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### 20320140506002 2

1. 1. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online), Volume 5, Issue 6, June (2014), pp. 10-15 © IAEME 10 INVESTIGATION OF THE CRITICAL DIRECTION OF SEISMIC FORCE FOR THE ANALYSIS OF R.C.C FRAMES Sohel Ahmed Quadri Mangulkar Madhuri N P.G Student, Dept. of Structural Asst Professor Dept. of Structural Engineering, J.N.E.C, Aurangabad Engineering, J.N.E.C, Aurangabad (M.S).India (M.S).India ABSTRACT A simple method which can be applied in seismic codes to determine the critical angle of seismic incidence is proposed in this paper. Two 4-story reinforced concrete buildings with moment resisting frames, one with square and the other with rectangular plan, have been analysed by Equivalent Static Method of analysis. A set of values from 0 to 90 degrees, with an increment of 10 degrees, have been used for angle of excitation. Buildings’ columns have been divided into three main categories, including corner, side, and internal columns, and axial force and bending moment values in different columns, have been investigated in all cases. The results show that the axial forces of columns may exceed the ordinary cases up to 13% by varying the angle of excitation. Each column gets its maximum axial force and moments with a specific angle of excitation, which is not 0 or 90 degree necessarily, and it varies from column to column. Keywords: Angle of Excitation, Equivalent Static method, IS 1893:2002 (Part-1) Provisions, Columns Axial Forces, Moments. 1. INTRODUCTION An earthquake can be explained in the horizontal plane as two orthogonal acceleration components of different intensities, which can excite a structure with any horizontal incidence angle. This situation is assumed in several codes considering two orthogonal components of equal intensities. Although in the seismic design of structures the directions of ground motion incidence are usually applied along the fixed structural reference axis, it is known that for most world tectonic regions the ground motion can act along any horizontal direction; therefore, this implies the existence of a possible different direction of seismic incidence that would lead to an increase of structural response. Critical angles are earthquake incidence angles producing critical responses. INTERNATIONAL JOURNAL OF CIVIL ENGINEERING AND TECHNOLOGY (IJCIET) ISSN 0976 – 6308 (Print) ISSN 0976 – 6316(Online) Volume 5, Issue 6, June (2014), pp. 10-15 © IAEME: www.iaeme.com/ijciet.asp Journal Impact Factor (2014): 7.9290 (Calculated by GISI) www.jifactor.com IJCIET ©IAEME
2. 2. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online), Volume 5, Issue 6, June (2014), pp. 10-15 © IAEME 11 The maximum structural response associated to the directions of ground seismic motions has been examined in several papers. Lopez and Torres (1997) have tried to present a simple method, which can be applied to determine the critical angle of seismic incidence and the corresponding peak response of structures subjected to two horizontal components applied along any arbitrary directions and to the vertical component of earthquake ground motion. In their method the seismic components are given in terms of response spectra that may be equal or have different spectral shapes. In that study the structures are discrete, linear systems with viscous damping. Their method, which is based on the response spectrum method of analysis, requires. For the general case of three arbitrary response spectra, their method requires the solution of five seismic loading cases. These procedures are usually identified in technical literature as complete quadratic combination rule with three seismic components or CQC3. A more accurate structural response can be obtained with equilibrium static method of analysis; however, for practical applications it requires the use of several ground motions and hence enormous numerical efforts. Several examples of this procedure are presented in technical literature. See for Fernández-Dávila (2000), Mahmood Hosseini and Ali salami (2008). In this study two set of 4-story reinforced concrete buildings with moment resisting frames, one with square and the other with rectangular plan, have been analysed by Equivalent Static Method of analysis. A set of values from 0 to 90 degrees, with an increment of 10 degrees, have been used for angle of excitation. The details of study and its result are described briefly in the following section of paper. 2. PARAMETRIC DETAILS OF MODELS WHICH ARE STUDIED In this work we consider the following two structures for the seismic analysis. Figure 1: Square Structure Figure 2: Rectangular Structure The basic specifications of above Structures are: In square structure dimensions of all the beams from B1 to B9 are =0.23m x 0.45m and all the columns from C1 to C9 are = 0.3m x 0.3 m. In rectangular structure dimensions of all the beams from B1 to B6 are = 0.23 m × 0.38 m; and all the beams from B7 to B12 are = 0.23 m × 0.45 m. M20, Fe415 materials are used for both the structure. The structures are assumed to be located in seismic Zone - V on a site with hard soil. Response reduction factor as 5 for special moment resisting frame is considered for seismic analysis.
