Strength of Material Sheet 21

1) Question.

If all the dimension of a prismatic bar elongating under its own weight are increased in the proportion $m : 1$ , then the total

elongation will increase in the ratio
Answer.
- 1
  
  $1 : m$
- 2
  
  $1 : m^{2}$
- 3
  
  $1 : m^{3}$
- 4
  
  $1 : m^{4}$
Answer: 4

Explanation:
2) Question.

Consider the following statements:

1. Welded structures are usually lighter than riveted structures.

2. Welding allows the arrangement of structural components in such a manner that the joint provides maximum efficiency

3. During welding, the members do not get distorted.

Of these statements
Answer.
- 1
  
  $1, 2$ and $3$ are correct
- 2
  
  $1$ and $2$ are correct
- 3
  
  $2$ and $3$ are correct
- 4
  
  $1$ and $3$ are correct
Answer: 2

Explanation:
3) Question.

A single direct stress $' p ‵$ acts along the longitudinal axis (x-axis) of a bar of rectangular cross section. $E$ is the Young's

modulus and $1 / m$ is the Poission's ratio of the material. Match list l with List ll and select the correct answer using the

codes given below the lists:

List l
Answer.
- 1
  
  $A B C D 1 2 3 4$
- 2
  
  $A B C D 1 2 4 3$
- 3
  
  $A B C D 2 1 3 4$
- 4
  
  $A B C D 2 1 4 3$
Answer: 4

Explanation:
4) Question.

A compound bar consisting of material $A$ and $B$ is tightly secured at the ends. The coefficient of thermal expansion of $A$ is

more than that of $B$ . when the temperature is increased the stresses induced will be
Answer.
- 1
  
  tensile in both the materials
- 2
  
  tensile in material $A$ and compressive in material $B$
- 3
  
  compressive in material $A$ and tensile in material $B$
- 4
  
  compressive in both the materials
Answer: 3

Explanation:
5) Question.

In a close coiled helical spring subjected to an axial load, other quantities remaining the same, if the wire diameter is

doubled, then the stiffness of the spring when compared to the original one, will become
Answer.
- 1
  
  twice
- 2
  
  four times
- 3
  
  eight times
- 4
  
  sixteen times
Answer: 4

Explanation:
6) Question.

Which one of the following statements about creep of metals is correct?
Answer.
- 1
  
  Creep is deformation due to high temperature under no stress condition
- 2
  
  Creep is independent of temperature
- 3
  
  Creep is time dependent deformation under stress
- 4
  
  For a given level of stress, the rate of creep is independent of time
Answer: 3

Explanation:
7) Question.

Given that the density of earth is $w$ , the angle of repose is $\emptyset$ and $h$ is the height of the wall and the earth retrained is

level, the active earth pressure $' P ‵$ on a retaining wall is given by
Answer.
- 1
  
  $\frac{w h^{2}}{3} x \frac{1 - \sin \emptyset}{1 + \sin \emptyset}$
- 2
  
  $\frac{w h^{2}}{2} x \frac{1 - \sin \emptyset}{1 + \sin \emptyset}$
- 3
  
  $\frac{w h^{2}}{2} x \frac{1 + \sin \emptyset}{1 - \sin \emptyset}$
- 4
  
  $\frac{w h^{2}}{3} x \frac{1 + \sin \emptyset}{1 - \sin \emptyset}$
Answer: 2

Explanation:
8) Question.
A bar $A B$ , $4 c m$ in diameter and $4 m$ long is rigidly fixed at its ends. A torque of $12, 000 k g$ . $c m$ is applied at a

section of the bar, one metre from end $A$ . The fixing couples Answer.
- 1
  $9000, 6000$
- 2
  
  $3000, 9000$
- 3
  
  $6000, 9000$
- 4
  
  $9000, 3000$
Answer: 4

Explanation:
9) Question.

Which of the following pairs are correctly matched ?

1. Shear stress ..... varies for different

distribution shapes of

diagram sections.

2. Bending stress ...... similar for different

distribution shapes of

diagram
Answer.
- 1
  
  $1, 2$ and $3$
- 2
  
  $1, 3 a n d 4$
- 3
  
  $1, 2$ and $4$
- 4
  
  $2, 3$ and $4$
Answer: 3

Explanation:
10) Question.

In order to produce bending and shear stresses of equal magnitudes at the extreme fibres of a circular cross section under

the action of combined bending and torsion, the ratio of bending to twisting moments must be
Answer.
- 1
  
  ¼
- 2
  
  ½
- 3
  
  1
- 4
  
  2
Answer: 2

Explanation:
11) Question.

