Seismic Response Reduction Factor Evaluation for Irregular RC Structures

Seismic Response Reduction Factor Evaluation for Irregular RC Structures

Sharjuban Jisha P.

M.Tech Scholar Assistant Professor

AWH Engineering College, Kozhikkode AWH Engineering College, Kozhikkode

Abstract

– Response reduction factor is invariably used by most seismic design codes to include the non-linear response of structure. The non-linear behaviour of the structure is taken into account due to this factor which permits the designer to use a linear elastic force-based design. It is a combined effect of over strength, ductility and redundancy. Response modification factors play a key, but controversial role in the seismic design process. No other parameter in the design base shear equation impacts the design actions in a seismic framing system as does the value assigned to R. Despite the profound influence of R on the seismic design process and ultimately on the seismic performance of buildings in India. No scientific basis exists for the values of R adopted in seismic design codes in India. Without such a basis, it will be difficult to advance the practice of force-based seismic design in its current form. In present work efforts has been made in estimating the actual value of response reduction factor (R) for reinforced concrete buildings having irregularity in plan by non-linear static pushover analysis using SAP2000 and compare results with codal values. The frames were designed as per guidelines of IS 456:2000.The lateral loads acting on the frames were obtained from the guidelines of IS 1893: 2002 (Part1).

1. INTRODUCTION

   The devastating effect of an earthquake can have major consequences on infrastructures and service life. The earthquake engineering community has been reassessing its procedures in the past few years due to such earthquakes which have caused extensive damage, loss of life and property. These procedures mainly consider assessment of seismic force demands on the structure and then developing design procedures for the structure to withstand the applied actions. The seismic design in most of the structures is based mainly on elastic force. The nonlinear response of structure is not incorporated in design process but its effect is integrated by using a reduction factor called Response Reduction factor (R). There are differences in the way the response reduction factor (R) is specified in different codes for different kinds of structural systems .The concept of response reduction factor is to reduce the seismic force and incorporate nonlinearity with the help of over strength, redundancy and ductility effects.

   The value of Response reduction factor varies from 3 to 5 in Indian code as per type of resisting frame, but previous studies does not provide information on what basis R values are considered. Most of the past research efforts in this area have focused on finding the ductility component and overstrength components of the response reduction factor. The present work takes a rational approach in determining R factor for irregular RC structures.

   Fig 1. Examples of Irregular structures

2. METHODOLOGY

   • Conduct literature review on response reduction factor of structures and effect of various parameters of response reduction factor on buildings.

   • Modelling of low, mid and high rise RC structures with stiffness irregularities.

   • Analysis to be done using SAP 2000 software.

   • Percentage variation in R value from code provisions are to be determine.

3. MODELLING OF BUILDINGS

   An ideal symmetric structures having the distribution of loads is uniform along each storey and three asymmetric structures were chosen for the study. Asymmetric structures includes an L shape, step shape and T shape floor. The buildings under consideration are low, mid and high rise buildings. All the structure had got the same perimeter for the plot they are compared for their irregular plan and mass distribution. The seismic analysis were carried out as per the code IS 1893: 2002. Zone IV and soil type II are considered for analysis. The performance of the structures are assessed as per the procedure prescribed in ATC-19, IS 1893-2002 and

   FEMA-356. The analysis of the structural model is done in SAP 2000.

   Three, seven and eleven storied RC structures which are symmetric and asymmetric in plan have been considered for the study. The building is assumed to be situated in Zone III as per IS 1893 (2000). The concrete floors are modelled as rigid. The details of the model is given in the table 1. The structures are assumed to be constructed on medium soil as per IS 1893. The design dead loads and live loads are calculated from IS 875 (Part 1) and IS 875 (Part 2) respectively.

