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

Six step procedure for determining the compressive stresses in steel and concrete:

Step One:

Find x by using the following formula:

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

Step two:

Find σ_cbcby:

σ’_cbc= σ_cbc(x – d’)/x

Step three:

Find Mr. Taking moments about tensile steel

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

Substitute the value of σ’_cbc in terms of σ_cbc

Step four:

Equate Mr to M and find σ_cbc

Step five:

σ_cbc/ (σst/m) = x/(d – x)

Step six:

Find σ_sc

σ_sc = 1.5m σ_cbc

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