A Chair for Dr Seuss - A Story Book

Volume/Area Volume/Area

A Storybook

ANALYSIS DRAFT DESIGNED AND WRITTEN BY 1-5 SAM VICKARS FOR ARCH 365 IN FALL 2013 ANALYSIS DRAFT 1-5(FALL OF 2013) DESIGNED BY SAM VICKARS IN 3B DESIGNED BY SAM VICKARS IN 3B (FALL OF 2013)

A CHAIR FOR DR SEUSS Designed and written by Sam Vickars, completed in December 2013 Final presentation submission for Elizabeth English’s ARCH 365 at the UNIVERSITY OF WATERLOO SCHOOL OF ARCHITECTURE in CAMBRIDGE ONTARIO Written with inspiration from Dr Seuss’s The Lorax, Oh the Place You’ll Go, and If I Ran the Zoo. Photos and biographical information from en.wikipedia.org and scholastic.com.

Fonts used throughout are Mission Gothic by Trevor Baum and James T Edmondson of Lost Type Co-op and Doctor Soos by Sean Trowbridge of DaFont.com

Volume/Area

e/Area

Oh the places you’ll sit, where there’s fun to be had, Conversations and laughing and sit-downs with Dad.

4 | A CHAIR FOR DR SEUSS

You’ll need somewhere to sit, take a load off your back: Four long pieces of wood, plus two more in your pack.

They all fit together and they make quite a sight, But when you start sitting, something feels not quite right...

So be sure when you sit, sit with care and great tact And remember that life’s a great balancing act.

It’s not so hard it really is not To sit right here, right here on this spot.

Except when you lean a bit far behind, The seat that you’re sitting on won’t be so kind.

A CHAIR FOR DR SEUSS | 5

But you’ll unlean yourself, I am sure that you will, Because if you do not, you’re sure in for a thrill!

A bit to the left, now back to the right, You’re just about there, you are almost, quite.

You’ve got it! You’ve done it! You are perfectly just!

You’re ready for anything! A stool you can trust!

But there’s more places to sit, there’s more fun to be had.

Debates and discussions and just looking not bad.

You’ll need somewhere to sit, so get packing your pack: Two round pieces of wood, plus four more on your back.

They’re all independent, yes they are at first sight, But they work together to make something just right.

A CHAIR FOR DR SEUSS | 7

So now that you’ve read the short story I wrote, A guide, a handbook, a manifesto to quote You’ve likely concluded and are wondering too, Is this chair built for Theo or is it for you?

Well you’re quite right to wonder, I think now you know, This stool’s built for you and the places you’ll go.

You see Dr Seuss (or Theodore to some) Wrote stories and stories with one rule of thumb: It’s all about you and the things that you do, Life can be tough, but you’ll always get through

8 | A CHAIR FOR DR SEUSS

But enough with the sap, let’s get on with the book, Some background on Seuss, a rhyming word cook: He was called by more names than the one often known, LeSieg, Theophrastus, and Rosetta Stone.

He was a great man and he wore many hats, From adverts and cartoons to stories of cats.

He was brainy and brilliant and soared to high heights, Two fish and some sneetches helped him teach reading right.

His political views changed when he heard a Who, Wrote an allegory for bombs post World War Two. Not too soon after, he returned to children’s lit, Taught lessons with butter battles and turtle wit.

He wrote of the world and what we must do To keep it intact, as if he ran the zoo.

His work spoke for itself (no matter how small!)

Anti-ism, schism, ageism, that’s all He passed far too soon, we should all give a damn, The Grinch can’t steal his heart, no he can’t (Sam-I-Am)!

A CHAIR FOR DR SEUSS | 9

Now on to the chair and why I did what I did, I’ll explain it you like I would to a kid: To get on your way to the places you’ll go, You must try your best to get on with the show.

If you don’t put in effort, no work and just play, Your whole world might crumble, it’s the price you may pay.

You must keep things in balance and keep your head high, If you keep that in mind, who knows where you’ll fly?

I built you this stool to remind you of that, Now get packing your pack, enough with this chat!