   Table 1: Structural details

   Contents	Description
   Type of structure	Multi storey structures (G+3, G+7 and G+11)
   Building plan dimension	15m x 15m
   Concrete Grade	M30
   Steel Grade	Fe 415
   Slab Thickness	120mm
   Height of each storey	3.5m
   Height of ground storey	2m
   Live load at floor & roof level	2 kN/m² & 0.75 kN/m²
   Type of soil	Medium soil
   Seismic zone	IV

   Table 2 gives the further details regarding the planar frames. The seismic weight calculation is done as per IS 1893. Based on the common practice of the engineers the models for the study have been selected. Same beam sections have been used throughout the structure whereas the column section have been varied as per the height of the buildings as is done in common practice. The RC design is based on IS-456 (2000) and the ductile designing is based on IS 13920 (2003). The reinforcement details of all the sections are not same in the three models.

   Table 2: Details of the RC frames considered for the study

   Number of storey	Height (m)	Time period (s)	Weight (kN)	Design base shear (kN)
   3	12.5	0.452	9654.50	387
   7	26.5	0.816	21682.54	543
   11	40.5	1.1106	35830.94	645

   b. Variation in plan shape

   It contains G+3, G+7 and G+11 structures with variation in plan shapes. Different plan shapes are L shape, T shape and stepp shape. All these structures have same base area. Fig 4 shows the different plan irregularities used for the thesis work

   1. Variation of height

      It contains rectangular plan shaped structure with variation in height. ie, G+3, G+7 and G+11 structures. The plan layout of the structures shown in the fig 2. Fig 3 shows the typical elevations for these structures.

      Fig 2. Plan of building

      Fig 3. Elevations of the structures

      1. L shape (b) T shape

   (C) stepp shape

   Fig 4. Plan irregularity

   1. Model Geometry

      In order to differentiate models from each other various abbreviations are used. For example, PL3: Model number 1 with 3 storey L shaped plan irregularity. Table 3 given below shows the model details of the thesis work. Fig 5 to 7 shows the three dimensional view of models used for the study.

      Table 3: Model details

      Designation	Details
      R3	3 storey regular structure
      PL3	3 storey L shaped plan irregular structure
      PS3	3 storey step shaped plan irregular structure
      PT3	3 storey T shaped plan irregular structure
      R7	7 storey regular structure
      PL7	7 storey L shaped plan irregular structure
      PS7	7 storey step shaped plan irregular structure
      PT7	7 storey T shaped plan irregular structure
      R11	11 storey regular structure
      PL11	11 storey L shaped plan irregular structure
      PS11	11 storey step shaped plan irregular structure
      PT11	11 storey T shaped plan irregular structure

      1. R3 (b) PL3

      2. PS3 (d) PT3

         Fig 5. Three dimensional view of 3 storey building

      3. PL7 (d) PT7

         Fig 6. Three dimensional view of 7 storey building

         1. R11 (b) PT11

   Fig 7. Three dimensional view of 11 storey building

4. ANALYSIS

   Pushover Analysis

   (a) R7 (b) PS7

   Pushover analysis is Non Linear Static Analysis done to determine the capacity of structure. In this procedure a predefined lateral load pattern is distributed along the building height. The lateral forces are then monotonically increased in constant proportion with a displacement control at the control node of the building until a certain level of deformation is reached. For this analysis nonlinear plastic hinges have been assigned to all of the primary elements. Default moment hinges (M3-hinges) have been assigned to beam elements and default axial-moment 2-moment3 hinges (PMM-hinges) have been assigned to column elements. The output of a nonlinear static analysis is generally presented in the form of a pushover curve, which is typically the base shear vs. roof displacement plot.

5. RESULTS AND DISCUSSIONS

   1. Comparison of Pushover curve

      Comparison of pushover curve having irregularity in plan is shown in fig 8 to fig 10. The figure describes the pushover curves of different models of rectangular shape, L shape, T shape and step shape. This shows that as percentage of irregularity goes on increasing push over curve drops down to the lower values. As we can clearly observe that graph of R3 is on lower value than PL3, PT3 and PS3. In case of mid and high rise structures, the base shear versus displacement graphs are almost similar.

      Fig 8. Comparison of pushover curve of 3 storey irregular structures

      Fig 9. Comparison of pushover curve of 7 storey irregular structures

      Fig 10. Comparison of pushover curve of 11 storey irregular structures

   2. Estimation of Performance point

      It is observed that the demand curve tend to intersect the capacity curve in the building performance level of Life Safety Level, which means substantial damage as occurred to the structure, thus it may lose a significant amount of its original stiffness. However, a substantial margin remains for additional lateral deformation before collapse would occur.

