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Design Guide of Geodesic Dome

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shui katrina

on 13 March 2014

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Transcript of Design Guide of Geodesic Dome

Easier Design Guide of Geodesic Dome
Background
Objective
Basic information
The Design is
NOT
so popular, especially in Hong Kong
The structure and loading distribution SEEMS complex
No specific design guideline for dome
To Boost the Geodesic Dome Design
1. Explain the idea in a simpler way
2. Ease the understanding and calculation of load distribution
3. Provide a specific design guideline
About Geodesic Dome...
How to divide sphere?
1. Paper model
-for display the idea in a simper way
2. Structural Analysis
-To understand the load distribution in Dome
-Discover a formula of Critical axial force against load and radius
3. Spread Sheet
- by using HONG Kong steel code 2011, check the suitability
- Spreadsheet which ease the user
Name:
Buckminster fuller

Year:
1950s

Qualification:
Engineering
Architecture
Geodesic
= Earth dividing
Dome
= Partial-spherical shell structure
Geodesic Dome =
Dividing a sphere into triangles
Sub-name of dome
2v dome
3v dome
4v dome
5v dome
frequency
Basic Division
-Telling about the number of members
paper model 1
By pentagons and hexagons
2 types of length!
By icosahedron
-The types of length depend on the number of frequency
- Length can be determined by coordinates

By SAP2000
By RISA 3D demonstrator
1. Mainly under
Compression
and
Tension
(continuous
tension
zone with
isolated
compression
member)
2. Negligible
Moment

Maximum Axial Force
under
different
Radius
of dome
Maximum Axial Force
under
different
Load
of dome
Result from two graphs
Maximum Axial Force(F)
α
loading(x)
Radius(r)
Proposed Equation:
where F is Maximum Axial Force (N)
k is a constant
r is radius (m)
x is loading (N/m)

F
= k *
r
*
x

F = k * r * x
Vertical UDL
For Maximum Tension,
k = 1.99
F = 1.99*radius*UDL load

For Maximum Compression,
k = -1.08
F = -1.08 * radius* UDL Load

Lateral UDL
For Maximum Tension,
k = 3.2
F = 3.2*radius*UDL load

For Maximum Compression,
k = -2.4
F = -2.4 * radius* UDL Load

F/x =
k
* r
- Spherical shape but all members are straight

- Use minimum of material
create maximum space

- Fully utilize the strength of members

- Good appearance
Special of the design
Inventor
Definition
Class of Division
Sub-division of triangles in icosahedron
Design Step 1 : Choice of geometric outlook

1. Choice of radius of dome
2. Choice the sub-division of dome


Gain the number of members
Design step 2: Choose material
- To generate the critical case of dome



Past: Modeling
Now: Formula


If I want to make a dome...
Reading numbers of paper to understand the principle and geometry
Run model to gain the critical section load
Check the code to ensure safety
Checking Safety by HKSC
1. Compression Capacity

2. Tension Capacity

3. Slenderness Ratio

4. Buckling
To understand the load distribution
adding point load on the top
Limitation
1. Only cover the quick formula of Max axial loading of 2v,3v,4v dome
2. Spread sheet is only suitable for circular hollow section of steel
How to determine the length of member?
Factor affecting
radius of dome

Frequency of Dome
Chord Factor
2v Dome
Type of member
Chord Factor
No. of member
Length = Radius * Chord Factor

3v dome
4v dome
Projection of line
center of dome
point of icosahedron
projection of sub-division point
Work Done
-Study Detail about loading in each member
Findings
fact: For same division,
Max. Axial Load (Compression, tension) when



Load adding
Radius
Conclusion
Applying same vertical UDL with various radius
Applying varies vertical UDL with same radius
Design Step3: Check Safety with code


Past: Read out from the code one by one
Now: Spreadsheet

Reason
by icosahedron
Design Step 1: Making Choice

1. Choice of radius of dome
2. Choice the sub-division of dome


Gain the number of members
Design step 2: Choose material
- To generate the critical case of dome



Past: Modeling
Now: Formula


Design Step3: Check Safety with code


Past: Read out from the code one by one
Now: Spreadsheet

Reference
G S Ramaswamy. Analysis, design and construction of steel space frames, first edition, 2002
Robert William Burkhardt, A practical guide to tensegrity design.
[Last Accessed: 19th February 2009], 2007. URL http://bobwb.tripod.com/tenseg/book/revisions.html.
R.C. Coates, M.G Coutie, and F.K. Kong, Structural Analysis. Chapman and Hall, third
edition, 1988.
Fiona Cobb. Structural Engineer’s Pocket Book. Blackwell House, 2007.
R. F. Craig. Craig’s Soil Mechanics. Spon Press, seventh edition, 2004.
Tom Davis, Geodesic dome, September 15,2004. URL: www.geometer.org/mathcircles

Thank you!
Q & A Section

TO boost the use of geodesic dome...
to ease the design...
Full transcript