a CHAIR for the PARKER BROTHERS

a CHAIR for the PARKER BROTHERS BRYCE CLAYTON & JACK LIPSON 2013

INDEX

02

INDEX

PART I : INTRODUCTION i MANIFESTO 04-05 ii THE PARKER BROTHERS 06-07 iii A PUZZLE 08-09

PART II : THE CHAIR iv INSTRUCTION MANUAL 12-15 v PUZZLE PIECES 16-43 vi PROCESS : CONSTRUCTION 44-51 vii A PUZZLE, A CHAIR, A GAME 52-57

PART III : ANALYSIS vii ANALYSIS I : WEIGHT & REACTIONS 60-75 ix ANALYSIS II : OVERTURNING 76-81 x ANALYSIS III : FRAME, STABILITY & RACKING 82-95 xi ANALYSIS IV : BEAMS & COLUMNS 96-107 xii ANALYSIS V : JOINTS 108-113

APPENDIX A : PRECEDENTS APPENDIX B : MATERIAL & COST

03

PART I

04

PART I

PART I : INTRODUCTION The design of the Parkers Brother chair, consists of six interlocking rectangular based components - unique yet similar puzzle pieces. As a chair for one, the pieces must be joined together following a precise order and method. However, once disassembled, the components may be reconfigured in countless ways to form accomodation for any activity, be it for the individual or a group. In the ‘Game’ configuration, the modular components can be stacked to form two seats and a table; a configuration allowing the Parker Brothers to take part in their favourite pastime. Restacked, the components become the ‘Shelf ’, a stand alone fixture to house the games as they await their next opportunity to be played. ~ “There shouldn’t be hidden morals buried within our games. A game should emphasize the time spent with friends: no lessons, just the enjoyment of playing.”

05

THE PARKER BROTHERS

[edward & charles parker]

06

THE PARKER BROTHERS

THE PARKER BROTHERS True pioneers in the board game industry, the Parker Brothers could be found in every American household throughout the turn of the century. Their groundbreaking games, including Clue, Sorry!, and most notably Monopoly, shaped the landscape of early 20th century pop-culture, while embracing Parker’s philosophy, which deviated from the common themes of board game design; that board games should be purely for enjoyment. Over 100 years later, the legacies of George, Charles and Edward Parker remain and their games continue to bring joy to millions.

07

A PUZZLE

[puzzle]

8

A PUZZLE

[p1]

[p2]

[p3]

[p4]

[p5]

[p6]

9

PART II

[p1]

[p2]

[p3]

[p4]

[p5]

[p6]

10

PART II

PART II : THE CHAIR INSTRUCTION MANUAL 12-15 PUZZLE PIECES 16-43 PROCESS : CONSTRUCTION 44-51 A PUZZLE, A CHAIR, A GAME 52-57

11

INSTRUCTIONS

step 2: [p3] & [p4] in vertical position

step 1: [p3] in vertical position

12

INSTRUCTIONS

step 3: slide [p2] in horizontal position

step 4: slide [p5] in horizontal position

13

INSTRUCTIONS

step 5: slide [p6] in horizontal position

step 6: slide [p1] in horizontal position

14

INSTRUCTIONS

step 7: enjoy!

15

COMBINED

16

COMBINED

679.60

609.60

679.60

304.80

17

COMBINED

18

COMBINED

19

PIECE I

20

PIECE I

304.80

615.60

679.60

240.80

21

PIECE I

22

PIECE I

23

PIECE I

24

PIECE I

25

PIECE II

26

PIECE II

615.60

679.60

304.80

27

PIECE II

28

PIECE II

29

PIECE II

30

PIECE II

31

PIECE III & IV

32

PIECE III & IV

615.60

679.60

304.80

33

PIECE III & IV

34

PIECE III & IV

35

PIECE III & IV

36

PIECE III & IV

37

PIECE V & VI

38

187.40

304.80

615.60

679.60

155.40

PIECE V & VI

304.80

39

PIECE V & VI

40

PIECE V & VI

41

PIECE V & VI

42

PIECE V & VI

43

PROCESS

44

PROCESS

PROCESS : CONSTRUCTION

45

PROCESS

[white ash]

[planing]

46

PROCESS

[gluing 6” ash boards]

[12” ash board]

47

PROCESS

[jig: finger joints]

test: finger joints]

48

PROCESS

top [cutting finger joints] bottom [spread ash pieces]

49

PROCESS

left [glue finger joints] top [filing, filing and more filing] bottom [it fits!]

50

PROCESS

top [clamping legs] bottom [sanding] right [finishing - walnut]

51

A PUZZLE, A CHAIR, A GAME

52

A PUZZLE, A CHAIR, A GAME

53

A PUZZLE, A CHAIR, A GAME

54

A PUZZLE, A CHAIR, A GAME

55

A PUZZLE, A CHAIR, A GAME

56

A PUZZLE, A CHAIR, A GAME

57

PART III

58

PART III

PART III : ANALYSIS ANALYSIS I : WEIGHT & REACTIONS 60-75 ANALYSIS II : OVERTURNING 76-81 ANALYSIS III : FRAME, STABILITY & RACKING 82-95 ANALYSIS IV : BEAMS & COLUMNS 96-107 ANALYSIS V : JOINTS 108-113

59

ANALYSIS I : WEIGHT & REACTIONS

60

ANALYSIS I : WEIGHT & REACTIONS

ANALYSIS I: WEIGHTS & REACTIONS [P3] and [P4] were identified as the most critical chair components in terms of likelihood of failure due to the distance of potential cantilever in a stool position and how all loads will be transferred through the finger joints without any load sharing. [P1] is also examined due to it being the only walnut component of the chair, as opposed to white ash. Analysis 1 will examine the self-weight and ground reactions of the assembled chair, and the aforementioned components in different loading conditions.

61

ANALYSIS I : WEIGHT & REACTIONS

Piece 1 Length (mm) Width (mm) Height (mm) Thickness (mm) Volume (m3)

679.60 304.80 304.80 32.00 0.06

Piece 2 Length (mm) Width (mm) Height (mm) Thickness (mm) Volume (m3)

679.60 304.80 304.80 32.00 0.06

Piece 3/4 Length (mm) Width (mm) Height (mm) Thickness (mm) Volume (m3)

679.60 304.80 304.80 32.00 0.06

Piece 5/6 Length (mm) Width (mm) Height (mm) Thickness (mm) Volume (m3)

679.60 304.80 304.80 32.00 0.06

Void Length Width Height Volume

615.60 304.80 240.80 0.05

Void Length Width Height Volume

615.60 304.80 240.80 0.05

Void Length Width Height Volume

609.60 304.80 272.80 0.05

Void1 Length Width Height Volume

609.60 304.80 272.80 0.05

(mm) (mm) (mm) (m3)

Net Volume

0.02

Black Walnut Density (kg/m3) Mass (kg)

Net Volume

52.96

0.02

White Ash Density (kg/m3)

550.00

9.87

Net Mass (kg) =

(mm) (mm) (mm) (m3)

Mass (kg) or

600.00

10.77

(mm) (mm) (mm) (m3)

Net Volume White Ash Density (kg/m3) Mass (kg)

0.01

600.00

7.17

(mm) (mm) (mm) (m3)

Net Volume White Ash Density (kg/m3) Mass (kg)

0.01

600.00

8.99

116.51 lbs

Board Feet of Black Walnut +10% Waste Price per Board Foot Cost + 13% HST

= = = =

12.50 13.75 $10.95 $170.14

Board Feet of White Ash +10% Waste Price per Board Foot Cost + 13% HST

= = = =

72.73 80.00 $4.12 $372.16

Miscellaneous =

$6.78

Total Cost =

$549.08

RCH 365 | ANALYSIS 1

W

SUMMARY 62

ANALYSIS I : WEIGHT & REACTIONS

X bi

Piece

(mm)

hi

(mm)

1 Solid Void

304.80 304.80

679.60 615.60

2 Solid Void

304.80 304.80

679.60 615.60

3 Solid Void

304.80 304.80

304.80 272.80

4 Solid Void

304.80 304.80

304.80 272.80

5 Solid Void Void

679.60 609.60 304.8

304.80 272.80 152.4

6 Solid Void Void

679.60 609.60 304.8

304.80 272.80 152.4

di

(mm)

Vi

2 (mm )

xi

304.80 63136906 240.80 45182479.1 17954426.9 304.80 63136906 240.80 45182479.1 17954426.9 679.60 63136906 609.60 50687898.6 12449007.4 679.60 63136906 609.60 50687898.6 12449007.4 304.80 63136906 304.80 50687898.6 152.40 7079211.65 5369795.71 304.80 63136906 304.80 50687898.6 152.4 7079211.65 5369795.71 71546459.9

Vixi

(mm)

0 0 0 0 152.4 136.4 -152.4 -136.4 0 0 0 0 0 0

3 (mm )

0 0 0 0 0 0 9622064472 6913829372 2708235100 -9.622E+09 -6.914E+09 -2.708E+09 0 0 0 0 0 0 0 0 0

X =

‫ڴ‬Vixi

=

0 mm

Vi

ARCH 365 | ANALYSIS 1

CENTROID CALCULATIONS 1 of

CENTROID CALCULATION: X 63

ANALYSIS I : WEIGHT & REACTIONS

Y bi

Piece

(mm)

hi

(mm)

1 Solid Void

304.80 304.80

304.80 615.60

2 Solid Void

304.80 304.80

679.60 615.60

3 Solid Void

304.80 304.80

304.80 272.80

4 Solid Void

304.80 304.80

304.80 272.80

5 Solid Void Void Void Void

679.60 609.60 609.60 304.80 304.80

304.80 152.40 88.40 32.00 32.00

6 Solid Void Void Void Void

679.60 609.60 609.60 304.80 304.80

304.80 152.40 88.40 32.00 32.00

Y =

‫ڴ‬Viyi

di

(mm)

Vi

2 (mm )

679.60 63136906 240.80 45182479.1 17954426.9 304.80 63136906 152.40 28595555.7 34541350.3 679.60 63136906 609.60 50687898.6 12449007.4 679.60 63136906 609.60 50687898.6 12449007.4 304.80 63136906 304.80 28316846.6 304.80 16425257.5 152.40 1486448.64 152.40 1486448.64 15421904.6 304.80 63136906 304.80 28316846.6 304.80 16425257.5 152.40 1486448.64 152.40 1486448.64 15421904.6 108237601

=

yi

Viyi

(mm)

0 0 0 0 0 0 0 0 152.4 120.4 228.6 168.4 288.8 -152.4 -120.4 -228.6 -168.4 -288.8

3 (mm )

0 0 0 0 0 0 0 0 0 0 0 0 9.622E+09 3.409E+09 3.755E+09 250317951 429286367 1.778E+09 -9.62E+09 -3.41E+09 -3.75E+09 -2.5E+08 -4.29E+08 -1.78E+09 0

0 mm

Vi

ARCH 365 | ANALYSIS 1

CENTROID CALCULATIONS 3 of

CENTROID CALCULATION: Y 64

ANALYSIS I : WEIGHT & REACTIONS X =

‫ڴ‬Vixi

=

0 mm

Vi

ARCH 365 | ANALYSIS 1

CENTROID CALCULATIONS 1 of

Z bi

Piece

(mm)

hi

(mm)

1 Solid Void

304.80 304.80

679.60 615.60

2 Solid Void Void

304.80 304.80 304.80

679.60 615.60 615.60

3 Solid Void

304.80 304.80

304.80 272.80

4 Solid Void

304.80 304.80

304.80 272.80

5 Solid Void Void

679.60 609.60 304.80

304.80 304.80 152.40

6 Solid Void Void

679.60 609.60 304.80

304.80 304.80 152.40

Z =

‫ڴ‬Vizi Vi

di

(mm)

Vi

2 (mm )

304.80 63136906 240.80 45182479.1 17954426.9 304.80 63136906 152.40 28595555.7 88.40 16586923.4 17954426.9 679.60 63136906 609.60 50687898.6 12449007.4 679.60 63136906 609.60 50687898.6 12449007.4 304.80 63136906 240.80 44742104.1 64.00 2972897.28 15421904.6 304.80 63136906 240.80 44742104.1 64.00 2972897.28 15421904.6 91650677.8

=

287.862 mm

=

288 mm

ARCH 365 | ANALYSIS 1

zi

(mm)

Vizi

3 (mm )

489.2 3.0887E+10 489.2 2.2103E+10 8783305630 152.4 9622064472 260.6 7452001819 184.4 3058628673 -888566020 339.8 2.1454E+10 339.8 1.7224E+10 4230172701 339.8 2.1454E+10 339.8 1.7224E+10 4230172701 339.8 2.1454E+10 339.8 1.5203E+10 416 1236725268 5013828424 339.8 2.1454E+10 339.8 1.5203E+10 416 1236725268 5013828424 2.6383E+10

CENTROID CALCULATIONS 2 of

CENTROID CALCULATION: Z 65

Total Cost =

$549.08

ANALYSIS I : WEIGHT & REACTIONS

CH 365 | ANALYSIS 1

WEIGHT CALCULA

W W a= 304.8mm

b= 304.8mm

a R1 + R3

R2 + R4

b

R1/R2

R3/R4

l= 609.6mm

l= 304.8mm

R1 + R3 = (b/L)xW = 259.762N

BY SYMMETRY R1 = R3 = (R1+R3)/2 = 129.881N

R2 + R4 = (a/L)xW = 259.762N

R2 = R4 = (R2+R4)/2 = 129.881N

W = 519.523N FRONT

RIGHT

*NOTE CHAIR IS NOT USED IN TORAGE POSITION

RCH 365 | ANALYSIS 1

REAC

REACTION CALCULATION: COMBINED CONFIGURATION 66

ANALYSIS I : WEIGHT & REACTIONS

xi

)

42 36

(mm)

Aixi

L L/3 b a P

3 (mm )

152.4 31568453 136.4 22906426.8

= = = = =

304.8 101.6 68.5 33.1 35.2

wCL =

6Pa

mm mm mm mm N

R = bW L b = RL W

=

220.934 mm

=

75.1037 N/m =

0.08 kN/m

=

348.878 N/m =

0.35 kN/m

= 339.8mm

l2

93 mm

w2 = 6Pa + 12Pb l2

= 339.8mm H=

304.8mm

WC = 70.34 N H= 304.8mm

a + R4

b

= 339.8mm

a

b

R2 + R4

R1 + R3

R1/R2

R3/R4

R1/R2

R3/R4

H= 304.8mm

l= 679.60mm

l= 304.8mm

R1 = (a/L)*W l= 679.60mm

R1 + R3 = (L/2)xWc = 35.17N R2 + R4 = (L/2)xWc R1 + R3

35.17N

= = R2 L = L/3 = R3 P = = R4w = =

l= 304.8mm

1

b

17.585N 17.585N 17.585N 17.585N

(a/L)*Wc = 17.6N RIGHT 304.8 mm (a/L)*W = 17.585N = 17.6N 101.6 mm c (b/L)*W = 17.585N = 17.6N 35.2 N c (b/L)*W = N/m 17.585N = 17.6N 2P = 230.767 = w c

l= 679.60mm

= = = =

2

L

+ R3 = (L/2)xWc = 35.17N L = ARCH 365 | ANALYSIS 1 + R4 = (L/2)xWc = 35.17N

w1 =

R1 R2 R3 R4

304.8 mm 101.6 mm 35.2 N

L/3 = P =

FRONT

a

R1/R2 R1

FRONT

= 35.17N

SIS 1

= 35.17N

R2 + R4

= c R2 = (a/L)*Wc = R3 = (b/L)*Wc = R4 = (b/L)*Wc = R3/R4 17.585N =

L = 2P= L/3 P =

304.8 mm = mm230.767 101.6 35.2 N

L

w1 =

2P

=

= = = =

(a/L)*Wc (a/L)*Wc (b/L)*Wc (b/L)*Wc

N/m = w2

= = = =

17.585N = 17.6N RIGHT 17.585N = 17.6N 17.585N = 17.6N 17.585N = 17.6N

17.6N 17.6N 17.6N 17.6N

R3 R4

231 N/m

R3 R4

231 N/m

R2

WORST CASE SCENARIO SELF WEI R3 R4

231 N/m

RIGHT

R R1

230.767 N/m = w2

R2

L

231 N/m

WORST CASE SCENARIO SELF

WORST CASE SCENARIO SELF WEIGHT 1 of 3

SELF WEIGHT: [P3] HORIZONTAL 67

L L/3 b a P

= = = = =

304.8 101.6 4.5 97.1 535.2

wCL =

6Pa

mm mm mm mm N

R = bW L b = RL W

ANALYSIS I : WEIGHT & REACTIONS =

156.904 mm

=

3356.14 N/m =

3.36 kN/m

=

3667.27 N/m =

3.67 kN/m

l2 w2 = 6Pa + 12Pb l2

5 kN/m

5 kN/m

5 kN/m

5 kN/m

5 kN/m

WC = 70.34 N WC = 70.34 N 1000 N WP = W = 1000 N P

H= 304.8mm

= 215.9mm

= 215.9mm

a R1 + R3 5 kN/m

R2 + R4

a R3/R4

R1/R2

R1/R2

b

R1/R2

BY SYMMETRY l= 679.60mm R1 = R3 = (R1+R3)/2 = 250N R2 = R4 = (R2+R4)/2 = 250N

l= 304.8mm = 500N

FRONT R1 R2 R3 R4

= = = =

R2 + R4 250N+17.6N 250N+17.6N 250N+17.6N 250N+17.6N

R1 + R3 = (L/2)xWc = = = = =

L = (L/2)xWcL/3 == R1/R2 P =

267.6N R2 + R4 = 267.6N 267.6N FRONT 267.6N BY

500NARCH

365 | ANALYSIS 1 R1 = 250N+17.6N l= 304.8mm

500N

= R2 = 250N+17.6N = R3 = 250N+17.6N = R4 = 250N+17.6N =

+ R3 = (L/2)xWc = 500N

+ R4 = (L/2)xWc

267.6N 267.6N 267.6N 267.6N

304.8 mm 101.6 mm 535.2 L = N

267.6N 267.6N 267.6N 267.6N

w1 =

2P L

L/3 = P = w1 =

=

l= 679.60mm 304.8 mm 500N101.6 mm 535.2 N

R3/R4

535.2 N

BY SYMMETRY w1 = 2P RIGHT = 250N R1 = R3 = (R1+R3)/2 L R2 = R4 = (R2+R4)/2 = 250N

R4

304.8 mm 101.6 mm 535.2 N

=

RIGHT

R3 WORST CASE SCENARIO PERSON CENTER

3511.61 N/m = R3

25 kPa 3.51 kN/m 3.51 kN/m

WORST CASE

25 kPa 3.51 kN/m

R1

3511.61 N/m = 3511.61 N/m =

3.51 kN/m 3.51 kN/m

L

R2

CENTER LOAD_PERSON: [P3] HORIZONTAL 68

R2

3.51

3.51 kN/m

CASE PERSON SCENARIO WORSTWORST CASE SCENARIO CENTEREDPERSON 2 of 3

1

25 kPa

3.51 kN/m

R2

R4 =

R4

R3

R1 = R3 = (R1+R3)/2 = 250N R2 = R4 = (R2+R4)/2 = 250N

1

RIGHT

2P

RIGHT BY SYMMETRY

b

P =

= 500N

L = L/3 = P =

a 500N

w = 2P = 3511.61 N/m = 3.51 kN/m SYMMETRY L R1 = R3 = (R1+R3)/2 = 250N L = 304.8 mm l= 679.60mm L/3 = 101.6 mm R2 = R4 = (R2+R4)/2 = 250N

