Strength of Material Sheet 28

1) Question.

Assertion $A$ : Macaulay's method to determine the slope and deflection at a point in a beam is suitable for beams subjected to concentrated loads and can be extended to unifomly distributed loads.

Reason $R$ : Macaulay's method is based upon the modification of moment area method. This is applicable to a simple beam carrying a single concentrated load
Answer.
- 1
  
  Both $A$ and $R$ are true and $R$ is the correct explanation of $A$
- 2
  
  Both $A$ and $R$ are true and $R$ is not a correct explanation of $A$
- 3
  
  $A$ is true but $R$ is false
- 4
  
  $A$ is false but $R$ is true
Answer: 2

Explanation:
2) Question.
Assertion $A$ : A bar tapers from a diameter of $d_{1}$ to a diameter of $d_{2}$ over its length $' l'$ and is subjected to a tensile

force $' p'$ . If extension is calculated based on treating it as a bar of average diameter, the calculated extension will be

more than the actual extension.

Reason 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: 2

Explanation:
3) Question.

Assertion $A$ : Bending moment may be defined as the algebraic sum of the moments of all forces on either side of the section.

Reason $R$ : The rate of change of bending moment is equal to shear force at the section.
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: 2

Explanation:
4) Question.

Assertion $A$ : The buckling load for a column of specified material, cross section and end conditions calculated as per Euler's formula varies inversely with the column length.

Reason $R$ : Euler's formula takes into account the end conditions in determining the effective length of column.
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: 2

Explanation:
5) Question.

Assertion $A$ : A beam of circular cross-section in comparison to rectangular section of the same material but of equal cross sectional area can resist a larger shear force.

Reason $R :$ The maximum intensities of shear stress in the sections of a beam of circular cross section and of a rectangular cross section are 1.33 times and 1.5 times the average shear stress respectively.
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: 2

Explanation:
6) Question.

Assertion $A$ : I-section is preferred to rectangular section for resisting bending moment.

Reason $R$ : In I-section more than $80 %$ of bending moment is resisted by flanges only.
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: 2

Explanation:
7) Question.

Assertion $A$ : The maximum bending moment occurs where the shear force is either zero or changes sign.

Reason $R$ : If the shear force diagram line between the two, points is horizontal, the $B M$ diagram line is inclined. But if

the $S F$ diagram is inclined, the $B M$ diagram is a parabola of second degree.
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: 2

Explanation:
8) Question.

Asserrtion $A$ : Strain is a fundamental behaviour of the material, while the stress is a derived concept.

Reason $R$ : Strain does not have a unit while the stress has a unit.
Answer.
- 1
  
  Both $A$ and $R$ are true and $R$ is the correct explanation of $A$
- 2
  
  Both $A$ and $R$ are tue 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: 2

Explanation:
9) Question.

Assertion $A$ : Bending moment in a beam is maximum at a section where shear force is zero.

Reason $R$ : Shear force at a section is given by the rate of change of bending moment
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: 2

Explanation:
10) Question.

Assertion $A$ : In a Mohr's circle, the vertical coordinates of the ends of any diameter are equal in magnitude and opposite in direction.

Reason $R$ : The shear stresses on two planes at right angles are equal in magnitude and tend to rotate the element in opposite directions.
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: 2

Explanation:
11) Question.

Match List I (Euler load formulae for different end restraints) with List II (conditions of end restraints) and select the correct answer using the codes given below the lists:

List I List II

A. $\frac{4 π^{2} E I}{L^{2}}$ 1. Pin-ended at both ends

B. $\frac{π^{2} E I}{4}$
Answer.
- 1
  $A B C D 4 3 2 1$
- 2
  
  $A B C D 3 4 2 1$
- 3
  
  $A B C D 3 4 1 2$
- 4
  
  $A B C D 4 3 1 2$
Answer: 3

Explanation:
12) Question.

A truss $A B C,$ carries two horizontal and two vertical loads, as shown in Fig. 10.76.

The horizontal and vertical components of the reaction at $A$ will be
Answer.
- 1
  
  $H_{A} = 1000 K N; V_{A} = 1706.25 K N$
- 2
  
  $H_{A} = 2000 K N; V_{A} = 2550 K N$
- 3
  
  $H_{A} = 1000 K N; V_{A} = 2550 K N$
- 4
  
  $H_{A} = 2000 K N; V_{A} = 1706.25 K N$
Answer: 2

Explanation:
13) Question.

Two similar round bars $A$ and $B$ are each $30 c m$ long as shown in Fig. 10.74.

The ratio of the energies stored by the bars $A$ and $B$ , $<$
Answer.
- 1
  $\frac{3}{2}$
- 2
  
  $1.0$
- 3
  
  $\frac{5}{8}$
- 4
  
  $\frac{2}{3}$
Answer: 1

Explanation:
14) Question.

A column section as indicated in Fig. 10.73 is loaded with a concentrated load at a point $' P'$ so as to produce maximum

bending stress due to eccentricities about XX axis and YY axis as $5 t / m^{2}$ and $8 t / m^{2}$ respectively.

If the direct stres
Answer.
- 1
  
  $2 t / m^{2}$ (Compressive)
- 2
  
  $12 t / m^{2}$ (Compressive)
- 3
  
  $18 t / m^{2}$ (tensile)
- 4
  
  $28 t / m^{2}$ (Compressive)
Answer: 2

Explanation:
15) Question.

Fig. 10.72 shows a retaining wall of base width $B_{1}$ and height $H_{1}$ . The sp. gravity of the material of construction is S. Further

$A B = B C = C D = \frac{B_{1}}{3}$
Answer.
- 1
  
  $A$ to $B$
- 2
  
  $B$ to $C$
- 3
  
  $C$ to $D$
- 4
  
  $B$ to $D$
Answer: 2

Explanation:
16) Question.

The 'Euler' load for a column is $1000 K N$ and crushing load is $1500 K N$ . The 'Rankine' load is equal to
Answer.
- 1
  
  $600 K N$
- 2
  
  $1000 K N$
- 3
  
  $1500 K N$
- 4
  
  $2500 K N$
Answer: 1

Explanation:
17) Question.

A timber beam of rectangular section $100 m m$ $x 50 m m$ is simply supported at the ends, has a

$30 m m x 10 m m$ steel strip securely fixed to the top surface as shown in Fig. 10. 71.

The centroid of the ''equivalent timber b
Answer.
- 1
  
  is $5 m m$
- 2
  
  is $30 m m$
- 3
  
  is $15 m m$
- 4
  
  cannot be predicted
Answer: 2

Explanation:
18) Question.

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

List I List II

A. Partial derivative 1. Equation for

of strain energy shear force

w.r.t. a load

B. Derivative of 2. Equation for

deflection slope

C. Derivative of 3. Equation f
Answer.
- 1
  
  $A B C D 4 3 2 1$
- 2
  
  $A B C D 2 1 3 4$
- 3
  
  $A B C D 4 2 3 1$
- 4
  
  $A B C D 2 3 1 4$
Answer: 3

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

(Beam with loading) (B.M. diagram)

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

Explanation:
20) Question.

The slope at the support $A$ of the overhanging beam shown in Fig. 10.69 is
Answer.
- 1
  
  $\frac{W l^{2}}{12 E I}$
- 2
  
  $\frac{W l^{2}}{24 E I}$
- 3
  
  $\frac{W l}{3 E I}$
- 4
  
  $\frac{W l}{6 E I}$
Answer: 2

Explanation:

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