Calculating Effective Span of a Continuous Slab

To find the effective span of a continuous slab, we consider the clear span, the effective depth of the slab, and the width of the supports. The effective span is determined based on specific rules provided in design codes like IS 456.

According to the relevant code provisions for continuous beams and slabs, the effective span is typically taken as the lesser of the following two values:

1. Clear span plus the effective depth of the slab ($\text{L}_{clear} + \text{d}$)
2. The distance between the centres of supports ($\text{L}_{center-to-center}$)

The distance between the centres of supports is equal to the clear span plus the width of the support ($\text{L}_{clear} + \text{w}$).

Given Data

• Clear span ($\text{L}_{clear}$) = 5 m = 5000 mm
• Effective depth of slab (d) = 150 mm
• Width of support (w) = 300 mm

Step-by-Step Calculation

We need to calculate the two possible values for the effective span:

Possibility 1: Clear span + effective depth

\(\text{Effective Span}_1 = \text{L}_{clear} + \text{d}\)

\(\text{Effective Span}_1 = 5000 \text{ mm} + 150 \text{ mm}\)

\(\text{Effective Span}_1 = 5150 \text{ mm}\)

Possibility 2: Distance between centres of supports

First, calculate the distance between centres of supports:

\(\text{L}_{center-to-center} = \text{L}_{clear} + \text{w}\)

\(\text{L}_{center-to-center} = 5000 \text{ mm} + 300 \text{ mm}\)

\(\text{L}_{center-to-center} = 5300 \text{ mm}\)

So, the second possibility for effective span is 5300 mm.

Determine the Effective Span

The effective span is the lesser of the two values calculated:

\(\text{Effective Span} = \text{Minimum}(\text{Effective Span}_1, \text{Effective Span}_2)\)

\(\text{Effective Span} = \text{Minimum}(5150 \text{ mm}, 5300 \text{ mm})\)

\(\text{Effective Span} = 5150 \text{ mm}\)

Conclusion

Based on the calculations, the effective span of the continuous slab is 5150 mm.