IS 1893 (Part 1): 2016 — Equivalent Static Method

What is the Equivalent Static Method?

IS 1893 §7.6

The Equivalent Static Method (ESM) — also called the Seismic Coefficient Method — is the simplest way IS 1893 (Part 1): 2016 allows you to analyse a building for earthquake forces.

Instead of solving complex dynamic equations, the method replaces the real, time-varying earthquake force with a single equivalent horizontal force (the design base shear, V_B) applied statically at the base, then distributed up the height following a parabolic pattern.

Think of it as asking: "If I pushed the building sideways with this much force, would it be safe enough?"

Key Limitation

IS 1893 imposes strict conditions on when ESM may be used. It is valid only for regular buildings in Seismic Zone II with height < 15 m, or buildings where the approximate period T_a < 0.4 s. For all other buildings, Dynamic Analysis is mandatory (Clause 7.7).

15 m

Max height in Zone II

0.4 s

Max period T_a

Zone II

Only applicable zone (basic)

5%

Damping ratio used

When ESM IS Permitted

IS 1893 §7.6, §7.7.1

The Golden Rule — Clause 7.6

"This method shall be applicable for regular buildings with height less than 15 m in Seismic Zone II."

Clause 7.7.1 confirms: dynamic analysis is needed for all buildings other than regular buildings < 15 m in Zone II. ESM also covers cases where T_a < 0.4 s.

Three Conditions — ALL must be met

Is the building REGULAR?

No plan or vertical irregularity per Tables 5 & 6. This means no torsional irregularity, no re-entrant corners >15%, no soft storey, no mass irregularity, etc.

Is the building in Seismic Zone II?

Location must fall in Zone II on the IS 1893 Zone Map (Z = 0.10). For Zones III, IV, V — Dynamic Analysis is mandatory for most situations.

Is the building height < 15 m?

Height h measured from base (Clause 4.10) to top of roof. Basements connected to ground floor slabs are excluded from h.

✅ ESM IS Allowed

Regular building — no irregularities

Seismic Zone II only

Height < 15 m

T_a < 0.4 s

Symmetric plan with balanced stiffness

Uniform distribution of mass & stiffness

❌ ESM NOT Allowed — Use Dynamic Analysis

Any irregular building (plan or vertical)

Buildings in Zones III, IV or V

Height ≥ 15 m (unless Zone II & regular)

T_a ≥ 0.4 s

Torsionally irregular buildings

Soft storeys, weak storeys, floating columns

When ESM is NOT Permitted

IS 1893 §7.7.1, Tables 5 & 6

Clause 7.7.1 — Mandatory Dynamic Analysis

"Linear dynamic analysis shall be performed… for all buildings, other than regular buildings lower than 15 m in Seismic Zone II."

Plan Irregularities (Table 5) — Any ONE triggers Dynamic Analysis

Type	Definition	Special Requirement
i) Torsional	Max displacement > 1.5× min displacement; AND torsional mode period > translational modes	Modal dynamic analysis; if ratio ≥ 2.0, revise config
ii) Re-entrant Corners	Projection > 15% of plan dimension in that direction	3D dynamic analysis
iii) Diaphragm Discontinuity	Cut-out area ≥ 50% of floor area	Model as flexible or rigid depending on openings
iv) Out-of-Plane Offsets	Lateral elements offset out-of-plane	3D structural analysis
v) Non-Parallel System	Lateral elements not parallel to principal axes	Full 3D load combinations per 6.3.2.2–6.3.4.1

Vertical Irregularities (Table 6) — Any ONE in Zones III–V triggers Dynamic Analysis

Type	Definition	Trigger Zone
i) Soft Storey	Storey lateral stiffness < storey above; SPD < 20% triggers explicit URM modelling	III, IV, V
ii) Mass Irregularity	Seismic weight at any floor > 150% of adjacent floors	III, IV, V
iii) Vertical Geometric	Lateral system dimension > 125% of storey below	III, IV, V
iv) In-plane Discontinuity	In-plane offset > 20% of plan length	III, IV, V
v) Weak Storey	Lateral strength < 80% of storey above	III, IV, V
vi) Floating/Stub Columns	Concentrated damage zones — avoid where possible	All zones
vii) Irregular Modes	First 3 modes < 65% mass participation; or periods within 10%	II & III (65%); IV & V (stricter)

Student Note — The Hierarchy

Zone II + Regular + H < 15m → ESM allowed.
Everything else → Response Spectrum Method or Time History Method (§7.7.3).
Dynamic analysis base shear must NOT be less than ESM base shear (§7.7.3) — ESM sets the minimum floor.

Seismic Zones & Zone Factor (Z)

IS 1893 §6.4, Table 3

II

Z = 0.10

Low seismicity
ESM can apply here

III

Z = 0.16

Moderate seismicity
Dynamic analysis required

IV

Z = 0.24

High seismicity
Dynamic analysis required

V

Z = 0.36

Very high seismicity
Dynamic analysis required

Z represents the Peak Ground Acceleration (PGA) for the Maximum Considered Earthquake (MCE). The factor of ½ in A_h = (Z/2)×… accounts for design using 50% of MCE.

Step-by-Step ESM Procedure

IS 1893 §7.6.1–§7.6.3

The 5-Step ESM Workflow

Calculate Approximate Natural Period T_a (§7.6.2)

Empirical formulas based on building type and height — no dynamic model needed.

Get Spectral Acceleration S_a/g (§6.4.2)

Design acceleration coefficient from ESM spectra (Fig. 2a) based on soil type and T_a.

Compute Design Horizontal Coefficient A_h (§6.4.2)

A_h = (Z/2) × (I/R) × (S_a/g). Fraction of g used as design acceleration.

