Elasticity - General Aptitude - General Aptitude (GA) Previous Year Questions

1

2012 · General Aptitude (GA) · General Aptitude · Elasticity

Mechanical Engineering (ME) 2012

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

A

\(\frac{ML^2}{2EI}\)

B

\(\frac{ML^2}{EI}\)

C

\(\frac{2ML^2}{EI}\)

D

\(\frac{4ML^2}{EI}\)

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2

2012 · General Aptitude (GA) · General Aptitude · Elasticity

Mechanical Engineering (ME) 2012

For a long slender column of uniform cross section, the ratio of critical buckling load for the case with both ends clamped to the case with both ends hinged is

A

1

B

2

C

4

D

8

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3

2012 · General Aptitude (GA) · General Aptitude · Elasticity

Mechanical Engineering (ME) 2012

The homogeneous state of stress for a metal part undergoing plastic deformation is T = \begin{pmatrix}10 & 5 & 0\\5 & 20 & 0\\0 & 0 & -10\end{pmatrix}, where the stress component values are in MPa. Using von Mises yield criterion, the value of estimated shear yield stress, in MPa is

A

9.50

B

16.07

C

28.52

D

49.41

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4

2012 · General Aptitude (GA) · General Aptitude · Elasticity

Mechanical Engineering (ME) 2012

A solid steel cube constrained on all six faces is heated so that the temperature rises uniformly by $\Delta T$. If the thermal coefficient of the material is $\alpha$, Young's modulus is $E$ and the Poisson's ratio is $\nu$, the thermal stress developed in the cube due to heating is

A

\(-\frac{\alpha(\Delta T)E}{(1-2\nu)}\)

B

\(-\frac{2\alpha(\Delta T)E}{(1-2\nu)}\)

C

\(-\frac{3\alpha(\Delta T)E}{(1-2\nu)}\)

D

\(-\frac{\alpha(\Delta T)E}{3(1-2\nu)}\)

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5

2014 · General Aptitude (GA) · General Aptitude · Elasticity

Mechanical Engineering (ME) 2014 [Session 2]

A steel cube, with all faces free to deform, has Young’s modulus, \(E\), Poisson’s ratio, \(\nu\), and coefficient of thermal expansion, \(\alpha\). The pressure (hydrostatic stress) developed within the cube, when it is subjected to a uniform increase in temperature, \(\Delta T\), is given by

A

0

B

\(\frac{\alpha (\Delta T) E}{1-2\nu}\)

C

\(-\frac{\alpha (\Delta T) E}{1-2\nu}\)

D

\(\frac{\alpha (\Delta T) E}{3(1-2\nu)}\)

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6

2015 · General Aptitude (GA) · General Aptitude · Elasticity

Mechanical Engineering (ME) 2015 [Session 1]

Consider a steel (Young's modulus E = 200 GPa) column hinged on both sides. Its height is 1.0 m and cross-section is 10 mm × 20 mm. The lowest Euler critical buckling load (in N) is ______

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7

2015 · General Aptitude (GA) · General Aptitude · Elasticity

Mechanical Engineering (ME) 2015 [Session 1]

A machine element is subjected to the following bi-axial state of stress: \(\sigma_x = 80\) MPa; \(\sigma_y = 20\) MPa; \(\tau_{xy} = 40\) MPa. If the shear strength of the material is 100 MPa, the factor of safety as per Tresca’s maximum shear stress theory is

A

1.0

B

2.0

C

2.5

D

3.3

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8

2015 · General Aptitude (GA) · General Aptitude · Elasticity

Mechanical Engineering (ME) 2015 [Session 2]

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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9

2015 · General Aptitude (GA) · General Aptitude · Elasticity

Mechanical Engineering (ME) 2015 [Session 2]

The flow stress (in MPa) of a material is given by
\[ \sigma = 500 \varepsilon^{0.1} , \]
where \( \varepsilon \) is true strain. The Young’s modulus of elasticity of the material is 200 GPa. A block of thickness 100 mm made of this material is compressed to 95 mm thickness and then the load is removed. The final dimension of the block (in mm) is ______

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10

2015 · General Aptitude (GA) · General Aptitude · Elasticity

Mechanical Engineering (ME) 2015 [Session 3]

A cylindrical tank with closed ends is filled with compressed air at a pressure of 500 kPa. The inner radius of the tank is 2 m, and it has wall thickness of 10 mm. The magnitude of maximum in-plane shear stress (in MPa) is __________

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