      E.g. For 3 storey regular building, on the above regular building frames the nonlinear static pushover analysis is performed to investigate the performance point of the building frame in terms of base shear and displacement. The various load combinations are also used for this purpose. After pushover analysis the demand curve and capacity curves are obtained to get the performance point of the structure. The performance point is obtained as per ATC 40 capacity spectrum method. The demand curve and capacity curve for regular building is shown in fig 11 – (ATC 40 Capacity Spectrum).

      Fig 11. ATC 40 Capacity Spectrum

      Performance point = 1175.967 kN

      The Performance points of all the buildings are obtained and stated in the table 4. The table specifies the performance points of all the buildings along with their designation.

      Table 4. Performance points for modelled buildings from capacity spectrum method

      Sl no	Designation	Performance point
      1	R3	1175.967
      2	PL3	810.17
      3	PS3	905.214
      4	PT3	806.689
      5	R7	1868.91
      6	PL7	1265.603
      7	PS7	1429.085
      8	PT7	1266.205
      9	R11	2030.085
      10	PL11	1362.236
      11	PS11	1547.119
      12	PT11	1364.118

   3. Estimation and Comparison of Response reduction factor

   Variation of Response reduction factor with respect to irregularities in plan is shown in the table 5.

   Table 5. Response reduction factor for modelled buildings

   Sl no	Designation	Rs	Rµ	Rr	R	Codal value
   1	R3	3.03	1.09	1	3.302	5
   2	PL3	2.264	1.127	1	2.553	5
   3	PS3	2.503	1.114	1	2.788	5
   4	PT3	2.223	1.04	1	2.31	5
   5	R7	3.44	1.163	1	4.002	5
   6	PL7	2.451	1.232	1	3.021	5
   7	PS7	2.881	1.198	1	3.452	5
   8	PT7	2.585	1.23	1	3.18	5
   9	R11	3.147	1.32	1	4.154	5
   10	PL11	2.261	1.347	1	3.046	5
   11	PT11	2.24	1.34	1	3.021	5
   12	PS11	2.583	1.312	1	3.389	5

6. CONCLUSIONS

On the above building frames the nonlinear static pushover analysis is performed to investigate the performance point of the building frame in terms of base shear and displacement. The various load combinations are also used for this purpose. After pushover analysis the demand curve and capacity curves are obtained to get the performance point of the structure. The performance point is obtained as per ATC

40 capacity spectrum method. From the aove study followings conclusions were drawn.

• The evaluated value of R in the present work were obtained by nonlinear static (pushover) analysis of structures with plan irregularities are found to be less than as those specified in the IS 1893.

• As number of storey increases, the value of response reduction factor goes on increasing.

• The performance point of T shape and L shape plan irregularity is almost nearer to each other. It may due to same base area.

• The performance point of step shape irregular structure is higher than that of other irregular structures. It may due to increased base area.

REFERENCES

1. Kruthi Thamboli, J.A. Amin (2016), Evaluation of Response Reduction Factor and Ductility Factor of RC Braced Frame Journal Of Materials And Engineering Structures 2 (2016) 120 129.

2. Keerthi. S, Vivek Philip (2017), Evaluation of Response Reduction Factor based on redundancy for high rise buildings. International Research Journal of Engineering and Technology (IRJET), Volume: 04 Issue: 05

3. Venkata Ramana R. L, Ingle R. K. (2016), Evaluation of Response Reduction Factor of RC framed buildings by Pushover analysis. International Journal of Advances in Mechanical and Civil Engineering, ISSN: 2394-2827 , Volume-3, Issue-4

4. Bholebhavi Rahul D., Inamdar V.M. (2016), An evaluation of seismic response reduction factor for irregular structures using nonlinear static analysis. International Journal of Innovative Research in Science, Engineering and Technology, Vol. 5, Issue

5. Deepak A L., jitendra babu N. (2015), Formulation of response reduction Factor for an RCC frame and study on difference in R factor based on seismic zones, International journal for scientific engineering and technology research, ISSN 2319-8885 Vol.04,Issue.37