Recent questions tagged mechanics-of-materials

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GATE2020-ME-2: 9
The process, that uses a tapered horn to amplify and focus the mechanical energy for machining of glass, is electrochemical machining electrical discharge machining ultrasonic machining abrasive jet machining

go_editor asked in Mechanics of Materials Sep 18, 2020

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GATE2020-ME-1: 7
The stress state at a point in a material under plane stress condition is equi-biaxial tension with a magnitude of $10\: MPa$. If one unit on the $\sigma -\tau$ plane is $1\: MPa$, the Mohr's circle representation of the state-of-stress is given by a circle with a ... of $10$ units on the $\sigma -\tau$ plane a point on the $\tau$ axis at a distance of $10$ units from the origin

go_editor asked in Applied Mechanics and Design Feb 19, 2020

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GATE2020-ME-1: 28
Bars of square and circular cross-section with $0.5\: m$ length are made of a material with shear strength of $20\: MPa$. The square bar cross-section dimension is $4\:cm \times$ $4\:cm$ and the cylindrical bar cross- ... the applied load as per maximum shear stress theory? Tensile and compressive load specimens Torsional load specimen Bending load specimen None of the specimens

go_editor asked in Mechanics of Materials Feb 19, 2020

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GATE2020-ME-1: 29
The $2$ kg block shown in the figure (top view) rests on a smooth horizontal surface and is attached to a massless elastic cord that has a stiffness $5\: N/m$. The cord hinged at $\text{O}$ is initially unstretched and always remains elastic. The block is given a velocity $v$ ... $0.4\: m$ is $0.83$ $1.07$ $1.36$ $1.50$

go_editor asked in Applied Mechanics and Design Feb 19, 2020

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GATE2020-ME-1: 38
A cam with a translating flat-face follower is desired to have the follower motion $y\left ( \theta \right )=4\left [ 2\pi \theta -\theta ^{2} \right ],\:\:\:0\leq \theta \leq 2\pi .$ Contact stress considerations dictate that the radius ... should not be less than $40\:mm$ anywhere. The minimum permissible base circle radius is _________$mm$ (round off to one decimal place).

go_editor asked in Mechanics of Materials Feb 19, 2020

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GATE2020-ME-1: 39
A rectangular steel bar of length $500\: mm$, width $100\: mm$, and thickness $15\: mm$ is cantilevered to a $200\: mm$ steel channel using $4$ bolts, as shown For an external load of $10\: kN$ applied at the tip of the steel bar, the resultant shear load on the bolt at $B$, is _______$kN$ (round off to one decimal place).

go_editor asked in Applied Mechanics and Design Feb 19, 2020

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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).

go_editor asked in Applied Mechanics and Design 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).

go_editor asked in Applied Mechanics and Design Feb 19, 2020

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GATE2019 ME-2: 6
Consider a linear elastic rectangular thin sheet of metal, subjected to uniform uniaxial tensile stress of $100$ MPa along the length direction. Assume plane stress conditions in the plane normal to the thickness. The Young's modulus $E=200$ MPa and Poisson's ratio $v=0.3$ are given. The principal strains in the ... are $(0.35, - 0.15)$ $(0.5, 0.0)$ $(0.5, - 0.15)$ $(0.5, - 0.5)$

Arjun asked in Mechanics of Materials Feb 9, 2019

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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

Arjun asked in Mechanics of Materials Feb 9, 2019

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GATE2019 ME-2: 21
The state of stress at a point in a component is represented by a Mohr’s circle of radius $100$ MPa centered at $200$ MPa on the thermal stress axis. On a plane passing through the same point, the normal stress is $260$ MPa. The magnitude of the shear stress on the same plane at the same point is _______ MPa

Arjun asked in Applied Mechanics and Design Feb 9, 2019

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GATE2019 ME-2: 22
A wire of circular cross-section of diameter $1.0$ mm is bent into a circular arc of radius. $1.0$ m by application of pure bending moments at its ends. The Young’s modulus of the material of the wire is $100$ GPa. The maximum tensile stress developed in the wire is ______ MPa

Arjun asked in Applied Mechanics and Design Feb 9, 2019

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GATE2019 ME-2: 29
A ball of mass $3$ kg moving with a velocity of $4 \:m/s$ undergoes a perfectly-elastic direct-central impact with a stationary ball of mass $m$. After the impact is over, the kinetic energy of the $3$ kg ball is $6$ J. The possible value(s) of $m$ is/are $1$ kg only $6$ kg only $1$ kg, $6$ kg $1$ kg, $9$ kg

Arjun asked in Applied Mechanics and Design Feb 9, 2019

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GATE2019 ME-2: 30
Consider two concentric circular cylinders of different materials $M$ and $N$ in contact with each other at $r=b$, as shown below. The interface at $r=b$ is frictionless. The composite cylinder is subjected to internal pressure $P$. Let $(u_r^M, u_{\theta}^M)$ ... $\sigma_{rr}^M = \sigma_{rr}^N \text{ and } \sigma_{\theta \theta}^M = \sigma_{\theta \theta}^N$

Arjun asked in Mechanics of Materials 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 $\dfrac{qL^4}{15EI} \\$ $\dfrac{qL^4}{30EI} \\$ $\dfrac{qL^4}{10EI} \\$ $\dfrac{qL^4}{60EI}$

Arjun asked in Mechanics of Materials 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).

