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Recent questions tagged mechanics-of-materials

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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 tens...
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311
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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 fr...
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325
325 views
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 o...
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231
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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 fin...
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268
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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 ...
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262
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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) measured from...
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235
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GATE2017 ME-2: 7
The state of stress at a point is $\sigma _{x}=\sigma _{y}=\sigma _{z}=\tau _{xz}=\tau _{zx}=\tau _{yz}=\tau _{zy}=0$ and $\tau _{xy}=\tau _{yx}=50$ MPa. The maximum norm...
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330
330 views
GATE2017 ME-1: 44
A horizontal bar, fixed at one end $(x=0)$, has a length of $1$ m, and cross-sectional area of $100 mm^{2}$. Its elastic modulus varies along its length as given by $E(x)...
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493
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GATE2017 ME-1: 42
A rectangular region in a solid is in a state of plane strain. The $(x, y)$ coordinates of the corners of the undeformed rectangle are given by $P(0, 0), Q(4, 0), R(4, 3)...
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418
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GATE2017 ME-1: 40
A point mass of $100$ kg is dropped onto a massless elastic bar (cross-sectional area $= 100 mm^{2}$, length $= 1$ m, Young's modulus$=100$ GPa) from a height $H$ of $10$...
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410
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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 ma...
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396
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GATE2017 ME-1: 25
In the engineering stress-strain curve for mild steel, the Ultimate Tensile Strength (UTS) refers toYield stressProportional limitMaximum stressFracture stress
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310
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GATE2017 ME-1: 21
In a metal forming operation when the material has just started yielding. the principal stresses are $\sigma_{1}=+180 MPa, \sigma_{2}=-100 MPa, \sigma_{3}=0$. Following v...
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255
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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}...
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278
278 views
GATE2017 ME-1: 15
A motor driving a solid circular steel shaft transmits $40$ kW of power at $500$ rpm. If the diameter of the shaft is $40$ mm, the maximum shear stress in the shaft is __...
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696
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GATE2017 ME-1: 13
The Poisson's ratio for a perfectly incompressible linear elastic material is$1$$0.5$$0$Infinity
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183
183 views
GATE2016-3-50
In a sheet metal of $2$ $mm$ thickness a hole of $10$ $mm$ diameter needs to be punched. The yield strength in tension of the sheet material is $100$ $MPa$ and its ultima...
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193
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GATE2016-3-36
Two masses m are attached to opposite sides of a rigid rotating shaft in the vertical plane. Another pair of equal masses $m_1$ is attached to the opposite sides of the s...
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396
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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 righ...
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346
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GATE2016-3-34
Two circular shafts made of same material, one solid (S) and one hollow (H), have the same length and polar moment of inertia. Both are subjected to same torque. Here, $\...
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470
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GATE2016-3-33
A square plate of dimension $L \times L$ is subjected to a uniform pressure load $p=250 \: MPa$ on its edges as shown in the figure. Assume plane stress conditions. The Y...
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237
237 views
GATE2016-3-20
Engineering strain of a mild steel sample is recorded as $0.100\%$. The true strain is$0.010\%$$0.055\%$$0.099\%$$0.101\%$
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202
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GATE2016-3-8
T he state of stress at a point on an element is shown in figure (a). The same state of stress is shown in another coordinate system in figure (b).The components $(\tau _...
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221
221 views
GATE2016-3-7
The cross-sections of two solid bars made of the same material are shown in the figure. The square cross-section has flexural (bending) rigidity $I_1$, while the circular...
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237
237 views
GATE2016-3-6
A force F is acting on a bent bar which is clamped at one end as shown in the figure.The CORRECT free body diagram is
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248
248 views
GATE2016-2-38
In a structural member under fatigue loading, the minimum and maximum stresses developed at the critical point are $50$ $MPa$ and $150$ $MPa$, respectively. The endurance...
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265
265 views
GATE2016-2-34
In the figure, the load $P=1 \: N$, length $L=1 \: m$, Young’s modulus $E=70 \: GPa$, and the cross-section of the links is a square with dimension $10 \: mm \times 10 \:...
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334
334 views
GATE2016-2-33
A simply supported beam of length $2L$ is subjected to a moment $M$ at the mid-point $x = 0$ as shown in the figure. The deflection in the domain $0 \leq x \leq L$ is giv...
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356
356 views
GATE2016-2-32
A rigid horizontal rod of length $2L$ is fixed to a circular cylinder of radius $R$ as shown in the figure. Vertical forces of magnitude $P$ are applied at the two ends a...
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206
206 views
GATE2016-2-23
The value of true strain produced in compressing a cylinder to half its original length is$0.69$$-0.69$$0.5$$-0.5$
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