Strength of Material Sheet 24

1) Question.

Given that for a channel section, the width of flange = $b$ , the depth of the web between centres of flanges = $h$ , the

thickness of flange = $t$ , the moment of inertia = $I$ , the distance 'e' of the shear centre outside the channel section from

the mid thickness of the web is
Answer.
- 1
  
  $\frac{t h^{2} b^{2}}{I}$
- 2
  
  $\frac{t^{2} h^{2} b}{4 I}$
- 3
  
  $\frac{t h^{2} b^{2}}{4 I}$
- 4
  
  $\frac{t^{2} h b^{2}}{4 I}$
Answer: 3

Explanation:
2) Question.

A material of Young's modulus $' E'$ and Poission's ratio $' μ'$ is subjected to two principal stress $σ_{1}$ and $σ_{2}$ at a point in a

two-dimensional stress system. The strain energy per unit volume of the material is
Answer.
- 1
  
  $\frac{1}{2 E} ({σ_{1}}^{2} + {σ^{2}}_{2} - 2 μ σ_{1} σ_{2})$
- 2
  
  $\frac{1}{2 E} ({σ^{2}}_{1} + {σ^{2}}_{2} + 2 μ σ_{1} σ_{2})$
- 3
  
  $\frac{1}{2 E} ({σ^{2}}_{1} - {σ^{2}}_{2} + 2 μ σ_{1} σ_{2})$
- 4
  
  $\frac{1}{2 E} ({σ^{2}}_{1} - {σ^{2}}_{2} - 2 μ σ_{1} σ_{2})$
Answer: 1

Explanation:
3) Question.

The state of stresses on an element is shown in the Fig. 10.49. The values of stresses are

$σ_{x} (= 32 M p a); σ_{y} (= 10 M p a)$ and major principal stress $σ_{1}$ $(= 40 M p a)$
Answer.
- 1
  
  $- 22 M p a$
- 2
  
  $- 18 M p a$
- 3
  
  $22 M p a$
- 4
  
  Indeterminable due to insufficient data
Answer: 2

Explanation:
4) Question.

The rectangular block shown in Fig. 10.48 is subjected to pure shear of intensity $' q'$ .

If $B E$ represents the principal plane and the principal stresses are $σ_{1,} σ_{2};$ then the values of $\emptyset$
Answer.
- 1
  $0 °, 90 °; + q$ and $- q$
- 2
  
  $30 °, 120 °; + q$ and $- q$
- 3
  
  $45 °, 135 °; + \frac{q}{2}$ and $- \frac{q}{2}$
- 4
  
  $45 °, 135 °; + q$ and $- q$
Answer: 4

Explanation:
5) Question.

A cylindrical bar of $20 m m$ diameter and $1 m$ length is subjected to a tensile test. Its longitudinal strain is $4$ times that

of its lateral strain. If the modulus of elasticity is $2 x 10^{5} N / m m^{2},$ then its modulus of rigidity will be&n
Answer.
- 1
  
  $8 x 10^{6} N / m m^{2}$
- 2
  
  $8 x 10^{5} N / m m^{2}$
- 3
  
  $0.8 x 10^{4} N / m m^{2}$
- 4
  
  $0.8 x 10^{5} N / m m^{2}$
Answer: 4

Explanation:
6) Question.

If a member is subjected to tensile stress of $p_{x}$ , compressive stress of $p_{y}$ and tensile stress of $p_{z}$ along the

$x, y a n d z$ directions respectively, then the resultant strain $' e_{x}'$
Answer.
- 1
  
  $\frac{1}{E} (p_{x} + μ p_{y} - μ p_{z})$
- 2
  
  $\frac{1}{E} (p_{x} + μ p_{y} + μ p_{z})$
- 3
  
  $\frac{1}{E} (p_{x} - μ p_{y} + μ p_{z})$
- 4
  
  $\frac{1}{E} (p_{x} - μ p_{y} - μ p_{z})$
Answer: 1

Explanation:
7) Question.

At a point in a steel member, the major principal stress is $200$ $M p a$ (tensile) and the minor principal stress is

compressive. If the uniaxial tensile yield stress is $250 M p a$ , then accroding to the maximum shear stress theory, the

magnitude of the minor principal stress (compressive) at which yielding will commence is
Answer.
- 1
  
  $200 M p a$
- 2
  
  $100 M p a$
- 3
  
  $50 M p a$
- 4
  
  $25 M p a$
Answer: 3

Explanation:
8) Question.

The rectangular column shown in Fig. 10.47 carries a load $' P'$ having eccentricity $e_{x}$ and $e_{y}$ along the x-axis and y-axis respectively.

The stress at any point (x,y) is given by
Answer.
- 1
  
  $\frac{P}{b d} [1 + \frac{12 e_{y} . y}{d^{2}} + \frac{12 e_{x .} x}{b^{2}}]$
- 2
  
  $\frac{p}{b d} [1 + \frac{12 e_{y} . y}{b^{2}} + \frac{12 e_{x} . x}{d^{2}}]$
- 3
  
  $\frac{p}{b d} [1 + \frac{6 e_{y} . y}{d^{2}} + \frac{6 e_{x} . x}{b^{2}}]$
- 4
  
  $\frac{p}{b d} [1 + \frac{6 e_{y} . y}{b^{2}} + \frac{6 e_{x} . x}{d^{2}}]$
Answer: 3

Explanation:
9) Question.

