Design of Beam Notes | EduRev

RCC & Prestressed Concrete

Civil Engineering (CE) : Design of Beam Notes | EduRev

The document Design of Beam Notes | EduRev is a part of the Civil Engineering (CE) Course RCC & Prestressed Concrete.
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Design stress-strain curve at the ultimate state

Design of Beam Notes | EduRev

Design value of strength For concrete

Design of Beam Notes | EduRev

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

Design of Beam Notes | EduRev

  • Limiting depth of the neutral axis (xu, lim)

Design of Beam Notes | EduRev

Design of Beam Notes | EduRev

Here d = effective depth of the beam 

  1. Actual depth of neutral axis (Xu)
    Design of Beam Notes | EduRev
  2. Lever arm = d – 0.42 Xu
  3. Ultimate moment of resistance

Some special cases

  1. When Xu < Xu,lim
    It is an under-reinforced section
    Mu = 0.36 fckbXu(d - 0.42Xu)
    or Mu = 0.87fyAst(d - 0.42Xu)
  2. 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)
  3. 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

Design of Beam Notes | EduRev

  1. Limiting depth of neutral axis.
  2. For actual depth of neutral axis (Xu)

Design of Beam Notes | EduRev

  • 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
  1. Effective width of flange Discussed in WSM
  2. Limiting depth of neutral axis

Design of Beam Notes | EduRev

Singly reinforced T-Beam

Case-1: When NA is in the flange area
i.e., Xu < Df

Design of Beam Notes | EduRev

(i) for Xu

Design of Beam Notes | EduRev

(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)

Design of Beam Notes | EduRev

Case (a) when Xu > Df and Design of Beam Notes | EduRev
i.e., depth of flange in less than the depth of the rectangular portion of the stress diagram.

  1. For actual depth of neutral, a is
    0.36fekbwxu + 0.45fek(bf - bw)Df = 0.87fyAst
  2. Ultimate moment of resistance

Design of Beam Notes | EduRev

Design of Beam Notes | EduRev

Special Case (2): When Xu > Df and Design of Beam Notes | EduRev

i.e., the depth of the flange is more than the depth of the rectangular portion of the stress diagram.

Design of Beam Notes | EduRev

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

Design of Beam Notes | EduRev

Design of Beam Notes | EduRev

Design of Beam Notes | EduRev

Design of Beam Notes | EduRev

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