Base Shear

Base shear (Vb) is the total horizontal force at the base of a structure caused by ground motion during a design earthquake. It represents the inertial reaction of the structure's mass to ground acceleration. Per IS 1893 Part 1:2016 Cl. 7.5, the design base shear is computed by the equivalent static method (for regular buildings up to 40 m height) as Vb = Ah × W, where Ah is the design horizontal seismic coefficient and W is the seismic weight of the structure (DL + 25-50% LL per Cl. 7.4.5).

The coefficient Ah = (Z/2) × (I/R) × (Sa/g) accounts for the four key parameters of seismic design: zone factor Z reflecting hazard (0.10-0.36), importance factor I reflecting consequence (1.0-1.5), response reduction factor R reflecting ductility (3-5), and Sa/g reflecting structural period (read from IS 1893 Fig. 2 for the building's natural period T computed via Cl. 7.6). For a typical residential 5-storey RCC SMRF in Mumbai (Zone III, I = 1.0, R = 5.0, T ≈ 0.5s for hard soil giving Sa/g ≈ 2.5): Ah = (0.16/2) × (1.0/5.0) × 2.5 = 0.04, so Vb ≈ 4% of seismic weight.

Once computed, Vb is distributed over the building height per Cl. 7.7.1 — the storey shear at level i: Qi = Vb × (Wi × hi²) ÷ Σ(Wi × hi²), placing larger storey shears near the top of the building (the 'inverted triangle' distribution). For irregular buildings (vertical or horizontal), tall buildings (>40 m), or buildings in Zone IV/V, dynamic analysis (response spectrum or time history) per Cl. 7.8 is mandatory and replaces the static method. Modern Indian design typically performs the static method as a first pass and the dynamic method as the design-of-record per software default.