When I first began, I made a quick sketch, I wanted a twist, I wanted a stretch!

A chair that could move and wobble and rock, A chair that could fall with just a quick knock.

A chair that was quick to pack up and take Was the chair in the end I wanted to make.

A few lucky guesses, though I was just one, I knew what I wanted to do could be done.

Studying and researching and thinking some more, I realized exactly how my chair could soar.

I needed four legs, a seat, and a dome, I built two versions of cardboard and foam.

It worked! It did! I could sit on my stool!

Now onto the final, it’s sure going to be cool!

I went to buy wood, but to my dismay, They don’t sell it that size, my plans they would sway.

The dome must be smaller, so smaller it was, Maybe it will look better... Hey! So it does!

I adjusted my drawings, as you’ll see coming soon, To match with the wood, but not change my tune.

10 | A CHAIR FOR DR SEUSS

I prepared all my drawings, then drew and redrew, While I was building, my design, it regrew.

The dimensions below are based on the text, Proportions and sizing just may have been flexed.

I figured out volumes and areas too, So that my reactions and weight would be true.

Made of cherry and birch and poplar as well, It cost a bit much, but the weight isn’t hell.

Now moving on, let’s put it together.

Will it really work without any teathers?

Dimensions SCALE 1:10 (mm) 41.4

346.1

345.2

568.3

17.5 38.1 17.5 76.2

125.6

77.5 330.2

12 | A CHAIR FOR DR SEUSS

Volume/Area SCALE 1:10

PIECE #1box

PIECE #3box+#4box

V1= .0051m

V2+3= 2(.0013m ) =.0026m

V4+5= 2(.0005m ) =.0010m

A2+3= 2(.0766m2) = .1532m2

A4+5= 2(.0296m2) = .0592m2

3

3

PIECE #2box

PIECE #5box+#6box 3

PIECE #7box-(10)

3

TOTAL

V6-9= 4(.0009m ) =.0036m

3

3

3

VTOTAL= .0138m3 ATOTAL= .2971m2

V2= .0015m3 A2= .0847m2

Total Weight V (m3)

AREA (m2) QUANTITY

TOTAL VOLUME (m3)

1

0.0051

0.0051

MATERIAL WEIGHT (kg/m)

TOTAL MATERIAL AREA (m2) CHERRY

TOTAL WEIGHT (kg)

595

3.0345

0.0847

1

0.0847 BIRCH PLYWOOD

12.6477

1.07

0.0766

2

0.1532 BIRCH PLYWOOD

12.6477

1.94

0.0296

2

0.0592 BIRCH PLYWOOD

12.6477

0.75

455

1.638

0.0009

4

0.0036

POPLAR

TOTAL WEIGHT

8.43 8.8

ACTUAL WEIGHT

19lbs 6.4oz

Total Cost WIDTH (mm)

WIDTH (in)

LENGTH (mm)

LENGTH (in)

THICKNESS (mm)

THICKNESS (in)

ADJUSTED (IN)

BOARD FEET

330.2

13.00

330.2

13.00

95

3.74

4

1219.2

48.00

609.6

24.00

17

0.67

0.67

50

1.97

457.2

18.00

48

SQUARE FEET

4.69 8.00

QUANTITY TOTAL NEEDED MATERIAL 1

4.69

5 POPLAR

1

1

1 BIRCH PLY

2

2

2 DOWELS

COST $14.10

$70.50

$33.95

$33.95

$7.95 TOTAL + 2hrs CNC

A CHAIR FOR DR SEUSS | 13

TOTAL COST

TOTAL

$15.90 $120.35 $16.00 $136.35

At first I modelled the dome on my screen, Then loaded the file into the machine.

I sanded it, smoothened it, and rounded it down, Then I cut up some dowels that I found out of town.

I cut out two discs and a thirteen inch seat, Made some cross-braces, and it looked pretty neat.

Screwed the disc to the brace and the brace to the dome, So I could take it apart for when I fly home.

I finished it, stained it and varnished it well, And when it was finished, I exclaimed with a yell!

