Dome Design Aiding and Abetting Spaghetti Domers

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Dome DesignAiding and Abetting Spaghetti Domers

• Ben Schafer
• 23 October 2002

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Objective

• Your design should be the most aesthetically
  pleasing structure that carries a 0.5 psi demand
  pressure using the least amount of building
  materials (spaghetti. and epoxy) while enclosing
  the greatest possible volume.

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LOADING APPARATUS
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UNDER LOAD
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Dome Design
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Dome Design

• REALIZATION
• Sketches and forms
• Think about construction too!
• DEMAND - GLOBAL
• Whats my target load (pressure)?
• DEMAND - LOCAL
• What does that mean in terms of forces on my
  members?
• CAPACITY
• What should I select for my material properties
• Are my members strong enough (sizing)

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A REALIZATION
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Starter example
I am dreaming up the small dome below, how do I
get started on designing it - at least
preliminarily?
REALIZATION!
view of my dome from above.
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Stress Demands
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Force Demands
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DEMAND - GLOBAL
SIMPLIFIED DEMAND FOR PRELIMINARY CALCULATION!
The pressure I want to withstand is 0.5 psi. The
vertical area I am covering is pd2/4 p(16
in.)2/4 200 in.2 The vertical load my dome
needs to support is 0.5psi 200 in.2 100 pounds
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DEMAND - LOCAL
My dome touches down in 5 places, so each
leg must support 100 lbf/5 20lbf.
20lbf
Here I assume each leg carries equal load,
sometimes correct, sometimes not.
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Compression Capacity
Pn compression capacity of one member E
Youngs modulus, also called modulus of
elasticity I moment of inertia of a member L
unsupported length of a member A cross-sectional
area of a member fb breaking stress of a member
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E
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sf
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CAPACITY - LOCAL
What amount of spaghetti do I need in each leg to
carry 20 lbf?
Assume, to start, members are well enough braced
that crushing instead of buckling controls.
Then PnAsf Based on the material data I
conservatively select 15 MPa as the fracture
stress 15MPa 2.175ksi 2000psi Required
Spaghetti area? A 20lbf/2000psi 0.01 in2
Required Spaghetti diameter 0.014/(p).5
0.11in. 2.86mm (at least 3 strands)
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CAPACITY - LOCAL
Realistic to use 0.11 in diameter spag?
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CAPACITY - LOCAL
Realistic to use 0.11 in diameter spag?
Well? Have to keep unbraced length 1 ¼ in. or
use more spaghetti and longer unbraced lengths
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multi-strand spag. members
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Moment of Inertia
consider cross-section of several strands of
connected spaghetti
one strand is
d1 Apd12/4 Ipd14/64
but that is not useful as we have many strands
together, in our example we might approximate
this as one big strand with a diameter of 3d1,
which we will call d3
d3 Apd32/4 Ipd34/64
so, use that A and I in your formulas!
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We can do better!

• DEMAND
• Use dome analysis presented here
• Consider bending demands!
• Use structural analysis to get forces in members
• CAPACITY
• Consider bending capacity
• Consider testing a portion of your substructure!

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What is Engineering? Spaghetti Dome Contest Fall
2001
Good dome that did not quite make the load.
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What is Engineering? Spaghetti Dome Contest Fall
2001
here enough I, is provided by using thicker and
more members.
certified for load
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What is Engineering? Spaghetti Dome Contest Fall
2001
here enough I is provided by using members with
depth, i.e., two sets of parallel members
1st Economic volume/weight
certified for load
1st Efficiency strength/wt ratio
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I and A of each bundled piece and I and A of
whole thing!
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Moment of inertia continued
d2

h
in cross-section we have several strands of spag.
on top and bottom separated by the diagonal
members. We want to know how strong the resulting
truss is for our example, d2 2d1
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Moment of inertia continued
d2

h
A2(pd22/4), full area is 2A2 I2(pd24/64),
full I depends! strong-axis (in-plane)
buckling/bending Istrong 2I2 2A2(h/2)2
weak-axis (out-of-plane) buckling/bending Iweak
2I2 Need to brace against weak-axis buckling!
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Checking bending?
make sure you provide enough I!!
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What is Engineering? Spaghetti Dome Contest Fall
2001
Take a look at what worked in years past!
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