Strength of Material Sheet 23

1) Question.

The shear centre of a section is defined as that point
Answer.
- 1
  
  through which load must be applied to produce zero twisting moment on the section
- 2
  
  at which shear force is zero
- 3
  
  at which the shear force is a maximum
- 4
  
  at which the shear force is a minimum
Answer: 1

Explanation:
2) Question.

According to the Distortion Energy Theory, failure will not occur when (Symbols have the usual meaning)
Answer.
- 1
  
  ${[\frac{{(σ_{1} - σ_{2})}^{2} + {(σ_{2} - σ_{3})}^{2} + {(σ_{3} - σ_{1})}^{2}}{2}]}^{\frac{1}{2}} \leq σ_{0}$
- 2
  
  ${[{(σ_{1} - σ_{2})}^{2} + 4 τ^{2}]}^{\frac{1}{2}} \leq σ_{0}$
- 3
  
  ${[({σ_{1}}^{2} + {σ^{2}}_{2} + {σ_{3}}^{2}) - \frac{1}{m} (σ_{1} σ_{2} + σ_{2} σ_{3} + σ_{3} σ_{1})]}^{\frac{1}{2}} \leq σ_{0}$
- 4
  
  $\frac{{(σ_{1} + σ_{2})}^{2} + {[{(σ_{1} - σ_{2})}^{2} + 4 τ^{2}]}^{\frac{1}{2}}}{2} \leq σ_{0}$
Answer: 1

Explanation:
3) Question.
A copper bar of $25 c m$ length is fixed by means of supports at its ends. Supports can yield (total) by 0.01 cm. If the

temperature of the bar is raised by $100 ° C$ , then the stress induced in the bar for $α_{c}$ $= 20 x 10^{- 6} / ° C$ and Answer.
- 1
  $2 x 10^{2} k g / c m^{2}$
- 2
  
  $4 x 10^{2} k g / c m^{2}$
- 3
  
  $8 x 10^{2} k g / c m^{2}$
- 4
  
  $16 x 10^{2} k g / c m^{2}$
Answer: 4

Explanation:
4) Question.

A round steel bar of overall length $40 c m$ consists of two equal portions of $20 c m$ each having diameters of $10 c m$

and $8 c m$ respectively. If the rod is subjected to a tensile load of $10 t o n n e s$ , the elongation will
Answer.
- 1
  
  $\frac{1}{10 π} (\frac{1}{25} + \frac{1}{16}) c m$
- 2
  
  $\frac{2}{10 π} (\frac{1}{25} + \frac{1}{16}) c m$
- 3
  
  $\frac{3}{10 π} (\frac{1}{25} + \frac{1}{16}) c m$
- 4
  
  $\frac{4}{10 π} (\frac{1}{25} + \frac{1}{16}) c m$
Answer: 4

Explanation:
5) Question.

Which one of the following pairs is not correctly matched?
Answer.
- 1
  
  Lame's constants: Thick cylinder
- 2
  
  Macaulay's method: deflection of beams
- 3
  
  Euler's method: Theory of columns
- 4
  
  Eddy's theorem: Torsion of shafts
Answer: 4

Explanation:
6) Question.

Two closed-coil springs of stiffness $s$ and $2 s$ are arranged in series in one case and in parallel in the other case. The ratio

of stiffness of springs connected in series to parallel is
Answer.
- 1
  
  $1 / 3$
- 2
  
  $1 / 9$
- 3
  
  $2 / 3$
- 4
  
  $2 / 9$
Answer: 4

Explanation:
7) Question.

A simply supported beam of span $l$ and flexural rigidity $E I$ , carries a unit point load at its centre. The strain energy in the

beam due to bending is
Answer.
- 1
  
  $\frac{l^{3}}{48 E I}$
- 2
  
  $\frac{l^{3}}{192 E I}$
- 3
  
  $\frac{l^{3}}{96 E I}$
- 4
  
  $\frac{l^{3}}{16 E I}$
Answer: 3

Explanation:
8) Question.

A column $A B C D$ $(2 y_{1} x 2 y_{2})$ of rectangular section carries a load $P$ at $Z$ having the coordinates $(x, y)$ as shown in

Fig. 10.42.

&n
Answer.
- 1
  
  $\frac{P}{A} + \frac{P y}{1_{x x}} y_{1} + \frac{P x}{1_{y y}} y_{2}$
- 2
  
  $\frac{P}{A} - \frac{P y}{1_{x x}} y_{1} - \frac{P x}{1_{y y}} y_{2}$
- 3
  
  $\frac{P}{A} + \frac{P y}{1_{y y}} y_{1} + \frac{P x}{1_{x x}} y_{2}$
- 4
  
  $\frac{P}{A} - \frac{P y}{1_{y y}} y_{1} - \frac{P x}{1_{x x}} y_{2}$
Answer: 2

Explanation:
9) Question.

A hollow circular column of internal diameter $d$ and external diameter $1.5 d$ is subjected to compressive load. The

maximum distance of the point of application of load from the centre for no tension is
Answer.
- 1
  
  $d / 8$
- 2
  
  $13 d / 48$
- 3
  
  $d / 4$
- 4
  
  $13 d / 96$
Answer: 2

Explanation:
10) Question.

