# Design of Beams - Principle of Design of Beams

By Aina Parasher|Updated : May 27th, 2022

Design of Beams: Beams are flexural members i.e, the beam takes load by bending, and flexural members carry bending moment and shear force. Therefore, the design of beams is for bending moment, shear force, and torsion. The design of beams can be done by various methods. The most prominent ones are Working Stress Method and Limit State Method.

The design of beams is done taking into consideration, many factors. We will see all the major factors, and the principles used in the design of beams. We will also learn about the moment of resistance, singly reinforced beams, and doubly reinforced beams.

## Principle of Design of Beams

When external loads are applied, moments are generated, and the maximum moment developed varies in each beam depending on the support conditions and loading combinations. For the below-shown beam, let M be the maximum moment which is also termed as unfactored moment/service moment/working moment.

Factored External Moment = 1.5 x Working Moment

Mu = 1.5M

Design of Beams is done for the factored external moment (Mu

Maximum internal resistance without failure or ultimate moment of resistance is called Moment of Resistance (MOR). The externally applied moment should be always less than or equal to the internal moment of resistance during the design of beams.

Mu≤MOR

Where, MOR = CZ or TZ

C- Compressive Force

Z- Lever Arm

T-Tensile Force

## Principle of Design of Beams for a Singly Reinforced Beam

If Mu > MORlim, the principle of design of beams will not get satisfied. Therefore, for the design of beams as singly reinforced beams of under reinforced type, Mu < MORlim. Limiting the moment of resistance can be increased by increasing fck or by increasing the depth, but both will increase the cost of construction. Therefore, in such cases beams are designed as doubly reinforced beams.

### Area of Steel

Mu=MOR

Mu=TZ

Mu=0.87 fyAst(d-0.42xu)

Ast=0.5 × fck/fy [1- √1- 4.6Mu/bd2fck]bd

Where, fck – Characteristic Compressive Strength of Concrete

fy – Yield Strength of Steel

Area of steel provided should be greater than the area of steel required.

Astmin < Astmin < Astmax

Maximum area of tension steel = Astmax = 0.04 x bD

Area of tension steel provided should be less than the maximum area of tension to avoid congestion during concreting.

Minimum area of tension steel = Ptmin % = Percentage minimum area of tensile steel

Ptmin= Ast min/bd ×100

Ptmin= 85%/fy

Ast min= 0.85bd/fy

Area of tension steel provided should be more than the minimum area of steel to avoid sudden failure.

 fy Pt min 250 0.34 415 0.205 500 0.17

For the design of beams (singly reinforced and under reinforced beam).

Ast < Astlim

Ast < Astmax

## Doubly Reinforced Beam

A beam is made doubly reinforced beam when a singly reinforced beam becomes over the reinforced beam, i.e, MOR > MORlim. An over-reinforced beam is sudden. In such a case, a beam is designed as doubly reinforced beam. Doubly reinforced beams are beneficial in case of stress reversal. The compression steel helps in bearing additional strain due to creep and shrinkage. Compression steel is found to reduce deflections. They are helpful in case of shock or impact loads. Overall more ductile compared to single reinforced beams.

Total Compressive Force C =C1 + C2

C=0.36fckbxu+(fsc-fcc)Asc

Where, fsc = Compressive Stress in compression steel

fcc = Stress in concrete at level of compression steel

fcc = 0.45 fck

Total Tensile Force T = 0.87 fy Ast

Doubly reinforced beams are not economical because compression steel is under stress.

## Design of Doubly Reinforced Beam

Doubly reinforced beams are designed for moment equal to

Mu= MORlim+(Mu- MORlim)

Area of tension steel Ast = Ast1 + Ast2

Ast2= Mu-MORlim/0.87 fy (d-d')

Area of compressive steel

Asc= Mu-MORlim/(fsc-fcc) (d-d')

### Flanged Beam

In case of monolithic casting of beams and slabs, part of slab behaves as a beam to take the compression, such beams are called flanged beams.

### Monolithically Casted T Beam

Effective flange width of T beam

bf= bw+ [6Df+ Lo/6]

Where,

bw = Web width

bf = Effective flange width

Df = Flange depth/Depth of slab

Lo = Distance between points of contra flexure

Maximum effective flange width (bfmax) = bw + Lc

bf < bfmax

Where Lc = Clear distance between adjacent beams

Monolithically Casted L Beam

bf= bw+ [3Df+ Lo/12]

(bfmax) = bw + Lc

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## FAQs on Design of Beams

• A beam is a flexural member that rests on a support on each end. The beam resists any kind of loading on itself by the resisting forces developed in these supports only.

• Beams are divided into singly reinforced beams and doubly reinforced beams based on steel provided. In singly reinforced beams, steel is provided only in the tension zone, whereas in doubly reinforced beams, steel is provided in both the tension and compression zone.

• To design a beam as an under the reinforced beam, we have to find the depth of neutral axis xu and the limiting depth of neutral axis xulim.

For a beam to be under reinforced, xu ≤ xulim.

• IS 456 is the code used for the design of beams. Some of the important IS codes are: