Maximum depth of stress block for balanced section of a beam

As per IS 456 recommendations, the maximum depth of stress block for a balanced section of a beam of effective depth d is 0.43d.

Explanation:

- A balanced section of a beam is one in which the depth of the neutral axis is at a distance of d/2 from the top and bottom faces of the beam.
- In a balanced section, the maximum compressive stress and the maximum tensile stress are equal and occur at the extreme fibres of the section.
- The stress distribution in a balanced section is assumed to be rectangular with a maximum compressive stress of 0.85fck and a maximum tensile stress of 0.85fy.
- The depth of the stress block is the distance from the extreme compression fibre to the neutral axis.
- To ensure a balanced section, the depth of the neutral axis should be at a distance of d/2 from the top and bottom faces of the beam.
- Therefore, the depth of the stress block can be calculated as:

Depth of stress block = d/2 - x

- where x is the distance of the extreme compression fibre from the top face of the beam.
- The maximum compressive stress occurs at the extreme compression fibre, which is at a distance of d/2 - x from the neutral axis.
- Equating the maximum compressive stress to 0.85fck, we get:

0.85fck = 0.85fy (d/2 - x)/x

- Solving for x, we get:

x = 0.416d

- Therefore, the maximum depth of the stress block is:

Depth of stress block = d/2 - x
= d/2 - 0.416d
= 0.084d

- Adding the distance of the neutral axis from the top face of the beam, we get:

Depth of stress block = 0.5d - 0.084d
= 0.416d

- Therefore, the maximum depth of stress block for a balanced section of a beam of effective depth d is 0.43d (approximately).