## Types of Problems | Design of Doubly Reinforced Sections

#### Stepwise procedure for calculating Moment of resistance and compressive stresses in steel and concrete

While we proceed with the article series for “Doubly reinforced sections”, I would like to categorize the problems into different types. This will make your understanding of the concept better and concrete. I recommend that you practice enough to be able to understand and confidently solve the problems. This will also help you in real time when you would get into practice.

#### In our article series for doubly reinforced sections, 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

Also check out: “Singly reinforced Sections” article series.

So let’s begin with different types of problems for “Doubly reinforced sections”.

#### Problem type 1

To find Moment of resistance (Mr)

In a problem where we have to find Mr, specific data is given so that you could calculate the Moment of resistance. The following data will be given in the problem. I suggest that you make notes of the points below.

Breadth of the beam = b

Effective depth of the beam = d

Area of tensile steel = Ast

Area of compressive steel = Asc

Permissible stress in concrete = σcbc

Permissible stress in steel = σst

Modular ratio = m

#### Four – step procedure to solving the problem:

Step one:

Find xc by the following formula,

σcbc/ (σst/m) = xc/(d-xc)

Step two:

Find x using the following formula,

bxx/2 + (1.5m – 1)Asc (x – d’) = m Ast (d – x)

## Guide to design of Doubly reinforced Sections | Civil Engineering

#### 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.

#### METHOD ONE:

Given that:

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,

## Guide to Doubly Reinforced RCC Beam Design

#### RCC Beams

RCC beams are cast in cement concrete reinforced with steel bars. Beams resist compression and tensile forces and add rigidity to the structure.

Beams generally carry vertical gravitational forces but can also be used to carry horizontal loads (i.e., loads due to an earthquake or wind). The loads carried by a beam are transferred to columns, walls, or girders, which then transfer the force to adjacent structural compression members. In light frame construction the joists rest on the beam.

In this article, we are going to discuss types of beam construction and RCC design of simply supportedreinforced beam.

#### Simply supported RCC beam construction is of two types:

• Singly reinforced beam
• Doubly reinforced beam