CHAIR FOR THE DECISIVE MOMENT A CHAIR FOR HENRI CARTIERBRESSON
ZAVEN TITIZIAN MACK PHILLIPS DECEMBER 19, 2015
A Chair for the Decisive Moment by Zaven Titizian and Mack Phillips
“The [chair] for us is a tool, not a pretty mechanical toy. In the precise functioning of the mechanical object perhaps there is an unconscious compensation for the anxieties and uncertainties of daily endeavor. In any case, people think far too much about techniques and not enough about [sitting].� -Henri Cartier-Bresson, on cameras and seeing The chair is both the photograph and the photographer the composition and the composer In photography, the chair is ubiquitous. The chair has always framed the moment Thus, the chair becomes part of the story The composition, but not the emphasis Nothing is staged, neither is the chair The photographer must blend in, to seem as if they were some permanent fixture Spontaneity and anonymity are paramount Also attention to proportion Attention to detail No other distractions Only the event expressed A precise organization of forms Simply. pragmatically and functionally reinterpreted Which give that event its proper expression Preserving this moment in time The smallest thing can be a great subject; the little human detail can become a leitmotiv The [chair] has a unique relationship with each individual subject There exists a back-and-forth, a conversation between the subject and the [chair] The resulting idiosyncrasies are brought forth in the subject Providing opportunities for the elusive and decisive moment
2
The Var Department, Hyeres, France, 1932
3
Place De L’Europe, Gare Saint Lazare, France, 1932
4
Naples, Italy, 1960
5
In a Train, Romania, 1975
6
Valencia, Spain, 1933
7
PRECEDENTS
The chair’s design and proportions are based on the ubiquituous schoolchair. Image courtesy of Oliver Apt.
8
Many of the original details of the original chair have been reinterpreted, such as the curvature of the bent legs and the placement of the rivets. Image courtesy of Oliver Apt.
9
The texture and materials used in the chair were inspired by the aesthetics of the Roundish Chair by Naoto Fukasawa.
10
The simplicity of parts and the functionality of the chair was inspired by the Folding Chair by Naoto Fukasawa.
11
DESIGN PROCESS
Chair breakdown options.
12
Sketch of chair brekdown of individual parts.
13
Testing bending techniques for front legs.
14
The tight radius and sharp angle required many thin plies – other thicker materials failed easily.
15
Progression of front leg test pieces.
16
Test peices, laminating front leg and cross piece.
17
Sketch of possible connection techniques.
18
Detailed sketch of connection of seat to frame.
19
Updated breakdown of chair parts.
20
Sketch of fabrication methods for individual chair parts.
21
Laminating back leg.
22
Vacuum-forming chair back.
23
Breakdown of parts, further updated.
24
Final arrangement of chair with connection details.
25
Sanding chair frame.
26
Zaven with assembled chair frame.
27
Sketch of anticipated seating position.
28
Sketch of alternate seating position.
29
First chair test.
30
Second chair test.
31
Finished chair.
32
Back of finished chair.
33
Final assembled chair.
34
Disassembled components of chair.
35
STRUCTURAL ANALYSIS
Orthographic views of finished chair. PLAN/ELEVATIONS 1:10 PLAN/ELEVATIONS 1:10
36
EXPLODED ISOMETRIC 1:5
Exploded axonometric view of finished chair.
37
testing materials 1/8� baltic birch plywood
$54.10
dowelling
$18.08
cnc time
$10.00
glue, etc.
$41.35
varathane
$25.00
____________________ total
total weight of chair
Final costing of chair.
38
$4.23
$151.87
2.5kg
11
10
6 9
7
12
5
2
8 4
1 3 Simplification of chair for structural analysis purposes.
