GATE AE Structures: Previous Year Questions

GATE AE 2026, Question 16 (1 mark, MCQ)

Structures - Strength of Materials

The number of independent elastic constants that a fully anisotropic linear elastic material can have is ______.

1. 36
2. 21
3. 10
4. 2

Official answer: B

GATE AE 2026, Question 17 (1 mark, MCQ)

Structures - Flight Vehicle Structures

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?

1. The beam undergoes only torsion
2. The beam undergoes only bending
3. The beam undergoes both torsion and bending
4. The beam undergoes neither torsion nor bending

Official answer: B

GATE AE 2026, Question 26 (1 mark, MSQ)

Structures - Strength of Materials

The state of stress at a point in a 2-D body, in the $x$-$y$ Cartesian coordinate system, is represented in matrix form as $[\sigma]$. The transformation matrix $[Q]$ rotates the coordinate system to a new $x'$-$y'$ Cartesian coordinate system. Select the CORRECT option(s) that represent(s) the state of stress in the new coordinate system.

1. $[Q][\sigma][Q]^T$
2. $[Q][\sigma][Q]^{-1}$
3. $([Q]^{-1})^T[\sigma][Q]^T$
4. $[Q]^{-1}[\sigma][Q]$

Official answer: A, B, C

GATE AE 2026, Question 33 (1 mark, NAT)

Structures - Structural Dynamics

The response $x(t)$ of a freely vibrating single degree of freedom underdamped system is given below. In the equation, $A$ and $\phi$ are constants. The damping ratio of the system is ________ (rounded off to 3 decimal places). $$x(t) = A e^{-5t}\sin(10t + \phi)$$

Official answer: 0.440 to 0.450

GATE AE 2026, Question 40 (2 marks, MCQ)

Structures - Strength of Materials

Consider a unit square body as shown in the figure below. The body is subjected to the deformation field $u = -ay$ and $v = ax$, where 'a' is a constant. Due to the application of this deformation field, the body undergoes ________ in the $x$-$y$ plane.

1. biaxial deformation
2. pure shear
3. pure bending
4. rigid body rotation

Official answer: D

GATE AE 2026, Question 45 (2 marks, MSQ)

Structures - Strength of Materials

The deformation of an open-section bar subjected to pure torsion can be solved by choosing an appropriate Prandtl stress function. Which of the following statements is/are true about the Prandtl stress function?

1. It satisfies the equilibrium equation
2. It is zero on the lateral surfaces of the bar
3. It satisfies the compatibility equation
4. It does not satisfy the equilibrium equation

Official answer: A, B, C

GATE AE 2026, Question 58 (2 marks, NAT)

Structures - Strength of Materials

A thin-walled circular tube is made of a material whose magnitude of the ultimate strength, both in tension and compression, is 200 MPa. The mean radius of the tube is 0.2 m and the wall thickness is 0.004 m. Based on the maximum stress criteria, the maximum torque that the tube can sustain is ________ kN-m (round off to the nearest integer).

Official answer: 197 to 202

GATE AE 2026, Question 59 (2 marks, NAT)

Structures - Structural Dynamics

A system comprising a bar, spring and mass is shown in the figure below. The bar, having negligible mass, is made of a material having Young's modulus $E = 200$ GPa, cross-sectional area $A = 100$ mm$^2$, and length $L = 100$ mm. The spring stiffness $k = 200$ kN/mm and the mass $M = 100$ kg. The natural frequency of free vibration of the system is ________ rad/s (rounded off to the nearest integer).

Official answer: 1000

GATE AE 2026, Question 60 (2 marks, NAT)

Structures - Strength of Materials

A stepped cantilever beam, made of a material having Young's modulus $E = 200$ GPa, is shown in the figure below. The length and the moment of inertia of the beam from point A to B are $L_1 = 100$ mm and $I_1 = 100$ mm$^4$, respectively. The length and the moment of inertia of the beam from point B to C are $L_2 = 100$ mm and $I_2 = 700$ mm$^4$, respectively. A shear force $P = 30$ N is applied at point A of the beam. The magnitude of the deflection of the beam at point A is ________ mm (rounded off to 1 decimal place).

Official answer: 0.9 to 1.1

GATE AE 2025, Question 26 (1 mark, MCQ)

Structures - Strength of Materials

For a homogeneous, isotropic material, the relation between the shear modulus ($G$), Young's modulus ($E$), and Poisson's ratio ($\nu$) is ____.

1. $G = 2E(1+\nu)$
2. $2G = E(1+\nu)$
3. $E = 2G(1+\nu)$
4. $2E = G(1+\nu)$

Official answer: C

GATE AE 2025, Question 27 (1 mark, MCQ)

Structures - Strength of Materials

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?

1. The magnitude of the vertical reaction force at A is larger than that at B.
2. The magnitude of the vertical reaction force at B is larger than that at A.
3. The magnitudes of the vertical reaction forces at A and B are equal.
4. The reactions at points A and B are indeterminate.

