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A MATLAB COMPUTER PROGRAM FOR 3- DIMENSIONAL DYNAMIC ANALYSIS OF MULTISTORY BUILDINGS

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OBJECTIVE To present a MTLAB program for conducting three dimensional dynamic analysis of multistory building by utilizing a simple and ‘easy to understand’ plane frame analysis program. To extend the program to do dynamic response spectrum analysis of buildings.

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Why MATLAB ? MATLAB has built-in functions that performs various computational tasks. This reduces, substantially, the program size. Matrix operation in MATLAB are conducted similar to scalar operation. With MATLAB graphic capability, it possible, with a little programming effort, to obtain a graphic display of the results including structure geometry, bending and shear force diagrams, deformed shape … etc.

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Shear an Moment Diagrams in a Member Deformed Shape

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Structural and General Purpose FE Software: SAP2000 ETABS STAAD/pro OTHERS : ANSYS, ABAQUS, ….ETC

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Three dimensional fully detailed finite element model of the building structure very expensive Three dimensional frame model large DOF Three dimensional frame model with rigid diaphragm constraint 3 DOF at each floor A set of orthogonal (two-way) planar frames with rigid diaphragm constraint Plane frame structure regular and symmetric building BUILDING MODELS FOR SEISMIC ANALYSIS

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THREE DIMENSIONAL FRAME WITH RIGID DIAPHRAGM CONSTRAINT ASSUMTIONS: 1. The floor diaphragm is rigid in its own plane. This Allows the horizontal displacements at a floor level to be defined in terms of floor horizontal translations and rotation about a vertical axis. 2. Building Structure Is Represented by a Set of Orthogonal planar Frames.

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1. RIGID DIAPHRAGM APPROXIMATION 3 DOF at each floor + 3 DOF at each node Mass center

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Analysis Procedure: 1. Identify Building Frames Six planar frame Two different types Typical Frame

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2. Construct Global Stiffness Matrix for each Typical frame 3. Apply displacement constraint to horizontal degrees of freedom at each level eliminate horizontal degrees of freedom but one at each floor

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4. Apply static condensation to eliminate all degrees of freedom but horizontal ones Number of degrees of freedom=Number of floor. Static Condensation

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5. Construct the global stiffness matrix for the 3D model by applying rigid diaphragm constraints to each plane frame stiffness matrices using the Number of degrees of freedom=3*Number of floor. Apply to frames in x-direction Apply to frames in y-direction

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5. Construct the diagonal Mass matrix

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Verification Examples (ETABS USER MANUALS) Two Story Three-Dimensional Unsymmetrical building Dynamic Response Spectrum Analysis Seismic excitation:Elcentro Response Spectrum at 30 to X

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Results Comparison 1.Structural periods ProgramReference 0.4500.4146 0.3960.3753 0.2470.2436 0.1340.1148 0.1200.1103 0.0870.0729

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2. DYNAMIC RESPONSE SPECTRUM BASE SHEARS:

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CONCLUSIONS Building Analysis using plane frame analysis programs with constraints gives results which are comparable to 3-dimensional analysis A plane frame representation of a three dimensional building structure is easier for visualization and preparation of data MATLAB is a powerful means that could be used for programming simple equations of design to the complicated structural analysis programs.

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