C V R Murty

Torsional response of buildings is attributed to poor structural configurations in plan, which arises due to two factors – torsional eccentricity and torsional flexibility. Usually, building codes address effects due to the former. This study examines both of these effects. Buildings with torsional eccentricity (e.g., those with large eccentricity) and with torsional flexibility (those with torsional mode as a fundamental mode) demand large deformations of vertical elements resisting lateral loads, especially those along the building perimeter in plan. Lateral-torsional responses are studied of unsymmetrical buildings through elastic and inelastic analyses using idealised single-storey building models (with two degrees of freedom). Displacement demands on vertical elements distributed in plan are non-uniform and sensitive to characteristics of both structure and earthquake ground motion. Limits are proposed to mitigate lateral-torsional effects, which guides in proportioning vertical elements and restricts amplification of lateral displacement in them and to avoid torsional mode as the first mode. Nonlinear static and dynamic analyses of multi-storey buildings are used to validate the limits proposed.

Seismic design codes permit the use of Equivalent Static Analysis of buildings considering torsional eccentricity e with dynamic amplification factors on structural eccentricity and some accidental eccentricity. Estimation of e in buildings is not addressed in codes. This paper presents a simple approximate method to estimate e in RC Moment Frame and RC Structural Wall buildings, which required no detailed structural analysis. The method is validated by 3D analysis (using commercial structural analysis software) of a spectrum of building. Results show that dynamic amplification factor should be applied on torsional eccentricity when performing Response Spectrum Analysis also. Also, irregular or mixed modes of oscillation arise in torsionally unsymmetrical buildings owing to poor geometric distribution of mass and stiffness in plan, which is captured by the mass participation ratio. These irregular modes can be avoided in buildings of any plan geometry by limiting the two critical parameters (normalised torsional eccentricity e/B and Natural Period Ratio τ =Tθ/T, where B is building lateral dimension, Tθ uncoupled torsional natural period and T uncoupled translational natural period). Suggestions are made for new building code provisions.

This article presents probabilistic seismic hazard analysis (PSHA) of India and adjoined region, carried out to develop a new national seismic hazard map for India. The hazard map is developed using fault oriented spatially smoothed seismicity approach. A catalog of earthquakes has been compiled for the region (Latitude 50N − 400 N and Longitude 650E − 1000E) from 2600BCE to 2019CE to estimate the seismicity parameters. Eighteen suitable ground motion prediction equations in the logic tree framework are used for the four major geological regions of the country. The hazard is estimated at rock sites (B-C boundary type) conditions in terms of peak ground acceleration (PGA), short-period (0.2 s), and long-period (1s) spectral acceleration maps and uniform hazard spectra, with 2% and 10% probabilities of exceedance in 50 years. Higher hazard values are observed in the Hindukush-Pamir regions and Northeast India, whereas central India and the southern peninsular regions are less prone to seismic threat. The proposed maps find their application in the seismic design of structures, risk assessment, and as an input for updating the existing code provisions.

An analytical method is presented to estimate lateral shear strength (and identify likely mode and location of failure) in reinforced concrete (RC) cantilever columns of rectangular cross-section under combined axial force, shear force and bending moment. Change in shear capacity of concrete with flexural demand at a section is captured explicitly and the shear resistance offered by concrete estimated; this is combined with shear resistance offered by transverse and longitudinal reinforcement bars to estimate the overall shear capacity of RC columns. Shear–moment (V-M) interaction capacity diagram of an RC column, viewed alongside the demand diagram, identifies the lateral shear strength and failure mode. These analytical estimates compare well with test data of 107 RC columns published in literature; the test data corresponds to different axial loads, transverse reinforcement ratios, longitudinal reinforcement ratios, shear span to depth ratios, and loading conditions. Also, the analytical estimates are compared with those obtained using other analytical methods reported in literature; in all cases, the proposed method gives reasonable accuracy when estimating shear capacity of RC columns. In addition, the method provides insights into the shear resistance mechanism in RC columns under the combined action of P-V-M, and it is simple to use.

