Beams and Slabs MCQ Quiz in मराठी - Objective Question with Answer for Beams and Slabs - मोफत PDF डाउनलोड करा

Concept:

RCC T-beam:

• The beam consists of a flange and a rib in the form of a T, generally made of RC concrete or metal is known as a T-beam.

• The top part of the slab which acts along the beam to resist compressive stress is called a flange.

• The part which lies below the slab and resists the shear stress is called the rib.

For continuous beams, the overall depth is assumed as follows :

1. For light loads = 1/15 to 1/20 of the span.
2. For medium loads = 1/12 to 1/15 of the span.
3. For heavy loads = 1/10 to 1/12 of the span.

Concepts:

When the comers of a slab are prevented from lifting, the maximum bending moments per unit width in a slab are given as:

M_x = α_x w l_x²

M_y = α_y w l_x²

Where

L_x is shorter span and l_y is the longer span

M_x and M_y are moments spanning l_x and L_y respectively

α_x and α_y are short and long span coefficients respectively.

W is total design load per unit area

Calculation:

Given:  l_x = 3.5 m and l_y = 4.5; W_L = 4.5 kN/m², α_x = 0.0912 and α_y = 0.0558

Dead Weight of Structure per unit area,

W_d = unit weight of concrete × thickness of slab

Or

W_d = 25 × 0.15 = 3.75 kN/m²

Design Load = 1.5(DL + LL)

W = 1.5 × (3.75 + 4.5) = 12.375 kN/m²

Short Span Moment, M_x

M_x = 0.0912 × 12.375 × 3.5² = 13. 8 kNm/m ≈ 15 kNm/m

Explanation:

RCC T-beam:

(i) The beam consists of a flange and a rib in the form of a T, generally made of RC concrete or metal is known as T-beam.

(ii) The top part of the slab which acts along the beam to resist the compressive stress is called flange.

(iii) The part which lies below the slab and resists the shear stress is called the rib.

Dimension of T-beam:

• The effective width of the flange is adopted as the minimum of c/c distance of the nearby ribs or beams.
• The overall thickness of the slab crossing over the beam is taken as flange thickness.
• The breadth of the rib is taken down earth ground. It should be adequate to hold the steel zone in it, effectively. It might be taken as between 1/3 to 2/3 of the rib depth of the beam.
• The depth of T-beam is taken between 1/10 to 1/20 of the span.

Concept:

As per IS 456 Cl 23.2.1, deflection can be limited, by controlling the span to effective depth ratio as given in the following table.

Calculation:

Given, Span = 12 m (> 10 m)

So, Span to effective depth ratio for a simply supported beam

 = 20 ×  =  = .

Hence, Span to effective depth ratio for a simply supported beam will be 50/3.

Explanation:

The overall depth of the beam depends upon the span as well as loading conditions.

In the case of simply supported beams, it may be assumed to be 1/12 to 1/15 of the span.

Additional Information

For continuous beams, the overall depth is assumed as follows :

For light loads = 1/15 to 1/20 of the span.
For medium loads = 1/12 to 1/15 of the span.
For heavy loads = 1/10 to 1/12 of the span.

Answer:

The design value of limiting span to effective depth ratio for deflection control of a beam is independent of: creep and shrinkage

Explanation:

The vertical deflection of limits: (IS: 456 Clause — 23.2.1)

1. Basic values of span to effective depth ratios for spans up to 10 metre;

2. For spans above 10 meter, the values in (1) may be multiplied by 10/span in meters, except for cantilever in which case deflection calculation should be made.

3. Depending on the area and the stress of steel for tension reinforcement the value in (1) or (2) shall be modified by multiplying with the modification factor.

4. Depending on the area of compression reinforcement, the value of span to depth ratio be further modified by multiplying with the modification factor.

Concept:

• For a restrained slab, the area of reinforcement in each of the four corner layers shall be three-quarters of the area required for the maximum mid span moment in the slab simply supported on both edges meeting at that corner.
• If the corner is contained by edges over only one of which the slab is continuous, torsion reinforcement equal to 0.375 or  times the area of reinforcement provided the mid-span in the same direction shall be provided.
• If both edges are continuous, no torsion reinforcement shall be provided.

Additional Information 

For Slab:

Minimum reinforcement criteria-

Mild steel- 0.15% of total C/S area

HYSD BARS- 0.12%  of total C/S area

Maximum diameter = d should not be greater than 1/8 ( thickness of slab)

For Columns:

Longitudinal reinforcement criteria-

It should not be less than 0.8%
It should not be greater than 6%

For Beams:

Tension Reinforcement criteria-

The minimum area of reinforcement  

Maximum area of reinforcement = 0.04bD

​Concept: 

According to IS 456: 2000, Annexure D, Cl no. D.1.0, When corners of the slab are prevented from lifting, the slab should be designed as follows.

M_x = α_x w l_x²

M_y  = α_y w l_x²

where, 

M_x = Ultimate B.M. per metre width along l_x

M_y = Ultimate B.M. per metre width along l_y

α_x , α_y = B.M. coefficients, w = factored load

l_x = effective span in the shorter span

l_y = effective span in the longer span

Calculation:

Data given:

l_y = 4.4 m, l_x = 4 m, w= 8 kN/m²

​^_⇒ l_y / l_x = 4.4/4 = 1.1

from the given table, α_x = 0.074, α_y = 0.061

⇒ M_x = 0.074 x 8 x 4² = 9.472 kN-m

⇒ M_y = 0.061 x 8 x 4² = 7.808 kN-m

Thus, the correct answer: 9.47 kN-m and 7.81 kN-m

Concept:

The ratio of limiting depth of neutral axis to the effective depth of the beam is given by

Note:

Without getting into the tedious calculation,

We know the standard values of the ratio of limiting depth of neutral axis to the effective depth (k) of the beam for different steel sections as following:

Calculation:

∴ For Fe 250, x_u ≈ 0.53 × 400 = 212 mm.

Explanation:
As per IS 456: 2000, the BM due to DL and LL at supports and mid-section of a continuous beam is given as:

M = K_d W_d L² + K_L W_L L²

Where,

K_d and K_L are the BM coefficients for dead load and live load respectively.

W_d and W_l are dead load and live load intensities respectively

 L is the effective length.

The BM coefficients for dead load and live load are given below:

For the given continuous beam

Span AB and CD are end spans; therefore, support C is the support next to end support. For C support BM coefficients are -1/10 and – 1/9 for DL and LL respectively. Furthermore, the BM at Support C is given as:

Confusion Points Why option C is incorrect?

The question is asking about the support C and in this particular case there is no interior support. Support A and D are end support.  Support B and C support next to the end support and in case we add another support between B and C, it can be called as an intermediate support.