Pushover Analysis for an Elevated Water Tanks

Transcription

1 Proceedings of International Conference on Advances in Architecture and Civil Engineering (AARCV 212), 21 st 23 rd June Pushover Analysis for an Elevated Water Tanks N. Vinay, Dr. Gopi Siddappa and Dr.G.S. Suresh Abstract--- Elevated water tanks are one of the most important lifeline structures in earthquake prone regions. In major cities and also in rural areas elevated water tanks forms an integral part of water supply scheme. These structures has large mass concentrated at the top of slender supporting structure, hence these structures are especially vulnerable to horizontal forces due to earthquake. Elevated water tanks that are inadequately analyzed and designed have suffered extensive damage during past earthquakes. Hence it is important to check the severity of these forces for particular region. The tanks are used to store water placed either on the ground or at an elevation. The need for a water tank is as old as civilization of man, providing storage of water for drinking, Irrigation, agriculture, fire suppression, agricultural farming both for plants and livestock, chemical manufacturing, food preparation as well as many other applications. All water tanks are designed as crack free structures to eliminate any leakage. The Analysis and Design of reinforced concrete structures to sustain static and dynamic loading is an important task facing structural engineers. The existing codes are based on elastic analysis which has no measure of the deformation capability of members or of structure. Thus the Non-Linear 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 purpose of this project is to summarize the basic concepts on which the pushover analysis can be based, assess the accuracy of pushover predictions, identify conditions under which the pushover will provide adequate information and perhaps more importantly to identify cases in which the pushover predictions will be inadequate or even misleading. The aim of this project is to provide relevant information and implementation of Non- linear Static [pushover] analysis for elevated water tanks. Keywords--- Water Tank, Pushover Analysis, Earthquake, Leakage E I. INTRODUCTION LEVATED water tanks are commonly used in public water distribution system. Being an important part of lifeline system, and due to post earthquake functional needs, seismic safety of water tanks is of considerable importance. Elevated water tanks also called as elevated service reservoirs N. Vinay, PG Student, vinaymtech21@gmail.com Dr. Gopi Siddappa, Professor, Department of Civil Engineering PESCE, Mandya, Karnataka, India. gopisiddappa@gmail.com Dr.G.S. Suresh, Professor & HOD Department of Civil Engineering, NIE, Mysore, Karnataka, India. gss_nie@yahoo.com (ESRs) typically comprises of a container and a supporting tower (also called as staging). Staging in the form of reinforced concrete shaft and in the form of reinforced concrete column-brace frame are commonly deployed. The column-brace frame type of staging is essentially a 3D reinforced concrete frame which supports the container and resists the lateral loads induced due to earthquake or wind. Aim of the present study is to bring out the differences in seismic behavior of column beam (Building) frame and column-brace (staging) frame in the post-elastic region and to quantify their ductility. In addition, nonlinear dynamic analysis is also performed to bring out the differences in the nonlinear dynamic behavior of two types of frames. Pushover analysis is an approximate analysis method in which the structure is subjected to monotonically increasing lateral forces with an invariant height-wise distribution until a target displacement is reached. Pushover analysis consists of a series of sequential elastic analysis, superimposed to approximate a force-displacement curve of the overall structure. A two or three dimensional model which includes bilinear or trilinear load-deformation diagrams of all lateral force resisting elements is first created and gravity loads are applied initially. Pushover Analysis option will allow engineers to perform pushover analysis as per FEMA -356 and ATC-4. Pushover analysis is a static, nonlinear procedure using simplified nonlinear technique to estimate seismic structural deformations. It is an incremental static analysis used to determine the force-displacement relationship, or the capacity curve, for a structure or structural element. The analysis involves applying horizontal loads, in a prescribed pattern, to the structure incrementally, i.e. pushing the structure and plotting the total applied shear force and associated lateral displacement at each increment, until the structure or collapse condition. Priestley et al (1988) describes a stress-strain model for confined as well as unconfined concrete subjected to uniaxial compressive loading. The unified stress-strain model for confined concrete is developed for members with circular and rectangular sections, under static or dynamic loading. The document given by Applied Technology Council (ATC-4, 1997) provides analytical procedures for evaluating the seismic performance of existing buildings. Simplified nonlinear analysis methods are provided. Use of nonlinear procedures in general has been discussed and capacity spectrum method is introduced. By using static pushover analysis method lateral force resisting capacity of structure is obtained. Habibullah et al.(1998) describe the steps involved in performing pushover analysis of simple three dimensional frame model using SAP2 software. The recent advent of performance based design has brought pushover analysis to forefront; hence, there is a need to have away to perform