Earthquake Resistant Design Philosophy seeks (a) no damage, (b) no significant structural damage, and (c) significant structural damage but no collapse of normal buildings, under minor, moderate and severe levels of earthquake shaking, respectively. A procedure is proposed for seismic design of low-rise reinforced concrete special moment frame buildings, which is consistent with this philosophy; buildings are designed to be ductile through appropriate sizing and reinforcement detailing, such that they resist severe level of earthquake shaking without collapse. Nonlinear analyses of study buildings are used to determine quantitatively (a) ranges of design parameters required to assure the required deformability in normal buildings to resist the severe level of earthquake shaking, (b) four specific limit states that represent the start of different structural damage states, and (c) levels of minor and moderate earthquake shakings stated in the philosophy along with an extreme level of earthquake shaking associated with the structural damage state of no collapse. The four limits of structural damage states and the three levels of earthquake shaking identified are shown to be consistent with the performance-based design guidelines available in literature. Finally, nonlinear analyses results are used to confirm the efficacy of the proposed procedure.

This paper presents the results of a study on the characteristics of vertical-to-horizontal ratio (V/H) of 5% damped acceleration spectra for Indian ground motion records. Preliminary analysis indicates that at least 50% of the records exceed the Indian seismic design code considered norm of 2/3 at both the short and long period ranges. In addition, currently there are no V/H spectral ratio models available for India and the global models do not capture the trend across all the periods efficiently. Therefore, new ground motion models for the V/H spectral ratio are derived for two of the active tectonic regions of India: the Western Himalayas and the North-East India. Moment magnitude, focal depth, distance, site soil class, and focal mechanism are considered while deriving these models for a wide range of spectral periods (0.01–10s). The goodness of these models is verified through comparison with other globally available V/H models.

A seismic design method is proposed for RC frame buildings, with focus on two of the seven virtues of earthquake resistant buildings, namely deformation capacity and desirable collapse mechanism. Fundamental lateral translation mode of the building and plastic rotation capacity of beams are included as input to estimate lateral force demand. Guidelines are provided to proportion beam and column cross-sections through: (a) closed-form expressions of flexural rigidities to maximize participation of the fundamental mode, and (b) relative achievable plastic rotation capacity using current design and detailing practice. This method is seen to surpass two prominent displacement-based design methods reported in literature. Results of nonlinear static pushover and nonlinear time history analyses of buildings of three different heights designed by this and the said two methods are used to make a case for the proposed method; the proposed method is able to control plastic rotation demand in beams and provide at least 20% more lateral deformation capacity than the said methods.

Torsionally flexible buildings (that have torsional mode as fundamental mode) twist during earthquake shaking, and may collapse partially or completely depending upon the direction and level of shaking. The problem is aggravated when the building is torsionally unsymmetrical. Some design codes (like Eurocode, Indian Code) explicitly prohibit the design of such buildings. This paper presents a simple approximate method to identify torsionally flexible RC Moment Frame and RC Structural Wall buildings at the initial proportioning stage itself without carrying out a detailed structural analysis. It is possible to identify whether or not the first mode is torsional mode of a building (i.e., torsionally flexible building) if Natural Period Ratio τ>1 by modelling the building with rigid diaphragm and distribution of mass & stiffness along the height of building, and estimating: (1) radius of gyration of rotational mass rm of each floor plan geometry by lumping the masses of slabs, beams and all vertical elements at each nodes, (2) radius of gyration of twisting stiffness rKθ of all vertical elements using their translational and torsional stiffnesses (considering flexibility of adjoining beams and vertical elements accounting for both flexural and shear deformations), and (iv) τ (=rm/rKθ). The method is validated with 3D Modal Analysis (using τ =Tθ/T, where Tθ is Uncoupled Torsional Natural Period and T Uncoupled Translational Natural Period) of hypothetical buildings using a commercial structural analysis software. Also, parameters are identified that lead to τ>1, and solutions suggested to avoid torsional flexibility in buildings. Further, the method helps identify vertical stiffness irregularity in buildings. Draft provisions are suggested for inclusion in seismic codes. Also, poor performance of multi-storey building (with τ>1) is demonstrated using nonlinear static and nonlinear time history analyses.