Official answer: A

GATE AE 2025, Question 28 (1 mark, MCQ)

Structures - Strength of Materials

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?

1. There is no body force per unit volume.
2. There is a constant body force per unit volume in the y-direction.
3. The body force per unit volume varies linearly in the y-direction.
4. The direction of the body force per unit volume depends on the value of $C_1$.

Official answer: B

GATE AE 2025, Question 29 (1 mark, MCQ)

Structures - Strength of Materials

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 _____.

1. $\dfrac{P^2L^3}{6EI}$
2. $\dfrac{PL^3}{3EI}$
3. $\dfrac{PL^3}{6EI}$
4. $\dfrac{P^2L^3}{3EI}$

Official answer: A

GATE AE 2025, Question 30 (1 mark, MCQ)

Structures - Strength of Materials

In the given figure, plate ABCD in its undeformed configuration (solid line) is a rhombus with all the internal angles being $90^\circ$. The lengths of the undeformed diagonals are 20 cm. Upon deformation, diagonal AC reduces to 19.96 cm and BD increases to 20.04 cm. In the given $x$-$y$ coordinate system, the engineering shear strain $\gamma_{xy}$ is equal to _____.

1. 0
2. 0.002
3. 0.004
4. -0.004

Official answer: A

GATE AE 2025, Question 37 (2 marks, MCQ)

Structures - Strength of Materials

A 1 m long rod is to be designed to support an axial tensile load $P$ ($P \gg$ 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? $$\begin{array}{|l|c|c|c|c|}\hline \text{Properties} & \text{Material } \alpha & \text{Material } \beta & \text{Material } \gamma & \text{Material } \delta \\ \hline \text{Density (kg/m}^3\text{)} & 2700 & 4500 & 7800 & 9000 \\ \text{Young's modulus (GPa)} & 70 & 115 & 200 & 130 \\ \text{Yield Strength (MPa)} & 270 & 900 & 520 & 540 \\ \hline\end{array}$$

1. Material $\alpha$
2. Material $\beta$
3. Material $\gamma$
4. Material $\delta$

Official answer: B

GATE AE 2025, Question 55 (2 marks, NAT)

Structures - Strength of Materials

A 1 m long rod of 1 cm $\times$ 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 $\times$ 0.998 cm. The Poisson's ratio of the material is ________ (rounded off to one decimal place).

Official answer: 0.4

GATE AE 2025, Question 56 (2 marks, NAT)

Structures - Strength of Materials

For a three-bar truss loaded as shown in the figure, the magnitude of the force in the horizontal member AB is ___N (answer in integer).

Official answer: 25

GATE AE 2025, Question 57 (2 marks, NAT)

Structures - Structural Dynamics

A uniform rigid bar of mass 3 kg is hinged at point F, and supported by a spring of stiffness k = 100 N/m, as shown in the figure. The natural frequency of free vibration of the system is ____ rad/s (answer in integer).

Official answer: 10

GATE AE 2025, Question 58 (2 marks, NAT)

Structures - Strength of Materials

A prismatic vertical column of cross-section $a \times 0.5a$ and length $l$ is rigidly fixed at the bottom and free at the top. A compressive force $P$ is applied along the centroidal axis at the top surface. The Young's modulus of the material is 200 GPa and the uniaxial yield stress is 400 MPa. If the critical value of $P$ for yielding and for buckling of the column are equal, the value of $\left(\dfrac{l}{a}\right)$ is _____ (rounded off to one decimal place).

Official answer: 5.0 to 5.1

GATE AE 2025, Question 59 (2 marks, NAT)

Structures - Strength of Materials

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).

Official answer: 1.25

GATE AE 2025, Question 60 (2 marks, NAT)

Structures - Flight Vehicle Structures

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).

Official answer: 1.20 to 1.22

GATE AE 2024, Question 13 (1 mark, MCQ)

Structures - Strength of Materials

The three-dimensional stress-strain relationship for an isotropic material is given as $$\begin{Bmatrix}\sigma_{xx}\\ \sigma_{yy}\\ \sigma_{zz}\\ \tau_{yz}\\ \tau_{zx}\\ \tau_{xy}\end{Bmatrix} = \begin{bmatrix} P & Q & Q & 0 & 0 & 0 \\ Q & P & Q & 0 & 0 & 0 \\ Q & Q & P & 0 & 0 & 0 \\ 0 & 0 & 0 & R & 0 & 0 \\ 0 & 0 & 0 & 0 & R & 0 \\ 0 & 0 & 0 & 0 & 0 & R \end{bmatrix}\begin{Bmatrix}\varepsilon_{xx}\\ \varepsilon_{yy}\\ \varepsilon_{zz}\\ \gamma_{yz}\\ \gamma_{zx}\\ \gamma_{xy}\end{Bmatrix}$$ where $P$, $Q$ and $R$ are the three elastic constants, $\sigma$ and $\tau$ represent normal and shear stresses and $\varepsilon$ and $\gamma$ represent normal and engineering shear strains. Which one of the following options is correct?

