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201

GATE2014-1-36
In a reinforced concrete section, the stress at the extreme fibre in compression is $5.80$ MPa. The depth of neutral axis in the section is $58$ mm and the grade of concrete is $M25$. Assuming linear elastic behavior of the concrete, the effective curvature of the section (in per mm) is $2.0 \times 10^{-6}$ $3.0 \times 10^{-6}$ $4.0 \times 10^{-6}$ $5.0 \times 10^{-6}$

In a reinforced concrete section, the stress at the extreme fibre in compression is $5.80$ MPa. The depth of neutral axis in the section is $58$ mm and the grade of concr...

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202

GATE2014-1-27
A box of weight $100$ kN shown in the figure is to be lifted without swinging. If all forces are coplanar, the magnitude and direction $( \theta)$ of the force $(F)$ with respect to $x$-axis should be $F=56.389$ kN and $\theta=28.28^{\circ}$ $F=-56.389$ kN and $\theta=-28.28^{\circ}$ $F=9.055$ kN and $\theta=1.414^{\circ}$ $F=-9.055$ kN and $\theta=-1.414^{\circ}$

A box of weight $100$ kN shown in the figure is to be lifted without swinging. If all forces are coplanar, the magnitude and direction $( \theta)$ of the force $(F)$ with...

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203

GATE2014-1-30
Mathematical idealization of a crane has three bars with their vertices arranged as shown in the figure with a load of $80$ kN hanging vertically. The coordinates of the vertices are given in parentheses. The force in the member $QR$, $F_{QR}$ will be $30$ kN Compressive $30$ kN Tensile $50$ Compressive $50$ kN Tensile

Mathematical idealization of a crane has three bars with their vertices arranged as shown in the figure with a load of $80$ kN hanging vertically. The coordinates of the ...

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204

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 ______

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 locate...

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205

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 ______

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

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206

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 $8$ $10$ $12$ $16$

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 o...

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207

GATE2014-1-26
If the following equation establishes equilibrium in slightly bent position, the mid-span deflection of a member shown in the figure is $\frac{d^2y}{dx^2}+\frac{P}{EI}y=0$ If $a$ is amplitude constant for $y,$ then $y=\dfrac{1}{P} \bigg( 1- a \cos \dfrac{2 \pi x}{L} \bigg) \\$ ... $y= a \sin \dfrac{n \pi x}{L} \\$ $y= a \cos \dfrac{n \pi x}{L}$

If the following equation establishes equilibrium in slightly bent position, the mid-span deflection of a member shown in the figure is$$\frac{d^2y}{dx^2}+\frac{P}{EI}y=0...

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208

GATE2014-1-7
The possible location of shear centre of the channel section, shown below, is $P$ $Q$ $R$ $S$

The possible location of shear centre of the channel section, shown below, is$P$$Q$$R$$S$

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209

GATE2014-1-8
The ultimate collapse load $(P)$ in terms of plastic moment $M_p$ by kinematic approach for a propped cantilever of length $L$ with $P$ acting at its mid-span as shown in the figure, would be $P=\dfrac{2M_p}{L} \\$ $P=\dfrac{4M_p}{L} \\$ $P=\dfrac{6M_p}{L}\\$ $P=\dfrac{8M_p}{L}$

The ultimate collapse load $(P)$ in terms of plastic moment $M_p$ by kinematic approach for a propped cantilever of length $L$ with $P$ acting at its mid-span as shown in...

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210

GATE2014-1-9
While designing, for a steel column of $Fe250$ grade, a base plate resting on a concrete pedestal of $M20$ grade, the bearing strength of concrete (in $N/mm^2$) in limit state method of design as per $IS:456-2000$ is ________

While designing, for a steel column of $Fe250$ grade, a base plate resting on a concrete pedestal of $M20$ grade, the bearing strength of concrete (in $N/mm^2$) in limit ...

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211

GATE2014-1-10
A steel section is subjected to a combination of shear and bending actions. The applied shear force is $V$ and the shear capacity of the section is $V_s$. For such a section, high shear force (as per $IS : 800 – 2007$) is defined as $V>0.6V_s$ $V>0.7V_s$ $V>0.8V_s$ $V>0.9V_s$

A steel section is subjected to a combination of shear and bending actions. The applied shear force is $V$ and the shear capacity of the section is $V_s$. For such a sect...

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212

GATE2014-1-11
The degree of static indeterminacy of a rigid joined frame $\text{PQR}$ supported as shown in the figure is zero one two unstable

The degree of static indeterminacy of a rigid joined frame $\text{PQR}$ supported as shown in the figure iszeroonetwounstable

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213

GATE2014-1-12
In a beam of length $L$, four possible influence line diagram for shear force at a section located at a distance of $\dfrac{L}{4}$ from the left end support (marked as $P, Q, R,$ and $S$) are shown below. The correct influence line diagram is $P$ $Q$ $R$ $S$

In a beam of length $L$, four possible influence line diagram for shear force at a section located at a distance of $\dfrac{L}{4}$ from the left end support (marked as $P...

