Codes referenced
Zone factor, importance factor, response reduction, analysis methods.
Pairs with IS 1893 for zones III, IV, V — R=5 requires IS 13920 ductility.
Seismic loads supplement to IS 875 Parts 1-4; the basis for Sa/g spectrum.
Code of practice for masonry buildings — companion to IS 1893 for low-rise.
The three factors every seismic design turns on
| Factor | What it controls | Values (typical) |
|---|---|---|
| Z — zone factor | Seismic hazard at the site | 0.10 / 0.16 / 0.24 / 0.36 (zones II/III/IV/V) |
| I — importance factor | Building use / post-disaster role | 1.0 / 1.2 / 1.5 (ordinary / important / post-disaster) |
| R — response reduction | Ductility of the lateral system | 3 (ordinary RC) / 5 (SMRF) / 4 (unreinforced masonry) |
| Sa/g | Spectral acceleration at the building period | 0 to 2.5 (depends on soil + period) |
Reference: IS 1893:2016 Tables 2-3 (zone + importance), Table 4 (R), Cl 6.4 (Sa/g spectrum by soil type).
The base shear formula
V_B = (Z · I · Sa/2g) / R × W
Where V_B is the design base shear at the bottom of the structure, Z the zone factor, I the importance factor, Sa/g the spectral acceleration at the fundamental period T, R the response reduction factor, and W the seismic weight (full dead load + 25% of live load for storage, 50% for assembly, etc. — per IS 875).
Source: IS 1893:2016 Cl 7.4.1 — Design Base Shear.
The formula works the same direction as the intuition: higher Z (more seismically active zone) raises the base shear; higher I (more critical building) raises it; higher R (more ductile detailing) lowers it. The trade-off is intentional — a ductile frame with IS 13920 detailing can absorb the same energy at a lower design force because it can deform without collapsing.
The three analysis methods
Single base shear distributed as inverted-triangle along height. Applicable to regular buildings up to 40 m (zone II/III) or 30 m (zone IV/V). Default for low-rise Indian construction. Output: storey shears and moments, peak base shear.
Modal analysis with Sa/g spectrum. Required for irregular or taller buildings (zone IV/V above 30 m, zone II/III above 40 m). Default for mid-rise. Output: storey shears, moments, drift, mode shapes.
Non-linear dynamic analysis with recorded ground motion. Required for very tall buildings or those with vertical irregularities. Output: full time-history response; reserved for signature projects.
Worked example — 4-storey residential, Delhi (Zone IV)
| Parameter | Value | Source |
|---|---|---|
| Zone | IV | Delhi NCR |
| Z | 0.24 | IS 1893 Table 3 |
| I | 1.2 | Residential — ordinary (1.0 base, +0.2 for residential) |
| R | 5 | SMRF per IS 13920 (which is mandatory in zone IV) |
| Sa/g (rocky soil, T = 0.6 s) | 2.0 | IS 1893 Cl 6.4.5 (rocky/ stiff soil, T < 0.55 s plateau; here at T = 0.6 reading interpolated) |
| W (seismic weight) | DL + 25% LL ≈ 3 500 kN | Per storey accumulation |
| V_B = (0.24 × 1.2 × 2.0/2) / 5 × 3 500 | ≈ 202 kN | Formula result |
Distribution along the building: inverted-triangular per Equivalent Static — storey shears from top (smallest) to base (largest). Each frame column in the lateral-load-resisting system is then sized for the cumulative storey shear.
Common deviations on Indian projects
IS 1893:2016 updated the zone map — some projects still use 2002 zones. Always quote the latest BIS revision.
Stilt parking without masonry infill at ground floor = soft storey. Without IS 13920 detailing + 2.5x column moment amplification, the building fails at that level.
R=5 is a credit for ductility — without the SCR, 135° hooks and joint hoops of IS 13920, the building cannot deform as designed. IS 1893 + IS 13920 must be paired.
Equivalent Static on a 60 m building in zone IV = audit finding. IS 1893 Cl 7.1 requires Response Spectrum for zone IV above 30 m.
Field-checklist blocks
A short questionnaire, an inspector's checklist, and three worked examples that show how a zone factor, a response reduction factor and an analysis method turn into a base shear the building has to survive.
Questionnaire — ask at design review, before the base shear is frozen
- Which seismic zone is the site in per the latest BIS map, and what zone factor Z does that give (0.10 for zone II, 0.16 for III, 0.24 for IV, 0.36 for V)?
