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Isaac Asimov Chair
A MANIFESTO for ISAAC ASIMOV There is no up or down in space, where gravity holds no domain. There are no directions either, what is right becomes left a moment later. Space is free, space is fun, space might be the ideal vacuum for thinking after all. Without orientation, we can see clearly , and without prejudice or bias. We gain versatility, we become truly neutral and open to all angles and points of view. Asimov embraced this freedom in his writing and the Asimov chair brings it forth to the physical realm. The chair rests in motion, every position is equally valid and all rotations are correct. It embraces the individual, acting as an extension of their body to carry them through physical and intellectual movement as well as welcomes multiple people to sit on it, becoming a platform for socio-political collision. There is no polarization, but only ideas, vision and revolution.
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Isaac Asimov Chair
contents INTRO
isaac asimov and design Process documentation
construction process part one
dead loading part two
live loading PART three
moment frame forces PART FOUR
combined loading and reflections
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“So the universe is not quite as you thought it was. You’d better rearrange your beliefs, then. Because you certainly can’t rearrange the universe.” -Isaac Asimov
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Isaac Asimov Chair
INTRO: THE LIFE OF ISAAC ASIMOV Sci-fi Writer, Humanist, Biochemist. January 2, 1920 – April 6, 1992 Isaac Asimov was a master writer and prominent intellectual from the golden era of science fiction. His magnum opus, the Foundation series, a science fiction epic, considered one of the greatest fiction series of the 20th century. Asimov was a prominent intellectual and popularized science through his writing and as the President of the American Humanists Association and a member of New York’s Sherlock Holmes’ Society. Asimov is best remembered for his contributions to science fiction, serious science and humanist philosophy. Isaac Asimov was born in what is now Smolensk Oblast, Russia (then RSFSR) in1920. His family emigrated to New York when he was three, and he grew up reading pulp science fiction at his parents’ candy stores. Though trained as a biochemist, his enduring interest in science fiction led him to become a prominent author. As an adult, Asimov participated in many science fiction conventions. He was known as an approachable public speaker and replied to many of his fans’ letters. In addition to his science fiction he wrote much non-fiction, and his work spans 9 of the 10 dewy decimal categories. Privately, he was a claustrophile and, though fascinated by space travel, Asimov was afraid of flying and preferred cruise ships over planes. An asteroid, a crater on Mars, and a literary award are named in his honour. 7
Spun Chair by David Heatherwick - Sitting and Upside down
Wooden Wagon Wheel, tension ring
Satellite from 2001: A Space Odyssey 8 Isaac Asimov Chair
Lunar Lander
NASA satellite concept
DESIGN INSPIRATION
The chair for Isaac Asimov is designed to embody Asimov’s spirit of fun, the openness of humanism, and the aesthetic of sci-fi spacecraft. We were initially drawn to the symbolism of circular shapes to the virtue of unbiasedness in humanist philosophy, and circles’ frequent use in real and fictional spacecraft. The chair is composed of two wooden wagon wheels joined by a steel tube inserted in both their axles. By spinning independently are the steel axle the wheels create gyroscopic action that simulates the disorientation of space movement in orbit mode, and a merry-go-round like spinning in spin mode. The rings not only allow rolling, but also hold the spokes in with tension to limit bending. We were primarily inspired by science fiction iconography from Isaac Asimov’s stories and the broader genre including the work of H.P. Lovecraft and Arthur C. Clarke. Our primary chair precedent was the Spun Chair by David Heatherwick, a spinning chair made by sculpting solid brass on a metal lathe. Lunar landers, real and fictitious satellites, the Death Star, Tron, and 2001: A Space Odyssey were all inspirations.
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Component Sketches
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Isaac Asimov Chair
Initial 3-D model
Cardboard Model
VERSION ONE
Our initial designs were inspired by spindly shapes like the original lunar landers and robotic arms and the symbolism of circular shapes. The initial designs conceived of the chair as a stool and a sculptural object imitating a spacecraft or landing pod more than as a chair. We initially conceived of the chair as being made up of one cross section shape copied around a central axis to give the chair its circular geometry. From the beginning we intended to build the chair from flat pieces that could be easily cut with the CNC. The curved geometry of the spokes was inspired by more contemporary science fiction imagery. We initially intended to split the chair into multiple smaller chairs. There are 12 spokes in this version in order to allow breaking into 4 stools with three feet each. This also made the spoke spacing dense enough to be used as a sitting surface to avoid filling the voids between spokes with seating members. The ring was introduced to pull back the spreading of the spokes. However, this version still had the issue of not having a comfortable sitting surface, and we did not find an appropriate connection to allow easily taking the chair apart into multiple chairs.
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Sketches of wheels and components
Spin Mode Elevation
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Isaac Asimov Chair
Cardboard Model
Flat Mode Elevation
Spin Mode Plan
Flat Mode Plan
VERSION TWO
In Version two the chair is usable in two positions - a large circular stool and the a spinning armchair. The design is heavily influenced by the Spun chair by David Heatherwick, which inspired us to introduce the spinning top motion by flipping the chair over and helped us calibrate the dimensions to achieve this. We reduced the number of spokes form 12 to 6 and made the rings the most prominent feature of the design. We straightened out the spokes to transfer loads more directly. Using wooden wagon wheels as precedents, we determined to use mortise and tenon joints to join the spokes to the rings. The major issues with this version are the absence of a sitting surface and the details of the component shapes. Because there are fewer spokes, the spaces between spokes are too great, and a seat piece must be introduced. The spokes are also individually implausibly thin. The rings are wider than they are thick, so the material is not resisting the spreading of the spokes efficiently, and when spinning, would experience high internal bending. Lastly, the axle has some pieces running parallel to its length, creating a weak point in both bending and compression. Our largest issue is that the chair is still conceived more as a sculpture than as a chair.
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3-D Model Views
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Isaac Asimov Chair
Cardboard Model
VERSION THREE
In version three we separate the base and top of the chair to create gyroscopic action in the orbit mode and developed the details of the pieces and joints. We introduced the axle spinning so that the chair’s rider can roll in orbit mode without getting flipped upside down. This creates the unintended positive of turning the flat circular stool into a sort of merry-go-round. The spinning is achieved by embedding a steel tube inside each part of the thick wood axle, and inserting another steel tube in both of them. The inner steel tube is shorter and narrower than the tube it sits inside of, so it experiences only bending, and the compression is taken by the whole wood cross section around it. The tension rings are much narrower and thicker than Version Two to resist spreading more efficiently. The axle is now made only of stacked crosssections of wood to minimize weakness. We developed the dimensions and details of the mortise and tenon joints based on research into the construction of traditional wagon wheels. This version has 12 spokes to try to provide a seating surface, but this is still an unsatisfactory solution.
