IS 456:2000 / IS 1893 Structural Design Guide
Quick-reference for concrete design per IS 456:2000, seismic design per IS 1893:2016, ductility detailing per IS 13920:2016, and loads per IS 875.
1.1 Concrete Grades — IS 456:2000 Cl. 6.1 & Table 2
IS 456 specifies concrete by characteristic cube strength (150 mm cube, 28 days). Design compressive strength: fcd = 0.67·fck/γc = 0.447·fck (γc = 1.5). Modulus: Ec = 5000√fck MPa (Cl. 6.2.3.1).
| Grade | fck (MPa) | fcd (MPa) | Ec (MPa) | Min. exposure use |
|---|---|---|---|---|
| M15 | 15 | 6.7 | 19,365 | Plain concrete only |
| M20 | 20 | 8.9 | 22,361 | Mild exposure (RC min) |
| M25 | 25 | 11.2 | 25,000 | Moderate exposure |
| M30 | 30 | 13.4 | 27,386 | Severe exposure |
| M35 | 35 | 15.6 | 29,580 | Very severe exposure |
| M40 | 40 | 17.9 | 31,623 | Extreme exposure |
| M45 | 45 | 20.1 | 33,541 | — |
| M50 | 50 | 22.4 | 35,355 | — |
Minimum grade for RC: M20 (Cl. 6.1.1). 0.67 factor accounts for cube-to-cylinder conversion (×0.8) and sustained loading (×0.85).
See Concrete Properties Reference for full IS 456 grade values.
1.2 Reinforcing Steel — IS 456:2000 Cl. 5.6
Design yield strength: fyd = 0.87·fy (γs = 1/0.87 ≈ 1.15)
| Grade | fy (MPa) | fyd (MPa) | Type |
|---|---|---|---|
| Fe 250 | 250 | 217 | Mild steel (plain bars) |
| Fe 415 | 415 | 361 | HYSD (deformed bars) |
| Fe 415D | 415 | 361 | HYSD — enhanced ductility |
| Fe 500 | 500 | 435 | HYSD (deformed bars) |
| Fe 500D | 500 | 435 | HYSD — enhanced ductility (seismic) |
| Fe 550 | 550 | 479 | HYSD |
Es = 200,000 MPa for all grades (IS 456 Cl. 5.6.3). Fe 500D / Fe 415D preferred for seismic primary elements (IS 13920:2016 Cl. 5.2).
→ Rebar Properties & Bar Size Reference
1.3 Minimum Cover (IS 456:2000 Table 16 / Cl. 26.4.1)
| Exposure Condition | Min. Cover (mm) |
|---|---|
| Mild | 20 |
| Moderate | 30 |
| Severe | 45 |
| Very Severe | 50 |
| Extreme | 75 |
2.1 Seismic Zones — IS 1893:2016 (Part 1) Table 3
| Zone | Zone Factor Z | Seismic Intensity |
|---|---|---|
| II | 0.10 | Low |
| III | 0.16 | Moderate |
| IV | 0.24 | Severe |
| V | 0.36 | Very Severe |
Zone maps in IS 1893:2016 Annex determine the applicable zone for a site.
2.2 Moment Frame Types & Response Reduction Factor (R)
IS 1893:2016 Table 9 (selected RC systems):
| System | R | Detailing Standard |
|---|---|---|
| Special RC Moment Resisting Frame (SMRF) | 5 | IS 13920:2016 |
| Ordinary RC Moment Resisting Frame (OMRF) | 3 | IS 456:2000 |
| RC Shear Walls + SMRF (dual system) | 5 | IS 13920:2016 |
| RC Shear Walls + OMRF | 4 | IS 13920:2016 (walls) |
| RC Load Bearing Shear Walls only | 3 | IS 13920:2016 |
IS 1893:2016 Cl. 7.2.1: OMRF is not permitted in Seismic Zones IV and V. SMRF required for Zone IV and V.