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214

GATE2014-1-6
Match the information given in Group - I with those in Group - II. ... $P-3; \: Q-4; \: R - 2;\: S - 1$ $P-4; \: Q-3; \: R - 2;\: S - 1$

Match the information given in Group – I with those in Group – II.$\begin{array}{llll} {} & \text{Group – I} & {} & \text{Group – II} \\ P & \text{Factor to decre...

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215

GATE Civil 2013 | Question: 44
Elevation and temperature data for a place are tabulated below: $\begin{array}{|c|c|} \hline \text{Elevation, m} & \text{Temperature, } ^{\circ}C \\ \hline 4 & 21.25 \\ \hline 444 & 15.70 \\ \hline \end{array}$ Based on the above data, lapse rate can be referred as Super-adiabatic Neutral Sub-adiabatic Inversion

Elevation and temperature data for a place are tabulated below:$$\begin{array}{|c|c|} \hline \text{Elevation, m} & \text{Temperature, } ^{\circ}C \\ \hline 4 & 21.25 \\ \...

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216

GATE Civil 2013 | Question: 48
A propped cantilever made of a prismatic steel beam is subjected to a concentrated load P at mid span as shown. If load $P=80$ kN, find the reaction $R$ (in kN) correct to $1$-decimal place) using elastic analysis ________

A propped cantilever made of a prismatic steel beam is subjected to a concentrated load P at mid span as shown.If load $P=80$ kN, find the reaction $R$ (in kN) correct to...

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217

GATE Civil 2013 | Question: 49
A propped cantilever made of a prismatic steel beam is subjected to a concentrated load P at mid span as shown. If the magnitude of load $P$ is increased till collapse and the plastic moment carrying capacity of steel beam section is $90$ kNm, determine reaction $R$ (in kN) (correct to $1$-decimal place) using plastic analysis _______

A propped cantilever made of a prismatic steel beam is subjected to a concentrated load P at mid span as shown.If the magnitude of load $P$ is increased till collapse and...

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218

GATE Civil 2013 | Question: 31
All members in the rigid-jointed frame shown are prismatic and have the same flexural stiffness $EI$. Find the magnitude of the bending moment at $Q$ (in kNm) due to given loading ________

All members in the rigid-jointed frame shown are prismatic and have the same flexural stiffness $EI$. Find the magnitude of the bending moment at $Q$ (in kNm) due to give...

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219

GATE Civil 2013 | Question: 32
A uniform beam $(EI = \textit{constant})PQ$ in the form of a quarter-circle of radius $R$ is fixed at end $P$ and free at the end $Q$, where a load $W$ is applied as shown. The vertical downward displacement, $\delta_q$, at the loaded point $Q$ is ... $\delta_q = \beta \bigg( \dfrac{WR^3}{EI} \bigg)$. Find the value of $\beta$(correct to $4$-decimal places). ______

A uniform beam $(EI = \textit{constant})PQ$ in the form of a quarter-circle of radius $R$ is fixed at end $P$ and free at the end $Q$, where a load $W$ is applied as show...

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220

GATE Civil 2013 | Question: 33
A uniform beam weighing $1800 \: N$ is supported at E and F by cable ABCD. Determine the tension (in $N$) in segment AB of this cable (correct to $1$- decimal place). Assume the cables ABCD, BE and CF to be weightless. _______

A uniform beam weighing $1800 \: N$ is supported at E and F by cable ABCD. Determine the tension (in $N$) in segment AB of this cable (correct to $1$- decimal place). Ass...

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221

GATE Civil 2013 | Question: 34
Beam $PQRS$ has internal hinges in spans $PQ$ and $RS$ as shown. The beam may be subjected to a moving distributed vertical load of maximum intensity $4 \:kN/m$ of any length anywhere on the beam. The maximum absolute value of the shear force (in $kN$) that can occur due to this loading just to the right of support $Q$ shall be $30$ $40$ $45$ $55$

Beam $PQRS$ has internal hinges in spans $PQ$ and $RS$ as shown. The beam may be subjected to a moving distributed vertical load of maximum intensity $4 \:kN/m$ of any le...

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222

GATE Civil 2013 | Question: 35
A rectangular concrete beam $250$ mm wide and $600$ mm deep is pre-stressed by means of $16$ high tensile wires, each of $7$ mm diameter, located at $200$ mm from the bottom face of the beamat a given section. If the effective pre- ... beam can with stand without causing tensile stress at the bottom face of of the beam? Neglect the effect of dead load of beam ______

A rectangular concrete beam $250$ mm wide and $600$ mm deep is pre-stressed by means of $16$ high tensile wires, each of $7$ mm diameter, located at $200$ mm from the bot...