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3-D Model Views
View of completed chair
N mode
n 1-10
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8
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8 2 10
10 1
ORBIT mod
Spin section 1-10 Plan 1-10
Orbit mode section 1-
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110 5 8
spin mode orbit mode
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Isaac Asimov Chair
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FINAL VERSION
In the final version, we simplified the structure to four spokes and designed seat pieces to fit on the spokes. The inner profile of the smaller ring had to be modified to suit the flat panels of the orbit mode seat. The rings that make the spin mode seat were simpler and designed to accentuate the circular, concentric design. All the pieces have thicknesses that are all multiples of 18.5mm. Every piece was cut by the CNC router from flat sheets of plywood and then laminated together. The only pieces that required profiles were the base of the spinner, which was specially CNC’d and the tenons, which were cut with a tenon attachment on the table saw. The joints are tight friction fits and not fastened by glue. The bolts in the rings are aesthetic accents and use as support pads so the ring in spin mode bears on points, not its whole surface. The steel rods inside the axle are also fit by friction inside the wood, which is continuously laminated to itself. The major challenges of the assembly were adjusting to the narrow tolerances of friction fits, forcing the pieces together, and maneuvering the large pieces of wood around the shop.
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Isaac Asimov Chair
DOCUMENTATION
MATERIALS AND COSTS CONSTRUCTION PROCESS DETAILS USE AND photography
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CNC cutting seat spokes and spindle 20
Isaac Asimov Chair
CONSTRUCTION Materials List and Costs Primary Costs
4’0” x 4’0“ x 3/4” maple and birch plywood CNC cut pattern
+ x2 Sanded Pine Plywood 4ftx8ft panels, 3/4in thick. // 47.75 CAD$ per panel, $95.50 total.
+ x1 Spruce Plywood 4ftx4ft panel, 3/4in thick. // 36.50 CAD$ per 8ftx4ft panel, $18.25 total (4ftx4ft used).
+ x1 Round Aluminum Tubing 1-1/4X3, // 14.98 CAD$
+ x1 Round Steel Tubing 1X.100X36, // 16.64 CAD$
4’0” x 4’0“ x 3/4” maple and birch plywood CNC cut pattern
+ x1 Box of Stainless Steel Bolts, 2in long (50 in a box) // 15.57 CAD$
+ x1 Box of Stainless Steel Nuts // 2.96 CAD$
+ x1 Box of Stainless Steel Washers // 6.35 CAD$
+ x2 Cold Rolled Steel Rods 3/8in thick, 3ft long. // 3.50 CAD$
4’0” x 4’0“ x 3/4” maple and birch plywood CNC cut pattern
Total Material Cost = 173.75 CAD$ + TAX Additional Costs + CNC Cutting (5Hours Total) // 50.00 CAD$
+ Printing and Design Models throughout the process: // 62.48 CAD$
+ Material Transportation // 20.40 CAD$
1’6” x 1’6” x 2 1/4” maple plywood CNC cut pattern
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Axle pieces prepared for application of glue, set of tools, and spokes cut on table saw 22
Isaac Asimov Chair
Axle pieces being clamped to laminate 23
Fitting aluminum tube into the axle 24
Isaac Asimov Chair
Fitting upper ring pieces together to laminate 25
Organizing the axle pieces 26
Isaac Asimov Chair
Pieces in the shop, in progress 27
Test assembling chair without seat 28
Isaac Asimov Chair
Chair spinning in test without seat 29
Detail: The inner edge of the ring is flattened out where it meets the seat so there is a minimal gap. The bolts create a machine aesthetic and, when flipped, provide contact pads so the ring will not be damaged.
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Isaac Asimov Chair
Detail: All the spokes are held in compression between the wheel and axle. Where the upper axle sits on the lower axle the axle thickens to help resist the bending that lamination would otherwise resist.
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Chair spinning with four people 32
Isaac Asimov Chair
Final chair critique 33
Orbit mode side view of rolling 34
Isaac Asimov Chair
Orbit mode side view of sitting 35
Spin mode one person sitting 36
Isaac Asimov Chair
Spin mode two people spinning 37
Orbit mode one person orbiting 38
Isaac Asimov Chair
Orbit mode one person orbiting 39
Spin and orbit mode, different ways to sit 40
Isaac Asimov Chair
Orbit mode time lapse of one revolution 41
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Isaac Asimov Chair
PART ONE: Dead Loading
DEAD LOAD WEIGHT ANALYSIS REACTIONS DUE TO DEAD LOAD OVERTURNING ANALYSIS
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spin mode Spin section 1-10
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6 5 8 13 12 6
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Isaac Asimov Chair
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8 4
30
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ORBIT mode Orbit mode section 1-10
115 27
10 3
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12 14 7
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SPIN mode Plan 1-10
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18 110 17
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Isaac Asimov Chair
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10 1
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orbit mode Plan 1-10
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SPIN mode Axonometric 1-10
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Isaac Asimov Chair
orbit mode Axonometric 1-10
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SPIN mode Exploded Axonometric 1-10
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Isaac Asimov Chair
orbit mode Exploded Axonometric 1-10
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DEAD LOAD ANALYSIS: PROCESS The volumes, weights, and centroids of each piece was calculated via a fully updateable grasshopper expression. Each column of the expression below solves for volume, weight, force mass, and one bar of the overall centroid. The volume and weight were summed to get the total for volume, weight, and force weight. By multiplying each piece’s N-bar by volume, we calculated a weighted average to produce the overall N-bar. By doing this three times we can determine the chair’s centroid in three dimensions.
