Equivalent spanL₀ = c · L — and the largest governs

Why do we need an 'equivalent' span? (30 seconds)

• The thickness is set by the deflection — how much the slab sags (bends downward) at mid-span.
• A continuous span sags less than a single span: the inner support 'holds' it → c less than 1.
• A cantilever sags much more — it has a support on one side only → c = 2.2.
• L₀ translates every span into 'the length of a single span that would sag the same' — and then they can be compared.

The coefficient table — by scheme type

The coefficients follow the order of the spans in the drawing — from the left span to the right · orange = cantilever

Scheme	Drawing	c
2 supports		1
3 supports		0.8 · 0.8
4 supports		0.8 · 0.6 · 0.8
2 supports + cantilever (cantilever on the right)		0.9 · 2.2
Cantilever + 2 supports (cantilever on the left)		2.2 · 0.9
Cantilever + 2 supports + cantilever		2.2 · 0.8 · 2.2
Cantilever + 3 supports (cantilever on the left)		2.2 · 0.7 · 0.8

Note: the coefficient depends on the position: in a scheme of 4 supports — 0.8 in the two end spans, 0.6 in the middle span. Cantilever on the other side? The same coefficients in reverse order — like '2 supports + cantilever' versus 'cantilever + 2 supports'.

A slab with two schemes — which one governs?

Scheme 1: 3 supports, 4 + 4 m. Scheme 2: 2 supports + cantilever, 4.5 m + cantilever 1.5 m.

• Scheme 1
  0.8 · 400 = 320 · 0.8 · 400 = 320 cm
• Scheme 2
  0.9 · 450 = 405 · cantilever: 2.2 · 150 = 330 cm
• Governs
  L₀(max) = 405 cm — the 4.5 m span ✓

That's it. A cantilever of a metre and a half is 'worth' 3.3 m — almost like the large span. So always check them all.

Next: the thickness with L₀(max) = 405

• Initial thicknessh₀ = max(L₀(max)25 , 15) = max(40525 , 15) = 17 cm
• Self-weightS.w = 2.5 · h100 = 2.5 · 17100 = 0.425 t/m²
• Service loadf_ser = S.w + Δg + q = 0.425 + 0.2 + 0.3 = 0.925 t/m²
• Load coefficientK₁₂ = 24.4∛(f_ser) = 24.4∛(0.925) = 25.04
• Slab type coefficient — solid, one-way spanningK₁₁ = 1
• Aggregate and concrete coefficientK₁₃ = 1
• Required thicknessh_req = L₀(max)K₁₁ · K₁₂ · K₁₃ = 4051 · 25.04 · 1 = 16.17 cm
• Thickness check (rounding up)h_req = 16.17 → 17 ≤ h = 17 cm ✓

Rounding: 405 / 25 = 16.2 → round up: h₀ = 17.

4 pitfalls

• The coefficient of the wrong span. The coefficients in the table go in order from left to right — as in the drawing.
• A cantilever with c = 1. A cantilever is always 2.2 — and it can set the thickness.
• Taking L₀ of the first scheme. What governs is L₀(max) of the whole slab.
• Metres and cm. In BST the spans are in cm — because h comes out in cm.