List of top Structures Questions on Material Properties

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).

 

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).

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).


 

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 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: 


 

For a homogeneous, isotropic material, the relation between the shear modulus (\( G \)), Young’s modulus (\( E \)), and Poisson’s ratio (\( \nu \)) is ________?

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 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 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}
For a homogeneous, isotropic material, the relation between the shear modulus (\( G \)), Young’s modulus (\( E \)), and Poisson’s ratio (\( \nu \)) is \_\_\_\_?
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 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 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}
For a homogeneous, isotropic material, the relation between the shear modulus (\( G \)), Young’s modulus (\( E \)), and Poisson’s ratio (\( \nu \)) is \_\_\_\_?
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 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 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}

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?

Which of the following options is/are correct?

The figure shows two yield loci for an isotropic material in the \((\sigma_I,\sigma_{II})\) plane. Here \(\sigma_I,\sigma_{II}\) are principal stresses and \(\sigma_Y\) is the uniaxial tensile yield stress. Which statements are correct?