List of top Structures Questions

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? 

In the figure shown below, the magnitude of internal force in member BC is .................. N (rounded off to 1 decimal place). 


 

The cross-section of a thin-walled beam with uniform wall thickness \(t\), shown in the figure, is subjected to a bending moment \(M_x = 10 \, \text{Nm}\).  
If \(h = 1 \, \text{m}\) and \(t = 0.001 \, \text{m}\), then the magnitude of the maximum normal stress in the cross-section is _______ N/m\(^2\) (answer as an integer).

The equations of motion for a two degrees of freedom undamped spring-mass system are: \[ m \ddot{x}_1 + 2k x_1 - k x_2 = 0 \] \[ m \ddot{x}_2 - k x_1 + 2k x_2 = 0 \] where $m$ and $k$ represent mass and stiffness, respectively, in SI units. The larger of the two natural frequencies is given by: \[ \omega = \alpha \sqrt{\frac{k}{m}} \, \, \text{rad/s} \] The value of $\alpha$ is .............. (rounded off to 2 decimal places).
Consider the plane strain field given by \(\varepsilon_{xx} = 10\,x y^{2}, \; \varepsilon_{yy} = -5\,x^{2}y \text{ and } \gamma_{xy} = A \, x y (2x - y)\) where \(A\) is a constant and \(\gamma_{xy}\) is the engineering shear strain. The value of \(A\) for the strain field to be compatible is .................. (rounded off to 1 decimal place).
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 rigid bar $AB$ of length 3 m is subjected to a uniformly distributed load of $100 \,\text{N/m}$. The bar is supported at $A$ (pin) and by rod $CD$ connected at $D$. The rod $CD$ has axial stiffness $40 \,\text{N/mm}$, and $C$ is pinned. Find the vertical deflection at point $D$ (in mm). 

A cantilever beam of length $2a$ is loaded at the tip with force $F$. The beam is supported in the middle by a roller (pin). Find the reaction moment at the built-in end of the beam as $\alpha Fa$, where $\alpha =$ ....................... (round off to one decimal place). 

The shear flow distribution in a single cell, thin-walled beam under a shear load $S_y$ is shown in the figure. The cell has horizontal symmetry with booms marked $1$ to $4$. The shear modulus $G$ is same for all walls, and the area of the cell is $135000 \,\text{mm}^2$. With respect to point $O$, find the distance of shear centre $S$ (in mm). (round off to nearest integer) 

A single degree-of-freedom spring–mass–damper system has viscous damping ratio $\zeta = 0.1$. The mass has initial displacement of $10$ cm without velocity. After exactly two complete cycles of damped oscillation, find amplitude of displacement (in cm, round off to two decimals).
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)
Which of the following statement(s) about the elastic flexural buckling load of columns is/are correct?
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)
For studying wing vibrations, a wing of mass \(M\) and finite dimensions has been idealized by assuming it to be supported using a linear spring of equivalent stiffness \(k\) and a torsional spring of equivalent stiffness \(k_\theta\) as shown in the figure. The centre of gravity (CG) of the wing (idealized as an airfoil) is marked. The number of degree(s) of freedom for this idealized wing vibration model is \underline{\hspace{1cm}}. \;(Answer in integer) \begin{center} \includegraphics[width=0.5\textwidth]{08.jpeg} \end{center}
Which of the following statement(s) is/are true about harmonically excited forced vibration of a single degree–of–freedom linear spring–mass–damper system?
Consider the four basic symmetrical flight loading conditions corresponding to the corners of a typical \(V\!-\!n\) diagram. For one condition it is observed that:
(i) the compressive bending stresses are maximum in the bottom aft region of the wing cross-section; and
(ii) the tensile bending stresses are maximum in the upper forward region of the wing cross-section (see figure).
Which flight loading condition corresponds to these observations? \begin{center} \includegraphics[width=0.5\textwidth]{06.jpeg} \end{center}
Which of the following statement(s) is/are true about the ribs of an airplane wing with semi–monocoque construction?
Which of the following statement(s) is/are true about the state of stress in a plane?