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.

5.2.1 The definitions given below shall apply for the purpose of earthquake resistant design of buildings, as enumerated in this Section.

5.2.2 Base — It is the level at which inertia forces generated in the building are considered to be transferred to the ground through the foundation. For buildings with basements, it is considered at the bottommost basement level. For buildings resting on,

a) pile foundations, it is considered to be at the top of pile cap;

b) raft, it is considered to be at the top of raft; and

c) footings, it is considered to be at the top of the footing.

For buildings with combined types of foundation, the base is considered as the bottom-most level of the bases of the constituent individual foundations as per definitions above.

5.2.3 Base Dimension (d) — It is the dimension (in metre) of the base of the building along a direction of shaking.

5.2.4 Centre of Mass (CM) — The point in the floor of a building through which the resultant of the inertia force of the floor is considered to act during earthquake shaking. Unless otherwise stated, the inertia force considered is that associated with the horizontal shaking of the building.

5.2.5 Centre of Resistance (CR)

5.2.5.1 For single storey buildings — It is the point on

the roof of a building through which when the resultant internal resistance acts, the building undergoes,

a) pure translation in the horizontal direction; and

b) no twist about vertical axis passing through the $CR$.

5.2.5.2 For multi-storey buildings — It is the set of points on the horizontal floors of a multi-storey building through which, when the resultant incremental internal resistances across those floors act, all floors of the building undergo,

a) pure translation in the horizontal direction; and

b) no twist about vertical axis passing through the $CR$.

5.2.6 Eccentricity

5.2.6.1 Design eccentricity ( $e_{di}$ ) — It is the value of eccentricity to be used for floor i in calculations of design torsion effects.

5.2.6.2 Static eccentricity $(e_{\mathrm{si}})$ — It is the distance between centre of mass (CM) and centre of resistance (CR) of floor $i$.

5.2.7 Design Seismic Base Shear ( $V_{B}$ ) — It is the horizontal lateral force in the considered direction of earthquake shaking that the structure shall be designed for.

5.2.8 Diaphragm — It is a horizontal or nearly horizontal structural system (for example, reinforced concrete floors and horizontal bracing systems), which transmits lateral forces to vertical elements connected to it.

5.2.9 Height of Floor ( $h_{i}$ ) — It is the difference in vertical elevations (in metre) of the base of the building and top of floor i of the building.

5.2.10 Height of Building (h) — It is the height of building (in metre) from its base to top of roof level,

a) excluding the height of basement storeys, if basement walls are connected with the ground floor slab or basement walls are fitted between the building columns, but

b) including the height of basement storeys, if basement walls are not connected with the ground floor slab and basement walls are not fitted between the building columns.

In step-back buildings, it shall be taken as the average of heights of all steps from the base, weighted with their corresponding floor areas. And, in buildings founded on hill slopes, it shall be taken as the height of the roof from the top of the highest footing level or pile cap level.

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

5.2.11 Horizontal Bracing System — It is a horizontal truss system that serves the same function as a diaphragm.

5.2.12 Joints — These are portions of columns that are common to beams/braces and columns, which frame into columns.

5.2.13 Lateral Force Resisting System — It is part of the structural system, and consists of all structural members that resist lateral inertia forces induced in the building during earthquake shaking.

5.2.14 Moment-Resisting Frame — It is an assembly of beams and columns that resist induced and externally applied forces primarily by flexure.

5.2.14.1 Ordinary moment-resisting frame (OMRF)—It is a moment-resisting frame designed and detailed as per relevant good practices [6-1(7)], but not meeting special detailing requirements for ductile behaviour as per good practices [6-1(8)] or [6-1(9)], as applicable.

5.2.14.2 Special moment-resisting frame (SMRF) — It is a moment-resisting frame designed and detailed as per relevant good practices [6-1(7)], and meeting special detailing requirements for ductile behaviour as per good practices [6-1(8)] or [6-1(9)], as applicable.

5.2.15 Number of Storeys $(n)$ — It is the number of levels of a building above the base at which mass is present in substantive amounts. This,

a) excludes the basement storeys, where basement walls are connected with the ground floor deck or fitted between the building columns; and

b) includes the basement storeys, when they are not so connected.

5.2.16 Core Structural Walls, Perimeter Columns, Outriggers and Belt Truss System — It is a structural system comprising a core of structural walls and perimeter columns, resisting the vertical and lateral loads, with

a) the core structural walls connected to select perimeter column element(s) (often termed outrigged columns) by deep beam elements, known as outriggers, at discrete locations along the height of the building; and

b) the outrigged columns connected by deep beam elements (often known as belt truss), typically at the same level as the outrigger elements.

A structure with this structural system has enhanced lateral stiffness, wherein core structural walls and perimeter columns are mobilized to act with each other

through the outriggers, and the perimeter columns themselves through the belt truss. The global lateral stiffness is sensitive to: flexural stiffness of the core element, the flexural stiffness of the outrigger element(s), the axial stiffness of the outrigged column(s), and the flexural stiffness of the outrigger elements connecting the core structural walls to the perimeter columns.

5.2.17 Principal Plan Axes — These are two mutually perpendicular horizontal directions in plan of a building along which the geometry of the building is oriented.

5.2.18 P- $\Delta$ Effect — It is the secondary effect on shear forces and bending moments of lateral force resisting elements generated under the action of the vertical loads, interacting with the lateral displacement of building resulting from seismic effects.

5.2.19 RC Structural Wall — It is a wall designed to resist lateral forces acting in its own plane.

5.2.19.1 Ordinary RC structural wall — It is a reinforced concrete (RC) structural wall designed and detailed as per good practice [6-1(10)], but not meeting special detailing requirements for ductile behaviour as per good practice [6-1(8)].

5.2.19.2 Special RC structural wall — It is a RC structural wall designed and detailed in accordance with and meeting special detailing requirements for ductile behaviour, as per good practice [6-1(8)].

5.2.20 Storey — It is the space between two adjacent floors.

5.2.20.1 Soft storey — It is one in which the lateral stiffness is less than that in the storey above. The storey lateral stiffness is the total stiffness of all seismic force resisting elements resisting lateral earthquake shaking effects in the considered direction.

5.2.20.2 Weak storey — It is one in which the storey lateral strength [cumulative design shear strength of all structural members other than that of unreinforced masonry (URM) infills] is less than that in the storey above. The storey lateral strength is the total strength of all seismic force resisting elements sharing the lateral storey shear in the considered direction.

5.2.21 Storey Drift — It is the relative displacement between the floors above and/or below the storey under consideration.

5.2.22 Storey Shear ( $V_{i}$ ) — It is the sum of design lateral forces at all levels above the storey i under consideration.

5.2.23 Storey Lateral Shear Strength $(S_{\mathrm{i}})$ — It is the total lateral strength of all lateral force resisting

elements in the storey considered in a principal plan direction of the building.

5.2.24 Storey Lateral Translational Stiffness ( $K_{i}$ ) — It is the total lateral translational stiffness of all lateral force resisting elements in the storey considered in a principal plan direction of the building.

5.2.25 RC Structural Wall Plan Density ( $\rho_{sw}$ ) — It is the ratio of the cross-sectional area at the plinth level of RC structural walls resisting the lateral load and the plinth of the building, expressed as a percentage.