Arjun asked in Applied Mechanics and Design Feb 9, 2019

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GATE2019 ME-2: 38
Two masses $A$ and $B$ having mass $m_a$ and $m_b$, respectively, lying in the plane of the figure shown, are rigidly attached to a shaft which revolves about an axis through O perpendicular to the plane of the figure. The radii of rotation of the masses $m_a$ ... $200$ mm is _________ kg (round off to two decimal places).

Arjun asked in Applied Mechanics and Design Feb 9, 2019

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GATE2019 ME-1: 20
A cylindrical rod of diameter $10$ mm and length $0.1$m fixed at one end. The other end is twisted by an angle of $10^{\circ}$ by applying a torque. If the maximum shear strain in the rod is $p \times 10^{-3}$, then $p$ is equal to ____ (round off to two decimal places).

Arjun asked in Applied Mechanics and Design Feb 9, 2019

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GATE2019 ME-1: 22
During a high cycle fatigue test, a metallic specimen is subjected to cyclic loading with a mean stress of $+140$ MPa, and a minimum stress of $-70$ MPa. The $R$-ratio (minimum stress to maximum stress) for this cyclic loading is _____ (round off to one decimal place)

Arjun asked in Applied Mechanics and Design Feb 9, 2019

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GATE2019 ME-1: 25
Consider the stress-strain curve for an ideal elastic-plastic strain hardening metal as shown in the figure. The metal was loaded in uniaxial tension starting from $O$. Upon loading, the stress-strain curve passes through initial yield point at $P$, and then ... specimen is reloaded in tension from point $R$, the value of stress at which the material yields again is _______ MPa.

Arjun asked in Applied Mechanics and Design Feb 9, 2019

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GATE2019 ME-1: 34
A plane-strain compression (forging) of a block is shown in the figure. The strain in the $z$-direction is zero. The yield strength $(S_y)$ in uniaxial tension/compression of the material of the block is $300 \: MPa$ and it follows the Tresca (maximum shear stress) ... $340 \: MPa$ (compressive) $340 \: MPa$ (tensile) $260 \: MPa$ (compressive) $260 \: MPa$ (tensile)

Arjun asked in Applied Mechanics and Design 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 ... $MPa$.

Arjun asked in Applied Mechanics and Design 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 _______$K$.

Arjun asked in Applied Mechanics and Design Feb 9, 2019

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GATE2019 ME-1: 41
In a UTM experiment, a sample of length $100 \: mm$, was loaded in tension until failure. The failure load was $40 \: kN$. The displacement, measured using the cross-head motion, at failure, was $15 \: mm$. The compliance of the UTM is constant and is given $5 \times 10^{-8} \: m/N$. The strain at failure in the sample is ______$\%$

Arjun asked in Applied Mechanics and Design Feb 9, 2019

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GATE2019 ME-1: 42
At a critical point in a component, the state of stress is given as $\sigma_{xx}=100 \: MPa, \: \sigma_{yy}=220 \: MPa, \: \sigma_{xy}= \sigma_{yx} = 80 \: MPa$ and all other stress components are zero. The yield strength of the material is $468 \: MPa$ The factor of safety on the basis of maximum shear stress theory is ___________ (round off to one decimal place)

Arjun asked in Applied Mechanics and Design Feb 9, 2019

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GATE ME 2012 | Question: 43
A solid circular shaft needs to be designed to transmit a torque of $50$ N.m. If the allowable shear stress of the material is $140$ MPa, assuming a factor of safety of $2$, the minimum allowable design diameter in mm is $8$ $16$ $24$ $32$

Andrijana3306 asked in Applied Mechanics and Design Mar 20, 2018

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GATE ME 2012 | Question: 34
The state of stress at a point under plane stress condition is $\sigma_{xx} = 40 \: MPa, \: \: \sigma_{yy} = 100 \: MPa \: \: \text{and }\tau_{xy} =40 \: Mpa$ The radius of the Mohr's circle representing the given state of stress in $MPa$ is $40$ $50$ $60$ $100$