2 Proceedings of International Conference on Advances in Architecture and Civil Engineering (AARCV 212), 21 st 23 rd June pushover analysis using standard software. The paper briefly describes each step of the procedure of pushover analysis in SAP2 which is a general purpose finite element structural analysis program. The paper uses default values of user defined hinge properties from the software. Inel and Ozmen (26) discuss the effects of plastic hinge properties on nonlinear response of reinforced concrete buildings. The paper discusses the results of pushover analysis with default and user defined hinge properties. Four storey building is considered and a study is carried out with the help of SAP2. The paper gives details of reinforcement as well as other structural features of the buildings under consideration. The study gives emphasis on the comparison of pushover curves with different plastic hinge lengths and other parameters such as spacing of transverse reinforcement are also included in the study. The paper by Kadid and Boumrkik (1987) is aimed at evaluating the performance of the framed structures under future expected earthquakes. Need was felt to evaluate the performance of structures after Boumerdes (23) earthquake which devastated a large part of Algeria. It is stated that pushover analysis is a viable method to assess the damage vulnerability of buildings. The paper explains pushover analysis of three framed buildings with 5, 8 and 12 stories representing low, medium and high rise buildings respectively. The study is carried out using general finite element software SAP2. IV. METHOD OF ANALYSIS For seismic performance evaluation, a structural analysis of the mathematical model of the structure is required to determine force and displacement demands in various components of the structure. Several analysis methods, both elastic and inelastic, are available to predict the seismic performance of the structures. There are two methods of analysis, elastic and inelastic methods. In the present study inelastic analysis is adopted. Inelastic analysis procedures basically include inelastic time history analysis and inelastic static analysis which is also known as pushover analysis. V. PUSH OVER ANALYSIS USING SAP 2 Consider a single bay single story frame with the same cross section throughout as shown in Figure 1(a) the frame is subjected to self weight only. The intention is to demonstrate the step by step procedure of pushover analysis in SAP2. II. PURPOSE OF DOING PUSH OVER ANALYSIS The pushover is expected to provide information on many response characteristics that cannot be obtained from an elastic static or dynamic analysis. The following are the examples of such response characteristics: 1. The realistic force demands on potentially brittle elements, such as axial force demands on columns, force demands on brace connections, moment demands on beam to column connections, shear force demands in reinforced concrete beams, etc. 2. Estimates of the deformations demands for elements that have to form inelastically in order to dissipate the energy imparted to the structure. 3. Estimates of the inter storey drifts that account for strength or stiffness discontinuities and that may be used to control the damages and to evaluate P-Delta effects. 4. Identification of the strength discontinuous in plan elevation that will lead to changes in the dynamic characteristics in elastic range. III. SCOPE OF PRESENT STUDY In the present study, modeling of the Elevated circular water tank (Base fixed) under loads has been analyzed using SAP2 software and the frame is analyzed using SAP2 software up to the failure and the load deformation curves and results are obtained. In this study default hinges are used in beams and columns and thus pushover graph is obtained from excel spread sheet Figure 1(a): Figure 1(b) Figure 1(a) and Figure 1(b) shows the example frame selected for demonstration and details of reinforcement of the cross-section provided. The step by step procedure of pushover analysis is as follows: Step 1: Geometry Step 2: Section and Material properties Step 3: Nonlinear hinge properties Step 4: Load patterns and load cases

