Very brief introduction to SAP2000 API and modelling of complex geometry structures using the API.

1. Modelling Complex Geometry Structures
Valerio Stuart

2. Modelling Complex Geometry Structures
Contents:
• Complex geometries
• Applications
• SAP2000 & API
• Case study
• Rhinoceros & Grasshopper
• Architects & Competitors
• Case studies

3. • Shells
• Helicoids
• Catenoids
• Gaussian surfaces
• Hyperboloids
• Surfaces of revolution
• Other weird stuff
Complex geometries

4. From math to the real world
Yas Viceroy, Abu Dhabi - Asymptote Architecture

5. From math to the real world
Aliyev Centre, Baku Azerbaijan - Zaha Hadid

6. From math to the real world
Walt Disney Concert Hall - Frank Gehry

7. From math to the real world (UK)
Aquatic Centre, London UK - Zaha Hadid
(Ove Arup & Partners)

8. From math to the real world (UK)
Savilll Garden Visitor Centre - Glen Howells
Architects (Buro Happold)

9. From math to the real world (UK)
Olympic Velodrome, London UK - Hopkins
Architects (Expedition Engineering)

10. SAP2000

11. Conventional modelling approach using SAP2000
• Draw the geometry in CAD
• Export the geometry in .dxf format
• Import the .dxf into SAP2000
• Mesh the geometry using the SAP2000 mesh generator
(or manually!)
Other approaches are possible, and there are other tools available in the market
to mesh complex geometries (other than the built-in SAP2000 mesh generator).
However, each program is different and might or might not be able to
communicate with SAP2000 or any other structural analysis software you
intend to use.

12. SAP2000 Application Programming Interface (API)
• Software library that offers access to a collection of objects and functions
capable of remotely controlling the way that SAP2000 behaves.
• Programming tool which allows to bind any third-party application to the
analysis software.
• Allows the user to develop plug-ins which can communicate with
SAP2000 and carry out routine tasks or other time consuming exercises.

13. Alternative approach using SAP2000 API
• Identify a surface that can reproduce the desired shape
• Define the type of coordinate system, depending on the type of surface
(e.g.: Cartesian, Polar, etc)
• Algebraically define the domain of the surface
• Discretise the surface into a finite number of nodes and define their position in
the 3D space
• Define others properties of the structure (e.g.: materials, loads, etc)
• Create a text file in .s2k format that can be imported into SAP2000
The API can also be used to run multiple analysis, export and manipulate results
to carry out different studies.

14. Case study
Kresge Auditorium, MIT Boston, USA - Eero Saarinen (Amman & Whitney)

15. The Kresge Auditorium
• Thin shell RC structure
• The structure can be reproduced as a portion
of a sphere cut by 4 planes
• The thickness of the shell varies:
• 90mm at the centre
• 130mm at the centre of the arches
• 540mm at the supports
• Radius of the sphere: 34.29m
• Maximum height of the shell: 14.5m
• Maximum height of the edges: 8.0m
• Distance between supports: 48.5m
Several models with different levels of mesh density were
required to carry out mesh sensibility studies.

16. Initial discretisations
• Discretisation of the surface
carried out using the AutoCAD
meshing tool
!
!
!
• Manual discretisation of the
surface

17. Initial discretisations
• Poor quality mesh, with
excessively deformed elements,
mix of triangular and quadrilateral
elements
• Highly time consuming procedure
• If a mesh with different density is
needed (e.g. coarse, fine, etc) the
procedure has to be repeated.
• Thickness of the elements to be
applied manually or approximated
with loss of accuracy.

18. Discretisation using the API
• Definition of the geometry of the structure
on plan, using the shape functions of the
ISO 6 element.
Nodes
Plan view

19. Modelling procedure
• Transformation of the coordinates
into x,y
!
• Definition of the coordinate z for each
node using the definition of a sphere:
!
• Definition of the nodes and triangular
shapes.
Elevation
Numbering of the
Area elements

20. Modelling procedure
• Once the coordinates of the joints are known, it is possible to define
them in the .s2k SAP2000 file:
!
!
• Define the Areas. Triangular elements were used in this study:

21. Modelling procedure
• Using the SAP2000 language it was
also possible to define:
• concrete grade
• type of supports
• element thickness
• load cases (wind, snow)
• load combinations
• other elements (i.e. frames)
and their thickness

22. Modelling procedure
Shell element thickness:
• The position of the centre of mass of each element is known
• It’s possible to define the thickness of each shell element in
relation to the position of its centre of mass

23. Modelling procedure
Wind load:
• The position of the centre of mass of
each element is known
• It’s possible to define the wind load for
each shell element in relation to the
position of its centre of mass

24. Modelling procedure
Snow load:
• The position of the centre of mass of each shell element is known and so is its
inclination
• As per the wind load, the snow load on each element can be defined in relation to the
position of its centre of mass
• It’s also possible to define different load situation, where the snow it’s on a portion of the
structure only.

25. Modelling procedure
• The Matlab script outputs an .s2k which can be imported into SAP2000, containing all
the parameters describing the structure and loads.

26. Results
Once the program to define all the parameters required in the .s2k file
has been set up, a different mesh, material properties, loads, etc. can
be selected in virtually no time.
Mesh density >>>

27. !9000$
!8000$
!7000$
!6000$
!5000$
!4000$
!3000$
!2000$
!1000$
0$
0$ 5$ 10$ 15$ 20$ 25$ 30$
Nmeridiano*[kN]*
*
ρ [m]*
Sforzo*Normale*2*sezione*B2B*
SAP2000$n=150$
SAP2000$n=135$
SAP2000$n=108$
SAP2000$n=75$
Sol.Anali7ca$
Results
• The .s2k files are text files which can be easily saved, stored, exchanged
between users thanks to their small size
• Different models can be easily created for the desired purpose (e.g.: mesh
studies, influence of the elements’ stiffness on the behaviour of the structure,
etc)
!1000$
0$
1000$
2000$
3000$
4000$
5000$
0$ 5$ 10$ 15$ 20$
Nparallelo([kN](
(
ρ [m](
Sforzo(Normale(di(Parallelo(3(sezione(A3A(
SAP2000$n=150$
SAP2000$n=135$
SAP2000$n=108$
SAP2000$n=75$
Sol.$Anali5ca$
9"
15"
30"
45"
75"
108$ 135" 150" 180"
0"
2"
4"
6"
8"
10"
12"
14"
0" 20" 40" 60" 80" 100" 120" 140" 160" 180" 200"
Errore$rela+vo$(%)$
Variazione$della$mesh:$parametro$n$
Errore$rela+vo$(%)$
9"
15"
30"
45"
75" 108" 135" 150" 180"
*1000"
*800"
*600"
*400"
*200"
0"
200"
400"
0" 20" 40" 60" 80" 100" 120" 140" 160" 180" 200"
Nmeridiano*[kN/m2]*
Variazione*della*mesh:*parametro*n*
Valore*dello*sforzo*N*di*meridiano,*nei*pressi*dell'appoggio*
Serie1"

28. Kresge Auditorium

29. SAP2000 Application Programming Interface (API)
• Compatibility with most major
programming languages
• Full control of element connectivity
• Ability to develop both pre- and post-
processing procedures tailored to the
user’s needs
• No need of using intermediate files,
which reduces significantly the time
needed for data exchange when
working on large models
• Once the procedures have been set up
it’s possible to use them for routine
operations, minimising time and human
errors
Advantages & Disadvantages
• Programming background/skills
required
• Learning curve
• Code robustness
• Routines designed for a specific
model might not be applicable to
others

30. Thank you