1. $R = \dfrac{P-Q}{2}$
2. $R = \dfrac{Q-P}{2}$
3. $Q = \dfrac{P-R}{2}$
4. $Q = \dfrac{R-P}{2}$

Official answer: A

GATE AE 2024, Question 14 (1 mark, MCQ)

Structures - Structural Dynamics

Consider the free vibration responses $P$, $Q$, $R$ and $S$ (shown in the figure) of a single degree of freedom spring-mass-damper system with the same initial conditions. For the different damping cases listed below, which one of the following options is correct? 1. Overdamped 2. Underdamped 3. Critically damped 4. Undamped

1. P – 1, Q – 4, R – 2, S – 3
2. P – 1, Q – 2, R – 4, S – 3
3. P – 3, Q – 4, R – 2, S – 1
4. P – 3, Q – 2, R – 4, S – 1

Official answer: C

GATE AE 2024, Question 15 (1 mark, MCQ)

Structures - Structural Dynamics

For a single degree of freedom spring-mass-damper system subjected to harmonic forcing, the part of the motion (response) that decays due to damping is known as:

1. transient response
2. steady-state response
3. harmonic response
4. non-transient response

Official answer: A

GATE AE 2024, Question 25 (1 mark, MSQ)

Structures - Strength of Materials

Which of the following options is/are correct?

1. The stress-strain graph for a nonlinear elastic material is as shown in the figure
2. Material properties are independent of position in a homogeneous material
3. An isotropic material has infinitely many planes of material symmetry
4. The stress-strain graph for a linear elastic material is as shown in the figure

Official answer: B, C, D

GATE AE 2024, Question 32 (1 mark, NAT)

Structures - Strength of Materials

A material has Poisson's ratio $\nu = 0.5$ and Young's modulus $E = 2500$ MPa. The percentage change in its volume when subjected to a hydrostatic stress of magnitude 10 MPa is ______ (answer in integer).

Official answer: 0

GATE AE 2024, Question 46 (2 marks, MSQ)

Structures - Strength of Materials

The figure shows plots of two yield loci for an isotropic material, where $\sigma_I$ and $\sigma_{II}$ are the principal stresses, and $\sigma_Y$ is the yield stress in uniaxial tension. Which of the following statements is/are correct?

1. Criterion P represents the von Mises criterion
2. Criterion Q represents the Tresca criterion
3. Criterion P represents the Tresca criterion
4. Criterion Q represents the von Mises criterion

Official answer: A, B

GATE AE 2024, Question 52 (2 marks, NAT)

Structures - Strength of Materials

The state of stress at a point is caused by two separate loading cases. One of them produces a pure uniaxial tension along the $x'$ direction, and other one produces a pure uniaxial compression along the $y'$ direction, as shown in the figure. The sum of maximum and minimum principal stresses for the resultant state of stress caused by both loads acting simultaneously is ___________ N/mm$^2$ (rounded off to 1 decimal place).

Official answer: 0

GATE AE 2024, Question 53 (2 marks, NAT)

Structures - Strength of Materials

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

Official answer: 141.0 to 141.5

GATE AE 2024, Question 54 (2 marks, NAT)

Structures - Flight Vehicle Structures

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

Official answer: 14900 to 15100

GATE AE 2024, Question 55 (2 marks, NAT)

Structures - Structural Dynamics

The equations of motion for a two degrees of freedom undamped spring-mass system are: $$m\ddot{x}_1 + 2kx_1 - kx_2 = 0$$ $$m\ddot{x}_2 - kx_1 + 2kx_2 = 0$$ where $m$ and $k$ represent mass and stiffness respectively, in corresponding SI units, and $x_1$ and $x_2$ are the degrees of freedom. The larger of the two natural frequencies is given by: $\omega = \alpha\sqrt{\dfrac{k}{m}}$ rad/s. The value of $\alpha$ is ________ (rounded off to 2 decimal places).

Official answer: 1.72 to 1.74

GATE AE 2024, Question 56 (2 marks, NAT)

Structures - Strength of Materials

Consider the plane strain field given by $$\varepsilon_{xx} = 10xy^2,\quad \varepsilon_{yy} = -5x^2y\quad \text{and}\quad \gamma_{xy} = A\,xy\,(2x - y)$$ where, $A$ is a constant and $\gamma_{xy}$ is the engineering shear strain. The value of the constant $A$ for the strain field to be compatible is _____________ (rounded off to 1 decimal place).

Official answer: 4.9 to 5.1

GATE AE 2023, Question 23 (1 mark, MCQ)

Structures - Flight Vehicle Structures

Consider the four basic symmetrical flight loading conditions corresponding to the corners of a typical $V$-$n$ diagram. For one of these flight loading conditions, it is observed that (i) the compressive bending stresses have a maximum value in the bottom aft region (see figure) of the wing cross-section; and (ii) the tensile bending stresses are maximum in the upper forward region (see figure) of the wing cross-section. For the preceding observations, select the corresponding flight loading condition from the options given.

