Recent questions and answers in Structural Analysis

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1

GATE Civil 2021 Set 2 | Question: 7
A single story building model is shown in the figure. The rigid bar of mass $\text{m}$' is supported by three massless elastic columns whose ends are fixed against rotation. For each of the columns, the applied lateral force $\text{(P)}$ ... $6\sqrt{\frac{6EI}{mL^{3}}}\text{rad/s}$ $\frac{2}{L}\sqrt{\frac{EI}{m}}\text{rad/s}$

asked Mar 1 in Structural Analysis by jothee (5.2k points)

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GATE Civil 2021 Set 2 | Question: 20
A propped cantilever beam $\text{XY}$, with an internal hinge at the middle, is carrying a uniformly distributed load of $\text{10 kN/m}$, as shown in the figure. The vertical reaction at support $\text{X}$ ( in $\text{kN}$, $\textit{in integer}$) is ___________

asked Mar 1 in Structural Analysis by jothee (5.2k points)

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GATE Civil 2021 Set 2 | Question: 38
A prismatic fixed-fixed beam, modelled with a total lumped-mass of $\text{10 kg}$ as a single degree of freedom $\text{(SDOF)}$ system is shown in the figure. If the flexural stiffness of the beam is $4 \pi ^{2}$ $\text{kN/m}$, its natural frequency of vibration (in $\text{Hz}$, $\textit{in integer}$) in the flexural mode will be ______________

asked Mar 1 in Structural Analysis by jothee (5.2k points)

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4

GATE Civil 2021 Set 2 | Question: 39
A perfectly flexible and inextensible cable is shown in the figure (not to scale). The external loads at $\text{F}$ and $\text{G}$ are acting vertically. The magnitude of tension in the cable segment $\text{FG}$ (in $\text{kN}, \textit{round off to two decimal places}$) is ________________________

asked Mar 1 in Structural Analysis by jothee (5.2k points)

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5

GATE Civil 2021 Set 1 | Question: 21
The equation of deformation is derived to be $y=x^{2}-xL$ for a beam shown in the figure. The curvature of the beam at the mid-span (in units, in integer) will be _________________

asked Feb 20 in Structural Analysis by Arjun (8.7k points)

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GATE Civil 2021 Set 1 | Question: 22
A truss $\text{EFGH}$ is shown in the figure, in which all the members have the same axial rigidity $\text{R}$. In the figure, $\text{P}$ is the magnitude of external horizontal forces acting at joints $\text{F}$ ... of the horizontal displacement of joint $\text{G}$ (in $\text{mm}, \textit{round off to one decimal place}$) is _____________________

asked Feb 20 in Structural Analysis by Arjun (8.7k points)

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7

GATE Civil 2021 Set 1 | Question: 41
Employ stiffness matrix approach for the simply supported beam as shown in the figure to calculate unknown displacements/rotations. Take length, $L=8\text{ m}$; modulus of elasticity, $E=3\times 10^{4} \text{N/mm}^{2}$ ... (in $\text{mm}, \textit{round off to integer}$) under $\text{P=100 kN}$ in downward direction will be _________________

asked Feb 20 in Structural Analysis by Arjun (8.7k points)

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8

GATE2020-CE-1-5
Consider the planar truss shown in the figure (not drawn to the scale) Neglecting self weight of the numbers, the number of zero-force members in the truss under the action of the load $P$, is $6$ $7$ $8$ $9$

asked Feb 28, 2020 in Structural Analysis by jothee (5.2k points)

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9

GATE2020-CE-1-41
A rigid, uniform, weightless, horizontal bar is connected to three vertical members P , Q and R as shown in the figure (not drawn to the scale). All three members have identical axial stiffness of $10\:kN/mm$ . The lower ends of bars $P$ and $R$ rest ... $W$ (in $kN$, round off to the nearest integer), is ______.

asked Feb 28, 2020 in Structural Analysis by jothee (5.2k points)

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10

GATE2020 CE-2-7
A weightless cantilever beam of span L is loaded as shown in the figure. For the entire span of the beam, the material properties are identical and the cross section is rectangular with constant width. From the flexure-critical perspective, the most economical longitudinal profile of the beam to carry the given loads among the options given below, is

asked Feb 13, 2020 in Structural Analysis by jothee (5.2k points)

