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.
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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