1. Positive high angle of attack
2. Positive low angle of attack
3. Negative high angle of attack
4. Negative low angle of attack

Official answer: D

GATE AE 2023, Question 25 (1 mark, MSQ)

Structures - Structural Dynamics

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?

1. The total response of the mass is a combination of free vibration transient and steady-state response.
2. The free vibration transient dies out with time for each of the three possible conditions of damping (under-damped, critically damped, and over-damped).
3. The steady-state periodic response is dependent on the initial conditions at the time of application of external forcing.
4. The rate of decay of free vibration transient response depends on the mass, spring stiffness and damping constant.

Official answer: A, B, D

GATE AE 2023, Question 26 (1 mark, MSQ)

Structures - Strength of Materials

Which of the following statement(s) is/are true about the state of stress in a plane?

1. Maximum or major principal stress is algebraically the largest direct stress at a point.
2. The magnitude of minor principal stress cannot be greater than the magnitude of major principal stress.
3. The planes of maximum shear stress are inclined at 90 degrees to the principal axes.
4. The normal stresses along the planes of maximum shear stress are equal.

Official answer: A, D

GATE AE 2023, Question 27 (1 mark, MSQ)

Structures - Flight Vehicle Structures

Which of the following statement(s) is/are true about the ribs of an airplane wing with semi-monocoque construction?

1. For a rectangular planform wing, the dimensions of the ribs DO NOT depend on their spanwise position in the wing.
2. Ribs increase the column buckling stress of longitudinal stiffeners connected to them.
3. Ribs increase plate buckling stress of the skin panels.
4. Ribs help in maintaining aerodynamic shape of the wing.

Official answer: B, C, D

GATE AE 2023, Question 30 (1 mark, NAT)

Structures - Structural Dynamics

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 in the figure. The number of degree(s) of freedom for this idealized wing vibration model is ________. (Answer in integer)

Official answer: 2

GATE AE 2023, Question 47 (2 marks, MSQ)

Structures - Strength of Materials

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

1. The buckling load increases with increase in flexural rigidity of the column.
2. The buckling load increases with increase in the length of the column.
3. The boundary conditions of the column affect the buckling load.
4. The buckling load is NOT directly dependent on the density of the material used for the column.

Official answer: A, C, D

GATE AE 2023, Question 48 (2 marks, NAT)

Structures - Strength of Materials

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 $\tau_{thin-wall}$ obtained using the thin-wall approximation is _______. (round off to one decimal place)

Official answer: 1.1 to 1.3

GATE AE 2023, Question 49 (2 marks, NAT)

Structures - Strength of Materials

A rigid bar AB is subjected to a uniformly distributed load of 100 N/m as shown in the figure. The bar is supported by rod CD, with A, C, and D as pin joints. The rod CD has axial stiffness of 40 N/mm. The vertical deflection at point D is __________ mm. (round off to nearest integer)

Official answer: 10

GATE AE 2023, Question 50 (2 marks, NAT)

Structures - Strength of Materials

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

Official answer: 0.5

GATE AE 2023, Question 51 (2 marks, NAT)

Structures - Structural Dynamics

A single degree-of-freedom spring-mass-damper system has viscous damping ratio of 0.1. The mass is given an initial displacement of 10 cm without imparting any velocity. After exactly two complete cycles of oscillation (i.e., after time $2T_d$, where $T_d$ is the period of the damped vibration), the amplitude of the displacement is ______ cm. (round off to two decimal place)

Official answer: 2.80 to 2.86

GATE AE 2023, Question 52 (2 marks, NAT)

Structures - Flight Vehicle Structures

The shear flow distribution in a single cell, thin-walled beam under the action of an arbitrary shear load $S_y$ applied at the shear centre S is shown in the figure. The cell has horizontal symmetry with booms marked by 1 to 4 that carry direct stresses. The shear modulus G is the same for all the walls, and the area of the cell is 135000 mm$^2$. With respect to the point O marked in the figure, the distance to the shear centre S is ______ mm. (round off to the nearest integer)

Official answer: 196 to 198

GATE AE 2023, Question 53 (2 marks, NAT)

Structures - Strength of Materials

Consider a thin-walled cylindrical pressure vessel made of an alloy with yield strength of 300 MPa. The vessel has end caps to contain the pressure. The ratio of radius of the vessel to its wall thickness is 100. As per the von Mises yield criterion, the internal pressure that would cause the failure of the vessel is _____ MPa. (round off to two decimal places)

Official answer: 3.40 to 3.50

GATE AE 2022, Question 20 (1 mark, MCQ)

Structures - Strength of Materials

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:

1. only at the top fibres of the cross-section
2. only at the bottom fibres of the cross-section
3. both at the top and bottom fibres of the cross-section
4. only at the centroidal fibres of the cross-section

Official answer: B

GATE AE 2022, Question 21 (1 mark, MCQ)

Structures - Strength of Materials

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

1. 0
2. $F$ (tensile)
3. $\dfrac{F}{\sqrt{2}}$ (compressive)
4. $\sqrt{2}F$ (tensile)

Official answer: B

GATE AE 2022, Question 22 (1 mark, MCQ)

Structures - Flight Vehicle Structures

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?