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11

GATE2020 CE-2-30
Joints $I,J,K,L,Q$ and $M$ of the frame shown in the figure (not drawn to the scale) are pins. Continuous members $IQ$ and $LJ$ are connected through a pin at $N$. Continuous members $JM$ and $KQ$ are connected through a pin at $P$. The frame has hinge ... positive $X$ direction. The magnitude of the horizontal component of reaction $\text{(in kN)}$ at $S,$ is $5$ $10$ $15$ $20$

asked Feb 13, 2020 in Structural Analysis by jothee (5.2k points)

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12

GATE2020 CE-2-42
The plane truss has hinge supports at $P$ and $W$ and is subjected to the horizontal forces as shown in the figure (not drawn to the scale) Representing the tensile force with $’+’$ sign and the compressive force with $’-’$ sign, the force in member $XW$ (in $kN$, round off to the nearest integer), is ________.

asked Feb 13, 2020 in Structural Analysis by jothee (5.2k points)

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13

GATE2017 CE-2-14
Consider the following frame in the figure: If the axial and shear deformations in different members of the frame are assumed to be negligible, the reduction in the degree of kinematical indeterminacy would be equal to $5$ $6$ $7$ $8$

asked Aug 7, 2019 in Structural Analysis by gatecse (4k points)

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14

GATE2017 CE-2-31
Two prismatic beams having the same flexural rigidity of $1000 \: kN-m^2$ are shown in the figures. If the mid-span deflections of these beams are denoted by $\delta_1$ and $\delta_2$ (as indicated in the figures), the correct option is $\delta_1 = \delta_2$ $\delta_1 < \delta_2$ $\delta_1 > \delta_2$ $\delta_1 >> \delta_2$

asked Aug 7, 2019 in Structural Analysis by gatecse (4k points)

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15

GATE2017 CE-2-32
Consider the prismatic beams with the clamped supports P, Q, and R as shown in the figures. Given that eh modulus of elasticity, $E$ is $2.5 \times 10^4$ MPa; and the moment of inertia, $I$ is $8 \times 10^8 \: mm^4$, the correct comparison of the magnitudes of the ... $M_P = M_Q>M_R$ $S_P < S_Q> S_R$; $M_P = M_Q=M_R$ $S_P < S_Q< S_R$; $M_P < M_Q < M_R$

asked Aug 7, 2019 in Structural Analysis by gatecse (4k points)

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16

GATE2017 CE-2-42
Consider the portal frame shown in the figure and assume the modulus of elasticity, $E=2.5 \times 10^4$ MPa and the moment of inertia, $I= 8 \times 10^8 \: mm^4$ for all the members of the frame. The rotation (in degrees, up to one decimal place) at the rigid joint Q would be ____________

asked Aug 7, 2019 in Structural Analysis by gatecse (4k points)

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17

GATE2019 CE-1: 5
A plane truss is shown in the figure (not drawn to scale). Which one of the options contains ONLY zero force members in the truss? $\text{FG,FI,HI,RS}$ $\text{FG,FH,HI,RS}$ $\text{FI,HI,PR,RS}$ $\text{FI,FG,RS,PR}$

asked Feb 14, 2019 in Structural Analysis by Arjun (8.7k points)

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18

GATE2019 CE-1: 7
Consider the pin-jointed plane truss shown in the figure $\text{(not drawn to scale)}$.Let $R_{P}, R_{Q}$ and $R_{R}$ denote the vertical reactions (upward positive) applied by the supports at $P, Q$ and $R,$ ... by $\text{(30,-30,30)kN}$ $\text{(20,0,10)kN}$ $\text{(10,30,-10)kN}$ $\text{(0,60,-30)kN}$

asked Feb 14, 2019 in Structural Analysis by Arjun (8.7k points)

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19

GATE2019 CE-1: 32
The rigid-jointed plane frame QRS shown in the figure is subjected to a load $P$ at the joint $R$. Let the axial deformations in the frame be neglected. If the support $S$ undergoes a settlement of $\Delta = \frac{PL^3}{\beta EI}$, the vertical reaction at the support $S$ will become zero when $\beta$ is equal to $0.1$ $3.0$ $7.5$ $48.0$

asked Feb 14, 2019 in Structural Analysis by Arjun (8.7k points)