2.3 Importance Factor (I) — IS 1893:2016 Table 8
| Building Category | I |
|---|---|
| General (residential, commercial, industrial) | 1.0 |
| Important (schools, hospitals, community halls) | 1.2 |
| Critical / post-disaster (emergency facilities) | 1.5 |
2.4 Site Soil Types — IS 1893:2016 Table 4
| Type | Description |
|---|---|
| Type I (Rock / Hard Soil) | Well-graded gravel/sand-gravel, hard/medium stiff clay, N > 30 throughout |
| Type II (Medium Soil) | All soils with N = 10 to 30; medium stiff clay 4 ≤ cu ≤ 50 kPa |
| Type III (Soft Soil) | Soft soil with N < 10; loose saturated sand; soft clay cu < 25 kPa |
3.1 Span-to-Effective-Depth Ratios — IS 456:2000 Cl. 23.2 (Table 15)
Basic l/d ratios for deflection control (Fe 415, ρ ≈ 0.5%, normalweight concrete):
| Support Condition | Beam | One-way Slab | Two-way Slab |
|---|---|---|---|
| Simply supported | 20 | 20 (≤ 3.5 m span) | 35×(Ly/Lx for continuous) |
| Continuous | 26 | 26 | — |
| Cantilever | 7 | 7 | — |
Modification factor for tension steel (Cl. 23.2.1): multiply l/d by fs-based factor from Fig. 4. For Fe 500 at ρ = 0.5%: factor ≈ 0.9 — effective l/d limit reduces. Flanged beams: additional 0.8 factor (Cl. 23.2.1).
→ Beam Flexural & Shear Design Calculator · Slab Design Calculator
3.2 Minimum Dimensions
| Element | Minimum | Reference |
|---|---|---|
| Beam width b | 200 mm (practical) | — |
| Column least lateral dimension | 200 mm | Cl. 26.5.3.1(a) |
| Slab thickness (one-way) | 100 mm (min per Cl. 24.1) | Cl. 24.1 |
| Flat slab drop panel depth | h + h/4 minimum | Cl. 31.2.1 |
3.3 Seismic Minimum Dimensions — IS 13920:2016
| Element | SMRF Requirement | Reference |
|---|---|---|
| Beam width bw | ≥ 200 mm; bw/D ≥ 0.3 | Cl. 6.1.2 |
| Column least dimension | ≥ 300 mm | Cl. 7.1.2 |
| Column aspect ratio | shortest/longest ≥ 0.4 | Cl. 7.1.2 |
| Column axial stress | Pu/(Ag·fck) ≤ 0.40 | Cl. 7.1.1 |
4.1 Dead Loads — IS 875 Part 1
Self-weight of materials. Unit weights (selected): RC 25 kN/m³; brick masonry 18–20 kN/m³; cement plaster 20.4 kN/m³; floor finishes 0.5–1.0 kN/m² (typical).
4.2 Imposed Loads — IS 875 Part 2 (selected values)
| Occupancy | UDL (kN/m²) | Point Load (kN) |
|---|---|---|
| Residential (bedrooms, living rooms) | 2.0 | 1.8 |
| Office (general) | 2.5 | 2.7 |
| Corridors, lobbies, stairs | 3.0–4.0 | 4.5 |
| Assembly hall (fixed seats) | 4.0 | 4.5 |
| Assembly hall (moveable) | 5.0 | 4.5 |
| Retail shops | 4.0 | 4.5 |
| Storage (general) | 5.0–10.0 | — |
4.3 Wind Loads (Overview) — IS 875 Part 3
Design wind speed: Vz = Vb·k1·k2·k3·k4
Design wind pressure: pz = 0.6·Vz² (N/m², Vz in m/s)
Vb = basic wind speed (IS 875 Fig. 1 — site map, 33–55 m/s), k1 = risk coefficient, k2 = terrain/height factor, k3 = topography, k4 = importance.
