Solid Mechanics

Question 1

Multiple choice

A frame of two arms of equal length L is shown in the adjacent figure. The flexural rigidity of each arm of the frame is EI. The vertical deflection at the point of application of load P is

$\frac{PL^3}{3EI}$
$\frac{2PL^3}{3EI}$
$\frac{PL^3}{EI}$

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Answer

$\frac{4PL^3}{3EI}$

Question 2

Multiple choice

Minimum shear strain in orthogonal turning with a cutting tool of zero rake angle is

0.0
0.5
1.0
2.0

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Answer

Both Young's modulus and shear modulus

Answer

variable with maximum of the neutral axis

Answer

$\frac{F(3L-2b)}{4b^3}$

Answer

$\frac{\sqrt{2}x^2EI}{L^2}$

Answer

The spindle rotational axis is parallel to the drill spindle taper hole axis.

Answer

2 kN, 20 kN

Answer

$\frac{4P^2L^3}{3EI}$

Question 3

Multiple choice

A 20؛ full depth involute spur pinion of 4 mm module and 21 teeth is to transmit 15 kW at 960 rpm. Its face width is 25 mm. Given that the tooth geometry factor is 0.32 and the combined effect of dynamic load and allied factors intensifying the stress is 1.5. The minimum allowable stress (in MPa) for the gear material is

242.0
166.5
121.0
74.0

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Question 4

Multiple choice

A rod of length L and diameter D is subjected to a tensile load P. Which of the following is sufficient to calculate the resulting change in diameter?

Young's modulus
Shear modulus
Poisson's ratio

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Question 5

Multiple choice

An axial residual compressive stress due to a manufacturing process is present on the outer surface of a rotating shaft subjected to bending. Under a given bending load, the fatigue life of the shaft in the presence of the residual compressive stress is

decreased
increased or decreased, depending on the external bending load
neither decreased nor increased
increased

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Question 6

Multiple choice

The transverse shear stress acting in beam of rectangular cross-section, subjected to a transverse shear load, is

variable with maximum at the bottom of the beam
variable with maximum at the top of the beam
uniform

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Question 7

Multiple choice

A solid circular shaft of diameter 100 mm is subjected to an axial stress of 50 MPa. It is further subjected to a torque of 10 kNm. The maximum principal stress experienced on the shaft is closest to

41 MPa
82 MPa
164 MPa
204 MPa

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Question 8

Multiple choice

For the component loaded with a force F as shown in the figure, the axial stress at the corner point P is

$\frac{F(3L-b)}{4b^3}$
$\frac{F(3L-b)}{4b^3}$
$\frac{F(3L-b)}{4b^3}$

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Question 9

Multiple choice

The rod PQ of length L and with flexural rigidity EI is hinged at both ends. For what minimum force F is it expected to buckle?

$\frac{\pi^2EI}{L^2}$
$\frac{x^2EI}{\sqrt{2}L^2}$
$\frac{x^2EI}{2L^2}$

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Question 10

Multiple choice

Consider a truss PQR loaded at P with a force F as shown in the figure. The tension in the member QR is

0.5 F
0.63 F
0.73 F
0.87 F

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Question 11

Multiple choice

A displacement sensor (a dial indicator) measures the lateral displacement of a mandrel mounted on the taper hole inside a drill spindle. The mandrel axis is an extension of the drill spindle taper hole axis and the protruding portion of the mandrel surface is perfectly cylindrical. Measurements are taken with the sensor placed at two positions P and Q as shown in the figure. The readings are recorded as R_x = maximum deflection minus minimum deflection, corresponding to sensor position at X, over one rotation.

If R_P = R_Q > 0, which one of the following would be consistent with the observation?

The spindle rotational axis is coincident with the drill spindle taper hold axis.
The spindle rotational axis intersects the drill spindle taper hole axis at point P.
The spindle rotational axis intersects the drill spindle taper hole axis at point Q.

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Question 12

Multiple choice

Orthogonal turning is performed on a cylindrical work piece with shear strength of 250 MPa. The following conditions are used cutting velocity is 180 m/min, feed is 0.20 mm/rev, depth of cut is 3 mm, chip thickness ratio = 0.5. The orthogonal rake angle is 7⁰. Apply merchant's theory for analysis.

The shear plane angle (in degrees) and the shear force respectively are

52; 320 N
52; 400 N
28; 400 N
28; 320 N

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Question 13

Multiple choice

A steel bar of 10 × 50 mm is cantilevered with two M 12 bolts (P and Q) to support a static load of 4 kN as shown in the figure:

The primary and secondary shear load on bolt P₁ respectively, are

20 kN, 2 kN
20 kN, 0 kN
0 kN, 20 kN

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Question 14

Multiple choice

A steel bar of 10 × 50 mm is cantilevered with two M 12 bolts (P and Q) to support a static load of 4 kN as shown in the figure:

The resultant shear stress on bolt is closest to

132 MPa
159 MPa
178 MPa
195 MPa

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Question 15

Multiple choice

The strain energy stored in the beam with flexural rigidity FL and loaded as shown in the figure is

$\frac{P^2L^3}{3EI}$
$\frac{2P^2L^3}{3EI}$
$\frac{8P^2L^3}{3EI}$

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Solid Mechanics

Solid Mechanics Questions