Static and Dynamic Analysis of Multi-storey Frame using Finite Element Method

Abstract

This study is devoted to understand the behavior of computer models and methods for predicting the static and dynamic response of multistorey buildings. To obtain the general objective of the study different two and three-dimensional multistorey shearwalled and wall-framed structures are taken and static and dynamic analysis procedure has been performed. The usefulness of walls in structural planning of multistorey buildings has long been recognized. The potential advantages of a wall-frame structure depend on the amount of horizontal interaction, which is governed by the relative stiffness of the walls and frames, and the height of the structure. Different multistorey shear walled frames with and without openings had been analyzed using SAP2000. Its parametric study includes formulation of storey displacements for multistorey shear wall-frame structures, top storey displacements with various percentage openings in shear wall, time period calculation, shear wall’s and shear walled frame’s stiffness with different percentage openings. In addition the stiffness reduction factor with different percentage openings in shear wall has been studied, which deliberately explains up to what percentage opening the shear wall remains effective in resisting lateral loads. It is observed that the stiffness of shear-walled frame does not equal to the addition of the stiffness of shear wall and stiffness of frame. Infill wall is playing a very important role in the behavior of structures when subjected to lateral loads. Different modeling techniques for infill wall with their example have been discussed. Static behavior of infill wall with opening on different positions has been studied. Multistorey infilled walls with various openings have been studied for static and dynamic condition. When walls are situated in advantageous positions in a building, they can be very efficient in resisting lateral loads originating from wind or earthquakes. Different IV symmetrical as well as unsymmetrical buildings with 5,10,20 and 30 storey and with different positioning of shear walls have been taken and response spectrum procedure has been implemented using SAP2000. The parametric study includes comparison of time period, storey displacements, earthquake forces in any particular direction taken by shear wall and frame. Analytical results have been presented in graphical form to understand the behavior of building with increasing storey height. The outcome of earthquake forces taken by frame and shear wall for different shear wall positions and for different building types has been discussed in detail. For unsymmetrical buildings eccentricities in both x and y directions for different position of shear walls have been found out using ETABS. How different positions of the shear wall affect the result for base shear in both x and a y direction is found out from the study made using SAP2000. A Visual C++ program has been developed for the static and dynamic analysis of multistorey frames and shear walls. Microsoft visual C++ environment provides the facility to write windows GUI (Graphical User Interface) programs in addition to console programs, which takes full advantage of the windows graphical user interface. For the dynamic analysis of framed structures the frame element has been taken for both stiffness and mass matrix formulation and for shear walled structure CST (Constant Strain Triangle) and Rectangular elements have been taken. The mass matrix is formulated using either of consistent mass technique or lumped mass technique. Program will develop the banded mass and stiffness matrices from the bandwidth calculation and from these banded matrices modal frequencies and time period for the user defined eigenvalues, using inverse iteration technique, are formulated.