FIND X-BAR (orbit) 52
Isaac Asimov Chair
FIND z-BAR (orbit)
FIND X-BAR (spin)
Breakdown of the Process
Find Volume and Centre of Gravity
Input Isolate Geometry Desired ex “Upper Component Spokes” x,y,z
Volume List Sum Volumes Total of Geometry Volume
Find Desired Component of Centre of Gravity of each element of Input Geometry
Average of Desired Component x,y,z-bar
Moment Force of Input Geometry relative to x,y,z-bar
Multiply Volume by Desired x,y,z-bar
Total Mass of Parts ex. “Upper Spokes”
Sum of Moment ∑(F•V) of Parts ex. “Upper Spokes”
Total Volume Convert Density of Density cm3 to m3 Material times (spruce/pine/fir Volume plywood)
Total Moment
Total Mass
Divide total z-bar Moment by total Volume
Simplification INPUT OF ALL PIECES
Axis Centroid
piece x/y/z-bar (MULTIPLY)
CHAIR PIECE
Moment Force on x/y/z-bar
Total Moment Total Volume
Piece Volume
Overall x/y/z-bar
(SUM)
500kg/m2 9.8 m/s2
Piece Weight
500kg/m2
Piece Force Mass
9.8 m/s2
Total Weight Total Force Mass
INPUT OF ALL PIECES
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DEAD LOAD ANALYSIS: DOCUMENTATIon of Weight of chair by part TOP
x-bar 550cm
y-bar 550cm
Origin
- Consider chair as groups of objects - Assume centre of gravity is located in the centre of circular components - Assume material is WISA spruce plywood: 500 kg/m3 (+/- 50 kg) WHOLE CHAIR (sum of below) total volume: 57989.42 cm3 (0.0580m3) total mass: 29.510 kg force mass: 289.2 N x-bar: 55.0cm y-bar: 55.0cm (55.0, 55.0, 34.2)
45.28cm
5.52cm
Upper Ring
5.52cm
Lower Ring
total volume: 0.00894 m3 weight: 4.47kg / 43.806N z-bar: 48.04 cm
total volume: 0.00899m3 weight: 4.45kg / 44.051N z-bar: 2.76 cm
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Isaac Asimov Chair
40.31cm
Lower Spokes
30.64cm
9.51cm
Upper Spokes total volume: 0.00717 m3 weight: 3.58kg / 35.133N z-bar: 46.54 cm total volume: 0.00575m3 weight: 2.87kg / 28.175N z-bar: 15.95 cm
Spinner
29.44cm
Top Axle Central Axle Bottom Axle
cm cm 11.04cm 9.2011.04
volume: 0.00656 m3 weight: 3.28kg / 32.144N z-bar: 65.16cm volume: 0.00309 m3 weight: 1.54kg / 15.141N z-bar: 45.3 cm volume: 0.00371 m3 weight: 1.85kg / 18.179N z-bar: 35.24 cm volume: 0.00309 m3 weight: 1.545kg / 15.141 z-bar: 25.12 cm Total Core Volume: 0.0164m3 weight: 8.225kg / 80.605N z-bar: 47.17 cm
Lower Seat
30.64cm
1.84cm
Upper Seat total volume: 0.00488 m3 weight: 2.44kg / 23.912N z-bar: 49.89 cm
total volume: 0.00580m3 weight: 2.90kg / 28.420N z-bar: 11.36 cm
Axle Core and Bolts total volume: 0.0001 m3 density: 7,750kg/m3 weight: 0.52kg / 5.1N
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overturning: spin mode
Overturning - Flat Mode
P= 289.2N
R1
P= 289.2N
R1 49.5cm
∑MR1=0 F • L = P • d1 F • 80.3cm = 289.2N • 49.5cm F overturning = 178.3 N
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F overturning=115.2N
80.3 cm
80.3 cm
F overturning=178.3N
Isaac Asimov Chair
32.0cm
∑MR1=0 F • L = P • d1 F • 80.3cm = 289.2N • 32.0cm F overturning = 115.2N
overturning: orbit mode
Overturning - Spin Mode
P= 289.2N
F overturning =119.6N
L2=96.7cm
L2=96.7cm
F overturning =49.0N
P= 289.2N
R1 d2 16.4cm
∑MR1=0 F • L2 = P • d3 F • 96.7cm = 289.2N • 16.4cm F overturning = 49.04 N
R2 d3 40cm
∑MR2=0 F • L2 = P • d3 F • 96.7cm = 289.2N • 40cm F overturning = 119.62 N
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Isaac Asimov Chair
PART TWO: Live loading
LIVE LOAD CONFIGURATIONS REACTIONS DUE TO LIVE LOAD TIPPING ANALYSIS lateral and racking ANALYSIS
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spin mode analysis
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Isaac Asimov Chair
LIVE LOAD REactions ANALYSIS : SPIN MODE : TWO SITTING Dead Load: 289.2N Torso: 642N + 642N Upper Legs: 200N + 200N
Lower Legs (not loading chair): 158N +158N Angle of Axis: 90ยบ
- Most basic intended sitting position in spin mode: multiple people - Position has loads well distributed nearly equally across four reactions
- Based on symmetry of loading, we know all reactions from live loading are equal. LL -> R1 = R2 = R3 = R4 = (LLtot/4) = (642N + 642N + 200N + 200N)/4 = (1684N/4) = 421N
Upper Legs 200N
Torso 642N
Centroid 289.2N
Torso 642N
Loads are distributed symmetrically about this axis
Upper Legs 200
Centroid, Torso, Upper Legs 1,373.2N
R3 = 421N + 79.9N = 500.9N R4 = 421N + 64.7N = 485.7N
Upper Legs 200N
Torso 642N
Centroid 289.2N
Upper Legs 200
Torso 642N
With dead load: R1 = 421N + 79.9N = 500.9N R2 = 421N + 64.7N = 485.7N
R4 = 500.9N
R3= 485.7N
32cm
32cm
R2 = 485.7N
8.0cm
11.0cm
R3 + R4
R1 + R2
R1 + R3
R2 + R4
21.0cm
32cm 21.0cm
32cm
11.0cm
32cm
8.0cm
32cm
R1 = 500.9N
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LIVE LOAD REactions ANALYSIS : SPIN MODE : TWO SITTING Dead Load: 289.2N Torso: 642N + 642N Upper Legs: 200N + 200N
Lower Legs: 158N +158N Angle of Axis: 90º
- Second intended sitting position: for chatting with friends - Loading is highest and thus causing the most critical compression - Load is not well distributed between the reactions, thus causing critical bending
22cm 10cm
Lower Legs 316N
Upper Legs 400N Centroid 289.2N
Loads are distributed symmetrically about this axis
R4
R3
R2
R1
22cm 10cm R3 + R4
R1 + R2
Isaac Asimov Chair
32cm
∑V=0 = R1R3 + R2R4 = liveload + deadload 598.1N + 1691.1N = 400.0N + 1284.0N + 316.0N + 298.2N 2,289.2N = 2,289.2N
Torso 1,284N
Centroid
Lower Legs 316N
32cm R1 + R3
R2 + R4
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32cm
Torso, Legs 1,000N
Conclusion: R1 = 299.1N R2 = 845.6N R3 = 299.1N R4 = 845.6N The chair is stable in this position, but experiencing high bending and compression.
Torso, Legs 1,000N
By symmetry we know loads are distributed equally. Therefore: R1 = R3 = 598.1N/2 = 299.1N R2 = R4 = 1,691.1N/2 = 845.6N
Upper Legs 400N Centroid 289.2N
∑MR1R3=0 R2R4 x64.0cm = (1,284Nx64cm) + (400.0Nx42cm) + (289.2Nx32cm) R2R4 = (82,176Ncm + 16,800Ncm + 9,254.4Ncm)/64cm R2R4 = 108,230.4Ncm/64cm R2R4 = 1,691.1N
Torsos 1,284N
∑MR2R4=0 R1R3 x64cm = (1284Nx0cm) + (400Nx22cm) + (289.2Nx32cm) + (316Nx64cm) R1R3 = (8800Ncm + 9254.4Ncm + 20224Ncm)/64cm R1R3 = 38,278.4Ncm/64cm R1R3 = 598.1N
32cm
LIVE LOAD ANALYSIS : SPIN MODE : TWO SITTING Dead Load: 289.2N Torso: 642N Upper Legs: 200N
Lower Legs (not loading chair): 158N Angle of Axis: 90º
- A very possible, but unintended sitting position -This position will result in tipping
∑MR3R4=0 R1R2 x64.0cm + (742Nx18cm)= (289.2Nx32cm) R1R2 = (9,254.4Ncm - 13,356Ncm)/64cm R1R2 = -4,101.6Ncm/64cm R1R2 = -64.1N
By symmetry we know loads are distributed equally. Therefore: R1 = R3 = 1,095.3N/2 = 547.7N R2 = R4 = 64.1N/2 = 32.1N
Conclusion: R1 = 547.7N R2 = 32.1N R3 = 547.7N R4 = 32.1N The chair is unstable in this position because it requires R1R2 to exert a downward reaction, which is impossible. The chair would tip over.
