Effective Span Calculation for Simply Supported Beams

The effective span is a key dimension used in structural design to calculate bending moments and shear forces for beams and slabs.

Determining Effective Span

For a simply supported beam or slab, the effective span ($L_{eff}$) is determined based on the geometry of the supports and the beam's dimensions. According to standard structural engineering practice and building codes (like IS 456), the effective span is calculated as the lesser of the following two values:

• The distance measured from the centre to centre of the supports ($L_{cc}$).
• The clear span ($L_{clear}$) between the supports plus the effective depth ($d$) of the member.

Mathematically, this is expressed as:

$L_{eff} = \min(L_{cc}, L_{clear} + d)$

Rationale for the Calculation Method

• Clear span: This is the unobstructed distance between the supports.
• Effective depth ($d$): This is the distance from the compression face of the beam/slab to the centroid of the tensile reinforcement.
• Centre to centre of supports ($L_{cc}$): This is the distance between the midpoints of the supports.

The calculation uses the minimum of the two values ($L_{cc}$ and $L_{clear} + d$) to ensure a conservative design, meaning it considers the span that leads to potentially higher design forces, thus ensuring safety.

Conclusion

Option 3 correctly identifies this standard calculation method: Clear span plus effective depth or centre to centre of supports, whichever is less.