39
centre of gravity Find centre of gravity: 11
Find volume:
10
6
9
12
5
7
8
2 1
4 3
Laminated Baltic Birch Plywood construction Leg diameter = 31.75mm Seat & back thickness = 9.5mm Density DBIRCH = 680kg/m3 Modulus of Elasticity E = 5900MPa Moment of Inertia of frame members I = 49882.11mm Allowable Bending Stress Fb = 10000KPa Allowable Shear Stress Fv = 1350KPa Allowable Compression Stress Fc = 8300KPa
V1234 = πr2h = π(15.9mm2)(419mm) = 332780.7mm3 V56 = πr2h = π(15.9mm2)(279mm) = 221589.1mm3 V78 = πr2h = π(15.9mm2)(267mm) = 212058.4mm3 V910 = πr2h = π(15.9mm2)(356mm) = 282744.5mm3 V11
= l•w•h = (191mm)(457mm) (6.35mm) = 829226.5mm3
V12
= l•w•h = (368mm)(432mm) (6.35mm) = 1510272mm3
V TOT
= 4V1234 + 2V56 + 2V78 + 2V910 + V11 + V12 = 4(332780.7mm3) + 2(221589.1mm3) + 2(212058.4mm3) + 2(282744.5mm3) + 829226.5mm3 + 1510272mm3 = 5103405.3mm3
Find individual centres of gravity x1 = 12.7mm x2 = 443.8mm x3 = 21.7mm x4 = 434.7mm x5 = 126.8mm x6 = 33.6mm x7 = 331.5mm x8 = 125mm x9 = 12.7mm x10 = 443.8mm x11 = 228.2mm x12 = 228.2mm 40
y1 = 492mm y2 = 492mm y3 = 12.7mm y4 = 12.7mm y5 = 320mm y6 = 320mm y7 = 116mm y8 = 116mm y9 = 480.3mm y10 = 480.3mm y11 = 511mm y12 = 228.6mm
z1 = 213.4mm z2 = 213.4mm z3 = 209.5mm z4 = 209.5mm z5 = 431.8mm z6 = 431.8mm z7 = 431.8mm z8 = 431.8mm z9 = 619.5mm z10 = 619.5mm z11 = 703.4mm z12 = 477.7mm
centre of gravity Find x ,̄ ȳ, z ̄
27 6m
6m 27
m
x ̄
432mm
m
26
7m
7m
26
m
m
y
= [V1234(x1+ x2 + x3+ x4) +V56(x5 + x6) + V78(x7 + x8)+V910 (x9 + x10) + V11x11+ V12x12] ÷ V TOT = [332780.7mm3(12.7mm+443.8mm+21.7mm+ 434.7mm)+221589.1mm3(126.8mm+336mm)+212058.4mm3 (331.5mm+125mm)+282744.5mm3(12.7mm + 443.8mm)+829226.5mm3(228.2mm)+1009498mm3(228.2mm)] ÷ 5103405.3mm3 = 228.4mm
x 368mm
ȳ
457mm
798mm
750mm
z ̄
z
x̄
= [V1234(z1+ z2 + z3+ z4) +V56(z5 + z6) + V78(z7 + z8)+V910 (z9 + z10) + V11z11+ V12z12] ÷ V TOT = [153536.4mm3(213.4mm+213.4mm+209.5mm+209.5mm)+ 102235mm3(431.8mm+431.8mm)+ 97838.2mm3(431.8mm+431.8mm)+ 130451mm3(619.5mm+619.5mm)+ 554272mm3(703.4mm)+1009498mm3(477.7mm)] ÷ 5103405.3mm3 = 470.4mm
191m m
x
= [V1234(y1+ y2 + y3+ y4) +V56(y5 + y6) + V78(y7 + y8)+V910 (y9 + y10) + V11y11+ V12y12] ÷ V TOT = [332780.7mm3(492mm+492mm+12.7mm+12.7mm)+ 221589.1mm3(320mm+320mm)+ 212058.4mm3(116mm+116mm)+ 282744.5mm3(480.3mm+480.3mm)+ 829226.5mm3(511mm)+ 1510272mm3 (228.6mm)] ÷ 5103405.3mm3 = 310.8mm
z y
m
The centre of gravity of the chair is located at the centre back of the chair, directly above the intersection of the planes of the frame.
z̄
356m m 419m
ȳ
41
dead load, tipping & reactions Fminx
Find mass of chair: mD
= VTOT DBIRCH = 0.0051034053m3 • 680kg/m3 = 3.47kg
This was slightly higher than what we measured (2.5kg), but was not far off.
798mm
PD
Find dead load of chair: PD
z x
x̄
= mDa = (3.47kg)(9.8m/s2) = 34.0N
Find minimum amount of force to tip chair resisted by dead load:
x̄ Fminy
PD ȳ
Fminx
= PD x ÷ ̄ zmax = (34.0N)(228.4mm)÷(798mm) = 9.73N
Fminy
= PD ȳ÷ zmax = (34.0N)(310.8)÷(798mm) = 13.24N
The chair is easiest to tip in the x-direction due to the proximity of the centre of gravity to the back of the chair, but either way requires very little effort to tip the chair.