It was time for my review, so please take a seat, The stool wobbled and rocked, it was really a treat.

A chair that was quick to pack up and easy to take, It was exactly the chair that I set out to make.

14 | A CHAIR FOR DR SEUSS

To begin with the math and it can be fun, We look at reactions in analysis one: The chair by itself, in twisted position, The reactions at the floor, that is our mission.

Reactions

CHAIR ALONE - SCALE 1:10 (mm)

POSITION 1 & 3 Step one: take the mass (9.8), Times by gravity, that’s the weight.

Wc = WEIGHT OF CHAIR x 9.8kg/m2

= 8.43kg x 9.8kg/m­2

= 82.614N w­c

= Wc / l = 82.614N / .3302m = 250.194N/m

FRONT VIEW

LEFT VIEW

WC = 82.614N

WC = 82.614N

wC = 250.194N/m

wC = 250.194N/m

330.2mm FRONT VIEW

LEFT VIEW

WC = 82.614N

WC = 82.614N

wC = 250.194N/m

wC = 250.194N/m

r = 1065.987

r = 1065.987

330.2mm

Across the seat at the top, we have a distributed load, Vertical equilibrium means at the bottom that’s owed. ∑V = 0 therefore

R

= wc x l = 250.194N/m x .3302m = 82.164N

77.5mm

r =R/l

= 82.614N / .0775m = 1065.987N/m In its straight position, we do the same thing, Up forces, down forces, what loads do we bring?

POSITION TWO Wc = WEIGHT OF CHAIR x 9.8kg/m2

= 8.43kg x 9.8kg/m­2

= 82.614N w­c

77.5mm

R = 82.614N

R= 82.614N

WC = 82.614N

WC = 82.614N

wC = 250.194N/m r = 1065.987

wC = 250.194N/m r = 1065.987

R = 82.614N

R= 82.614N

WC = 82.614N

WC = 82.614N

wC = 250.194N/m

wC = 250.194N/m

r = 1065.987N/m

r = 1065.987N/m

R = 82.614N

R = 82.614N

r = 1065.987N/m

r = 1065.987N/m

R = 82.614N

R = 82.614N

= Wc / l = 82.614N / .3302m = 250.194N/m

∑V = 0 therefore

R

= wc x l = 250.194N/m x .3302m = 82.164N

r =R/l

= 82.614N / .0775m = 1065.987N/m

16 | A CHAIR FOR DR SEUSS

Reactions

CHAIR + PERSON - SCALE 1:10 (mm) FRONT VIEW

LEFT VIEW

WC = 82.614N

WC = 82.614N

WP = 1000N

WP = 1000N

wP = 3028.47N/m

wP = 3028.47N/m

wC = 250.194N/m

wC = 250.194N/m

330.2mm

Continuing on, we add the weight of you, One hundred and two kilos, that’s how we do.

POSITION 1 & 3 Wc = 82.614N WP = 1000N w­c = 250.194N/m wP = WP / l

= 1000N / .3302m = 3028.47N/m WP+C = 1082.61N

∑V = 0 therefore

R = (wc x l) + (wP x l)

= (250.194N/m x .3302m)

+ (3028.47N/m x .3302m)

= 1082.61N r =R/l

= 1082.61 / .0775m = 13969.2N/m

77.5mm r = 13969.2

r = 13969.2

R = 1082.61N

R= 1082.61N

WC = 82.614N

WC = 82.614N

WP = 1000N

WP = 1000N

wP = 3028.47N/m wC = 250.194N/m

wP = 3028.47N/m wC = 250.194N/m

POSITION TWO Wc = 82.614N WP = 1000N w­c = 250.194N/m wP = WP / l

= 1000N / .3302m = 3028.47N/m WP+C = 1082.61N

∑V = 0 therefore

A CHAIR FOR DR SEUSS | 17

r = 13969.2

r = 13969.2

R = 1082.61N

R= 1082.61N

R = (wc x l) + (wP x l)

= (250.194N/m x .3302m)

+ (3028.47N/m x .3302m)

= 1082.61N r =R/l

= 1082.61 / .0775m = 13969.2N/m

Centre of Gravity The centre of gravity is simple enough, I’d suggest in the middle just off the cuff.

