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Design of Beam
Design stress-strain curve at the ultimate state
Design value of strength For concrete
where, ymc = Partial factor of safety for concrete = 1.5
fd = design value of strength
For steel
fd = fy / 1.15 = 0.87fy
Singly Reinforced Beam
- Limiting depth of the neutral axis (xu, lim)
Here d = effective depth of the beam
- Actual depth of neutral axis (Xu)
- Lever arm = d - 0.42 Xu
- Ultimate moment of resistance
Some special cases
- When Xu < Xu,lim
It is an under-reinforced section
Mu = 0.36 fckbXu(d - 0.42Xu)
or Mu = 0.87fyAst(d - 0.42Xu) - When Xu = Xu,lim
It is a balanced section
Mu = 0.36fckbXu,lim(d - 0.42Xu,lim)
or Mu = 0.87fyAst(d - 0.42Xu,lim) - When Xu > Xu,lim
It is over reinforced section. In this case, keep Xu limited to Xu,lim and moment of resistance of the section shall be limited to limiting moment of resistance, (Mu,lim)
Doubly Reinforced Section
- Limiting depth of neutral axis.
- For actual depth of neutral axis (Xu)
- Ultimate moment of resistance
Mu = 0.36fckbXu(d - 0.42Xu) + (fsc - 0.45fek)Asc(d - dc)
where fSC = stress in compression steel and it is calculated by strain at the location of compression steel (fSC)
T-Beam
- Effective width of flange Discussed in WSM
- Limiting depth of neutral axis
Singly reinforced T-Beam
Case-1: When NA is in the flange area
i.e., Xu < Df
(i) for Xu
(ii) Ultimate moment of resistance
Mu = 0.36fckbfXu(d - 0.42Xu)
or Mu = 0.87 fyAst(d - 0.42Xu)
Case-2: When NA is in the web area (Xu > Df)
Case (a) when Xu > Df and 
i.e., depth of flange in less than the depth of the rectangular portion of the stress diagram.
- For actual depth of neutral, a is
0.36fekbwxu + 0.45fek(bf - bw)Df = 0.87fyAst - Ultimate moment of resistance
Special Case (2): When Xu > Df and 
i.e., the depth of the flange is more than the depth of the rectangular portion of the stress diagram.
As per IS 456 : 2000
(bf - bw) Df portion of the flange is converted into (bf - bw)yf section for which stress is taken constantly throughout the section is 0.45 fck.
As per IS 456 : 2000
yf = 0.15Xu + 0.65Df < Df
For actual depth of neutral axis
0.36fekbwXu + 0.45fek(bf - bw) yf = 0.87fyAst1 + 0.87fyAst2
or 0.36fckbwXu + 0.45fck(bf - bw)yf = 0.87fyAst
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FAQs on Design of Beam
| 1. What is the purpose of beam design in civil engineering? |  |
Ans. Beam design in civil engineering is crucial for ensuring the structural integrity and safety of buildings and other structures. Its purpose is to determine the appropriate size, shape, and reinforcement of beams to withstand the applied loads and prevent structural failure.
| 2. What are the key factors considered in beam design? | |
Ans. Several factors are considered in beam design, including the magnitude and type of loads, the span length of the beam, the material properties, and the desired deflection and strength criteria. These factors help engineers determine the appropriate cross-sectional dimensions and reinforcement requirements for the beam.
| 3. What are the different types of beams used in civil engineering? | |
Ans. In civil engineering, various types of beams are used depending on the structural requirements. Some common types include simply supported beams, cantilever beams, continuous beams, and reinforced concrete beams. Each type has its own advantages and limitations, and engineers select the most suitable type based on the specific project's needs.
| 4. How is beam design affected by different load types? | |
Ans. Beam design is influenced by different types of loads, such as dead loads, live loads, wind loads, and seismic loads. Each load type has a different effect on the beam's behavior, and engineers must consider their combinations and magnitudes while determining the beam's design parameters. Proper analysis and consideration of load types are crucial to ensure a safe and reliable beam design.
| 5. What are the common methods used for beam design in civil engineering? | |
Ans. In civil engineering, beam design can be carried out using various methods, including the working stress method, the ultimate strength method, and the limit state design method. These methods involve different approaches and assumptions to determine the beam's capacity and ensure adequate safety factors. The choice of method depends on the design codes and standards followed in a particular region.
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Apr 19, 2026 Last updated
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