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20

GATE2019 CE-1: 39
A portal frame shown in figure (not drawn to scale) has a hinge support at joint P and a roller support at joint R. A point load of $50 \: kN$ is acting at joint in R in the horizontal direction. The flexural rigidity. EI, of each number is $10^6 \: kNm^2$. Under the applied load, the horizontal displacement (in mm, round off to $1$ decimal place) of joint R would be _________

asked Feb 14, 2019 in Structural Analysis by Arjun (8.7k points)

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21

GATE2019 CE-2: 20
The degree of static indeterminacy of the plane frame as shown in the figure is ________

asked Feb 12, 2019 in Structural Analysis by Arjun (8.7k points)

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22

GATE2019 CE-2: 37
A plane frame shown in the figure (not to scale) has linear elastic springs at node H. The spring constants are $k_x = k_y = 5 \times 10^5 kN/m$ and $k_{\theta} =3 \times 10^5 \: kNm/rad$. For the externally applied moment of $30 \: kNm$ at node F, the rotation (in degrees, round off to $3$ decimals) observed in the rotational spring at node H is ______

asked Feb 12, 2019 in Structural Analysis by Arjun (8.7k points)

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23

GATE2019 CE-2: 38
A rolled $I$-section beam is supported in a $75 \: mm$ wide bearing plate as shown in the figure. Thicknesses of flange and web of the $I$ section $20 \: mm$ and $8 \: mm$, respectively. Root radius of the $I$-section is $10 \: mm$. Assume: material ... $IS: 800-2007$, the web bearing strength (in $kN$, round off to $2$ decimal places) of the beam is __________

asked Feb 12, 2019 in Structural Analysis by Arjun (8.7k points)

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24

GATE2016-2-33
The portal frame shown in the figure is subjected to a uniformly distributed vertical load $w$ (per unit length). The bending moment in the beam at the joint ‘Q’ is zero $\dfrac{wL^2}{24}$ (hogging) $\dfrac{wL^2}{12}$ (hogging) $\dfrac{wL^2}{8}$ (sagging)

asked Mar 28, 2018 in Structural Analysis by Milicevic3306 (11.9k points)

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25

GATE2016-1-6
Consider the plane truss with load P as shown in the figure. Let the horizontal and vertical reactions at the joint $\textbf{B}$ be $H_B$ and $V_B$, respectively and $V_C$ be the vertical reaction at the joint $\textbf{C}$. Which one of the following sets gives the correct values of $V_B$, $H_B$ ... $V_B=P; \: H_B = P (\cos 60^{\circ}); \: V_C=0$

asked Mar 28, 2018 in Structural Analysis by Milicevic3306 (11.9k points)

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26

GATE2016-1-31
A $3$ m long simply supported beam of uniform cross section is subjected to a uniformly distributed load of $w=20$kN/m in the central $1$ m as shown in the figure. If the flexural rigidity (EI) of the beam is $30 \times 10^6 \: N-m^2$, the maximum slope (expressed in radians) of the ... is $0.681 \times 10^{-7}$ $0.943 \times 10^{-7}$ $4.310 \times 10^{-7}$ $5.910 \times 10^{-7}$

asked Mar 28, 2018 in Structural Analysis by Milicevic3306 (11.9k points)

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27

GATE2016-1-32
Two beams $PQ$ (fixed at $P$ and with a roller support at $Q$, as shown in Figure I, which allows vertical movement) and $XZ$ (with a hinge at $Y$) are shown in the Figures I and II respectively. The spans of $PQ$ and $XZ$ are $L$ and $2L$ respectively. Both the ... $\delta_{\text{max1}} = \delta_{\text{max2}}$ and $\theta_{\text{max1}} = \theta_{\text{max2}}$

asked Mar 28, 2018 in Structural Analysis by Milicevic3306 (11.9k points)

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28

GATE2016-1-33
A plane truss with applied loads is shown in the figure. The members which do not carry any force are FT, TG, HU, MP, PL ET, GS, UR, VR, QL FT, GS, HU, MP, QL MP, PL, HU, FT, UR

asked Mar 28, 2018 in Structural Analysis by Milicevic3306 (11.9k points)