4.4 Snow Loads — IS 875 Part 4
S = μ·S0 where S0 = ground snow load (site map), μ = roof shape coefficient (0.8 for flat roofs). Applicable primarily to Himalayan regions and high-altitude sites.
5.1 Design Horizontal Seismic Coefficient — IS 1893:2016 Cl. 6.4.2
Ah = (Z/2) · (I/R) · (Sa/g)
Z = zone factor, I = importance factor, R = response reduction factor, Sa/g = spectral acceleration coefficient.
Minimum: Ah ≥ Z·I/(2R) regardless of computed Sa/g.
5.2 Spectral Acceleration (Sa/g) — IS 1893:2016 Cl. 6.4.5 (5% damping)
| Period T (s) | Type I (Rock) | Type II (Medium Soil) | Type III (Soft Soil) |
|---|---|---|---|
| 0 < T ≤ 0.1 | 1 + 15T (all soil types) | ||
| 0.1 < T ≤ 0.40 | 2.5 | — | — |
| 0.1 < T ≤ 0.55 | — | 2.5 | — |
| 0.1 < T ≤ 0.67 | — | — | 2.5 |
| 0.40 < T ≤ 4.0 | 1.0/T | — | — |
| 0.55 < T ≤ 4.0 | — | 1.36/T | — |
| 0.67 < T ≤ 4.0 | — | — | 1.67/T |
5.3 Fundamental Period — IS 1893:2016 Cl. 7.6.2
Ta = 0.075·h0.75 (RC frame buildings)
Ta = 0.085·h0.75 (steel frame buildings)
Ta = 0.09·H/√d (shear wall buildings — H = height, d = base dimension in direction of shaking)
5.4 Base Shear & Vertical Distribution — IS 1893:2016 Cl. 7.7
VB = Ah · W (W = total seismic weight — Cl. 7.4)
Lateral force distribution: Qi = VB · (Wi·Hi²) / Σ(Wj·Hj²) — parabolic distribution (Cl. 7.7.1)
6.1 IS 456:2000 Limit State Design — Cl. 18.2.3.1
| Combination | Equation |
|---|---|
| DL + IL | 1.5(DL + IL) |
| DL + IL + WL/EL | 1.2(DL + IL ± WL) or 1.2(DL + IL ± EL) |
| DL + WL/EL | 1.5(DL ± WL) or 1.5(DL ± EL) |
| DL uplift check | 0.9DL ± 1.5WL or 0.9DL ± 1.5EL |
DL = Dead Load, IL = Imposed (Live) Load, WL = Wind Load, EL = Earthquake Load. Identical factors for US and SI units (dimensionless).
6.2 IS 1893:2016 Seismic Combinations — Cl. 6.3.1.2
In seismic combinations, earthquake and wind are not combined simultaneously. The governing combination is used:
- 1.2(DL + IL + Eh) — where Eh is horizontal seismic force
- 1.5(DL + Eh)
- 0.9DL + 1.5Eh
Vertical seismic component: Ev = 0.5·Ah·Wi — added to dead load effect (Cl. 6.4.4).
7.1 Flexural Design — IS 456:2000 Cl. 38
Singly reinforced section (parabolic-rectangular stress block):
As = (0.5·fck/fy) · [1 − √(1 − 4.6·Mu/(fck·b·d²))] · b·d
Limiting moment of resistance (Fe 415): Mu,lim = 0.138·fck·b·d²
Limiting neutral axis depth: xu,max/d = 0.48 (Fe 415), 0.46 (Fe 500), 0.53 (Fe 250)
Min. steel — Cl. 26.5.1.1: As,min = 0.85·b·d/fy
Max. steel — Cl. 26.5.1.2: As,max = 0.04·b·D
→ Beam Flexural Design Calculator
7.2 Shear Design — IS 456:2000 Cl. 40
Nominal shear stress: τv = Vu/(b·d)
Design shear strength τc: from Table 19 (function of 100As/bd and fck). Maximum permitted: τc,max from Table 20 (M20: 2.8, M25: 3.1, M30: 3.5 MPa).
