Multistorey RC framed buildings, irregular in plan, often exhibit unfavorable seismic behaviour. In this study, the influence of the earthquake incidence angle on the seismic response of irregular RC framed buildings is examined. Three multistory RC buildings, One regular in plan and Two plan irregular buildings (C-shape, L-shape) are investigated for critical seismic incidence angle. For a good comparison, all the three buildings having the same floor plan area are modeled. The Linear Time History Analysis (LTHA) has been carried out for these three buildings by considering the twelve different earthquake directions and rotating the direction by 15o for each analysis, ranging from 0o to 180o . All these three buildings are modeled using ETABS Software and are subjected to Northridge earthquake accelerogram. It is observed from the study that, the seismic behavior of these three buildings is considerably influenced by the seismic incidence angle. The various parameters observed in this study are axial forces in columns, storey drift, storey shear and maximum storey displacement. The results reveal that the direction of earthquake incidence angle considerably influences the response of multistorey RC buildings.
Buildings having simple regular geometry and uniformly distributed mass and stiffness in plan as well as in elevation suffer much less damage than buildings with irregular configurations. It is learnt from the past earthquakes that the multistorey buildings irregular in plan, is one of the most frequent sources of severe damage. In this study, multistory RC buildings are analyzed by Linear Time History Analysis. In this technique, the mathematical model of the building is subjected to accelerations from earthquake records that represent the expected earthquake at the base of the structure.
Three multistorey RC buildings, One regular in plan and two plan irregular models are considered in the present study. Three buildings i.e. Regular, C-shaped and L-shaped buildings are modeled in ETABS. The seismic input has been applied in 12 different directions ranging from 0o to 180o with an increment of 15o . Three multistorey RC buildings are analyzed by Linear Time History Analysis for ground acceleration data recorded at the station Los Angeles- Baldwin hills for Northridge Earthquake occurred on January 17, 1994. The various parameters observed in this study are axial forces in columns, storey drift, storey shear and maximum storey displacement.
The primary objective of this study is to investigate the influence of earthquake incidence angle on seismic response of the multi-storey RC buildings. The buildings are subjected to Northridge earthquake accelerogram in twelve directions ranging from 0o and 180o degrees, with an increment of 15o .
The main objectives of the present study are as follows:
Mahmood Hosseini and Ali Salemi (2008) carried out the Nonlinear Time History Analysis (NLTHA) on two 5-storey steel buildings with square and rectangular plan configurations using the accelerograms of two horizontal components of previously recorded earthquakes. Accelerograms used in this study are having the same PGA level and angle of excitation varies from 0o to 90o with an increment of 10o . It was observed that column axial forces enhanced by around 50% by varying the seismic angle of excitation.
Paolo Emidio Sebastiani, Laura Liberatore, Andrea Lucchini and Fabrizio Mollaioli (2014) studied the effect of directionality on the building response by means of nonlinear dynamic analyses. The seismic incidence angles are varied from 0o to 180o , with an increment of 22.5o. They observed that the equivalent linear and nonlinear two d.o.f. models are adequate to predict the most critical angle of incidence.
Antonio Bruno Rigato (2007) investigated the influence of seismic angle of incidence of the applied bi-directional ground motions on various parameters for inelastic structures. The models considered plan irregularities, various degrees of inelasticity, 5% damping ratios, and fundamental periods that ranged from 0.2 sec. to 2.0 sec. They observed that the critical seismic incidence angle is varying with the increase in degree of inelasticity.
C. Cantagallo, G. Camata and E. Spacone (2012) studied the seismic directionality effects by considering four different structures subjected to different scaled and unscaled bi-directional ground motion records oriented along nine incidence angles, whose values are from 0o and 180o , with an increment of 22.5o.
I.-K.M. Fontara, K.G. Kostinakis and A.M. Athanatopoulou (2012) investigated the influence of orientation of the ground-motion reference axes, the seismic incidence angle and the seismic intensity level on the inelastic response of asymmetric RC buildings.
A study considering the bi-directional effects and the seismic angle variations in building design is carried out by Iván Fernandez-Davila, Silvana Cominetti and Ernesto F Cruz (2000). Different parameters such as the transverse seismic component and the variation of incidence angle of the ground motion are studied. They observed that the maximum response in any structural element due to the application of a bi-directional seismic movement with the angle of variable incidence may not coincide with any of the two principal directions of the building.
M.A. Archila and C.E. Ventura (2012) studied the effect of ground motion directionality on seismic response of tall buildings. Their work demonstrates the sensitivity of the nonlinear dynamic response of tall buildings to the horizontal ground motion directionality. A 44 storey RS building located in downtown Vancouver, British Columbia, Canada is taken for the case study. Numerous Non-linear Time History Analyses were performed on the structural models considered using the recorded horizontal groundmotion orthogonal components. Their study reveals that the ground motion directionality is very important for the non-linear analysis of tall buildings and this has to be taken into account, for better seismic resistance.
SriKanya and B D V Chandra Mohan Rao (2015) studied the influence of earthquake incidence angle on the seismic response of irregular RC framed buildings (+ Shape, HShape).
