List of top Structures Questions asked in GATE AE

For a thin-walled I section, the width of the two flanges as well as the web height are the same, i.e., \( 2b = 20 \, \text{mm} \). Thickness is 0.6 mm.
The second moment of area about a horizontal axis passing through the centroid is _________ mm\(^4\).
Given: The tip deflection and tip slope for a tip-loaded cantilever of length \( L \) are: \[ \delta = \frac{NL^3}{3EI} \quad \text{and} \quad \theta = \frac{NL^2}{2EI}, \] where \( N \) is the tip force and \( EI \) is the flexural rigidity.
A cantilever \( PQ \) of rectangular cross-section is subjected to transverse load, \( F \), at its mid-point. Two cases are considered as shown in the figure. In Case I, the end \( Q \) is free and in Case II, \( Q \) is simply supported.
The ratio of the magnitude of the maximum bending stress at \( P \) in Case I to that in Case II is _________ (rounded off to one decimal place).
A 0.5 m long thin-walled circular shaft of radius 2 cm is to be designed for an axial load of 7.4 kN and a torque of 148 Nm applied at its tip, as shown in the figure.
The allowable stress under uniaxial tension is 100 MPa.
Using the maximum principal stress criterion, the minimum thickness, \( t \), of the shaft so that it does not fail is _________ mm (rounded off to the nearest integer).
A 10 kN axial load is applied eccentrically on a rod of square cross-section (1 cm $\times$ 1 cm) as shown in the figure.
The strains measured by the two strain gages attached to the top and bottom surfaces at a distance of 0.5 m from the tip are \( \varepsilon_1 = 0.0016 \) and \( \varepsilon_2 = 0.0004 \), respectively.
The eccentricity in loading, \( e \), is _________ mm.
A conventional airplane of mass 5000 kg is doing a level turn of radius 1000 m at a constant speed of 100 m/s at sea level.
Taking the acceleration due to gravity as 10 m/s\(^2\), the bank angle of the airplane is _________ degrees.
A convergent-divergent nozzle with adiabatic walls is designed for an exit Mach number of 2.3. It is discharging air to atmosphere under the conditions indicated in the figure.
Flow through the nozzle is inviscid, the characteristic gas constant for air is 287 J/(kg-K), and \( \gamma = 1.4 \).
When the reservoir pressure is 25 bar (absolute), and temperature is 300 K, Prandtl-Meyer expansion waves appear at the nozzle exit as shown.
The minimum percentage change in the reservoir pressure required to eliminate the wave system at the nozzle exit under steady state is _________ %.
Consider a circulation distribution over a finite wing given by the equation below.
\[ \Gamma(y) = \begin{cases} \Gamma_0 \left(1 - \frac{2y}{b}\right) & \text{if } 0 \leq y \leq \frac{b}{2}, \\ \Gamma_0 \left(1 + \frac{2y}{b}\right) & \text{if } -\frac{b}{2} \leq y \leq 0, \end{cases} \] The wingspan \( b \) is 10 m, the maximum circulation \( \Gamma_0 \) is 20 m\(^2\)/s, density of air is 1.2 kg/m\(^3\), and the free stream speed is 80 m/s.
The lift over the wing is _________ N (rounded off to the nearest integer).
A horizontal load \(F\) is applied at point R on a two-member truss, as shown in the figure. Both the members are prismatic with cross-sectional area \(A_0\), and made of the same material with Young's modulus \(E\). The horizontal displacement of point R is:
The two-dimensional plane-stress state at a point is: \[ \sigma_{xx} = 110\,\text{MPa},\quad \sigma_{yy} = 30\,\text{MPa},\quad \tau_{xy} = 40\,\text{MPa}. \] The normal stress $\sigma_n$ on a plane inclined at $45^\circ$ as shown is (round off to the nearest integer).
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:
An isotropic linear elastic material point under plane strain condition in the x–y plane always obeys:
A three-member truss is simply supported at Q and R, and loaded at P by a horizontal force \( F \) as shown. The force in QR is
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:
The closed thin-walled rectangular channel shown in figure (i) is opened by introducing a sharp cut at the center of the bottom edge, as shown in figure (ii). Which one of the following statements is correct?

A 3 m × 1 m signboard is subjected to a wind pressure of 7.5 kPa. It is supported by a hollow square pole of outer dimension 250 mm and inner dimension $d$ (unknown). The yield strength is 240 MPa. Find $d$ (round off to nearest integer).

Two cantilever beams AB and DC touch at their free ends through a roller. Both beams have a 50 mm × 50 mm square cross section and modulus \(E = 70\ \text{GPa}\). Beam AB carries a UDL of 20 kN/m. Determine the compressive force at the roller (round off to one decimal place). 

A two-cell wing box has wall thickness 1.5 mm and shear modulus \(G = 27\ \text{GPa}\). A torque of 12 kNm is applied. Determine the shear stress in wall AD (round off to one decimal place). 

A rigid horizontal bar ABC is supported by two columns BD and CE. BD is fixed at D, CE is pinned at E. A load $P$ is applied at distance $a$ from $B$. The columns are steel with $E = 200$ GPa and cross-section $1.5 \text{ cm} \times 1.5 \text{ cm}$. The lengths are: BD = 75 cm, CE = 125 cm. The value of $a$ for which both columns buckle simultaneously is \(\underline{\hspace{2cm}}\) cm (round off to one decimal place). 

A rigid massless rod pinned at one end has a mass $m$ attached to its other end. The rod is supported by a linear spring of stiffness $k$ as shown in the figure. The natural frequency of this system is: 

For the state of stress as shown in the figure, what is the orientation of the plane with maximum shear stress with respect to the x-axis? 

Uniaxial tension test (see the figure) is conducted on two different samples prepared with homogeneous, isotropic materials. One of the materials is brittle, whereas the other is ductile.

Assuming that there is no stress concentration at loading points, the failurewould initiate:

A two degree of freedom spring–mass system undergoes free vibration with natural frequencies \( \omega_1 = 233.9 \,\text{rad/s} \) and \( \omega_2 = 324.5 \,\text{rad/s} \). The mode shapes are \[ \phi_1 = \begin{bmatrix} 1 \\ -3.16 \end{bmatrix}, \phi_2 = \begin{bmatrix} 1 \\ 3.16 \end{bmatrix}. \] Given zero initial velocities, identify which initial deflections produce pure or mixed mode oscillations. \\
A thin-walled cylindrical tank is internally pressurized. If the hoop strain is thrice the axial strain, the Poisson's ratio of the material is \(\underline{\hspace{1cm}}\) (correct to one decimal place).
Two cantilever beams of same material & cross-section have lengths $l$ and $2l$. Find the ratio of their first natural frequencies (round off to nearest integer).
A spring-mass-damper system (m = 10 kg, k = 17400 N/m) has natural frequency 13.2 rad/s. Find the damping coefficient $c$ for critical damping (round off to nearest integer).