Strength of Material Sheet 29

1) Question.

In the analysis of a closely coiled helical spring under axial load, which of the following is/are negligible?

1. Torsion

2. Bending

3. Axial force in the wire

Select the correct answer using the codes given below

Codes:
Answer.
- 1
  
  $1$ alone
- 2
  
  $2$ and $3$
- 3
  
  $1$ and $2$
- 4
  
  $1$ and $3$
Answer: 2

Explanation:
2) Question.

The plane of maximum shear stress has normal stress that is
Answer.
- 1
  
  maximum
- 2
  
  minimum
- 3
  
  zero
- 4
  
  none of the above
Answer: 4

Explanation:
3) Question.

In the truss shown in Fig. 10.65 the forces in the members $A B$ and $B C$ will be respectively (plus denotes tension)
Answer.
- 1
  
  Zero and Zero
- 2
  
  $- W / \cos 60 °$ and $+ W \tan 60 °$
- 3
  
  $- W / \cos 60 °$ and Zero
- 4
  
  Zero and $+ W \tan 60 °$
Answer: 1

Explanation:
4) Question.

A three-hinged symmetric parabolic arch is hinged at the springings and at the crown. The span and rise are $40 m$ and

$10 m$ respectively. The left half of the arch is loaded with $U . D . L$ . of $3 t / m$ . The horizontal thrust at the springings

will be
Answer.
- 1
  
  $15 t$
- 2
  
  $20 t$
- 3
  
  $30 t$
- 4
  
  $40 t$
Answer: 3

Explanation:
5) Question.

A section of a flitched beam is shown in Fig. 10.64.

The main role of the steel plate placed between the two timber sections is to
Answer.
- 1
  
  increase the axial resistance of the section
- 2
  
  increase the density
- 3
  
  increase shear and bending resistance of the section
- 4
  
  avoid development of shear stress in the two timber sections
Answer: 3

Explanation:
6) Question.

A beam of square section $' a'$ is used with its diagonal horizontal. The modulus of section of the beam is given by
Answer.
- 1
  
  $\frac{a^{4}}{6 \sqrt{2}}$
- 2
  
  $\frac{a^{4}}{12 \sqrt{2}}$
- 3
  
  A3/6 root 2
- 4
  
  $\frac{a^{3}}{12 \sqrt{2}}$
Answer: 3

Explanation:
7) Question.

Figure 10.62 shows a simply-supported beam overhanging to the left. The beam carries a uniformly distributed load of $w / m$ throughout.

The correct bending moment diagram for the beam is
Answer.
- 1
- 2
- 3
- 4
Answer: 1

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

(Principal stress) (Max. shearing stress)

A. $\{+ 50, + 50\}$ 1. $25$

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

Explanation:
9) Question.

The ratio of total elongation of a bar of uniform cross-section produced under its own weight to the elongation produced by an external load equal to the weight of the bar is
Answer.
- 1
  
  $2$
- 2
  
  $1$
- 3
  
  $\frac{1}{2}$
- 4
  
  $\frac{1}{4}$
Answer: 3

Explanation:
10) Question.

For the compound bar shown in Fig. 10.61, the ratio of stresses in the portions $A B : B C : C D$ will be
Answer.
- 1
  
  $4 : 1 : 2$
- 2
  
  $1 : 2 : 4$
- 3
  
  $1 : 4 : 2$
- 4
  
  $4 : 2 : 1$
Answer: 3

Explanation:
11) Question.

A shaft of diameter $' d'$ is subjected to bending moment $' M'$ and twisting moment $' T' .$ The developed principal stress will be
Answer.
- 1
  
  $\pm \frac{16}{π d^{3}} \sqrt{M^{2} + T^{2}}$
- 2
  
  $\frac{16}{π d^{3}} (M \pm \sqrt{M^{2} + T^{2}})$
- 3
  
  $\frac{16}{π d^{3}} (T \pm \sqrt{M^{2} + T^{2}})$
- 4
  
  $\frac{16}{π d^{3}} \sqrt{M^{2} + T^{2}} \pm M$
Answer: 2

Explanation:
12) Question.

A hollow steel shaft of external diameter $100 m m$ and internal diameter $50 m m$ is to be replaced by a solid alloy

shaft. Assuming the same value of polar modulus for both, the diameter of the solid alloy shaft will be
Answer.
- 1
  
  $10 x \sqrt[3]{9375} m m$
- 2
  
  $10 x \sqrt[3]{9375 x 10} m m$
- 3
  
  $10 x \sqrt[3]{\frac{9375}{10}} m m$
- 4
  
  $\sqrt[3]{9375} m m$
Answer: 3

Explanation:
13) Question.

A shaft turns at $150 r p m$ under a torque of $1500 N m$ . Power transmitted is
Answer.
- 1
  
  $15 π k W$
- 2
  
  $10 π k W$
- 3
  
  $7.5 π k W$
- 4
  
  $5 π k W$
Answer: 3

Explanation:
14) Question.

Match List I with List II and select the correct answer using the codes given below the lists: ( No. of members $' m',$ No. of

joints $' n',$ No. of reaction elements $' r'$ )

List I List II

(Types of structure) &nb
Answer.
- 1
  
  $A B C 1 2 3$
- 2
  
  $A B C 4 3 2$
- 3
  
  $A B C 2 1 3$
- 4
  
  $A B C 4 1 2$
Answer: 4

Explanation:
15) Question.

The three-hinged arch shown in Fig. 10.60 will have value of $H$ as
Answer.
- 1
  
  $20 K N$
- 2
  
  $30 K N$
- 3
  
  $40 K N$
- 4
  
  $50 K N$
Answer: 3

Explanation:
16) Question.

The shear stress distribution shown in Fig. 10.58 represents a beam with cross section.
Answer.
- 1
- 2
- 3
- 4
Answer: 1

Explanation:
17) Question.

The cross section of a beam is shown in Fig. 10.57(a). Its $I_{x x}$ is equal to $3 x 10^{6} m m^{4}$ . It is subjected to a load as

shown in Fig. 10.57(b).

The maximum tensile stress in the beam would be
Answer.
- 1
  
  indeterminable as data is insufficient
- 2
  
  $21 M N / m^{2}$
- 3
  
  $21 K N / m^{2}$
- 4
  
  $21 N / m^{2}$
Answer: 2

Explanation:
18) Question.
A mild steel flat of width $120 m m$ and thickness $10 m m$ is bent into an arc of a circle of radius $10 m$ by applying a
pure moment 'M'. If E is
2 x 105
Answer.

1
$2 x 10^{6} N - m m$

2

$2 x 10^{5} N - m m$

3

$0.2 x 10^{5} N - m m$

4

$0.2 x 10^{4} N - m m$

Answer: 2

Explanation:

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19) Question.

A simply supported beam of constant width and varying depth and uniform strength is subjected to a central concentrated

load. The depth of the beam $d_{x}$ at a distance $x$ from one of the supports is proportional to
Answer.
- 1
  
  $x^{\frac{1}{2}}$
- 2
  
  $x^{\frac{1}{3}}$
- 3
  
  $x$
- 4
  
  $x^{2}$
Answer: 1

Explanation:
20) Question.

The bending moment diagram of the beam shown in Fig. 10.55 is
Answer.
- 1
- 2
- 3
- 4
Answer: 4

Explanation:

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