1. Centroids of (i) and (ii) coincide while shear centers do not
2. Shear centers of (i) and (ii) coincide while centroids do not
3. Both centroids and shear centers of (i) and (ii) coincide
4. Neither centroids nor shear centers of (i) and (ii) coincide

Official answer: A

GATE AE 2022, Question 28 (1 mark, MSQ)

Structures - Strength of Materials

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 pure bending is/are:

Official answer: B, C

GATE AE 2022, Question 29 (1 mark, MSQ)

Structures - Strength of Materials

An isotropic linear elastic material point under plane strain condition in the x-y plane always obeys:

1. out-of-plane normal strain, $\epsilon_{zz} = 0$
2. out-of-plane normal stress, $\sigma_{zz} = 0$
3. out-of-plane shear stress, $\tau_{xz} = 0$
4. out-of-plane shear strain, $\gamma_{xz} = 0$

Official answer: A, C, D

GATE AE 2022, Question 33 (1 mark, NAT)

Structures - Strength of Materials

The two-dimensional plane-stress state at a point is: $\sigma_{xx} = 110$ MPa; $\sigma_{yy} = 30$ MPa; $\tau_{xy} = 40$ MPa. The normal stress, $\sigma_n$, on a plane inclined $45^\circ$ as shown in the figure is ____ MPa (round off to the nearest integer).

Official answer: 109 to 111

GATE AE 2022, Question 41 (2 marks, MCQ)

Structures - Strength of Materials

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:

1. 0
2. $\dfrac{Fl}{EA_0}$
3. $\sqrt{2}\dfrac{Fl}{EA_0}$
4. $2\dfrac{Fl}{EA_0}$

Official answer: C

GATE AE 2022, Question 57 (2 marks, NAT)

Structures - Strength of Materials

Given: The tip deflection and tip slope for a tip loaded cantilever of length $L$ are: $\dfrac{NL^3}{3EI}$ and $\dfrac{NL^2}{2EI}$, respectively, 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).

Official answer: 2.6 to 2.7

GATE AE 2022, Question 58 (2 marks, NAT)

Structures - Strength of Materials

A simply supported Aluminium column of length 1 m and rectangular cross-section $w \times t$ with $t \le w$, is subjected to axial compressive loading. Young's modulus is 70 GPa. Yield stress under uniaxial compression is 120 MPa. The value of $t$ at which the failure load for yielding and buckling coincide is ________ mm.

Official answer: 43 to 48

GATE AE 2022, Question 59 (2 marks, NAT)

Structures - Strength of Materials

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 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).

Official answer: 1

GATE AE 2022, Question 60 (2 marks, NAT)

Structures - Strength of Materials

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 $\epsilon_1 = 0.0016$ and $\epsilon_2 = 0.0004$, respectively. The eccentricity in loading, $e$ is _________ mm.

Official answer: 0.95 to 1.05

GATE AE 2022, Question 61 (2 marks, NAT)

Structures - Flight Vehicle Structures

For a thin-walled I section, the width of the two flanges as well as the web height are the same, i.e., $2b = 20$ mm. Thickness is 0.6 mm. The second moment of area about a horizontal axis passing through the centroid is ______ mm$^4$.

Official answer: 2700 to 2960

GATE AE 2022, Question 62 (2 marks, NAT)

Structures - Structural Dynamics

A damper with damping coefficient, $c$, is attached to a mass of 5 kg and spring of stiffness 5 kN/m as shown in figure. The system undergoes under-damped oscillations. If the ratio of the 3$^{\text{rd}}$ amplitude to the 4$^{\text{th}}$ amplitude of oscillations is 1.5, the value of $c$ is ____ Ns/m (rounded off to the nearest integer).

Official answer: 19 to 21

GATE AE 2022, Question 63 (2 marks, NAT)

Structures - Structural Dynamics

A uniform rigid prismatic bar of total mass $m$ is suspended from a ceiling by two identical springs as shown in figure. Let $\omega_1$ and $\omega_2$ be the natural frequencies of mode I and mode II respectively ($\omega_1 < \omega_2$). The value of $\omega_2/\omega_1$ is _________ (rounded off to one decimal place).

Official answer: 1.7 to 1.8

GATE AE 2018, Question 27 (1 mark, MCQ)

Structures - Flight Vehicle Structures

Determine the correctness or otherwise of the following statements, [a] and [r]: [a] A closed-section box beam configuration is used in aircraft wings. [r] Closed-section box beam configuration is capable of resisting torsional loads.

1. Both [a] and [r] are true and [r] is the correct reason for [a].
2. Both [a] and [r] are true but [r] is not the correct reason for [a].
3. Both [a] and [r] are false.
4. [a] is true but [r] is false.