3 Base Shear (kn) Base Shear(kN) Proceedings of International Conference on Advances in Architecture and Civil Engineering (AARCV 212), 21 st 23 rd June Step 5: Analysis. Step 6: Results Figure 2 shows the capacity curve for the example frame considered (Inel and Ozmen). The base shear is linear upto 4 kn force corresponding to roof displacement.1m Roof Displacement (m) Figure 2: Capacity Curve for the Example Frame (Base Shear versus Roof Displacement) VI. BENCKMARK PROBLEM FOR VALIDATION AND DISCUSSIONS Inel and Ozmen (26) have studied the effects of plastic hinge properties in nonlinear analysis of reinforced concrete buildings. SAP 2 Nonlinear Version 8 has been used for pushover analysis by Inel and Ozmen (26). Pushover analysis is carried out for default as well as user defined hinge properties. A 4-story building of plan dimensions 16m x 12m is used for study as shown in Figure 3(a). This consists of typical beam-column RC frame building with no shear walls. Typical floor to floor height is 2.8m. The building is 11.2 m in elevation. Material properties are assumed to be 16 MPa for the concrete compressive strength and 22MPa for yield strength of both longitudinal and transverse reinforcements. Types of column sections are given in Figure 3(b) All beams are of 2mm x 5mm and amounts of top and bottom reinforcement is shown in Figure 3(c) and column dimensions are given in the Figure 3(d). Transverse reinforcement spacing of 1mm has been considered. The dead and participating live loads (3% of live load) on the frame are 1976 kn and 36 kn. Since there is no torsional effect in the selected structure, two-dimensional modeling is employed. The first mode period is.755 s. Modal properties of first three modes are given in Table 1. Figure 4 shows the capacity curve for benchmark problem given by Inel and Ozmen. Table 1: Dynamic Characteristics of the Benchmark Problem Mode No Period (s) Mass participation factor Figure 3: Details of Structure (Inel and Ozmen, 26) PUSHOVER Displacement (m) Figure 4: Capacity Curve for Benchmark Problem The present study is as follows: a water tank of 9 litres capacity with height of staging 16m upto the bottom of the tank. The tank is supported with 8 columns symmetrically placed on a circle of 1.6m mean diameter. The staging of the tank is divided into 4 panels each of 4m height. The columns are connected to foundation by means of ring beam, the top of which is provided at 1m below the ground level so that actual height of first panel is 5m. Modulus of Elasticity of steel, E s (MPa) Table 2: Basic Material Properties Modulus of Elasticity of concrete, E c(mpa) Characteristic strength of concrete, f ck(mpa) Yield stress for steel, f y(mpa) Ultimate strain in bending, Ƹ cu

4 Proceedings of International Conference on Advances in Architecture and Civil Engineering (AARCV 212), 21 st 23 rd June Table 3: Typical Dimensions of Brace and Reinforcement Adopted B (m m) D (mm ) Top Cover Botto m Cover Top steel diamet er Botto m steel stirrup s Diam eter of stirrup Spacin g of stirrups The plan and sectional elevation of the elevated water tank considered for the present study is shown in Figure. 5(a) and 5(b). The skeleton 3D View of bracings, columns and bottom ring beam is shown in Figure 6(a) and the details of the bottom ring beam is given in Figure 6(b). Figures 6(c) and 6(d) shows the details of circular column detailing of bracings respectively Figure 6(a): 3D View of Bracings, Columns Figure 5(a): Plan of Water Tank Figure 6(b): Details of Bottom Ring Beam and Bottom Ring Beam Figure 6(c): Details of Circular Column Figure 5(b): Sectional Elevation of the Structure Figure 6(d): Details of Bracings

