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

2. 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.

3. 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.

5. Shear an Moment Diagrams in a Member
Deformed Shape

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

7. 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

8. 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.

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

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

11. 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

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

13. 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

14. 5. Construct the diagonal Mass matrix

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

16. Results Comparison
1 .Structural periods
Program Reference

17. 2. DYNAMIC RESPONSE SPECTRUM BASE SHEARS:

18. 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.