Official answer: A

GATE AE 2018, Question 32 (1 mark, NAT)

Structures - Structural Dynamics

For a damped single degree of freedom system with damping ratio of 0.1, ratio of two successive peak amplitudes of free vibration is ___________ (accurate to two decimal places).

Official answer: 1.75 to 1.95

GATE AE 2018, Question 33 (1 mark, NAT)

Structures - Structural Dynamics

The natural frequency (in rad/s) of the spring-mass system shown in the figure below is _____ (accurate to one decimal place). (Springs $k_1 = k_2 = 20$ N/m; masses $m_1 = 6$ kg and $m_2 = 4$ kg joined by a rigid link.)

Official answer: 2

GATE AE 2018, Question 39 (2 marks, MCQ)

Structures - Strength of Materials

A solid circular shaft of diameter $d$ is under pure torsion of magnitude $T$. The maximum tensile stress experienced at any point on the shaft is

1. $\dfrac{32T}{\pi d^3}$
2. $\dfrac{16T}{\pi d^4}$
3. $\dfrac{32T}{\pi d^4}$
4. $\dfrac{16T}{\pi d^3}$

Official answer: D

GATE AE 2018, Question 40 (2 marks, MCQ)

Structures - Strength of Materials

A clamped-clamped beam, subjected to a point load $P$ at the midspan, is shown in the figure below. The magnitude of the moment reaction at the two fixed ends of the beam is

1. $PL/2$
2. $PL/4$
3. $PL/8$
4. $PL/16$

Official answer: C

GATE AE 2018, Question 41 (2 marks, MCQ)

Structures - Strength of Materials

Which of the following statement(s) is/are true about the state of a body in plane strain condition? P: All the points in the body undergo displacements in one plane only, for example the x-y plane, leading to $\varepsilon_{zz} = \gamma_{xz} = \gamma_{yz} = 0$. Q: All the components of stress perpendicular to the plane of deformation, for example the x-y plane, of the body are equal to zero, i.e. $\sigma_{zz} = \tau_{xz} = \tau_{yz} = 0$. R: Except the normal component, all the other components of stress perpendicular to the plane of deformation of the body, for example the x-y plane, are equal to zero, i.e. $\sigma_{zz} \neq 0$, $\tau_{xz} = \tau_{yz} = 0$.

1. P only
2. Q only
3. P and Q
4. P and R

Official answer: D

GATE AE 2018, Question 59 (2 marks, NAT)

Structures - Strength of Materials

A thin-walled tube with external radius of 100 mm and wall thickness of 2 mm, is fixed at one end. It is subjected to a compressive force of 1 N acting at a point on the circumference parallel to its length. The maximum normal stress (in kPa) experienced by the structure is _____________ (accurate to two decimal places).

Official answer: -2.50 to -2.20

GATE AE 2018, Question 60 (2 marks, NAT)

Structures - Structural Dynamics

A 1 m long massless cantilever beam oscillates at 2 Hz, while a 60 kg mass is attached at the tip of it. The flexural rigidity of the beam (in kN-m$^2$) is _________________ (accurate to two decimal places).

Official answer: 3.10 to 3.20

GATE AE 2018, Question 61 (2 marks, NAT)

Structures - Strength of Materials

A cantilever beam having a rectangular cross-section of width 60 mm and depth 100 mm, is made of aluminum alloy. The material mechanical properties are: Young's modulus, $E = 73$ GPa and ultimate stress, $\sigma_u = 480$ MPa. Assuming a factor of safety of 4, the maximum bending moment (in kN-m) that can be applied on the beam is _____ (accurate to one decimal place).

Official answer: 12

GATE AE 2018, Question 62 (2 marks, NAT)

Structures - Strength of Materials

The components of stress in a body under plane stress condition, in the absence of body forces, is given by: $\sigma_{xx} = Ax^2;\ \sigma_{yy} = 12x^2 - 6y^2$ and $\sigma_{xy} = 12xy$. The coefficient, $A$, such that the body is under equilibrium is _____ (accurate to one decimal place).

Official answer: -6

GATE AE 2016, Question 21 (1 mark, NAT)

Structures - Strength of Materials

The total number of material constants that are necessary and sufficient to describe the three dimensional Hooke's law for an isotropic material is ____.

Official answer: 2

GATE AE 2016, Question 22 (1 mark, MCQ)

Structures - Strength of Materials

Determine the correctness or otherwise of the following statements, [a] and [r]: [a]: In a plane stress problem, the shear strains along the thickness direction of a body are zero but the normal strain along the thickness is not zero. [r]: In a plane stress problem, Poisson effect induces the normal strain along the thickness direction of the body.

1. Both [a] and [r] are true and [r] is the correct reason for [a].
2. Both [a] and [r] are true but [r] is not the correct reason for [a].
3. Both [a] and [r] are false.
4. [a] is true but [r] is false.

Official answer: A

GATE AE 2016, Question 23 (1 mark, MCQ)

Structures - Flight Vehicle Structures

Consider four thin-walled beams of different open cross-sections, as shown in the cases (i-iv). A shear force of magnitude 'F' acts vertically downward at the location 'P' in all the beams. In which of the following case, does the shear force induce bending and twisting?