798mm
Find the reactions in the legs from the dead load: R1 , R2 = PD (0.5)(ȳ÷ℓ) = (34.0N)(0.5)(310.8mm÷425.4mm) = 12.4N
z y
425.4mm
R3 , R4 = PD (0.5)[(ℓ-ȳ)÷ℓ] = (34.0N)(0.5)[(425.4mm-310.8mm)÷425.4mm] = 4.6N
R2 42
R1 R3
R4
live load reactions case # 1 Find reactions in chair under live load for upright position: Find live loads:
PL1 PL2 PD PL3 y
332mm
PL1
PL2
166mm
PD
305.4mm
PL3
PL2
= upper legs = 200N
PL3
= lower legs + feet = 130N + 28N = 158N
RL3
= PL3 = 158N
Ma R12
=0 = (PL1ℓL1+ PL2ℓL2+ PDℓD)÷(ℓR12) = ((642N)(332mm)+(200N)(166mm)+(34.0N)(305.4mm)) ÷(465mm) = 552.1N
R34
= PL1+ PL2+ PD - R12 = 642N+200N+34.0N - 543.8N =332.2N
465mm z a
= head + torso + arms = 90N + 420N + 92N + 40N = 642N
PD = 34.0N Find reactions
z
150mm
PL1
y
RL3 R34
R12 PL1
PL2
PD
223.2mm 223.2mm
R1 = R2 R1 , R2 = R12÷2 = 552.1N÷2 = 276N R3 = R4 R3 , R4 = R34÷2 = 332.2N÷2 = 166.1N
z
Because chair is symmetrical in x-direction, reactions are equal on either sides.
Most of the force when sitting upright is carried by the back legs.
x
R1 R3
R2 R4
43
live load reactions case # 2 Find reactions in chair under live load for slouching position: Find live loads: PL1V = 642N PL2V
PL1H
PL1V
PL1H = PL1V tanθ FfL12 = (PL1V+ PL2V) µLEATHER ON WOOD = 642N tan30 = (200N + 642N) (0.45) = 371N = 378.9N
PD
PL3V = 158N Ff3 = RL3 µRUBBER ON CONCRETE = 158N (0.6) = 94.8N PL3H = PL3V tanθ = 158N tan30 = 91N RL3 = PL3H = 158N
PL2
PL3V PL3H
z y
225mm
FfL12
453mm
465mm
PL3H
z a
y
R34
R12 PL1
PD
223.2mm 223.2mm
z x
44
Ma R12
R2 R4
=0 = (PL1VℓL1V+ PL1HℓL1H+ PL2VℓL2V+ PDℓD+ RL3ℓL3- FfL12ℓfL12 - (PL3Vℓ3V)÷(ℓR12) = [(642N)(225mm)+(371N)(798mm)+(34.0N)(305.4mm)+(158N) (450mm)-(378.9N)(453mm)-(200N)(450mm)]÷(465mm) = 559.9N
R34
= PL1V+ PL2V+ PD + PL3V - R12 - RL3 = 642N+200N+158 N+34.0N - 562.5N - 158N =316.1N
PL2
R1 R3
= 34.0N
Find reactions:
PL2V
305.4mm
PL3V
RL3
PD
PD
450mm
Ff3
PL1V PL1H
798mm
83mm
= 200N
Because chair is symmetrical in x-direction, reactions are equal on either sides.
R1 = R2 R1 , R2 = R12÷2 = 559.9N÷2 = 279.95N R3 = R4 R3 , R4 = R34÷2 = 316.1N÷2 = 158.05N
live load reactions case # 3 Find reactions in chair under live load for upright position on edge of seat: Find live loads:
PL1
PD
z y
PL1
PD
500mm
305.4mm
PL2 z
RL2
PL2
= lower legs + feet + (upper legs ÷ 2) = 130N + 28N + (200÷2) = 258N
RL2
= PL2 = 258N
Ma R12
=0 = (PL1ℓL1+ PDℓD)÷(ℓR12) = [(742N)(50mm)+(34.0N)(305.4mm)]÷(465mm) = 102.1N
R34
= PL1+ PL2+ PD - R12 - RL2 = 742N+258N+34.0N - 93.8N - 258N = 673.9N
Because chair is symmetrical in x-direction, reactions are equal on either sides.
