List of top Structures Questions

Two designs A and B, shown in the figure, are proposed for a thin-walled closed section that is expected to carry only torque. Both A and B have a semi-circular nose, and are made of the same material with a wall thickness of 1 mm. With strength as the only criterion for failure, the ratio of maximum torque that B can support to the maximum torque that A can support is \_\_\ (rounded off to two decimal places).
\includegraphics[width=0.5\linewidth]{60.png}
A thin flat plate is subjected to the following stresses: \[ \sigma_{xx} = 160 \, {MPa}; \, \sigma_{yy} = 40 \, {MPa}; \, \tau_{xy} = 80 \, {MPa}. \] Factor of safety is defined as the ratio of the yield stress to the applied stress. The yield stress of the material under uniaxial tensile load is 250 MPa. The factor of safety for the plate assuming that material failure is governed by the von Mises criterion is \_\_\_\_\_\_\_ (rounded off to two decimal places).
\includegraphics[width=0.5\linewidth]{59.png}
A 1 m long rod of 1 cm × 1 cm cross section is subjected to an axial tensile force of 35 kN. The Young’s modulus of the material is 70 GPa. The cross-section of the deformed rod is 0.998 cm × 0.998 cm. The Poisson’s ratio of the material is \_\_\_\_\_\_\_\_ (rounded off to one decimal place).
For a three-bar truss loaded as shown in the figure, the magnitude of the force in the horizontal member AB is \_\_\_\_ N (answer in integer).
\includegraphics[width=0.5\linewidth]{56.png}
A uniform rigid bar of mass 3 kg is hinged at point F, and supported by a spring of stiffness \( k = 100 \, {N/m} \), as shown in the figure. The natural frequency of free vibration of the system is \_\_\_\_\_\_ rad/s (answer in integer).
\includegraphics[width=0.5\linewidth]{57.png}
A 1 m long rod is to be designed to support an axial tensile load \( P \) (\( P >> \) weight of the rod). The material for the rod is to be chosen from one of the four provided in the table. Using strength-based failure criterion for design, which material results in the lowest weight of the rod? % Given Properties Properties:
\includegraphics[width=0.7\linewidth]{37.png}
A stress field is given by \( \sigma_{xx} = \sigma_{zz} = C_1 y \); \( \sigma_{yy} = C_2 y \); \( \tau_{xy} = \tau_{yz} = \tau_{zx} = 0 \), where \( C_1 \) and \( C_2 \) are non-zero constants. If the stress field satisfies equilibrium, which one of the following options is correct?
For a homogeneous, isotropic material, the relation between the shear modulus (\( G \)), Young’s modulus (\( E \)), and Poisson’s ratio (\( \nu \)) is \_\_\_\_?
In the given figure, plate ABCD in its undeformed configuration (solid line) is a rhombus with all the internal angles being 90°. The lengths of the undeformed diagonals are 20 cm. ABCD deforms as shown by the dotted lines. Upon deformation, diagonal AC reduces to 19.96 cm and BD increases to 20.04 cm. In the given x-y coordinate system, the engineering shear strain \( \gamma_{xy} \) is equal to \_\_\_\_\_.
\includegraphics[width=0.5\linewidth]{30.png}
A simply supported horizontal beam is subjected to a distributed transverse load varying linearly from \( q_0 \) at A to zero at B, as shown in the figure. Which one of the following options is correct?
\includegraphics[width=0.5\linewidth]{27.png}
A uniform symmetric cross-section cantilever beam of length \( L \) is subjected to a transverse force \( P \) at the free end, as shown in the figure. The Young’s modulus of the material is \( E \) and the moment of inertia is \( I \). Ignoring the contributions due to transverse shear, the strain energy stored in the beam is \_\_\_\_\_.
\includegraphics[width=0.5\linewidth]{29.png}
A prismatic vertical column of cross-section \( a \times 0.5a \) and length \( l \) is rigidly fixed at the bottom and free at the top. A compressive force \( P \) is applied along the centroidal axis at the top surface. The Young’s modulus of the material is 200 GPa and the uniaxial yield stress is 400 MPa. If the critical value of \( P \) for yielding and for buckling of the column are equal, the value of \( \frac{l}{a} \) is \_\_\_\_ (rounded off to one decimal place).
\includegraphics[width=0.5\linewidth]{58.png}
Two designs A and B, shown in the figure, are proposed for a thin-walled closed section that is expected to carry only torque. Both A and B have a semi-circular nose, and are made of the same material with a wall thickness of 1 mm. With strength as the only criterion for failure, the ratio of maximum torque that B can support to the maximum torque that A can support is \_\_\ (rounded off to two decimal places).
\includegraphics[width=0.5\linewidth]{60.png}
A thin flat plate is subjected to the following stresses: \[ \sigma_{xx} = 160 \, {MPa}; \, \sigma_{yy} = 40 \, {MPa}; \, \tau_{xy} = 80 \, {MPa}. \] Factor of safety is defined as the ratio of the yield stress to the applied stress. The yield stress of the material under uniaxial tensile load is 250 MPa. The factor of safety for the plate assuming that material failure is governed by the von Mises criterion is \_\_\_\_\_\_\_ (rounded off to two decimal places).
\includegraphics[width=0.5\linewidth]{59.png}
A 1 m long rod of 1 cm × 1 cm cross section is subjected to an axial tensile force of 35 kN. The Young’s modulus of the material is 70 GPa. The cross-section of the deformed rod is 0.998 cm × 0.998 cm. The Poisson’s ratio of the material is \_\_\_\_\_\_\_\_ (rounded off to one decimal place).
A uniform rigid bar of mass 3 kg is hinged at point F, and supported by a spring of stiffness \( k = 100 \, {N/m} \), as shown in the figure. The natural frequency of free vibration of the system is \_\_\_\_\_\_ rad/s (answer in integer).
\includegraphics[width=0.5\linewidth]{57.png}
A 1 m long rod is to be designed to support an axial tensile load \( P \) (\( P >> \) weight of the rod). The material for the rod is to be chosen from one of the four provided in the table. Using strength-based failure criterion for design, which material results in the lowest weight of the rod? % Given Properties Properties:
\includegraphics[width=0.7\linewidth]{37.png}
In the given figure, plate ABCD in its undeformed configuration (solid line) is a rhombus with all the internal angles being 90°. The lengths of the undeformed diagonals are 20 cm. ABCD deforms as shown by the dotted lines. Upon deformation, diagonal AC reduces to 19.96 cm and BD increases to 20.04 cm. In the given x-y coordinate system, the engineering shear strain \( \gamma_{xy} \) is equal to \_\_\_\_\_.
\includegraphics[width=0.5\linewidth]{30.png}
A uniform symmetric cross-section cantilever beam of length \( L \) is subjected to a transverse force \( P \) at the free end, as shown in the figure. The Young’s modulus of the material is \( E \) and the moment of inertia is \( I \). Ignoring the contributions due to transverse shear, the strain energy stored in the beam is \_\_\_\_\_.
\includegraphics[width=0.5\linewidth]{29.png}
A stress field is given by \( \sigma_{xx} = \sigma_{zz} = C_1 y \); \( \sigma_{yy} = C_2 y \); \( \tau_{xy} = \tau_{yz} = \tau_{zx} = 0 \), where \( C_1 \) and \( C_2 \) are non-zero constants. If the stress field satisfies equilibrium, which one of the following options is correct?