- What importance factor I applies to the building's use (1.0 ordinary, 1.2 important such as a school or hospital, 1.5 post-disaster function)?
- What response reduction factor R is claimed, and if it is 5, is the IS 13920 detailing actually drawn (SCR, 135° hooks with 10d extension, joint hoops)?
- What Sa/g has been used, at what fundamental period and for what soil type, per Cl 6.4 and Cl 6.4.5?
- Which analysis method is being used, and does the building height fit it (Equivalent Static up to 40 m in zone II/III and 30 m in zone IV/V, Response Spectrum beyond, Time History for the tall or vertically irregular cases) per Cl 7.1?
- Is there a soft storey on the ground floor (stilt parking, open lobby), and which route is taken: columns designed to remain elastic, or IS 13920 detailing with the 2.5x column moment amplification?
- How is the seismic weight W built up from the dead load plus the permitted fraction of live load per IS 875?
- Has the hand-calculated base shear (Z · I · Sa/2g / R) · W been reconciled with the base shear the model actually delivers?
Inspector's checklist — what to verify in the drawings and on site
- Seismic zone and the BIS revision of the zone map noted on the drawings, not an inherited zone from an earlier project.
- Base shear recomputed on paper from Cl 7.4.1 with the Z, I, Sa/g, R and W on the sheet, and compared with the model's base storey shear.
- Sa/g read at the building's actual period and soil type rather than taken from the plateau by habit.
- Analysis method checked against height and regularity per Cl 7.1 before anything is fixed in the reinforcement.
- R = 5 matched to the IS 13920 detailing on the same drawing set, not claimed on a calculation sheet and absent from the bar bending schedule.
- Soft-storey condition checked against IS 1893 Table 5 and the chosen route (elastic columns or 2.5x amplification with IS 13920 detailing) written down.
- Seismic weight built up in the calculation as dead load plus the permitted live-load fraction, storey by storey.
- Model mass reconciled with the hand-built W, since a mismatch in weight quietly scales every storey shear.
What happens if… three worked examples
What happens. Take the 4-storey Delhi frame: Z = 0.24, I = 1.2, R = 5, Sa/g = 2.0, W = 3,500 kN, giving V_B = (0.24 × 1.2 × 2.0/2) / 5 × 3,500 = 0.0576 × 3,500 = 201.6 kN, about 202 kN. Read the zone from a superseded map and use Z = 0.16 for zone III: V_B = (0.16 × 1.2 × 2.0/2) / 5 × 3,500 = 0.0384 × 3,500 = 134.4 kN.
Likely outcome. 134 kN against 202 kN is 67 kN of missing base shear, a 33% shortfall, spread over every column and beam of the lateral system. The frame is sized for a third less demand than the site can produce, and nothing on the drawing reveals it because the zone factor looks plausible. Check the zone against the current BIS map before anything else on the seismic design.
What happens. The same frame, but the reinforcement drawings carry ordinary IS 456 detailing: no SCR, 90° stirrup hooks, no joint hoops. R = 5 is a credit for ductility, and without IS 13920 the frame is an ordinary RC frame with R = 3: V_B = (0.24 × 1.2 × 2.0/2) / 3 × 3,500 = 0.096 × 3,500 = 336 kN.
Likely outcome. 336 kN against the 202 kN on the drawing is 134 kN of understated demand, about 66% more than the frame was designed for, and the frame also has no ductility to spend. Either the detailing is upgraded to IS 13920 so R = 5 is earned, or the design is redone for R = 3 and the members are resized.
What happens. The height limit for Equivalent Static in zone IV is 30 m per Cl 7.1. At 60 m the building is twice the permitted height, and the base shear distributed as an inverted triangle down the height is no longer a valid description of its behaviour.
Likely outcome. The audit finding is written on the day the drawing is reviewed, not on the day the building shakes. The model has to be rebuilt as a Response Spectrum analysis and every member re-checked against the corrected storey shears, drifts and moments, which usually means rework of the lateral system and a fresh look at the foundations.
Frequently Asked Questions
What is the difference between Z, I and R in IS 1893?
Which IS 1893 analysis method should be used?
Why does IS 1893 limit soft storey design?
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Amit Haridas
Founder & Proprietor, ConcreteInfo. 25+ years experience in construction QA/QC, concrete technology, RMC plant operations, consulting and technical training across India. For a seismic-design audit or capacity verification, contact amit@concreteinfo.in.
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