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Two-Way Slab — Direct Design Method

Minimum thickness, total static moment M0, span distribution (interior / exterior), column-strip vs middle-strip moments, reinforcement design, and a live slab plan + section diagram per ACI 318-19 / NSCP 2015.

Inputs

Geometry

m
m (perp.)
mm

Loads

kPa
kPa

Materials

MPa
MPa
mm

System

0 if no beams

Reinforcement

Method & assumptions
  • wu = 1.2 D + 1.6 L (kPa).
  • M0 = wu · ℓ2 · ℓn² / 8.
  • Interior span: 0.65 M0 negative @ supports, 0.35 M0 positive @ midspan.
  • Exterior span (no edge beam): exterior neg = 0.26, positive = 0.52, interior neg = 0.70 of M0.
  • Column strip width = 0.5 · min(ℓ1, ℓ2) total (0.25 each side of column line).
  • Min thickness h: per ACI 318-19 Table 8.3.1.1, adjusted for fy.
  • Flexure design: ρ = (0.85 f'c / fy)·[1 − √(1 − 2 Rn / (0.85 f'c))], Rn = Mu / (φ b d²), φ = 0.9.
  • As,min = 0.0018 b h (Grade 60); max spacing = min(2 h, 450 mm) per ACI 8.7.2.2.
  • DDM applicability: 3+ spans, ratio ≤ 2, LL ≤ 2 DL, gravity uniform loads only.

Results (per design direction strip)

Min thickness hmin (≈)
Effective depth d
Factored Load wu
Total Static Moment M0
Column Strip Width
Middle Strip Width
As,min per metre
Max spacing smax

Moment Distribution

SectionTotal (kN·m)Col. StripMid Strip

Reinforcement Design (As per metre of strip)

SectionStripMu/m (kN·m/m)As,req (mm²/m)Spacing (mm)

Slab Design Diagram

Plan view — column & middle strips

Column strip Middle strip Column Bottom bars (midspan) Top bars (supports)

Section A–A — through column line

Rebar schedule (representative)

LocationBarSpacing (mm)Direction
Top bars run continuous over column lines for the negative-moment region (≥ 0.30 ℓn each side of support, ACI 8.7.4.1). Bottom bars are placed within the positive-moment region between columns; extend at least 150 mm into supports. All spacing rounded to the nearest 25 mm for practical placement.