But we’ll do the math and see what we find, In this second analysis of mine: X I 1 2 3 ∑

Vi Xi ViXi .0033m3 .1651m .00054483m4 .0069m3 .1651m .00113919m4 .0036m3 .1651m .00059436m4 .0138m3 .0027838m4

Y I 1 2 3 ∑

Vi Yi ViXi .0033m3 .53105m .001752465m4 .0069m3 .3219m .0019314m4 .0036m3 .07465m .00026874m4 .0138m3 .003952605m4

X

= (∑ViXi) / ∑Vi = .0027838m4 / .0138m3 = .1651m = 165.1mm

Y

= (∑ViYi) / ∑Vi = .003952605m4 / .0138m3 = .2864m = 286.4mm

FRONT VIEW - SCALE 1:10 (mm) 17.5 38.1 17.5

①

17.5 38.1 345.2 17.5

①③

17.5 38.1 345.2 17.5

②③ ②

76.2

125.6

77.5

125.6

330.2

17.5 38.1 17.5 76.2

531.05

321.9 286.4 531.05 74.65

321.9 165.1

286.4

74.65

165.1

125.6

①

77.5

125.6

330.2

17.5 38.1 17.5

165.1

165.1 LEFT VIEW - SCALE 1:10 (mm)

Yes it turns out, I guessed almost right, The X was the centre, the Y, lower by slight.

17.5 38.1 345.2 17.5

①③

17.5 38.1 345.2 17.5

②③ ②

76.2

125.6

77.5

125.6

330.2

17.5 38.1 17.5 76.2

531.05

321.9 286.4 531.05 74.65

321.9 165.1

286.4

74.65

165.1

125.6

77.5

125.6 165.1

330.2 165.1

18 | A CHAIR FOR DR SEUSS

Overturning FRONT VIEW

F = .0127kN

CHAIR ALONE - SCALE 1:10 2614kN

WC = .082614kN

W C = .08 F

wC = 250.194N/m

When you sit on your chair, right in the middle You‘re not going to tip, just don’t you diddle.

But as soon as you lean to the left or the right, The chair will fall over and you’re in for a fright.

0.194N/m

w C = 25

330.2mm

The drawings I’ve done show you on the edge, With half of your weight hanging over the ledge.

In theory it’s the same as if you were to lean How much force do you need before you make a scene?

ML = WC (lW) - RR (lR)

= WC (lW) - ¼WC (lR)

= .082614kN x .03875m .0206535kN x .0775m = .0016kN·m RB

77.5mm RL= RR= .02065kN

RL

RR RF

ASSUME 4 POINTS OF CONTACT

CHAIR + PERSON - SCALE 1:10 FRONT VIEW WP = 1000N WC = 82.614N wP = 6406N/m wC = 250.194N/m

∑ML = 0

clockwise = counter-clockwise

RR (lR) + F (lF) = WC (lW) = [WC (lW) - RR (lR)] / lF = [(.082614kN x .03875m)

- (.0206535kN x .0775m)] / .1264m

= .0127kN = 12.7N

F

0N .614N W C = 82

W P = 100

06N/m

w P = 64

0.194N/m

w C = 25

After doing the math, it’s really quite clear, The stool will tip with less force than a tear.

330.2mm

12.7 Newtons to be exact, Keeping balanced is really quite the act.

Anything more than that, say a person that leans Will flip the stool over, that’s what that means.

77.5mm r = 13969.2

R = 1082.61N

A CHAIR FOR DR SEUSS | 19

R= 1082.61N

The next step in understanding How this stool is still standing

Frame Analysis POSITION 1 & 3 - SCALE 1:10

Is analyzing the frame (The third part of the game.)

We look first at positions one and three, The legs are twisted, that’s how they must be.

POSITION 1 & 3 Wc = 82.614N WP = 1000N WC+P = 1082.61N chair is symmetrical

PV1 = PV2 = PV3 = PV4

PV = ¼WC+P

= ¼(1082.61N) = 270.6525N All legs are the same, but two of them back, Vertical horizontal, a practical hack.