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223

GATE Civil 2013 | Question: 26
The state of $2D$-stress at a point is given by the following matrix of stresses: $\begin{bmatrix} \sigma_{xx} & \sigma_{xy} \\ \sigma_{xy} & \sigma_{yy} \end{bmatrix} = \begin{bmatrix} 100 & 30 \\ 30 & 20 \end{bmatrix} MPa$ What is the magnitude of the maximum shear stress in MPa $50$ $75$ $100$ $110$

The state of $2D$-stress at a point is given by the following matrix of stresses:$$\begin{bmatrix} \sigma_{xx} & \sigma_{xy} \\ \sigma_{xy} & \sigma_{yy} \end{bmatrix} = ...

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224

GATE Civil 2013 | Question: 8
The ‘plane section remains plane’ assumption in bending theory implies strain profile is linear stress profile is linear both strain and strain profiles are linear shear deformations are neglected

The ‘plane section remains plane’ assumption in bending theory impliesstrain profile is linearstress profile is linearboth strain and strain profiles are linearshear ...

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225

GATE Civil 2013 | Question: 9
Two steel columns P (length $L$ and yield strength $f_y=250$ MPa) and Q (length $2L$ and yield strength $f_y=500$ MPa) have the same cross-sections and end-conditions. The ratio of buckling load of column P to that of column Q is $0.5$ $1.0$ $2.0$ $4.0$

Two steel columns P (length $L$ and yield strength $f_y=250$ MPa) and Q (length $2L$ and yield strength $f_y=500$ MPa) have the same cross-sections and end-conditions. Th...

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226

GATE Civil 2013 | Question: 10
The pin-jointed $2-D$ truss is loaded with a horizontal force of $15 \: kN$ at joint S and another $15 \: kN$ vertical force at joint U, as shown. Find the force in member RS (in $kN$) and report your answer taking tension as positive and compression as negative _________

The pin-jointed $2-D$ truss is loaded with a horizontal force of $15 \: kN$ at joint S and another $15 \: kN$ vertical force at joint U, as shown. Find the force in membe...

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227

GATE Civil 2013 | Question: 11
A symmetric I-section (with width of each flange $=50$ mm, thickness of each flange $=10$ mm, depth of web $=100$ mm, and thickness of web $=10$ mm) of steel is subjected to a shear force of $100$ kN. Find the magnitude of the shear stress (in $N/mm^2$) in the web at its junction with the top flange _______

A symmetric I-section (with width of each flange $=50$ mm, thickness of each flange $=10$ mm, depth of web $=100$ mm, and thickness of web $=10$ mm) of steel is subjected...

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228

GATE Civil 2013 | Question: 4
Maximum possible value of Compacting Factor for fresh (green) concrete is $0.5$ $1.0$ $1.5$ $2.0$

Maximum possible value of Compacting Factor for fresh (green) concrete is$0.5$$1.0$$1.5$$2.0$

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229

GATE Civil 2013 | Question: 5
As per $IS \: 800:2007$, the cross-section in which the extreme fiber can reach the yield stress, but cannot develop the plastic moment of resistance due to failure by local buckling is classified as plastic section compact section semi-compact section slender section

As per $IS \: 800:2007$, the cross-section in which the extreme fiber can reach the yield stress, but cannot develop the plastic moment of resistance due to failure by lo...

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230

GATE Civil 2013 | Question: 6
The creep strains are caused due to dead loads only caused due to live loads only caused due to cyclic loads only independent of loads

The creep strains arecaused due to dead loads onlycaused due to live loads onlycaused due to cyclic loads onlyindependent of loads

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231

GATE Civil 2013 | Question: 7
As per $IS \: 456:2000$ for $M20$ grade concrete and plain barsin tension the design bond stress $\tau_{bd}=1.2$ MPa. Further, $IS \: 456:2000$ permits this design bond stress value to be increased by $60 \%$ for HSD bars. The stress ... tension, $\sigma_s=360$ MPa. Find the required development length, $L_d$, for HSD barsin terms of the bar diameter, $\phi$ ________

As per $IS \: 456:2000$ for $M20$ grade concrete and plain barsin tension the design bond stress $\tau_{bd}=1.2$ MPa. Further, $IS \: 456:2000$ permits this design bond s...