If τv > τc: Vus = (τv − τc)·b·d. Stirrup: Asv·0.87·fy·d/sv = Vus
Minimum stirrup — Cl. 26.5.1.5: Asv/(b·sv) ≥ 0.4/(0.87·fy)
→ Beam Shear Design Calculator
7.3 Column Design — IS 456:2000 Cl. 39
Short column, axially loaded — Cl. 39.3: Pu = 0.4·fck·Ac + 0.67·fy·Asc
Combined axial + bending: P-M interaction diagram. See Column PMM Design Calculator.
Min. eccentricity — Cl. 25.4: emin = max(L/500 + D/30, 20 mm)
Steel limits — Cl. 26.5.3.1: Asc,min = 0.8%·Ag, Asc,max = 4%·Ag (6% at laps).
7.4 Torsion — IS 456:2000 Cl. 41
Equivalent shear: Ve = Vu + 1.6·Tu/b. Equivalent moment: Mt = Tu·(1 + D/b)/1.7.
Design for Me1 = Mu + Mt (main steel face) and Me2 = Mt − Mu (opposite face if positive).
8.1 Non-Seismic Detailing (OMRF) — IS 456:2000
Standard cover (Cl. 26.4), development length (Cl. 26.2), lap length (Cl. 26.2.5), stirrup spacing (Cl. 26.5.1.5 / 26.5.3.2). No special ductile detailing required.
Development length: Ld = φ·fs/(4·τbd) where τbd from Table 5 (M20: 1.2 MPa plain, ×1.6 for deformed).
→ Development Length Calculator (IS 456)
8.2 SMRF Beam Detailing — IS 13920:2016 Cl. 6
Confinement region: lo = 2d from face of column at each end.
Hoop spacing in confinement: so ≤ min(d/4, 8·dbL, 100 mm) — Cl. 6.3.5
Outside confinement: s ≤ d/2
Min. 2 bars top and bottom throughout beam length; positive moment capacity at joint face ≥ 50% negative moment capacity — Cl. 6.2.2.
8.3 SMRF Column Detailing — IS 13920:2016 Cl. 7
Confinement region lo = max(Lc/6, max column dimension, 450 mm) from each end — Cl. 7.3.1
Hoop spacing in confinement: so ≤ min(b/4, 100 mm) — Cl. 7.3.4
Hoop spacing outside confinement: s ≤ min(b/2, 200 mm)
Strong column–weak beam: ΣMu,col ≥ 1.4·ΣMu,beam at each joint — IS 13920:2016 Cl. 7.2
8.4 Shear Wall Detailing — IS 13920:2016 Cl. 9
Boundary elements required when extreme fibre compressive stress > 0.2·fck under seismic + gravity load combinations — Cl. 9.4.1.
9.1 Storey Drift Limits — IS 1893:2016 Cl. 7.11.1
Allowable storey drift: Δa = 0.004·hs (hs = storey height)
For buildings with brittle non-structural elements: checked under design seismic forces. Drift is computed using the elastic deflection amplified by response reduction factor R where required.
9.2 Diaphragm Design — IS 1893:2016 Cl. 7.9
Floor and roof slabs assumed to act as rigid diaphragms to transfer seismic forces to lateral-resisting elements. Flexible diaphragm analysis required for timber/metal deck systems.
9.3 Soft / Weak Storey Check — IS 1893:2016 Cl. 4.15 & Table 6
Soft storey: lateral stiffness < 70% of storey above or < 80% of average of 3 storeys above.
Weak storey: storey strength < 80% of storey above. Buildings with soft/weak storeys in Zones III–V require special design per IS 1893:2016 Cl. 7.10.