Bending moment coefficients (αx, αy) for two-way slabs are tabulated in IS 456:2000 Annex D — Table 26 for two-way restrained slabs (with corner-holding) and Table 27 for simply supported slabs (no corner restraint). Use the formulas Mx = αx × w × lx² (moment per metre width about the long-span axis, steel runs in short direction) and My = αy × w × lx² (moment per metre width about the short-span axis, steel runs in long direction). Here lx is the shorter clear span between supports, ly is the longer span, and w is the total ultimate (factored) uniformly distributed load including slab self-weight, floor finish, partitions, and imposed live load. Table 26 covers 9 distinct edge condition cases — interior panel (all edges continuous), one edge discontinuous, two adjacent edges discontinuous, two opposite edges discontinuous, three edges discontinuous, and four edges discontinuous (corner panel). The ratio ly/lx ranges from 1.0 to ≥ 2.5 in tabulated intervals. When ly/lx exceeds 2.0, slab action transitions toward one-way behaviour and the long span carries minimal moment — beyond ly/lx = 2.0, IS 456 Cl. 24.4 recommends designing as one-way spanning the shorter direction.
Notes
• lx is the shorter clear span (centre-to-centre of supports or clear span + effective depth, whichever is less per IS 456 Cl. 22.2); ly is the longer span; w is the total factored design load in kN/m² (1.5 × DL + 1.5 × LL for limit state, including self-weight + finishes + partitions + imposed live load).
• Mx = αx × w × lx² is the bending moment per metre width about the long-span (ly) axis — the reinforcement to resist this moment runs along the SHORT direction (perpendicular to the moment axis). Mx is the dominant moment; the shorter span carries the higher proportion of load.
• My = αy × w × lx² is the bending moment per metre width about the short-span (lx) axis — reinforcement runs along the LONG direction. Note: My is also multiplied by lx² (not ly²) because the coefficient αy already accounts for the lx² basis. My is always smaller than Mx for the same panel.
• When ly/lx exceeds 2.0, the slab behaves predominantly as one-way — the longer direction carries little moment. Design as one-way slab spanning the shorter direction per IS 456 Cl. 24.4. Minimum reinforcement in the longer direction (per Cl. 26.5.2.1) still required for shrinkage + temperature control.
• Restrained slabs (Table 26) require torsion reinforcement at corners per IS 456 Cl. D-1.8 + D-1.9. Without proper corner detailing, cracks develop at corners under load. Specifically: at corners formed by two discontinuous edges, provide torsion bars in 4 layers (two top + two bottom) at right angles to each other, each layer steel = 0.75 × area of main span steel, over a square zone of side equal to 0.2 × lx.
• Table 26 assumes supports (beams or walls) are infinitely stiff. If supports deflect significantly (e.g., very long beams with shallow depth), the slab moments redistribute toward the supports. For accurate analysis of slabs on flexible beams, use FEA / yield-line / direct design method per IS 456 Cl. 31.
• For continuous slabs over multiple bays, each panel is analysed individually using the Case that matches its actual edge condition. Adjacent panels' supports are 'continuous' for inner edges, 'discontinuous' for outer edges. Negative moments at common supports of two adjacent panels can be averaged or designed for the larger value.
• Table 26 has 9 standard cases — the JSON tables above show the most common (Case 1, 2, 3, 4, 9). Cases 5, 6, 7, 8 (involving combinations of three discontinuous edges or two opposite discontinuous edges) are detailed in IS 456 Annex D Table 26 — refer to the original code for those.
• Once moments are calculated, steel area: Ast = M / (0.87 × fy × jd) where jd ≈ 0.87 × effective depth d. For slab design, check minimum steel (0.12% of cross section for Fe415, 0.15% for Fe250) per IS 456 Cl. 26.5.2.1 + maximum spacing (3d or 300 mm) per Cl. 26.3.3.
• Deflection control is often the governing criterion for slab thickness, not moment capacity. Use IS 456 Cl. 23.2 — span/effective-depth ratio limits (typically 26 for simply supported one-way, 32 for continuous two-way, modified by tension steel percentage).
• For practical design, use IS 875 Part 2 for live loads: residential 2.0 kN/m², office 2.5-3.0 kN/m², classroom 3.0 kN/m², commercial 4.0 kN/m², assembly 5.0 kN/m². Add 1.0-1.5 kN/m² for floor finish + partitions if applicable.