7 step procedure for “Design of Doubly reinforced sections”
In our article series for “Design of Doubly reinforced sections”, we covered the following:
In our previous article, we discussed a detailed 6 step procedure for determining stresses in steel and concrete followed by a numerical example. Now we shall move on with the “design procedure for doubly reinforced sections”.
Generally the following data are given:
Breadth of the beam = b
Effective depth of the beam = d
Permissible stress in concrete = σcbc
Permissible stress in steel = σst
Modular ratio = m
Bending moment = M
To solve a problem, the following procedure may be followed.
Design the beam as a singly reinforced one (balanced section)
Find xc by
σcbc/ (σst/m) = xc/(d – xc)
Find Ast by:
C = T
b xc σcbc /2 = σst.Ast1
Find the Mr of singly reinforced balanced beam
Mr = b xc σcbc /2[d – (xc/3)]
Find the remaining bending moment ‘M1’
M1 = M – Mr
Find Ast2 for M1
M1 = T x lever arm
= Ast2. σst x (d – d’)
= M1 / σst x (d – d’)
Ast = Ast1 + Ast2
Equating moments of equivalent area of tensile and compressive steel about Neutral axis(N.A)
mAst (d – xc) = (1.5m – 1) Asc (xc – d’)
Asc = mAst (d – xc)/ (1.5m – 1)(xc – d’)
In our next article, we shall proceed with a numerical example using the same procedure.
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