Beams and Slabs MCQ Quiz - Objective Question with Answer for Beams and Slabs - Download Free PDF

Concept:

One-way slab:

(i) If a slab is supported only on two opposite supports, it is called a one-way slab.

(ii) If the slab is opposite on all four sides and span ratio 'ly/lx > 2', it is called a one-way slab.

(iii) Main reinforcement is provided along a shorter span.

(iv) Distribution reinforcement is provided along a longer span.

(v) maximum moment in the slab is along a shorter span direction.

(vi) When simply supported along two opposite edges square slab will behave as the one-way slab.

The maximum moment for the simply supported slab is given by,

\({M_x} = \frac{{wl_x^2}}{8}\)

Where lx = shorter span length 

Explanation:

In a singly reinforced beam, the reinforcement is provided only in the tension zone. Here's the reasoning:

1. Tension Zone:

   • In a bending moment scenario, the bottom portion of a beam (in the case of simply supported beams) experiences tension, while the top portion experiences compression. 

   • To resist the tension, reinforcement (usually steel bars) is provided in the tension zone (the bottom half of the beam).

2. Compression Zone:

   • Concrete is strong in compression but weak in tension. In a singly reinforced beam, the compression zone (the upper part of the beam) does not require reinforcement because concrete can resist compression without any issues.

   • Only the bottom portion, which is under tension, requires tensile reinforcement.

3. Design Approach:

   • In design, the reinforcement is placed in such a way as to resist tensile forces that occur in the beam while the concrete takes care of the compressive forces. This is why the reinforcement is only provided in the tension zone, not in the compression zone.

Additional Information

Concept of RCC (Reinforced Cement Concrete)

• RCC is a composite material that is widely used in construction, combining the high compressive strength of concrete with the high tensile strength of steel reinforcement.
• This combination allows RCC to effectively resist both tension and compression, making it suitable for various structural applications like buildings, bridges, roads, and more.

Types of RCC:

• Singly Reinforced Concrete: Only one type of reinforcement (usually in the tension zone).

• Doubly Reinforced Concrete: Reinforcement in both the tension and compression zones for more strength.

• Pre-stressed Concrete: Concrete is pre-stressed with high-strength steel tendons to counteract tensile stresses before applying any external load.

Explanation:

1. In a one-way slab, the main reinforcement is provided in the shorter span direction (the direction in which the slab bends the most).
2. This is because in a one-way slab, the bending occurs primarily along the shorter span, and the slab acts like a beam spanning in one direction.
3. Therefore, the bottom reinforcement is placed in the direction of the shorter span to resist the bending.

 Additional InformationOne-Way Slab:

1. Load Distribution: Loads are carried in one direction (along the shorter span).

2. Reinforcement: Main reinforcement is provided in the shorter span direction (bottom reinforcement).

3. Support: Supported by beams or walls on opposite sides, typically on all four edges.

4. Shape: Slab is longer in one direction, and the other direction is much shorter (like a rectangular slab).

5. Usage: Common in smaller structures, floors of residential buildings, and simple slabs with longer spans in one direction.

Two-Way Slab:

1. Load Distribution: Loads are carried in both directions (along both spans).

2. Reinforcement: Main reinforcement is provided in both directions, with bottom reinforcement generally in both the shorter and longer spans.

3. Support: Supported on all four edges, with the slab bending in both directions.

4. Shape: The length and width of the slab are relatively equal (square or nearly square).

5. Usage: Common in large structures, such as commercial buildings, parking garages, and large floor areas.

Explanation:

At the ultimate limit state of flexure for a singly reinforced beam, the ultimate tensile force (Tu) in the tensile reinforcement (As) is derived from the stress-strain relationship of steel in tension at its yield strength.

• f_y is the characteristic yield strength of steel.

• A_s is the area of tensile reinforcement.

At ultimate limit state:

• The stress in the tensile reinforcement is typically assumed to be 0.87 fy (the stress corresponding to the yield strength of steel).

• The tensile force in the reinforcement, Tu, is given by: Tu = 0.87 fy As​​

Additional Information

Singly Reinforced Beam:

• A singly reinforced beam is a beam where the tensile reinforcement is placed in the bottom (tensile region) of the beam, while the compression reinforcement is either absent or negligible.

• The beam is subjected to bending, and the tensile reinforcement helps resist the bending stress.

Explanation:

• Moment of Resistance (MR) is the internal resisting moment developed in a structural member (like a beam) due to bending stresses.

• It is equal in magnitude and opposite in direction to the external bending moment at a section in equilibrium.

Additional Information

MR is the maximum internal bending moment a section of a beam or structural member can resist without failing.

It depends on:

• Material strength (e.g., yield stress of steel, compressive strength of concrete)

• Section properties (especially the section modulus, Z)

Concept:

Spacing between the bars for 1 m(1000 mm) width:

\({s} = \frac{a}{{{A_{st}}}} \times 1000\)

Where, a = Area of one bar = \(\frac{\pi \ \times \ ϕ^2}{4}\)

ϕ = Diameter of bar

s = spacing of bars

A_st = Area of total main reinforcement

Calculations:

Given, 

Case 1: when ϕ = 10 mm then spacing(s₁) = 10 cm = 100 mm

Case 2: when ϕ = 12 mm then spacing(s₂) = ?