WC = 82.614N WP = 1000N

They are not quite two-force, there’s an F from the plate, But those balance out, Nine-Seven-One and an 8

PV = 270.6N

wP = 3028.47N/m wC = 250.194N/m

x = 94.5mm F = 475.3N

PH

= (94.5/445.6) x PV = (.21207) x 270.6525N = 57.40N

1

3 4

P=276.67N P=276.67N P=276.67N P=276.67N

y = 26.91mm

LEG 1 All 4 legs the same

P=276.67N P=276.67N P=276.67N P=276.67N

therefore force in each leg is equal to force =

2

F = 475.3N 445.6mm

similar triangles can be used:

PH = 57.40N

1

√PV + PH = √(270.65252) + (57.402) = √76547.54 = 276.67N 2

2

3 4

F = 475.3N

2

I’m sure you’ve noticed, all legs are the same, I lucked out with that one, yes I’ll take the blame.

F = 475.3N y = 26.91mm

PH = 57.40N r = 13969.2N/m PV = 270.6N

R= 1082.61N

To find the magnitude of F, we calculate the moment around the centre of the leg. where the moment is equal to zero and no horizontal force or shear is transferred. ∑MCL = 0 MCLOCKWISE = MCOUNTER-CLOCKWISE 2Px = 2Fy F = (2Px) / 2y F = [2(270.6525N)(94.5mm)] / 2(26.908mm) F = 950.5N / 2 = 475.3N WC = 82.614N

∑M = 0 ∑H = 0 ∑V = 0

WP = 1000N

wP = 3028.47N/m wC = 250.194N/m

A

B

C D

20 | A CHAIR FOR DR SEUSS

x = 94.5mm F = 475.3N

2

3 4

F = 475.3N

Frame Analysis

P=276.67N P=276.67N P=276.67N P=276.67N

LEG 1 All 4 legs the same

POSITION 2 - SCALE 1:10

P=276.67N P=276.67N P=276.67N P=276.67N 1

2

y = 26.91mm

445.6mm

1

PH = 57.40N

3 4

F = 475.3N

F = 475.3N y = 26.91mm

PH = 57.40N

To keep it all going, the math remains few, We must look again, at the chair in mode two.

r = 13969.2N/m

It’s almost the same, the legs remain straight Vertical forces will take all the weight.

PV = 270.6N

R= 1082.61N

POSITION 2 Wc = 82.614N WP = 1000N WC = 82.614N

WC+P = 1082.61N

WP = 1000N

chair is symmetrical therefore

wP = 3028.47N/m

A = B = C = D = E = F = G = H

wC = 250.194N/m

= ¼WC+P

= ¼(1082.61N) = 270.6525N force

A

270.65N

B

C D

270.65N270.65N 270.65N

270.65N270.65N 270.65N

A

B

C

D

E

F

G

H

270.65N

270.65N

270.65N

270.65N270.65N E

270.65N270.65N

F

G H

r = 13969.2

R= 1082.61N

A CHAIR FOR DR SEUSS | 21

270.65N

270.65N

(ae) (bf) (cg) (dh) = TWO-FORCE force in each

= 270.6525N

We start looking at beams in analysis four, And then we see columns, and then joints and more.

Beam Analysis BEAM 1 - SCALE 1:10

To begin on this trip, we’ll look at piece five, The same as piece six, the load is all live.

R3 R4 R2

Let’s take it apart, let’s look at the middle, The piece that we want isn’t much of a riddle.

R1

PIECE #5box+#6box

CHOOSE PIECE 5 (SAME AS 6) CENTRE BEAM (l = 250mm)

WP = 500N

Ignoring self-weight, to make it more easy, More easy is good, so it will be breezy.

wP = 2000N/m

We do this because The weight is so small, There’s nothing above which Weighs nothing at all.

RL = 250N 55

55 250

Chair legs make contact between the supports, So R on each side must then take a quart.

