What are Doubly reinforced sections?
Sections that have tensile as well as compressive reinforcement are called doubly reinforced sections.
Necessity of design of doubly reinforced sections
When the dimensions of the beam are restricted for architectural or structural considerations, the section has insufficient area of concrete which results in inability of the beam to take sufficient compressive stresses. If not paid attention to, it could result in structural failure.
To solve this problem, steel is placed in the compressive area of the section to help the concrete section in resisting compressive stresses. (Steel is good at taking up both compression and tension.)
In this way, the moment of resistance of the section is increased without altering its dimensions.
Three important conditions where doubly reinforced sections are to be used:
1) When the dimensions of the beam are restricted for architectural or structural purposes.
2) Sections that are subjected to the reversal of bending moment (piles, braces in water towers etc.
3) The portion of the beam over middle support in continuous T beams has to be designed as doubly reinforced section.
We are now going to begin with a series of articles on “Design of Doubly reinforced sections”. In our previous series of articles for “Singly reinforced sections“, we have covered every step in detail for the design and analysis of Singly reinforced sections.
We would be covering the following for “Doubly reinforced Sections”:
So let us begin with understanding the methods for determining the neutral axis for doubly reinforced sections.
Methods of determining Neutral axis for doubly reinforced sections
Dimensions of the beam:
b = width of the beam, d = depth of the beam
Permissible stresses in concrete = σcbc
Permissible stress in steel = σst
Modular ratio = m
From similar triangles in the equivalent concrete stress diagram,
σcbc/ (σst/m) = xc/(d – xc)
Width of the beam = b
Effective depth of the beam = d
Distance of compressive steel from the top edge of the beam to the centre of the steel = d’
Area of tensile steel = Ast
Area of compressive steel = Asc
Modular ratio = m
Since neutral axis is situated at the centre of gravity of a given section, the moments of areas on either side of Neutral axis (NA) are equal.
Therefore, Moment of area on compression side = moment of area on tension side
Moment of area on compression side – concrete area above N.A. is to be considered and equivalent concrete ares of steel in compression is also to be taken into account.
According to IS: 456-1978;
“Compression in bars, where the compressive resistance of the concrete is taken into account, shall be the calculated stress in the surrounding concrete multiplied by 1.5times the modular ratio or σcbc whichever is lower.”
Moment of area on compression side = bxx/2 – Asc(x-d’) + 1.5mAsc (x – d’)
Where, 1.5mAsc is the equivalent concrete area of compressive steel.
On simplification, we get,
bxx/2 + (1.5m – 1)Asc(x – d’)
Moment of area of tension side about N.A is given by,
mAst (d – x)
Therefore, bxx/2 + (1.5m – 1) Asc (x – d’) = mAst(d – x)