The three-dimensional stress-strain relationship for an isotropic material is given as \[ \begin{Bmatrix} \sigma_{xx} \sigma_{yy} \sigma_{zz} \tau_{yz} \tau_{xz} \tau_{xy} \end{Bmatrix} = \begin{bmatrix} P & Q & Q & 0 & 0 & 0 \\ Q & P & Q & 0 & 0 & 0 \\ Q & Q & P & 0 & 0 & 0 \\ 0 & 0 & 0 & R & 0 & 0 \\ 0 & 0 & 0 & 0 & R & 0 \\ 0 & 0 & 0 & 0 & 0 & R \end{bmatrix} \begin{Bmatrix} \varepsilon_{xx} \varepsilon_{yy} \varepsilon_{zz} \gamma_{yz} \gamma_{xz} \gamma_{xy} \end{Bmatrix}, \] 

where \(P, Q, R\) are elastic constants; \(\sigma,\tau\) are normal and shear stresses; and \(\varepsilon,\gamma\) are normal and engineering shear strains. Which relation is correct?

Four free-vibration responses \(P,Q,R,S\) of a single-DOF spring-mass-damper with the same initial conditions are shown. Identify which curve corresponds to: (1) Overdamped, (2) Underdamped, (3) Critically damped, (4) Undamped. 

For a single degree of freedom spring-mass-damper system subjected to harmonic forcing, the part of the motion (response) that decays due to damping is known as:

Which of the following options is/are correct?

A material has Poisson's ratio \(\nu=0.5\) and Young's modulus \(E=2500\ \text{MPa}\). Under a hydrostatic stress of magnitude \(10\ \text{MPa}\), the percentage change in its volume is _________,(answer in integer).