ARCH 365 | ANALYSIS 1

FRONT

R3/R4

= 215.9mm

R1 + R3 = (L/2)xWc = 500N

1 + R3

R3/

l= 679.60mm H= 304.8mm

l= 304.8mm

R2 + R4 = (L/2)xWc

b

5 kN/m

a

R4

b

R2 + R4

R1 + R3

= 215.9mm

H= 304.8mm

CENTERED 2 ARCH 36

ANALYSIS I : WEIGHT & REACTIONS

5 kN/m

5 kN/m

5 kN/m = 70.34 N WCD= 100mm WP = 1000 N

5 kN/m

D= 100mm

5 kN/m

5 kN/m

WC = 70.34 N WP = 1000 N

D= 100mm

D= 100mm

D= 100mm

5 kN/m

D= 100mm

R2 + R4

R1 + R3

R2 + R4

R1 + R3

R1 + R3

R3 + R3 + R4

l= 304.8mm l= 304.8mm

R2 + R4 4.8mm

R1 + R3

R3 + R4

b

b R1 +

R1 + R2

R1 + R2

l= 679.60mm

l= 679.60mm

b

b

a

l= 679.60mm

R1 = [(Width-D)/L]*W = 573.15N = 573N R3 = [D/L]*W = 98.77N = 99N

R2 + R4 = 328.08N 328.08N

= 573N+17.6N = 590.8N = 280N+17.6N = 297.4N = 99N+17.6N = 116.4N R1 = 573N+17.6N L = mm = R590.8N = bW = 48N+17.6N =304.8 65.9N L/3 = 101.6 mm L

L L/3 b 3b P

= = = = =

w1-2 =

R2 = 280N+17.6N b = 50.1 mm = b297.4N = RL = 254.672 mm W = 116.4N = 65.9N 9403.81 N/m = 9.40 kN/m

304.8 101.6 50.1 150.4 707.1 2P b

mm mm mm mm NL =

L/3 b L3b = L/3 = P b = 3b = wP1-2 =

= 590.8N 3b = 150.4 mm 99N+17.6N P = 707.1 ARCHR3 365= | ANALYSIS 1N = 297.4N = 116.4N R4 = 48N+17.6N w = 2P b = 65.9N

R2 = [(Width-D)/L]*Wp = 279.81N = 280N R3 = 48N R4 = [D/L]*Wp = 48.28N R = bW L b = RL W

97.7 mm 293.0 mm 363.2 2P N

=

2P

304.8 101.6 50.1 150.4 707.1 2P

mm mm mm mm N

b

L L/3 b 3b P

254.672 mm

mm R = bW mm L mm9.40 kN/mb = RL R = bW mm W L N b = RL W

=

=

304.8 101.6 97.7 293.0 R4 363.2

mm mm mm mm N

w3-4 = 254.672 mm2P b

97.671 mm

9403.81 N/m =

2479.42 N/m =

= = = = =

9.40 kN/m

R = bW L b = RL W

L L/3 2479.42 N/m b 3b P

25 kP

= 97.671 mm 2.48kN/m

= = == = =

304.8 mm 25 kPa 101.6 mm 2.48 97.7 kN/m mm 293.0 mm 363.2 N

R = bW L b = RL W

=

97.671 mm

R2

R1 WORSTw3-4CASE SCENARIO PERSON FROM CORN = 2P 2479.42 N/m = 100mm 2.48 kN/m b

2.48 kN/m

R2

9.40kN/m

b

R4

WORST CASE SCENARIO PE

ARCH 365 | ANALYSIS 1 = = = = =

=

304.8 = 101.6 = =9403.81 N/m50.1 304.8150.4 mm = 101.6 mm = 707.1

w3-4 =

1-2

w1-2 =

H= 304.8mm

R1 + R2 R1 = [(Width-D)/L]*W = 573.15N = 573N = 573.15N = 573N p R1 = [(Width-D)/L]*W p R3 = [D/L]*Wp = 98.77N = 99N R3 = [D/L]*Wp = 98.77N = 99N l= 679.60mm R2 + R4 = 328.08N R2 = [(Width-D)/L]*Wp = 279.81N = 280N R2 =p =[(Width-D)/L]*W = 279.81N = 280N R4 = [D/L]*W 48.28N = 48N p R1 = [(Width-D)/L]*Wp = 573.15N = 573N R4 =p [D/L]*Wp = 48.28N = 48N R3 = [D/L]*Wp = 98.77N = 99N p R3 2.48kN/m R2 = [(Width-D)/L]*Wp = 279.81N = 280N R4 R4 = [D/L]*Wp = 48.28N = 48N

671.92N

L L/3 b 3b P

R4

R1 + R3 R1 =+671.92N R3 = 671.92N R2 + R4 = 328.08N

R1 + R3 = 671.92N

IS 1

a

a

R3 + R4

l= 304.8mm

R1 R2 R3 R4

a

D= 100mm

H= 304.8mm

D= 100mm

5 kN/m

WORST CASE SCENARIO PERSON 100mm FROM CORNER 3 of 3 R = bW L b = RL W

=

L L/3 b 3b P

254.672 mm

9403.81 N/m =

= = = = =

w3-4 =

9.40 kN/m

b

304.8 101.6 97.7 293.0 363.2 2P

mm mm mm mm N

R = bW L b = RL W

=

2479.42 N/m =

97.671 mm

2.48 kN/m

b

WORST CASE SCENARIO PERS CORNER LOAD_PERSON: [P3] HORIZONTAL 69

H ANALYSIS I : WEIGHT & REACTIONS

REACTIONS

WC = 70.34 N

= 220.93mm H= 679.6mm

a

b

R2 + R4

R1 + R3

220.93mm l== 304.8mm

R1/R2

a b H= 679.6mm

R1 + R3 = (L/2)xWc = 35.17N R2 + R4 = (L/2)xWc

R2 + R4

R1 + R3

R1 + R3 = (L/2)xWc = 35.17N

FRONT

bi

R2

Solid Void

(mm)

Ai

(mm)

hi (mm) Ai (mm ) 304.8 xi (mm) Aixi 679.6 (mm ) Solid 304.8 679.6 207142 152.4 31568453 Void 272.8 615.6 + R4 272.8 615.6 167936 136.4 22906426.8 2

(mm)

3

2 (mm )

xi

(mm)

207142 167936

3 i i (mm )

L L/3 b a P

= = = = =

136.4 22906426.8 R1/R2 wCL =

304.8 101.6 68.5 33.1 35.2

6Pa l

X =

.8mm

‫ڴ‬Aixi Ai

=

220.93 mm

‫ڴ‬Aixi

X =

=

220.93 mm

xWc

T

L/3 b a P

304.8 101.6 68.5 33.1 35.2

= = = =

wCL =

mm mm mm mm N

6Pa l

L L/3 b a P

2 = = = = =

304.8 101.6 68.5 33.1 35.2

l2

6Pa

=

=

220.934 mm

R3/R4

75.1037 N/m =

wCL =

0.08 kN/m

=

348.878 N/m =

0.35 kN/m

75.1037 N/m =

mm mm mm mm N

=

R = bW L b = RL W

= = = =

9.677N 9.677N 25.49N 25.49N

348.878 N/m = 75.1037 N/m =

0.08 kN/m

=

348.878 N/m =

0.35 kN/m

mm mm mm mm N

=

= = = =

=

0.35

kN/m

R3

220.934 m

R2

75.1037 N/m 0.08 =

0.08 k

=

348.878 N/m =

0.35 k

9.7N 9.7N 25.5N 25.5N

R3 R1

0.35

0.35 kN/m

R = bW L b = RL R4 W

l2

0.08 kN/m

220.934 mm

=

6Pa

w2 = 6Pa + 12Pb

R4 =

304.8 101.6 68.5 33.1 35.2

9.7N 9.7N 25.5N 25.5N

RIGHTWORST CASE SCENARIO SELF WEIGHT 1

l2

= (a/L)*Wc = (a/L)*Wc R3 = (b/L)*Wc R4 =mm(b/L)*Wc 220.934

= = = = =

= = = =

l2

kN/m

l2 w2 = 6Pa + 12Pb

=

RIGHT

=

w2 = 6Pa + 12Pb wCL =

R = bW L b = RL W

R = bW L b = RL W

l= 304.8mm

R1 ARCH 365 | ANALYSIS 1R2

= 35.17N L =

mm mm mm mm N

L L/3 b a P

2

w2 = 6Pa + 12Pb

A ARCH 365 | ANALYSISi 1

)xWc = 35.17N

R3/R4

R1 = (a/L)*W = 9.677N R2 =FRONT (a/L)*Wc = 9.677N = RIGHT 25.49N R3a = (b/L)*W b c A x R4 = (b/L)*Wc = 25.49N 152.4 31568453

17N hi

R1/R2

R1 = (a/L)*Wc = 9.677N = 9.7N R2 = (a/L)*Wc = 9.677N = 9.7N c = 25.49N = 25.5N R3 = (b/L)*W c R4 = (b/L)*Wc = 25.49N = 25.5N

= 35.17N

R2 + R4 = (L/2)xWc

bi

l== 35.17N 304.8mm l= 304.8mm

l= 304.8mm

7N

R3/R4

R2 0.08

WORST CASE SCENA

l2

WORST CASE SCENARIO SELF WEIGHT 1 of 3 SELF-WEIGHT: [P3] VERTICAL 70

H= ANALYSIS I : WEIGHT & REACTIONS

5 kN/m

5 kN/m

WC = 70.34 N WP = 1000 N 5 kN/m

5 kN/m

WC = 70.34 N WP = 1000 N

= 220.9

= 220.93mm

/m

5 kN/m

H= 679.6mm

a

b

= 220.93mm

R1/R2 R1 + R3

R1 + R3

R2 + R4

R2 + R4

l= 304.8mm

R1/R2

0N

= = = = =

wCL =

304.8 101.6 4.5 97.1 535.2

6Pa

mm mm mm mm N

R = bW L b = RL W

w2 = 6Pa + 12Pb

3356.14 N/m =

=

3667.27 N/m =

2)xWc =

)xWc

T

= 500N wCL =

L L/3 b 3.36 kN/m a P 3.67 kN/m

= = = = =

wCL =

304.8 101.6 4.5 97.1 535.2

6Pa

=

=

w2 = 6Pa + 12Pb l

304.8 101.6 4.5 97.1 535.2

3356.14 N/m =

=

6Pa l

mm mm mm mm N

3.67

=

kN/m

156.904 mm

25 kPa

3356.14 N/m =

RIGHT

R = bW L b = RL W

= 156.904 3667.27 N/m = mm

3.67 kN/m

WORST CASE SCENARIO PERSON CENTERED 2 3.67 kN/m

RIGHT =

3667.27 N/m =

WORST CASE

R3 R4

R1

3.67 kN/m

=

3356.14 N/m =

3.36 kN/m

=

3667.27 N/m =

3.67 kN/m

R2 3.36

WORST CASE SCENARIO P

l2

CENTER LOAD_PERSON: [P3] VERTICAL

R2 3.36

3.36 kN/m

3.36 kN/m

2

w2 = 6Pa + 12Pb

=

R = bW L b = RL W

BY SYMMETRY 156.904 mm R1 = R3 = (R1+R3)/2 = 250N R2 = R4 = (R2+R4)/2 = 250N

l2 L = L/3 = b = a = 2 P =

mm mm mm mm N

l2

l2

6Pa

wCL =

156.904 mm

l= 304.8mm l2

=

R3

w2 = 6Pa + 12Pb

304.8 mm R = bW | ANALYSIS 1L 101.6 mm 4.5 mm b = RL 97.1 mm W 535.2 N

365

=

=

ARCH 365 | ANALYSIS 1 L = ARCH L/3 = b = 500N a = P =

25 kPa

R4

l2

R3 = 250N+25.5N = 275.5N R4 = 250N+25.5N = 275.5N

.8mm

R3/R

R2 = R4 = (R2+R4)/2

BY SYMMETRY RIGHT FRONT R1 = R3 = (R1+R3)/2 = 250N RIGHT R4 = (R2+R4)/2 = 250N R1/R2 R2 = R3/R4

= 500N

L L/3 b a P

R2 = 250N+9.7N = 259.7N R1 = 250N+9.7N = 259.7N + R4 R3 R2 = 250N+25.5N = 275.5N R2 = 250N+9.7N = 259.7N R4 = 250N+25.5N = 275.5N

R1/R2

BY SYMMETRY

BY SYMMETRY R1 = R3 = (R1+R3)/2 = 250N R1 = R3 = (R1+R3)/2 = R2 = R4 = (R2+R4)/2 = 250N

R2 + R4 = (L/2)xWc = 500N a b

FRONT

b

l= 304.8mm

l= 304.8mm

R1 + R3 = (L/2)xWc = 500N

NR1 = 250N+9.7N = 259.7N

R3/R4

l= 304.8mm

l= 304.8mm

R1 + R3 = (L/2)xWc = 500N R2 + R4 = (L/2)xWc

H=

a

R3/R4 679.6mm a b

WORST CASE SCENARIO PERSON CENTERED 2 of 3

71

A

ANALYSIS I : WEIGHT & REACTIONS

5 kN/m

5 kN/m

WC = 70.34 N WP = 1000 N

5 kN/m

WC = 70.34 N WP = 1000 N

5 kN/m

D= 100mm

D=

D= 100mm

D= 100mm H= 679.6mm

5 kN/m

a

5 kN/m

b

.34 N 00 N

R2 + R4

a

a

b

R1/R2

D= 100mm

R1 R2 ++ R3 R4

R1 + R3

.8mm

l= 304.8mm

D= 100mm R1/R2

R2 + R4

b

R3/R4

R1/R2

R3/R4

R3/R

l= 304.8mm l= 304.8mm

25 kPa

H= 679.6mm l= 304.8mm

l= 304.8mm

R1 = [(Width-D)/L]*Wp = 451.47N = 451N

R1 + R3 R2 + R4 = 328.08N

328.08N R1 = 451N+9.7N

= 671.92N

L L/3 b a P

= = = = =

wCL =

T

304.8 101.6 46.4 55.2 707.1 6Pa

mm mm mm mm N

R = bW L b = RL W

=

=

2521.45 N/m =

w2 = 6Pa + 12Pb

=

6757.88 N/m =

l2

wCL =

55.2 + R4 = mm328.08N

=

L L/3 b a P

198.785 mm

l2

R = bW L b = RL W

=

193.092 mm

bW L= 1428.92 N/m = 1.43 kN/m RL = 198.785 mm W = 3338.18 N/m =

3.34 kN/m

=

2521.45 N/m =

2.52 kN/m

L L/3 b a P

R3/R4

= = = = =

wCL =

304.8 101.6 40.7 60.9 363.3

6Pa

mm mm mm mm N

R = bW L b = RL W

=

193.092 mm

= 1428.92 N/m =

=

= = = = =

304.8 101.6 46.4 55.2 707.1

mm mm mm mm N

6757.88 N/m =

wCL =

6Pa

=

R = bW L b = RL W

6.76 kN/m =

198.785 mm

2521.45 N/m =

2.52 kN/m

l2 w2 = 6Pa + 12Pb

L L/3 b a P

= = = = =

wCL =

=

2

2

40.7 mm

b = RL

=

RIGHT = 1428.92 N/m =

6Pa

304.8 101.6 2 40.7 60.9 363.3

w

6Pa

mm mm mm mm N

R = bW L b = RL W

= 6Pa + 12Pb l2

=

= 3338.18 N/m =

193.092 mm

WORST CASE SCENARIO

193.092 mm

1.43 kN/m

=

6757.88 N/m =

6.76 kN/m

w2 = 6Pa + 12Pb

= 1428.92 N/m =

1.43 kN/m

= 3338.18 N/m =

3.34 kN/m

l2

3.34 kN/m

R3 3.34

R4 6.76 kN/m

l2

l2

1.43 kN/m

kPa WORST CASE SCENARIO PERSON25100mm FROM CORNER 3 w = 6Pa + 12Pb = 3338.18 N/m = 6757.88 N/m = 6.76 kN/m 3.34 kN/m l= 304.8mm l l2

l2 L L/3 b a P

2.52

RIGHT =

= 60.9 mm W = 220.45N = 220N R2 = [(Width-D)/L]*W p = N = 107.64N = 108N R4363.3 = [D/L]*W p

wCL =

2.52 kN/m

mm mm mm mm N

R1 = [(Width-D)/L]*W = 451.47N = 451N = 304.8 mm R = bW p = 220.45N = 220N R3101.6 = [D/L]*W = mm p L

l2 w2 = 6Pa + 12Pb

R1/R2

l2

W

2521.45 N/m =

304.8 101.6 40.7 60.9 363.3

l2

6Pa

w2 = 6Pa + 12Pb

707.1 N

6PaFRONT=

R3 R2 = [(Width-D)/L]*Wp R4=RIGHT 220.4 3.34 6.76 a R4 b = [D/L]*W = 107.64N = R2 p kN/m

l2

R = bW

=R1 + R3 46.4=mm671.92N b = RL

= = = = =

304.8 mm R = 101.6 wCL =mm 6Pa 46.4 mm l2 b = 55.2 mm w2 =N 6Pa + 12Pb 707.1

wCL =

ARCH 365 101.6 | ANALYSIS 1 L/3 = mm L

N = 461N N = 230N 5N = 246N 5N = 133N

LYSIS 1

304.8 mm

L L/3 b a P

L = 2.52 L/3 kN/m = b = a = 6.76 kN/m P =

l2

p

R4 = [D/L]*Wp = 107.64N

RIGHT

198.785 mm

= 108N+25.5N = 133N ARCH 365 |R4 ANALYSIS 1 l= 304.8mm

b a =R2 P =

p

p

FRONT

= 461N R2 = 220N+9.7N = 230N R3 = 220N+25.5N = 246N R1 = 451N+9.7N = 461N R4 = 108N+25.5N = 133N R2 = 220N+9.7N = 230N R2 + R1 =+ 220N+25.5N R3 R3 = R4 246N