1. (i)
2. (ii)
3. (iii)
4. (iv)

Official answer: B

GATE AE 2016, Question 24 (1 mark, NAT)

Structures - Structural Dynamics

The effective stiffness of the spring-mass system as shown in the figure below is ____ N/mm.

Official answer: 5

GATE AE 2016, Question 25 (1 mark, MCQ)

Structures - Strength of Materials

A structural member supports loads, which produce at a particular point, a state of pure shear stress of 50 N/mm$^2$. At what angles are the principal planes oriented with respect to the plane of pure shear?

1. $\pi/6$ and $2\pi/3$
2. $\pi/4$ and $3\pi/4$
3. $\pi/4$ and $\pi/2$
4. $\pi/2$ and $\pi$

Official answer: B

GATE AE 2016, Question 47 (2 marks, NAT)

Structures - Strength of Materials

A bar made of linear elastic isotropic material is fixed at one end and subjected to an axial force of 1 kN at the other end. The cross-sectional area of the bar is 100 mm$^2$, length is 100 mm and the Young's Modulus is $1 \times 10^5$ N/mm$^2$. The strain energy stored in the bar is ____ Nmm.

Official answer: 5

GATE AE 2016, Question 48 (2 marks, NAT)

Structures - Strength of Materials

A cantilever beam-spring system is shown in the figure. The beam is made with a material of Young's modulus $1 \times 10^5$ N/mm$^2$ and geometry such that its moment of inertia is 100 mm$^4$ and length $l = 100$ mm. It is supported by a spring of stiffness $K = 30$ N/mm and subjected to a load of $P = 100$ N at the point 'B'. The deflection at the point 'B' due to the load P is ____ mm.

Official answer: 1.5 to 1.7

GATE AE 2016, Question 49 (2 marks, MCQ)

Structures - Flight Vehicle Structures

Determine the correctness or otherwise of the following statements, [a] and [r]: [a]: Ribs, used in airplane wings, increase the column buckling strength of the longitudinal stiffeners. [r]: Ribs distribute concentrated loads into the structure and redistribute stresses around discontinuities.

1. Both [a] and [r] are true and [r] is the correct reason for [a]
2. Both [a] and [r] are true but [r] is not the correct reason for [a]
3. Both [a] and [r] are false
4. [a] is true but [r] is false

Official answer: B

GATE AE 2016, Question 50 (2 marks, NAT)

Structures - Flight Vehicle Structures

A channel section shown in the figure has uniform thickness. It is subjected to an anticlockwise torque of $62.5 \times 10^3$ Nmm. The maximum possible thickness of the channel section, such that the shear stress induced in it does not exceed 100 N/mm$^2$, is ____ mm.

Official answer: 2.4 to 2.6

GATE AE 2016, Question 51 (2 marks, NAT)

Structures - Structural Dynamics

The governing differential equation of motion of a damped system is given by $m\dfrac{d^2x}{dt^2} + c\dfrac{dx}{dt} + kx = 0$. If $m = 1$ kg, $c = 2$ Ns/m and $k = 2$ N/m then the frequency of the damped oscillation of this system is ____ rad/s.

Official answer: 0.99 to 1.01

GATE AE 2016, Question 52 (2 marks, NAT)

Structures - Strength of Materials

The two dimensional state of stress in a body is described by the Airy's stress function: $\phi = 5\dfrac{x^4}{12} + \dfrac{x^3y}{6} + 3\dfrac{x^2y^2}{2} + 7\dfrac{xy^3}{6} + E\dfrac{y^4}{12}$. The Airy's stress function will satisfy the equilibrium and the compatibility requirements if and only if the value of the coefficient E is ____.

Official answer: -11

GATE AE 2014, Question 21 (1 mark, MCQ)

Structures - Strength of Materials

It is desired to measure the Young's modulus and the Poisson's ratio of a given homogeneous, isotropic material. A bar of length 20 cm and square cross-section (10 mm $\times$ 10 mm) of this material is subjected to a tensile load of 40 kN. Under this load, length increases to 20.1 cm while the cross-section reduces to 9.98 mm $\times$ 9.98 mm. Young's modulus and Poisson's ratio of the material are:

1. 80 GPa & 0.4 respectively
2. 40 GPa & -0.4 respectively
3. 80 GPa & -0.2 respectively
4. 40 GPa & 0.2 respectively

Official answer: A

GATE AE 2014, Question 22 (1 mark, MCQ)

Structures - Strength of Materials

In general, for any given solid subjected to arbitrary loading, which of the following statements is always true:

1. Volume does not vary with loading
2. Mass does not vary with loading
3. Density does not vary with loading
4. Volume, mass and density vary with loading

Official answer: B

GATE AE 2014, Question 23 (1 mark, MCQ)

Structures - Strength of Materials

Which one of the following objects with inclined face at $45^\circ$, subjected to the given stresses, are in static equilibrium:

Official answer: B

GATE AE 2014, Question 24 (1 mark, NAT)

Structures - Structural Dynamics

A damped single degree of freedom system whose undamped natural frequency, $\omega_n = 10$ Hz, is subjected to sinusoidal external force. Power is half of the maximum for the two frequencies of 60.9469 rad/s and 64.7168 rad/s. The damping factor associated with the vibrating system (in %) is _______.