32cm
32cm
18cm
32cm
Torso and Half Upper Legs
∑V=0 = R3R4 = liveload + deadload + R1R2 1,095.3N= 642N + 100N+ 289.2N + 64.1N 1,095.3N = 1,095.3N
Centroid
Centroid, Torso, and Half Upper Legs 1,031.2N
Centroid 289.2N
Torso and Half Upper Legs 742N
∑MR1R2=0 R3R4 x64cm = (289.2Nx32cm) + (742Nx82cm) R3R4 = (9,254.4Ncm + 60,844.0Ncm)/64cm R3R4 = 70,098Ncm/64cm R3R4 = 1,095.3N
Loads are distributed symmetrically about this axis
R4 = 500.9N
R3= 485.7N
R2 = 485.7N
R1 = 500.9N
32cm
32cm
32cm
18cm R3 + R4
R1 + R2
R3 + R4
R1 + R2
R3 + R4
R1 + R2
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orbit mode analysis
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Isaac Asimov Chair
LIVE LOAD ANALYSIS : ORBIT MODE : ONE SITTING Dead Load: 289.2N Torso: 642N Upper Legs: 200N
Lower Legs (not loading chair): 158N Angle of Axis: 60º
∑MR1=0 R2 x57.0cm = (200Nx60.0cm) + (642Nx 40.0cm) + (289.2Nx16.0cm) R2 = (12000Ncm + 25680Ncm + 4627.2Ncm)/57cm R2 = 42 307.2Ncm/57cm R2 = 742N
- Most basic intended sitting position in orbit mode: single person - Chair is stable in this position when symmetrically loaded as shown ∑MR2=0 R1 x57.0cm + 200Nx3cm = (289.2Nx41cm) + (642Nx17cm) R1 = (11,857.2Ncm + 10,914.0Ncm - 600.0Ncm)/57cm R1 = 22,175.3Ncm/57cm R1 = 389.0N
∑V=0 = R2 + R1 = liveload + deadload 742.2N + 389.0N = 289.2N + 200N + 642N 1,131.2N = 1,131.2N
Upper Legs 200N
Torso 642N
Centre of Gravity 289.2N
17.0cm
24.0cm
3.0cm
Torso, Centroid, Upper legs: 1,131.2N
16.0cm
3.0cm
17.0cm
24.0cm
R2
R1, R2
R1
R2
R1 16.0cm
Upper Legs 200N
Torso 642N
Centre of Gravity 289.2N
Conclusion: R1 = 389.0N R2 = 742N The chair is stable in this position, and the live load is moderately well distributed between the two reactions.
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LIVE LOAD ANALYSIS : ORBIT MODE : LOUNGING Dead Load: 289.2N Torso: 642N Upper Legs: 200N
Lower Legs (not loading chair): 158N Angle of Axis: 60º
∑MR1=0 R2 x57.0cm = (642Nx14cm) + (289.2Nx16cm) + (200Nx60cm) R2 = (8988Ncm + 4627.2Ncm + 12000Ncm)/57cm R2 = 26,615Ncm/57cm R2 = 449.4N
-Relaxed sitting, the secondary intended sitting position - Chair is stable in this position when symmetrically loaded as shown
∑MR2=0 R1 x57.0cm + 200Nx3cm = (289.2Nx41cm) + (642Nx43cm) R1 = (11,857.2Ncm + 27,606Ncm - 600.0Ncm)/57cm R1 = 38,863Ncm/57cm R1 = 681.8N
∑V=0 = R2 + R1 = liveload + deadload 449.4N + 681.8N = 289.2N + 200N + 642N 1,131.2N = 1,131.2N
Upper Legs 200N
Torso: 642N Centre of Gravity 289.2N
3.0cm
41.0cm
2cm
14.0cm
3.0cm
41.0cm
2cm
14.0cm
R2
Isaac Asimov Chair
R1, R2
R1
R2
R1
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Torso, Centroid, Upper legs: 1,131.2N
Upper Legs 200N
Torso: 642N Centre of Gravity 289.2N
Conclusion: R1 = 681.8N R2 = 449.2N The chair is stable in this position, and the live load is well distributed between the two reactions.
LIVE LOAD ANALYSIS : ORBIT MODE : FLYING Dead Load: 289.2N Torso: 642N Upper Legs: 200N
Lower Legs: 158N Angle of Axis: 60º
∑MR1=0 R2 x57.0cm = (289.2Nx41cm) + (348Nx27cm) + (289.2Nx16.0cm) R2 = (36,594Ncm + 9,666Ncm + 4,771.2Ncm)/57cm R2 = 51,031Ncm/57cm R2 = 895.3N
- A late-discovered, unintended sitting position, near impossible to balance laterally, and holdable only for a moment. ∑MR2=0 R1 x57.0cm = (289Nx41cm) + (358Nx30cm) + (642Nx0cm) R1 = (11,857.2Ncm + 10,740Ncm + 0Ncm)/57cm R1 = 22,597.2Ncm/57cm R1 = 396.4N
∑V=0 = R2 + R1 = liveload + deadload 895.2N + 396.4N = 289.2N + 358N + 642N 1291.7N = 1291.7N
Torso 642N
Centre of Gravity 289.2N Legs 200N 30.0cm
11.0cm
16.0cm
30.0cm
11.0cm
R2
R1, R2
R1
R2
R1 16.0cm
Torso, Centroid, Upper legs: 1,131.2N
Torso 642N
Centre of Gravity 289.2N Legs 200N
Conclusion: R1 = 396.4N R2 = 895.3N The chair is stable in this position, and the live load is moderately well distributed between the two reactions. This is the worst-case loading scenario for orbit mode.
67
Tipping and Friction : ORBIT MODE Dead Load: 289.2N Torso: 642N Upper Legs: 200N
Lower Legs (not loading): 158N Angle of Axis: 60º
- The chair must be pivoted around R1 in order to tip, therefore R2 is not in contact with the floor and should be disregarded. F=µxN F=P µ = 0.5 for Wood on Wood surfaces.
