Recent questions tagged deflection-of-beams

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GATE2020-ME-1: 40
The barrier shown between two water tanks of unit width $(1\: m)$ into the plane of the screen in modeled as a cantilever. Taking the density of water as $1000\:kg/m^{3}$ , and the acceleration due to gravity as $10\:m/s^{2}$ , the maximum absolute bending moment developed in the cantilever is _________$kN\cdot m$ (round off to the nearest integer).

The barrier shown between two water tanks of unit width $(1\: m)$ into the plane of the screen in modeled as a cantilever.Taking the density of water as $1000\:kg/m^{3}$ ...

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go_editor asked Feb 19, 2020

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GATE2020-ME-1: 41
The magnitude of reaction force at joint $C$ of the hinge-beam shown in the figure is __________$kN$ (round off to $2$ decimal places).

The magnitude of reaction force at joint $C$ of the hinge-beam shown in the figure is __________$kN$ (round off to $2$ decimal places).

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go_editor asked Feb 19, 2020

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GATE2019 ME-2: 8
Endurance limit of a beam subjected to pure bending decreases with decrease in the surface roughness and decrease in the size of the beam increase in the surface roughness and decrease in the size of the beam increase in the surface roughness and increase in the size of the beam decrease in the surface roughness and increase in the size of the beam

Endurance limit of a beam subjected to pure bending decreases withdecrease in the surface roughness and decrease in the size of the beamincrease in the surface roughness ...

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Arjun asked Feb 9, 2019

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GATE2019 ME-2: 31
A prismatic, straight, elastic, cantilever beam is subjected to a linearly distributed transverse load as shown below. If the beam length is $L$, Young’s modulus $E$, and area moment of inertia $I$, the magnitude of the maximum deflection is $\dfrac{qL^4}{15EI} \\$ $\dfrac{qL^4}{30EI} \\$ $\dfrac{qL^4}{10EI} \\$ $\dfrac{qL^4}{60EI}$

A prismatic, straight, elastic, cantilever beam is subjected to a linearly distributed transverse load as shown below. If the beam length is $L$, Young’s modulus $E$, a...

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Arjun asked Feb 9, 2019

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GATE2019 ME-2: 37
A horizontal cantilever beam of circular cross-section, length $1.0$ m and flexural rigidity $EI=200 \: N \cdot m^2$ is subjected to an applied moment $M_A = 1.0 \: N \cdot m$ at the free end as shown in the figure. The magnitude of the vertical deflection of the free end is ______ mm (round off to one decimal place).

A horizontal cantilever beam of circular cross-section, length $1.0$ m and flexural rigidity $EI=200 \: N \cdot m^2$ is subjected to an applied moment $M_A = 1.0 \: N \cd...

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Arjun asked Feb 9, 2019

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GATE2019 ME-1: 39
Consider an elastic straight beam of length $L= 10 \pi \: m$, with square cross-section of side $a=5 \: mm$, and Young's modulus $E=200 \: GPa$. This straight beam was bent in such a way that the two ends meets, to form a ... $MPa$.

Consider an elastic straight beam of length $L= 10 \pi \: m$, with square cross-section of side $a=5 \: mm$, and Young’s modulus $E=200 \: GPa$. This straight beam was ...

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Arjun asked Feb 9, 2019

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GATE2019 ME-1: 40
Consider a prismatic straight beam of length $L=\pi \: m$, pinned at the two ends as shown in the figure. The beam has a square cross-section of side $p=6 \: mm$. The Young’s modulus $E=200 \: GPa$, and the coefficient of thermal expansion $\alpha = 3 \times 10^{-6} K^{-1}$. The minimum temperature rise required to cause Euler buckling of the beam is _______$K$.

Consider a prismatic straight beam of length $L=\pi \: m$, pinned at the two ends as shown in the figure. The beam has a square cross-section of side $p=6 \: mm$. The You...

