# Design steps for a doubly reinforced beam section

To start the design of doubly reinforced beam with you should have an idea about doubly reinforced section. As the name implies doubly reinforced beams means we are providing the reinforcement in both the zones. In the case of a beam the zone is basically compression and tension zone.

Check this post to know more about a doubly reinforced beam section.

As in this type of beams, the beam dimension is a constrain. Our main aim is only to calculate the area of reinforcement required in each zone of the beam section. The step by step procedure to design a doubly reinforcement beam as per IS:456:2000 is as follows:

### Step 1: Calculate the depth of neutral axis.

Apply the equilibrium condition for the beam section. $$C_{uc} +C_{us} = T_{u}$$

where Cuc and Cus are the compressive force in concrete and steel respectively. And Tu is the tensile force in the reinforcement.

The depth of neutral axis is $$x_u = \frac{f_{st} A_{st} – (f_{sc} – 0.447 f_{ck}) A_{sc}}{0.362 f_{ck} b}$$

### Step 2 : Calculate the factored moment

In this case, we split the total bending moment into two component.

$$M_u = M_{u lim} + \Delta M_{u}$$

where Mu lim is the limiting moment capacity which is equal to the moment of resistance of a balanced singly reinforced beam section. and the second component is for the additional moment capacity which should be taken care by the compression reinforcement.

### Step 3 : Design of compression reinforcement

The value of area of reinforcement in compression zone is calculated using :

$$A_{sc} =\frac{\Delta M_{u}}{f_{sc}(d -d ‘)}$$

Area of reinforcement in tension zone is the sum of area of reinforcement to resist the compressive and tensile forces in tension zone.

$$A_{st } = A_{st1} + A_{st2}$$

$$A_{st1} = \frac{0.362 f_{ck} b x_{u}}{0.87 f_y}$$

$$A_{st2} = \frac{A_{sc}f_{sc}}{0.87f_y}$$

This is not the end of the design procedure.

Then you have to check for shear reinforcement and deflection control of the RCC beam section. This part I will discuss in the upcoming posts.

## Beam design

• RCC Beam Design is a free app for designing reinforced concrete beams as per Indian Standards.
• RCC Design and detailing could be performed by Limit State Method specified in IS456:2000
• Option to save the design projects in local storage.
• Detailed calculation steps presented for verification and validation.