Calculate Total Seismic Base Shear V_B (§7.6.1)

V_B = A_h × W, where W = full dead load + % imposed load per Table 10.

Distribute V_B Along Height (§7.6.3)

Q_i = V_B × (W_ih_i²) / Σ(W_jh_j²). Higher floors receive greater lateral force.

Key Formulas

IS 1893 §6.4.2, §7.6.1–7.6.3

Formula 1 — Design Horizontal Seismic Coefficient (§6.4.2)

A_h = (Z/2) × (I/R) × (S_a/g)

ZZone Factor (Table 3): II=0.10, III=0.16, IV=0.24, V=0.36. Halved because Z is for MCE; design uses 50%.

IImportance Factor (Table 8): 1.0 ordinary, 1.2 occupancy >200, 1.5 hospitals/schools/lifeline.

RResponse Reduction Factor (Table 9): 1.5–5.0 depending on structural system ductility.

S_a/gSpectral Acceleration Coefficient from Fig. 2(a) ESM spectra, based on soil type and T_a.

Formula 2 — Design Base Shear (§7.6.1)

V_B = A_h × W

V_BDesign Seismic Base Shear — total equivalent horizontal earthquake force at the base.

WSeismic Weight = Dead Load + % Imposed Load (Table 10: 25% for IL ≤ 3 kN/m², 50% for IL > 3 kN/m²).

Formula 3 — Vertical Distribution (§7.6.3)

Q_i = V_B × (W_ih_i²) / Σ(W_jh_j²)

Q_iDesign lateral force at floor i — floor's share of total base shear.

h_iHeight of floor i from base (m). The h² term produces a parabolic distribution matching first-mode shape.

Approximate Natural Period T_a (§7.6.2)

Building Type	Formula
RC Bare MRF (no masonry infills)	`Tₐ = 0.075 × h⁰·⁷⁵`
RC-Steel Composite MRF	`Tₐ = 0.080 × h⁰·⁷⁵`
Steel MRF	`Tₐ = 0.085 × h⁰·⁷⁵`
RC with structural walls	`Tₐ = 0.075×h⁰·⁷⁵/√Aw ≥ 0.09h/√d`
All other buildings	`Tₐ = 0.09h / √d`

h = building height (m); d = base dimension along shaking direction (m)

Spectral Acceleration S_a/g for ESM, 5% Damping — §6.4.2(a)

Soil Type	T < 0.1 s	Plateau (T_c)	T_c < T ≤ 4.0 s	T > 4.0 s
Type I — Hard/Rocky	1 + 15T	2.5 (T_c=0.40s)	1.00/T	0.25
Type II — Medium	1 + 15T	2.5 (T_c=0.55s)	1.36/T	0.33
Type III — Soft	1 + 15T	2.5 (T_c=0.67s)	1.67/T	0.40

Minimum Design Base Shear (§7.2.2, Table 7)

Zone	Minimum V_B
Zone II	0.7% of W
Zone III	1.1% of W
Zone IV	1.6% of W
Zone V	2.4% of W

Understanding Structural Irregularities

IS 1893 Tables 5 & 6

Why Do Irregularities Matter?

Irregular buildings experience complex, amplified responses that ESM's single-force approach cannot capture. Torsional coupling, mode shape complexity, and storey-wise amplification all demand dynamic analysis. Tables 5 and 6 define the precise thresholds.

🏗️ Regular — ESM Eligible

Symmetric plan in both directions

Uniform storey height and stiffness

Mass distributed evenly per floor

No projection > 15% of plan dimension

All lateral elements parallel to axes

⚡ Irregular — Must Use Dynamic Analysis

L-shaped, T-shaped, U-shaped plans

Piloti / open ground floor (soft storey)

Heavy water tanks on roof (mass irregularity)

Setback buildings (vertical geometric)

Floating columns (concentrated damage)

ESM Eligibility Checker & Base Shear Calculator

IS 1893 (Part 1): 2016 · Equivalent Static Method

Project Information

Project Title optional

Author / Designer optional

Seismic Zone IS 1893 Table 3

Building Height h metres

Structural Type Clause 7.6.2

Soil Type Clause 6.4.2

Importance Factor I Table 8

Response Reduction Factor R Table 9

Base Dimension d m, along shaking direction

Building Regularity Tables 5 & 6

Floor-wise Seismic Weights

Floor	Height h_i (m)	Seismic Weight W_i (kN)

📋 Step-by-Step Calculations

📌 Assumptions: 5% damping (§7.2.4); ESM spectra Fig. 2(a); I & R from Tables 8 & 9; min V_B per Table 7.

Key Takeaways for Students

Remember These 5 Points for Exams

1. ESM is for regular buildings, height <15m, Zone II only (§7.6).
2. Even when using ESM, minimum V_B from Table 7 must always be satisfied.
3. Any one irregularity (Tables 5 or 6) forces Dynamic Analysis in Zones III–V.
4. The factor Z/2 accounts for design at 50% of the Maximum Considered Earthquake.
5. Dynamic analysis base shear must NOT be less than ESM base shear (§7.7.3).

Why the Parabolic Distribution (W_ih_i²)?

The first mode shape of a regular building is approximately linear — displacement increases with height. Since inertia force ∝ mass × acceleration, and acceleration ∝ displacement in harmonic motion, Q_i ∝ W_i × h_i. The squared term (h_i²) is the parabolic approximation of mode shape × height, better representing multi-storey dynamic response.

What Happens When ESM and Dynamic Analysis Disagree?

Clause 7.7.3 requires: when V_B,dynamic < V_B,ESM, all dynamic force quantities must be scaled up by V_B,ESM / V_B,dynamic. ESM always provides a conservative lower bound.