# Determining stresses in Steel and Concrete | Doubly reinforced Sections

#### Six step procedure for determining stresses in steel and concrete

In our article series for “Doubly reinforced Sections design guide”, we have 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

Determining stresses in steel and concrete

Numerical example | Stresses in steel and concrete

Now we shall proceed with a simple 6 step procedure for determining compressive stresses in steel and concrete. Further in our next article, we shall also solve a numerical using the same method.

Generally, the following data is given for reference with the help of which we can determine the stresses in steel and concrete

Breadth of the beam = b

Effective depth of the beam = d

Area of tensile steel = Ast

Area of compressive steel = Asc

Modular raito = m

Bending moment = M

#### Step One:

Find x by using the following formula:

bx.x/2 + (1.5m – 1)Asc (x – d’) = mAst(d-x)

#### Step two:

Find σcbc by:

σ’cbc  = σcbc (x – d’)/x

#### Step three:

Find Mr. Taking moments about tensile steel

Mr = bx σcbc/2 (d – x/3) + (1.5m – 1) Asc σcbc (d – d’)

Substitute the value of σ’cbc in terms of σcbc

#### Step four:

Equate Mr to M and find σcbc

#### Step five:

σcbc/ (σst/m) = x/(d – x)

#### Step six:

Find σsc

σsc = 1.5m σcbc

Further, we shall solve a numerical using the above “six step procedure”.

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