List of top Structures Questions on Beam Analysis asked in GATE AE

A cantilever beam with an unsymmetric cross-section is subjected to a transverse shear force (P) at its free end. P acts at the shear center of the beam cross-section. Which one of the following statements is TRUE about the deformation of this beam?

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 ___________.

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?

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 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}

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).

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)

Which of the following statement(s) about the elastic flexural buckling load of columns is/are correct?

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?