Assessment of Response Reduction Factor for High Rise Irregular Structures

1. INTRODUCTION

An earthquake is the result of a sudden release of stored energy in the Earth's crust that creates seismic waves. The destructive effect of an earthquake can cause adverse effect on infrastructure as well as social and economic life of society. The community related seismology and earthquake has been reassessing its procedures, in the past few years, due to such earthquakes which have caused hazardous damage, loss of life and property. These studies fundamentally consider evaluation of seismic force demands on the structure and then developing design procedures for the structure to withstand the applied actions. Elastic force is the important factor for seismic design in most of the structures. Now a days many existing structures are designed and to be constructed containing irregularities in their plan as well as in elevation, but some of them are designed and purposefully constructed to be irregular to fulfill various needs and functions such as basements for mercantile purposes created by eliminating central columns. Also, by adjusting the sizes of structural members in the upper story‘s to fulfill necessary requirements and for other functions like storing heavy machines and equipment‘s etc. This difference in usage of a particular floor with respect to adjacent floors results in uneven distributions of mass, stiffness and strength along the building dimensions. Generally nonlinear response of structure is not encompasses in design process but its effect is considered by using a reduction factor called Response Reduction factor (R). There is a variations in the method the response reduction factor (R) is specified in various codes. The value of response reduction factor varies from 3 to 5 in IS code, the present work takes a rational approach in

The response reduction factor, R represents the ratio of the maximum lateral force if structure remains elastic to the lateral force which it has been designed to withstand. Commonly, the response reduction factor is expressed as a function of various parameters of the structural system, such as strength, ductility, damping and redundancy. R=Rs*Rμ*Rr Where ‗Rs‘ is the strength factor, ‗Rr‘ is the redundancy factor, ‗Rμ‘ is the ductility factor.

The extra strength after the design strength is called the over strength. Most of the structures show significant over strength. Subsequentconcurrence of unfavourable zones, Over strength of material, strain hardening, capacity depletion factors are the emergence of Over strength (Rs). Over strength is to be engage to reduce the forces that are used in the design, hence directing to more reasonable structures.. The Over strength, which is specified as member or structural capacity, is usually defined using Over strength factor, which may be defined as the ratio of maximum base shear in actual behavior to first significant yield strength in structure. Rs = Vu/Vd Where,‗Vu‘ is the maximum base shear and ‗Vd‘ is the design base shear.

Ductility of a structure, is the capacity to hold up large unyielding deformations without considerable loss of strength and stiffness. Ductile structures functions better than that of the fragile structures. Structures with high ductility can relatively tolerate large distortion and permit the structure to go under high possible strength, in turn, dissolving a substantial amount of energy. The ductility factor (Rμ) is a scale of the universal nonlinear response of the structures in view of its inelastic distortion capacity. It is estimated as the ratio of the base shear considering an elastic response to the ultimate base shear considering an inelastic response. Rμ = Ve/Vu Where,‗Ve‘ is the base shear with elastic response and ‗Vu‘ is the base shear with inelastic response. horizontal load resisting system. The moment resisting frames, shear walls are the mostselected horizontal load resisting systems in reinforced concrete structures. The RC structures with multiple lines of horizontal load resisting frame type is normally considered in the class of redundant type of structures cause the frames are indicated and categorized to convey the seismic inertia loads to the foundation. The horizontal load is retained by various frames depending upon the comparative strength and stiffness property of relevant frames for redundant system of frames. When independent the accuracy of framing system is greater for the structures with multiple lines of frames while it decreases when resisting criteria are accurately correlated. ATC 19 fixed a association between lines of vertical seismic frame and drift redundancy factor as shown in table.

It is a factor to obtain the design spectrum depending on the perceived maximum seismic risk characterized by Maximum Considered Earthquake ( MCE ) in the zone in which the structure is located. The basic zone factors included in this standard are reasonable estimate of effective peak ground acceleration. From the above table we know that intensity of an earthquake is mainly depends on the seismic zone. As values of zone factors are in fractions and does not have much difference amongst them zone wise but on the front of seismic intensity it may cause huge effect on loss of economic and social life of society.

It is a factor denoting the acceleration response spectrum of the structure subjected to earthquake ground vibrations, and depends on natural period of vibration and damping of the structure. 1.4 Fundamental Natural Period (Ta):- Theapproximate fundamental natural period of vibration (T,) in seconds, of a moment-resisting frame building without brick infill panels may be estimated by the empirical expression. i) Ta = 0.075h^0.75 (for RC MRF building) iii) Ta = 0.085h^0.75 (for Steel MRF building) Where, h = Height of building, in m. This excludes the basement stores, where basement walls are connected with the ground floor deck or fitted between the building columns.

