Chapter 5Seismic Force

This clause primarily deals with earthquake hazard assessment and earthquake-resistant design of buildings.

All structures, like parking structures, security cabins and ancillary structures need to be designed for

10A VALUES OF THE CROSS WIND FORCE SPECTRUM COEFFICIENT FOR SQUARE SECTION BUILDINGS

10B VALUES OF THE CROSS WIND FORCE SPECTRUM COEFFICIENT FOR 2:1 AND 1:2 RECTANGULAR SECTION BUILDINGS

FIG. 10 WIND FORCE SPECTRUM COEFFICIENT

appropriate earthquake effects as per this clause. Also, temporary elements, such as scaffolding and temporary excavations, need to be designed as per this clause. This clause does not deal with construction features relating to earthquake-resistant buildings and other

structures. For guidance on earthquake-resistant construction of buildings, reference may be made to the latest revisions of the following good practice [6 1(6)].

The provisions of this clause are applicable even to critical and special structures, like nuclear power plants and petroleum refinery plants. For such structures, additional requirements may be imposed based on special studies, such as site-specific hazard assessment. In such cases, the earthquake effects specified by this clause shall be taken as at least the minimum.

For the purpose of this clause the symbols given at Annex G are applicable.

For the purpose of this clause, definitions given below shall apply to all structures, in general. For definition of terms pertaining to soil mechanics and soil dynamics, reference may be made to Part 6 ‘Structural Design, Section 2 Soils and Foundations’ of the Code; and for definition of terms pertaining to ‘Loads’, 3.2 and 4.3 may be referred.

5.1.1 Closely-Spaced Modes — Closely-spaced modes of a structure are those of the natural modes of oscillation of a structure, whose natural frequencies differ from each other by 10 percent or less of the lower frequency.

5.1.2 Critical Damping — The damping beyond which the free vibration motion will not be oscillatory.

5.1.3 Damping — The effect of internal friction, inelasticity of materials, slipping, sliding, etc, in reducing the amplitude of oscillation; it is expressed as a fraction of critical damping (see 5.1.2).

5.1.4 Design Acceleration Spectrum — Design acceleration spectrum refers to an average smoothened graph of maximum acceleration as a function of natural frequency or natural period of oscillation for a specified damping ratio for the expected earthquake excitations at the base of a single degree of freedom system.

5.1.5 Design Horizontal Acceleration Coefficient $(A_{\mathrm{h}})$ — It is a horizontal acceleration coefficient that shall be used for design of structures.

5.1.6 Design Horizontal Force — It is the horizontal seismic force prescribed by this Section that shall be used to design a structure.

5.1.7 Ductility — It is the capacity of a structure (or its members) to undergo large inelastic deformations without significant loss of strength or stiffness.

5.1.8 Epicentre — It is the geographical point on the

PART 6 STRUCTURAL DESIGN — SECTION 1 LOADS, FORCES AND EFFECTS

surface of earth vertically above the point of origin of the earthquake.

5.1.9 Floor Response Spectrum — It is the response spectrum (for a chosen material damping value) of the time history of the shaking generated at a floor of a structure, when the structure is subjected to a given earthquake ground motion at its base.

5.1.10 Importance Factor (I) — It is a factor used to estimate design seismic force depending on the functional use of the structure, characterized by hazardous consequences of its failure, post-earthquake functional needs, historical value, or economic importance.

5.1.11 Intensity of Earthquake — It is the measure of the strength of ground shaking manifested at a place during the earthquake, and is indicated by a roman capital numeral on the MSK scale of seismic intensity (see Annex H).

5.1.12 Liquefaction — It is a state primarily in saturated cohesionless soils wherein the effective shear strength is reduced to negligible value for all engineering purposes, when the pore pressure approaches the total confining pressure during earthquake shaking. In this condition, the soil tends to behave like a fluid mass (see Annex J).

5.1.13 Lithological Features — Features that reflect the nature of the geological formation of the earth's crust above bed rock characterized on the basis of structure, mineralogical composition and grain size.

