List of top Applied Mechanics and Structures Questions

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?