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Arjun asked Feb 9, 2019

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GATE ME 2012 | Question: 22
A cantilever beam of length $L$ is subjected to a moment $M$ at the free end. The moment of inertia of the beam cross section about the neutral axis is $I$ and the Young's modulus is $E$. The magnitude of the maximum deflection is $\dfrac{ML^2}{2EI} \\$ $\dfrac{ML^2}{EI} \\$ $\dfrac{2ML^2}{EI} \\$ $\dfrac{4ML^2}{EI}$

A cantilever beam of length $L$ is subjected to a moment $M$ at the free end. The moment of inertia of the beam cross section about the neutral axis is $I$ and the Young'...

1.5k points

Andrijana3306 asked Mar 19, 2018

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GATE2018-1-19
A steel column of rectangular section ($15$ mm $\times \: 10$ mm) and length $1.5$ m is simply supported at both ends. Assuming modulus of elasticity, $E=200$ GPa for steel, the critical axial load (in kN) is ______ (correct to two decimal places).

A steel column of rectangular section ($15$ mm $\times \: 10$ mm) and length $1.5$ m is simply supported at both ends. Assuming modulus of elasticity, $E=200$ GPa for ste...

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Arjun asked Feb 17, 2018

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GATE2017 ME-2: 9
The cantilever beam of Length $L$ and Flexural modulus $EI$ is subjected to a point load $P$ at the free end. The elastic strain energy stored in the beam due to bending (neglecting transverse shear) is $\dfrac{P^{2}L^{3}}{6EI} \\$ $\dfrac{P^{2}L^{3}}{3EI} \\$ $\dfrac{PL^{3}}{3EI} \\$ $\dfrac{PL^{3}}{6EI}$

The cantilever beam of Length $L$ and Flexural modulus $EI$ is subjected to a point load $P$ at the free end. The elastic strain energy stored in the beam due to bending ...

28.5k points

Arjun asked Feb 26, 2017

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GATE2017 ME-1: 16
Consider a beam with circular cross-section of diameter $d$. The ratio of the second moment of area about the neutral axis to the section modulus of the area is $\dfrac{d}{2} \\$ $\dfrac{\pi d}{2} \\$ $d \\$ $\pi d$

Consider a beam with circular cross-section of diameter $d$. The ratio of the second moment of area about the neutral axis to the section modulus of the area is$\dfrac{d}...

28.5k points

Arjun asked Feb 26, 2017

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GATE2016-3-35
A beam of length $L$ is carrying a uniformly distributed load w per unit length. The flexural rigidity of the beam is $EI$. The reaction at the simple support at the right end is $\dfrac{wL}{2} \\$ $\dfrac{3wL}{8} \\$ $\dfrac{wL}{4} \\$ $\dfrac{wL}{8}$

A beam of length $L$ is carrying a uniformly distributed load w per unit length. The flexural rigidity of the beam is $EI$. The reaction at the simple support at the righ...

28.5k points

Arjun asked Feb 24, 2017

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GATE2016-2-33
A simply supported beam of length $2L$ is subjected to a moment $M$ at the mid-point $x = 0$ as shown in the figure. The deflection in the domain $0 \leq x \leq L$ is given by $w=\dfrac{-Mx}{12EIL}(L-x)(x+c)$ where $E$ is the Young's modulus, $I$ is the area moment ... is a constant (to be determined) . The slope at the center $x$ = $0$ is $ML/(2EI)$ $ML/(3EI)$ $ML/(6EI)$ $ML/(12EI)$

A simply supported beam of length $2L$ is subjected to a moment $M$ at the mid-point $x = 0$ as shown in the figure. The deflection in the domain $0 \leq x \leq L$ is giv...

