Recent questions and answers in Solid Mechanics - GATE Civil Q&A

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1

GATE Civil 2021 Set 2 | Question: 6
Strain hardening of structural steel means experiencing higher stress than yield stress with increased deformation strengthening steel member externally for reducing strain experienced strain occurring before plastic flow of steel material decrease in the stress experienced with increasing strain

asked Mar 1 in Solid Mechanics by jothee (5.2k points)

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2

GATE Civil 2021 Set 2 | Question: 19
A solid circular torsional member $\text{OPQ}$ is subjected to torsional moments as shown in the figure (not to scale). The yield shear strength of the constituent material is $\text{160 MPa}$. The absolute maximum shear stress in the member (in $\text{MPa}$, $\textit{round off to one decimal place}$) is __________________________

asked Mar 1 in Solid Mechanics by jothee (5.2k points)

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3

GATE Civil 2021 Set 2 | Question: 29
A frame $\text{EFG}$ is shown in the figure. All members are prismatic and have equal flexural rigidity. The member $\text{FG}$ carries a uniformly distributed load $\text{w}$ per unit length. Axial deformation of any member is neglected. Considering the joint $\text{F}$ being ... $\text{0.375 wL}$ $\text{0.453 wL}$ $\text{0.482 wL}$ $\text{0.500 wL}$

asked Mar 1 in Solid Mechanics by jothee (5.2k points)

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4

GATE Civil 2021 Set 2 | Question: 37
An elevated cylindrical water storage tank is shown in the figure. The tank has inner diameter of $\text{1.5 m}$. It is supported on a solid steel circular column of diameter $\text{75 mm}$ and total height $\text{(L)}$ of $\text{4m}$ ... $\text{(h)}$ of the water permissible (in $\text{m}$, $\textit{round off to one decimal place}$) is ________________________

asked Mar 1 in Solid Mechanics by jothee (5.2k points)

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5

GATE Civil 2021 Set 1 | Question: 4
A propped cantilever beam $\text{EF}$ is subjected to a unit moving load as shown in the figure (not to scale). The sign convention for positive shear force at the left and right sides of any section is also shown. The $\text{CORRECT}$ qualitative nature of the influence line diagram for shear force at $\text{G}$ is

asked Feb 20 in Solid Mechanics by Arjun (8.7k points)

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6

GATE Civil 2021 Set 1 | Question: 20
The state of stress in a deformable body is shown in the figure. Consider transformation of the stress from the $\text{x-y}$ coordinate system to the $\text{X-Y}$ coordinate system. The angle $\theta$, locating the $\text{X}$-axis, is ... $\text{MPa}, \textit{round off to one decimal place}$) in $\text{x-y}$ coordinate system is ______________________

asked Feb 20 in Solid Mechanics by Arjun (8.7k points)

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7

GATE Civil 2021 Set 1 | Question: 38
Refer the truss as shown in the figure (not to scale). If load, $F=10\sqrt{3}\text{ kN}$, moment of inertia, $I=8.33\times 10^{6}\text{ mm}^4$, area of cross-section, $A=10^{4}\text{ mm}^2$, and length, $L=2\text{ m}$ ... members of the truss, the compressive stress (in $\text{kN/m}^2, \textit{in integer}$) carried by the member $\text{Q-R}$ is _______________

asked Feb 20 in Solid Mechanics by Arjun (8.7k points)

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8

GATE2020-CE-1-19
A planar elastic structure is subjected to uniformly distributed load, as shown in the figure (not drawn to the scale) Neglecting self-weight, the maximum bending moment generated in the structure (in $kN.m$, round off to the nearest integer), is _______.

asked Feb 28, 2020 in Solid Mechanics by jothee (5.2k points)