A three hinged parabolic arch rib with hinges at abutments and at crown is under the action of uniformly distributed load

$' W ‵$ per unit length over its entire span $' L ‵$ through its crown. The bending moment at quarter span is
Answer.
- 1
  
  zero
- 2
  
  $W L^{2} / 8$
- 3
  
  $W L^{2} / 12$
- 4
  
  $W L^{2} / 24$
Answer: 1

Explanation:
12) Question.

A circular shaft subjected to torsion undergoes a twist of $1 °$ in a length of $120 c m$ . If the maximum shear stress

induced is limited to $1000 k g / c m^{2}$ and if modulus of rigidity $G = 0.8 \times 10^{6} k <$
Answer.
- 1
  $π / 18$
- 2
  
  $18 / π$
- 3
  
  $π / 27$
- 4
  
  $27 / π$
Answer: 4

Explanation:
13) Question.

A load $P$ is acting on the diagonal of a square column of size $' D ‵,$ as shown in Fig. 10.19. For no tension, the maximum

distance of the load from the centre $' O ‵$ is
Answer.
- 1
  
  $D / 8$
- 2
  
  $D / 6$
- 3
  
  $D \sqrt{2} / 6$
- 4
  
  $D \sqrt{2} / 12$
Answer: 3

Explanation:
14) Question.

If $K$ is defined as the ratio of Young's modulus of elasticity and the permissible stress in compression of a material used in

the construction of a column, then the Rankine's constant used in finding the load carrying capacity of columns is

proportional to
Answer.
- 1
  
  $1 / K$
- 2
  
  $K$
- 3
  
  $\sqrt{K}$
- 4
  
  $1 / \sqrt{K}$
Answer: 1

Explanation:
15) Question.

A wooden beam of width $B$ and depth $D$ is strengthened by two steel plates of thickness $' t ‵$ and depth $' D ‵$ on both sides

of the beam. The allowable bending stress in wood is $σ$ and modular ratio of steel to wood is $' m ‵$ . The allowable bending

moment
Answer.
- 1
  
  $\frac{σ}{6} D^{2} (B + m t)$
- 2
  
  $\frac{σ}{6} D^{2} (B + 2 m t)$
- 3
  
  $\frac{σ}{6} D^{2} (2 B + m t)$
- 4
  
  $\frac{σ}{6} D^{2} (2 B + 2 m t)$
Answer: 2

Explanation:
16) Question.

An overhanging beam of overall length $L$ and uniform flexural rigidity $E I$ is loaded by two concentrated loads at the two

ends. The beam is supported symmetrically on two supports with overhang $' a ‵$ on each side as shown in Fig. 10.18.

The vertical deflection upwards at the centre of the beam is given
Answer.
- 1
  
  $P a {(L - 2 a)}^{2} / 8 E I$
- 2
  
  $P a^{2} (L - 2 a) / 8 E I$
- 3
  
  $P a L^{2} / 8 E I$
- 4
  
  $P a^{2} (L - a) / 8 E I$
Answer: 1

Explanation:
17) Question.

A simply supported beam of span $' L ‵$ and uniform flexural rigidity $E l$ , carries a central load $' W'$ and total uniformly

distributed load $' W ‵$ throughout the span. The maximum deflection is given by
Answer.
- 1
  
  $13 W L^{3} / 96 E I$
- 2
  
  $5 W L^{3} / 384 E I$
- 3
  
  $5 W L^{3} / 96 E I$
- 4
  
  $13 W L^{3} / 384 E I$
Answer: 4

Explanation:
18) Question.

The shear stress distribution over a rectangular cross section of a beam follows
Answer.
- 1
  
  a straight line path
- 2
  
  a circular path
- 3
  
  a parabolic path
- 4
  
  an elliptical path
Answer: 3

Explanation:
19) Question.

Consider the following statements:

$A :$ For beams, l-section are more economical than rectangular sections.

$R :$ Most of the material is concentrated away from the centoid.

Of these statements
Answer.
- 1
  
  both $A$ and $R$ are true and $R$ is the correct explanation of $A$
- 2
  
  both $A$ and $R$ are true but $R$ is not a correct explanation of $A$
- 3
  
  $A$ is true but $R$ is false
- 4
  
  $A$ is false but $R$ is true
Answer: 1

Explanation:
20) Question.

An l-section beam, made of structural steel has an overall depth of $30 c m$ . If the developed flange stresses at the top

and bottom of the beam are $1200 k g / c m^{2}$ and $300 k g / c m^{2}$ respectively, then the depth of the neutral axis

from the top of the beam would be
Answer.
- 1
  
  $25 c m$
- 2
  
  $24 c m$
- 3
  
  $20 c m$
- 4
  
  $18 c m$
Answer: 2

Explanation:

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