# Structural and General Purpose FE Software SAP ETABS

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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 ?
 MATLAB has built-in functions that performs
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.
• 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  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
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

uxi )  uxm)  y (i )um)
(       (            (
z             3 DOF at each floor
+ 3 DOF at each node
u   (i )
y      u   ( m)
y       x u z
(i ) ( m)
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  eliminate
horizontal degrees of
freedom but one at each
floor
4. Apply static condensation to eliminate all
degrees of freedom but horizontal ones 
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 Number of degrees of
freedom=3*Number of floor.

uxi )  uxm)  y (i )um)
(       (            (
z
Apply to frames in x-direction

u(yi )  u(ym)  x(i )um)
(
z
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:

MODE   DIRECTION-X            DIRECTION-Y

program    reference   program    reference
1    0.0        0.652       105.4418   100.016
2    162.7916   168.372          0     -1.127
3    3.2791     2.12             0     .01
4    0.0        .048          9.2353   10.295
5    14.1575    15.329           0     -.065
6    0.420      .01              0     0
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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 views: 40 posted: 10/4/2012 language: English pages: 19