3. 3. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online), Volume 5, Issue 6, June (2014), pp. 10-15 © IAEME 12 3. METHOD OF ANALYSIS The present study undertaken deals with Linear Static Method of Analysis or Equivalent Static Method of Analysis of 3D frames that can be used for regular structure with limited height. For the 3D modelling and analysis of the Structure standard software package is used. Seismic force is applied with incidence angle of 0 to 90 degrees, with an increment of 10 degrees and column forces have been investigated in all cases. The columns have been divided into three main categories, including corner, side, and internal columns. The natural period of the building is calculated by the expression, T=0.09H/√D as per IS 1893:2002(part1), where H is the height and D is the base dimension of the building in the considered direction of vibration. The lateral load calculation and its distribution along the height are done as per B.I.S provisions. The seismic weight is calculated using full dead load plus 25% of live load. Load combinations as per clause 6.3.1.2 of IS 1893:2002 (Part-1) are considered. 4. NUMERICAL RESULTS AND DISCUSSION Among different internal forces following variation were observed in axial forces of columns. Figure 3: Axial force variation for corner columns of square plan Figure 4: Axial force variation for corner columns of rectangular plan.
4. 4. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online), Volume 5, Issue 6, June (2014), pp. 10-15 © IAEME 13 Figure 3 and 4 represents the increase in axial force with respect to angle of seismic incidence from 0 to 90 degrees with an increment of 10 degrees in all the corner columns of square and rectangular structure respectively. Table 1 shows the percent variation of axial force of columns of the first storey for various maximizing cases with respect to the base case. Table 1: Percentage of variation of axial force in column in various cases Building Plane Shape Column Category Critical Angle Variation Percent Square Corner 49 12.55% Side 10 0.34% Middle 90 - Rectangular Corner 52 7.84% Side 10 0.31 Middle 90 - It can be seen in Table 1 that the maximum axial force in each column may occur by a specific angle of seismic incidence, which is different from the critical angle for other columns. It should be mentioned that the maximum variations does not necessarily belong to the same column in each category. The variation in moments due to the effect of critical direction of seismic force for square structure is shown in table 2. Table 2: variation of moments in columns for square structure COLUMN CATEGORY COLUMN NAME Critical angle Moments in KN for (0 or 90 degree) Moments in KN for critical angle My Mz My Mz Corner C1 49 -3.193 -65.108 -49.923 -43.814 C7 49 65.108 -3.193 43.814 -49.923 C3 49 -3.193 65.108 -43.814 49.923 C9 49 65.108 3.193 49.923 43.814 SIDE C2 10 -66.259 0 -65.292 13.087 C4 10 0 -66.259 -13.087 -65.292 C6 10 0 66.259 13.087 65.292 C8 10 66.259 0 65.292 -13.087 It is seen in table 2 that maximum bending moment in the entire corner columns were obtained by applying seismic force at an angle of 49 degree. It is observed for column one and seven that bending moments in one direction decreases by 32.70% but bending moments in other direction increases 15.635 times, similarly for column three and nine the bending moments in one direction decreases by 23.29% but bending moments in other direction increases13.712 times which makes seismic incidence angle 49 degree critical. Maximum bending moment in the entire side columns
5. 5. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online), Volume 5, Issue 6, June (2014), pp. 10-15 © IAEME 14 were obtained by applying seismic force at an angle of 10 degree. All the side columns which were uni-axial become biaxial column. This makes seismic incidence angle 10 degree critical. The bending moment in central column occurs mainly by applying seismic force at an angle of incidence of either 0 or 90 degree. Table 3: variation of moments in columns for rectangular structure Column Category Column Name Critical angle Moments in KN for (0 or 90 degree) Moments in KN for critical angle My Mz My Mz Corner C1 52 -9.248 -72.562 -66.712 -57.773 C7 52 72.562 -9.248 57.773 -66.712 C3 52 -9.248 72.562 -57.773 66.712 C9 52 72.562 9.248 66.712 57.773 SIDE C2 10 -191.932 0 -189.149 28.782 C4 10 0 -141.245 -38.618 -139.125 C6 10 0 141.245 38.618 139.125 C8 10 191.932 0 189.149 -28.782 It is seen in table 3 that maximum bending moment in the entire corner columns were obtained by applying seismic force at an angle of 52 degree. It is observed for column one and seven that bending moments in one direction decreases by 20.381% but bending moments in other direction increases 7.213 times similarly for column three and nine the bending moments in one direction decreases by 8% but bending moments in other direction increases by 6.247 times which makes seismic incidence angle 52 degree critical. Maximum bending moment in the entire side columns are obtained by applying seismic force at an angle of 10 degree. All the side columns which were uni-axial become biaxial columns. This makes seismic incidence angle 10 degree critical. The bending moment in central column occurs mainly by applying seismic force at an angle of incidence of either 0 or 90 degree. 5. CONCLUSIONS Based on the numerical results it can be concluded that: • The axial forces of column may exceed the ordinary cases up to 13% in corner columns. This critical direction is very close to the diagonal direction of the structure. • Critical direction for columns on edge is very close to the conventional direction we normally follow as far as Axial Forces are considered. • There is increase in moments for columns on edge if we apply Seismic force other than the conventional directions. • There is no unique specific angle of incidence for each structure which increases the value of internal forces of all structural members together; each member gets its maximum value of internal forces by a specific angle of incidence. • It is recommended to apply Seismic force in a set of different angle ranging between 0 to 90 degrees for safe design.