465mm a
= head + torso + arms + (upper legs ÷ 2) = 90N + 420N + 92N + 40N + (200÷2) = 742N
PD = 34.0N Find reactions:
PL2
50mm
PL1
y
R34
R12 PL1
R1 = R2 R1 , R2 = R12÷2 = 102.1N÷2 = 51.05N R3 = R4 R3 , R4 = R34÷2 = 673.9N÷2 = 336.75N
PD
223.2mm 223.2mm
PL2 z x
R1 R3
R2 R4
45
live load tipping cases 1-3
332mm
PL2
Find minimum amount of force to tip chair resisted by live loads:
Fa PL1
Case # 1: Sitting upright, centred 798mm
166mm
PD
150mm
305.4mm
PL3
Fa
240mm
159.6mm
465mm
z y
PD
305.4mm
PL2
465mm z a
y
= (PL1VℓL1V - PL1HℓL1H+ PL2VℓL2V+ PL3VℓL3V+FfL12ℓfL12 + PDℓD)÷ zmax = [(642N)(240mm) - (371N)(798mm)+(200N)(382mm)+(158N) (915mm)+(378.9N)(453mm)+(34.0N)(159.6mm)]÷(798mm) = 320.9N
Fa Case # 3: Sitting upright, at front
PL1
50mm
Fa
b
798mm
PL3V
PD
798mm
915mm
382mm
453mm
PL2V
500mm
Case # 2: Slouching
PL1V PL1H
FfL12
46
b
y
PL3H
= (PL1ℓL1+ PL2ℓL2+ PL3ℓL3+ PDℓD) ÷ zmax = [(642N)(332mm)+(200N)(166mm)+(158N) (150mm)+(34.0N)(305.4mm)] ÷ (798mm) = 351.4N
465mm z
Ff3
Fa
Fa
= (PL1ℓL1 - PL2ℓL2+ PDℓD)÷ zmax = [(742N)(50mm)+(258N)(500mm)+(34.0N)(305.4mm)] ÷(798mm) = 221.2N
S Pin-frame analysis section cut location.
47
pin-frame analysis case #1 Find the load take-down for members in chair for case #1: 101.5mm
*Dead load excluded due to negligible weight
PL1 C
400mm
D
∑MA VB
=0 = PL1 (347.5mm÷624mm) = 742N (347.5mm÷624mm) = 414N
VA
= PL1 (276mm÷624mm) = 742N (276mm÷624mm) = 328N
HA
A
VA
HB
B
245mm
205mm
174mm
400mm
AC
VB
245mm Find reactions:
CD MC =8.82Nm
PL1
MD =8.82Nm HD =201N
HC =201N
HA=201N
∑V = 0 ∑H =0 VC = VA HC = HA = 328N = 201N CD
VC =328N VD =414N AC
VA=328N
175mm
350mm
347.5mm
∑V VD
DB VD =414N HD=201N
= 0 ∑H = PL1 - VC HD = 742N - 328N = 414N
DB ∑H HD
VC =328N HC =201N
= 0 = HB = 201N
Find moment in joints C & D: HB =201N MC VB =414N HA =201N VA =328N 48
MD
= VD (205mm) - PL1 (102.5 mm) = 409N (144mm) - 742N (102.5mm) = 8.82Nm = MC = 8.82Nm
=0 = HC = 201N
pin-frame analysis case #2 Find the load take-down for members in chair for case #2:
PL1H
350mm
347.5mm
175mm
101.5mm
PL1V C
D
∑V VA
=0 = 642N
HA
= PL1H (tipping force) = 689N
400mm
AC ∑V VC
=0 = HA -PL1H = 689N - 689N = 642N = 0N
HA
A
VA
HB
B 205mm
245mm
CD MC =70.6Nm
174mm
VB
CD ∑V VD
PL1V
MD =70.6Nm
= 0 ∑H =0 = VC-PL1V HD = HC = 642N 642N = 0N = 0N
HD =0
HC =0
BC
VC =642N VD =0 AC
= 0 ∑H = VA HC
DB PL1H =689N
∑V = 0 ∑H =0 VB = VD HB = HD = 0N = 0N
VD =0
(since chair is tipping there will be no reaction forces in point B)
HD =0 VC =642N
Find moment in joints C & D:
HC =0
∑M
=0
∑MC MD
=0 = PL1V (0.1025m) = 70.6Nm
HB =0 VB =0
HA
=689N VA =642N
MC
= MD = 70.6Nm
Under this loading would cause the maximum amount of stress and deflection in member AC.
