Design steps for a doubly reinforced beam section | IS 456: 2000

When we provide reinforcement on both sides of a beam section, we call it a doubly reinforced beam.

In most basic beam design, we learn that steel is required mainly to resist tension, since concrete is weak in tension.
So a natural question arises—why do we provide reinforcement in the compression zone?

The answer lies in capacity.

When bending moments are high or beam dimensions are restricted, the compression capacity of concrete alone is not sufficient.
By introducing steel in the compression zone, we increase the beam’s ability to resist compressive stresses.

In other words, compression reinforcement is provided not because concrete cannot take compression, but because we want the beam to carry more moment than what a singly reinforced section can offer.

This is the fundamental idea behind a double reinforced beam.

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

As in this type of beams, the beam size is a constrain. Our main aim is only to calculate the area of reinforcement required in each zone of the beam section.

Procedure to design a doubly reinforced beam

The step by step procedure to design a beam section as per IS:456:2000 are as follows:

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 resp. and Tu is the tensile force in the steel.

The depth of neutral axis is

$$x_u = frac{f_{st} A_{st} - (f_{sc} - 0.447 f_{ck}) A_{sc}}{0.362 f_{ck} b}$$

Calculate the factored moment

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

$$M_u = M_{ur.max} + \Delta M_{u}$$

where Mur maxis the limiting moment capacity which is equal to the moment of resistance of a balanced RCC beam section and the second component is for the moment capacity which should be taken care by the compression reinforcement.

First calculate

$$M_{ur.max} = R_{u.max} bd^2$$

If $M_u < M_{ur.max}$, obtain $A_{st}$ as of the SRB section (Check this post for the same), or else proceed to obtain $A_{st}$ as per the DRB section.

Design of reinforcement

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

$$A_{st } = A_{st1} + A_{st2}$$ $$A_{st1} = \frac{M_{ur.max}}{0.87f_y(d-0.42x_{u.max})}$$ $$A_{st2} = \frac{M_u - M_{ur.max}}{0.87f_y(d -d_c)}$$

Calculate the value of the area of steel in the compression zone using :

$$A_{sc} =\frac{0.87 f_y A_{st2}}{(f_{sc}-f_{cc})} = \frac{0.87 f_y A_{st2}}{f_{sc}}$$

For HYSD bars obtain $f_{sc}$ corresponding $varepsilon_{sc}=0.0035left(1-frac{\frac{d_c}{d}}{k_{u cdot max }}right)$ from IS 456:2000.

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 have explained in this post.  

Conclusions

In conclusion, designing a doubly R.C.C. beam section is a simple process that requires a thorough understanding of the Indian standard codes. Additionally, it is important to consider the potential for creep, and temperature effects when designing a doubly RCC beam. By following these steps, engineers can design a doubly R.C.C. beam section that is both efficient and effective.

In this post you have learned the following points:

• Importance of DRBs: In scenarios where the dimension of the beam is a constrain, it may be because of any reason (architectural or for head space), we have to go for these beams.

• Adhering to IS 456:2000: Following the Indian Standard code for R.C.C. design is imp. to ensure the integrity and safety of beams, as it is specific to the Indian context.

• Contribution to Safety: Properly designed beams leads to the overall safety, and durability of structures, and ensures the well being of users.

Check this post to know more about min. and max. steel of a beam section