L =

p

R2 + R4 = 328.08N

FRONT

p

p

R1 + R3 = 671.92N

671.92N

R1 = [(Width-D)/L]*W = 451 = 220N = [D/L]*W = 220.45N R1 = R3[(Width-D)/L]*W = 451.4 R3 = [D/L]*W = 220.45N p = 220.45N = = 220N R2 =R3 [(Width-D)/L]*W 220.45N = = [D/L]*W p 108N = R4 = [D/L]*W = 107.64N R2 = [(Width-D)/L]*W = 220

R2 2.52

R1 1.43

WORST CASE SCENARIO PER

WORST CASE SCENARIO PERSON 100mm FROM CORNER 3 of 3

CORNER LOAD_PERSON: [P3] VERTICAL 72

L/3 = P =

101.6 mm 35.2 N

w1 =

2P

230.767 N/m = w2

=

ANALYSIS I : WEIGHT & REACTIONS

L

= 152.8mm

H= 679.6mm

WC = 96.85 N

H= 679.6mm

= 152.8mm

R2 + R4

R1 + R3

l= a 304.8mmb R2 + R4

R1 + R3

R4

FRONT

bi (mm)

hi (mm)

Solid Void

304.8 304.8

X =

!Aixi Ai

+ R3

Ai (mm2)

679.6 609.6

b

xi (mm)

Aixi (mm3)

h

i (mm)152.4 31568452.99 i (mm) 207142 185806 152.4 28316846.59

SolidR2 + R4 304.8 = 152.40 mm Void 304.8

Ai (mm2)

679.6 609.6

xi (mm)

207142 185806

i

!Ai1 xi ARCH 365X|= ANALYSIS Ai

152.4 28316846.59 w1 = 2P

=

152.40 mm

R3 = (L/2)xWc = 48.42N = 48.42N

L = ARCH L/3 = FRONT P =

3 i (mm )

L

l= 304.8mm

4 = (L/2)xWc

R1 = (a/L)*Wc = 24.21N 24.21N c 24.21N c 24.21N c

R2 = (a/L)*W = l= 304.8mm R3 = (b/L)*W = FRONT R4 = (b/L)*W = RIGHT R1 = (a/L)*Wc = 24.21N R2 = a(a/L)*W = 24.21N b c L = 304.8 mm R3 101.6 = (b/L)*W = 24.21N c mm A xL/3 = P = R4 = 48.4 (b/L)*W N = 24.21N 152.4 31568452.99 c R1/R2 R3/R4

= 48.42N

48.42N

99 59

H= 679.6mm R1 + R3 = (L/2)xWcR1/R2 = 48.42N R3/R4

R1 + R3 = (L/2)xWc = 48.42N

8.42N

365

b

=l=48.42N R2 + R4 = (L/2)xWc R3/R4 R1/R2 304.8mm

l= 304.8mm

R2 + R4 = (L/2)xWc

a

304.8 mm | ANALYSIS 101.6 mm 48.4 N

1

R1 R2 R3 R4

= = = =

=

317.747 N/m = w2

RIGHT l= 304.8mm = = = =

(a/L)*Wc (a/L)*Wc (b/L)*Wc (b/L)*Wc

R3 R4

L = L/3 = P =

304.8 mm 101.6 R2 mm 318 48.4 N

318 N/m

WORST CASE SCENARIO SELF WEIGHT 1

w1 =

24.21N 24.21N 24.21N 24.21N

2P

318 N/m

RIGHT

mm =304.8 317.747 N/m = w2

2P

L = L/3 = L P= w1 =

R2

R4 318 N/m

101.6 mm 48.4 N

2P

=

=

L R4

R3

w1 =

N

R2

R1 318 N/m

WORST CASE SCENARIO SELF WEI

317.747 N/m = w2

L

WORST CASE SCENARIO SELF WEIGHT 1 of 3 SELF WEIGHT: [P1] VERTICAL 73

ANALYSIS I L = L/3 = P =

WC = 96.85 N W = 1000 N

304.8 mm 101.6 mm 535.2 N

w1 =

2P

5 kN/m

=

5 kN/mL

5 kN/m

3511.61 N/m =

3.51 kN/m

= 152.8mm

5 kN/m

WC = 96.85 N W = 1000 N

H= 679.6 = 152.8mm H= 679.6mm

5 kN/m

5 kN/m

6.85 N 00 N a

a R2 + R4

R1 + R3

l= 304.8mm

R2 + R4

25 kPa

R1/R2

R3/R4

R3/R4

l= 304.8mm

2

l= R1 =304.8mm R3 = (R1+R3)/2

R1 + R3 = (L/2)xWc = 500N R2 + R4 = (L/2)xWc

= 250N SYMMETRY R2 = R4 = (R2+R4)/2 =BY 250N

= 500N

R1 + R3 = (L/2)xWc = 500N

FRONT R2 + R4 = (L/2)xWc = = = = c

)xW = 500N

xW

w1 =

2P L

= 500N

= = = =

274.21N 274.21N 274.21N 274.21N

ALYSIS 1

2P L

=

L = L/3 = P = w1 =

R1 = R3 = (R1+R3)/2 = 2 R2 = R4 = (R2+R4)/2 =R3 2

BY SYMMETRY L = 304.8 mm = R1 3598.59 N/m = 3.60 (R1+R3)/2 kN/m = = 250N L/3 = = R3 101.6 mm R1/R2 R3/R4 P = 548.4 N 25 kPa R2 = R4 = (R2+R4)/2 = 250N b

R4 3.60 kN/m

RIGHT R2

3.60 k

WORST CASE SCENARIO PERSON CENTERED 2

2Pl= 304.8mm = 3598.59 N/m = L

3.60 kN/m

RIGHT

WORST CASE S

R4 3.60 kN/m

BY SYMMETRY R1 = R3 = (R1+R3)/2 = 250N R2 = R4 = (R2+R4)/2 = 250N

L/3 101.6 mm R1 + =R3 = (L/2)xW = 500N c = = (L/2)xW 548.4 N = 500N R2 P+ R4 c FRONT

RIGHT

a

w1 =

ARCHL 365 = | ANALYSIS 304.8 1mm

w1 =

= 500N

L = 304.8 mm L/3 = 101.6 mm PFRONT = 548.4 N

250N+24.21N = 274.21N 250N+24.21N = 274.21N 250N+24.21N = 274.21N 250N+24.21N = 274.21N = 274.21N R1 = 250N+24.21N R2 =+ 274.21N R4 R3 R2 R1 = +250N+24.21N ARCH | ANALYSIS 1 c 365 R3 = 250N+24.21N = 274.21N l= 304.8mm = 274.21N R4 = 250N+24.21N

.21N .21N .21N .21N

b

BY SYMMETRY

8mm

R1 R2 R3 R4

a

l= 304.8mm H= 679.6mm

R1/R2

l= 304.8mm

b

= 152.8mm R3/R4

R1/R2

R2 + R4

R1 + R3

b

3598.59 304.8 mm N/m = 101.6 mm 548.4 N

2P

=

3.60 kN/m

RIGHT

R3 R4 3.60 kN/m R2

3598.59 N/m =

3.60 kN/m

L

R1 3.60 kN/m

WORST CASE SCENARIO PERSON WORST CASE SCENARIO PERSON CENTERED 2 of 3

CENTER LOAD_PERSON: [P1] VERTICAL 74

5 kN/m

5 kN/m

ANALYSIS I

L L/3 b 3b P

= = = = =

w1-2 =

304.8 101.6 50.1 150.4 707.1

mm mm mm mm N

2P

R = bW L b = RL W

5 kN/m L = =

254.672 mm

9403.81 N/m =

b WC = 96.85 N W = 1000 N

L/3 b 3b P

304.8 101.6 97.7 293.0 363.2

= = = =

w3-4 =

9.40 kN/m

mm mm mm mm N

2P

5 kN/m

R = bW L b = RL W

=

97.671 mm

2479.42 N/m =

2.48 kN/m

b

5 kN/m

5 kN/m

D= 100mm

D= 100mm

D= 100mm

D= 100mm

WC = 96.85 N W = 1000 N

H= 679.6

D= 100mm

D= 100mm

H= 679.6mm

5 kN/m

5 kN/m

6.85 N 00 N

a D= 100mm R1 + R3

+ R3

R2 + R4R1

R2 + R4

b

a

b

R1 + R3 = 671.92N

R1/R2

H= 679.6mm R3/R4

R1/R2

l= 304.8mm

R3/R4 l= 304.8mm

l= 304.8mm

R1 R3/R4 = [(Width-D)/L]*Wp25=kPa 451

R1/R2

+ R3 = 671.92N

R1 = [(Width-D)/L]*Wp = 451.47N = 451N R3 = [D/L]*W = 220.45N p R3 = [D/L]*Wp = 220.45N = 220N

R2 + R4 = 328.08N

R2 + R4 = 328.08N

l= 304.8mm

R2 = [(Width-D)/L]*W = 220 l= 304.8mm p = 220.45N = 220N R2 = [(Width-D)/L]*W p R4 = [D/L]*W = 107.64N R4 = [D/L]*Wp = 107.64N = 108N p

FRONT

R2 + R4 = 328.08N

R1 = [(Width-D)/L]*Wp = 451.47N = 451N RIGHT RIGHT R3 =a [D/L]*W = 220.45N = 220N p b

FRONT

R3

= = = =

L L/3 b 3b P

= = = = =

304.8 101.6 83.0 249.1 720.3

R1 + R3 451N+24.21N = 475.68N R2 + R4 220N+24.21N = 244.66N = 475.68N R1 = 451N+24.21N 220N+24.21N =l=244.66N R2 = 220N+24.21N 304.8mm = 244.66N w = 108N+24.21N = 131.85N FRONT R3 = R1 220N+24.21N = 244.66N + R3 = 671.92N

mm mm mm mm N

2P

1-2

b

R4 = 108N+24.21N = 131.85N

R = bW L L = b = RL = L/3 = W

R2 = [(Width-D)/L]*Wp = 220.45N = 220N R4 3.72kN/m R3/R4 L = 304.8 mm R R1/R2 = bW 304.8 mm R = bW R4 = [D/L]*W = 107.64N = 108N 101.6 mm L 101.6 mm L p L/3 =

221.765 mm

b = 3b = 5783.45 P N/m= =

83.0 mm 249.1 mm 5.78 kN/mN 720.3

w1-2 =

R2 + R4 = 328.08N ARCH 365 | ANALYSIS 1

1N 1N 1N 1N

R2 + R4

l= 304.8mm

1 + R3 = 671.92N

R1 R2 R3 R4

R1 + R3

a

D= 100mm

b

2P b

ARCH 365 | ANALYSIS 1 L L/3 b 3b P

= = = =

= = = = =

w1-2 =

475.68N 244.66N 244.66N 131.85N

304.8 mm 101.6 mm FRONT 83.0 mm 249.1 mm 720.3 N

2P b

L L/3 b 3b P

= = = = =

w1-2 =

R = bW L b = RL W

304.8 mm

=

R = bW L b = RL W

5783.45 101.6 mm N/m = 83.0 mm 249.1 mm 720.3 N 2P

5.78 kN/m =

221.765 mm

5783.45 N/m =

b

5.78 kN/m

L L/3 b 3b P

= w3-4 = = = =

w3-4 =

W

w3-4 =

304.8 mm 101.6 mm 67.5 mm 202.6 mm 221.765 376.5 N mm

R = bW L b = RL W

l= 304.8mm 2P

=

237.267 mm

b = 3b = 3.72 P =kN/m

RIGHT

3716.76 N/m =

67.5 mm 202.6 mm 376.5 N

b = RL W

=

237.267 mm

R2

5.

25 kPa

b R1 = [(Width-D)/L]*W = 451.47N = 451N p = 5783.45 N/m = 2P 3716.76 N/m = 3.72 kN/m =kN/m 220.45N =w3-4220N R3 = [D/L]*W5.78 p b WORST CASE SCENARIO PERSON 100mm FROM CORNER 3 R2 = [(Width-D)/L]*Wp = 220.45N = 220N WORST CASE SCENARIO P R4 = [D/L]*Wp = 107.64N = 108N

L L/3 b 3b P

221.765 mm

L = L/3 = b = 3b = b = RL P = =

= = = = =

304.8 101.6 67.5 202.6 376.5

304.8 101.6 67.5 202.6 376.5

=

2P b

ALYSIS 1 CORNER LOAD_PERSON: [P1] VERTICAL

mm mm2P mmb mm N

mm mm mm mm N

R = bW L b = RL W

R = bW

RIGHTL

b = RL W

R4 =

237.267 mm

R3 3716.76 N/m = =

237.267 mm

3.72 kN/m

R4

3.72kN/m R2

R1 5.78kN/m

WORST CASE SCENARIO PERSON 100mm FRO

3716.76 N/m =

3.72 kN/m

WORST CASE SCENARIO PERSON 100mm FROM CORNER 3 of 3

75

ANALYSIS II: OVERTURNING

76

ANALYSIS II: OVERTURNING

ANALYSIS II: OVERTURNING Pieces [p3] and [p4] were selected for the overturning analysis. The natural tipping resistance of the chair is a function of the dead weight of the chair and the frictional resistance of contact points. Both of these parameters are directly related to the weight of the chair, and [p3]/[p4] have the smallest mass generating the least overturning and frictional resistance.

77

YSIS 2

ARCH 365 | ANALYSIS 2

CENTROID CALCULATIONS

ANALYSIS II: OVERTURNING

F

WC D

WC D

o

99 N

00 N

Xc

80 mm

40 mm

60 mm Positive = Clockwise =

YSIS 2

Wc =

518.99N(0.3048 m)

518.99 0.6796 m

Wp =

1000 N

xc =

304.80 mm

xp =

152.40 mm

d =

679.60 mm ‫ڴ‬Mo =

0 0 = Wcxc - Fd F =

Wcxc

=

N

232.77 N

o OVERTURNING - STORAGE Xc

Positive = Clockwise =

d

518.99N(0.3048 m) 0.6796 m

ARCH 365 | ANALYSIS 2 OVERTURNING: COMBINED CONFIGURATION 78

=

232.77 N

ANALYSIS II: OVERTURNING

Coefficient of Friction Wood on wood = 0.30-0.70 Assumption: Bottoms of chair legs are not sanded smooth to improve grip. However, hardwood flooring is finished smooth, and the bottom of the legs are cut relatively smooth so assume a value of 0.4 to represent the condition that the interface is smoother than the median value of the provided range.

Leather on wood = 0.20-0.50 Assumption: An approximation will be used on this interface to represent the contact between the fabric a person is wearing and the surface of the chair. As leather typically has superior grip compared to fabrics such as cotton or wool, and the finish on the chair seating surfaces is quite smooth, a value of 0.30 will be used for friction calculations Coefficient of Friction between person Wood and onchair. wood = 0.30-0.70

Wc = Wp = WN = Empty Chair

Assumption: Bottoms of chair legs are not sanded smooth to improve grip. However, hardwood flooring is finished smooth, and the bottom of the legs are cut relatively smooth so assume a value of 0.4 to represent the condition that the interface is smoother than the median 70.34 N the provided range. value of

336.2 N

602 N

Leather on wood = 0.20-0.50 672.34 N Assumption: An approximation will be used on this interface to represent the contact between the fabric a person is wearing and the surface of the chair. As leather typically has superior grip compared to fabrics such as cotton or wool, and the finish on the chair Chair seating surfaces is quite smooth, a value of 0.30 will be used for friction calculations to Floor between person and chair.

Fs = µsN = 0.4 x 70.34N Wc = = 28.13508 N Wp = = N W28.1 N =

70.34 N

336.2 N

602 N

180.6 N

672.34 N

268.9 N

Empty Chair Since Fs is less than the force required to tip the chair in its bench position it will Chair to Floor slide, not tip. However, in it's stool position, the friction force exceeds the tipping Fs = µsN force, therefore the =base 0.4 x will 70.34N grip and the stool can topple. = 28.13508 N = 28.1 N

Occupied Chair Since Fs is less Chair to Floor slide, not tip.

Fs = µsN force, therefore

than the force required to tip the chair in its bench position it will Person to Chair However, in it's stool position, the friction force exceeds the tipping Fs = µsN the base will grip and the stool can topple.

= 0.4 x 672.34N Occupied = 268.93508 N Chair Chair to = 268.9 N Floor

Fs = µsN = 0.4 x 672.34N Again in the bench position, = 268.93508 the N = 268.9 N the frictional resistance of the

= 0.3 x 602N = 180.6 N Chair = 180.6 N

Person to Fs = µ sN = 0.3 x 602N force required to tip the person and the chair exceeds = 180.6 N = 180.6 N occupant's clothing, and of the frictional resistance

both

between the chair and the floor. First the occupant would merely slide backwards before the Again in the bench position, the force required to tip the person and the chair exceeds both chair moved, but the friction between clothing andfrictional chair was not exceeded, the the if frictional resistanceresistance of the occupant's clothing, and of the resistance between the chair before and the floor.