5 Base Shear (kn) Proceedings of International Conference on Advances in Architecture and Civil Engineering (AARCV 212), 21 st 23 rd June VII. RESULTS AND DISCUSSIONS In the present study, non-linear response of elevated water tank modeled as per details mentioned above. The objective of this study is to see the variation of load-displacement graph and check the maximum base shear and displacement of the frame. Figure 7 shows the capacity curve obtained from the present study using SAP2. Table 4 gives the list of displacement and base force for various steps of analysis from which capacity curved is obtained PUSHOVE R CURVE Displacement (m) Figure7: Capacity Curve for Elevated Water Tank Table 4: Tabular Data for Capacity Curve Step Displacement Base Force (m) (kn) Figure 8: Elevated Circular Liquid Storage Tank with Columns Rigid at Top and Fixed at Footings An elevated circular liquid storage tank with columns rigid at top and fixed at footings is shown in Figure 8. Figures 9 to 14 describes the deformed shapes of the frames at various steps of analysis and also the formation of hinges on the columns and braces. The colour code at the bottom of the figures helps in identifying the intensity of the hinge formation. At step and 1 (Figures 9 and 1 ), ie, in the early steps of analysis, there is no deformation and hence hinges are not observed and also colour code do not appear at the bottom of the figure. Figure 9: Deformed Shape of the Frame at Step-

6 Base Shear(kN) Proceedings of International Conference on Advances in Architecture and Civil Engineering (AARCV 212), 21 st 23 rd June Figure 1: Deformed Shape of the Frame at Step-1 Figure 13: Deformed Shape of the Frame at Step-15 Figure 11: Deformed Shape of the Frame at Step-5 Figure 14: Deformed Shape of the Frame at Step Comparison between the SAP 2 model and the bench mark problem (Inel and Ozmen) Present study Inel and ozmen Displacement (m) Figure 12: Deformed Shape of the Frame at Step-1 Figure 15: Combined Capacity Curve

7 Proceedings of International Conference on Advances in Architecture and Civil Engineering (AARCV 212), 21 st 23 rd June Base shear v/s roof displacement are plotted in Figure 15. From the present study it is seen from Figure 15, the maximum displacement has been obtained as 34mm and the average top drift is therefore equal to about 2.5% of the total height of the building. And for the bench mark problem the maximum displacement has been obtained as 21mm and the average top drift is therefore equal to about 2% of the total height of the building. VIII. CONCLUSIONS In the present study, the non-linear response of RCC frame of an elevated circular liquid storage tank using SAP 2 under the loading has been carried out with the intention to study the relative importance of several factors in the nonlinear analysis of RC frames. The frame behaved linearly elastic up to a base shear value of around 31 kn. At the value of base-shear 91 kn, it depicted non-linearity in its behavior. Increase in deflection has been observed to be more with load increments at base-shear of 91 kn showing the elasto-plastic behavior. The joints of the structure have displayed rapid degradation and the inter storey deflections have increased rapidly in non-linear zone. The frame has shown variety of failures like beam-column joint failure, flexural failures and shear failures. Prominent failures are joint failures. REFERENCES [1] ATC (1997)., NEHRP Guidelines for the Seismic Rehabilitation of Buildings. FEMA 273 Report, prepared by the Applied Technology Council for the Building Seismic Safety Council, published by the Federal Emergency Management Agency, Washington, D.C. [2] Habibullah, Ashraf., Stephen and Pyle.(1998). Practical Three- Dimensional Nonlinear Static Pushover Analysis. Structure Magazine, U.S.A, 1-2. [3] Kadid and Boumrkik. (1987). Pushover Analysis of Reinforced Concrete Frame Structures, Asian Journal of Civil Engineering (building and housing). [4] Mehmet Inel and Hayri Baytan Ozmen.(26). Effects of plastic hinge properties in nonlinear analysis of reinforced concrete buildings. Department of Civil Engineering, Pamukkale University, 27 Denizli, Turkey. [5] Priestley, M. J. N., and Park R. (1987). Strength and Ductility of Concrete Bridge Columns under Seismic Loading. ACI Structural Journal, Technical paper, Title n 84-S8, 79(1),