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Arjun asked Feb 24, 2017

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GATE2016-1-34
A simply-supported beam of length $3L$ is subjected to the loading shown in the figure. It is given that $P=1\: N$, $L=1\:m$ and Young's modulus $E=200\:GPa$. The cross-section is a square with dimension $10\:mm\times10\:mm$. The ... at a distance of $1.5L$ from the left end is _____________ (Indicate compressive stress by a negative sign and tensile stress by a positive sign.)

A simply-supported beam of length $3L$ is subjected to the loading shown in the figure.It is given that $P=1\: N$, $L=1\:m$ and Young’s modulus $E=200\:GPa$. The cross-...

28.5k points

Arjun asked Feb 24, 2017

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GATE2016-1-9
A cantilever beam having square cross-section of side $a$ is subjected to an end load. If $a$ is increased by $19\%$, the tip deflection decreases approximately by $19\%$ $29\%$ $41\%$ $50\%$

A cantilever beam having square cross-section of side $a$ is subjected to an end load. If $a$ is increased by $19\%$, the tip deflection decreases approximately by$19\%$$...

28.5k points

Arjun asked Feb 24, 2017

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GATE2015-3-48
A cantilever bracket is bolted to a column using three M$12×1.75$ bolts P, Q and R. The value of maximum shear stress developed in the bolt P (in $MPa$) is ________

A cantilever bracket is bolted to a column using three M$12×1.75$ bolts P, Q and R. The value of maximum shear stress developed in the bolt P (in $MPa$) is ________

28.5k points

Arjun asked Feb 24, 2017

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GATE2015-3-46
For the overhanging beam shown in figure, the magnitude of maximum bending moment (in $kN$-$m$) is ________

For the overhanging beam shown in figure, the magnitude of maximum bending moment (in $kN$-$m$) is ________

28.5k points

Arjun asked Feb 24, 2017

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GATE2015-2-33
A cantilever beam with square cross-section of $6 \: mm$ side is subjected to a load of $2 \: kN$ normal to the top surface as shown in the figure. The Young’s modulus of elasticity of the material of the beam is $210 \: GPa$. The magnitude of slope (in radian) at $Q$ ($20 \: mm$ from the fixed end) is ________

A cantilever beam with square cross-section of $6 \: mm$ side is subjected to a load of $2 \: kN$ normal to the top surface as shown in the figure. The Young’s modulus ...

28.5k points

Arjun asked Feb 24, 2017

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GATE2015-2-31
A cantilever beam OP is connected to another beam PQ with a pin joint as shown in the figure. A load of $10$ $kN$ is applied at the mid-point of PQ. The magnitude of bending moment (in $kN$-$m$) at fixed end O is $2.5$ $5$ $10$ $25$

A cantilever beam OP is connected to another beam PQ with a pin joint as shown in the figure. A load of $10$ $kN$ is applied at the mid-point of PQ. The magnitude of bend...

28.5k points

Arjun asked Feb 24, 2017

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GATE2015-1-44
A cantilever beam with flexural rigidity of $200$ $N.m^2$ is loaded as shown in the figure. The deflection (in $mm$) at the tip of the beam is _______

A cantilever beam with flexural rigidity of $200$ $N.m^2$ is loaded as shown in the figure. The deflection (in $mm$) at the tip of the beam is _______

28.5k points

Arjun asked Feb 24, 2017

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GATE2015-1-15
Consider a stepped shaft subjected to a twisting moment applied at $B$ as shown in the figure. Assume shear modulus, $G$ = $77$ $GPa$. The angle of twist at $C$ (in degrees) is __________

Consider a stepped shaft subjected to a twisting moment applied at $B$ as shown in the figure. Assume shear modulus, $G$ = $77$ $GPa$. The angle of twist at $C$ (in degre...

28.5k points

Arjun asked Feb 24, 2017

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GATE Mechanical 2014 Set 3 | Question: 35
A force $P$ is applied at a distance $x$ from the end of the beam as shown in the figure. What would be the value of $x$ so that the displacement at ‘$A$’ is equal to zero? $0.5L$ $0.25L$ $0.33L$ $0.66L$

A force $P$ is applied at a distance $x$ from the end of the beam as shown in the figure. What would be the value of $x$ so that the displacement at ‘$A$’ is equal to...

