{xy}$ is multiplied by 2

Explanation

GATE→2023→Applied Mechanics and Structures→Engineering Mechanics & Mechanics of Materials

Q30

NAT[2 Marks]

Consider a truss as shown in the following figure. The length of each member is 2 m. The area of cross section of each member is $100\text{ mm}^2$ and Young's modulus is $2 \times 10^5\text{ N/mm}^2$.\nThe vertical deflection at C is mm (round off to one decimal place)

Explanation

GATE→2022→Applied Mechanics and Structures→Engineering Mechanics & Mechanics of Materials

Q31

MSQ[1 Mark]

A simply supported beam is loaded with a uniformly distributed load (UDL) acting vertically downwards. Which of the following statements are TRUE with regard to strain energy?

(A)

It increases with increase in UDL

(B)

It increases with increase in cross-sectional area of the beam

(C)

It is independent of the length of the beam

(D)

It is dependent on Young's modulus of elasticity

Explanation

GATE→2022→Applied Mechanics and Structures→Engineering Mechanics & Mechanics of Materials

Q32

NAT[1 Mark]

The beam fixed at end A and simply supported at C with a roller is shown in the figure. If B is an internal hinge and a concentrated load of 10 kN is acting at D and a uniformly distributed load (UDL) of $10\text{ kN/m}$ is acting on member AB, then the magnitude of bending moment at the fixed end A is kNm.

Explanation

GATE→2022→Applied Mechanics and Structures→Engineering Mechanics & Mechanics of Materials

Q33

MCQ[2 Marks]

A column of height 20 m is fixed at both ends. If Young's modulus of elasticity is $17 \times 10^9\text{ N/m}^2$ and moment of inertia is $3.255 \times 10^{-4}\text{ m}^4$, then the first critical load of buckling of the column lies between kN.

(A)

501 and 520

(B)

521 and 540

(C)

541 and 560

(D)

561 and 580

Explanation

GATE→2022→Applied Mechanics and Structures→Engineering Mechanics & Mechanics of Materials

Q34

MSQ[2 Marks]

Which of the following statements are TRUE about the assumptions adopted in Euler's column theory?

(A)

Length of the column is very large in comparison to its cross-sectional dimensions

(B)

Effect of the axial compressive stress is smaller than the effect of bending stress on column buckling

(C)

Column fails only by transverse loads

(D)

Column fails only by buckling

Explanation

GATE→2022→Applied Mechanics and Structures→Engineering Mechanics & Mechanics of Materials

Q35

NAT[2 Marks]

An element, as shown in the figure, is subjected to stresses $\sigma_{x}=500\text{ N/m}^{2}$, $\sigma_{y}=300\text{ N/m}^{2}$ and $\tau=120\text{ N/m}^{2}$.\nIf $\sigma_{1}$ and $\sigma_{2}$ are the principal stresses, then the absolute value of the angle $\phi$ is degree (rounded off to one decimal place).

Explanation

Vibrations & Machine Design

10 Questions

GATE→2026→Applied Mechanics and Structures→Vibrations & Machine Design

Q36

MSQ[2 Marks]

For a dynamic system with single degree of freedom, choose the CORRECT statement(s).

(A)

Damped natural frequency is greater than the undamped natural frequency.

(B)

Dynamic response is always greater than static response at all excitation frequencies.

(C)

Damping ratio can be estimated using logarithmic decrement method.

(D)

A non-zero phase lag is always observed between the excitation and response for a damped system.

Explanation

GATE→2025→Applied Mechanics and Structures→Vibrations & Machine Design

Q37

MCQ[1 Mark]

The dynamic response amplitude $|H(\omega)|$ of a single degree of freedom system subjected to support motion is given by the expression. $|H(\omega)|$ increases with an increase in damping ratio ($\zeta$) if the excitation frequency ($\omega$) is ______ the natural frequency ($\omega_n$) of the system.

(A)

less than $0.75$ times

(B)

less than $\frac{\sqrt{3}}{2}$ times

(C)

less than $\sqrt{2}$ times

(D)

greater than $\sqrt{2}$ times

Explanation

GATE→2025→Applied Mechanics and Structures→Vibrations & Machine Design

Q38

NAT[2 Marks]

A single degree of freedom system is undergoing free oscillation. The natural frequency and damping ratio of the system are $1\text{ rad/sec}$ and 0.01 respectively.\nThe reduction in peak amplitude over three cycles is % (rounded off to one decimal place).

Explanation

GATE→2024→Applied Mechanics and Structures→Vibrations & Machine Design

Q39

NAT[2 Marks]

A single degree of freedom system has a mass, stiffness and damping of 200 kg, $20\text{ N/m}$ and $62\text{ N-s/m}$ respectively. For a forced oscillation system, if the excitation frequency is equal to the undamped natural frequency, then the dynamic magnification factor is (rounded off to three decimal places).

Explanation

GATE→2023→Applied Mechanics and Structures→Vibrations & Machine Design

Q40

MSQ[2 Marks]

For a given time varying load applied on a single degree of freedom system, the dynamic response amplitude is always less than the static response amplitude if

(A)

the applied loading frequency is greater than 1.5 times the natural frequency of the system

(B)

the damping is greater than 70% of critical damping

(C)

the damping is exactly $1/3^{rd}$ of critical damping

(D)

the applied loading frequency is less than the natural frequency of the system for an undamped system

Explanation

GATE→2023→Applied Mechanics and Structures→Vibrations & Machine Design

Q41

NAT[2 Marks]

A buoy of virtual mass 30 kg oscillates in a fluid medium as a single degree of freedom system. If the total damping in the system is set as $188.5\text{ N-s}/\text{m}$, such that the oscillation just ceases to occur, then the natural period of the system is s (round off to one decimal place)

Explanation

GATE→2022→Applied Mechanics and Structures→Vibrations & Machine Design

Q42

MCQ[1 Mark]

Let $\omega_{f}$ be the excitation frequency of a sinusoidal load and $\omega_{n}$ be the natural frequency of a single degree of freedom system. Then the dynamic response of the system is highly affected by the stiffness of the system when

(A)

$\omega_{f}=\omega_{n}$

(B)

$0<\omega_{f}<\omega_{n}$

(C)

$0<\omega_{n}<\omega_{f}$

(D)

$\omega_{f}=0$

Explanation

GATE→2022→Applied Mechanics and Structures→Vibrations & Machine Design

Q43

NAT[1 Mark]

If the maximum static deflection of a shaft is 5 mm, then the estimated critical speed using Rayleigh-Ritz method is RPM (rounded off to nearest integer).

Explanation

GATE→2022→Applied Mechanics and Structures→Vibrations & Machine Design

Q44

NAT[2 Marks]

An under-damped single degree of freedom system is freely oscillating with an initial amplitude A. The initial velocity of the system is zero. After five cycles of oscillation, the amplitude reduces to $A/2$.\nThen the damping ratio of the system is % (rounded off to one decimal place) of critical damping.

Explanation

GATE→2022→Applied Mechanics and Structures→Vibrations & Machine Design

Q45

NAT[2 Marks]

A system with two degrees of freedom, as shown in the figure, has masses $m_{1}=200\text{ kg}$ and $m_{2}=100\text{ kg}$ and stiffness coefficients $k_{1}=k_{2}=200\text{ N}/\text{m}$.\nThen the lowest natural frequency of the system is rad/s (rounded off to one decimal place).

Explanation