Strength of Material Sheet 26

1) Question.

The structure shown in Fig. 10.81 is stable if
Answer.
- 1
  
  $x = 2 y$
- 2
  
  $2 x = y$
- 3
  
  $\sqrt{2 x} = y$
- 4
  
  $x = \sqrt{2} y$
Answer: 4

Explanation:
2) Question.
$A B C D$ is a beam of length $5 l$ which is supported at $B$ and $C$ (having supported length $B C =$ $1)$ and having two equal overhangs $A B$ and Answer.
- 1
  
  at $B$ and $C$
- 2
  
  at the mid point of $B C$
- 3
  
  nowhere in the beam
- 4
  
  at the mid point of $A B$ and $C D$
Answer: 3

Explanation:
3) Question.

The shear force diagram for a simply supported beam of span 'l' is given in Fig. 10.79.

The maximum bending moment is
Answer.
- 1
  
  $\frac{W l}{2}$
- 2
  
  $W (\frac{1}{2} - l_{1})$
- 3
  
  $W l_{1}$
- 4
  
  $W (l - 2 l_{1})$
Answer: 3

Explanation:
4) Question.

The shear force diagram for a simply supported beam of span 'l' is given in Fig. 10.79.

The maximum bending moment is
Answer.
- 1
  
  $\frac{W l}{2}$
- 2
  
  $W (\frac{1}{2} - l_{1})$
- 3
  
  $W l_{1}$
- 4
  
  $W (l - 2 l_{1})$
Answer: 3

Explanation:
5) Question.

In Fig. 10.78, the maximum bending moment at the fixed end of the cantilever caused by the $U D L$ is $M .$

The bending moment at a section $l / 5$ from the free end is
Answer.
- 1
  
  $4 %$ of $M$
- 2
  
  $5 %$ of $M$
- 3
  
  $10 %$ of $M$
- 4
  
  $20 %$ of $M$
Answer: 1

Explanation:
6) Question.

The deflection at the free end of a cantilever subjected to a couple $M$ at its free end and having a uniform flexural rigidity $E I$ throughout its length $' L'$ is equal to
Answer.
- 1
  
  $\frac{M L^{2}}{2 E I}$
- 2
  
  $\frac{M L^{2}}{3 E I}$
- 3
  
  $\frac{M L^{2}}{6 E I}$
- 4
  
  $\frac{M L^{2}}{8 E I}$
Answer: 1

Explanation:
7) Question.

Match List I with List II and select the correct answer using the codes given below the lists:

List I List II

(Nature of beam) (Max.deflection)

A. Cantilever beam 1. $\frac{W L^{3}}{15 E I}$

subjected to a

concentrated

load $W$ at free end

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

Explanation:
8) Question.

Match List I with List II and select the correct answer using the codes given below the lists:

List I List II

A. Impulse 1. shear centre

B. Torsion 2. plane motion

C. Plane of loading 3. Modulus of

D. Instantaneous rigidity

centre of rotation 4. Time effect of a

force

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

Explanation:
9) Question.

Match the items in List I with those in List II (with reference to Fig. 10.75 ) and select the correct answer using the codes given below the lists:

List I List II

A. Maximum principal 1. 9.0

stress

B. Minimum prin
Answer.
- 1
  
  $A B C D 4 3 5 2$
- 2
  
  $A B C D 4 2 5 3$
- 3
  
  $A B C D 4 5 1 2$
- 4
  
  $A B C D 2 5 1 3$
Answer: 2

Explanation:
10) Question.

A thick cylinder is subjected to external pressure. The magnitude of hoop stress at internal radius will be
Answer.
- 1
  
  equal to the magnitude of hoop stress at external radius
- 2
  
  less than the magnitude of hoop stress at external radius
- 3
  
  greater than the magnitude of hoop stress at external radius
- 4
  
  equal to the magnitude of radial stress at internal radius
Answer: 3

Explanation:
11) Question.
A column $A B C D$ of rectangular section is subjected to an eccentric load at $Z$ as shown in Fig. 10.68.
Under the compressive load, the direct stress is 400 t/m2 and bending stresses are
σ
Answer.

