Pushover Analysis of RC Bare Frame: Performance Comparison between Ductile and Non-ductile detailing by Narender Bodige, Pradeep Kumar Ramancharla in Urban Safety of Mega Cities in Asia (USMCA) Report No: IIIT/TR/2012/-1 Centre for Earthquake Engineering International Institute of Information Technology Hyderabad - 500 032, INDIA October 2012
Pushover Analysis of RC Bare Frame: Performance Comparison between Ductile and Non-ductile detailing B. Narender 1 and Ramancharla Pradeep Kumar 2 1 P.hD Student, Computer Aided Structural Engineering, IIIT Hyderabad, Hyderabad, India. Narender.b@research.iiit.ac.in 2 Associate Professor, Earthquake Engineering Research Centre, IIIT Hyderabad, Hyderabad, India. ramancharla@iiit.ac.in ABSTRACT The objective of this paper is to compare pushover response of ductile and non-ductile frames using AEM (Applied Element Method). Pushover analysis is non linear static analysis, a tool for seismic evaluation of existing structures. Unlike FEM, AEM is a discrete method in which the elements are connected by pair of normal and shear springs which are distributed around the elements edges and each pair of springs totally represents stresses and deformation and plastic hinges location are formed automatically. In the present case study a 1 x 1 bay four storied building is modeled using AEM. Gravity loads and laterals loads as per IS 1893-2002 are applied on the structure and designed using IS 456 and IS 13920. Displacement control pushover analysis is carried out. The effect of ductile detailing, change in grade of concrete and bar sizes in columns is also compared. Keywords: Pushover analysis, AEM, ductile detailing. 1. INTRODUCTION There is an urgent need to assess the seismic vulnerability of buildings in urban areas of India as an essential component of a comprehensive earthquake disaster risk management policy. Detailed seismic vulnerability evaluation is a technically complex and expensive procedure and can only be performed on a limited number of buildings. It is therefore very important to use simpler procedures that can help to rapidly evaluate the vulnerability profile of different types of buildings, so that the more complex evaluation procedures can be limited to the most critical buildings.
Nonlinear static (pushover) analysis is used to quantify the resistance of the structure to lateral deformation and to gauge the mode of deformation and intensity of local demands. The static pushover analysis is becoming a popular tool for seismic performance evaluation of existing and new structures. The expectation is that the pushover analysis will provide adequate information on seismic demands imposed by the design ground motion on the structural system and its components. The existing building can become seismically deficient since seismic design code requirements are constantly upgraded and advancement in engineering knowledge. Further, Indian buildings built over past two decades are seismically deficient because of lack of awareness regarding seismic behavior of structures. The widespread damage especially to RC buildings during earthquakes exposed the construction practices being adopted around the world, and generated a great demand for seismic evaluation and retrofitting of existing building stocks. The objective of this paper is to study the performance of building designed without considering earthquake forces and by considering the earthquake forces. A newly developed method called AEM is used for this study. In the present case study a 1 x 1 bay four storied building is modeled. Gravity loads and laterals loads as per IS 1893-2002 are applied on the structure and designed it using IS 456 and IS 13920. Displacement control pushover analysis is carried out in both cases and the pushover curves are compared. The effect of ductile detailing, change in grade of concrete and bar sizes in columns is also compared. 2. Applied Element Method Numerically, it is important to know the damage of the structure till collapse. Applied element method (AEM) is an efficient technique to deal this kind of problems accurately. In Figure 1: Element shape and degrees of the freedom
this method, the elements are connected by pair of normal and shear springs which are distributed around the element edges. These springs represents the stresses and deformations of the studied element. The elements motion is rigid body motion and the internal deformations are taken by springs only. It is advisable to increase the number of elements than connecting springs for improving the accuracy. The general stiffness matrix components corresponding to each degree of freedom are determined by assuming unit displacement and the forces are at the centroid of each element. The element stiffness matrix size is 6x6. The first quarter portion of the stiffness matrix is given by equation (1). The stiffness matrix components diagram is shown in Figure.1. However the global stiffness matrix is generated by summing up all the local stiffness matrices for each element. Case study Description of structure A ground plus three storey RC building of plan dimensions 3.3 m x 3.3 m and height of building is 12 m located in seismic zone II and on hard soil is considered. It is assumed that there is no parking floor for this building. Seismic analysis is performed using the IS 1893-2002 seismic coefficient method. Since the structure is a regular building with a height less than 12 m, as per Clause 7.8.1 of IS 1893 (Part 1): 2002, a dynamic analysis need not be carried out. Detailed design of the beams along longitudinal and transverse as per recommendations of IS 13920:1993 has been carried out. Plan of the building and sectional elevations of four story RC frames are shown in Figures 2. The sizes of the beams and columns are given in Table 1. Material property For this study material property has been used as follows Grade of concrete: M20, M25 and M30 Grade of steel = Fe 415 and Fe250 Live load on floors = 2 kn/m 2 Floor finish = 1 kn/m 2 Brick wall on peripheral beams = 230 mm thick Density of concrete = 25 kn/m 3 Density of brick wall including plaster = 20 kn/m 3
Figure 2 Plan of building (All dimension are in meters) Load Combinations Load combinations are considered as per IS 456: 2000 and are given in Table 2. EQX implies earthquake loading in X direction and EQY stands for earthquake loading in Y direction. The emphasis here is on showing typical calculations for ductile design and detailing of building elements subjected to earthquakes. In practice, wind load should also be considered in lieu of earthquake load and the critical of the two load cases should be used for design. This analysis only three combination were used. Beams parallel to the Y direction are not significantly affected by earthquake force in the X direction (except in case of highly unsymmetrical buildings), and vice versa. Beams parallel to Y direction are designed for earthquake loading in Y direction only. Torsion effect is not considered in this example. The dead load of slab, beam and wall and live load and floor finishing load on slab were calculated and total load of dead load and live load on beam have been used 22.7 kn/m and 9.9 kn/m respectively. Due to symmetry plan all floor beams had same load. The seismic weights are calculated in a manner similar to gravity loads. The weight of columns and walls in any storey shall be equally distributed to the floors above and below the storey. Seismic analyses were evaluated and base shear was calculated and it is distributed according to IS: 1893 which were from first floor to top floor distribution like inverted triangle.
