List of top Applied Mechanics and Structures Questions on Strength of Materials

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