List of top Applied Mechanics and Structures Questions asked in GATE NM

A freely-floating rectangular barge of length 200 m is divided into five equal compartments. In light-weight condition, the weight and buoyancy are uniformly distributed along the length of the barge. Assume \( g = 9.81 \, {m/s}^2 \). If 500 tonne of liquid cargo is added to each of the two end compartments as shown in the figure, then the maximum bending moment is {98.10 MN·m (rounded off to two decimal places).

 

The displacement field of a body is given by \( \vec{u} = yx \hat{i} + yz \hat{j} + (z + x^2) \hat{k} \). The shear strain \( \gamma_{xy} \) at \( (2, 1, 5) \) is:
A single degree of freedom system is undergoing free oscillation. The natural frequency and damping ratio of the system are \(1 \, {rad/sec}\) and \(0.01\) respectively.
The reduction in peak amplitude over three cycles is ________ % (rounded off to one decimal place).
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 m \(\times\) 0.5 m. The magnitude of maximum tensile stress in the beam is ________ N/m\(^2\) (answer in integer).

A freely-floating rectangular barge of length 200 m is divided into five equal compartments. In light-weight condition, the weight and buoyancy are uniformly distributed along the length of the barge. Assume \( g = 9.81 \, {m/s}^2 \). If 500 tonne of liquid cargo is added to each of the two end compartments as shown in the figure, then the maximum bending moment is {98.10 MN·m (rounded off to two decimal places).


 

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

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


 

A square‑shaped body is subjected to only direct tensile stresses \(\sigma_x\) and \(\sigma_y\) as shown. If \(\sigma_x > \sigma_y\), then the value of normal stress (\(\sigma_{\theta}\)) and shear stress (\(\tau_{\theta}\)) respectively are ________.


 

The midship section of a barge of breadth \( W \) and depth \( H \) is shown in the figure. All plate thicknesses are equal. The barge is subjected to a longitudinal bending moment in the upright condition. Which one of the following statements is correct?


 

In the stress-strain curve of mild steel, plastic deformation starts at the ________.
The dynamic response amplitude \( |H(\omega)| \) of a single degree of freedom system subjected to support motion is given by the following expression: \[ |H(\omega)| = \sqrt{\frac{1 + 4 \zeta^2 \left( \frac{\omega}{\omega_n} \right)^2 }{\left[ 1 - \left( \frac{\omega}{\omega_n} \right)^2 \right]^2 + 4 \zeta^2 \left( \frac{\omega}{\omega_n} \right)^2} } \] Where the damping ratio is \( \zeta \), the excitation frequency is \( \omega \), and the natural frequency of the system is \( \omega_n \). The amplitude \( |H(\omega)| \) increases with an increase in damping ratio (\( \zeta \)) if the excitation frequency (\( \omega \)) is ________ the natural frequency (\( \omega_n \)) of the system.
A single degree of freedom system is undergoing free oscillation. The natural frequency and damping ratio of the system are \(1 \, {rad/sec}\) and \(0.01\) respectively.
The reduction in peak amplitude over three cycles is ________ % (rounded off to one decimal place).
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 m \(\times\) 0.5 m. The magnitude of maximum tensile stress in the beam is ________ N/m\(^2\) (answer in integer).
For a butt weld joint of two plates, which one of the following loading scenarios has the least permissible stress?
Consider a ship with one half of its midship cross-section with moulded breadth \(B = 30\ \text{m}\) and moulded depth \(D = 9\ \text{m}\). The deck, side-shell, and bottom plate have the same thickness. The yield stress of the material is \(240\ \text{MPa}\). The section is subjected to a vertical bending moment of \(712.8\ \text{MN·m}\). Ignore the self-moment of inertia of deck and bottom plating. The distance of the farthest fiber from the neutral axis is taken excluding plate thickness. If maximum bending stress equals yield stress, the required plate thickness is ____________ mm (rounded off to one decimal place).
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).
An under-damped single-degree-of-freedom system is freely oscillating with an initial amplitude \(A\). The initial velocity is zero. After five cycles of oscillation, the amplitude reduces to \(A/2\). Then the damping ratio of the system is ________________ % (rounded off to one decimal place) of critical damping.
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 \(k_1 = k_2 = 200\ \text{N/m}\). Then the lowest natural frequency of the system is ____________ rad/s (rounded off to one decimal place).
Which of the following statements are TRUE about the assumptions adopted in Euler’s column theory?
A column of height 20 m is fixed at both ends. If Young’s modulus is \(E = 17\times 10^{9}\ \text{N/m}^2\) and moment of inertia \(I = 3.255\times 10^{-4}\ \text{m}^4\), then the first critical buckling load lies between ________________ kN.
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).
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 10 kN point load acts at D, and a UDL of 10 kN/m acts on AB, the magnitude of bending moment at the fixed end A is ____________ kNm.
Which of the following flows are represented by the velocity field, \[ \mathbf{V} = (x^2 - y^2) \hat{i} - 2xy \hat{j}? \]
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: