Solid Mechanics

Question 1

Multiple choice

Match the following metal forming processes with their associated stresses in the work piece.


Metal forming process
	Type of stress

1. Coining
	P. Tensile

2. Wire Drawing
	Q. Shear

3. Blanking
	R. Tensile & Compressive

4. Deep Drawing
	S. Compressive

1 - S, 2 - P, 3 - R, 4 - Q
1 - P, 2 - Q, 3 - S, 4 - R
1 - P, 2 - R, 3 - Q, 4 - S

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Answer

1 - S, 2 - P, 3 - Q, 4 - R

Question 2

Multiple choice

A solid circular shaft needs to be designed to transmit a torque of 50 Nm. 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

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Answer

stress developed in the rod is E^_$\alpha$ ^$\triangle$T and strain developed in the rod is zero

Answer

1 kN downward, 1 kN upward

Answer

$\Big( \frac{18TL}{\pi \theta G} \Big)^{\frac{1}{4}}$

Answer

$\frac{bxt^3}{12I}$

Answer

$\frac{6pI^3}{Ebt^3}$

Answer

P-M, Q-N, R-L

Answer

torsional yield strength (Ssy)

Answer

$\frac{12 T_0}{\pi d^3}$

Question 3

Multiple choice

A circular rod of length ‘L’ and area of cross-section ‘A’ has a modulus of elasticity ‘E’ and coefficient of thermal expansion ‘^_$\alpha$’. One end of the rod is fixed and other end is free. If the temperature of the rod is increased by ^$\triangle$T, then

stress developed in the rod is E^_$\alpha$ ^$\triangle$T and strain developed in the rod is ^_$\alpha$ ^$\triangle$T
both stress and strain developed in the rod are zero
stress developed in the rod is zero and strain developed in the rod is ^_$\alpha$^$\triangle$T

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Question 4

Multiple choice

A simply supported beam PQ is loaded by a moment of 1 kN-m at the mid-span of the beam as shown in the figure. The reaction forces P R and Q R at supports P and Q respectively are

0.5 kN upward, 0.5 kN downward
0.5 kN downward, 0.5 kN upward
1 kN upward, 1 kN upward

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Question 5

Multiple choice

A torque T is applied at the free end of a stepped rod of circular cross-sections as shown in the figure. The shear modulus of the material of the rod is G. The expression for d to produce an angular twist $\theta$at the free end is

$\Big( \frac{32TL}{\pi \theta G} \Big)^{\frac{1}{4}}$
$\Big( \frac{16TL}{\pi \theta G} \Big)^{\frac{1}{4}}$
$\Big( \frac{2TL}{\pi \theta G} \Big)^{\frac{1}{4}}$

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Question 6

Multiple choice

The sheer strength of a sheet metal is 300 MPa. The blanking force required to produce a blank of 100 mm diameter from a 1.5 mm thick sheet is close to

45 kN
70 kN
141 kN
3500 kN

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Question 7

Multiple choice

A triangular-shaped cantilever beam of uniform-thickness is shown in the figure. The Young's modulus of the material of the beam is E. A concentrated load P is applied at the free end of the beam.

The area moment of inertia about the neutral axis of a cross-section at a distance x measured from the free end is

$\frac{bxt^3}{6I}$
$\frac{bxt^3}{24I}$
$\frac{xt^3}{12}$

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Question 8

Multiple choice

A triangular-shaped cantilever beam of uniform-thickness is shown in the figure. The Young's modulus of the material of the beam is E. A concentrated load P is applied at the free end of the beam.

The maximum deflection of the beam is

$\frac{24pI^3}{Ebt^3}$
$\frac{12pI^3}{Ebt^3}$
$\frac{8pI^3}{Ebt^3}$

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Question 9

Multiple choice

Match the following criteria of material failure, under biaxial stresses $\sigma_1$ and $\sigma_2$ and yield stress $\sigma_y$, with their corresponding graphic representations: P. Maximum-normal-stress criterion

Q. Maximum-distortion-energy criterion R. Maximum-shear-stress criterion

P-M, Q-L, R-N
P-N, Q-M, R-L
P-N, Q-L, R-M

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Question 10

Multiple choice

A thin cylinder of inner radius 500 mm and thickness 10 mm is subjected to an internal pressure of 5 MPa. The average circumferential (hoop) stress (in MPa) is

100
250
500
1000

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Question 11

Multiple choice

A single-point cutting tool with 12⁰ rake angle is used to machine a steel work- piece. The depth of cut, i.e. uncut thickness is 0.81 mm. The chip thickness under orthogonal machining condition is 1.8 mm. The shear angle is approximately

22⁰
26⁰
56⁰
76⁰

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Question 12

Multiple choice

If the principal stresses in a plane stress problem, are $\sigma_1$= 100MPa, $\sigma_2$= 40MPa, the magnitude of the maximum shear stress (in MPa) will be

60
50
30
20

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Question 13

Multiple choice

A solid circular shaft of diameter d is subjected to a combined bending moment M and torque, T. The material property to be used for designing the shaft using the relation $\frac{16}{\pi d^3} \sqrt{M^2 + T^2}$is

ultimate tensile strength (Su)
tensile yield strength (Sy)
endurance strength (S_e)

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Question 14

Multiple choice

A solid shaft of diameter, d and length L is fixed at both the ends. A torque, T₀ is applied at a distance L/4 from the left end as shown in the figure given below:

The maximum shear stress in the shaft is

$\frac{16 T_0}{\pi d^3}$
$\frac{8 T_0}{\pi d^3}$
$\frac{4 T_0}{\pi d^3}$

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Question 15

Multiple choice

A forged steel link with uniform diameter of 30 mm at the centre is subjected to an axial force that varies from 40 kN in compression to 160 kN in tension. The tensile (S_u), yield (S_y) and corrected endurance (S_e) strengths of the steel material are 600 MPa, 420 MPa and 240 MPa respectively. The factor of safety against fatigue endurance as per Soderberg's criterion is

1.26
1.37
1.45
2.00

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Solid Mechanics

Solid Mechanics Questions