49
pin-frame analysis case #3 Find the load take-down for members in chair for case #3 175mm
350mm
347.5mm
101.5mm
PL1 C
∑MA VB
=0 = PL1 (522.5mm÷624mm) = 742N (522.5mm÷624mm) = 621N
VA
= PL1 (101.5mm÷624mm) = 742N (101.5mm÷624mm) = 121N
400mm
D
VA
HB
B 205mm
245mm
174mm
VB
CD MC =14.1Nm
MD =14.1Nm HD =74N
HC =74N
VC =121N VD =121N AC
DB VD =121N
PL1
=74N HD VC
=121N HC =74N
245mm Find reactions
CD ∑V = 0 ∑H =0 VD = VC HD = HC = 121N = 74N DB ∑V VB
VA =121N 50
= 0 ∑H = PL1 - VD HB = 742N - 121N = 621N
=0 = HD = 74N
Find moment in joints C & D
VB =621N MD
=74N
HA=74N
∑V = 0 ∑H =0 VC = VA HC = HA = 121N = 74N
MC HB =74N HA
400mm
A
HA
VA=121N
AC
= VD (205mm) = 98N (205mm) = 14.1Nm = MC = 14.1Nm
Under this loading would cause the maximum amount of stress and deflection in member DB.
frame analysis case #1
MC =8.8Nm
PL1
MD =8.8Nm HD =202N
HC =201N
VC =328N VD =414N
I = πr4 ÷ 4 = π(15.875mm)4 ÷ 4 = 49882.11mm4
102.5mm PL1
MC =8.8Nm
MD =8.8Nm
P VC =328N
VD =414N
VC =328N
V
0
0 VD =414N Mmax =29.2Nm
M
0
0
-8.8Nm
*Assuming that because the members are glue-laminated birch ply, their modulus of elasticity is half of a solid member of a similar size E =11800MPa ÷ 2 =5900MPa
205mm 102.5mm
Find the load, shear, moment and deflection in critical case (#1) for CD
-8.8Nm
PL1
∆
VC
= 328N
VD
= 414N
Mmax
= (Pℓ ÷ 4) - 8.8Nm = [(742N)(205mm) ÷ 4] - 8.8Nm = 17.4Nm
ƒb
=m÷s = 17400Nmm ÷ 3142.2mm3 = 5537.5kPa
ƒc
=P÷A = 202N ÷ π(15.875mm)2 = 255.1KPa
Fcr = π2E ÷ (ℓ ÷ r) = π2(5900MPa) ÷((205mm) ÷ (7.94mm))2 = 1127.7 MPa ƒv
= 3VD ÷ 2A = 3(414N) ÷ 2(791.7mm2) = 784.4kPa
∆max
= Pℓ3 ÷ 48EI = (742N)(205mm)3 ÷ (48)(5900MPa)(49882.11mm4) = 0.45mm
VC =328N
VD =414N
ƒc ÷ Fc + ƒb ÷ Fb ≤ 1.0 = 255.1kPa ÷ 8300kPa + 5537.5kPa ÷ 10000kPa = 0.585 Under this loading the shear, moment and deflection within the member would be negligible. This member falls within the acceptable limits for compression and bending stress. 51
frame analysis case #2 Find the actual and allowable axial stress, critical buckling load, and deflection in critical case (#2) for AC
RC =642N
ƒc
= VAp ÷ A = (548N + 548N) ÷ π(15.875mm)2 = 1384.3 KPa
Fcr = π2E ÷ (kℓ ÷ r) = π2(5900MPa) ÷(2(430mm) ÷ (7.94mm))2 = 537.61 MPa 400mm
VA =642N
245mm
RC =548N
438mm
∆max VAp =548N
52
HAp =335N
Pcr
= Fcr x A = (537.61 MPa)(π(0.015875m)2) =425.6 KN
ƒb
=m÷s
s
= 3πr3 ÷ 4 = 3π(15.875mm)3 ÷ 4 = 3142.2mm3
ƒb
=m÷s = 70600Nmm ÷ 3142.2mm3 = 22468kPa
ƒv
= 3HAp ÷ 2A = 3(335N) ÷ 2(791.7mm2) = 397.8kPa
∆max
= Pℓ3 ÷ 3EI = (335N)(438mm)3 ÷ (3)(5900MPa)(49882.11mm4) = 31.9mm
ƒc ÷ Fc + ƒb ÷ Fb ≤ 1.0 = 1384.3kPa ÷ 8300kPa + 22468kPa ÷ 10000kPa = 2.41
Under this loading the axial stress within the member would be negligible and there would be a small amount of deflection. This member falls outside of the acceptable limits for compression and bending stress, however, the chair is stable under normal use.
