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Recent questions and answers in 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, iselectrochemical machiningelectrical discharge machiningultrasonic machiningabrasive jet machining
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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 $20\: MPa$ ... theory?Tensile and compressive load specimensTorsional load specimenBending load specimenNone of the specimens
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GATE2020-ME-1: 38
A cam with a translating flat-face follower is desired to have the follower motion ... The minimum permissible base circle radius is _________$mm$ (round off to one decimal place).
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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 ... $(0.5, - 0.5)$
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GATE2019 ME-2: 8
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 ... beamdecrease in the surface roughness and increase in the size of the beam
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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. ...
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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 ... $\dfrac{qL^4}{60EI}$
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GATE2018-2-20
A hollow circular shaft of inner radius $10 \: mm$ outer radius $20 \: mm$ length $1 \: m$ is to be used as a torsional spring. If the shear modulus of ... stiffness of the shaft (in $kN-m/rad$) is ________ (correct to two decimal places).
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GATE2018-2-21
Fatigue life of a material for a fully reversed loading condition is estimated from $\sigma_a=1100N^{-0.15}$, where $\sigma_a$ is teh stress amplitude ... cycles under the same loading condition is ________ (correct to two decimal places).
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GATE2018-2-46
The true stress (in MPa) versus true strain relationship for a metal is given by $\sigma=1020 \varepsilon^{0.4}$. The cross sectional-area at the start of ... time of necking ( in $mm^2$) is ______________ correct to two decimal palces.
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GATE2018-2-37
A thin-walled cylindrical can with rigid end caps has a mean radius $R=100\:mm$ and a wall thickness of $t=5 \: mm$. The can is pressurized and an ... , the pressure (in $MPa$) inside the can is ___________ (correct to two decimal places)
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GATE2018-2-33
A bimetallic cylindrical bar cross sectional area $1 \: m^2$ is made by bonding Steel (Young's modulus $= 210 \: GPa$ ... $ (in $kN$) along the indicated direction is$70$140$210$280$
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GATE2018-2-31
A bar of circular cross section is clamped at ends P and Q as shown in the figure. A torsional moment $T=150 \: Nm$ is applied at a distance of $100 \: mm$ from end $P$ ... P$ and $Q$ respectively are$(50, 100)$(75, 75)$(100, 75)$(120, 30)$
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GATE2018-2-5
The minimum axial compressive load, $P$, required to initiate buckling for a pinned-pinned slender column with bending stiffness $EI$ and length $L$ is$P=\dfrac{\pi^2 EI}{4L^2} \\$P= ... =\dfrac{3\pi^2 EI}{4L^2} \\$P=\dfrac{4\pi^2 EI}{L^2}$
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GATE2018-1-50
A bar is compressed to half to its original length. The magnitude of true strain produced in the deformed bar is __________ (correct to two decimal places)
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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 ... strain at point B$(\varepsilon_B)$ is _____ (correct to three decimal places)
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GATE2018-1-39
A simply supported beam of width $100$ mm, height $200$ mm and length 4 m is carrying a uniformly distributed load of intensity $10 \: kN/m$. The maximum bending stress (in MPa) in the beam is _________ (correct to one decimal place)
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GATE2018-1-11
In a linearly hardening plastic material, the true stress beyond initial yieldingincreases linearly with the true straindecreases linearly with the true ... increases linearly and then decreases linearly with the true strainremains constant
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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 ... $-0.69$-0.75$-1.0$
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GATE2017 ME-2: 8
For a loaded cantilever beam of uniform cross-section, the bending moment (in N.mm) along the length is $M(x)=5x^{2}+10x$, where $x$ is the distance (in mm ... magnitude of shear force (in N) in the cross-section at $x=10$ mm is __________.
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GATE2017 ME-1: 39
An initially stress-free massless elastic beam of length $L$ and circular cross-section with diameter $d$ $(d << L)$ is held fixed between two walls as shown. The beam material ... $d^{2}$d^{3}$d^{4}$
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GATE2016-2-23
The value of true strain produced in compressing a cylinder to half its original length is$0.69$-0.69$0.5$-0.5$
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GATE2016-1-51
A cylindrical job with diameter of $200$ $mm$ and height of $100$ $mm$ is to be cast using modulus method of riser design. Assume that the bottom surface of cylindrical ... $) is$150$200$100$125$
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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\%$50\%$
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GATE2015-3-50
The dimensions of a cylindrical side riser (height = diameter) for a $25 \: cm \times 15 \: cm \times 5 \: cm$ steel casting are to be determined. For the tabulated shape factor ...