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232

GATE Civil 2012 | Question: 52
The cross-section at mid-span of a beam at the edge of a slab is shown in the sketch. A portion of the slab is considered as the effective flange width for the beam. The grades of concrete and reinforcing steel are $M25$ and $Fe415$, respectively. The total area of ... mm) computed as per the Limit State Method of $IS \: 456:2000$ is $200.0$ $223.3$ $236.3$ $273.6$

The cross-section at mid-span of a beam at the edge of a slab is shown in the sketch. A portion of the slab is considered as the effective flange width for the beam. The ...

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233

GATE Civil 2012 | Question: 53
The cross-section at mid-span of a beam at the edge of a slab is shown in the sketch. A portion of the slab is considered as the effective flange width for the beam. The grades of concrete and reinforcing steel are M25 and Fe415, respectively. The total area of reinforcing ... , as per the Limit State Method of $\text{IS } 456:2000$ is $475.2$ $717.0$ $756.4$ $762.5$

The cross-section at mid-span of a beam at the edge of a slab is shown in the sketch. A portion of the slab is considered as the effective flange width for the beam. The ...

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234

GATE Civil 2012 | Question: 33
A concrete beam prestressed with a parabolic tendon is shown in the sketch. The eccentricity of the tendon is measured from the centroid of the cross-section. The applied prestressing force at service is $1620$ kN. The uniformly distributed load of $45$ kN/m ... in the bottom fibre at mid-span is tensile $2.90$ compressive $2.90$ tensile $4.32$ compressive $4.32$

A concrete beam prestressed with a parabolic tendon is shown in the sketch. The eccentricity of the tendon is measured from the centroid of the cross-section. The applied...

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235

GATE Civil 2012 | Question: 34
A symmetric frame $PQR$ consists of two inclined members $PQ$ and $QR$, connected at $‘Q’$ with a rigid joint, and hinged at $‘P’$ and $‘R’$. The horizontal length $PR$ is $l$. If a weight $W$ is suspended at $‘Q’$, the bending moment at $‘Q’$ is $\dfrac{Wl}{2} \\$ $\dfrac{Wl}{4} \\$ $\dfrac{Wl}{8} \\$ zero

A symmetric frame $PQR$ consists of two inclined members $PQ$ and $QR$, connected at $‘Q’$ with a rigid joint, and hinged at $‘P’$ and $‘R’$. The horizontal l...

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236

GATE Civil 2012 | Question: 35
Two plates are connected by filler welds of size $10$ mm and subjected to tension, as shown in the sketch. The thickness of each plate is $12$ mm. The yield stress and the ultimate tensile stress of steel are $250$ MPa and $410$ MPa, respectively. The welding is done ... mm) of each weld to transmit a force $P$ equal to $270$ kN is $100$ mm $105$ mm $110$ mm $115$ mm

Two plates are connected by filler welds of size $10$ mm and subjected to tension, as shown in the sketch. The thickness of each plate is $12$ mm. The yield stress and th...

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237

GATE Civil 2012 | Question: 31
A simply supported beam is subjected ti a uniformly distributed load of intensity $w$ per unit length, on half of the span from one end. The length of the span and the flexural stiffness are denoted as $l$ and $EI$ ... $\dfrac{5}{384} \dfrac{wl^4}{EI} \\$ $\dfrac{5}{192} \dfrac{wl^4}{EI}$

A simply supported beam is subjected ti a uniformly distributed load of intensity $w$ per unit length, on half of the span from one end. The length of the span and the fl...

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238

GATE Civil 2012 | Question: 32
The sketch shows a column with a pin at the base and rollers at the top. It is subjected to an axial force $P$ and a moment $M$ at mid-height. The reaction(s) at R is/are a vertical force equal to $P$ a vertical force equal to $P/2$ a vertical force equal to $P$ an a horizontal force equal to $M/h$ a vertical force equal to $P/2$ and a horizontal force equal to $M/h$

The sketch shows a column with a pin at the base and rollers at the top. It is subjected to an axial force $P$ and a moment $M$ at mid-height. The reaction(s) at R is/are...

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239

GATE Civil 2012 | Question: 13
As per the Indian Standard soil classification system, a sample of silty clay liquid limit of $40\%$ and plasticity index of $28\%$ is classified as CH CI CL CL-ML

As per the Indian Standard soil classification system, a sample of silty clay liquid limit of $40\%$ and plasticity index of $28\%$ is classified asCHCICLCL-ML

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240

GATE Civil 2012 | Question: 14
A smooth rigid retaining wall moves as shown in the sketch causing the backfill material to fail. The backfill material is homogeneous and isotrophic, and obeys the Mohr-Coulomb failure criterion. The major principal stress is parallel to the ... acting downwards normal to the wall face oblique to the wall face acting downwards oblique to the wall face acting upwards

A smooth rigid retaining wall moves as shown in the sketch causing the backfill material to fail. The backfill material is homogeneous and isotrophic, and obeys the Mohr-...

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