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29

GATE2017 CE-1: 7
The figure shows a two-hinged parabolic arch of span $L$ subjected to a uniformly distributed load of intensity $q$ per unit length. The maximum bending moment in the arch is equal to $\dfrac{qL^2}{8} \\$ $\dfrac{qL^2}{12} \\$ zero $\dfrac{qL^2}{10}$

asked Mar 26, 2018 in Structural Analysis by Milicevic3306 (11.9k points)

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30

GATE2017 CE-1: 29
A planar truss tower structure is shown in the figure. Consider the following statements about the external and internal determinacies of the truss. Externally Determinate External Static Indeterminacy $=1$ External Static Indeterminacy $=2$ Internally Determinate Internal Static Indeterminacy $=1$ ... S-False; T-False; U- True P-True; Q- True; R-False; S-True; T-False; U- True

asked Mar 26, 2018 in Structural Analysis by Milicevic3306 (11.9k points)

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31

GATE2017 CE-1: 40
The value of $M$ in the beam ABC shown in the figure is such that the joint B does not rotate. The value of support reaction (in kN) at B should be equal to _________.

asked Mar 26, 2018 in Structural Analysis by Milicevic3306 (11.9k points)

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32

GATE2015-2-6
A horizontal beam $ABC$ is loaded as shown in the figure below. The distance of the point of contraflexure from end $A$ (in m) is _________

asked Mar 26, 2018 in Structural Analysis by Milicevic3306 (11.9k points)

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33

GATE2015-2-8
A guided support as shown in the figure below is represented by three springs (horizontal, vertical and rotational) with stiffness $k_x, k_y$ and $k_{\theta}$ respectively. The limiting values of $k_x, k_y$ and $k_{\theta}$ are: $\infty, 0, \infty$ $\infty, \infty, \infty$ $0, \infty, \infty$ $\infty, \infty, 0$

asked Mar 26, 2018 in Structural Analysis by Milicevic3306 (11.9k points)

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34

GATE2015-2-33
A simply supported beam AB of span, $L=24$ m is subjected to two wheel loads acting at a distance, $d=5$ m apart as shown in the figure below. Each wheel transmits a load, $P=3$ kN and may occupy any position along the beam. If the beam is an $I$-section having section modulus, $S=16.2 \:cm^3$, the maximum bending stress (in GPa) due to the wheel loads is _______.

asked Mar 26, 2018 in Structural Analysis by Milicevic3306 (11.9k points)

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35

GATE2015-1-7
For the beam shown below, the stiffness coefficient $K_{22}$ can be written as $\dfrac{6EI}{L^2} \\$ $\dfrac{12EI}{L^3} \\$ $\dfrac{3EI}{L} \\$ $\dfrac{EI}{6L^2}$

asked Mar 26, 2018 in Structural Analysis by Milicevic3306 (11.9k points)

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36

GATE2015-1-33
Consider the singly reinforced beam section given below (left figure). The stress block parameters for the cross-section from $IS:456-2000$ are also given below (right figure). The moment of resistance for the given section by the limit state method is _______ kN-m

asked Mar 26, 2018 in Structural Analysis by Milicevic3306 (11.9k points)

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37

GATE2015-1-37
For the $2D$ truss with the applied loads shown below, the strain energy in the member $XY$ is _____ kN-m. For member $XY$, assume $AE=30$ kN, where $A$ is cross-section area and $E$ is the modulus of elasticity.

asked Mar 26, 2018 in Structural Analysis by Milicevic3306 (11.9k points)

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38

GATE2014-2-35
The tension (in kN) in a $10$ m long cable, shown in the figure, neglecting its self-weight is $120$ $75$ $60$ $45$

asked Mar 26, 2018 in Structural Analysis by Milicevic3306 (11.9k points)

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39

GATE2014-1-32
For the truss shown below, the member $PQ$ is short by $3$ mm. The magnitude of vertical displacement of joint $R$ (in mm) is ______

asked Mar 26, 2018 in Structural Analysis by Milicevic3306 (11.9k points)

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40

GATE2014-1-31
For the cantilever beam of span $3$ m (shown below) m concentrated load of $20 \: kN$ applied at the free end causes a vertical displacement of $2$ mm at a section located at a distance of $1$ m from the fixed end. If a concentrated vertically downward load ... m from the fixed end (with no other load on the beam), the maximum vertical displacement in the same beam (in mm) is ______

asked Mar 26, 2018 in Structural Analysis by Milicevic3306 (11.9k points)