**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 concrete 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 load 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

Q & A Section

to ease the design process