The base shears of structure were obtained 26.73KN. Due to symmetry similar frame can be used for further analysis Design and Detailing The design of all beams and columns are based on IS: 456 and IS 13920. The longitudinal, transverse reinforcement and spacing of both beam and column as shown in Figures 3 (a)-(b) respectively. Figure 3 (a) IS: 456 design details Figure 3 (b) IS: 13920 ductile design details Pushover Analysis Pushover Analysis is performed using applied element method on a 2D frame to obtain the capacity curve for three frames, viz., design only for gravity loads, designed earthquake loads without ductile detailing and designed for earthquake loads and also with ductile detailing. Case I: Gravity Design Pushover Curve Lateral displacement is applied according to force distribution given in IS 1893. A total of 0.2 m is applied in 100 load steps. Base shear at every displacement step is captured. Maximum base shear obtained 32 kn at 10mm of displacement pushover (See Figure 4). After reaching maximum load, frames lost its capacity significantly, which can be seen as a steep fall in load carrying capacity. It is obvious that without considering the earthquake forces, frame s capacity to resist lateral displacement is very low.
Figure 4: Load vs displacement curve Case II: Non Ductile Detailing Pushover Curve Second case study was for non-ductile detailing structure. The members were design according IS: 456 and reinforcement details were shown in Figure 3(a). Ductile detailing is not considered in this frame. Pushover analysis is performed on this frame using displacement pushover approach. Maximum displacement applied at top of roof element as 2.4m and its collapse behavior as shown in Figure 5. Maximum base shear occurred at 118KN and drift ratio of 0.019 %. After reaching the drift ratio, the first failure occurred at top roof beam joint members in, hinges forming at top floor elements. The sequence of failure shown in Figure 5 as top beam joint element to bottom beams joint and it followed by left column joint. In figure vertical drops indicate the steel failure and incline lines indicate the elements behavior. Figure 5: Non ductile detailing Load vs displacement curve Case III: Ductile detailing Pushover Curve Members were design according IS: 13920 and reinforcement details were shown in Figure 3(b). Pushover analysis has been performed and the results were shown in Figure 6. It can be clearly seen from the results that ductile detailing is increasing the capacity of the frame significantly. Up to significant
deformation, structure is not loosing is load carrying capacity. The maximum base shear was obtained as 125KN but this base shear is maintained same up 1.3m after that sudden drop took place. This sudden vertical drop indicate that joint member failed at time and the sequence of failure like beam-column joint at top to bottom beam but column joint still stand. The resistance capacity more compare to non ductile design. Case IV: Effect of concrete grade As a case study affect of concrete grade on load deformation capacity of the frame is studied. Three cases were considered i.e., M20, M25 and M30 grade. Figure 6, it can be clearly seen that the yield strength of the structure is higher for higher grades of concrete however; the capacity to deform is lower when the grade of the concrete is higher. It was found that M 25 grade of concrete slight to high base shear and smooth decreasing curve compare to other grade of concrete. From observation of all combination, M25 grade of concrete has slight high resistance capacity compared M20 and M30. It can be concluded that grade of the concrete has less affect on the capacity of building under lateral loads. Figure 6: Effect of grade of concrete Case V: Effect of change in diameter of column bars As a second case study affect of steel grade on load deformation capacity of the frame is studied. Two cases were considered i.e., Fe 250 and Fe 415 grade. Results are illustrated in Figure 7. It indicates that load deformation curve is same for both the cases upto 115 kn, there after as the deformation is increasing, the load carrying capacity of Fe 250 is lower than Fe 415, however ductility is higher. Along with this another study has also been conducted to understand the affect of number of reinforcing bars. It can be concluded from the analysis that if the number of bars are
increasing, capacity is also increasing slightly, however, care must be taken because large number of reinforcing bars increase congestion in concreting. Figure 7: Effect of Steel Grade Conclusion In the present case study a 1 x 1 bay 2D four storied building is modeled using AEM (applied element method). Gravity loads and laterals loads as per IS 1893-2002 are applied on the structure and designed it using IS 456 and IS 13920. Displacement control pushover analysis is carried out in both cases and the pushover curves are compared. As an observation it is found that AEM give good representation capacity curve. From the case studies it is found that capacity of the building significantly increases when ductile detailing is adopted. Also, it is found that affect on concrete grade and also steel are not that significant. REFERENCES 1. Hatem Tagel-Din and Kimiro Meguro: Applied Element Method for Simulation of Nonlinear Materials: Theory and Application for RC Structures, Structural Eng./Earthquake Eng., International Journal of the Japan Society of Civil Engineers (JSCE) Vol. 17, No. 2, 137s-148s, July 2000. 2. IS 456: 2000; Criteria for Plain and Reinforced Concrete Design of Structures, BIS, India. 3. IS 1893: 2002; Criteria for Earthquake Resistant Design of Buildings, BIS, India. 4. IS 13920: 1993; Code of Practice for Ductile Detailing of Buildings, BIS, India.