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9

GATE2020-CE-1-30
A cantilever beam $\textbf{PQ}$ of uniform flexural rigidity (EI) is subjected to a concentrated moment M at $\textbf{R}$ as shown in the figure The deflection at the free end $\textbf{Q}$ is $\large\frac{ML^2}{6EI} \\$ $\large\frac{ML^2}{4EI} \\$ $\large\frac{3ML^2}{8EI} \\$ $\large\frac{3ML^2}{4EI} $

asked Feb 28, 2020 in Solid Mechanics by jothee (5.2k points)

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10

GATE2020-CE-1-42
The flange and web plates of the doubly symmetric built-up section are connected by continuous $10\:mm$ thick fillet welds as shown in figure (not drawn to the scale). The moment of inertia of the section about its principal axis $X-X$ ... welds. The maximum shear force (in $kN$ , round off to one decimal place ) that can be carried by the section, is ______.

asked Feb 28, 2020 in Solid Mechanics by jothee (5.2k points)

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11

GATE2020 CE-2-28
A prismatic linearly elastic bar of length $L$, cross-sectional area $A$, and made up of a material with Young's modulus $E$, is subjected to axial tensile force as shown in the figures. When the bar is subjected to axial tensile forces $P_1$ and $P_2$, the strain energies stored ... the correct relationship is $U = U_1 + U_2$ $U = U_1 - U_2$ $U < U_1 + U_2$ $U > U_1 + U_2$

asked Feb 13, 2020 in Solid Mechanics by jothee (5.2k points)

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12

GATE2020 CE-2-29
The planar structure $RST$ shown in the figure is roller-supported at $S$ and pin-supported at $R.$ Members $RS$ and $ST$ have uniform flexural rigidity $(EI)$ and $S$ is a rigid joint. Consider only bending deformation and neglect effects of self-weight and axial stiffening. When the ... $R,$ is $\dfrac{PL^3}{12EI}$ $\dfrac{PL^2}{12EI}$ $\dfrac{PL^2}{6EI}$ $\dfrac{PL}{6EI}$

asked Feb 13, 2020 in Solid Mechanics by jothee (5.2k points)

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13

GATE2017 CE-2-16
In a material under a state of plane strain, a $10 \times 10$ mm square centered at a point gets deformed as shown in the figure. If the shear strain $\gamma_{xy}$ at this point is expressed as $0.001k$ (in rad), the value of $k$ is $0.50$ $0.25$ $- 0.25$ $- 0.50$

asked Aug 7, 2019 in Solid Mechanics 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 Solid Mechanics 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 Solid Mechanics by gatecse (4k points)

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16

GATE2017 CE-2-38
Two towers, A and B, standing vertically on a horizontal ground, appear in a vertical aerial photograph as shown in the figure. The length of the image of the tower A on the photograph is $1.5$ cm and the tower B is $2.0$ cm. The distance of the top tower A ( ... point $p$ of the photograph. If the height of the tower B is $80$ m, the height (in meters) of the tower A is ________

asked Aug 7, 2019 in Solid Mechanics by gatecse (4k points)

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17

GATE2017 CE-2-39
A hallow circular shaft has an outer diameter of $100 $ mm and inner diameter of $50 $ mm. If the allowable shear stress is $125$ MPa, the maximum torque (in kN-m) that the shaft can resist is _______

asked Aug 7, 2019 in Solid Mechanics by gatecse (4k points)

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18

GATE2019 CE-1: 6
An element is subjected to biaxial normal tensile strains of $0.0030$ and $0.0020$. The normal strain in the plane of maximum shear strain is Zero $0.0010$ $0.0025$ $0.0050$

asked Feb 14, 2019 in Solid Mechanics by Arjun (8.7k points)

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19

GATE2019 CE-1: 8
Assuming that there is no possibility of shear buckling in the web, the maximum reduction permitted by $\text{IS 800-2007}$ in the (low-shear) design bending strength of a semi-compact steel section due to high shear is zero $\text{25 %}$ $\text{50 %}$ governed bye the area of the flange

asked Feb 14, 2019 in Solid Mechanics by Arjun (8.7k points)

