Moments in a slab BuildingCoefficient × F × L² — no diagrams from scratch

Why is there a ready formula? (30 seconds)

• A slab scheme is a continuous beam with a uniform load — the same cases come back again and again.
• A beam on 2 supports? 0.125 · F · L² = F · L² / 8 — exactly the Mmax from the beams binder.
• With 3 supports or more the beam is not statically determinate — so we use coefficients from the table.

The table

Moment coefficients — equal spans

Scheme	Over a support (−)	In the span (+)
2 supports	—	0.125 · F · L²
3 supports, equal spans	B: −0.125 · F · L²	0.07 · F · L²
4 supports, equal spans	B, C: −0.1 · F · L²	End: 0.08 · F · L² · Middle: 0.025 · F · L²
Cantilever (of length Lz)	At the cantilever root: −0.5 · F · Lz²	—

Unequal spans? 3 supports — over B: −F · (L₁ + L₂)² / 36, in the spans: F · L₁² / 11, F · L₂² / 11. 4 supports — over B: −F · (L₁ + L₂)² / 36, over C: −F · (L₂ + L₃)² / 36; in the spans: F · L₁² / 11, F · L₂² / 15, F · L₃² / 11.

The slab from the track: F = 1.285 t/m², L = 4 m

• Reactions
  R_A = 0.375·F·L = 1.927 · R_B = 1.25·F·L = 6.425 t/m — t per 1 m of slab width
• Over B
  −0.125 · 1.285 · 4² = −2.57 t·m → top reinforcement
• In the span
  0.07 · 1.285 · 4² = 1.439 t·m → bottom reinforcement
• Check
  R_A + R_B + R_C = 10.28 = 1.285 · 8 — all the load reached the supports ✓

That's it. Three numbers — and you know where every bar goes.

4 pitfalls

• F = f_ser. For moments — only F_d,max.
• L in cm. In the formula L is in metres — otherwise the moment grows 10,000 times.
• Ignoring the minus. The minus tells where the reinforcement goes: on top.
• Equal-span coefficients when the spans differ. Check first.