For a circular column having its ends hinged, the slenderness ratio is $160$ . The $l / d$ ratio of the column is
Answer.
- 1
  
  $80$
- 2
  
  $57$
- 3
  
  $40$
- 4
  
  $20$
Answer: 3

Explanation:
11) Question.

A cantilever of constant depth carries a uniformly distributed load on the whole span. To make the maximum stress at all

sections the same, the breadth of the section at a distance $x$ from the free end should be proportional to
Answer.
- 1
  
  $x$
- 2
  
  $\sqrt{x}$
- 3
  
  $x^{2}$
- 4
  
  $x^{3}$
Answer: 3

Explanation:
12) Question.

For the cantilever beam shown in Fig. 10.40, which one of the following pairs is not correctly matched?
Answer.
- 1
  
  $T h e o r e m$ $(E I) t i m e s o f d e f l e c t i o n a t B$
  
  Mohr's Theorem Area of $B M D$ $x$ distance of centroid of $B M D$ from $B$
- 2
  
  $T h e o r e m$ $(E I) t i m e s o f d e f l e c t i o n a t B$
  
  Castigliano's theorem $\int_{0}^{1} W x^{2} d x$
- 3
  
  $T h e o r e m$ $(E I) t i m e s o f d e f l e c t i o n a t B$
  
  Conjugate beam theorem Shear force at the fixed end of conjugate beam
- 4
  
  $T h e o r e m$ $(E I) t i m e s o f d e f l e c t i o n a t B$
  
  Successive integration $\int \int - W x d x$
Answer: 3

Explanation:
13) Question.

The cantilever frame shown in Fig. 10.34 is supported by vertical links at $B$ and $C$ and carries loads as shown. The

Force in the bar $A E$ is
Answer.
- 1
  
  $500 k g$
- 2
  
  $1000 k g$
- 3
  
  $z e r o$
- 4
  
  $2500 k g$
Answer: 3

Explanation:
14) Question.

The maximum deflection of a fixed beam carrying a central load $W$ is equal to
Answer.
- 1
  
  $\frac{W L^{3}}{48 E I}$
- 2
  
  $\frac{W L^{3}}{96 E I}$
- 3
  
  $\frac{W L^{3}}{192 E I}$
- 4
  
  $\frac{5}{384} \frac{W L^{3}}{E I}$
Answer: 3

Explanation:
15) Question.

Match $L i s t I$ with $L i s t I I$ and select the correct answer using the codes given below the lists:

$L i s t I$
Answer.
- 1
  $A B C D 4 3 2 1$
- 2
  
  $A B C D 3 1 4 2$
- 3
  
  $A B C D 4 1 2 3$
- 4
  
  $A B C D 4 2 3 1$
Answer: 1

Explanation:
16) Question.

A certain steel has proportionality limit of $3000 k g / c m^{2}$ in simple tension. It is subjected to principal stresses of

$1200 k g / c m^{2}$ (tensile), $600 k g / c m^{2}$ (tensile) and $300 k g / c m^{2}$
Answer.
- 1
  $1.50$
- 2
  
  $1.75$
- 3
  
  $1.80$
- 4
  
  $2.00$
Answer: 4

Explanation:
17) Question.

On an element shown in Fig. 10.33, the stress are (in Mpa)

$σ_{x} = 110$

$σ_{y} = 30$

$τ_{x y} = 30 = τ_{y x}$

The radius of Moh
Answer.
- 1
  
  $R a d i u s — r$ $σ_{1}$ $σ_{2}$
  
  $50$ $20$ $120$
- 2
  
  $R a d i u s — r$ $σ_{1}$ $σ_{2}$
  
  $55$ $110$ $30$
- 3
  
  $R a d i u s — r$ $σ_{1}$ $σ_{2}$
  
  $60$ $20$ $140$
- 4
  
  $R a d i u s — r$ $σ_{1}$ $σ_{2}$
  
  $70$ $20$ $140$
Answer: 1

Explanation:
18) Question.

If all the dimensions of a prismatic bar of square cross section suspended freely from the ceiling of a roof are doubled,

then the total elongation produced by its own weight will increase
Answer.
- 1
  
  eight times
- 2
  
  four times
- 3
  
  three times
- 4
  
  two times
Answer: 2

Explanation:
19) Question.

The side $A D$ of the square block $A B C D$ as shown in Fig. 10.32 is fixed at the base and it is under a state of simple

shear causing shear stress τ and shear strain $\emptyset$ , where

$\emptyset$ =
Answer.
- 1
  $\frac{\emptyset}{2}$
- 2
  
  $\frac{\emptyset}{\sqrt{2}}$
- 3
  
  $\emptyset \sqrt{2}$
- 4
  
  $\emptyset$
Answer: 1

Explanation:
20) Question.

The length, coefficient of thermal expansion and Young's modulus of bar $' A ‵$ are twice that of bar $' B ‵$ . If the temperature

of both bars is increased by the same amount while preventing any expansion, then the ratio of stress developed in bar $A$

to that in bar $B$ will be
Answer.
- 1
  
  $2$
- 2
  
  $4$
- 3
  
  $8$
- 4
  
  $16$
Answer: 2

Explanation:

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