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”:
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
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)