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20

GATE2019 CE-1: 31
The cross-section of a built-up wooden beam as shown in the figure (not drawn to scale) is subjected to a vertical shear force of $8 \: kN$. The beam is symmetrical about the neural axis (N.A.) shown, and the moment of inertia about N.A. is $1.5 \times 10^9 \: mm^4$. ... , each of the nails at P will be subjected to the shear force of $60 \: N$ $120 \: N$ $240 \: N$ $480 \: N$

asked Feb 14, 2019 in Solid Mechanics by Arjun (8.7k points)

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21

GATE2019 CE-2: 5
A closed thin-walled tube has thickness, $t$, mean enclosed area within the boundary of the centerline of tube’s thickness, $A_m$, and shear stress, $\tau$. Torsional moment of resistance, $T$, of the section would be $0.5 \tau A_m t$ $\tau A_m t$ $2 \tau A_m t$ $4 \tau A_m t$

asked Feb 12, 2019 in Solid Mechanics by Arjun (8.7k points)

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22

GATE2019 CE-2: 8
For a channel section subjected to a downward vertical shear force at its centroid, which one of the following represents the correct distribution of shear stress in flange and web?

asked Feb 12, 2019 in Solid Mechanics by Arjun (8.7k points)

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23

GATE2019 CE-2: 29
For a plane stress problem, the state of stress at a point P is represented by the stress element as shown in figure. By how much angle $( \theta)$ in degrees the stress element should be rotated in order to get the planes of maximum shear stress? $13.3$ $26.6$ $31.7$ $48.3$

asked Feb 12, 2019 in Solid Mechanics by Arjun (8.7k points)

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24

GATE2019 CE-2: 36
A long uniformly distributed load of $10 \: kN/m$ and a concentrated load of $60 \: kN$ are moving together on the beam ABCD shown in the figure (not drawn to scale). The relative positions of the two loads are not fixed. The maximum shear force (in $kN$, round off to the nearest integer) caused at the internal hinge B due to the two loads is _________

asked Feb 12, 2019 in Solid Mechanics by Arjun (8.7k points)

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25

GATE2019 CE-2: 39
When a specimen of $M25$ concrete is loaded to a stress level of $12.5 \: MPa$, a strain of $500 \times 10^{-6}$ is recorded. If this load is allowed to stand for a long time, the strain increases to $1000 \times 10^{-6}$. In ... with the provisions of $IS:456-2000$, considering the long-term effects, the effective modulus of elasticity of the concrete (in $MPa$) is _________

asked Feb 12, 2019 in Solid Mechanics by Arjun (8.7k points)

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26

GATE2016-2-16
Group I contains the types of fluids while group II contains the shear stress - rate of shear relationship of different types of fluids, as shown in the figure. ... $P-2, Q-5, R-4, S-1$ $P-2, Q-4, R-5, S-3$ $P-2, Q-1, R-3, S-4$

asked Mar 28, 2018 in Solid Mechanics by Milicevic3306 (11.9k points)

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27

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 Solid Mechanics by Milicevic3306 (11.9k points)

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28

GATE2016-2-35
A haunched (varying depth) reinforced concrete beam is simply supported at both ends, as shown in the figure. The beam is subjected to a uniformly distributed factored load of intensity $10 \: kN/m$. The design shear force (expressed in $kN$) at the section X-X of the beam is ________

asked Mar 28, 2018 in Solid Mechanics 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 Solid Mechanics by Milicevic3306 (11.9k points)

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30

GATE2017 CE-1: 41
Consider the beam ABCD shown in the figure. For a moving concentrated load of $50$ kN on the beam, the magnitude of the maximum bending moment (in kN-m) obtained at the support C will be equal to ________.

asked Mar 26, 2018 in Solid Mechanics by Milicevic3306 (11.9k points)

