NONLINEAR STATIC ANALYSIS OF R.C.C. FRAMES (Software Implementation ETABS 9.7) Mrugesh D. Shah M.E Structure student, B.V.M Engineering College Abstract:- Nonlinear static analysis is an iterative procedure so it is difficult to solve by hand calculation and that s why software is required to do nonlinear static analysis. ETABS 9.7 have features to perform nonlinear static analysis. This paper is an approach to do nonlinear static analysis in simplify and effective manner. Keyword:- ETABS 9.7, modeling, static analysis, Designing, Pushover analysis I. Introduction The nonlinear analysis of a structure is an iterative procedure. It depends on the final displacement, as the effective damping depends on the hysteretic energy loss due to inelastic deformations, which in turn depends on the final displacement. This makes the analysis procedure iterative. Difficulty in the solution is faced near the ultimate load, as the stiffness matrix at this point becomes negative definite due to instability of the structure becoming a mechanism. Software available to perform nonlinear static (pushover) analysis are ETABS, SAP, ADINA, SC-Push3D Extended Three Dimensional Buildings Systems (ETABS) and Structural Analysis Program finite element program that works with complex geometry and monitors deformation at all hinges to determine ultimate deformation. It has built-in defaults for ACI 318 material properties and ATC-40 and FEMA 273 hinge properties. Also it has capability for inputting any material or hinge property. ETABS 9.7 deals with the buildings only. The analysis in ETABS 9.7 involves the following four step.1)modeling,2)static analysis, Designing 4)Pushover analysis Steps used in performing a pushover analysis of a simple three-dimensional building. 1. Creating the basic computer model (without the pushover data) in the usual manner. 2. Define properties and acceptance criteria for the pushover hinges. The program includes several built-in default hinge properties that are based on average values from ATC-40 for concrete members Sumant B. Patel Associate prof. B.V.M Engineering College and average values from FEMA-273 for steel members. These built in properties can be useful for preliminary analyses, but user defined properties are recommended for final analyses. 3. Locate the pushover hinges on the model by selecting one or more frame members and assigning them one or more hinge properties and hinge locations. 4. Define the pushover load cases. In ETABS 9.7 more than one pushover load case can be run in the same analysis. Also a pushover load case can start from the final conditions of another pushover load case that was previously run in the same analysis. Typically a gravity load pushover is force controlled and lateral pushovers are displacement controlled. 5. Run the basic static analysis and, if desired, dynamic analysis. Then run the static nonlinear pushover analysis. 6. Display the pushover curve and the table. 7. Review the pushover displaced shape and sequence of hinge formation on a step-by-step basis. II. BASIC STEPS A) Create the model 1) Create the basic grid system This step shows how to create the basic grid system. The structural objects are set relative to the grid system. Begin creating the grid system by clicking the File menu > New model button, the form shown in fig.1 will be Fig.1 New Model Initialization form Select the Default.edb button on the form shown in fig..1, form shown in fig.2 will be
displayed and in this form define Grid dimension, Story dimension and Units. Fig.5 Material Property Data Form 4) Define section properties Begin defining various section properties used in the model by clicking the Define menu > Frame Section command, the form shown in fig.6 will be Fig.2 Building Plan Grid System and Story Data Definition form 2)RC frame code selection Select the Option menu > Preferences > Concrete frame design command. Select the appropriate Design code. Define the material properties 3) Begin defining various material properties used in the model by clicking the Define menu > Material properties command, the form shown in fig.4 Will be Fig.6 Define Frame Properties form Select the Add Rectangular button on the form shown in fig.6, form shown in fig.7 will be displayed and in the form add Section Name, Dimensions, and Material. Fig.7 Rectangular Section form Fig.4 Define Materials form Select Add new Material or Modify/Show Material button on the form shown in fig.4, form shown in fig.5 will be displayed, Define material property data. 5) By clicking the Define menu > Wall/Slab/Deck Sections command, the form shown in fig.8 will be Fig.8Define Wall/Slab/Deck Section form
Select the Modify/show section or Add new Deck button on the form shown in fig.8, form shown in fig.9 will be displayed and in the form add Deck type, Geometry. Fig.11 Define Static load cases Names form In case of Earth Quake Load, Changes the Direction and Eccentricity, Seismic Coefficients select Modified Load form shown in fig.12 will be Fig.9 Deck Section form 6). Draw Beam, Column, Slab Begin Draw various elements are used in the model by clicking the Draw menu > Draw Line Objects > Create Lines in Region or at click command, the form shown in fig.10 Will be Fig.12 IS 1893:2002 Seismic loading form Fig.10 Create Lines in Region or at click form Similarly slabs and columns are draw. 7. Define the Static load cases Add a static load case, click the Define menu > Static Load Cases command button, to access the Define Static Load Case Names the form Shown in fig.11 Complete the following action using that form: 1. Type the name of the load case in the Load edit box. The program does not allow use of duplicate names. 2. Select a load type from the Type dropdown names. 3. Type a self-weight multiplier in the Self-weight Multiplier edit box. 4. If the load type specified in Quake or wind, Select an option from the Auto Lateral Load drop-down list. 5. Click the Add New Load button. 8. Assign Structural Loads The load cases define are required in order to be able to assign loads to points/joints, lines/frames, and areas/shells. The user must first select the object before a load can assigned to the object. After the object has been selected, Click the Assign menu > Shell/Area load > Uniform command. Form shown in fig.13 will be Fig.13 Uniform Surface loads form Select the Load Case Name, Magnitude of load and Direction. 9. Define Analysis option To Define analysis option select Analysis menu > Set Analysis Option command. III Run static analysis