First the occupant chair would slide backwards tipping could occur.would merely slide backwards before the

157.86 N 157.86 N

180.6 N

chair moved, but if the friction resistance between clothing and chair was not exceeded, the chair would slide backwards before tipping could occur.

In the stool position, the force required to tip the chair is less than both the friction In the and stoolthe position, theand force required tipthe the chair is less both the between the person chair, the chairtoto floor.

If than a force of friction at least 157.34 between the person and the chair, and the chair to the floor. If a force of at least 157.34 N were applied at the top of the stool, the chair would tip backwards without the occupant N were applied at the top of the stool, the chair would tip backwards without the occupant of the chair sliding. of the chair sliding.

ARCH 365 | ANALYSIS 2

268.9 N

FRICTION - ANALYSIS

ARCH 365 | ANALYSIS 2

FRICTIO

FRICTION ANALYSIS: [P3] VERTICAL + HORIZONTAL 79

ANALYSIS II: OVERTURNING

Wp Wp

Wp

Wp

Xp = 152.40 mm

mm mm Xp = 152.40 Xp = 152.40

W3

F

232.77 N

F

W3

= 215.9mm

o 304.8304.8 mm mm

Wc =

Wc =

70.34 N 70.34 N

Wp =

Wp =

1000 N 1000 N

xc =

xc = 152.40 mm 152.40 mm

xp =

xp = 152.40 mm 152.40 mm

d =

d =

= 215.9mm = 215.9mm

Wp

D= 304.80 mm o

F

F

W3

D= 304.80 D= 304.80 mm mm

Wp

679.60 679.60 mm mm

o

Reduction�of�body�weight�for�sitting�position:�Feet,�lower�legs,�lower�arms,�and�half�the�upper�leg�will�be�supported�by�the�floor.

Reduction�of�body�weight�for�sitting�position:�Feet,�lower�legs,�lower�arms,�and�half�the�upper�leg�will�be�supported�by�the�floor.

1000N���F ���FLLeg���Ffeet ���F���1/2F Wp�=� 1000N���F Wp�=�feet LArm LLeg���FULeg LArm���1/2FULeg

304.8 mm

= 1000N���28N���130N���40�N���1/2(200N) = 1000N���28N���130N���40�N���1/2(200N) =

602 N =

602 N

304.80 mm 304.80 mm

‫ڴ‬Mo =

‫ڴ‬Mo0 = Positive Positive = Clockwise = Clockwise 0 0 = Wcxc 0- W =Fd c - Fd 70.34 N cWcx= WFcx= W cx c = = 70.34N x 70.34N 0.1524m x 0.1524m F = c W =d 1000 N d p 0.3048m 0.3048m

‫ڴ‬Mo = =

‫ڴ‬Mo = 0 Positive = Clockwise = Clockwise 0 Positive Wpxp - Fd 0 = Wcxc 0+ =WpWxcpxc -+ Fd WFcx=c + WWpx 70.34 = N 70.34 x 0.1524m N x 0.1524m + 602 N +x 602 0.3048 N x m 0.3048 m= F = cx p c + Wp=xp d d 0.3048 m 0.3048 m

35.16885 35.16885 N N =

= 336.17 N336.17 N

Reduction�of�body�weight�for�sitting�p Wp�=

xc =

152.40 mm

=

xp =

152.40 mm

=

d =

304.80 mm

ARCH ARCH 365 |365 ANALYSIS | ANALYSIS 2 2 ‫ڴ‬Mo =

0 0 = Wcxc - Fd Wcxc F = d

Positive = Clockwise =

OVERTURNING OVERTURNING - PIECE - PIECE 3 BENCH 3 BENCH CONFIGURATION CONFIGURA ‫ڴ‬Mo =

0 0 = Wcxc + Wpxp - Fd Wcxc + Wpxp F =

679.60 mm

70.34N x 0.1524m 0.3048m

=

35.16885 N

d

Reduction�of�body�weight�for�sitting�position:�Feet,�lower�legs,�lower�arms,�and�half�the�upper�leg�will�be�supported�by�the�floor.

Wp�=� 1000N���Ffeet���FLLeg���FLArm���1/2FULeg = 1000N���28N���130N���40�N���1/2(200N) =

602 N

‫ڴ‬Mo 365 = Positive 0 ARCH | ANALYSIS 2 0 = Wcxc + Wpxp - Fd Wcxc + Wpxp F = d

=

= Clockwise

70.34 N x 0.1524m + 602 N x 0.3048 m 0.3048 m

=

336.17 N

OVERTURNING: [P3] HORIZONTAL

Wp

80

OVERTURNING - PIECE 3 BENCH CONFIGURATION

F

= 1000N Ͳ 28N Ͳ 130N Ͳ 40 N Ͳ 1/2(200N) =

602 N

Wp

ANALYSIS II: OVERTURNING Positive = Clockwise

‫ڴ‬Mo =

0 0 = Wcxc + Wpxp - Fd Wcxc + Wpxp F = d

=

= 220.93mm

70.34 N x 0.1524m + 602 N x 0.3048 m 0.3048 m 3

W

Wp

Wp

mm Xp = 152.40 mm Xp = 152.40

F

D= 679.60 mm

336.17 N

=

Wp

Wp

F

= 220.93mm = 220.93mm

W3

W3

W3

W3

W3

D= 679.60 mm D= 679.60 mm

o o Wc =

Wp =

xc = x

xc =

c xp = x

xp =

d =d

=d

p

304.8304.8 mm

mm

mm

1000 N

Wc =

Wp =

304.8304.8 mm

mm

70.34 N

Wp = Wc =

o

304.8

Reduction of body weight for sitting p

70.34 N 70.34 N 1000 N 1000 N

220.93 mm

= 220.93 mm 220.93 mm 152.40 = 152.40 mm 152.40 mm

=

679.60 mm 679.60 679.60 mm

304.8

Wp

mm mm

Wp = Reduction of body weight for sitting position: Feet, lower legs, lower arms, and half the upper leg will be supported by the flo Reduction of body weight for sitting position: Feet, lower legs, lower arms, and half the upper leg will be supported by the floor.

1000N Ͳ F Ͳ FLLeg Ͳ FULeg Wp = feet LArm Ͳ 1/2FULeg Ͳ FLLeg Ͳ Ffeet Wp = 1000N Ͳ F = LArm Ͳ 1/2F

mm

‫ڴ‬Mo0 = Positive = Clockwise 0 Positive = Clockwise Positive = Clockwise =FdWcxc - Fd 0 Wcxc 0- = 0 =‫ڴ‬Mo Wx = 70.34N x 0.1524m F = 70.34N x 0.1524m F = c Fd = Wcxcc c0Wcx= d d 0.6796m 0.6796m

= 1000N Ͳ 28N Ͳ 130N Ͳ 40 N Ͳ 1/2(200N) = 1000N Ͳ 28N Ͳ 130N Ͳ 40 N Ͳ 1/2(200N) = 602 N = 602 N

‫ڴ‬Mo =

F =

Wcxc

=

‫ڴ‬Mo = 0 Positive = Clockwise 0 Positive = Clockwise Wpxp - Fd ‫ڴ‬Mo = 0 = Wcxc 0+ =WpWxcpxc -+ Fd + Wp=xp = N x 0.1524m N x 0.3048 m cx WFcx=c + WWpx 70.34 N 70.34 x 0.1524m + 602 N +x 602 0.3048 F = pc 0 = mWcxc += d 0.6796 m d 0.6796 m

‫ڴ‬Mo = =

22.86637 N = 22.86637 N

70.34N x 0.1524m 0.6796m

d

=

22.86637 N

F =

ARCH 365 | ANALYSIS 2 = 1000N Ͳ 28N Ͳ 130N Ͳ 40 N Ͳ 1/2(200N)

0 0 = Wcxc + Wpxp - Fd Wcxc + Wpxp F =

Wcxc + Wpxp

OVERTURNING - PIECE 3 STOOL CO OVERTURNING - PIECE 3 STOOL CONFIG

Reduction of body weight for sitting position: Feet, lower legs, lower arms, and half the upper leg will be supported by the floor.

Wp = 1000N Ͳ Ffeet Ͳ FLLeg Ͳ FLArm Ͳ 1/2FULeg

‫ڴ‬Mo =

0 157.86 N1 Wpxp = Fd d

| ANALYSIS 2 ARCH ARCH 365 |365 ANALYSIS 2

=

=

602 N

Positive = Clockwise =

d

OVERTURNING: [P3] VERTICAL

70.34 N x 0.1524m + 602 N x 0.3048 m 0.6796 m

W3OVERTURNING

=

157.86 N

- PIECE 3 STOOL CONFIGURATION 81

ANALYSIS III: FRAME, STABILITY & RACKING

82

ANALYSIS III: FRAME, STABILITY & RACKING

ANALYSIS III: FRAME, STABILITY & RACKING [P1] will be split into four segments for free body diagram analysis. Because each component is intended to be used in either a bench or stool orientation, the analysis will be conducted in both positions to examine the difference in resultant forces.

83

ANALYSIS III: FRAME, STABILITY & RACKING

l= 679.6mm 100 mm

l= 679.6mm 5 kN/m

100 mm a

Wdl(walnut) = 96.85N

b

5 kN/m a

b l= 679.6mm 100 mm moment connections providing lateral stability

c

d 5 kN/m

Wdl(walnut) = 96.85N

moment connections providing lateral stability

a

c

iece - B - C - D - D

b

d

Length (mm) Width (mm) Thickness 679.60 304.80 234.80 304.80 234.80 304.80 679.60 304.80 c

(mm) Density (kg/m3) Weight (N) 32.00 550.00 35.764 32.00 550.00 12.356 32.00 550.00 12.356 32.00 550.00 35.764

) Width (mm) Thickness (mm) Density (kg/m3) Weight (N) CH 365 | ANALYSIS 3 60 304.80 32.00 550.00 35.764 80 304.80 32.00 550.00 12.356 80 304.80 32.00 550.00 12.356 FREE-BODY DIAGRAM: [P1] HORIZONTAL 60 304.80 32.00 550.00 35.764 3

84

Piece

Length (mm)

Width (mm)

Thickness (mm)

mo pr st d

POS 1 |FREE BODY DIAGRA

POS 1 |FREE BODY DIAGRAM|1:5

Density (kg/m3)

Weight (N)

5 kN/m Wdl(walnut) = 96.85N

a

ANALYSIS III: FRAME, STABILITY & RACKING

c

Piece A - B A - C B - D C - D

Length (mm) Width (mm) Thickness (mm) Density (kg/m3) Weight (N) 679.60 304.80 32.00 550.00 35.764 234.80 304.80 32.00 550.00 12.356 234.80 304.80 32.00 550.00 12.356 679.60 304.80 32.00 550.00 35.764

ARCH 365 | ANALYSIS 3

DATA CHART: [P1] 85

1000 N

108.3 mm

ARCH 339.80 365 | ANALYSIS1036 3 N

870.7 N

ANALYSIS III: FRAME, STABILITY & RACKING

100.00

108.3 mm 339.80 5 kN/m

ARCH 365 | ANALYSIS 3

A - B Piece A - B Fi Dead Piece Live

Dead Live

xi

(N)

Vixi

(mm)

35.764 Fi (N) 1000 35.764 1035.764323

339.8 xi (mm) 100

1000 ‫ڴ‬Fixi 1035.764323

X =

X = Fi Piece Dead Live

Piece

100

=

Y = Dead Live

A - B l =Y

35.764 1000 1035.764323

3 (mm )

mm 5450.48282 100000 105450.4828

l R2 ==

‫ڴ‬F 679.6 iyimm

=

101.809

mm

L/3 =

304.8 mm / 3

571.32 mm x 1045 N = 870.74 N = 679.6 mm

870.7 N

1000 N

Dead Live

35.764 N

165.0 N

571.32 mm x 1045 N = 870.74 N = 679.6 mm

Y =

339.80

A - B

1000 1035.764323

100

‫ڴ‬F x X = ARCH 365 | ANALYSIS 3 F i i

=

mm

304.8 mm / 3 Fi (N) Piece 35.764 1000 -0.2091035.764323 mm

L/3 - Y = Vixi 339.8 100

12152.71694 870.7 100000 112152.7169

=

R1 = 1/2 w x d

108.280

Vixi 152.4 100

X = b =

3 (mm )

101.809

5450.48282 100000 centre105450.4828 portion.

R2 =

mm

108.280 mm 571.320 mm

=

101.809

w x d

= 870.74 N =

= 165.03 N =

870.7 N

165.0 N

-0.209 mm

mm

5713.5 N/m 165.0 N

304.8

L/3 - Y = 870.7 N

108.28 mm x 1045 N = 165.03 N = 679.6 mm

165.0 N

-

R1 = 1/2 w 870.7 N = 0.5 x

1

Assume centroid is along L/3 line.

R2 = 1/2 w x d W =

165.0 N 304.8 mm / 3mm 152.4

L/3 - Y =

165.0 N

35.764 N

Ne

ARCH 365 | ANALYSIS 3

mm

L/3 =

108.28 mm x 1045 N = 165.03 N = 679.6 mm

L/3 - Y =

= 1082.9 N

L/3 =

-0.209 mm

= 1082.9 N/m =

101.6 mm

into centre portion.

R1 = 1/2 w x d 870.7 N = 0.5 x W x 304.8 mm 870.7 N W = = 152.4 mm

=

86

R1 = 1/2 w x d 870.7 N = 0.5 x W x 304.8 mm 870.7 N W = = 152.4 mm

Negligible distance.

1036 N

5713.5 N/m

Assume centroid is along L/3 line.

R2 = 1/2 w x d

165.0 N = 0.5 x W x 304.8 mm 5713.5 N/m

W =

165.0 N 152.4 mm

= 1082.9 N/m

Assume centroi

R2 = 1/2 w x d

101.6 mm

into centre portion.

Negligible distance.

PO

165.0 N = 0.5 x W x 304.8 mm

ARCH 365 | ANALYSIS 3

1000 N

W = mm 165.0 N 101.6152.4 mm mm

165.0 N = 0.5 x W x 304.8 mm

870.7 N

304.8 mm / 3

870.7 N

into centre portion.

571.32 mm x 1045 N = 870.74 N = 679.6 mm

Negligible distance.

5713.5 N/m

571.32 mm x 1045 N = 870.74 N = 679.6 mm

A-B: [P1] HORIZONTAL L/3 =

R2 = 1/2 w x d

W = R2 =

108.280 mm 571.320 mm

R1 =

5450.48282 100000 105450.4828

152.4 100

Fi

N = 0.5 x W x 304.8 mm 870.7 N W = = A - B l 152.4 = mm 679.6 mm mm

679.6 mm

X = b =

3 101.6 Viximm (mm )

into

‫ڴ‬Fiyi

Y =

3 (mm )

xi=(mm)

Dead Live

l =

Assume centroi 108.3 mm

5450.48282 100000 105450.4828

870.7 = 0.5 x= W x 304.8 mm ‫ڴ‬FiyN 101.809 i 108.3 mm Fi 870.7 N W = = 152.4 mm

R1 =

i

L/3 =

3

152.4 100

=

870.7 N A - B

100000 112152.7169

108.280

108.280

Vixi (mm ) -0.209 mm

(mm)

35.764 1000 1035.764323 R1 = 1/2

870.7 N

3 108.28 mm x 1045 165.03 N =Vixi 165.0 N Fi (N) N = x Piece i (mm) (mm ) Dead 35.764 339.8 12152.71694 679.6 mm

Live

xi

Negligible distance.

12152.71694 100000 112152.7169

165.0 N = 0.5 x W x 304.8 mm

5713.5= N/m

L/3 Fi-(N)Y =

Dead Live

339.8 100

304.8 mm / 3

Piece

ARCH 365 | ANALYSIS 3

R2 =

3 )

Vixi (mm (mm) intoxi centre portion.

35.764 339.80 1000 1035.764323

R1 = 1/2 w x d

100.00

mm

1036 N

101.6 mm

870.7 N = 0.5 x W x 304.8 mm 870.7 N ‫ڴ‬Fixi = W = X = N L/3 mm = 1036 152.4 Fi

571.320 mm

R1 =

35.764 N

=

A - B Piece i (N) -0.209F100.00 mm

L/3 - Y =

679.6 108.28 mm x 1045 Nmm= 165.03 N = 108.280 mm 679.6 mm

X = b =

1000 N

52.63 N/m

108.280 Fi mm 571.320 mm

A - B

52.63 N/m

Vixi

101.809 152.4 100

=

mm

5450.48282 100000 105450.4828

5 kN/m (mm)

xi

(N)

108.280

3 (mm )

152.4 100

Fi

=

R1 =

mm

= Vixi

‫ڴ‬Fiyi

X = b =

52.63 N/m

100000 mm 112152.7169

108.280

(mm)

35.764 Fi 1000 1035.764323

Fi

10

12152.71694 3 Vixi (mm ) 100000 339.8 112152.716912152.71694

100.00

‫ڴ‬Fixi xi

(N)

870.7 N

3 (mm )

Fi

IS 3

=

100.00

35.764 N

W =

165.0 N 152.4 mm

= 1082.9 N

870.7 N

ANALYSIS III: FRAME, STABILITY & RACKING 5.7135 kN/m 5.7135 kN/m

5.7135 5.7135kN/m kN/m

870.7 N

870.7 N

870.7 N

5.7135 kN/m

5.7135 kN/m

870.7 N

12.356 N 40.5 N/m

883.1 N

12.356 N

883.1 N

5.7135 kN/m

40.5 N/m

5.7135 kN/m

A - C Piece

870.7 N

12.356 N

xi

FiN/m 40.5 (N)

Dead 152.40

304.80

152.4

1883.127378

870.7 883.1

101.6

88466.85704 5.7946 kN/m 90349.98441

202.55

1883.127378

152.40

12.356 N

102.311

mm

A - C Piece

Fi

xi

(N)

12.356

Live

152.4

870.7 L/3 = 883.1 ‫ڴ‬Fiyi

Y =

mm

1883.127378

-0.711 mm 102.311

152.40

304.80

101.6 88466.85704 304.8 mm /90349.98441 3 =

L/3 - Y ==

102.311

202.55

A - C Pdead =

Vixi (mm3)

(mm)

=

Fi

883.1 N

304.80

40.5 N/m

Dead

mm

‫ڴ‬Fiyi

Y =

88466.85704 90349.98441

202.55

12.356 N

YAͲC =

101.6 mm

into centremmportion.

