Introduction
To compute the beam depth for controlling deflection in a simply supported beam, we need to consider the span, material properties, and permissible deflection limits.

Given Data
- Length of the beam (L): 6 m
- Steel grade: Fe500 (yield strength = 500 MPa)
- Percentage of steel reinforcement: 0.9%

Deflection Criteria
- For simply supported beams, the permissible deflection (Δ) is typically limited to L/250 for live load or L/360 for total load.
- For L = 6000 mm, permissible deflection is:
- Live Load: Δ ≤ 6000/250 = 24 mm
- Total Load: Δ ≤ 6000/360 = 16.67 mm

Moment of Inertia (I)
- The deflection (Δ) for a simply supported beam under a uniform load can be calculated using the formula:
Δ = (5wL^4) / (384EI)
- Where:
- w = load per unit length (N/m)
- E = Modulus of Elasticity (approximately 200 GPa for steel)
- I = Moment of Inertia

Calculating Beam Depth (h)
- For a rectangular beam, the moment of inertia (I) is given by:
I = (b * h^3) / 12
- Assuming a width (b) of 230 mm for standard beams, we can rearrange the equations to solve for h.

Steps to Determine Depth
1. **Estimate Load (w)**: Calculate load based on service conditions.
2. **Substitute in Deflection Formula**: Use the calculated w to find h from Δ.
3. **Check Feasibility**: Ensure h is practical for construction.

Conclusion
The beam depth should be determined based on the allowable deflection limits and should ensure structural integrity while adhering to building codes and standards.