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

Explanation:

• A slab is considered one-way slab if the longer span is more than twice the shorter span (i.e., ratio of long span to short span > 2).

• In one-way slabs, loads are primarily carried by the shorter span, and reinforcement is provided mainly in that direction.

• If the ratio is less than or equal to 2, the slab behaves more like a two-way slab, distributing loads in both directions.

• This classification helps in deciding the design approach and reinforcement detailing for slabs.

Additional InformationOne-Way Slab

• Load is primarily carried in one direction (shorter span).

• Occurs when the ratio of long span to short span is greater than 2.

• Reinforcement is provided mainly in the short span direction.

• Supported on two opposite sides only (usually beams on two sides).

• Simpler design and less reinforcement compared to two-way slabs.

Two-Way Slab

• Load is carried in both directions (long and short spans).

• Happens when the ratio of long span to short span is less than or equal to 2.

• Reinforcement is provided in both directions.

• Supported on all four sides (beams or walls).

• More complex design, with bending moments distributed in two directions.

Explanation:

Beam-columns are structural elements that are subjected to both axial compression and bending moment simultaneously.

• They are columns that carry axial loads, but due to lateral loads, eccentricities, or moment connections, they also experience bending.

• Commonly found in multi-storey frames, bridges, and pylon structures.

• Their design must consider interaction effects between compression and bending using interaction curves or design codes (e.g., IS 800 for steel or IS 456 for RCC).

 Additional Information

• Beam-columns are structural members that simultaneously carry axial loads (usually compression) and bending moments.

• They are commonly found in framed structures where columns also experience bending due to lateral loads like wind or earthquake forces.

• The combination of axial compression and bending moment influences their design because the axial load affects the bending capacity and vice versa.

• Beam-columns require special design considerations to ensure stability, strength, and serviceability.

• Unlike simple beams or columns alone, beam-columns demand analysis for interaction effects between axial force and bending.

Explanation:

• A deep beam is characterized by having a small span-to-depth ratio, meaning it is relatively deep compared to its span.

• According to IS 456:2000 and common structural engineering practice, a beam is considered deep if  the ratio of effective span to overall depth is less than 2.5.

Additional InformationContinuous Beam 

• A continuous beam is a beam that spans over more than two supports without any hinges or joints in between.

• Unlike simply supported beams, continuous beams provide moment redistribution and greater structural efficiency.

• Because of multiple supports, the beam experiences negative moments over supports and positive moments at mid-spans.

• Continuous beams generally have lower maximum bending moments and deflections compared to simply supported beams of the same span and loading.

• Used widely in building floors, bridges, and other structures for better load-carrying capacity and economy.

Explanation:

• A beam curved in plan (such as those found in circular balconies or curved bridge decks) experiences not only bending and shear, but also torsion, due to the geometry.

• The curvature in plan causes eccentricity between the applied load and the beam’s centerline, introducing a torsional moment.

• Therefore, when designing such beams, all three forces—bending moment, shear force, and torsional moment—must be considered.

Additional Information

A curved beam is a structural member that follows a curved path in plan (horizontal view). It is common in circular structures like tanks, silos, curved balconies, and ring beams around circular columns or wells.\

Behavior:

• When loaded vertically, a curved beam experiences:

  • Shear forces (due to vertical loads)

  • Bending moments (due to eccentric loading or restraint)

  • Torsional moments (due to the plan curvature and radial distance between the load and the support path)

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,

Where lx = shorter span length 

Concept:

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

Where, a = Area of one bar = 

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

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

Shortcut Trick

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 =  =  = 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, but this factor is not multiplied for the cantilever beam

Therefore,

When Simply supported beam with effective span > 10 m

 = 20 x  = 20 x  = 16.67

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:

or, 

= 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.

Concept:

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

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

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,

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:

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 ():

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.