Slab thicknessDeflection decides, not strength

Why assume a thickness? (30 seconds)

• The slab also carries its own weight — and that depends on a thickness that is not known yet.
• So assume h, calculate S.w and f_ser from it, and check: is the required thickness that came out ≤ the thickness we assumed?
• K₁₂: large load → small K₁₂ → large required thickness. K₁₃: strong concrete and dolomite aggregate → smaller thickness.
• K₁₁ — the slab type. In a solid slab spanning in one direction K₁₁ = 1.
• B30 — the concrete grade, by its strength. Aggregate — the type of gravel in the concrete: limestone or dolomite.

Given thickness 18 cm — fails

A single span of 4.6 m (L₀ = 1.0 · 460 = 460), q = 0.3, Δg = 0.2, B30 limestone. The exercise gives h = 18.

• S.w
  2.5 · 18 / 100 = 0.45 t/m²
• f_ser
  0.45 + 0.2 + 0.3 = 0.95 t/m²
• K₁₂
  24.4 / ∛0.95 = 24.82
• Required h
  460 / (1 · 24.82 · 1) = 18.53 → 19 > 18 fails ✗

The thickness we assumed is too small. But with a larger thickness the self-weight grows too — so '19' is not enough. Calculate again.

Iteration: +1 cm and recalculate

• h
  18 + 1 = 19 cm
• S.w
  2.5 · 19 / 100 = 0.475
• f_ser
  0.475 + 0.2 + 0.3 = 0.975
• K₁₂
  24.4 / ∛0.975 = 24.61
• Required h
  460 / 24.61 = 18.69 → 19 ≤ 19 passes ✓

That is it. h = 19 cm — and this time the calculation includes the weight of 19 cm.

A 'check' question: if the question only asks to check whether the given thickness is enough — 'fails' is the answer. Increase only when asked to design.

How much to increase? BST suggests +1, +2 or +3 cm — the smallest step that reaches the rounded required thickness. Even +3 was not enough? Another iteration, from the new thickness.

Passed by a wide margin? If the thickness we assumed is more than 5 cm larger than required — it is worth reducing it and calculating again: the self-weight drops, and the slab is more economical.

K₁₃ table — aggregate and concrete

K₁₃ by aggregate type and concrete grade

Aggregate	B20	B30	B40	B50
Limestone	0.97	1	1.02	1.05
Dolomite	1.01	1.04	1.07	1.09

4 pitfalls

• Comparing without rounding. 18.53 ≤ 18? No. Round to 19 and then compare.
• Increasing the thickness without recalculating. S.w changed → f_ser → K₁₂ → everything.
• √ instead of ∛. K₁₂ uses the cube root of f_ser.
• K₁₃ from the wrong row. First the aggregate (row), then the concrete (column).