224.9N = 0.5N 224.9N/0.5= N VN = 449.8N
Upper Legs 200N
Torso: 642N Centre of Gravity 289.2N
∑MR1=0 P x 85.6cm = (200N x 57.0cm) + (289.2N x 16.0cm) + (642N x 14.0cm) P = (5640Ncm + 4,627Ncm + 8,988Ncm)/120cm P = 19,255Ncm /85.6cm P = 224.9N
∑V=0
VR + N= P + Live Loads VR + 449.8N = 289.2N + 642N + 200N VR = 581.2N
Force of Feet Ff = √(449.8N2 + 224.9N2) Ff = 502.9N
P = 224.9N
85.62 cm
The force required to tip backward (509.2N) is higher than is reasonable to expect the sitter to exert, and the force friction is required to exert (224.9N) are both unreasonably high, thus the chair is very hard to tip backward in this position.
Ffoot = 224.9N
VR= 581.2N
Isaac Asimov Chair
41.0cm
68
14.0cm 2.0cm
R1
VN= 449.8N 63.0cm
HR = 224.9N
HN = 224.9N Ff = 502.9N
Tipping and Friction : SPIN MODE Dead Load: 289.2N Torso: 642N Upper Legs: 200N
Lower Legs (not loading): 158N Angle of Axis: 60º
- The chair must be pivoted around the back tip of the ring in order to tip, therefore R1, R2, R3, and R4 are not in contact with the floor and should be disregarded. F=µxN µ = 0.5 for Wood on Wood surfaces. F=P 901.4N = 0.5xN 901.4N/0.5 = N
VN = 1,802.9N
Upper Legs 200N
Torso 642N
Centroid 289.2N
∑MR1=0 P x 80.3cm = (200N x 85.0cm) + (642N x 66cm) + (289.2N x 45cm) P = (17,000Ncm + 42,372Ncm + 13,014Ncm)/120cm P = 72,386Ncm /120cm P = 901.4N
R = P + Live Loads VR + 1,802.9N = 289.2N + 642N + 200N VR = -771.7N
Force of Feet Ff = √(901.4N2 + 1,802.9N2) Ff = 2014.9N
In order to tip backward the sitter must exert over 2000N of force down with the feet and the back reaction must pull down (catch on the floor) The force required to push and the reaction pulling down are both unreasonable to expect to happen and we must conclude that the chair is practically impossible to tip in this position.
80.3 cm
P=901.4N
Ffoot = 901.4N HR = 901.4N 63.0cm
8.0cm
11.0cm
21.0cm
VR = 1,802.9N
45.0cm
HN = 901.4N VN = 1,802.9N
Ff = 2014.9N
69
LATERAL Stability and Racking: ORBIT MODE
SHEAR The spin mode of the chair is inherently unstable in the x-y plane and is designed to roll sideways at even slight lateral force. In the x-z and y-z planes, it relies on the strength of the spokes and to resist compression and relies on the rings to resist spreading with tension in order to provide resistance to vertically loaded forces. LATERAL In Orbit mode, the Asimov chair has intentionally high lateral instability. The base is designed to roll sideways about a 60º axis like a spinning top on its two points of contact. The top is designed to rotate about the same axis counter to the base to keep the seat upright. The sitter’s feet provide the non-axial points of contact to prevent spinning, but if feet are
z
y 70
Isaac Asimov Chair
x
LATERAL STABILITY AND RACKING: SPIN MODE
SHEAR The flat mode of the chair is the more stable and resistant to shear. Because the upper ring rotates, it does not resist any lateral force, but spins. The large diameter of the lower ring creating the base gives the chair lateral resistance in the x-z and y-z planes. The deep spokes and rings are designed to resist shearing in the x-y directions by preventing the spreading of the spokes. The strength of the system is mostly due to the high friction and rigidity of the mortise and tenon joints at the ends of the spokes. LATERAL The Asimov chair has a lot of inherent lateral stability due to its width, symmetrical geometry and wheel-and-spoke structural system. Dynamic rotational movement sloughs off lateral forces exerted against it.
z
y
x 71
72
Isaac Asimov Chair
PART THREE: moment frame forces
MOMENT FRAME ANALYSIS ANALYSIS of member reactions overview of forces in members
73
Chair Dead Weight: 289.2N Torso: 642N Upper Legs: 200N Lower Legs (not loading chair): 158N Angle of Axis: 60ยบ
Upper Legs
Torso
Centroid
Chair Loading and Dimensions:
Torso
Upper Legs
FRAME ANALYSIS : SPIN MODE : TWO SITTING
Q11 R= 500.9N
Q11 R = 485.7N
32cm
Q1
Q2 32cm
Upper Spoke
Lower Spoke
Q21 R = 485.7N
Q21 R = 500.9N 14.5cm 14.5cm 32cm
Isaac Asimov Chair
485.7N
500.9N
74
14.5cm
14.5cm 14.5cm 32cm
14.5cm
Q1 1a
Centre of Gravity 289.2N
Q2 3
1a 1b
2
Chair Components and Weights (Each Quarter)
Torso = 642N Upper Legs = 200N
1. Upper Wheel 1a. outer: 10.95N 1b. middle: 3.83N 1c. inner: 2.16N 2. Upper Spoke: 8.77N 3. Upper Axle: 16.35 4. Lower Axle: 3.88N
3 4. Axle
1c R4 = 500.9N
4 Q2b
4
1a
3 1c
Q2a
2
1b
3 4
Q2c R2 = 485.7N
1c
Torso = 642N Upper Legs = 200N
1b
Q2a
2. Q1 Lower Spoke
Q2b
Q2 Components Q2a. Q2 Seat: 2.88N Q2b. Q2 Lower Spoke: 7.05N Q2c. Q2 Lower Wheel: 9.87N
2
1a
1. Q1 Upper Spoke
Q2
Q1 Components Q1a. Q1 Seat: 11.37N Q1b. Q1 Lower Spoke: 7.05N Q1c. Q1 Lower Wheel: 12.14N
Q2c
Q2 485.7N
Q1 500.9N
Q1 500.9N
Q2 485.7N
R3 = 485.7N
Q1b Q1a 3. Q2 Lower Spoke
Q1c Q1 R1 = 500.9N
75
Outer Ring
AXLE
Torso and Inner Ring Spoke Centroid
Q1
Upper Legs and Middle Ring
1. Q1 Upper Spoke (identical to Q2 upper spoke)
14.5cm
2.4cm 12.1cm
14.5cm
HA = 0Ncm
Q1
11.0
100N + 3.9N
8.77N
321N + 2.2N
500.9N
MA = 9,731.3 Ncm
A
VA = 446.8Ncm
∑V=0 VA = 321 + 8.62 + 8.77 + 100 + 15.3 + 43.8 VA= 446.8N ∑MA=0 MA = (323.2N x 14.5cm) + (8.77N x 16.9cm) + (103.9N x 29cm) + (43.8N x 43.5cm) MA = 4686.4Ncm + 148.2Ncm + 3013.1Ncm + 1905.2Ncm MA = 9,731.3 Ncm
76
Isaac Asimov Chair
7.05N + 23.4N = 30.5N
446.8N + 20.2N = 467.0N
AXLE
1. Q1 Lower Spoke
Q1
500.9N N
A
Q1 Lower spoke and Q1 seat weight
Axle weight Q1 Upper spoke load
Vertical Forces P 39.1
R1
22.5cm
AXLE
19.55cm
32
39.1
=
H 22.5
=
V 32
17.6N
287.7
V 382.2N
25.0N
409.2N
N
22.5
H 268.7N
0.9
VA = 0Ncm
50
500.9N
HA = 0Ncm
.5N
7.0
30
46
MA = 15,511.0Ncm
∑V=0 = 382.2N + 25.0N = 409.2N 407.2N = 409.2N Forces are close, OK. Discrepancy due to negligible misplaced dead load
= ∑H=0 268.7N + 17.5N = 287.7N 286.2N= 287.7N Forces are close, OK. Discrepancy due to negligible misplaced dead load
∑MA=0 MA + (25.0 x 19.55) = (409.2N x 39.1cm) MA = 15,999.7Ncm - 488.75Ncm MA = 15,511.0Ncm
19.55cm
77
AXLE
3. Q2 Lower Spoke 452.6N + 20.2N = 472.8N
Q2
2.88N + 9.87N = 12.75N
Q2 Ring tension 482.7N
485.7N
20.5cm
Q2 Lower spoke and Q2 seat weight
N
2.7
48
Axle weight Q2 Upper spoke load
N
23 34.5
41 23cm
AXLE
N
.75
2.8
A
Vertical Forces P 41 34.5cm
12
47
MA = 16,325Ncm
20.5cm
R1
=
H 23
=
V 34.2
H
265.12
7.15N
272.2N
V
397.7N
10.7N
408.4N
∑V=0 = 397.7N + 10.7N = 408.4N 408.4N = 408.4N
∑H=0 = 365.12N + 7.15N = 272.2N 272.3N = 272.2N
Verticals are balanced, OK
Horizontals are close, OK
∑MA=0 MA + (10.7 x 20.5) = (408.4N x 41cm) MA = 16,744.4Ncm - 419.35Ncm MA = 16,325Ncm
78
Isaac Asimov Chair
10 393Ncm
Verticals are balanced, OK
Verticals are balanced, OK
∑MA=0 10 393Ncm + 15,511.0Ncm = 10 393Ncm + 15,511.0Ncm 25,904Ncm = 25,904Ncm
∑MA=0 10 393Ncm + 15,511.0Ncm = 10 393Ncm + 15,511.0Ncm 25,904Ncm = 25,904Ncm
15,511.0Ncm 4 x 472.8N
Moment is balanced, OK
15,511.0Ncm
Moment is balanced, OK
Q1 and Q2 upper spokes
20.2N
4 x 452.6N
Q1 and Q2 lower spokes
∑V=0 = 4(452.6N) + 4(20.2N) = 4(472.8N) 1,891.2N = 1,891.2N
Q1 and Q2 lower spokes
Q2
Spinner Weight
Q1
10 393 Ncm
10 393 Ncm
16,325Ncm
16,325Ncm 4 x 472.8N
10 393Ncm
20.2N
4 x 452.6N
∑V=0 = 4(452.6N) + 4(20.2N) = 4(472.8N) 1,891.2N = 1,891.2N
Q1
Q1 and Q2 upper spokes
Q12 upper spokes
Q22
Q2
Q12 lower spokes
Q11
Spinner Weight
Q12
Q11 lower spokes
Q21
Q11 upper spokes
4. Axle for All Quarters
79
24.0cm
Chair Dead Weight: 289.2N Torso: 642N Upper Legs: 200N Lower Legs (not loading chair): 158N Angle of Axis: 60ยบ
Upper Legs
Chair Loading and Dimensions:
Torso
Centre of Gravity
FRAME ANALYSIS : ORBIT MODE : ONE SITTING
R2
R1 16.0cm
Isaac Asimov Chair
742.2N
389.0N
80
24.0cm
17.0cm
3.0cm
Chair Components and Weights (Each Quarter) Q1c
Back Quarter
Side Quarter
Q1b 2
1a
Q1a
Q2b Q2c
1b 4
1c
Q1 (Front and Back) Components Q1a. Q1 Seat: 11.37N Q1b. Q1 Seat Spoke: 7.05N Q1c. Q1 Seat Wheel: 12.14N
Q2a 4
Side Quarter
3 Q2c
Q2 (Side) Components Q2a. Q2 Seat: 2.88N Q2b. Q2 Seat Spoke: 7.05N Q2c. Q2 Seat Wheel: 9.87N
3 Q2a
4
Q2b
2 1b 1a
Q1a
Q1b Q1c
3
1c
1c R1 = 389.0N
Q2 64.4N
1. Support Wheel 1a. outer: 10.95N 1b. middle: 3.83N 1c. inner: 2.16N 2. Support Spoke: 8.77N 3. Spinning Axle: 16.35 4. Upper Axle: 3.88N
Front Quarter
1b 1a R2 = 742.2N
81
Q1 Seating Ring
Q1 Seating Ring (tension)
AX LE
Torso
Q1: Seat
Seat and Spoke Centroid
3. Seat Spoke - assume seat is flat
Upper Legs
1. Q1 Seat spoke
∑V=0 = VA + VR = 642N + 18.4N + 200N + 12.1N VR = 872.5N - VA VR = 872.5N - 531.7N VR = 340.8N
MA = 1.5Ncm HA = 426N
82
Isaac Asimov Chair
12.1N
R
200.0N
10.0cm
A
VA = 531.7N
6.4
4 5
∑MA=0 MA + VR•(37cm) = (642N x 10cm) + (18.4N x 18.5cm) + (200N x 27cm) + (12.1N x 37cm) MA = 12,608.1Ncm - 340.8x37cm MA = 12,608.1Ncm - 12,609.6Ncm MA = -1.5Ncm
8.5cm
18.4N
∑MR=0 VA•(37cm) = 642Nx27.0cm + 18.4Nx18.5cm + 200Nx10cm VA = 19,674.4Ncm/37cm VA = 531.7N
8.5cm
642.0N
10.0cm
HR = VR 5 4 ∑H=0 = HA = HR HA = 426N
Ring R 6.4
=
H 5
=
V 4
HR = 5(340.8N) 4 PR = 6.4(340.8) 4
HR = 426N PR = 545.28N
2. Tension Ring and 3. back spoke Q1: Back
3. Back Spoke
Q1: Seat
426.0N
Ring Tension 340.8N 16cm
Ring Weight
12.1N 18.4N
16cm
Spoke + Seat Weight
742.2N
A
HA = 426.0N
LE AX
389.0N
9.25cm 9.25cm
MA = 6,933.1Ncm
2. Tension Ring
VA = 371.3N
VR = 340.8N
√3
HR = 426N T
1
TR = 545.3N
HR = 426N
VR = 340.8N
6.4
4 5
HR = VR = TR 5 4 6.4
Ring R 6.4
=
H 5
=
The ring is in 545.3N of tension
R 2
=
H 1
=
V √3
L = 2(18.5) L = 37cm
∑MA=0 MA + (12.1N x 18.5cm) + (18.4N x 9.25cm) + (340.8Nx18.5cm) = 426.0Nx32cm MA = 13,632Ncm - 223.9Ncm - 170.2Ncm - 6,304.8Ncm MA = 6,933.1Ncm ∑V=0 = VA = 12.1N + 340.8N + 18.4N VA = 371.3N
V 4
TR = 6.4(340.8N) 4
2
TR = 545.3N
∑H=0 = HA = HR HA = 426.0N
83
Q1: Seat
8.7N 2.2N
3.8N
Q1: Back
11.0N
4. Lower back spoke
7.25cm 6.25cm 1.0cm 7.25cm
Spoke Centroid Inner Ring
Middle Ring
Outer Ring
12.6cm
1.7cm
10.9cm
742.2N
389.0N
12.6cm
A
MA = 633.27Ncm HA = 0N VA = 25.7N
∑V=0 = VA = 11.0N + 3.8N+ 8.7N + 2.2N VA = 25.7N ∑MA=0 MA = (11.0N x 37.8cm) + (3.8N x 25.2cm) + (8.7N x 14.3cm) + (2.2N x 12.6cm) MA = 4158Ncm + 95.76Ncm + 124.41 + 27.7Ncm MA = 663.7Ncm
84
Isaac Asimov Chair
5. Lower Front Spoke
VA = 716.3N
MA = 27,313.1Ncm
A
12.6cm 11.0N
HA = 0N
3.8N
Q1: Seat
2.2N 8.7N
Q1: Back
12.6cm
Outer Ring
2
1
√3 = ∑V=0 742.2N = VA + 2.2N + 8.7N + 3.8N+ 11.0N 716.3N = VA
R 2
=
H √3
=
V 1
L = 2(18.5) L = 37cm
∑MA=0 MA + (8.62Nx12.6cm) + (8.7Nx14.3cm) + (3.8N x 25.2cm) + (10.95N x 37.8cm) = (742.2N x 37.8cm) MA = 28,055.2Ncm - 108.6Ncm - 124.4Ncm - 95.8Ncm - 413.9Ncm MA = 27,313.1Ncm R2
Middle Ring
Inner Ring Spoke Centroid
Axle Weight Seat Spoke Load Back Spoke Load Lower Back Spoke Load
12.6cm
10.9cm
1.7cm
12.6cm
742.2N
389.0N
742.2N
7.25cm
85
18.1cm
9.9cm Q2 Lower Ring: 11.0
A
VA = 25.7N
14.5cm
∑V=0 = VA = 11.0N + 3.8N+ 8.7N + 2.2N VA = 25.7N
Isaac Asimov Chair
Spoke Weight: 8.7N
Inner Ring: 2.2N
742.2N 389.0N
MA = 664.8Ncm
86
18.1cm
∑MA=0 MA = (9.9N x 36.1cm) + (7.1N x 18.1cm) MA = 357.4Ncm + 128.5Ncm MA = 485.9Ncm
∑V=0 = VA = 2.9N + 7.1N+ 9.9N VA = 19.9N
HA = 0Ncm
9.9cm
MA = 485.9Ncm
Middle Ring: 3.8N
AXLE
350
Spoke Weight : 7.1N
Q1: Side Q2 Seat Weight : 2.9N
Q2: Side
Q2 Ring: 9.9N
6. UPPER SIDE SPOKE and 7. lower side spoke
2.4cm 12.1cm
14.5cm
∑MA=0 MA = (11.0N x 37.8cm) + (3.8N x 25.2cm) + (8.7N x 14.3cm) + (2.2N x 12.6cm) MA = 415.8Ncm + 95.8Ncm + 124.4Ncm + 27.7Ncm MA = 664.8Ncm
371.3N + 545.3N + 19.9N + 19.9N
8. AXLE FOR ALL QUARTERS
Q1: Seat
∑V=0 = 389.0N + 716.3N = 371.3N + 345.3N + 19.9N + 19.9N + 25.7N + 25.7N + 25.7 + 80.6N 1,105.3N = 1,134.0N
716.3N
25.7N+ 25.7N+ 25.7N
Q1: Back
80.6N
Close, discrepancy due to margins of error. OK.
389.0N
742.2N
389.0N
Back Spoke Load Upper Side Spoke Loads Seat Spoke Load
N
9.0
38
Lower Back Spoke Lower Side Spoke Loads
.6N
80
N
9.2
63
H
336.0N
69.8N
553.4N
828.3N
V
194.5N
40.3N
319.5N
478.2N
R1
Lower Leg Spoke
Axle Dead Load
N
6.4
95
87
SPIN MODE: FORCES ON MEMBERS COMPONENTS 1. Upper Wheel 1a. outer: Tension parallel and perpendicular to grain to grain and minor Bending 1b. middle: Bending 1c. inner: Bending 2. Upper Spoke: Bending and Compression parallel to grain 3. Upper Axle: Compression perpendicular to grain 4. Lower Axle: Compression perpendicular to grain Q1 Components Q1a. Q1 Seat: no loading Q1b. Q1 Lower Spoke: Compression parallel to grain and bending Q1c. Q1 Lower Wheel: no loading (but realistically, in tension) Q2 Components Q2a. Q2 Seat: no loading Q2b. Q2 Lower Spoke: compression parallel to grain and bending Q2c. Q2 Lower Wheel: no loading (but realistically, in tension)
Torso = 642N Upper Legs = 200N
Q1 1a Q2
Centre of Gravity 289.2N
3
1a 1b
2
3 4. Axle
1c R4 = 500.9N
4 Q2b
4 1c
Q2a 4
Q2c R2 = 485.7N
1c
Torso = 642N Upper Legs = 200N
1b
Q2
Q2a
Q2b
2
1a
2. Q1 Lower Spoke
Q2c R3 = 485.7N
Q1b Q1a Q1c
3. Q2 Lower Spoke Q1
R1 = 500.9N
Isaac Asimov Chair
2
1b
3
1. Q1 Upper Spoke
88
1a
3
ORBIT: FORCES ON MEMBERS
Q1c
Back Quarter
Side Quarter
Q1b 2
1a
Q1a
Q2b Q2c
1b 4
1c
Q2a 4
Side Quarter
3 Q2c
3 Q2a
4
Q2b
2
1a
1c R1 = 389.0N
Q2 64.4N
Q1 (Front and Back) Components Q1a. Q1 Seat: compression perpendicular to grain Q1b. Q1 Seat Spoke: compression parallel to grain and bending Q1c. Q1 Seat Wheel: tension parallel to grain only Q2 (Side) Components Q2a. Q2 Seat: compression perpendicular to grain Q2b. Q2 Seat Spoke: compression parallel to grain and bending Q2c. Q2 Seat Wheel: tension only
Q1b Q1c
3
1c 1b
Q1a
COMPONENTS 1. Support Wheel 1a. outer: tension parallel to grain and bending 1b. middle: not loaded 1c. inner: not loaded 2. Support Spoke: compression parallel to grain and bending 3,4. Axle: compression perpendicular to grain and bending
Front Quarter
1b 1a R2 = 742.2N
89
90
Isaac Asimov Chair
PART FOUR: combined loading
combined loading analysis shear and moment analysis actual vs allowable stresses
91
Combined Loading calculations for lower spoke in spin miode
+ Axle Weight + Spoke Weight + Live Loads
+ Self-weight + Seat weight + Ring weight
A
39.1cm
Q2
B 500.9N
446.8N + 20.2N = 467.0N
R2
A MA = 15,511.0Ncm
7.50 + 23.4N = 30.5N
22.5
Section of the Member 55.2mm
32
39.1
Vertical Forces
B 500.9N
92
Isaac Asimov Chair
R2
P 39.1
=
H 22.5
=
V 32
90mm
A: 4968mm2 2 S = bh 6 2 2 S = 55.2mm x 90 mm 6 S = 74520mm3
19.55cm
19.55cm
467.0N
30.5N
B
A
500.9N
MA = 15,511.0Ncm
H
268.7N
17.6N
287.7
V
382.2N
25.0N
409.2N
382.2N 268.7N
17.6N
A
fb = M/S M = 15,511.0Ncm 2 S = bh 6 2 2 S = 55.2mm x 90 mm 6 S = 74520mm3
Fb = Mr/S
25.0N
B
W
2) Allowable Bending Stress Mr = Φ . mp . bp
Φ = 0.95
409.2N
287.7N
bp = 82.5 mm (width of the member at center) Mr = 0.95 x 2790Nmm/mm x 82.5mm Mr = 218666.25Nmm Fb =
fb = 0.20814Nmm2 fb = 208.14kPa
Fb = 2934.32 kPa
4) Allowable Axial Stress
3) Axial Stress Member is in compression. fc = P/A P = 287.20N A=axb A=axb A = 55.2mm x 90.0mm A = 4968mm2 fc = 0.05780 N/mm2
V
Fc = Pr/A
Pr = Φ . Pp . bp
Φ = 0.95 Pp= 510N/mm* A = 4968mm2 bp = 82.5 mm (width of the member at center) Pr = 0.95 x 510N/mm x 82.5mm
fc = 57.80 kPa -382.2N -407.2N
fc
+
fb
Fc Fb
8054.5Nmm
Pr = 39971.25 N Fc =
5) Combined Loading Criteria
15 511.0Nmm
218666.25Nmm 74520mm3
Fb = 2.93432 N/mm2
R2 B
S = 74520mm3
mp= 2790Nmm/mm*
fb = 15,511.0Ncm 74520mm3
A MA = 15,511.0Ncm
1) Bending Stress
39971.25 N 4968mm2 Fc = 8.04574 N/mm2 Fc = 8045.74 kPa
≤ 1.0
57.80 kPa 208.14 Kpa + 8045.74 kPa 2934.32 kPa
M A
B MA = 15,511.0Ncm
0.0071
+
0.0709 = 0.0823
≤ 1.0
Member meets criteria! 93
* (mp for laminated plywood, 18.4 x 3 layers at mp=930Nmm/mm) * (Pp for member 170N/mm x 3 layers of 18.4mm plywood)
Combined Loading calculations for lower spoke in spin miode
MA = 6933.1Ncm 63cm
Upper Back Spoke
A
MC = 663.7Ncm Lower Back Spoke
B C
Deadload
Q1: Back
MB = 1.5Ncm Upper Front Spoke
Q1: Seat
D F
MD = 27313.1Ncm Lower Front Spoke
E 742.2N
389.0N
956.4N A,B
77.1N
Section of Smallest Member
C,D 716.3N
80.6N
2
F
A: 17671.45mm2
1
S=
√3 R 2
=
H √3
=
E
94
Isaac Asimov Chair
3
4 S = 331.34cm3
V 1
r = 7.5cm 389.0N
�r
31.5cm
5.0cm
26.5cm
956.4N
80.6N
E
F 389.0N
A,B
C,D 639.2N
H
336.0N
69.8N
553.4N
828.3N
V
194.5N
40.3N
319.5N
478.2N
1) Bending Stress
2) Allowable Bending Stress
fb = M/S � r3 S= 4
Fb = Mr/S S = 331.34cm3
M = -20.68Ncm r = 7.5cm
W
336.0N E
553.4N
69.8N 194.95N
C,D 319.5N
F 40.3N
MA = 6931.6Ncm 828.3N 478.2N
A,B
V
E
C,D
3975750Nmm 331339mm2
Fb = 11.99900N/mm2 Fb = 11999.00kPa
4) Allowable Axial Stress Fc = Qr/A
Qr = Φ . Qp . Ab
Φ = 0.95 Qp= 4.5Mpa (Standard Value) A = 17671mm2 Qr = 0.95 x 4.5Mpa(4500kPa) x 17671mm2 Qr = 75543525 kPa mm2
fc = 828.3N 17671mm2 fc = 0.04687N/mm2
A,B
6884Ncm 6111Ncm
M
Mr = 0.95 x 27900Nmm/mm x 150mm Mr = 3975750Nmm
fb = 63.64N/cm2 fb = 636.4N/mm2
fc = P/A P = 828.3N A = � r2 A = 176.71cm2 F
bp = 150 mm (at the smallest/weakest member)
Fb =
Member is in compression.
194.5N 154.6N
S = 331.34cm3
fb = 21092.8Ncm 331.34cm3
3) Axial Stress 474.1N
Φ = 0.95
mp*= 27900Nmm/mm
fb = 21092.8Ncm � 7.53 4 MD = 27976.8Ncm
Mr = Φ . m p . b p
Fc = 75543525 kPa mm2 17671mm2 Fc = 4275 kPa
fc = 46.87kPa
5) Combined Loading Criteria F -1598.8Ncm
E,D
G
C
fc
+
fb
Fc Fb -8529.8Ncm
≤ 1.0
46.87kPa 636.40kPa + 4275 kPa 11999.00kPa 0.0109
-21092.8Ncm
+
*(for 30 layers of 1.85mm Plywood at mp = 930Nmm/mm laminated)
0.0530 = 0.0640 ≤ 1.0
Member meets criteria!
95
96
Isaac Asimov Chair