Beam Design: Reinforced Concrete Beam, Beam Steel Design
By BYJU'S Exam Prep
Updated on: September 25th, 2023
Design of Beams: Beams are flexural members, i.e., the beam takes to 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 and doubly reinforced beams.
Table of content
How to Design a Beam?
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. Let M be the maximum moment, 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
Singly Reinforced Beam
If Mu > MORlim, the beam design principle will not be 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
The 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
The area of tension steel provided should be less than the maximum area of tension to avoid congestion during concreting.
The 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
The 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
Some special cases
- When Xu < Xu,lim
It is an under-reinforced section
- When Xu = Xu,lim
It is a balanced section
- When Xu > Xu,lim
It is over reinforced section. In this case, keep Xu limited to Xu,I’m, and the moment of resistance of the section shall be limited to limiting moment of resistance (Mu,lim)
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 a 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 the 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 a 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 the case of the monolithic casting of beams and slabs, part of the 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 Cast L Beam
bf = bw+ [3Df+ Lo/12]
(bfmax) = bw + Lc
Design of Beams Sample Question for Gate
Question: Minimum area of tension steel depends on
a.) Grade of concrete b.) Grade of steel c.) Both a and b d.)None of these
Answer: a. Grade of Concrete
Solution: We know that,
Ast min= 0.85bd/fy
Therefore, we can say that area of steel depends on the grade of concrete.