To run analysis select the Analysis menu > Run Analysis command. Once the analysis is performed successfully, the results like deformations, shear forces, bending moments of each element can be displayed or listed for each load cases and load combinations cases defined in the Display menu. III Design the structure The ETABS 9.7 design include the following Steel Frame Design Concrete Frame Design Composite Beam Design Steel Joist Design Shear Wall Design To perform the design, first run the analysis, then click on the Option menu > Preface to select the Design code and then click the Design menu and select the appropriate design from the drop down menu. For an example, Let us take design of concrete frame. Firstly select frame members then select Design menu > Concrete Frame Design > Start design/check. IV Pushover analysis 1) Define hinge properties Frame nonlinear properties are used to define nonlinear force-displacement and/or moment rotation behavior that can be assigned to discrete locations along the length of frame elements. These nonlinear hinges are only used during static nonlinear analysis. For all other types of analysis, these hinges are rigid and have no effect on the linear behavior of element. Types of hinge properties: There are three types of hinge properties in the software: Default hinge property, User defined hinge property and generated hinge property. Only default hinge property and user defined hinge property can be assigned to the frame elements. When a default or user defined hinge property is assigned to any frame element, it will automatically creates a new generated hinge property for each hinge. Fig.14 shows the default hinge properties available with the software. Default hinge properties are as per ATC-40 and FEMA 273. Fig.14 Define Frame Hinge Properties form Assign hinge properties: To assign hinge properties, after selection the frame elements, click the Assign menu > Frame/Line > Frame Nonlinear hinges. For beam default M3 and Default V2 hinges and for column default P-M-M hinges are assign. 2) Define static push over cases: Pushover analysis is a powerful feature available with the software. To add a static pushover cases, click the Define menu > Static Nonlinear/Pushover cases command, the Define static Nonlinear Cases form as shown in fig.15 will be Fig.15 Define Static Nonlinear Cases form Select the Add new case button on the form shown in fig.15, form shown in fig.16 will be As shown in Fig.16 and Fig.17 for defining the Static Nonlinear Cases (Pushover Cases) requires the understanding of following points:
GF 600x600 230 500 2 1st floor 600x600 230x500 2 2nd floor 500x500 230x450 1.5 3rd floor 500x500 230x450 1.5 4th floor 450x450 230x450 1.5 The storey height was 3m and the support condition at base was assumed to be fixed. VI RESULTS Fig.16 Static Nonlinear Case Data PUSH1 The ultimate base shear is around 2794 kn and the corresponding roof displacement is 243mm. The capacity spectrum curve of the same model is shown in Fig.16. Red curve in the Fig. 16 shows the response spectrum curve for various damping values. The base shear at performance point is 1269 kn and corresponding displacement is 64 mm. Fig 18. Capacity spectrum curve for EQ-X dir Fig.17 Static Nonlinear Case Data PUSH2 V Example In the model, the support condition was assumed to be fixed and soil condition was assumed as medium soil. Building was a symmetric structure with respect to both the horizontal directions. It was X- direction and Y-direction, each of 4m in length. All the slabs were considered as shell element of 150mm thickness. The model was the bare frame having beams, columns and slabs. The geometric properties are listed in Table. M25 grade concrete and Fe415 steel.. Floor Column Size mm mm Beam size mm mm Live Load KN/ m2 The pushover analysis was including ten steps. It has been observed that, on subsequent push to building, hinges started forming in beams first. Initially hinges were in B-IO stage and subsequently proceeding to IO-LS and LS-CP stage. At performance point, where the capacity and demand meets, out of 330 assigned hinges 261 were in A-B stage, 31, 38, and 0 hinges are in B- IO, IO-LS and LS-CP stages respectively. As at performance point, hinges were in IO-LS range,
overall performance of building is said to be Immediate occupancy to Life Safety. VII Conclusion Software used for nonlinear static analysis ETABS 9.7 having features of performing performance based analysis by going through some simple steps. Refrances:-1. ATC-40 - Seismic Evaluation and Retrofit of Concrete Buildings, Applied Technology Council, November 1996. 2.FEMA-273 - NEHRP Guidelines for the Seismic Rehabilitation of Buildings, Federal Emergency Management Agency, October 1997. 3. ETABS User s Manual, Integrated Building Design Software, Computer and Structure Inc. Berkeley, USA 4. Code and Commentary on IS:1893-2002 (Part1) IITK- GSDMA-EQ05-V2