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31

GATE2015-2-7
For the plane stress situation shown in the figure, the maximum shear stress and the plane on which it acts are: $-50$ MPa, on a plane $45^{\circ}$ clockwise w.r.t. $x$-axis $-50$ MPa, on a plane $45^{\circ}$ anti-clockwise w.r.t. $x$-axis $50$ MPa at all orientations Zero, at all orientations

asked Mar 26, 2018 in Solid Mechanics by Milicevic3306 (11.9k points)

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32

GATE2015-2-40
Stress path equation for tri-axial test upon application of deviatoric stress is, $q=10 \sqrt{3}+0.5p$. The respective values of cohesion, $c$ (in kPa) and angle of internal friction, $\phi$ are: $20$ and $20^{\circ}$ $20$ and $30^{\circ}$ $30$ and $30^{\circ}$ $30$ and $20^{\circ}$

asked Mar 26, 2018 in Solid Mechanics by Milicevic3306 (11.9k points)

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33

GATE2015-1-6
Consider the singly reinforced beam shown in the figure below: At cross-section $XX$, which of the following statements is TRUE at the limit state? The variation of stress is linear and that of strain is non-linear The variation of strain is linear and that of stress is non-linear The variation of both stress and strain is linear The variation of both stress and strain is non - linear

asked Mar 26, 2018 in Solid Mechanics by Milicevic3306 (11.9k points)

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34

GATE2014-2-46
A suspension of sand like particles in water with particles of diameter $0.10$ mm and below is flowing into a settling tank at $0.10 \: m^3/s$. Assume $g=9.81 \: m/s^2$, specific gravity of particles $=2.65$ ... are (in $m^2$) required for this settling tank to remove particles of size $0.06$ mm and above with $100 \%$ efficiency is ___________

asked Mar 26, 2018 in Solid Mechanics by Milicevic3306 (11.9k points)

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35

GATE2014-2-30
The values of axial stress $(\sigma)$ in $kN/m^2$, bending moment $(M)$ in kNm, and shear force $(V)$ in kN acting at point P fr the arrangement shown in the figure are respectively. $1000, 75$ and $25$ $1250, 150$ and $50$ $1500, 225$ and $75$ $1750, 300$ and $100$

asked Mar 26, 2018 in Solid Mechanics by Milicevic3306 (11.9k points)

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36

GATE2014-2-10
The flexural tensile strength of $M25$ grade of concrete, in $N/mm^2$, as per $IS:456-2000$ is _______

asked Mar 26, 2018 in Solid Mechanics by Milicevic3306 (11.9k points)

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37

GATE2014-2-7
The first moment of area about the axis of bending for a beam cross-section is moment inertia section modulus shape factor polar moment of inertia

asked Mar 26, 2018 in Solid Mechanics by Milicevic3306 (11.9k points)

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38

GATE2014-2-6
Group I contains representative stress-strain curves as shown in the figure, while Group II gives the list of materials. Match the stress-strain curves with the corresponding materials. ... $P-3; \: Q - 1; \: R-2$ $P-3; \: Q - 2; \: R-1$

asked Mar 26, 2018 in Solid Mechanics by Milicevic3306 (11.9k points)

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39

GATE2014-1-34
The tension and shear force (both in kN) in each bolt of the joint, as shown below, respectively are $30.33$ and $20.00$ $30.33$ and $25.00$ $33.33$ and $20.00$ $33.33$ and $25.00$

asked Mar 26, 2018 in Solid Mechanics by Milicevic3306 (11.9k points)

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40

GATE2014-1-33
A rectangular beam of width $(b)$ $230$ mm and effective depth $(d)$ $450$ mm is reinforced with four bars of $12$ mm diameter. The grade of concrete is $M20$ and grade of steel is $Fe500$. Given that for $M20$ ... diameter (in mm) of $Fe500$ steel two legged stirrups to be used at spacing of $375$ mm, should be $8$ $10$ $12$ $16$

asked Mar 26, 2018 in Solid Mechanics by Milicevic3306 (11.9k points)

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