Andrijana3306 asked in Applied Mechanics and Design Mar 20, 2018

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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 $\dfrac{ML^2}{2EI} \\$ $\dfrac{ML^2}{EI} \\$ $\dfrac{2ML^2}{EI} \\$ $\dfrac{4ML^2}{EI}$

Andrijana3306 asked in Applied Mechanics and Design Mar 20, 2018

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GATE ME 2012 | Question: 2
Match the following metal forming process with their associated stresses in the workpiece. ... $1-S; 2-P; 3-R; 4-Q$ $1-P; 2-Q; 3-S; 4-R$ $1-P; 2-R; 3-Q; 4-S$

Andrijana3306 asked in Applied Mechanics and Design Mar 20, 2018

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GATE2018-1-48
The true stress $(\sigma)$ - true strain $(\varepsilon)$ diagram of a strain hardening material is shown in figure. First, there is loading up to point A, i.e., up to stress of $500$ MPa and strain of $0.5$. Then from point A, there is unloading ... . Given that the Young's modulus $E=200$ GPa, te natural strain at point B$(\varepsilon_B)$ is _____ (correct to three decimal places)

Arjun asked in Mechanics of Materials Feb 17, 2018

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GATE2018-1-31
A carpenter glues a pair of cylindrical wooden logs by bonding their end faces at an angle of $\theta = 30^{\circ}$ as shown in the figure. The glue used at the interface fails is Criterion 1: the maximum normal stress exceeds $2.5$ MPa Criterion 2: the ... fails only because of criterion $1$ fails only because of criterion $2$ fails because of both criterion $1$ and $2$ does not fail

Arjun asked in Applied Mechanics and Design Feb 17, 2018

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GATE2018-1-29
The state of stress at a point, for a body in plane stress, is shown in the figure below. If the minimum principal stress is $10$ kPa, then the normal stress $\sigma_y$ (in kPa) is $9.45$ $18.88$ $37.78$ $75.50$

Arjun asked in Applied Mechanics and Design Feb 17, 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).

Arjun asked in Applied Mechanics and Design Feb 17, 2018

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GATE2018-1-11
In a linearly hardening plastic material, the true stress beyond initial yielding increases linearly with the true strain decreases linearly with the true strain first increases linearly and then decreases linearly with the true strain remains constant

Arjun asked in Mechanics of Materials Feb 17, 2018

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GATE2018-1-6
If $\sigma_1$ and $\sigma_3$ are the algebraically largest and smallest principal stresses respectively, the value of the maximum shear stress is $\dfrac{\sigma_1 +\sigma_3}{2} \\$ $\dfrac{\sigma_1 -\sigma_3}{2} \\ $ $\sqrt{\dfrac{\sigma_1 +\sigma_3}{2}} \\$ $\sqrt{\dfrac{\sigma_1 -\sigma_3}{2}}$

Arjun asked in Applied Mechanics and Design Feb 17, 2018

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GATE2017 ME-2: 50
A rod of length $20$ mm is stretched to make a rod of length $40$ mm. Subsequently, it is compressed to make a rod of final length $10$ mm. Consider the longitudinal tensile strain as positive and compressive strain as negative. The total true longitudinal strain in the rod is $-0.5$ $-0.69$ $-0.75$ $-1.0$

Arjun asked in Mechanics of Materials Feb 27, 2017

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GATE2017 ME-2: 38
The rod $PQ$ of length $L=\sqrt{2}$ m, and uniformly distributed mass of $M=10$ kg, is released from rest at the position shown in the figure. The ends slide along the frictionless faces $OP$ and $OQ$. Assume acceleration due to gravity, $g=10 m/s^{2}$. ... figure is $(ML^{2}/12)$. At this instant, the magnitude of angular acceleration (in radian/$s^{2}$) of the rod is __________.

Arjun asked in Applied Mechanics and Design Feb 27, 2017

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GATE2017 ME-2: 37
The principal stresses at a point in a critical section of a machine component are $\sigma _{1}=60$ MPa, $\sigma _{2}=5$ MPa and $\sigma _{3}=-40$ MPa. For the material of the component, the tensile yield strength is $\sigma _{y}=200$ MPa. According to the maximum shear stress theory, the factor of safety is $1.67$ $2.00$ $3.60$ $4.00$

Arjun asked in Applied Mechanics and Design Feb 27, 2017

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GATE2017 ME-2: 23
For a single server with Poisson and exponential service time, the arrival rate is $12$ per hour. Which one of the following service rates will provide a steady state finite queue length? $6$ per hour $10$ per hour $12$ per hour $24$ per hour

Arjun asked in Applied Mechanics and Design Feb 27, 2017

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

Arjun asked in Applied Mechanics and Design Feb 27, 2017

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