frame analysis case #3 Find the actual and allowable axial stress, critical buckling load, and deflection in critical case (#3) for BD VD =121N
ƒc
PL1 =621N
HD=74N
=P÷A = (680N + 599N) ÷ π(15.875mm)2 = 1026 KPa
400mm
Fc = π2E ÷ (ℓ ÷ r) = π2(5900MPa) ÷((436mm) ÷ (15.875mm))2 = 79.9MPa
HB =74N 174mm V
B
=621N
30N
Pcr
= Fc x A = (79.9MPa)(π(0.015875m)2) = 67.87KN
ƒb
=m÷s = 14100Nmm ÷ 3142.2mm3 = 4487.3kPa
ƒv
= 3HBp ÷ 2A = 3(180N) ÷ 2(791.7mm2) = 213.8kPa
∆max
= Pℓ3 ÷ 3EI = (180N)(436mm)3 ÷ (3)(5900MPa)(49882.11mm4) = 17.3mm
111N
ƒc ÷ Fc + ƒb ÷ Fb ≤ 1.0 = 1026kPa ÷ 8300kPa + 4487.3kPa ÷ 10000kPa = 0.57
680N 421mm
∆max
Under this loading the axial stress within the member would be negligible and there would be a small amount of deflection. This member falls within the acceptable limits for compression and bending stress.
HBp =180N
VBp =599N
53
53
54
55
56
57
58
59
60
61
IMAGE CREDITS
Place De L’Europe, Gare Saint Lazare, France, 1932 Cartier-Bresson, Henri. Place De L’Europe. Gare Saint Lazare. 1932. FRANCE, Paris. Magnum Photos. Web. 19 Dec. 2015. <http://www.magnumphotos.com/Asset/2S5RYDI9CNRQ.html>. The Var Department, Hyeres, France, 1932 Cartier-Bresson, Henri. The Var Department. Hyeres. 1932. FRANCE, Paris. Magnum Photos. Web. 19 Dec. 2015. <http://www.magnumphotos.com/Asset/-2S5RYDZCKY50. html>. Valencia, Spain, 1933 Cartier-Bresson, Henri. Valencia. 1933. SPAIN, Paris. Magnum Photos. Web. 19 Dec. 2015. <http://www.magnumphotos.com/Asset/-2S5RYDI0Q9GT.html>. In a Train, Romania, 1975 Cartier-Bresson, Henri. In a Train. 1975. ROMANIA, Paris. Magnum Photos. Web. 19 Dec. 2015. <http://www.magnumphotos.com/Asset/-2S5RYDIFH5B6.html>. Naples, Italy, 1960 Cartier-Bresson, Henri. Naples. 1960. ITALY, Paris. Lomography. Web. 19 Dec. 2015. <http://www.lomography.com/magazine/64790-best-of-the-best-henri-cartier-bresson>. The Steward, courtesy of Oliver Apt. The Steward. 2010. Edmonton. Oliver Apt. By Max Hurd. Web. 19 Dec. 2015. <http://www.oliverapt.com/team/>. Roundish Chair by Naoto Fukasawa Fukasawa, Naoto. Roundish Chair. 2015. Mjolk, Japan. Mjolk. Web. 19 Dec. 2015. <http://store.mjolk.ca/index.php?product=Roundish+web&shop=1&c=44.45>.
62
63