Design procedure for designing doubly reinforced section

7 step procedure for “Design of Doubly reinforced sections”

In our article series for “Design of Doubly reinforced sections”, we covered the following:

What are doubly reinforced sections?

Methods for determining Neutral Axis?

Solved numerical examples for determining Neutral Axis

Numerical examples for practice (Find Neutral axis)

Methods for calculating Moment of Resistance

Numerical example for calculating Moment of resistance

Types of problems in Doubly reinforced sections

6 step prodecure for determining stresses in steel and concrete 

Numerical example | Stresses in steel and concrete

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 = σ_cbc

Permissible stress in steel = σ_st

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)

Step One:

Find x_c by

σ_cbc/ (σ_st/m) = x_c/(d – x_c)

Step two:

Find A_st by:

C = T

b x_c σ_cbc /2 = σ_st.A_st1

Step three:

Find the Mr of singly reinforced balanced beam

Mr = b x_c σ_cbc /2[d – (x_c/3)]

Step four:

Find the remaining bending moment ‘M1’

M1 = M – M_r

Step five:

Find A_st2 for M1

M1 = T x lever arm

= A_st2. σ_st x (d – d’)

= M1 / σ_st x (d – d’)

Step six:

Ast = Ast1 + Ast2

Step seven:

Find Asc

Equating moments of equivalent area of tensile and compressive steel about Neutral axis(N.A)

mAst (d – x_c) = (1.5m – 1) Asc (x_c – d’)

A_sc = mAst (d – x_c)/ (1.5m – 1)(x_c – d’)

 In our next article, we shall proceed with a numerical example using the same procedure.