Solid Mechanics

Question 1

Multiple choice

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) criterion, which one of the following statements is true?

I yields after II
II yields after I
Nothing can be said about their relative yielding

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Answer

Both yield simultaneously

Question 2

Multiple choice

The relationship between true strain (^$\in_T$) and engineering strain (^$\in_E$) in a uniaxial tension test is given as

^$\in_E$ = ln(1 + ^$\in_T$)
^$\in_E$ = ln(1 - ^$\in_T$)
^$\in_T$ = ln(1 - ^$\in_E$)

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Answer

^$\in_T$ = ln(1 + ^$\in_E$)

Question 3

Multiple choice

In a statically determinate plane truss, the number of joints (j) and the number of members (m)are related by

j = 2m – 3
m = 2j + 1
m = 2j – 1

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Answer

m = 2j – 3

Question 4

Multiple choice

In a rolling process, the maximum possible draft, defined as the difference between the initial and the final thickness of the metal sheet, mainly depends on which pair of the following parameters? P: Strain Q: Strength of the work material R: Roll diameter S: Roll velocity T: Coefficient of friction between roll and work

Q, S
R, T
S, T
P, R

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Answer

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

Answer

$\frac{ML^2}{2EI}$

Answer

$\frac{\alpha (\triangle T)E}{(1 - 2u)}$

Answer

1.0104 x 10⁵

Question 5

Multiple choice

A frame is subjected to a load P as shown in the figure. The frame has a constant flexural rigidity EI. The effect of axial load is neglected. The deflection at point A due to the applied load P is

$\frac{1}{3}$ $\frac{PL^3}{EI}$
$\frac{2}{3}$ $\frac{PL^3}{EI}$
$\frac{PL^3}{EI}$

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Question 6

Multiple choice

A thin walled spherical shell is subjected to an internal pressure, if the radius of the shell is increased by 1% and the thickness is reduced by 1%, with the internal pressure remaining the same, the percentage change in the circumferential (hoop) stress is

0
1
1.08
2.02

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Question 7

Multiple choice

The homogenous 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

9.50
16.07
28.52
49.41

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Question 8

Multiple choice

The state of stress at a point under plane stress condition is $\sigma_{xx}$= 40 MPa, $\sigma_{yy}$= 100 MPa and $\tau_{xy}$= 40 MPa The radius of the Mohr's circle representing the given state (in MPa) is

40
50
60
100

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Question 9

Multiple choice

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 l and the Young's modulus is E. The magnitude of the maximum deflection is

$\frac{ML^2}{EI}$
$\frac{2ML^2}{EI}$
$\frac{4ML^2}{Ei}$

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Question 10

Multiple choice

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

1
2
4
8

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Question 11

Multiple choice

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

$\frac{2\alpha (\triangle T)E}{(1 - 2u)}$
$\frac{3\alpha (\triangle T)E}{(1 - 2u)}$
$\frac{\alpha (\triangle T)E}{3(1 - 2u)}$

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Question 12

Multiple choice

Two steel truss members, AC and BC, each having cross sectional area of 100 mm² are subjected to a horizontal force F as shown in figure, all the joints are hinged.

If F = 1 kN, the magnitude of the vertical reaction force developed at the point B (in kN) is

0.63
0.32
1.26
1.46

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Question 13

Multiple choice

Two steel truss members, AC and BC, each having cross sectional area of 100 mm² are subjected to a horizontal force F as shown in figure, all the joints are hinged.

The maximum force F in kN that can be applied at C such that the axial stress in any of the truss members DOES NOT exceed 100 Mpa is

8.17
11.15
14.14
22.30

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Question 14

Multiple choice

A filled welded joint is subjected to transverse loading F as shown in the figure. Both legs of the fillets are of 10 mm size and the weld length is 30 mm. If the allowance shear stress of the weld is 94 MPa, considering the minimum throat area of the weld, the maximum allowable transverse load (in kN) is

14.44
17.92
19.93
22.16

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Question 15

Multiple choice

Details pertaining to an orthogonal metal cutting process is as below:


Chip thickness ratio	0.4
Undeformed thickness	0.6 mm
Rake angle	+ 10⁰
Cutting speed	2.5 m/s
Mean thickness of primary shear zone	25 microns

The shear strain rate (in s^-1) during the process is

0.1781 x 10⁵
0.7754 x 10⁵
4.397 x 10⁵

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Solid Mechanics

Solid Mechanics Questions