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1. Concrete Grades — IS 456:2000
Grade fck (MPa) f'ck (= fck+1.65s, MPa) Design compressive strength (0.45fck, MPa) Tensile strength (0.7√fck, MPa) E = 5000√fck (MPa) M10 10 15.78 4.50 2.21 15,811 M15 15 20.78 6.75 2.71 19,365 M20 20 26.60 9.00 3.13 22,361 M25 25 31.60 11.25 3.50 25,000 M30 30 38.25 13.50 3.83 27,386 M35 35 43.25 15.75 4.14 29,580 M40 40 48.25 18.00 4.43 31,623 M50 50 58.25 22.50 4.95 35,355
Minimum grade: M20 for RCC in mild exposure; M30 for prestressed concrete; M35 for seawater / aggressive environments per IS 456 Table 5.
2. Steel (Reinforcement) Grades — IS 1786
Grade fy (MPa) Fu (MPa, min) Elongation (%) IS Code Typical Use Fe 250 (Mild Steel) 250 410 ≥23% IS 432 Tie bars, stirrups (rare today) Fe 415 (Deformed) 415 485 ≥14.5% IS 1786 General RCC work Fe 500 (Deformed) 500 545 ≥12% IS 1786 Most common now Fe 500D (Ductile) 500 565 ≥16% IS 1786 Seismic zones Fe 550 550 585 ≥10% IS 1786 High rise structures Fe 550D 550 600 ≥14.5% IS 1786 Seismic zones, high rise
3. Limiting Neutral Axis Depths (IS 456 Cl. G-1.1)
xu,max / d = 0.0035 / (0.0035 + fy/(1.15 × Es))
Steel Grade fy (MPa) xu,max/d Mu,lim / bd² (MPa) Remarks Fe 250 250 0.53 2.24 Rarely used now Fe 415 415 0.48 2.76 (M20), 3.45 (M25) Singly reinforced Fe 500 500 0.46 2.66 (M20), 3.33 (M25) Singly reinforced Fe 550 550 0.44 2.57 (M20), 3.21 (M25) —
4. Moment of Resistance Coefficients (Mu,lim / bd²) — SP:16
Mu = 0.87 × fy × Ast × d × [1 - (Ast × fy) / (b × d × fck)]
Concrete Grade Fe 250 (xu/d=0.53) Fe 415 (xu/d=0.48) Fe 500 (xu/d=0.46) M20 2.24 2.76 2.66 M25 2.80 3.45 3.33 M30 3.36 4.14 3.99 M35 3.92 4.83 4.66 M40 4.48 5.52 5.32
If Mu > Mu,lim, design as doubly reinforced section. Mu,lim = R × b × d² where R is from the table above.
5. Nominal Cover Requirements — IS 456:2000 Table 16
Exposure Condition Nominal Cover (mm) Min Concrete Grade Mild 20 mm M20 Moderate 30 mm M25 Severe 45 mm M30 Very Severe 50 mm M35 Extreme 75 mm M40
For slabs: Reduce cover by 5mm (IS 456 Cl.26.4.1). Min cover = greater of bar diameter or 15mm. Fire resistance may require additional cover per IS 456 Table 16A.
6. Development Length — IS 456:2000 Cl. 26.2
Ld = (φ × σs) / (4 × τbd)
Bar φ (mm) Ld (mm) Fe415, M20 Ld (mm) Fe415, M25 Ld (mm) Fe500, M20 Ld (mm) Fe500, M25 8 392 336 472 405 10 490 420 590 506 12 588 504 708 607 16 784 672 944 809 20 980 840 1180 1012 25 1225 1050 1475 1265 32 1568 1344 1888 1619
These Ld values assume M20/M25 concrete with deformed bars (bond stress multiplied by 1.6 factor). For plain bars (Fe250), divide by 1.6.
7. Standard Hooks and Bends — IS 456:2000 Cl. 26.2.2
Type Bend Angle Minimum Bend Radius Extension beyond bend Equivalent Ld Provided Standard Hook (180°) 180° 2φ (4φ for Fe500) 4φ 16φ Standard Bend (90°) 90° 4φ 12φ 8φ Standard Bend (135°) — stirrups 135° 2φ 8φ —
8. Span-to-Depth Ratios — IS 456:2000 Cl. 23.2
Support Condition Cantilever Simply Supported Continuous Basic ratio (l/d) 7 20 26
Modification factors:
For fs < 240 MPa: multiply by tension reinforcement factor (MF1) from IS 456 Fig.4
For T/L beams: multiply by 0.8 for flanged beams
For spans > 10m: multiply basic ratio by 10/span
Effective span = lesser of (clear span + d) and (c/c of supports)
9. Reinforcement Limits
Member Min Steel (%) Max Steel (%) Remarks Beam (tension side) 0.85bd/fy (IS 456 Cl.26.5.1.1) 4% of bd Min = 0.12% for M25 & Fe415 Slab (main steel) 0.12% of total cross-section (HYSD) 4% of bd 0.15% for plain bars Column (longitudinal) 0.8% of Ag (IS 456 Cl.26.5.3) 6% of Ag (4% preferred) Ag = gross cross-section Column (lateral ties) As per IS 456 Cl.26.5.3.2 — Spacing: lesser of 300mm, 16φlong, least lateral dim. Slab (distribution/temp) 0.12% (HYSD) or 0.15% (MS) 4% Transverse to main steel
10. Column Slenderness — IS 456:2000
Slenderness ratio = l_eff / D (or l_eff / b for rectangular)
End Condition Effective Length l_eff Both ends fixed (rotation & translation) 0.65L One end fixed, other pinned 0.80L Both ends pinned 1.00L One end fixed, other free (cantilever) 2.00L Both ends fixed (rotation fixed, one translates) 1.20L
11. Load Combinations — IS 456:2000 Cl. 18.2 (Limit State)
Combination Formula Use Case DL + LL 1.5 DL + 1.5 LL Gravity loading DL + LL + EL 1.2 DL + 1.2 LL + 1.2 EL With earthquake load DL + EL only 1.5 DL ± 1.5 EL Earthquake dominant DL + WL only 1.5 DL ± 1.5 WL Wind load dominant DL + LL + WL 1.2 DL + 1.2 LL ± 1.2 WL Wind combined DL uplift check 0.9 DL ± 1.5 EL (or WL) Check for tension/uplift
Serviceability (SLS): Unfactored loads. Check deflection, crack width, stress.Strength (ULS): Factored loads as above. Check strength & stability.