# faculty.ksu.edu.saaldeghaitherPubsdynamic_pres.ppt by yurtgc548

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```									A MATLAB COMPUTER PROGRAM FOR 3-
DIMENSIONAL DYNAMIC ANALYSIS OF
MULTISTORY BUILDINGS
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.
Why MATLAB ?
q MATLAB has built-in functions that performs
substantially, the program size.
q Matrix operation in MATLAB are conducted
similar to scalar operation.
q 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.
• Shear an Moment
Diagrams in a Member

• Deformed Shape
Structural and General Purpose FE
Software:

• SAP2000
• ETABS
• OTHERS : ANSYS, ABAQUS, ….ETC
BUILDING MODELS FOR SEISMIC
ANALYSIS
• Three dimensional fully detailed finite element
model of the building structure Þ very expensive
• Three dimensional frame model Þ large DOF
• Three dimensional frame model with rigid
diaphragm constraint Þ 3 DOF at each floor
• A set of orthogonal (two-way) planar frames
with rigid diaphragm constraint
• Plane frame structure Þ regular and symmetric
building
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
2. Building Structure Is Represented by a Set
of Orthogonal planar Frames.
1. RIGID DIAPHRAGM APPROXIMATION

Mass
center

3 DOF at each floor
+ 3 DOF at each node
Analysis Procedure:
• Six planar frame
1. Identify Building
Frames                 • Two different types

Typical Frame
2. Construct Global
Stiffness Matrix for
each Typical frame

3. Apply displacement
constraint to horizontal
degrees of freedom at
each level Þ eliminate
horizontal degrees of
freedom but one at each
floor
4. Apply static condensation to eliminate all
degrees of freedom but horizontal ones Þ
Number of degrees of freedom=Number of floor.

Static Condensation
5. Construct the global stiffness matrix for the
3D model by applying rigid diaphragm
constraints to each plane frame stiffness
matrices using the ÞNumber of degrees of
freedom=3*Number of floor.

Apply to frames in x-direction

Apply to frames in y-direction
5. Construct the diagonal Mass matrix
Verification Examples (ETABS USER MANUALS)

Two Story Three-Dimensional Unsymmetrical building
Dynamic Response Spectrum Analysis
Seismic excitation:Elcentro Response Spectrum at 30 to X
Results Comparison

1 .Structural periods
Program   Reference
0.450     0.4146
0.396     0.3753
0.247     0.2436
0.134     0.1148
0.120     0.1103
0.087     0.0729
2. DYNAMIC RESPONSE SPECTRUM BASE SHEARS:
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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