Solid Mechanics

Question 1

Multiple choice

A continuous beam is loaded as shown in the figure below. Assuming a plastic moment capacity equal to M_P, the minimum load at which the beam would collapse is

$\dfrac{4M_p}{L}$
$\dfrac{8M_p}{L}$
$\dfrac{10M_p}{L}$

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Answer

$\dfrac{6M_p}{L}$

Question 2

Multiple choice

In the design of a reinforced concrete bean the requirement for bond is not getting satisfied. The economical option to satisfy the requirement for bond is by

bundling of bars
providing larger diameter bars less in number
providing same diameter bars more in number

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Answer

providing smaller diameter bars more in number

Question 3

Multiple choice

The span(s) to be loaded uniformly for maximum positive (upward) reaction at support P, as shown in the figure below, is (are)

PQ only
PQ and QR
QR and RS
PQ and RS

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Answer

increasing the length of the rod

Answer

$\frac{b}{H} = \frac{1}{\sqrt{G - K}}$

Answer

$\dfrac{\tau}{2}$

Answer

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

Answer

$\frac{8P}{bd}$

Question 4

Multiple choice

A vertical PQ of length L is fixed at its top end P and has a flange to the bottom end Q. A weight W is dropped vertically from a height h (<L) on to the flange. The axial stress in the rod can be reduced by

decreasing the length of the rod
decreasing the area of cross-section of the rod
increasing the modulus of elasticity of the material

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Question 5

Multiple choice

The base width of an elementary profile of gravity dam of height H is b. The specific gravity of the material of the dam is G and uplift pressure coefficient is K. The correct relationship for no tension at the heel is given by

$\frac{b}{H} = \sqrt{G - K}$
$\frac{b}{H} = \frac{1}{G - K}$
$\frac{b}{H} = \frac{1}{K \sqrt{G - K}}$

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Question 6

Multiple choice

Unfactored maximum bending moments at a section of a reinforced concrete beam resulting from a frame analysis are 50, 80, 120 and 180 kNm under dead, live, wind and earthquake loads respectively. The design moment (kNm) as per IS: 456- 2000 for the limit state of collapse (flexure) is

195
250
345
372

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Question 7

Multiple choice

A rigid bar GH of length L is supported by a hinge and a spring of stiffness K as shown in the figure below. The buckling load (P_cr) for the bar will be

0.5 KL
0.8 KL
1.0 KL
1.2 KL

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Question 8

Multiple choice

The maximum shear stress in a solid shaft of circular cross section having diameter subjected to a torque T is $\tau$ . If the torque is increased by four times and the diameter of the shaft is increased by two times, the maximum shear stress in the shaft will be

$2\tau$
$\tau$
$\dfrac{\tau}{4}$

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Question 9

Multiple choice

The members EJ and IJ of a steel truss (shown in the figure below) are subjected to a temperature rise of 30^oC. The coefficient of thermal expansion of steel is 0.000012 per ^oC per unit length. The displacement (mm) of joint E relative to joint H along the direction HE of the truss is

0.255
0.589
0.764
1.026

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Question 10

Multiple choice

A reinforced concrete column contains longitudinal steel equal to 1 percent of net cross sectional area of the column. Assume modular ratio as 10. The loads carried (using the elastic theory) by the longitudinal steel and the net area of concrete are P_s and P_c respectively. The ratio P_s/P_c expressed as percent is

0.1
1
1.1
10

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Question 11

Multiple choice

Cross section of a column consisting of two steel strips, each of thickness t and width b is shown in the figure below. The critical loads of the column with perfect bond and without bond between the strips are P and P₀ respectively. The ratio P/P_o is

2
4
6
8

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Question 12

Multiple choice

The stepped cantilever is subjected to movements, M as shown in the figure below. The vertical deflection at the free end (neglecting the self weight) is

$\frac{ML^2}{8EI}$
$\frac{ML^2}{4EI}$
Zero

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Question 13

Multiple choice

The maximum tensile stress at the section X-X shown in the figure below is

$\frac{6P}{bd}$
$\frac{4P}{bd}$
$\frac{2P}{bd}$

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Question 14

Multiple choice

Rivets and bolts subjected to both shear stress $\tau_{vf_{cal}}$ and axial tensile stress $\tau_{tf_{cal}}$shall be so proportioned that the stresses do not exceed the respective allowable stresses ^$\tau_{vf}$and $\sigma_{tf}$and the value of $\left( \dfrac{\tau_{vf_{cal}}}{\tau_{vf}} + \dfrac{\sigma_{vf_{cal}}}{\sigma_{vf}} \right)$does not exceed

1.0
1.2
1.4
1.8

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Question 15

Multiple choice

Beam GHI is supported by the pontoons as shown in the figure below. The horizontal cross sectional area of each pontoon is 8 m², the flexural rigidity of the beam is 10000 kN-m² and the unit weight of water is 10 kN-m³.

When the middle pontoon is removed, the deflection at H will be

0.2 m
0.4 m
0.6 m
0.8 m

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Solid Mechanics

Solid Mechanics Questions