1
$800 t / m^{2}$ (Compressive)

2

$1600 t / m^{2}$ (tensile)

3

$800 t / m^{2}$ (tensile)

4

$2000 t / m^{2}$ (Compressive)

Answer: 1

Explanation:

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12) Question.

The modular ratio of the materials used in the flitched beam is $10$ and the ratio of the allowable stresses is also $10$ . Four different sections of the beam are shown in Fig. 10.67. The material shown hatched has larger modulus of elasticity and allowable stress than the rest.

Which one of the following statements is true for the beam under consideration?
Answer.
- 1
  
  All the given sections would support the same magnitude of load.
- 2
  
  Sections 2, 3 and 4 would support equal loads which is more than what section 1 would support
- 3
  
  Sections 1 and 2 would support equal loads which is more than what sections 3 and 4 would support
- 4
  
  Section 2 would support the greatest load
Answer: 4

Explanation:
13) Question.

A simply supported truss shown in Fig. 10.66 carries load as shown. The force in member $B E$ is
Answer.
- 1
  
  $\sqrt{2} t$ (tensile)
- 2
  
  $\sqrt{2} t$ (compressive)
- 3
  
  $1 t$ (tensile)
- 4
  
  $1 t$ (Compressive)
Answer: 3

Explanation:
14) Question.

Given that

$P_{E} =$ the cripping load given by Euler,

$P_{C} =$ the load at failure due to direct compression

$P_{R} =$ the load in accordance with the Rankine's criterion of failure,

$P_{R}$ is given by
Answer.
- 1
  
  $(P_{E} + P_{C}) / 2$
- 2
  
  $\sqrt{P_{E} x P_{C}}$
- 3
  
  $P_{C} P_{E} / (P_{C} + P_{E})$
- 4
  
  None of the above
Answer: 3

Explanation:
15) Question.

System $A$ is a simply supported beam with a load $P$ at mid span. System $B$ is the same beam but the load is replaced by

a $u d l$ of intensity $P / L$ wherein $L$ is the span. The mid span deflection of system $B$ will
Answer.
- 1
  
  be the same as that of system $A$ at mid span
- 2
  
  be less than that of system $A$ at mid span
- 3
  
  be more than that of system $A$ at mid span
- 4
  
  bear no relation to that of system $A$
Answer: 2

Explanation:
16) Question.
A straight wire $15 m$ long is subjected to a tensile stress of $2000 k g f / c m^{2}$ . Elastic modulus is

$1.5 x 10^{6} k g f / c m^{2} .$ Coefficient of linear expansion for the material is Answer.
- 1
  
  $40$
- 2
  
  $80$
- 3
  
  $120$
- 4
  
  $160$
Answer: 2

Explanation:
17) Question.

Two closedly-coiled springs $A$ and $B$ of the same material, same wire and same number of turns ar subjected to an axial

load of $W$ . The mean diameter of spring $A$ is half that of spring $B$ . The ratio of deflection on spring $B$ to that of spring $A$

will be&nb
Answer.
- 1
  
  $8$ $4$
- 2
  
  $4$
- 3
  
  $\frac{1}{4}$
- 4
  
  $\frac{1}{8}$
Answer: 1

Explanation:
18) Question.

The ratio of torsional moments of resistance of a solid circular shaft of diameter $D$ and a hollow shaft having external diameter $D$ and internal diameter $' d'$ is given by
Answer.
- 1
  
  $\frac{D^{4}}{D^{4} - d^{4}}$
- 2
  
  $\frac{D^{4} - d^{4}}{D^{4}}$
- 3
  
  $\frac{D^{3}}{D^{3} - d^{3}}$
- 4
  
  $\frac{D^{3} - d^{3}}{D^{3}}$
Answer: 1

Explanation:
19) Question.

The deflection at the free end of a cantilever of rectangular cross-section due to certain loading is $0.8 c m .$ If the depth

of the section is doubled keeping the width the same, then the deflection at the free end due to the same loading will be
Answer.
- 1
  
  $0.1 c m$
- 2
  
  $0.4 c m$
- 3
  
  $0.8 c m$
- 4
  
  $1.6 c m$
Answer: 1

Explanation:

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