A thin cylindrical shell of internal diameter $' D'$ and thickness $' t'$ is subjected to internal pressure $' p'$ . The change in

diameter is given by
Answer.
- 1
  
  $\frac{p D^{2}}{4 t E} (2 - μ)$
- 2
  
  $\frac{p D^{2}}{4 t E} (1 - 2 μ)$
- 3
  
  $\frac{p d^{2}}{4 t E} (1 - 2 μ)$
- 4
  
  $\frac{p d^{2}}{2 t E} (2 - μ)$
Answer: 1

Explanation:
10) Question.

If the strain energy absorbed in a cantilever beam in bending under its own weight is $' K'$ times greater than the strain

energy absorbed in an identical simply supported beam in bending under its own weight, then the magnitude of $' K'$ is
Answer.
- 1
  
  $2$
- 2
  
  $4$
- 3
  
  $6$
- 4
  
  $8$
Answer: 3

Explanation:
11) Question.

If the diameter of a shaft subjected to torque alone is doubled, then the horse power $P$ can be increased to
Answer.
- 1
  
  $16 P$
- 2
  
  $8 P$
- 3
  
  $4 P$
- 4
  
  $2 P$
Answer: 2

Explanation:
12) Question.

Consider the following statements regarding a beam of uniform cross section simply supported at its ends and carrying a

concentrated load at one of its third points:

A) Its deflection under the load will be maximum.

B) The bending moment under the load will be maximum.

C) The deflection at the mid-point of the span will be maximum.

D) The slope at the nearer support will be maximum.

Of these statements
Answer.
- 1
  
  $1$ and $3$ are correct
- 2
  
  $2$ and $4$ are correct
- 3
  
  $1$ and $2$ are correct
- 4
  
  $3$ and $4$ are correct
Answer: 2

Explanation:
13) Question.

A simply supported rectangular beam of span $' L'$ and depth $' d'$ carries a central load $' W'$ . The ratio of maximum

deflection to maximum bending stress is
Answer.
- 1
  
  $L^{2} / 6 E d$
- 2
  
  $L^{2} / 8 E d$
- 3
  
  $L^{2} / 48 E d$
- 4
  
  $L^{2} / 12 E d$
Answer: 1

Explanation:
14) Question.

A three hinged semicircular arch of radius $R$ carries a uniformly distributed load $' W'$ per unit run over the whole span.

The horizontal thrust is
Answer.
- 1
  
  $W R$
- 2
  
  $W R / 2$
- 3
  
  $- \frac{4}{3 π} W R$
- 4
  
  $\frac{2}{3 π} W R$
Answer: 2

Explanation:
15) Question.

A short column of external diameter $D_{1}$ and internal diameter $D_{2}$ carries an external load $W$ . For no-tension condition,

the eccentricity will be
Answer.
- 1
  
  $({D^{2}}_{1} - {D^{2}}_{2}) / 8 D_{2}$
- 2
  
  $({D^{2}}_{2} + {D^{2}}_{1}) / 8 D_{2}$
- 3
  
  $({D^{2}}_{1} + {D^{2}}_{2}) / 8 D_{1}$
- 4
  
  ${(D_{1} + D_{2})}^{2} / 8 D_{1}$
Answer: 3

Explanation:
16) Question.

The ratio of the flexural strength of two beams of square cross-section, the first beam being placed with its top and bottom

sides horizontally and the second beam being placed with one diagonal horizontally, is
Answer.
- 1
  
  $\sqrt{3}$
- 2
  
  $1 / \sqrt{3}$
- 3
  
  $1 / \sqrt{2}$
- 4
  
  $\sqrt{2}$
Answer: 4

Explanation:
17) Question.

If the area under the shear curve for a beam between the two points $X_{1}$ and $X_{2}$ is $' K',$ then the difference between the

moments at the two points $X_{1}$ and $X_{2}$ will be equal to
Answer.
- 1
  
  $k$
- 2
  
  $2 k$
- 3
  
  $k / 2$
- 4
  
  $k^{2}$
Answer: 1

Explanation:
18) Question.

In a strained body, three principal stresses at a point are denoted by $σ_{1,} σ_{2}$ and $σ_{3}$ such that $σ_{1} > σ_{2} > σ_{3}$ . If $σ_{0}$

denoted yield stress, then according to the maximum shear stress theory
Answer.
- 1
  
  $σ_{1} - σ_{2} = σ_{0}$
- 2
  
  $σ_{1} - σ_{3} = σ_{0}$
- 3
  
  $σ_{2} - σ_{3} = σ_{0}$
- 4
  
  $\frac{σ_{1} + α_{3}}{2} = σ_{0}$
Answer: 2

Explanation:
19) Question.

Two closed thin vessels, one cylindrical and the other spherical with equal internal diameter and wall thickness are

subjected to equal internal fluid pressure. The ratio of hoop stresses in the cylindrical to that of spherical vessels is
Answer.
- 1
  
  $4.0$
- 2
  
  $2.0$
- 3
  
  $1.0$
- 4
  
  $0.5$
Answer: 2

Explanation:
20) Question.

A cantilever carries a load $P$ at $C$ as shown in Fig. 10.41.

The deflection at $B$ is
Answer.
- 1
  
  $\frac{P l^{2}}{2 E I} (L - 1)$
- 2
  
  $\frac{P l^{2}}{3 E I} (L - 1)$
- 3
  
  $\frac{P l^{2}}{2 E I} (L + 1 / 3)$
- 4
  
  $\frac{P l^{2}}{2 E I} (L - 1 / 3)$
Answer: 4

Explanation:

Question Pallet

Time Left -