List of top Applied Mechanics and Structures Questions

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 \(6 \times 10^{-4}\) m\(^4\).
The total twist at the free end is ______ \(\times 10^{-4}\) rad (rounded off to one decimal place).

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 \(2 \times 10^5\) N/mm\(^2\).

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

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?

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 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).

The weight of a ship is uniformly distributed along its length.
Under which ONE or MORE of the following conditions will the ship be subjected to hogging moment?
Note: The weight is equal to buoyancy in all of the following conditions.

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

The state of plane stress in an element is shown in the figure.

The maximum shear stress in the element is ______ \(\text{N/mm}^2\).

The virtual work principle states that ______.