Official answer: 2.95 to 3.05

GATE AE 2014, Question 25 (1 mark, MCQ)

Structures - Structural Dynamics

The boundary conditions for a rod with circular cross-section, under torsional vibration, are changed from fixed-free to fixed-fixed. The fundamental natural frequency of the fixed-fixed rod is $k$ times that of fixed-free rod. The value of $k$ is

1. 1.5
2. $\pi$
3. 2.0
4. 0.5

Official answer: C

GATE AE 2014, Question 48 (2 marks, NAT)

Structures - Strength of Materials

A 1.8 m long steel beam of rectangular cross section (10 mm $\times$ 6 mm) is simply supported with a length of 1.2 m between the supports and an overhang of 0.3 m on either side. Young's modulus for the material of the beam is 200 GPa. For a 50 N load applied at the center of the beam, magnitude of the slope of the beam at tip $S$ is _______.

Official answer: 0.12 to 0.13

GATE AE 2014, Question 49 (2 marks, MCQ)

Structures - Strength of Materials

There are 2 designs proposed for a shaft of length $l$, with a torque carrying capacity of $T$. Design I is a solid circular cross-section shaft of diameter 30 mm. Design II is a thin-walled circular shaft of average diameter 40 mm. Thickness of the wall in Design II has to be determined such that maximum shear stress is the same in both the designs for the given torque $T$ (so that same material can be used for manufacturing both the shafts). Ratio of mass of shaft using Design I to the mass of shaft using Design II is

1. 2.68
2. 5.36
3. 1.79
4. 3.58

Official answer: A

GATE AE 2014, Question 50 (2 marks, MCQ)

Structures - Strength of Materials

A structural member of rectangular cross-section 10 mm $\times$ 6 mm and length 1 m is made of steel (Young's modulus is 200 GPa and coefficient of thermal expansion is $12 \times 10^{-6}/{}^\circ$C). It is rigidly fixed at both the ends and then subjected to a gradual increase in temperature. Ignoring the three dimensional effects, the structural member will buckle if the temperature is increased by $\Delta T\ ^\circ$C which is

1. 19.74
2. 9.87
3. 78.96
4. 39.48

Official answer: B

GATE AE 2014, Question 51 (2 marks, MCQ)

Structures - Strength of Materials

A gas cylinder (closed thin-walled cylindrical pressure vessel) of diameter 30 cm and wall thickness 1 mm is subjected to a design maximum internal pressure of 5 bar (0.5 MPa). The material used for manufacturing this cylinder has a failure stress of 260 MPa. Assuming von Mises failure criterion, the factor of safety (with respect to maximum allowable stress) for this cylinder is

1. 2.8
2. 2.0
3. 6.9
4. 4.0

Official answer: D

GATE AE 2014, Question 52 (2 marks, MCQ)

Structures - Strength of Materials

A cantilevered beam is subjected to a parabolic distribution of shear traction at the right edge while the top and bottom surfaces are traction free. To solve this problem, following Airy's stress function is proposed: $\phi = C_1xy + C_2xy^3 + C_3x^2y^2 + C_4x^3y$. This is an admissible Airy's function that would satisfy the bi-harmonic equation as well as the boundary conditions if and only if

1. $C_1 = 0, C_2 = \lambda, C_3 = 0, C_4 = \dfrac{\lambda}{3d^2}$
2. $C_1 = \lambda, C_2 = \dfrac{\lambda}{3d^2}, C_3 = 0, C_4 = 0$
3. $C_1 = 0, C_2 = 0, C_3 = \lambda, C_4 = -\dfrac{\lambda}{3d^2}$
4. $C_1 = \lambda, C_2 = -\dfrac{\lambda}{3d^2}, C_3 = 0, C_4 = 0$

Official answer: D

GATE AE 2014, Question 53 (2 marks, MCQ)

Structures - Structural Dynamics

A 1 kg mass is hanging from a spring of stiffness 500 N/m attached to a massless, symmetric beam of length 0.6 m, moment of inertia about the bending axis $I = 8.33 \times 10^{-10}$ m$^4$ and Young's modulus $E = 210$ GPa as shown in the figure. The fundamental natural frequency (in rad/s) of the system is

1. 3.24
2. 20.36
3. 22.36
4. 3.56

Official answer: B

GATE AE 2014, Question 54 (2 marks, MCQ)

Structures - Structural Dynamics

A single degree of freedom system is vibrating with initial (first cycle) amplitude of 5 cm. The viscous damping factor associated with the vibrating system is 2%. Vibration amplitude of the fifth cycle (in cm) is

1. 1.65
2. 4.41
3. 2.67
4. 3.02

Official answer: D