R­L

RR

RR = 250N

W

= (R1 + R2) / 2 = (270.6N + 270.6N)/2 = 250N = (R2 + R3) / 2 = (270.6N + 270.6N)/2 = 250N

140N 110N

V

In each direction, see there goes a beam, So half of the weight is part of this scheme.

a2

0N

a4

a1

0N

a3 -110N

WP = 500N wP = (WP) / l = 500N / .250m = 2000N/m

-140N

1.875N/m

M

We take all this figuring And make tables show, All the math that I’ve outlined, And shown below: SHEAR Start at 0N Go down 2000N/m x .055m = -110N Go up 250N at reaction (140N) Go down 2000N/m x .14m = -140N Go up 250N at reaction (110N) Go down 2000N/m x .055m = -110N (0N) MOMENT m1 = a1 = -110N x .055m = -3.025n/m m2 = m1 + a2 = -3.025N/m + (140N x .07m)

= 1.875N/m m3 = m2 + a3 = 1.875N/m + (-140N x .07m)

= -3.025N/m m4 = m3 + a4 = -3.025N/m + (110N x .055m)

= 0N/m

0N/m

0N/m

-3.025N/m

fb

-3.025N/m

= M/S S = 1.875N/m / .000004091m3 = .001875kN/m / .000004091m3 = 458.323kPa

= (bh2) / 6 = (.017m x (.038m)2 / 6 = .00002455m3 / 6 = .000004091m3

FbPOPLAR = 7000kPa fb < Fb fv

= 3V / 2A = 3(.14kN) / 2(646mm2) = .42kN / 1292mm2 = 325kPa

FvPOPLAR = 1000kPa fv = Fv

VMAX = 140N MMAX = 1.875N/m

22 | A CHAIR FOR DR SEUSS

Column Analysis POSITION 2 - SCALE 1:10

Next we see columns in position two, Simple enough is the math we must do.

The columns are straight, as we’ve already seen, We ignore friction, self-weight, and keep it all clean.

COLUMN IN POSITION 2 (STRAIGHT) We are assuming pin-ends (so K = 1) An assumption we assume to make it more fun.

The columns are thick, six inches around, It will crush before buckling and then falling down.

standard axial calculation

m

=

250N

FC= = 6200kPa fc= < Fc=

431.3m

+

P =5

56.8N

=

243

=P/a P 2 100.6m .3N 2 = 250N / 1963mm = 250N=2/43(pi)r m = .25kN / .00195m2 = 127.55kPa

6.8N

P=250N

P=250N

442.9mm

fC=

.05m

P =5

Now onwards and upwards, let’s look at some more!

P=250N We still have another in analysis four! +

P= =24 3.3N

6.8N

The column is straight, with no movement at all, No moment is transferred, no matter how small.

P = 270.65N

F = 475.4N

F = 475.4N

F = 475.4N

F = 475.4N

R = 270.65N

A CHAIR FOR DR SEUSS | 23

MC

MC

Modes one and three are tougher it seems, Columns, oh columns, are tougher than beams.

COLUMN IN POSITION 1 & 3 (ANGLED) Let’s start with assuming pin-ends again, Ignoring friction and self-weight is simpler then.

Column Analysis POSITION 1 & 3 - SCALE 1:10

They will crush before buckling, they’re still pretty thick, Look at compression, it’s a quick poplar trick.

Edges of holes prevent much rotation, Tops of the legs will keep them in station.

We can assume assumptions, it’s simple enough, Zero moment at centre, and some other stuff: Moment’s minus at bottom and plus at the top, Point of inflection at centre, that’s where we’ll chop.