Negligible distance.

R1 = PAssume D+R1 =

3 (mm )

12.356

Live

3 (mm )

Vixi

(mm)

152.4 mm 870.7 N centroid 883.1 is along N L/3 line.@

102.31 mm

Fi

152.40

RC = 1/2 w x d

883.1 N = 0.5 x W x 304.8 mm A - C 304.80 202.55 883.1 N W = = 5794.6 N/m Pdead = 12.356 N 152.4 mm YAͲC = 152.4 mm

R1 =

870.7 N

L/3 = = P

304.8 mm @ /102.31 3

883.1 N

D+R1

L/3 - Y =

mm

-0.711 mm

=

101.6 mm

5.7946 kN/m

L/3 = L/3 - Y =

304.8 mm / 3

=

-0.711 mm

101.6 mm

into centre portion.

Negligible distance.

Assume centro

POS 1 | A-C

ARCH 365 | ANALYSIS 3

into centre portion.

RC = 1/2 w xdistance. d Negligible

883.1 N = 0.5 x W x 304.8 mm 883.1 N W = = 152.4 mm

Assume centroid is along L/3 line.

5794.6 N/m

RC = 1/2 w x d

ARCH 365 |= 0.5 ANALYSIS 3 = N101.6 mm x W x 304.8 883.1 mm

304.8 mm / 3

-0.711 mm

W =

883.1 N = 5794.6 N/m Negligible distance. Assume 152.4 mm

into centre portion.

= 1/2 w x d

= 0.5 x W x 304.8 mm 883.1 N = = 152.4 mm

centroid is along L/3 line.

PO

870.7 N 5794.6 N/m

POS 1 | A-C A-C: [P1] HORIZONTAL 87

5.7135 kN/m

165.0 N

165.0 N

165.0 N

ANALYSIS III: FRAME, STABILITY & RACKING 1.0829 kN/m

1.0829 kN/m

1.0829 kN/m1.0829 kN/m

165.0 N

1.0829 kN/m

1.0829 kN/m

165.0 N

1.0829 kN/m1.0829 kN/m

12.356 N 1.0829 kN/m 40.5 N/m

40.5 N/m

165.0 N

165.0 N

165.0 N

12.356 N

1.0829 kN/m 165.0 N

12.356 N

177.4 N

12.356 N

40.5 N/m

177.4 N

1.0829 kN/m

177.4 N

177.

165.0 N

40.5 N/m

1.0829 kN/m

3 ixi (mm )

Vixi

165.0 N

304.80

3 (mm )

304.80

152.40

152.40

202.55

304.80

7378 152.4 1883.127378 1883.127378

40.5 N/m

=

105.139 mm 105.139

B - D Piece

mm

Fi

Dead

xi

(N)

Vixi

(mm)

3 (mm )

1.1639 kN/m1.1

12.356

152.4

1883.127378

Live

165.0 177.4

101.6

16766.79818 18649.92556

202.55

177.4 N

‫ڴ‬Fiyi

=

Fi

202.55

B - D Pdead =

101.6=mm 101.6 mm

105.139 152.40

304.80

3 (mm )

12.356 152.4 1883.127378 L/3 = 165.0L/3 304.8 = mm101.6 L/3 / 3304.8 = mm16766.79818 = 304.8 / 3101.6 mm mm /= 3

Live

xi

(N)

Dead

202.55

Vixi

(mm)

Fi

Y =

304.80

mm

202.55

152.40

12.356 N 1.1639 kN/m

152.40

12.356 N

9818 101.6 16766.79818 16766.79818 2556 18649.92556 18649.92556

B - D Piece 40.5 N/m

12.356 N

YAͲC =

152.4 mm

1.1639 kN/m

177.4 18649.92556 R1 = 165.0 N L/3 - Y = L/3 - -3.539 Y =L/3mm - Y -3.539 = intomm centre -3.539into portion. mm centre into Negligible portion. centre portion. distance.

Negligible Negligible Assume distance. centroid distance.

Assume is centroid along Assume L/3centroid isline. along is L/3along line.L/3 line.

mm

14 @mm 105.14 mmY =

‫ڴ‬Fiyi

=

105.139

152.40

PD+R1 =

mm

177.4 N

@ 105.14 mm

Fi

B - D Pdead =

L/3 =

SIS 3

RD = 1/2 w xRDb = 1/2 wRDx =b1/2 w x b 304.80 202.55 177.4 N = 0.5 177.4 177.4 NW =x0.5 x W Nx =304.8 0.5 xmm 304.8 x W mm x 304.8 mm 177.4N 177.4N W = W = W177.4N = 1163.9 N/m = 1163.9=N/m1163.9 N/m 152.4 mm 152.4 mm 152.4 mm 12.356 N L/3 =

304.8 mm / 3

YAͲC =

R1 = P D+R1 =L/3

=

152.4 mm 165.0 N

Y =

177.4 N

304.8 mm / 3

101.6 mm

L/3 - Y = @ 105.14 -3.539 mm

mm

into centre portion.

-3.539 mm

L/3 -

=

101.6 mm

177.4 N = 0.5 x W x 304.8 mm 177.4N W mm = Y = -3.539 into centre portion.= ARCH 365 | ANALYSIS 3 152.4 mm

1163.9 N/m Negligible distance.

Negligible centr POS 1 distance. | POS B-D 1 Assume POS | B-D 1 |

Assume centroid is along L/3 line.

ARCH 365 | ANALYSIS 3

177.4 N = 0.5 x W x 304.8 mm 177.4N W = = 152.4 mm

RD = 1/2 w x b

304.8 mm / 3

101.6 mm

into centre portion.

Negligible distance.

RD = 1/2 w x b

L/3 =

=

1163.9 N/m

Assume centroid is along L/3 line.

RD = 1/2 w x b 177.4 N = 0.5 x W x 304.8 mm 177.4N W = = 152.4 mm

PO

1163.9 N/m

POS 1 | B-D

165.0 N

B-D: [P1] HORIZONTAL 88

1.0829 kN/m

1096.2 N

1.1639 kN/m

ANALYSIS III: FRAME, STABILITY & RACKING

52.63 N/m

177.4 N

35.764 N

177.4 N

35.764 N

5.7946 kN/m

2.7616 kN/m

ARCH 365 | ANALYSIS 3

1.1639 kN/m

C - D C - D Fi (N) Piece Fi (N) Piece

Dead

Dead Live Live Live Live

xi

x

i (mm) 35.764

35.764 883.1 883.1 177.4 177.4 1096.2 1096.2 ‫ڴ‬Fixi

X =

(mm)

Piece Live Live

177.4 ‫ڴ‬Fiyi 1096.241604 F

Y =

132.318

=

ARCH Piece 365 | FiANALYSIS x3 (N) i (mm) Live Dead Live

Vixi

mm

mm

POS 1

3 (mm )

101.6

=

103.257

‫ڴ‬Fiyi

C -YD =

132.318

=

X = Y =

l =

679.6 mm

X = Y =

132.318 mm 103.257 mm

mm

i (mm)

i (mm)

52.63 N/m

52.63 N/m

883.1 N

ARCH 365 | ANALYSIS 3

Dead Live Live

L/3 =

679.6 mm / 3

L/3 - Y = Therefore: b = 3X =

X =

123.276 mm

Piece

Fi

xi

(N)

C - D Piece

Live

RC-D = 1/2 w x b Fi 1096.2 (N)

Fi

Piece

Fi

Vixi

(mm)

Dead 35.764 Vixi (mm3) Live 883.1 152.4 5450.48282 Live 177.4 101.6 1096.241604 89722.27529 101.6 18022.21643 113194.9745 Y = 883.1‫ڴ‬F Niyi

152.4 101.6 101.6

C-D: [P1] HORIZONTAL

=

Fi 103.257

=

‫ڴ‬Fixi

Fi

xi

Vixi

(mm)

152.4 101.6 101.6

883.1 177.4 1096.241604 ‫ڴ‬Fiyi

xi

679.6 mm

X = Y =

132.318 mm 103.257 mm

b = 3X =

Y =

mm

3 (mm )

RC-D

=

‫ڴ‬F y

i i 123.276 mm

=

F

C - D

5450.48282 89722.27529 1096.2 N 18022.21643 226.53 mm 113194.9745

2.7

103.257 Case II Loading for mm distr

396.955 mm 679.6 mm

X = =Y =1/2

w x

L

132.318 mm b 103.257 mm

(mm )

L T b

2761.6 N/m

| A-C

2.7616 kN/m

ARCH 365 | ANALYSIS 3

2.7616 kN/m

103.257

mm

Fi

2761.6 N/m 679.6 mm

L/3 =

132.318 mm 103.257 mm mm

679.6 mm / 3

L/3 - Y = Therefore: b = 3X =

123.276 mm

=

226.53 mm

POS 1

Case II Loading for distributed reactions.

396.955 mm

RC-D = 1/2 w x b 1096.2 N = 0.5 x W x 396.955 mm 1096.2 N W = = 396.955 mm

365 mm | ANALYSIS 3

mm

1096.2 N

89 L/3 =

35.764 N

Vixi

152.4 101.6 101.6

177.4 NN/m i 2761.6

l =

5450.48282 89722.27529 18022.21643 113194.9745

L/3 =

177.4 N

132.318

(mm)

35.764 883.1 177.4 679.61096.241604 mm / 3 1096.2 N

1096.2 N = 0.5 x W x 396.955 L/3 - Y = mm 1096.2 N W = = Therefore: 35.764 N mm 177.4 396.955 N

5450.48282 89722.27529 18022.21643 113194.9745

=

3 (mm )

12152.71694 15454.13206 117445.9596 145052.8086

=

(N)

C - D l =

339.8 17.5 662.1

35.764 N

Dead Live Live

L/3 =

12152.71694 15454.13206 117445.9596 145052.8086

Vixi

(mm)

Case II Loading for distributed reactions.

396.955 mm

3 (mm )

103.257 ARCH

Piece

123.276 mm

mm xi

(N)

l = 145052.8086 X = Y = 132.318

=

Fi 132.318

=

Y =

(N)

Nxi = Wixix(mm3396.955 mm (mm)0.5 x V ) 339.81096.2 12152.71694 N = 17.5 15454.13206 396.955 mm C - D 662.1 117445.9596

Dead 35.764W = Vixi (mm3) Live 883.1 339.8 12152.71694 Live 177.4 17.5 15454.13206 1096.2 662.1 117445.9596 145052.8086 ‫ڴ‬Fixi X =

3 i i (mm )

339.8 17.5 662.1

35.764 883.1 177.4 1096.2

1096.2 N = 0.5 x W x 396.955 mm = 226.53 mm 1096.2 N W = = ‫ڴ‬Fixi = 132.318 mm 396.955 mm Fi Case II Loading for distributed reactions.

POS 1 3

Dead ARCH 365 | ANALYSIS 3 35.764

396.955 mmLive

35.764 V xN

(mm)

35.764 883.1 177.4 1096.2

xi

(N)

226.53 mm Fi

=

RC-D = 1/2 w x b

1.1639 kN/m

C - D Piece

Fi

X =

679.6 mm / 3

L/3 - Y = Therefore: 883.1 N b = 3X =

1.1639 kN/m

mm

C - D Piece Dead Live Live

L/3 =

C - D 5.7946 kN/m

1.1639 kN/m

103.257

132.318 mm 103.257 mm

POS 1 | A-C

883.1 N

18022.21643 52.63 N/m mm 113194.9745

679.6 Fi mm

l =

2.7616 kN/m

152.4 5.7946 kN/m 5450.48282 3 xi101.6 Vixi (mm ) (mm) 89722.27529 152.4 101.6 18022.21643 5450.48282 113194.974589722.27529 101.6

i

mm

52.63 N/m

3 (mm )

339.8 12152.71694 12152.71694 17.5 15454.1320615454.13206 117445.9596117445.9596 662.1 145052.8086145052.8086

339.8 17.5 662.1

Fi

35.764 Fi (N)883.1 35.764 177.4 1096.241604 883.1

Vixi

Vixi (mm3)

=

Fi ‫ڴ‬Fixi

X =

ALYSIS 3 Dead

m

ARCH 365 | ANALYSIS 3

883.1 N

m

m

883.1 N

52.63 N/m

5.7946 kN/m

679.6 mm / 3

679.6 mm / 3

= 226.53 mm L/3 177.4 - Y =N 123.276 mm Therefore:

=

226.53 mm

Case II Loading for distributed reactions.

2761.6 N/m

t)

ANALYSIS III: FRAME, STABILITY & RACKING

5 kN/m a

b

100 mm

= 96.85N

Wdl(walnut) = 96.85N moment connections providing lateral stability c

l= 304.8mm

d

th (mm) Width (mm) Thickness (mm) Density (kg/m3) Weight (N) 304.80 304.80 32.00 550.00 16.040 304.80 609.60 32.00 550.00 32.081 304.80 609.60 32.00 550.00 32.081 304.80 304.80 32.00 550.00 16.040

ALYSIS 3

POS 2 |FREE BODY DIAGRAM|1:5

FREE-BODY DIAGRAM: [P1] VERTICAL 90

Piece A - B A - C B - D

Length (mm) Width (mm) Thickness (mm) 304.80 304.80 32.0 304.80 609.60 32.0 304.80 609.60 32.0

Wdl(walnut) = 96.85N

ANALYSIS III: FRAME, STABILITY & RACKING

moment co providing stability c

Piece A - B A - C B - D C - D

l= 304.8mm

d

Length (mm) Width (mm) Thickness (mm) Density (kg/m3) Weight (N) 304.80 304.80 32.00 550.00 16.040 304.80 609.60 32.00 550.00 32.081 304.80 609.60 32.00 550.00 32.081 304.80 304.80 32.00 550.00 16.040

ARCH 365 | ANALYSIS 3

DATA CHART: [P1] 91

3 0 7

52.6 52.6 N/m

5 kN/m

ANALYSIS III: FRAME, STABILITY & RACKING

1000 N

5 kN/m

52.6 N/m A - B Piece

Fi

A - B Dead Piece Live

Fi

Dead Live

xi

(N)

Vixi

(mm)

16.040

152.4 (mm) 100

1016.040267 16.040

1000 ‫ڴ‬Fixi 1016.040267

X =

3 (mm )

2444.536733 3 V100000 ixi (mm ) 102444.5367 152.4 2444.536733

xi

(N) 1000

100

=

100000 mm 102444.5367

100.827

Fi

Piece X = Fi Dead Live

‫ڴ‬Fixi xi

(N)

16.040 Fi 1000 1016.040267

Fi

Piece

152.4 100

xi

(N)

‫ڴ‬Fiyi

Y = Dead Live

16.040 1000 1016.040267

V =ixi

l = R2 =

3 (mm )

mm 2444.536733 100000 102444.5367

5 kN/m

=

mm 100.827 mm F304.80 i x 1016 N = 304.8 mm 100.827 mm

X = b =Piece

Fi

(N)

Dead Live365 ARCH

336.1 N =

(mm) 203.973ximm

R1 =

304.8 mm

‫ڴ‬Fiyi

Y =

100.827 mm x 1016 N = 304.8 mm

R2 =

=

0.773 mm

into outer 1000portion.

N

101.6 mm Negligible distance.

mm

52.6 N/m

Assume centroid

R2 = 1/2 w x d

679.9 N = 0.5 x W x 304.8 mm 679.9 N W = = L/3 mm = 152.4

3 (mm )

336.1 N =

mm / 3

R1 = 1/2 w x d 4461.5 N/m16.04

304.8 mm / 3

L/3 - Y = N

100.827

Fi

mm304.8

L/3 - Y =

2444.536733 100000 679.94 N = 679.9 102444.5367

=

L/3 =

100.827

336.1 N

Vixi

16.040 152.4 1000 100 | ANALYSIS 3 203.973 mm x 1016 N = 1016.040267

mm

679.9 N

Vixi (mm3) Fi100.827 (N) mm xi (mm) F16.040 i mm 152.4 2444.536733 203.973 1000 100 100000 1016.040267 102444.5367 203.973 mm x 1016 N = 679.94 N = 679.9 R1 = N 304.8 mm A - BX = ‫ڴ‬Fixi = 100.827

X = Piece b = Dead Live

mm

100.827

100.827 152.4 100

i i

52.6 N/m

2444.536733 100000 102444.5367

Vixi

=

304.80 ‫ڴ‬F y mm

Y =

3 (mm )

(mm)

Fi

A - B l = A - B

mm

(mm)

6

16.04 N

336.1 N = 0.5 x W x 304.8 mm

N

=

0.773 mm

W =

336.1 N

101.6152.4 mm

= 2205.4 N

mm

into outer portion.

Negli

R1 = 1/2 w x d 679.9 N = 0.5 x W x 304.8 mm 679.9 N W = = 152.4 mm

mm

336.1 N

679.9 N

4461.5 N/m

336.1 N

A - B l =

304.80 mm

X = b =

100.827 mm 203.973 mm

L/3 =

ARCH 365 | ANALYSIS 3 L/3 =

304.8 mm / 3

R1 =

L/3 - Y = mm

R2 =

=

203.973 mm x 1016 N = 679.94 N = 304.8 mm

0.773 mm

100.827 mm x 1016 N = 304.8 mm d R1 = 1/2 w x

679.9 N

0.773 mm

=

101.6 mm

into outer portion.

R1 = 1/2 w x d

Assume centr

R2 = 1/2 w x d

679.9 N = 0.5 x W x 304.8 mm Negligible Assume centroid 679.9 N W = distance. = 4461.5 N/m

336.1 N = 0.5 x W x 304.8 mm

is along L/3 336.1 W =line.

152.4 mm

336.1 N

Negligible distance.