28.5k points

Arjun asked Feb 19, 2017

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GATE Mechanical 2014 Set 3 | Question: 32
Consider a simply supported beam of length, $50h$, with a rectangular cross-section of depth, $h$, and width, $2h$. The beam carries a vertical point load, P, at its mid-point. The ratio of the maximum shear stress to the maximum bending stress in the beam is $0.02$ $0.10$ $0.05$ $0.01$

Consider a simply supported beam of length, $50h$, with a rectangular cross-section of depth, $h$, and width, $2h$. The beam carries a vertical point load, P, at its mid-...

28.5k points

Arjun asked Feb 19, 2017

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GATE Mechanical 2014 Set 2 | Question: 31
A cantilever beam of length, $L$, with uniform cross-section and flexural rigidity, $EI$, is loaded uniformly by a vertical load, $w$ per unit length. The maximum vertical deflection of the beam is given by $\dfrac{wL^4}{8EI} \\$ $\dfrac{wL^4}{16EI} \\$ $\dfrac{wL^4}{4EI} \\$ $\dfrac{wL^4}{24EI}$

A cantilever beam of length, $L$, with uniform cross-section and flexural rigidity, $EI$, is loaded uniformly by a vertical load, $w$ per unit length. The maximum vertica...

28.5k points

Arjun asked Feb 19, 2017

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GATE Mechanical 2014 Set 2 | Question: 30
The flexural rigidity $(EI)$ of a cantilever beam is assumed to be constant over the length of the beam shown in figure. If a load $P$ and bending moment $PL/2$ ... $\dfrac{PL^2}{EI} \\$ $\dfrac{3}{2}\dfrac{PL^2}{EI} \\$ $\dfrac{5}{2}\dfrac{PL^2}{EI}$

The flexural rigidity $(EI)$ of a cantilever beam is assumed to be constant over the length of the beam shown in figure. If a load $P$ and bending moment $PL/2$ are appli...

28.5k points

Arjun asked Feb 19, 2017

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GATE Mechanical 2014 Set 1 | Question: 33
Consider a cantilever beam, having negligible mass and uniform flexural rigidity, with length $0.01$ $m$. The frequency of vibration of the beam, with a $0.5$ $kg$ mass attached at the free tip, is $100$ $Hz$. The flexural rigidity (in $N$.$m^2$) of the beam is _______

Consider a cantilever beam, having negligible mass and uniform flexural rigidity, with length $0.01$ $m$. The frequency of vibration of the beam, with a $0.5$ $kg$ mass a...

28.5k points

Arjun asked Feb 19, 2017

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GATE ME 2013 | Question: 41
A simply supported beam of length $L$ is subjected to a varying distributed load $\sin(3\pi x/L) Nm^{-1}$ , where the distance $x$ is measured from the left support. The magnitude of the vertical reaction force in $N$ at the left support is $\text{zero}$ $L/3\pi$ $L/\pi$ $2L/\pi$

A simply supported beam of length $L$ is subjected to a varying distributed load $\sin(3\pi x/L) Nm^{-1}$ , where the distance $x$ is measured from the left support. The ...

1.4k points

piyag476 asked Feb 19, 2017

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GATE ME 2013 | Question: 33
A pin jointed uniform rigid rod of weight $W$ and length $L$ is supported horizontally by an external force $F$ as shown in the figure below. The force $F$ is suddenly removed. At the instant of force removal, the magnitude of vertical reaction developed at the support is $\text{zero}$ $W/4$ $W/2$ $W$

A pin jointed uniform rigid rod of weight $W$ and length $L$ is supported horizontally by an external force $F$ as shown in the figure below. The force $F$ is suddenly re...

1.4k points

piyag476 asked Feb 19, 2017

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