Case 1:

When the main reinforcement of an RC slab consists of 10 mm bars at 10 cm spacing, A_st will be

\({s_1} = \frac{a}{{{A_{st}}}} \times 1000\)

\(\Rightarrow {A_{st}} = \frac{{\frac{{\pi \times 10^2 }}{4}}}{{100}} \times 1000 = 785.4\;m{m^2}\)

Case 2:

⇒ If 10 mm bars is to be replaced by 12 mm bars, then the spacing of 12 mm bars

As the Area of the main reinforcement will be the same so A_st = 785.4 mm²

\({s_2} = \frac{a}{{{A_{st}}}} \times 1000\)

\(\Rightarrow \;{s_2} = \frac{{\frac{{\pi \times 12^2}}{4}}}{{785.4}} \times 1000 = 14.40\;cm\)

Shortcut Trick

\(S_2 \ ={\left( {\frac{{{d_2}}}{{{d_1}}}} \right)^2} \times {S_1} = {\left( {\frac{{12}}{{10}}} \right)^2} \times 10 = 14.4\;cm\)

One-way slab:

Design of one way RCC slab is similar to design of beam but the only difference is during the design of one way slab we take unit width of slab as a beam width.

Slabs are designed for bending and deflection and not designed for shear.

1. Slabs have much small depth than beams.
2. Most of slabs subjected to uniformly distributed loads.

Note:
In one way slab, the maximum bending moment at a support next to end support.

Explanation:

Explanation:

Given,

Clear span = 5 m, Effective depth = 0.5 m
Uniformly distributed load(W) = 100 KN/m

The shear force of the beam in case of uniformly distributed load,

V = \(\frac{W\ × \ l}{2}\) = \(\frac{100\ × \ 5}{2}\) = 250 KN

The location of critical section for shear design is determined based on the conditions at the supports. The location of critical shear is at a distance of effective depth d.

Design shear force for the beam:

V_u = 250 - 100 × 0.5 = 200 KN

Concept:

Where

bf = effective width of flange

lo = distance between points of zero moments in the beam

bw = breadth of the web

df = thickness of the flange, and

b = actual width of the flange

Explanation:

Data given,

The effective span of SS beam = 12 m

As per IS 456 -2000 criteria for effective depth:

NOTE: When span > 10 m, multiply the span/depth coefficient with, \(10 \over Effective \ span\) but this factor is not multiplied for the cantilever beam

Therefore,

When Simply supported beam with effective span > 10 m

 = 20 x \(10 \over Eff. \space span\) = 20 x \(10 \over 12\) = 16.67

Concept:

As per IS 456:2000 clause 26.5.1.1, Minimum tension reinforcement (Ast) in a beam  provided is given by:

\(\frac{{{A_{st}}}}{{bd}} = \frac{{0.85}}{{fy}}\)

Where,

b & d are width, effective depth of the beam

f_y is the yield stress

Calculation:

Given,

b = 450 mm, d = 550 mm

Grade of Steel is Fe 500

\({A_{st}} = \frac{{0.85}}{{fy}} \times bd = \frac{{0.85}}{{500}} \times 450\times550\\=420.75\; mm^2\)

Concept:

Effective Width of Flange of the different section:

Where,

bf = Effective width of flange

lo = Distance between points of zero moments in the beam

bw = Breadth of the web

df = Thickness of the flange

b = Actual width of the flange

Explanation:

Given,

lo = 6m = 6000mm, b = 1000mm, bw = 300mm, 

Walkway is the case of isolated T-Beam. Then,

\({b_f} = {b_w} + \frac{{{l_o}}}{{\frac{{{l_o}}}{b} + 4}}\)

\({{\bf{b}}_{\bf{f}}} = 300 + \frac{{6000}}{{\frac{{6000}}{{1000}} + 4}}\)

bf = 300 + 600 = 900mm

Concept:

Nominal Shear stress:

IS code recommends the use of nominal shear stress for RCC structures. The nominal shear stress in beams or slabs of uniform depth is calculated as:

\({{\bf{\tau }}_{\bf{v}}} = \frac{{{{\bf{V}}_{\bf{u}}}}}{{{\bf{bd}}}}\) 

Where

V_u = Shear force due to design loads,

b = breadth of beam or slab,

d = effective depth

Shear stress for slabs is very low since b is large. Therefore no shear reinforcement is provided in slabs except that the alternate bars are bent up near the supports.

Bond stress (\({{\bf{\tau }}_{{\bf{bd}}}}\)):

Bond stress is the shear stress developed along the contact surface between the reinforcing steel and the surrounding concrete which prevents the bar from slipping out of concrete.

It depends upon the grade of concrete and type of steel only.

Explanation:

• A minimum area of tension steel is required in flexural members (like beams) in order to resist the effect of loads and also control the cracking in concrete due to shrinkage and temperature variations.
• Minimum flexural steel reinforcement in beams: CI. 26.5.1.1 of IS 456:2000 specify the minimum area of reinforcing steel as:

\(\frac{{{A_{st\min }}}}{{bd}} \ge \frac{{0.85}}{{{f_y}}}\)

or, \({p_{t\min }} \ge \frac{{85}}{{{f_y}}}\)

= 0.34% for Fe 250

= 0.205% for Fe 415

= 0.17% for Fe 500

For flanged beams, replace 'b' with the width of web 'b_w'

Important Points

• The maximum area of tension steel in beams(Intension beams as well as compression beam) provided as per IS 456:2000 = 4% of gross area
• The minimum area of tension steel in the slab as per CI. 26.5.2 of IS 456:2000 
  • A_stmin = 0.15% of gross area for Fe 250
  • A_stmin = 0.12% of gross area for Fe 415

Confusion Points 

• Minimum flexural steel reinforcement in the slab is based on shrinkage and temperature consideration and not on strength consideration because, in slabs, there occurs a better distribution of loads effects unlike in beams, where minimum steel requirement is based on strength consideration.