N

= 2205

152.4 mm

R2 = 1/2 w x d

679.9 N = 0.5 x W x 304.8 mm 679.9 N 3 W = | ANALYSIS = ARCH 365 152.4 mm

3 0 7

L/3 - Y =

101.6 mm

into outer portion.

336.1 N =

304.8 mm / 3

336.1 N = 0.5 x W x 304.8 mm 4461.5 N/m

W =

336.1 N

= 2205.4 N/m

152.4 mm

mm

POS 5 kN/m L/3 =

304.8 mm / 3

L/3 - Y =

A-B: [P1] VERTICAL

0.773 mm

=

101.6 mm

into outer portion.

Negligible distance.

R1 = 1/2 w x d 679.9 N = 0.5 x W x 304.8 mm 679.9 N W = = 152.4 mm

Assume centroid is along L/3 N line.

1000

R2 = 1/2 w x d 336.1 N = 0.5 x W x 304.8 mm 4461.5 N/m

52.6 N/m

W =92 336.1 N 152.4 mm

= 2205.4 N/m

16.04 N

POS 2 | A-B

679.9 N

ANALYSIS III: FRAME, STABILITY & RACKING 679.9 N

679.9 N

4.4615 kN/m

679.9 N

679.9 N

4.4615 kN/m

4.4615 kN/m 679.9 N

4.4615 kN/m 4.4615 kN/m 679.9 N

4.4615 kN/m

4.4615 kN/m 4.4615 kN/m

679.9 N

4.4615 kN/m 679.9 N

4.4615 kN/m

712.0 N

32.081 N

105.3 N/m

Vixi

3 (mm )

2.4

4889.073465

1.6

69081.51224 73970.58571

A - C

Dead Live Live

xi 32.081 679.9 679.9 712.0 712.0

Y =

Vixi

(mm)

x105.3 i (mm)N/m 32.081

Vixi 152.4

3 (mm )

3 32.081 N (mm )

152.4 4889.073465 101.6 L/3 = 304.8 mm69081.51224 / 3 = 101.6 69081.51224

101.6 mm

73970.58571

73970.58571 -2.289 mm

L/3 - Y =

‫ڴ‬Fiyi

‫ڴ‬Fiyi

=

FiFi

=

into centre portion.

103.889

103.889

mm

3

3 =

3 - Y =

R1 R1 == PD+R1 = PD+R1 = 304.8 mm / 3

-2.289 mm

L/3 =

L/3w Y = RC = 1/2 x d

mm

Negligible distance. Assume centroid is along L/3 line.

304.80 304.80

POS 2 | A-B

RC = 1/2 w x d

L/3 =

into centre portion.

=

679.9 N

-2.289 mm

ARCH 365 | ANALYSIS 3

into centre portion.

101.6 mm

4.672 kN/m

L/3 - Y L/3 = -2.289 mm -2.289 into portion.

Negligible Assume centroi - Y = mm centreinto centre portion.distance.

Negligible distance.

Negligible distance.

101.6 mm

mm 304.8 / 3 L/3 304.8 = mm = / 3 101.6 mm=

POS 2 | A-C

679.9 N N 679.9 712.0 N @ 103.89 mm 712.0 N @ 103.89 mm = 101.6 mm

304.8 mm / 3

4.672 kN/m

4672 N/m

AA -- CC 304.80 PPdead 32.081 N N 32.081 dead == 304.80 YYAͲC == 152.4 mm mm 152.4 AͲC

712.0 N

32.081 N

4889.073465

712.0 N = 0.5 x W x 304.8 mm 712.0 N W = = 152.4 mm

mm

4.672 kN/m

712.0 N

304.80

mm

FiN/m APiece - C 105.3 (N) Fi (N) Piece Dead

Y =

32.081 N

105.3 N/m

103.889

103.89 mm

32.081 N

105.3 N/m

RC = 1/2 w x d RC = 1/2 w x d Assume 712.0 centroid line.

N = is 0.5along x W xL/3 304.8 mm N712.0 = 0.5N x W x= 304.8 mmN/m W 712.0 = 4672 W152.4 = = mm 712.0 N

Negligible distance.

4672 N/m Assume centroid 152.4 mmis along L/3 line.

712.0 N = 0.5 x W x 304.8 mm 712.0 N W = = 4672 N/m 152.4RCmm= 1/2 w x d

ARCH 365 | ANALYSIS 3 712.0 N = 0.5 x W x 304.8 mm 712.0 N W = = 152.4 mm

POS 2 | A-C

4672 N/m

POS 2 | A-C A-C: [P1] VERTICAL

4.4615 kN/m

4.4615 kN/m

679.9 N

93

336.1 N

336.1 N

ANALYSIS III: FRAME, STABILITY & RACKING

2.2054 kN/m 336.1 N 338.1 N

2.2054 kN/m

336.1 N

2.2054 kN/m

336.1 N

338.1 N

2.2054 kN/m 2.2054 kN/m 338.1 N

2.2054 kN/m

2.2054 kN/m 2.2054 kN/m

338.1 N

2.2054 kN/m

338.1 N

2.2054 kN/m

368.2 N

32.081 N

105.3 N/m

Vixi

3 (mm )

52.4

4889.073465

01.6

34148.17891 39037.25238

105.3 N/m 304.80

106.026

Dead Piece

Fi

xi

32.081 xi (mm) 336.1 32.081 336.1 368.2 368.2

368.2 N

Fi

=

Fi

32.081 N 32.081 N304.80

YYAͲCAͲC ==

32.081 N

4889.073465

39037.25238 -4.426 mm

=

101.6 mm

into centre portion.

106.026

106.026

mm

368.2 N = 0.5 x W x 304.8 mm 368.2 N W = = 152.4 mm

L/3 - Y =

304.80

2.4159 kN/m

2415.9 N/m L/3 =

L/3 304.8 = mm =/ 3 101.6 mm= mm 304.8 / 3

101.6 mm

152.4 152.4 mm mm

-4.426 mm

L/3 =

into centre portion.

304.8 mm / 3

RD = 1/2 w x b

L/3 - Y =

-4.426 mm

368.2 N = 0.5 x W x 304.8 mm 368.2 N336.1 N = W = 152.4 mm

=

L/3 - Y L/3 = -4.426 mm -4.426 into portion.

Negligible Assume centroi - Y = mm centreinto centre portion.distance.

Negligible distance.

Negligible distance.

101.6 mm

into centre portion.

2.4159 kN/m

POS 2 | B-D

R1 336.1 N N R1 == 336.1 = PPD+R1 368.2 N N @ 106.03 mm mm 368.2 @ 106.03 D+R1 = 304.8 mm / 3 = 101.6 mm

L/3 =

Negligible distance.

304.80 Assume centroid is along L/3 line.

mm

RD = 1/2 w x b

304.80

BB -- DD dead= = PPdead

152.4

L/3 - Y =

‫ڴ‬Fiyi

Y =

3 (mm )

Vixi (mm3)

4889.073465 L/3 152.4 = 101.6 304.8 mm34148.17891 / 3 = 101.6 34148.17891 39037.25238

‫ڴ‬Fiyi

Y =

Vixi

(mm)

105.3 N/m

Live

mm

2.4159 kN/m

32.081 N

(N)

Live Dead

3

32.081 N 368.2 N

mm

B - D 105.3 N/m Fi (N) BPiece - D

106.03 mm

32.081 N

105.3 N/m

RD = 1/2 w x b = 1/2 x b Assume centroid isRDalong L/3w line.

368.2 N = 0.5 x W x 304.8 mm 368.2 N = 0.5 x W x 304.8 mm 368.2 N W = = 2415.9 N/m 368.2 N W152.4 = = 2415.9 N/m mm

Negligible distance.

152.4 mm is along L/3 line.

Assume centroid

ARCH 365 | ANALYSIS 3 2415.9 N/m

ARCH 365 | ANALYSIS 3 RD = 1/2 w x b

368.2 N = 0.5 x W x 304.8 mm 368.2 N W = = 152.4 mm

B-D: [P1] VERTICAL

POS 2 | B-D

2415.9 N/m

POS 2 | B-D

2.2054 kN/m 2.2054 kN/m

338.1 N

94

712.0 N

2.4159 kN/m ANALYSIS III: FRAME, STABILITY & RACKING 4.672 kN/m

16.04 N

52.6 N/m

4.672 kN/m

712.0 N

2.4159 kN/m

24.672 kN/mkN/m 4.672 kN/m

712.0 N

2.4159 kN/m

2.4159 kN/mkN/m 2.4159 kN/m 2.4159

712.0 N

2.4159 kN/m

52.6 N/m

1096.2 N

17.50 17.50

C - D Piece

Fi

xi

(N)

(mm)

Dead

3

7.3529 kN/m

16.040 3 712.0 11392.26686 xi (mm) Vixi16 Fi (N) (mm ) 3 xi (mm) Vixi288.8 Fi (N) Piece (mm ) Live 368.2 106331.7291 Dead 16.040 152.4 2444.536733 Dead 16.040 152.4 2444.536733 Live 712.0 16 11392.26686 1096.2 120168.5327

Live 712.0 Live 3 368.2 368.2 VLive ixi (mm ) 1096.2 1096.2 2444.536733 ‫ڴ‬Fixi X 2444.536733 = 152.4 2444.536733 11392.26686 16 11392.26686 F 11392.26686 x i = ‫ڴ‬F‫ڴ‬F XX =106331.7291 106331.7291 ixi i i 288.8 106331.7291

16 288.8 288.8

3 mm Vi)xi (mm3) m)

= =

120168.5327 FiFi 120168.5327 120168.5327

Piece

Fi

=

xi

(N)

101.60 101.60 7.3529 kN/mkN/m 7.3529 kN/m 7.3529

11392.26686 106331.7291 106331.7291 120168.5327 120168.5327 109.619

109.619 109.619

(mm)

Vixi

mm

mm 102.343

lC =- D Xl C ==- D Y =

mm

YSIS 3

X l == Y X ==

Y =

L/3 =

101.60

3 (mm )

mm

mm

mm 304.80 mm

L/3 =

109.619 mm mm 304.80 102.343 mm

679.6 mm / 3

L/3 =

109.619 mm mm 304.80 102.343 mm mm L/3 = L/3 mm mm L/3679.6 = / 3mm /679.6 /= 3 101.6 =mm 109.619 = 679.6 3 = mm101.6

L/3 - Y =

=

101.6 mm

679.6 mm / 3

-0.743 mm

L/3 - Y = 101.6 mm

L/3 =

=

101.6 mm

into centre portion.

-0.743 mm

679.6 mm / 3

Negligible distance.

=

into centre portion.

Assume centroid is a

101.6 mm

Negligible distance.

RC-D = 1/2 w x b 304.8- mm 1096.2 N = 0.5 x W xL/3 Y = -0.743 mm into centre portion.

102.343 mm = Negligible 1/2 b =distance.

L/3 - L/3 Y = - Y = L/3 -0.743 centre portion.

Negligible distance. centroid is along L/3 line.

1096.2 Nw xAssume - Y-0.743 =mm -0.743 mm centre into centre centroid is along W portion. = RC-D 7193.2 N/mAssume mminto into portion.

Negligible distance.

Assume centroid is along L/3 line. L/3 line.

1096.2 N152.4 = 0.5mmx W x 304.8 mm RC-D N= 1/2 =w 7193.2 x b RC-D =RC-D 1/2 =w 1/2 x bRC-D 1096.2 W = N/m w x = b 1/2 w x b W x 101.6 mm x Wmmx 304.8 mm 1096.2 NW =x 0.5 x304.8 304.8 1096.2 N =x1096.2 152.4 Nmm= 0.5 x W x 304.8 mm 679.6 mm 1096.2 / N3 = 0.5 =0.5 mm W = W = 1096.21096.2 7193.2 N/m =N/m7193.2 N/m N = 1096.2 WN = = N7193.2

ARCH 365 | ANALYSIS 3 L/3 - Y =

101.60

mm

Fi F i

C - D

7.3529 kN/m

mm

3 3 xi x Vixi V(mm FF Piece 109.619 i mm (mm) ) (mm ) Piece = 109.619 109.619 i(N) (N) mm 16.040 imm (mm) ixi Dead 152.4 2444.536733 Dead 16.040 152.4 Dead 16.040 152.4 2444.536733 2444.536733 Live 712.0 101.6 Live 712.0 101.6 72340.89455 72340.89455 Live 712.0 101.6 72340.89455 3 Live 368.2368.2 101.6 37407.56122 37407.56122 Live 101.6 3 3 mm Vi)xi (mm ) VLive 368.2 101.6 37407.56122 m) ixi (mm ) 1096.2 112192.9925 1096.2 112192.9925 2444.536733 mm 152.4 2444.5367331096.2 2444.536733 112192.9925 72340.89455 101.6 72340.89455 72340.89455 ‫ڴ‬Fiyi Y = = 102.343 mm 37407.56122 101.6 37407.56122 yi iyi ‫ڴ‬Fi‫ڴ‬F YY 37407.56122 == = 102.343 102.343 mm = F i 112192.9925 112192.9925 112192.9925

102.343 = 102.343

287.30 287.30

Vixi (mm ) 152.40 152.4 2444.536733 287.30

C - D Live CPiece - D

152.40

152.40

17.5017.50 17.50 152.40 152.40 152.40 287.30 287.30 287.30

17.50

152.40 287.30

368.2 N

16.04 N

m

1096.2 N 1096.2 N1096.2 N 368.2 N 16.04 N 17.50

368.2368.2 N N 368.2 N 16.0416.04 N N 16.04 N

52.6 N/m 52.6 N/m52.6 N/m

368.2 N

16.04 N

712.052.6 N N/m 712.0 N 712.0 N

-0.743 mm

152.4 mm 152.4 mm Negligible distance.

152.4 mmportion. into centre

ARCH 365 | ANALYSIS 3

W =

1096.2 N

Assume centroid is along L/3 line.

=

Assum

Negl

7193.2 N/m

152.4 mm

POS POS 2 | 2C-D POS 2 | | C-D

RC-D = 1/2 w x b 1096.2 N = 0.5 x W x 304.8 mm 1096.2 N W = = 152.4 mm

ARCH 365 | ANALYSIS 3N/m 7193.2

POS 2 | C-D

5 kN/m 1000 N

C-D: [P1] VERTICAL 95

52.6 N/m

16.04 N

ANALYSIS IV: BEAMS & COLUMNS

96

ANALYSIS IV: BEAMS & COLUMNS

ANALYSIS IV: BEAMS & COLUMNS The structural capacity for the chair must now be examined. At the beginning of the analyses, [P3] and [P4] were identified as the most critical components in terms of structure due to the cantilever of the shorter members with no internal member for load sharing or moment reduction.

It stands to reason that if [P3] and [P4] have sufficient shear, crushing, and bending resistance, then all other members will either meet or exceed these values. However, [P5] and [P6] have a reduced cross section in the middle, and the shorter cantilever can actually amplify the compression load carried by the internal member. As such, this internal member will also be examined for column failure.

97

ANALYSIS IV: BEAMS & COLUMNS

l= 679.6mm

l= 679.6mm l= 679.6mm

Wdl(ash) = 69.9N

a

b

a

Wdl(ash) = 69.9N

b

a

b

l= 679.6mm

moment connections providing lateral stability

c

d Wdl(ash) = 69.9N

c

c

moment connections providing lateral stability

a

mome prov stab d

d

iece - B - C - D

Length (mm) Width (mm) Thickness (mm) Density (kg/m3) Weight (N) 679.60 304.80 32.00 600.00 39.016 269.80 304.80 32.00 600.00 15.489 269.80 15.489 Piece Length304.80 (mm) Width (mm) 32.00 Thickness (mm)600.00 Density (kg/m3) Weight (N) A - B 679.60 304.80 32.00 600.00 39.016 CHWidth 365 |(mm) ANALYSIS POS 1 |FREE BODY DIAGRAM (mm) 269.80 Density (kg/m3) A Thickness - 4C 304.80 Weight (N) 32.00 600.00 15.489 c 600.00 0 304.80B - D 32.00 39.016 269.80 304.80 32.00 600.00 15.489 0 304.80 32.00 600.00 15.489 ARCH 365 | ANALYSIS POS 1 | 0 304.80 32.00 4 600.00 15.489 POS 1 |FREE BODY DIAGRAM|1:5

FREE-BODY DIAGRAM: [P3][P4] HORIZONTAL Piece A - B A - C B - D

Length (mm) Width (mm) Thickness (mm) Density (kg/m3) Weight (N) 679.60 304.8098 32.00 600.00 39.016 269.80 304.80 32.00 600.00 15.489 269.80 304.80 32.00 600.00 15.489

POS 1 | A-B | SHEAR ARCH 365||ANALYSIS ANALYSIS44 ARCH 365

POS 1 | A-B | SH

ARCH 365 | ANALYSIS 4

ANALYSIS IV: BEAMS & COLUMNS

887.9 N

88 887.

887.9 N

Resistance) 15.489 NA A- -C C Piece 872.4 NPiece Dead 887.9 NDead

F Fi (N)

i (mm) xix(mm) 15.489 15.489

i (N)

Live Live

872.4 872.4 887.9 887.9

3 π MPa x 1089025 mm4 V2ixxi (mm11800 ) 2 (269.8 mm) x (304.8 mm x 32 mm) 6 247.8261481

A = E(Ash) = I

9753.6 mm!

3 MPa ixi 3 (mm ) ViV x11800 i (mm ) 247.8261481 =1616 bh" 247.8261481 = 832307.2 mm4 16 13957.79893 12 16 13957.79893 A - C (Buckling Resistance) 14205.62507 14205.62507 = 136.526 MPa Pdead = 15.489 N

A - C 6 -C C(Buckling (Buckling Resistance) f xA A13957.79893 V=xResistance) P0.091028 1026.7 = MPa = 0.0910281 -N Piece Fi (N) xi (mm) MPa 14205.62507 5.341 16.00 565.4624787 P == 15.489 a NN 04.8 mm x 32P mm 15.489 Dead 15.489 i (mm)

a

i

3 i (mm )

dead dead

= 872.4 017.5 π16279.97557 EI N f=16.00 = R1R1 Live872.4 N 872.4 ore this member has sufficient P = 887.9 l 052.8 16845.43805 P = 887.9A N Nbuckling resistance 887.9 efore this member has sufficient crushing resistance f = 7.6 MPa 2

CR

2

D+R1 D+R1

C(Ash)

A = 16 A = E(Ash)= = E(Ash) 16 II ==

PD+R1= = PD+R1 fC(Ash)

872.4 N f f= = A - C (Buckling Resistance) 887.9 A- -C C N Pdead =N A35.341

R1 = Vixi (mm3)

Res a(Buckling = Resi P A A- -C Cf (Buckling P 15. a dead = Pdead = 15.4 2 R1 = 87 π f = CR R1 = 872E

CR

PD+R1 = ! !

