Strength of Material Sheet 27

1) Question.

A simply supported truss shown in Fig. 10.92 carries a load of $20 K N$ at $F$ .

The forces in the members $E F$ and $B E$ are respectively.
Answer.
- 1
  
  Zero and $10 K N$ (Compression)
- 2
  
  Zero and $10 K N$ (tension)
- 3
  
  $10 K N$ (tension) and $10 K N$ (compression)
- 4
  
  $10 K N$ (compression) and $10 K N$ (tension)
Answer: 2

Explanation:
2) Question.

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

List I List II

(Beam/column and (Number of points

loading) of contraflexure)

A. Propped cantilever 1. Two

beam under mid point

loading

B. Fixed beam under 2. Three

uniformly

C. Fixed beam subjected 3. One <
Answer.
- 1
  
  $A B C D 3 2 1 3$
- 2
  
  $A B C D 3 2 3 1$
- 3
  
  $A B C D 2 3 3 1$
- 4
  
  $A B C D 2 3 1 3$
Answer: 2

Explanation:
3) Question.

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

List I List II

A. Ratio of lateral strain 1. Strain

to linear strain

B. Ratio of stress to strain 2. Poisssion's ratio

C. Ratio of extension to 3. Tensile stress

original length

D. Ratio of axial pull to area 4. Young's modulus

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

Explanation:
4) Question.

In order to produce a maximum shearing stress of $75 M N / m^{2}$ in the material of a hollow circular shaft of $25 c m$

outer diameter and $17.5 c m$ inside diameter, the torque that should be applied to the shaft is
Answer.
- 1
  
  $87.4 K N . m$
- 2
  
  $17.49 K N . m$
- 3
  
  $174.9 K N . m$
- 4
  
  $349.7 K N . m$
Answer: 3

Explanation:
5) Question.
Consider the following statements about flitched beams:
1. A flitched beam has a composite section made of two or more materials joined together in such a manner that they behave as a unit piece and each material bends to the same radius of curvature.
2. The total moment of resistance of a flitched beam is equal to the sum of the moments of resistance of individual sections.
  1. Flitched beams are used when a beam of one material, if used alone, would require quite a large cross sectional area. &
Answer.
- 1
  
  $1, 2$ and $3$ are correct
- 2
  
  $1$ and $2$ are correct
- 3
  
  $1$ and $3$ are correct
- 4
  
  $2$ and $3$ are correct
Answer: 1

Explanation:
6) Question.

A $4 - m e t r e$ long beam, simply supported at its ends, carries a point load $' W'$ at its centre. If the slope at the ends of

the beam is $1 °$ , then the deflection at the centre of the beam will be
Answer.
- 1
  
  $10.56 m m$
- 2
  
  $18.32 m m$
- 3
  
  $23.27 m m$
- 4
  
  $39.37 m m$
Answer: 3

Explanation:
7) Question.

Match List I (deflection) with List II (Expressions for deflection in different types of beams of span $' l'$ subjected to total load $' w'$ ) and select the correct answer using the codes given below the lists:

List I List II

A. Central deflection in a 1. $<$
Answer.
- 1
  $A B C D 4 3 1 2$
- 2
  
  $A B C D 3 4 2 1$
- 3
  
  $A B C D 3 4 1 2$
- 4
  
  $A B C D 4 3 2 1$
Answer: 4

Explanation:
8) Question.

A rectangular beam $10 c m$ wide, is subjected to a maximum shear force of $50000 N$ , the corresponding maximum

shear stress being $3 N / m m^{2}$ . The depth of the beam is
Answer.
- 1
  
  $25 c m$
- 2
  
  $22 c m$
- 3
  
  $16.67 c m$
- 4
  
  $30 c m$
Answer: 1

Explanation:
9) Question.

In a simply supported beam shown in Fig. 10.88, if dimensions $a c$ and $a b$ are doubled, then the bending moment and the shear force at $' c'$ will be such that
Answer.
- 1
  
  both $S F$ and $B M$ are doubled
- 2
  
  $S F$ is half and $B M$ is double
- 3
  
  $S F$ is double and $B M$ is half
- 4
  
  $S F$ is double and $B M$ is four times
Answer: 4

Explanation:
10) Question.
Consider the following statements:

The theory of simple bending assumes that
1. the material of the beam is homogenous, isotropic and obeys Hook's law
2. plane sections of the beam remain plane after bending
3. Each cross section of the beam is symmetric about the loading plane
  1. Young's moduli are the same for tension and compression
Answer.
- 1
  
  $1$ and $2$ are correct
- 2
  
  $1, 3$ and $4$ are correct
- 3
  
  $2, 3$ and $4$ are correct
- 4
  
  $1, 2, 3$ and $4$ are correct
Answer: 4

Explanation:
11) Question.

