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Published byMicah Yelton Modified over 2 years ago

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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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**BUILDING MODELS FOR SEISMIC ANALYSIS**

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

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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**

Mass center 3 DOF at each floor + 3 DOF at each node

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**1. Identify Building Frames**

Analysis Procedure: Six planar frame Two different types 1. Identify Building Frames 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 Program Reference

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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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