9753.6 9753.6 mmmm 247.8261481 11800 MPa 11800 MPa

13957.79893

" fCR = = " bhbh = 14205.62507 1212

88 l2 887 7.

2 π2π x (269 (269.

Piece fNF=iF(N) 1017.5 i (N) Piece f = 101 Dead 35.34 304.8 PD+R1 = 1052.8 N Dead 35.341 304.8 4 π2 x 11800 MPa x 1089025 mm1017.5 Live 1017.

832307.2 Live 832307.2 mmmm 2 f, ,xtherefore therefore (269.8 mm) x (304.8 mm 32 1052.8 mm) 1052.

F F <<<<f t 2 F <<f f , MPa ,therefore therefor fCR = πF x<<11800 x 1089 R1 =

a

4

A - C

CR

=

a

4

a a

a a

CR

CR

C(Ash) C(Ash)

3 fa Fi (N) xi (mm) N (679.60 PieceMPa 136.526 ) P 11800MPa MPax x1089025 1089025 A =π π x x11800 9753.6 mm! mm) m fMPa 1026.7 =V=ixi x(mm (304.8 0.0910 a = = = 136.526 mmmm (269.8 mm) x (304.8 mm x 32 mm) Dead 35.341 16.00 565.46 E(Ash)(269.8 = 11800 MPa a mm) x (304.8 mm x 32 mm) 304.8 mm x 32 mm A - C (Buckling Resistance) f = 1026.7 =N 2 Live 1017.5 π16279.

EI = I = bh" = 832307.2 mm4 f16.00 ! CR f = 1026.7 N = 0.091028 MPa = 0.0910281 MPa P = 15.489 N A = 9753.6 mm dead 304.8 mm x 32 mm f = 1026.7 = 0.091028 MPa = 0.0910281 MPafCR, therefore 2 Fa << this member has sufficient 12 N l16845.

A bu 1052.8 304.8 R1 mm =mmx x3232mmmm 872.4 N E 11800 MPa 304.8 (Ash) = Fa << fC(Ash), therefore this member fC(Ash) has sufficient = 7.6 M this member has PD+R1136.526 = 887.9 N I = F << bh"f , therefore = 832307.2 mm4 suf 4 = MPa 89025 mm thereforethis thismember memberhas hassufficient sufficientbuckling bucklingresistance resistance F F <<<<f f, ,therefore F << 12f , therefore this member has su mm x 32 Fmm) << f , therefore this member has sufficient crushing resistance CR = fCRf=

2

2

4

2

4

2

2

a

a

a

a

a

CR

CR

a

CR

a

C(Ash)

C(Ash) Fa a<< fC(Ash) , therefore this member has sufficient crushing resistance

fCR =

π2 x 11800 MPa x 1089025 mm4

0.091028 MPa = 0.0910281 MPa S= 1 | A-C | CRUSHING RESISTANCE (269.8 mm) x (304.8 mm x 32 mm) ARCH365 365||ANALYSIS ANALYSIS44 ARCH

=

136.526 MPa

2

POS11| POS

1026.7 N = 0.091028 MPa = 0.0910281 MPa a = sufficient buckling fresistance 304.8 mm x 32 mm s sufficient crushing resistance CRUSHING RESISTANCE: [P3][P4] HORIZONTAL - AC Fa << fCR, therefore this member has sufficient buckling resistance Fa << fC(Ash), therefore this member has 99 sufficient crushing resistance

POS 1 | A-C | CRUSHING RESISTA

ANALYSIS IV: BEAMS & COLUMNS

SIS 4 ANALYSIS 4

(N)

ARCH 365 | ANALYSIS 4

P

100 mm

644.6 mm

100 mm 200 mm

644.6 mm

200 mm 100 mm

WLL =5kN/m

WLL =5kN/m

644.6 mm 200 mm

WDL = 60.454 NWDL = 60.454 N

a

WLL =5kN/m

a

b

WDL = 60

a 872.4 N

166.7 N

872.4 N

166

872.4 N

xi (mm)

A - B 9.016 39.016 Piece 1000 1000 Dead 15625 1039.015625 Live

xi

POS 1 |POS A-B1 || MOM A-B

Vixi (mm3) Vixi (mm3) xi (mm) 339.8 339.8 13257.50939 13257.50939 F x Vx 100 100000 100000 100 39.016 339.8 113257.5094 113257.5094 i (N)

i (mm)

i

1000 1039.015625

= !Fixi Fi X =

=

100

=

x) Shear) 679.60 A mm- B (Max Fv(Ash) = 679.60 mm Shear) l 679.60 mm 09.005109.005 mm= mm X 109.005 mm 953742 mm= 570.5953742 mm

V

0

0

V

3 i (mm )

109.005109.005

!Fixi Fi

V 13257.50939 100000 113257.5094

mm

Vmax = 0.134 MPa Vmax = 0.134 MPa

- B (Max A - BShear) (Max Shear) V = 0.13 = 679.60 mm l = 679 A - B (Ma = 109.005109. mm X = l = 0 = mm b = 570.5953742 570.5953 max

R1 =

X = b =

644.6 mm x 10m 644.6 679.6 mm 6

R1 =

mm

R1 =

109.005

Fv(Ash) =

A l X b

mm

R2 =

15 MPa 15 MPa

100 mm 100 x 106 mm 679.6 mm 6 R2 =

R2 =

f = f = 3 x (1005.8 3 x A - B A - B F = 15 MPa = 2 x 304.8 2 fx mm 304x Fi (N) Vixi (mm3) Vixi (mm3) Piece Piece Fi (N)A - B xi (mm) xi (mm) F x Vx Piece17.498 Dead Dead 17.498 152.4 F152.4 2666.767345 2666.76734 b = 570.5953742 mm >> Ff , therefore this >> f , therefor Dead 17.498 152.4 26 .6 mm x 1060.5 N Live 204.8 204800 F 20480 >> f 644.6 mm x 1060.5 = N N = N 872.4 N872.4 N 1000 1000 Live 204.8 = 872.362872.362 = Live 1000 204.8 = = 872.362 N = 872.4 N 679.6R1mm 679.6 mm 644.6 mm x 1060.5 N 1017.498473 207466.7673 1017.498473 207466.767 v

v

v(Ash)

v

i (N)

i (mm)

v(Ash)

i

v v(Ash)

3 i (mm )

v

v(Ash)

679.6 mm

1017.498473

0 mm 100 x 1060.5 N mm x 1060.5 =N N = N 166.7 N = 166.653166.653 = N !F X = 166.7 = i 100 mm x 1060.5 N = = X = 166.653 N ixi = !Fix166.7 N = X = !Fixi 679.6R2mm 679.6 mm

Fi

679.6 mm

x (1005.8 N) 0.134 MPa 3 x (1005.8 N)= = 0.134 MPa f = 3 x (1005.8 N) = 304.8 x 32mmmmx 32 mm 2 x mm 304.8 2 x 304.8 mm x 32 mm v

Fi

v

20

203.899 203.899 =

203

Fi

0.134 MPa

this member has sufficient shear has resistance ,fore therefore this hasthis sufficient shear resistance F >> f , member therefore member sufficient shear resistance v(Ash)

v

SIS 4 ARCH 4 ANALYSIS 365 | ANALYSIS 4

POS 1 |POS A-B1 || SA

SHEAR ANALYSIS : [P3][P4] HORIZONTAL - AB 100

200 mm

4 NALYSIS 4 ARCH 365 | ANALYSIS 4

POS 1 |FREE POS 1 BODY |FREEDIAGRAM|1 BODY DIA POS

WLL =5kN/m

ANALYSIS IV: BEAMS & COLUMNS WDL = 39.016

a

b

POS 1 |FREE BODY DIAGRAM|1:5 200Nmm 519.5

519.5N

200 mm

200 m

Mmax = 353.1 Nm WLL =5kN/m

13257.50939

A - B (Max Moment) l = 679.60 mm a X = 339.8 mm

200 mm

M

339800 353057.5094

0

b =

WLL =5kN/m

39.800

Mmax =

mm

WDL = 39.016

a

WLL =5kN/m WLL =5kN/m WDL = 39.016 W = 39.016 DL

Fb(Ash) = c=

a

a

339.8 mm 519.5N 1060.5 519.5N N x 679.60 mm 2

b I =

=

b

w=

353.058

8.3 MPa b 16 mm

0.128 N/mm

Nm =

519.5 N 353.1

519.5 Nm N

519.5N

Mmax = 353.1 Nm M

max

= 353.1 Nm

= 832307 mm4 (32 mm)3 - B (Max A -Moment) B (Max Moment) 3 xi (mm) = 679.60 mm679.60 Vixi (mm3) l = A x-i (mm) B Vixi (mm ) A mm - B (Max Moment) Fb 6 39.016Piece 339.8 Fi (N) 13257.50939 =x 16 mm 339.8 mm 339.8 339.8 13257.50939 X = " mm fbA= - B xi (mm) Vixi (mm3) lMPa = = 6.787061 6.787 679.

MPa 519.5N 519.5 N 3 fbb = F1000 = 339.8 8.339.016 MPa339800 339800 = 339.8 M c mm b(Ash)Dead #i (mm) Fi M x V Piece 0 b = (N) ixi (mm ) 339.8 13257.50939 X = 339 M 0 339.8 339.8 mm 0 10809025 mm c Live = 16 mm1000 353057.5094 Dead 17.498 152.4 I 2666.767345 539.015625 353057.5094 339.8 339800 b = 339 M 0 Mmax = 353.1 Nm ! w= 0.128 N/mm bh1060.5 Mmax = I 1060.5 N x 679.60 mm679.60 = mm353.058 Live 1000 204.8 Mmax == N x204800 = 3 1039.015625 353057.5094 Fb(Ash) > fb, therefore this member has sufficient bending 12 2 207466.7673 = mm 1017.498473 !Fixi = A 339.800 mm 2 Mmaxresistance = 1060.5 N - B (Max339.800 Moment) 3.058 Nm 353.1 ∆max1MPa = 5wl4 Fi X == = 339.800 i l =!FixNm 679.60 mm Fb(Ash) =mm 8.3 4 ∆max1 X= = 5 !F x i0.198 N/mm x (679.60 mm)x = =0.0362001 mm 384EI I = x = 203.899 mm i = mm (32 mm mm)x3 (32 =83230 304.8 mm)3 X = Fi 339.8 mm c= 16 mm I 304.8 4 384Fix 11800 MPa x 1089025 mm 12 12 I = 304.8 m b = 339.8 mm w= 0.128 N/mm M 0 ∆max2 = Pl3 832307 mm4 ∆total = 0.04215 mm oment) fbA= -mmB + f0.5004 360342 mm Nmm x 16 Nmm mm x =16 " mm 0.70 6.78706 360342 " bA= - B 48EI Mmax = F 1060.5 N x 679.60 mm = 353.058 Nm = 353.1 Nm 3 f 0 mm679.60 = 8.3 MPa = M c b f b(Ash) # mm F = 8.3 MPa = b FPiece xi (mm) fbA=xVi360342 xi (mm ) Piece A - B (Max Moment) b(Ash) i (N) Fi (N) 10809025 10809025 mm mm#i (mm)B 2 16 mm 8 mm 339.8 mm c= 16 mmFb(Ash) = Dead E(Ash)Dead 17.498 152.4 I 266 lMPa = = 8.3 MPa = 11800 MPa 17.498Piece 6.787061 6.787 679.60 MPa c =mm Fi 152.4 (N) 1080 !

I I 8 mm 339.8 w =mm 0.128 N/mm = bh X mm = 339.8 c = 16 mm Live 1000 204.8 w= 0.128 N/mm = Live 1000Dead 204.8 I = = 832307 mm4 304.8 mm x (32 mm)3 Fb(Ash) > fb,Fb(Ash) therefore this1017.498473 member sufficient be > f1017.498473 thishas member has 12 suffi b, therefore 207 b = 339.8 mm w= 0.128 N/mm Live 12 4 x 679.60 mm = 353.058 Nm = 353.1 Nm ∆ = 5wl F > f , therefore max1 1060.5 N x 679.60 mm = 353.058 Nm = 353.1 Nm ∆b max1 = b(Ash) 1017.

4 ∆max1 X= = ∆max1 5= !F x 0.198 N/mm x (679.60 mm) ient bending x i0.198 (679.60 2 = N/mm x384EI 2 Mmaxresistance X = ixi 5 !F xi = A -203. = 1060.5 353.058 Nm = 353.1 Nm B3 fbA= - NB x 679.60 360342 mm Nmm x= 16 mm " 6.787061 MPa = 6.787 MPa 4 384Fix 11800 x ∆1089025 384FMPa x 11800 1089025 = = x mm 5 !F x i max1 MPa 3 2 X f i = M c b # F x V x l = Piece i (N) i (mm) i i (mm ) 4 10809025 mm )x = =0.0362001 mm ∆max2 = 1000 N x (679.60 mm)3 = 0.66581 mm ∆ 4 4 mm832307 =∆max2 Pl3 X=384 832307 (32 mm mm)x3 (32 max2 mm =Dead 304.8 mm)3 17.498 152.4 I 2666.767345 = F 4 4 ∆ 0.04215 mm + 0.5004 mm 48 x 11800 MPa x 1089025 mm total = ∆ = 0.04215 mm 48EI +mm0.5004 total 4!

12 3 12 I = 4 mm = 832307 304.8 I = bh wdead = Livemm x (32 mm) 1000 204.8 204800 ∆total = 12 Fb(Ash) >mm fb, therefore this member has sufficient bending resistance 12 1017.498473 207466.7673 mmm x 16 Nmm mm x =16 " mm 0.70 6.787061 MPa = 6.787 E(Ash) = 360342 = MPa " 6.787061 MPa = MPa6.787 MPa E11800 (Ash) ∆max1 = 5wl4 Mmax 4 = fbmm =# 360342 " 6.787061 MPa 6.787 MPa 9025 10809025 mm# ∆max1 X= =Nmm x 16 5 !F xmmi0.198 N/mm x (679.60 mm) = 0.0362001 mm ∆ 1 max2 = 384EI 203.899 xi = mm # 4 384 x 11800 MPa x 1089025 mm 48 x 10809025 mm Fi I ∆max2 = Pl3 his member sufficient bending resistance erefore thishas member has∆total sufficient bending resistance POS 1 | A-B | MOMENT = 0.04215 mm + 0.5004 mm = 0.70 mm 48EI Fb(Ash) > fb, therefore this member has sufficient bending resistance 4 3 .1985 N/mm x (679.60 = 0.0362001 mm ∆max2 = N x 1000 (679.60 = 3 0.66581 x 0.198 N/mm x mm) (679.60 mm)4 = 0.0362001 mm ∆max2 1000 = N x mm) (679.60 mm) = mm 0. f = 11800 MPa E 4 4 (Ash) 4 4 4 11800 x ∆1089025 mm 48 x 11800 MPa x 1089025 mm 384 MPa x 11800 MPa x 1089025 mm 48 x 11800 MPa x 1089025 mm = 5 x 0.198 N/mm x (679.60 mm) = 0.0362001 mm ∆ = 1000 N x (6 max1 max2 384 x 11800 MPa x 1089025 mm4 48 x 11800 MPa 0.04215 mm + 0.5004 = 0.70 0.04215 mm +mm0.5004 mm = mm 0.70 mm Fb(Ash) > ∆total = 0.04215 mm + 0.5004 mm = 0.70 mm ∆max2 =

1000 N x (679.60 mm)3

4 48 x 11800 MPa x 1089025 mm NALYSIS 4 ARCH 365 | ANALYSIS 4

=

304.8 mm x A 12 l X 360342 Nmm

0.66581 mm

4

MOMENT ANALYSIS : [P3][P4] HORIZONTAL - AB

POS 1 | A-B | 101 MOMENT

POS 1 |POS A-B1 || MOMEN A-B

ANALYSIS IV: BEAMS & COLUMNS

a

a

b

b

a

b

69.9N Wdl(ash) = 69.9N

Wdl(ash) = 69.9N

c

c

l= 304.8mm l= 304.8mm

d

d

moment connections providing lateral moment connections providing stability lateral stability

moment providi stabili

c d l= 304.8mm ength (mm) Width (mm) Thickness (mm) Density (kg/m3) Weight (N) ) Width (mm) Thickness Density Weight (N) 304.80 304.80 (mm) 32.00(kg/m3) 600.00 17.498 .80 304.80 32.00 600.00 17.498 615.60 304.80 32.00 600.00 35.341 Piece Length (mm) (mm) 600.00 Thickness (mm) (kg/m3) Weight (N) .60 304.80 32.00 Width 35.341 Density 304.80 304.80 32.00 600.00 17.498 A B 304.80 304.80 32.00 600.00 17.498 .80 304.80 32.00 600.00 17.498 A C 615.60 304.80 32.00 600.00 35.341 ANALYSIS 4 POS 2 |FREE BODY DIAGRAM|1:5 C - D 304.80 304.80 32.00 600.00BODY DIAGRAM|1:5 17.498 4 POS 2 |FREE

POS 2 |

ARCH 365 | ANALYSIS 4

FREE-BODY DIAGRAM: [P3][P4] VERTICAL 102

Piece A - B A - C C - D

Length (mm) Width (mm) Thick 304.80 304.80 615.60 304.80 304.80 304.80

ARCH 365 | ANALYSIS 4

POS 2 | A-B | SHEAR ARCH 365 | ANALYSIS 4 ARCH 365 | ANALYSIS 4

ARCH 365 | ANALYSIS 4

ANALYSIS IV: BEAMS & COLUMNS

1052.8 N

1052.8 N

kling Resistance) A - CN = 35.341 A - C Piece N Fi (N) 1017.5 Piece F Dead N i (N) = 1052.8 Dead Live Live

xi (mm)fa xi (mm)fa

35.341 35.341 1017.5 fCR 1017.5 fCR 1052.8 1052.8 565.4624787 4 C(Ash) π2 x 11800 MPa x 1089025 fmm 6577 fC(Ash) (679.60 mm)2 x (304.8 mm x 32 mm) 16279.97557

A = 9753.6 mm!

