Solid Mechanics

Question 1

Multiple choice

The shear stress at the neutral axis in a beam of triangular section with a base of 40 mm and height of 20 mm, subjected to a shear force of 3 kN is

3 MPa
6 MPa
10 MPa
20 MPa

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Answer

U > U₁ + U₂

Answer

$\frac{5 \omega L}{4}$

Answer

2.5 N/mm² (compression), 10 N/mm² (compression)

Answer

I, II and III

Question 2

Multiple choice

A metal bar of length 100 mm is inserted between two rigid supports and its temperature is increased by 10°C. If the coefficient of thermal expansion is 12 ^_x10^–6 per °C and the Young’s modulus is 2 ^_x10⁵ MPa, the stress in the bar is

zero
12 MPa
24 MPa
2400 MPa

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Question 3

Multiple choice

U₁ and U₂ are the strain energies stored in a prismatic bar due to axial tensile forces P₁ and P₂ respectively. The strain energy stored in the same bar due to combined action of P₁ and P₂ will be

U = U₁ + U₂
U = U₁U₂
U < U₁+ U₂

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Question 4

Multiple choice

The right triangular truss is made of members having equal cross-sectional area of 1550 mm² and Young’s modulus of 2 ^_x10⁵ MPa. The horizontal deflection of the joint Q is

2.47 mm
10.25 mm
14.1 mm
15.68 mm

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Question 5

Multiple choice

A steel flat of rectangular section of size 70 mm ^_x6 mm is connected to a gusset plate by three bolts each having a shear capacity of 15 kN in holes having diameter 11.5 mm. If the allowable tensile stress in the flat is 150 MPa, the maximum tension that can be applied to the flat is

42.3 kN
52.65 kN
59.5 kN
63.0 kN

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Question 6

Multiple choice

A bracket connection is made with four bolts of 10 mm diameter and supports a load of 10 kN at an eccentricity of 100 mm. The maximum force to be resisted by any bolt will be

5 kN
6.5 kN
6.8 kN
7.16 kN

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Question 7

Multiple choice

The plastic collapse load W_p for the propped cantilever supporting two point loads as shown in the figure in terms of plastic moment capacity M_p, is given by

3M_p/L
4M_p/L
5M_p/L
6M_p/L

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Question 8

Multiple choice

What is the ultimate capacity in kN of the pile group shown in the figure assuming the group to fail as a single block?

921.6
1177.6
2438.6
3481.6

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Question 9

Multiple choice

The width of the expansion joint is 20 mm in a cement concrete pavement. The laying temperature is 20°C and the maximum slab temperature in summer is 60°C. The coefficient of thermal expansion of concrete is 10 ^_x10^–6 mm/mm/°C and the joint filler compresses upto 50% of the thickness. The spacing between expansion joints should be

20 m
25 m
30 m
40 m

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Question 10

Multiple choice

A singly reinforced rectangular concrete beam has a width of 150 mm and an effective depth of 330 mm. The characteristic compressive strength of concrete is 20 MPa. Adopt the stress block for concrete as given in IS 456-2000 and take limiting value of depth of neutral axis as 0.48 times the effective depth of the beam.

The limiting value of the moment of resistance of the beam in kNm is

0.14
0.45
45.08
156.82

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Question 11

Multiple choice

A singly reinforced rectangular concrete beam has a width of 150 mm and an effective depth of 330 mm. The characteristic compressive strength of concrete is 20 MPa. Adopt the stress block for concrete as given in IS 456-2000 and take limiting value of depth of neutral axis as 0.48 times the effective depth of the beam. The limiting area of tension steel in mm² is

473.9
412.3
373.9
312.3

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Question 12

Multiple choice

A two span continuous beam having equal spans each of length L is subjected to a uniformly distributed load ^_$\omega$ per unit length. The beam has constant flexural rigidity.

The reaction at the middle support is

^_$\omega$L
$\frac{5 \omega L}{2}$
$\frac{\omega L^2}{16}$

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Question 13

Multiple choice

A concrete beam of rectangular cross section of size 120 mm (width) and 200 mm (depth) is pre-stressed by a straight tendon to an effective force of 150 kN at an eccentricity of 20 mm (below the centroidal axis in the depth direction). The stresses at the top and bottom fibres of the section are

10 N/mm² (tension), 3.75 N/mm²
3.75 N/mm² (tension), 3.75 N/mm² (compression)
2.75 N/mm² (compression), 3.75 N/mm² (compression)

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Question 14

Multiple choice

Consider the following statements: I. Modulus of elasticity of concrete increases with increase in compressive strength of concrete. II. Brittleness of concrete increases with decrease in compressive strength of concrete. III. Shear strength of concrete increases with increase in compressive strength of concrete. The TRUE statements are

II and III
I and II
I and III

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Question 15

Multiple choice

The percentage loss of pre-stress due to anchorage slip of 3 mm in a concrete beam of length 30 m which is post-tensioned by a tendon with an initial stress of 1200 N/mm² and modulus of elasticity equal to 2.1 ^_x10⁵ N/mm² is

0.0175
0.175
1.75
17.5

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Solid Mechanics

Solid Mechanics Questions