List of top Structures Questions on Stress Equilibrium asked in GATE AE

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).

 

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).


 

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).
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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?
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 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?
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 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?
Two separate load cases act at a point. Case I: pure uniaxial tension of \(10\ \text{N/mm}^2\) along the \(x'\)-axis; Case II: pure uniaxial compression of \(10\ \text{N/mm}^2\) along the \(y'\)-axis. The axes \((x',y')\) are rotated by \(45^\circ\) with respect to the \((x,y)\) axes. Find the sum of the maximum and minimum principal stresses for the combined loading (rounded to 1 decimal place). \begin{center} \includegraphics[width=0.7\textwidth]{15.jpeg} \end{center}
A thin-walled cylindrical pressure vessel of yield strength $300$ MPa has radius-to-thickness ratio $R/t = 100$. Using von Mises yield criterion, find internal pressure at failure. (round off to two decimals)
The thickness of a uniform hollow circular shaft is equal to the difference between the outer radius and the inner radius. The ratio of the inner diameter to outer diameter of the shaft is $0.5$. For the shaft reacting to an applied torque, the ratio of the maximum shear stress $\tau$ to the maximum shear stress $\tau_{\text{thin-wall}}$ obtained using the thin-wall approximation is ............. (round off to one decimal place)
Which of the following statement(s) is/are true about the state of stress in a plane?
Let \(\sigma\) and \(\tau\) represent the normal stress and shear stress on a plane, respectively. The Mohr circle(s) that may possibly represent the state of stress at points in a beam of rectangular cross-section under \textit{pure bending} is/are:
A beam with a symmetrical T-shaped cross-section, as shown in the figure, is subjected to pure bending. The maximum magnitude of the normal stress is realised: