Basic span-to-effective-depth (L/d) ratios per IS 456 to control deflection without explicit calculation. Multiply by modification factors based on tension steel %, compression steel %, and flange (for T/L beams). Useful for preliminary depth selection during conceptual design.
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Basic L/d Ratios (Cl 23.2.1)
Member / Case Value Limit Note Cantilever 7 10 m span For span > 10 m, deflection must be calculated Simply supported 20 10 m span Single span beams and slabs Continuous 26 10 m span Multi-span beams and slabs Cantilever (>10 m) Calculate — Use IS 456 Annex C deflection check Simply supported (>10 m) 20 × 10/L — Reduce ratio for long spans Continuous (>10 m) 26 × 10/L — Reduce ratio for long spans
Modification Factor — Tension Steel (kt) — Cl 23.2.1(c)
Multiply basic L/d by kt based on % steel and service stress fs
Member / Case Value Limit Note fs (MPa) → Pt = 0.4% Pt = 0.8% Pt = 1.0% / 1.5% / 2.0% 120 (Fe 250) 1.68 1.42 1.30 / 1.10 / 1.00 145 (Fe 415, working) 1.55 1.33 1.22 / 1.04 / 0.95 190 (Fe 415, ULS) 1.40 1.20 1.10 / 0.95 / 0.85 240 (Fe 500) 1.25 1.07 0.98 / 0.85 / 0.78 290 (Fe 550) 1.10 0.95 0.87 / 0.75 / 0.68
Modification Factor — Compression Steel (kc) — Cl 23.2.1(d)
Multiply by kc when compression reinforcement provided
Member / Case Value Limit Note Pc = 0.25% 1.08 — Compression bars increase L/d slightly Pc = 0.50% 1.16 — — Pc = 0.75% 1.22 — — Pc = 1.00% 1.27 — — Pc = 1.25% 1.31 — — Pc = 1.50% 1.34 — Maximum factor
Modification Factor — Flanged Beams (kf) — Cl 23.2.1(e)
For T-beams and L-beams; bw/bf = web width / flange width
Member / Case Value Limit Note bw / bf = 0.10 0.80 — Wide flange — biggest reduction bw / bf = 0.20 0.81 — — bw / bf = 0.30 0.82 — — bw / bf = 0.50 0.85 — — bw / bf = 0.70 0.92 — — bw / bf = 1.00 1.00 — Rectangular beam
Quick Preliminary Depth Selection
Member / Case Value Limit Note One-way slab (SS) L / 25 to L / 30 Span 3–5 m Depth in mm for L in metres Two-way slab (SS) L / 30 to L / 35 Span 3–6 m Use shorter span Two-way slab (cont) L / 35 to L / 40 Span 3–6 m — Beam (SS) L / 12 to L / 15 Span 4–8 m Total depth Beam (continuous) L / 15 to L / 20 Span 4–10 m Total depth Cantilever beam L / 7 to L / 10 Span ≤ 3 m Total depth Flat slab L / 30 to L / 36 Span 6–9 m — Waffle slab L / 20 to L / 25 Span 8–14 m Overall depth including topping
Notes
• Permissible L/d = basic ratio × kt × kc × kf
• fs at service load = 0.58 × fy × (Ast required / Ast provided) — use 0.58 × fy if Ast = required
• If actual L/d ≤ permissible L/d, deflection check is satisfied without computation
• For long spans (>10 m), explicit deflection check per Annex C is mandatory regardless of L/d
• These ratios are for 'normal' loading and Indian conditions — reduce by 10% for heavily loaded slabs
• Cantilever ratios are conservative — long cantilevers always need deflection calculation
• For two-way slabs, use the shorter span lx as L
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