A cantilever beam of span $L$ carries concentrated load $' W'$ at the free end. If the width $' b'$ of the beam is constant throughout the span, then for the beam to have uniform strength, the depth $' d'$ at the free end should be
Answer.
- 1
  
  $\frac{6 W L}{b f}$
- 2
  
  $\frac{3 W L}{b f}$
- 3
  
  $\sqrt{\frac{3 W L}{b f}}$
- 4
  
  $\sqrt{\frac{6 W L}{b f}}$
Answer: 4

Explanation:
12) Question.

For the system of springs shown in Fig. 10.87, the equivalent spring stiffness is
Answer.
- 1
  
  $58 K N / m$
- 2
  
  $62 K N / m$
- 3
  
  $78 K N / m$
- 4
  
  $90 K N / m$
Answer: 1

Explanation:
13) Question.

A simply supported beam $A B$ of span $4 m$ carries loads as shown in Fig. 10.85.

The corresponding $S F D$ and $B M D$ for the beam will be as shown in
Answer.
- 1
- 2
- 3
- 4
Answer: 4

Explanation:
14) Question.
A steel rod of circular section tapers from $2 c m$ diameter to $1 c m$ diameter over a length of $50 c m .$ If the modulus of

elasticity of the material is $2 x 10^{6} k g / c m^{2}$ , then the increase in length under a pull of Answer.
- 1
  $\frac{0.3}{2 π} c m$
- 2
  
  $\frac{30}{π} c m$
- 3
  
  $\frac{300}{π} c m$
- 4
  
  $750 c m$
Answer: 1

Explanation:
15) Question.

A simply supported beam of span 'l' is loaded (as shown in Fig. 10.84) with a uniformly varying load of intensity $w_{l}$ /unit length at $' A'$ to $w_{2}$ /unit length at $' B'$ .

The shear force at the support 'B' is given by
Answer.
- 1
  
  $\frac{(w_{1} + w_{2}) 1}{3}$
- 2
  
  $\frac{(w_{1} + w_{2}) 1}{6}$
- 3
  
  $\frac{w_{l} l}{6} + \frac{w_{2} l}{3}$
- 4
  
  $\frac{w_{l} l}{3} + \frac{w_{2} l}{6}$
Answer: 3

Explanation:
16) Question.

Figure 10.82 shows a beam cantilevering out at one end. It carries a uniformly distributed load $W$ over the cantilever.

Which one of the following figures correctly represents the shear force diagram for the beam?
Answer.
- 1
- 2
- 3
- 4
Answer: 1

Explanation:
17) Question.

Two simply supported beams $B_{1}$ and $B_{2}$ have spans $l$ and $2 l$ respectively. Beam $B_{1}$ has a cross section of $1 x 1$ units

and beam $B_{2}$ ha
Answer.
- 1
  
  $4$
- 2
  
  $2$
- 3
  
  $^{\frac{1}{2}}$
- 4
  
  $^{\frac{1}{4}}$
Answer: 1

Explanation:
18) Question.

A propped cantilever of span $' l'$ carries a uniformly distributed load of $' w'$ per unit run over its entire span. The value of prop reaction to keep the beam horizontal is
Answer.
- 1
  
  $\frac{w l}{3}$
- 2
  
  $\frac{3}{8} w l$
- 3
  
  $\frac{w l}{2}$
- 4
  
  $\frac{5}{8} w l$
Answer: 2

Explanation:
19) Question.

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

List I List II

(Name of person whom (Method)

the methods of analysis

are associated)

A. Clapeyron 1. Moment distribution

method

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

Explanation:
20) Question.

In the cantilever truss shown in Fig. 10.77, the reaction at $A$ is
Answer.
- 1
  
  $10$ t
- 2
  
  $20$ t
- 3
  
  $30$ t
- 4
  
  $40$ t
Answer: 3

Explanation:

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