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GATE2015-3-5
The strain hardening exponent $n$ of stainless steel SS $304$ with distinct yield and UTS values undergoing plastic deformation is$n < 0$n = 0$0 < n < 1$n = 1$
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GATE2015-2-38
A hollow shaft ($d_o$ = $2d_i$ where $d_o$ and $d_i$ are the outer and inner diameters respectively) needs to transmit $20$ $kW$ power at $3000$ $RPM$. If the maximum permissible ... MPa$, do is$11.29$ $mm$22.58$ $mm$33.87$ $mm$45.16$ $mm$
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GATE2015-2-37
A hollow shaft of $1 \: m$ length is designed to transmit a power of $30\: kW$ at $700 \text{rpm}$. The maximum permissible angle of twist in the shaft ... rigidity is $80 \: GPa$. The outside diameter (in $mm$) of the shaft is__________
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GATE2015-2-34
In a plane stress condition, the components of stress at a point are $\sigma_x =20$ $MPa$, $\sigma _y=80$ $MPa$ and $\tau_ {xy}$=$40$ $MPa$ The maximum shear stress (in $MPa$) at the point is$20$25$50$100$
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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 ... of slope (in radian) at $Q$ ($20 \: mm$ from the fixed end) is ________
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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$25$
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GATE2015-2-19
A rope-brake dynamometer attached to the crank shaft of an $I.C$. engine measures a brake power of $10$ $kW$ when the speed of rotation of the shaft is $400$ $rad/s$. The shaft torque (in $N$-$m$) sensed by the dynamometer is ___________
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GATE2015-2-8
A gas is stored in a cylindrical tank of inner radius $7$ $m$ and wall thickness $50$ $mm$. The gage pressure of the gas is $2$ $MPa$. The maximum shear stress (in $MPa$) in the wall is$35$70$140$280$
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GATE2015-2-7
A rod is subjected to a uni-axial load within linear elastic limit. When the change in the stress is $200$ $MPa$, the change in the strain is $0.001$. If ... ratio of the rod is $0.3$, the modulus of rigidity (in $GPa$) is ________________
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GATE2015-2-11
The uniaxial yield stress of a material is $300$ $MPa$. According to von Mises criterion, the shear yield stress (in $MPa$) of the material is _______
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GATE Mechanical 2014 Set 3 | Question: 53
The diameter of a recessed ring was measured by using two spherical balls of diameter $d_2$ = $60$ $mm$ and $d_1$ = $40$ $mm$ ... $20.55$ $mm$. The diameter ($D$, in $mm$) of the ring gaugeis _______
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GATE Mechanical 2014 Set 3 | Question: 12
Consider a long cylindrical tube of inner and outer radii, $r_i$ and $r_o$ , respectively, length, $L$ and thermal conductivity, $k$. Its inner and outer surfaces are maintained ... \$\dfrac{1}{4\pi kL}\ln \bigg (\dfrac{r_o}{r_i} \bigg )$
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GATE Mechanical 2014 Set 2 | Question: 38
Consider the two states of stress as shown in configurations I and II in the figure below. From the standpoint of distortion energy (von-Mises) ... yields after $I$Both yield simultaneouslyNothing can be said about their relative yielding
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GATE Mechanical 2014 Set 2 | Question: 19
A component can be produced by any of the four processes $I$, $II$, $III$ and $IV$. The fixed cost and the variable cost for each of the processes are listed below. The most ... 2 \\ \hline IV & 10 & 4 \\ \hline \end{array}$$I$II$III$IV$
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GATE Mechanical 2014 Set 2 | Question: 11
A thin plate of uniform thickness is subject to pressure as shown in the figure belowUnder the assumption of plane stress, which one of the following ... stress is compressive in the z-directionNormal stress varies in the z-direction
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