The connection’s a pin, And that makes things good, Transfer shear and compression, Yes, yes we could. look at forces parallel and perpendicular to axis

P=250N P= =24 3.3N

6.8N

= P x (100.6mm / 442.9mm) P=250N = 250N x (100.6mm / 442.9mm) = 68.8N = P x (431.3mm / 442.9mm) = 250N x (431.3mm / 442.9mm) = 243.3n

100.6m

56.8N

m

243.3N

250N

m

=

431.3m

442.9mm

+

P =5

P+

P=

fC=

= P= / a = 243.3 / (pi)r2 = 250N / 1963mm2 .05m = .2433kN / .00195m2 = 124.13kPa

P= =24 3.3N

+

P=250N

P = 270.65N

FC= = 6200kPa fc= < Fc= fC+

P =5

standard axial calculation

6.8N

Both P+ and P= (perpindicular and parallel) are looked at in terms of axial (compression) loads, as the column will crush before it buckles due to its thickness (2”)

MC F = 475.4N

F = 475.4N

= P+ / a = 56.8 / (pi)r2 = 250N / 1963mm2 = .0568kN / .00195m2 = 28.6kPa

FC+ = 3000Pa fc+ < Fc+ MTOP = (.0568kN)(.4313m)+(.2433kN)(.1006m)

= .0490kN/m MBOT. = MTOP = .0490kN·m = 49N·m

F = 475.4N

F = 475.4N

R = 270.65N

MC

24 | A CHAIR FOR DR SEUSS

P = 270.65N

Joint Analysis POSITION 2 - SCALE 1:2

p = 5106.6N/m

Last but not least is analysis five, A study of joints, go ahead, take a dive: COLUMN IN POSITION 2 (STRAIGHT) Looking first at the straight, up and down yes they are, The force stays the same, it’s vertically par.

Look back at the last page, maybe the two, No moment is transferred when the movement is few.

The allowable axial load is so high, The columns won’t fail and the chair will not die.

The load at the top of the column is P, It’s ditributed over .053.

Same at the bottom, the joints are the same, In position one, things are quite tame.

P = 270.65N p = 270.65N / .053m = 5106.6N/m COLUMN IN POSITION 1 & 3 (ANGLED)

x/2 = 47.25

POSITION 1 & 3 - SCALE 1:2

The chair legs, they’re twisted and spun forth and back, So we rotate the forces and have them unpack.

P = 270.65N

H versus V, but they’re rotated slightly, To align with the axis that sits nice and tightly.

The Newtons in V we already know, Same with H, we found long ago.

V equals two-four-three and one third, And H is less than sixty, or that’s what I heard.

F = 475.3N F = 475.3N

y = 26.91mm

The legs slide through holes in piece four and three, The edge exerts force, I think that is key.

The bottom of one edge, the top of the other, Stop the legs moving toward one another.

P = 270.65N

x/2 Cut it in half, that’s what we must do, The top joint is one piece, look good to you?

M=0 (Point of inflection) R = 270.65N

What’s up’s also down and what’s left’s also right, It’s all equilibrium, an opposite fight.

So everything’s equal, like the force from the edge, The force on the leg is forcing a wedge.

Now have a close look at the leg in rotation, Counter is offset by clockwise causation.

Cut chair leg at centre, where M = 0

R=250N

A CHAIR FOR DR SEUSS | 25

Find moment around centre MC = P(x/2) MC = Fy Fy = P(x/2) F = [P(x/2)] / y = 270.65N (47.2mm) / 26.91mm F = 475.3N

The leg is now angled, so the top load’s a point, Add the force from the disc, it’s all part of the joint.

The load times it’s distance (X over two), That equals moment and gives us what’s due.

Then to find F, we divide that by Y, The distance between where the two are applied.

Well that’s it for the math, I did all I could, The end was quite pleasing, it looks pretty good.

Would I do anything different next time if I could?

Not a chance! Not a chance! Not a chance that I would!

There’s many ways you can sit, so let’s have a look, At the ways you can use it, and sit down with a book.

But there’s more places to sit, there’s more fun to be had.

Debates and discussions and just looking not bad.

You’ll need somewhere to sit, so get packing your pack: Two round pieces of wood, plus four more on your back.

They’re all independent, yes they are at first sight, But they work together to make something just right.

You’re off to great places, Today is your day!

Your mountain is waiting, So get on your way!

a e r

A / e m u

That’s it, that’s a wrap! We’re done with this book!

Thank-you, oh thank-you for having a look!

)

-5 T1

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A AN ED

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F RA D S

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N SI R A CK

3B

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