Mechanics of Materials - Applied Mechanics and Structures - Naval Architecture & Marine Engineering Previous Year Questions

1

2022 · Naval Architecture & Marine Engineering · Applied Mechanics and Structures · Mechanics of Materials

Naval Architecture & Marine Engineering (NM) 2022

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 on the length of the beam

D

It is dependent on Young's modulus of elasticity

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2

2022 · Naval Architecture & Marine Engineering · Applied Mechanics and Structures · Mechanics of Materials

Naval Architecture & Marine Engineering (NM) 2022

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 kN/m is acting on member AB, then the magnitude of bending moment at the fixed end A is ______ kNm.

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3

2022 · Naval Architecture & Marine Engineering · Applied Mechanics and Structures · Mechanics of Materials

Naval Architecture & Marine Engineering (NM) 2022

A column of height 20 m is fixed at both ends. If Young's modulus of elasticity is 17 × 10⁹ N/m² and moment of inertia is 3.255 × 10⁻⁴ m⁴, 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

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4

2022 · Naval Architecture & Marine Engineering · Applied Mechanics and Structures · Mechanics of Materials

Naval Architecture & Marine Engineering (NM) 2022

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

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5

2022 · Naval Architecture & Marine Engineering · Applied Mechanics and Structures · Mechanics of Materials

Naval Architecture & Marine Engineering (NM) 2022

Consider the midship section of a vessel with the centerline (CL) and neutral axis (NA) as shown in the figure. Assume that the cross-section is symmetric about the centerline, the plate thickness is uniform throughout the section and \( h_1 < h_2 \).
When the vessel is subjected to a vertical bending moment in its upright condition, which of the following statements are TRUE?

A

Magnitude of shear stress is maximum at points P and S

B

Magnitude of shear stress is minimum at points Q and U

C

Magnitude of bending stress is maximum at points S and T

D

Magnitude of bending stress is minimum at points Q and U

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6

2022 · Naval Architecture & Marine Engineering · Applied Mechanics and Structures · Mechanics of Materials

Naval Architecture & Marine Engineering (NM) 2022

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 \(\tau = 120 \text{ N/m}^2\).
If \(\sigma_1\) and \(\sigma_2\) are the principal stresses, then the absolute value of the angle \(\varphi\) is ______ degree (rounded off to one decimal place).

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7

2023 · Naval Architecture & Marine Engineering · Applied Mechanics and Structures · Mechanics of Materials

Naval Architecture & Marine Engineering (NM) 2023

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

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8

2023 · Naval Architecture & Marine Engineering · Applied Mechanics and Structures · Mechanics of Materials

Naval Architecture & Marine Engineering (NM) 2023

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

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9

2023 · Naval Architecture & Marine Engineering · Applied Mechanics and Structures · Mechanics of Materials

Naval Architecture & Marine Engineering (NM) 2023

The stress field,
\sigma_x = 4x^3 + 3x^2y + 5xy^2
\sigma_y = -x^3 + 6x^2y - 7xy^2
\tau_{xy} = -5x^2y - 3xy^2
would satisfy the strain compatibility condition if

A

both \sigma_x and \sigma_y are multiplied by 1/2

B

both \sigma_x and \sigma_y are multiplied by 2

C

\tau_{xy} is multiplied by 1/2

D

\tau_{xy} is multiplied by 2

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10

2024 · Naval Architecture & Marine Engineering · Applied Mechanics and Structures · Mechanics of Materials

Naval Architecture & Marine Engineering (NM) 2024

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

\(\frac{2\pi^2 EI}{L^2}\)

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11

2024 · Naval Architecture & Marine Engineering · Applied Mechanics and Structures · Mechanics of Materials

Naval Architecture & Marine Engineering (NM) 2024

For a plane strain problem in the \(x-y\) plane, it is necessary that

A

normal stress \(\sigma_z\) is zero

B

normal strain \(\varepsilon_z\) is zero

C

both the normal stresses \(\sigma_x\) and \(\sigma_y\) are zero

D

shear strain \(\gamma_{xy}\) is equal to \(\frac{(\sigma_x - \sigma_y)}{2}\)

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12

2024 · Naval Architecture & Marine Engineering · Applied Mechanics and Structures · Mechanics of Materials

Naval Architecture & Marine Engineering (NM) 2024

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

A

2

B

3

C

9

D

21

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13

2024 · Naval Architecture & Marine Engineering · Applied Mechanics and Structures · Mechanics of Materials

Naval Architecture & Marine Engineering (NM) 2024

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

\(\frac{M}{2}\)

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14

2024 · Naval Architecture & Marine Engineering · Applied Mechanics and Structures · Mechanics of Materials

Naval Architecture & Marine Engineering (NM) 2024

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

\(\frac{\partial^2 w}{\partial y^2} = \frac{p_0}{D} \sin \left( \frac{\pi y}{a} \right) \)

C

\(\frac{\partial^2 w}{\partial y^2} = \frac{p_0}{D} \sin \left( \frac{\pi y}{a} \right) \)

D

\(\frac{\partial^4 w}{\partial x^4} = \frac{p_0}{D} \sin \left( \frac{\pi y}{a} \right) \)

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15

2024 · Naval Architecture & Marine Engineering · Applied Mechanics and Structures · Mechanics of Materials

Naval Architecture & Marine Engineering (NM) 2024

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

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16

2024 · Naval Architecture & Marine Engineering · Applied Mechanics and Structures · Mechanics of Materials

Naval Architecture & Marine Engineering (NM) 2024

A ship travelling in head seas experiences a bending moment of 200 MN·m. The ship’s cross section is assumed to be a box girder of 30 m beam and 10 m depth with a 10 mm plate thickness. The maximum bending stress is ______ MPa (rounded off to the nearest integer).

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17

2024 · Naval Architecture & Marine Engineering · Applied Mechanics and Structures · Mechanics of Materials

Naval Architecture & Marine Engineering (NM) 2024

Consider a thin-walled closed cylindrical steel vessel with an internal pressure of 2 N/mm². The inner diameter is 1 m, and the thickness of the wall is 10 mm. The hoop stress is ______ N/mm² (rounded off to one decimal place).

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18

2024 · Naval Architecture & Marine Engineering · Applied Mechanics and Structures · Mechanics of Materials

Naval Architecture & Marine Engineering (NM) 2024

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 \(\theta = 45^0\), and the principal stresses are \(\sigma_x = 8 \text{ N/mm}^2\) and \(\sigma_y = 3 \text{ N/mm}^2\), then the corresponding \(\tau_{xy} =\) ________ N/mm².

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19

2025 · Naval Architecture & Marine Engineering · Applied Mechanics and Structures · Mechanics of Materials

Naval Architecture & Marine Engineering (NM) 2025

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

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20

2025 · Naval Architecture & Marine Engineering · Applied Mechanics and Structures · Mechanics of Materials

Naval Architecture & Marine Engineering (NM) 2025

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 are ______.

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 \(\frac{\sigma_x - \sigma_y}{2}\)

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