RCC Sheet 23

1) Question.

For a balanced reinforced section, the depth of critical neutral axis from the top of the beam $(n_{c})$ is given by the relation
Answer.
- 1
  
  $\frac{m σ_{c b}}{σ_{s t}} = \frac{n_{c}}{d - n_{c}}$
- 2
  
  $\frac{m σ_{c b}}{σ_{s t}} = \frac{d - n_{c}}{n_{c}}$
- 3
  
  $\frac{m σ_{c b}}{σ_{s t}} = \frac{n_{c}}{d + n_{c}}$
- 4
  
  $\frac{m σ_{c b}}{σ_{s t}} = \frac{d + n_{c}}{n_{c}}$
Answer: 1

Explanation:
2) Question.

If the tensil stress in steel reinforcement is $σ_{s t}$ area of tensile reinforcement is $A_{s t}$ depth of neutral axis is n and the effective depth is d, then the moment of resistence of an under-reinforced section is equal to
Answer.
- 1
  
  $σ_{s t} x A_{s t} [\frac{d - n}{3}]$
- 2
  
  $σ_{s t} x A_{s t} [\frac{2 d - n}{3}]$
- 3
  
  $σ_{s t} x A_{s t} [\frac{3 d - n}{3}]$
- 4
  
  $σ_{s t} x A_{s t} [\frac{4 d - n}{3}]$
Answer: 3

Explanation:
3) Question.

The lever arm in a singly reinforced beam is equal to
Answer.
- 1
  
  $\frac{d - n}{3}$
- 2
  
  $\frac{2 d - n}{3}$
- 3
  
  $\frac{3 d - n}{3}$
- 4
  
  $\frac{4 d - n}{3}$
Answer: 3

Explanation:
Where d = Distance between the top of beam and the centre of steel bars, and

n = Depth of neutral axis below the top of beam
4) Question.

If the breadth of a singly reinforced beam is b, effective depth is d, depth of neutral axis below the top of beam is n and the compressive stress in the extreme fiber of concrete is $σ_{c b}$ then the moment of resistance of the beam is equal to
Answer.
- 1
  
  $\frac{σ_{c b}}{2} x b n (\frac{d - n}{3})$
- 2
  
  $\frac{σ_{c b}}{2} x b n (\frac{2 d - n}{3})$
- 3
  
  $\frac{σ_{c b}}{2} x b n (\frac{3 d - n}{3})$
- 4
  
  $\frac{σ_{c b}}{2} x b n (\frac{4 d - n}{3})$
Answer: 3

Explanation:
5) Question.

In a Singly reinforced beam, the depth of neutral axis below the top of the beam ( $n_{c}$ ) is given by
Answer.
- 1
  
  $n_{c} = \frac{m x σ_{c b}}{m x σ_{c b} + σ_{s t}} x d$
- 2
  
  $n_{c} = \frac{m x σ_{c b}}{m x σ_{c b} - σ_{s t}} x d$
- 3
  
  $n_{c} = \frac{m x σ_{c b} + σ_{s t}}{m x σ_{c b}} x d$
- 4
  
  $n_{c} = \frac{m x σ_{c b} - σ_{s t}}{m x σ_{c b}} x d$
Answer: 1

Explanation:
where m = Modular ratio

$σ_{c b}$ = Compressive stress in extreme fiber of concrete

$σ_{s t}$ = Tensile stress in steel reinforcement and

d = Distance between the top of the beam and the centre of steel bars ( also known as effective depth)
6) Question.

A simply supported concrete beam, prestressed with a force of 2500 kN is designed by load balancing concept for an effective span of 10 m and carry a total load of 40 kN/m. The central dip of the cable profile should be
Answer.
- 1
  
  100 mm
- 2
  
  200 mm
- 3
  
  300 mm
- 4
  
  400 mm
Answer: 2

Explanation:
7) Question.

It is required to completely balance a bent tendon of span L carring a point load W at the centre. The minimum central dip should be equal to
Answer.
- 1
  
  $\frac{W L}{P}$
- 2
  
  $\frac{W L}{2 P}$
- 3
  
  $\frac{W L}{3 P}$
- 4
  
  $\frac{W L}{4 P}$
Answer: 4

Explanation:
Where P = Tension in the bent tendon
8) Question.

The diagonal tension in a pre-stressed concrete member will be ........ shear stress
Answer.
- 1
  
  equal to
- 2
  
  less than
- 3
  
  more than
Answer: 2

Explanation:
9) Question.

In the previous question, the minimum stress in the beam section will be
Answer.
- 1
  
  $\frac{W}{A} + \frac{M}{Z}$
- 2
  
  $\frac{W}{A} - \frac{M}{Z}$
- 3
  
  $\frac{A}{W} + \frac{Z}{M}$
- 4
  
  $\frac{A}{W} - \frac{Z}{M}$
Answer: 2

Explanation:
10) Question.

When the tendon of a rectangular pre-stressed beam of cross-sectional area A is subjected to a load W through the centroidal longitudinal axis of beam, then the maximum stress in the beam section will be
Answer.
- 1
  
  $\frac{W}{A} + \frac{M}{Z}$
- 2
  
  $\frac{W}{A} - \frac{M}{Z}$
- 3
  
  $\frac{A}{W} + \frac{Z}{M}$
- 4
  
  $\frac{A}{W} - \frac{Z}{M}$
Answer: 1

Explanation:
Where M = Maximum bending moment, and

Z = Section modulus

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