Time-History Analysis is a step-by-step analysis of the dynamic response of a structure to a specified loading that may vary with time. The analysis may be linear or nonlinear. This study describes Time-History Analysis in general, and linear time-history analysis in particular. Time - history analysis is used to determine the dynamic response of a structure to arbitrary loading. The dynamic equilibrium equations to be solved are given by:
where, K is the stiffness matrix; C is the damping matrix; M is the diagonal mass matrix; u, u&, and u&& are the displacements, velocities, and accelerations of the structure respectively; and r is the applied load. If the load includes ground acceleration, the displacements, velocities, and accelerations are relative to this ground motion.
The load, r(t), applied in a given time-history case may be an arbitrary function of space and time. It can be written as a finite sum of spatial load vectors, pi, multiplied by time functions, f i (t), as:
The program uses load patterns and/or acceleration loads to represent the spatial load vectors. The time functions can be arbitrary functions of time or periodic functions such as those produced by wind or sea wave loading.
If acceleration loads are used, the displacements, velocities, and accelerations are all measured relative to the ground. The time functions associated with the acceleration loads mx, my, and mz are the corresponding components of uniform ground acceleration, u&&gx, u&&gy, and u&&gz respectively.
In the present study, 5 storey building frame is considered for performing Time History Analysis of ground acceleration data recorded at station Los Angeles - Baldwin Hills for Northridge earthquake occurred on January 17, 1994. The same analysis is performed for the following models of buildings:
The general specifications of the buildings are given in Table 1.
Table 1. General Specifications of Buildings
The 3D view of regular building is shown in Figure 1. Typical plan views of all buildings are shown from Figure 2 to Figure 4 and Accelerogram of Northridge Earthquake is shown in Figure 5.
Figure 1. 3D View of Regular Building
Figure 2. Plan View of Regular Building
Figure 3. Plan View of C-Shape Building
Figure 4. Plan View of L-Shape Building
Figure 5. Accelerogram of Northridge Earthquake
The results of Time History Analysis in the form of maximum column forces, maximum displacement and storey shear for all the buildings and their percentage variation with respect to regular building were studied.
The values of maximum column forces and the variation with incidence angle is shown in Figure 6 and Table 2.
Figure 6. Column Axial Forces Variation with Incidence Angle
Table 2. Maximum Column Axial Forces
For Regular building, the maximum column forces occurred when the peak ground acceleration is applied at 135 degrees, the value increased by 54% with respect to 0 degrees. For C shaped building, the maximum column forces have occurred when the peak ground acceleration is applied at 45 degrees, the value increased by 32% with respect to 0 degrees. For L shaped building, the maximum column forces have occurred when the peak ground acceleration is applied at 45 degrees, the value increased by 40% with respect to 0 degrees. Sri Kanya M. and Chandra Mohan Rao (2015).
The values of maximum storey displacement and the variation with incidence angle is shown in Figure 7 and Table 3.
Figure 7. Maximum Storey Displacement Variation with Incidence Angle
Table 3. Maximum Storey Displacement
For Regular shaped building, the maximum storey displacement occurred when the peak ground acceleration is applied at 180 degrees, the value increased by 10% with respect to 0 degrees. For C shaped building, the maximum storey displacement occurred when the peak ground acceleration is applied at 180 degrees, the value increased by 4% with respect to 0 degrees. For L shaped building, the maximum storey displacement occurred when the peak ground acceleration is applied at 180 degrees, the value increased by 5% with respect to 0 degrees.
The values of maximum storey shear and the variation with incidence angle is shown in Figure 8 and Table 4.
Figure 8. Maximum Storey Shear Variation with Incidence Angle
Table 4. Maximum Storey Shear
For Regular shaped building, the maximum storey shear has occurred when the peak ground acceleration is applied along with principal axes (0 and 90 degrees), no percentage variation was observed with respect to 0 degrees. For C shaped building, the maximum storey shear have occurred when the peak ground acceleration is applied at 0 degrees itself. For L shaped building, the maximum storey shear has occurred when the peak ground acceleration is applied at 0 degrees itself.
The values of maximum storey drift and the variation with incidence angle is shown in Figure 9 and Table 5.
Figure 9. Maximum Storey Drift Variation with Incidence Angle
Table 5. Maximum Storey Drift
For Regular shaped building, the maximum storey drift has occurred when the peak ground acceleration is applied at 180 degrees, the value increased by 2% with respect to 0 degrees. For C shaped building, the maximum storey drift has occurred when the peak ground acceleration is applied at 180 degrees, the value increased by 7% with respect to 0 degrees. For L shaped building, the maximum storey drift has occurred when the peak ground acceleration is applied along with principal axes (0 and 90 degrees).
It is concluded that regular and irregular buildings have shown a considerable increase in maximum column forces when the peak ground acceleration is subjected to various incidence angles. There has been no considerable changes in maximum storey displacement, maximum storey shear and storey drift.
It is observed that the internal forces of structural elements depend on the angle of incidence of seismic wave with respect to the axes of the building plan. Among various internal forces, the axial forces of columns are more sensitive to the angle of incidence.
For regular shape building, the maximum column forces occur at an incidence angle 135 degrees whereas for C and L shape buildings, the maximum column forces occur at 45 degrees.
It can be inferred that C and L shaped building is more vulnerable to earthquakes than the regular shaped buildings.
The present study may be helpful to the structural engineering community while planning the buildings for better seismic resistance.
The present research work can be further extended