It is a factor ddepending upon the functional use of the structures, characterized by hazardous consequences of its failure, post-earthquake functional needs, historical value, or economic importance

VB = Ah*W Where, VB= Design horizontal acceleration spectrum value, using the fundamental natural period Ta, in the considered direction of vibration. W= Seismic weight of the building. The base shear plays vital role in the estimation of various factors mentioned above such as over strength factor. The value of ‗R‘ factor varies from 3 to 5 in IS code depending on type of resisting frame, but previous studies related this does not provide analysis that on what basis values of Response Reduction Factor are considered. Most of the previous studies in this area have focused on finding the Over strength and ductility components of the response reduction factor. The present work takes a reasonable perspective in determining R factor for irregular high rise RC structures with various irregularities in plan.

uniform load distribution along each storey individually and three structures having various irregularities were selected for the study. Irregular structures contains an L-shaped, T-shaped and stepped-shaped plan irregularities. The buildings under consideration are 3-storey, 7-storey and 11-storey buildings. All the buildings are having same perimeter of the plot for irregular plan and mass distribution. The seismic evaluation were carried out as per the code IS 1893: 2002. Buildings are to be situated in medium stiff soil are to be considered for analysis. The performance of the buildings are evaluated as per the procedure specified in ATC-19 and IS 1893-2002. The structural analysis of the model is carried out in SAP 2000. The buildings are assumed to be situated in Zone V as per IS 1893 (2000). The concrete floors are designed as rigid. The specifications of the model are to be given in the table below.

For Plan Irregularities: SYM: Symmetric Structure LI: L-shape Irregularity TI: T-shape Irregularity For Vertical Irregularities: SI: Stepped Irregularity For Example: LPI: Model with L-shape plan irregularity. TPI: Model with T-shape plan irregularity. SPI: Model with Stepped-shape irregularity.

It is noticed that the capacity curve is to be intersected by the demand curve in the structural performance level, it means significant damage is takes place to the structure, thus it may be possible to lose considerable amount of its actual stiffness. However, a significant margin rests for supplementary horizontal deformation before actual collapse would occur. Such as for3-storey symmetric building, on the above regular building frames the nonlinear static pushover analysis is conducted to evaluate the performance point of the structural frame in terms of base shear and displacement. The different load combinations are also used for this purpose. After the nonlinear pushover analysis the demand curve and capacity curves are obtained to get the performance point of the buildings. The performance point is obtained as per ATC 40 capacity spectrum method. The demand curve and capacity curve for symmetric building is shown in fig below.

(Graph of Demand curve VS Capacity curve) Performance point =2365.0352KN. along with their designations and also shows the base shear values of different type of buildings based on which the comparison between the codal values of response reduction factor and estimated values are also specifies.

As location of the building changes it may influence the seismic behaviour of the structure in different ways in other words we can say that as the seismic zone of the building where the structure is actually to be situated changes, the zone factor of the respective seismic zone also changes which may turn to effect on the base shear value. We know that the base shear is an estimate of the maximum expected lateral force on the base of the structure due to seismic activity. It is calculated using the seismic zone, soil material, and building code lateral force equations.The table below shows results based on seismic zone II, zone III and zone IV.

Following are the salient conclusions obtained from the present study:- 1. A persistent value of response reduction factor for any of above case of building are not justified. Precise methodology are essential to estimate the ―R‖ value accounting for strength, ductility and redundancy for specific type of building; present work takes efforts in the same direction. 2. On behalf of results obtained we can conclude that the value of response reduction factories overestimated in IS-1893 (2000), which may leads to the potentially hazardous underestimation of the design base shear. 3. As number of storey that is as height of building goes on increases, the value of response reduction factor goes on increasing. 4. The performance point of T-shaped and L-shaped plan irregularity is almost alike might be due to the same base area.

6. There is a necessity to estimate the accurate values of response reduction factor as, many factors causes substantial effect on R-factor. Also there is a need to specify concern values ductility and over strength factors. 7. The obtained results are based on only few considerations and methodology such as we performed our analysis by considering specific seismic zone; specific type of soil etc. and only non-linear static pushover analysis is conducted. 8. If we changes our above specifications and will adopted other modes of analysis such as non-linear dynamic pushover analysis, time history analysis etc., then there may be a possibility to obtain different types of results based on the considerations.

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PG Student, Department of Civil Engineering, SVERI‘s College of Engineering, Pandharpur, Maharashtra, India