## Disclaimer

- This calculator is intended for educational purpose only.
- Any commercial or on site use has to be warranted by a qualified engineer.
- As we put a lot of efforts in maintaining the correctness of calculator, however DCBA Online website does not take responsibility for any error in calculator.
- For singly reinforced beam design check this calculator.
- For doubly reinforced beam design check this calculator.

## Calculator

## How to use calculator

- Quantities marked with ‘*’ are essential without which the calculations will not be performed.
- Width (B), Total Depth (D) are essential, length however is optional and only required to find the safe loading on the beam.
- Concrete grade and steel grade are also essential. The steel grade is to be chosen from the dropdown list, and you get 3 grades option of 250, 415 and 500.
- For a singly reinforced beam the compression reinforcement needs to be put 0, i.e 0 numbers of bars.
- Exposure needs to be selected for durability criteria and to specify nominal cover.
- Clear cover and effective cover are calculated by the program however, user gets the option to specify them manually as well.
- In results, the effective depth is calculated by the program, however the user is given option to specify user defined effective depth.

## What is moment capacity

A concrete beam is designed to resist forces like shear, moment, torsion etc. which satisfies the limit state of collapse. The moment carrying capacity of the beam is determination of maximum safe allowable moment that a beam can carry.

It is the resisting moment produced by the compression stress block or tension stress block about the neutral axis.

This moment capacity of concrete beam calculator is intended to find the moment of resistance of singly reinforced and doubly reinforced sections for simply supported beam condition.

## Singly Reinforced beam moment capacity

A singly reinforced beam is a concrete beam with reinforcement only on the tension side.

### Step 1: Find actual neutral axis

By equating the compression stress block to tension stress block we can find the actual depth of neutral axis.

### Step 2: Find maximum neutral axis depth

The maximum neutral axis depth depends on the grade of steel used.

The moment capacity formula depends on whether the actual neutral axis is greater than maximum neutral axis or less than maximum neutral axis.

Maximum neutral axis is also called as balanced neutral axis.

Maximum neutral axis depths as given by IS 456:2000

- For Fe 250 = 0.53d
- For Fe 415 = 0.48d
- For Fe 500 = 0.46d

If actual neutral axis is greater than balanced neutral axis then neutral axis needs to be limited to maximum neutral axis.

### Step 3: Find Moment of Resistance

The moment capacity formula is given as follows:

The moment capacity of concrete beam when neutral axis is greater than balanced neutral axis is given as follows:

## Doubly Reinforced Beam Moment capacity

A doubly reinforced beam is a concrete beam in which the reinforcement is provided on both tension and compression side.

### Step 1: Find actual neutral axis

The neutral axis of doubly reinforces section for moment capacity of concrete beam is given as follows:

where fsc = stress in compression steel, fcc is stress in concrete at the level of steel. Asc and Ast are compression and tension steel respectively.

### Step 2: Find maximum neutral axis depth

This step remains the same as for singly reinforced beam with the maximum neutral axis depending on the grade of steel.

### Step 3: Find Moment of Resistance

Moment capacity of concrete beam with double reinforcement is given as follows: