A Chair for Isaac Asimov

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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.

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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

8

8 2 10

10 1

ORBIT mod

Spin section 1-10 Plan 1-10

Orbit mode section 1-

115

110 5 8

spin mode orbit mode

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7 115

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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

110 5

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6 5 8 13 12 6

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Isaac Asimov Chair

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30

4 7

8 4

30

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5

ORBIT mode Orbit mode section 1-10

115 27

10 3

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SPIN mode Plan 1-10

110 5 8 10

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Isaac Asimov Chair

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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