5.1.14 Modal Mass ( $M_{k}$ ) in Mode (k) of a Structure — It is a part of the total seismic mass of the structure that is effective in natural mode k of oscillation during horizontal or vertical ground motion.

5.1.15 Modal Participation Factor ( $P_{k}$ ) in Mode (k) of a Structure — The amount by which natural mode k contributes to overall oscillation of the structure during horizontal or vertical earthquake ground motion. Since the amplitudes of mode shapes can be scaled arbitrarily, the value of this factor depends on the scaling used for defining mode shapes.

5.1.16 Modes of Oscillation — See 5.1.19.

5.1.17 Mode Shape Coefficient ( $\phi_{ik}$ ) — It is the spatial deformation pattern of oscillation along degree of freedom i, when the structure is oscillating in its natural mode k. A structure with N degrees of freedom possesses N natural periods and N associated natural mode shapes. These natural mode shapes are together presented in the form of a mode shape matrix [ $\phi$ ], in which each column represents one natural mode shape. The element $\phi_{ik}$ is called the mode shape coefficient

associated with degree of freedom $i$, when the structure is oscillating in mode $k$.

5.1.18 Natural Period ( $T_{k}$ ) in Mode (k) of Oscillation — The time taken (in second) by the structure to complete one cycle of oscillation in its natural mode k of oscillation.

5.1.18.1 Fundamental lateral translational natural period $(T_{1})$ — It is the longest time taken (in second) by the structure to complete one cycle of oscillation in its lateral translational mode of oscillation in the considered direction of earthquake shaking. This mode of oscillation is called the fundamental lateral translational natural mode of oscillation. A three-dimensional model of a structure will have one such fundamental lateral translational mode of oscillation along each of the two orthogonal plan directions.

5.1.19 Normal Mode of Oscillation — The mode of oscillation in which there are special undamped free oscillations in which all points on the structure oscillate harmonically at the same frequency (or period), such that all these points reach their individual maximum responses simultaneously.

5.1.20 Peak Ground Acceleration — It is the maximum acceleration of the ground in a given direction of ground shaking. Here, the acceleration refers to that of the horizontal motion, unless specified otherwise.

5.1.21 Response Reduction Factor(R) — It is the factor by which the base shear induced in a structure, if it were to remain elastic, is reduced to obtain the design base shear. It depends on the perceived seismic damage performance of the structure, characterized by ductile or brittle deformations, redundancy in the structure, or overstrength inherent in the design process.

5.1.22 Response Spectrum — It is the representation of maximum responses of a spectrum of idealized single degree freedom systems of different natural periods but having the same damping, under the action of the same earthquake ground motion at their bases. The response referred to here can be maximum absolute acceleration, maximum relative velocity, or maximum relative displacement.

5.1.23 Response Acceleration Coefficient of a Structure $(S_{\mathrm{a}}/\mathrm{g})$ — It is a factor denoting the normalized design acceleration spectrum value to be considered for the design of structures subjected to earthquake ground shaking; this value depends on the natural period of oscillation of the structure and damping to be considered in the design of the structure.

5.1.24 Seismic Mass of a Floor — It is the seismic

weight of the floor divided by acceleration due to gravity.

5.1.25 Seismic Mass of a Structure — It is the seismic weight of a structure divided by acceleration due to gravity.

5.1.26 Seismic Weight of a Floor (W) — It is the sum of dead load of the floor, appropriate contributions of weights of columns, walls and any other permanent elements from the storeys above and below, finishes and services, and appropriate amounts of specified imposed load on the floor.

5.1.27 Seismic Weight of a Structure $(W)$ — It is the sum of seismic weights of all floors.

5.1.28 Seismic Zone Factor (Z) — It is the value of peak ground acceleration considered by this Section for the design of structures located in each seismic zone.

5.1.29 Time History Analysis — It is an analysis of the dynamic response of the structure at each instant of time, when its base is subjected to a specific ground motion time history.