3 V x 11800 MPa = E(Ash)iP=i (mm3 ) ViP xi (mm ) = 16.00 565.4624787 I a= bh" = 832307.2 mm4 16.00 a 565.4624787 A - C (Buckling Resistance) 16.00 π2EI 16279.97557 = 12 16.00 16279.97557 A - C (Buckling π2EI = Pdead = Resistance) 35.341 N 16845.43805 l2A - C 16845.43805 P AR1 = 26.5921017.5 N l2A = N = 7.6 MPa26.224 MPa A - C = F 1361.3 N x R1Piece = = 7.6 MPa

0.96 A - C 16845.43805 3466 A - C (Buckling fa - P C = A Resistance)

A - C f(Buckling a = A - C (Buckling R Pdead = Pdead = π fCRR1 == R1 = PD+R1 = PD+R1 = fC(Ash) = 7

A = Vixi (mm3) E(Ash) = PD+R1 = Fi (N) 1052.8xNi (mm) V x 3 fCR = Piece Dead 16.00 i i (mm ) 425.4746577 fCR =I = PD+R1 = 1387.9 26.592 N Dead 26.592 16.00 425.4746577 Live 1361.3 16.00 21780.96 0.108 MPa 1361.3 16.00 21780.96 ViP xi (mm3) Live !

1387.9 22206.43466 = A 9753.6 mm 3= VixiA(mm=) fa = 4 !

1387.9 22206.43466 2 4 mm f=CR565.4624787 =fCR =9753.6 = 16.00 aE(Ash) x 1089025 π2 x MPa 11800 MPa x mm 1089025 fa mm = 11800 π x 11800 MPa 16.00 E 425.4746577 2 = 11800 MPa (679.60 mm) x (304.8 mm x 32 mm) 2 (Ash) 2 " (679.60 mm) x (304.8 mm x 32 mm) 4 dead

i (N)

9

i (mm)

b 1(

N Piece = Fi 0.107943721 A 1026.7 - C (Buckling Resistance) xi =(mm)fa (N) Pdead = 35.341 N a F xi (mm) i (N) 304.8 mm P xdead 32= mm Piece N 2 Dead 35.341 35.341 R1 1017.5 N π2EI fCR = = Dead 26.592 R1 = 1017.5 N 3 1017.5 resistance 16.00 π EI 16279.97557 .2 mm4 this member fCR = PD+R1 = Live 1052.8 N buckling bh" = 832307.2 mm l2A herefore has sufficient Live 1361.3 16.00 II == 21780.96 4 PD+R1 = 1052.8 N bh = 832307.2 mm 2 l A f 16845.43805 12 Fa << fCR, therefo =has 7.6 MPa 1052.8 therefore thisfmember sufficient crushing resistance C(Ash) ! = 1026.7 N A - fCa = = 0.1422964 = 1387.9 22206.43466 A = 9753.6 mm Pa <<0.107943721 F f , therefo fa =12 1026.7 N = Fa << fCRC(Ash), there fC(Ash) = 7.6 MPa 304.8 mm x 32 mm F xi ,(mm)theref Piece F 11800 MPax 1089025 mm4 aa << fC(Ash) fCR E =(Ash) = = 26.224 MPa π2 x 11800 MPa 304.8 mm x 32 mmi (N) fCR = = 26.224 MPa π2" x 118002 MPa x 1089025 mm4 Dead 26.592 2 (679.60 mm) x mm x 32 mm) πbuckling EI I = bh = (304.8832307.2 mm4 F << f , therefore this member has fCR sufficient = resistanc (679.60 mm)2 x Resistance) (304.8 mm x 32 mm) Live 1361.3 A - C (Buckling

MPa

a

a

CR

F F<< << f f, ,therefore thisthis member has sufficient crushing resista 12 l 2A therefore member has sufficient buckli a CR !

1387.9 f = 1026.7 N = 0.107943721 = 0.108 MPa Pdead = 35.341 N A = 9753.6 mm f = 7.6 MPa F << f , therefore this member has sufficient crus C(Ash) a = C(Ash) f = 1026.7 N = 0.107943721 0.108 MPa 304.8 mm x 32 mm1017.5 N 4 R1 = E = 11800 MPa = 26.224 5 mm 304.8 mm xMPa 32 mm f = 3 x (Ash) (1387.9 N) = 0.427 MPa " PD+R1 = 1052.8 N I mm = x 32 bh = 832307.2 x 32 mm) 2 x 152.4 mm F << f , therefore this member has sufficient buckling resistance F << f , therefore this member has sufficient buckling resistance 12 F << f , therefore this member has sufficient crushing resistance F >> f , therefore this member has sufficient shear resistance F << f , = therefore this MPa member has sufficient crushing resistance 0.107943721 0.108 = = 26.224 MPa π2 x 11800 MPa x 1089025 mm4 OS 2 | A-C | CRUSHINGfCRRESISTANCE (679.60 mm)2 x (304.8 mm x 32 mm) ARCH 365 | ANALYSIS 4 POS 2 ARCH 365 | ANALYSIS 4 POS 2 | ient buckling resistance fa = 1026.7 N = 0.107943721 = 0.108 MPa icient crushing resistance 304.8 mm x 32 mm a

C(Ash)

a

a

v

a

a

a

a

CR

CR C(Ash)

v(Ash)

C(Ash)

v

CRUSHING RESISTANCE: [P3][P4] HORIZONTAL - AC

Fa << fCR, therefore this member has sufficient buckling POS 2 |resistance A-C | CRUSHING RESISTANCE 103sufficient crushing resistance Fa << fC(Ash), therefore this member has

NALYSIS 4 4 ARCH 365 | ANALYSIS 4

A-B POS 2 | POS A-B 2| |MOMENT ANALYSIS IV: BEAMS & COLUMNS

ARCH 365 | ANALYSIS 4

WLL =5kn/m

WDL = 17.498N WDL = 17.498N

a

a

b

WDL

b

a

WDL = 17.4

a

1017.49 N

1017.49 N

1017.49

1017.49 N

A -xiB(mm) Vixi (mm ) x Vix V V F x2666.767345 Vixi (mm3) Piece i (mm) 7.498 17.498 152.4 i (N)152.42666.767345 152.4 2666.767345 A1000 -Dead B 204.8 204.817.498 1000 204800 204800 15 MPa 3 Live Fi (N) 1000 204.8 204800 xi (mm)207466.7673 Vixi (mm ) Piece 1017.498473 98473 207466.7673 1017.498473 207466.7673 17.498 152.4 2666.767345 72.4 N Dead

(N)

WLL =5kn/m

3 i (mm )

i (mm) 15 MPa

!FixiLive = X = .4 N Fi

66.7 N

X =

.7Shear) N

3

= 203.899204.8 1000 203.899 !F x = i i 1017.498473 Fi !Fixi Fi

=

mm

0

0

Therefore: VTherefore: 0

mm 204800 203.899 207466.7673 203.899

A - Shear) B (Max A - B (Max l = l = Fv(Total) V = Fv(Total) =0 10

mm

RA =

RA = 10

fv =

fv = 3 2 x

mm

>> fv, Fv(Ash) >> F fv(Ash) v, therefo

A - B mm (Max Shear) 304.80 304.80 mm Fv(Ash) = Fv(Ash) = 15 MPa 15 MPa l = 304.80 mm Fv(Ash) = 15 MPa 1017.498 N 017.498 N A -Fv(Total) B (Max = Shear) 1017.498 N ce l = 304.80 mm Fv(Ash) = 15 MPa Fv(Total) = N 1017.498 N 1017.498 017.498 NTherefore: 1017.498 N RA = Therefore: 3 x (1027.114 N) = 0.156 MPa 0.156 MPa x (1027.114 N) = 1017.498 N R f = 3 x (1027.114 N) = 0.156 MPa A = v 2 xmm 304.8 304.8 x 35mm mmx 35 mm 2 x 304.8 mm x 35 mm fthis 3 has x (1027.114 0.156 MPa v = therefore member sufficient shear=resistance ore this member has sufficient shearN)resistance 2 x 304.8 this mm x member 35 mm has sufficient shear resistance Fv(Ash) >> fv, therefore F

>> f , therefore this member has sufficient shear resistance

v(Ash) v NALYSIS 4 4 ARCH 365 | ANALYSIS 4

SHEAR ANALYSIS : [P3][P4] VERTICAL - AB ARCH 365 | ANALYSIS 4 104

A-B POS 2 | POS A-B 2| |SHEAR

T ANALYSIS IV: BEAMS & COLUMNS

4 ARCH ANALYSIS 4 365 | ANALYSIS 4

POS 2 |FREE DIAGRAM|1: POS 2BODY |FREE BODY PO DI

POS 2 |FREE BODY DIAGRAM|1:5 200 mm

200 mm WLL =5kn/m

WLL =5kn/m

WDL = 17.498N W = 17.498N DL

a

200 mm

WDL = 17.498

ba

a

b

WLL =5kn/m

WDL = 17.498N

a

1017.49 N

b

A - B 1017.49 N fb = fb MVixci (mm= = MVixci (mm3) MVixci (mm3) xi (mm) Piece Fi (N) 3) xi (mm) I I 8 152.4 2666.767345 Dead 17.498 152.4 I 2666.767345 17.498 152.4 2666.767345 ! !

I !

I bh = I bh =F bh = 0 304.80 204.8 204800 mm = Live 1000 204.8 204800 1000 204.8 204800v(Ash) 12 12 12 3 207466.7673 1017.498473 207466.7673 017.498473 207466.7673 017.498 N= 4 ∆max1 4 ∆max1 = 5wl4 (Max Moment) ∆max1 5wl A= - B5wl 384EI 384EI = mm mm !F384EI 203.899 ixi !Fixi = X = = l 203.899 203.899 =304.80 mm X = 203.899 mm F i Fi 3 3 ∆max2 ∆max2 0.05741 = Pl 017.498 N= ∆Mmax2 Pl w=dead = Pl03 n/mm 48EI 48EI 48EI

A - B (Max A Moment) - B (Max Moment) A - B (Max Momen l = 304.80 mm 304.80 l = mm l = X = 203.899 mm203.899 X = mm X = wdeadM= 0 wdead = 00.05741 M n/mm 0 wdead =n/mm 0.05741

fb xi (mm)

Mmax = 1027.114 N x 304.8 mm A -= B (Max Moment) 11800 E(Ash) oment) = 11800 E(Ash) x (1027.114 N) = 0.156 MPa MPa =MPa 11800 MPa E (Ash) .80 mm 304.80 Fb(Ash) = mm Fb(Ash) = 8.3 MPa l = mm 304.80 8.3 304.8 mm x 35 mm 899 mm203.899 c = mm 16 mm X = mm 203.899 c = 16 Mmax = 207.5Nm I =E 304.8 mm x (32 mm)3 741 n/mm = 11800 MPa (Ash) w = 0.05741 n/mm dead 0.05741 n/mm E(Ash) = 11800 12

=

15 MPa M

207.467

Fb(Ash) = MPa mm c = = E(Ash) = MPa

ore this member has sufficient shear resistance

N1027.114 x 304.8 NmmMxmax304.8 207.467 = 207.5 == 1027.114 NNm x 304.8 mm 207.467Nm mm = 207.467 Nm == Nm207.5 3 fb = Nmm x 16 mm mm = 30.66581 " ∆ 1000 N =xmm(679.60 mm)3 308932 0.66581 max2 = xmm) (679.60 mm) 0.66581 mm f= = M c b 4 9025 4 48 x mm 11800 MPa x 1089025 mm4 10809025 mm# I MPa xmm1089025

Mmax =

Fb(Ash) mm= c= E(Ash)

= Nm

8.3 16 mm4 832307 11800

Nm = 207.5 3.988273 MPa

N x 304.8 Nmm 207 Mmax == 102 M1027.114 1027.114 x 304.8 mm max = 8.3 MPa 16 mm

= 207.5NmM = 207.5Nm Mmax = 2 max 3 I =11800MMPa max x (32 mm) I = = mm I 304.8 = 304.8 mm x (32 mm)3 3 12 12 = 207.5 Nm fb = x 16 mm 33 fb308932 = 308932 f Nmm = c f=bx= "16M mm MPa fM Nmm c # # 10809025 mm I mm 10809025 mm I !

I = Ibh MPa = sufficien bh!

Fb(Ash) > fb, Ftherefore this member has F12 fb, theref b(Ash) > member has b(Ash) > fb, therefore this 12 ∆ = Nm ∆ wl x = wl mm)4 ∆3.988 (304.8 max1 = ∆max1 = x (3 = MPa∆max1 =0.08896 N/mm 0.08896 N/mm 8EI 8EI 4 8 x 11800 8MPa x 1089025 x 11800 MPa xmm 10

4 3 3 4 832307 == mm)3 304.8 mm x304.8 (32 mm) Imm mmmmx 832307 (32 mm) = bh! 832307 mm4 = mm xI (32 ∆total = Fb(Ash) > fb, therefore this member has sufficient bending resistance 12 12 12 12

∆max1 = wl4 ∆max1 =Nmm 0.08896 N/mm x (304.8 MPa mm)4= = 0.00630651 mm 3.988273 MPa = 3.988 MPa 308932 x 16 mm " 3.988273 3.988 MPa " 3.988273 MPa = 3.988 MPa 8EI 4 8 x 11800 MPa x 1089025 mm 10809025 mm# ∆max2 = Pl3 ∆total this = 0.000765 mm +bending 0.7223resistance mm = 0.30 mm his member hasmember bending resistance Fb(Ash) > sufficient fb, therefore member has sufficient erefore this has sufficient bending resistance 3EI

Nmm308932 x 16 mm Nmm fxb ="16 mm # 09025 mm 10809025 mm#

08896 N/mm x (304.8 mm)4 =N/mm 0.00630651 mmmm)4 ∆N/mm x (304.8 max1 = x (304.80.08896 0.08896 mm)4 = 0.00630651 mm 4 x 11800 8MPa x 1089025 4 8 x mm 11800 MPa x 1089025 mm4 x 11800 MPa xmm1089025 0.000765 mm + ∆0.7223 mm mm mm mm +0.30 total =mm + 0.7223 0.000765 0.000765 mm = =0.7223 0.30 mm ∆max2 = 1000 N x (304.8 mm)3 = 3 x 11800 MPa x 1089025 mm4

1017.49 N

1017.49 N

b

max1

∆ ∆total =

max2

b

4

max1

4

= ∆ Plmm =+ 0.7223 Pl 0.000765 ∆total = mm mm + 3EI0.000765 3EI 3

max2

3

∆max2 = 3

3 ∆max2 mm = 1000 =∆max2 0.29154 = 0.00630651 = 3 1000 N x (304 ∆max2 N= x (304.8 1000 N mm) x (304.8 mm) =mm0.29154 mm 4 3 x 11800 3MPa x 1089025 4 3 x mm 11800 MPa x x 11800 MPa xmm1089025

=

0.30 mm

0.29154 mm

R 4 ARCH ANALYSIS 4 365 | ANALYSIS 4

POS 2 | POS A-B 2| |MOMEN A-B

MOMENT ANALYSIS : [P3][P4] VERTICAL - AB 105 POS 2 | A-B | MOMENT

ANALYSIS IV: BEAMS & COLUMNS

l= 152.4mm l= 152.4mm a

b

e

e

304.8mm

l= 152.4mm b

a

304.8mm

200 mm

152.4 mm l= 152.4 152.4mm mm

b

e

WLL =5kN/m

a

l= 152.4mm

WDL = 17.498N W =e 17.498N DL

a

304.8

200 mm

a

b

e

b

304.8mm

WLL =5kN/m WDL = 17.498N

b 200 mm a 152.4 mm

a

b

WLL =5kN/m

WDL = 17.498N

PLL =1000N

a

PDL =17.498N

b

PLL =1000N P =17.498N DL

PDL =17.498N

Wdl(ash) = 88.18N

l= 152.4mm Wdl(ash) = 88.18N

RA =343.88N

DL

a

88.18N

PLL =1000N

RE =1361.32N P =17.498N

e

R =343.88N

RE = PDL + RA + PLLA

RA =343.88N

b

RE =13

RE =1361.32N RE = PDL + RA + PLL

∑MA = 0

RA =343.88N RE =1361.32N ∑MA = 0 RE (152.4mm) = 17.498N(152.4mm)+1000N(204.8mm)

RE = P=DL17.498N(152.4mm)+1000N(204.8mm) + RA + PLL RE (152.4mm)

RE (152.4mm) = 17.498N(152.4mm

RE = 1361.32 N

RE (152.4mm) = 17.498N(152.4mm

∑MA = 0

RE = PDL + RA + PLL

RE = 1361.32 N

RE (152.4mm) ∑M= =17.498N(152.4mm)+1000N(204.8mm) 0 A = 17.498N(152.4mm)+1000N(204.8mm) RE (152.4mm) RE (152.4mm) = 17.498N(152.4mm)+1000N(204.8mm) REN(152.4mm) = 17.498N(152.4mm)+1000N(204.8mm) RE = 1361.32

ns l

moment connections providing lateral f stability c nt connections l= 304.8mm iding lateral connections ility ing lateral ity

RE = 1361.32 N

Wdl(ash) = 88.18N

c

d

momentf connections providing lateral stability l= 304.8mm

d

f c

l= 304.8mm

f Notch (m3)

d

Width (mm) Thickness (mm) Density (kg/m3) Weight (N) f Piece Length (mm) Thickness (mm) 600.00 Notch (m3) 17.498 Density (kg/m3) Weight (N) 304.80 32.00 Width (mm) n/a c d A B 304.80 304.80 32.00 n/a 600.00 17.498 304.80 32.00 0.001486 600.00 26.592 l= 304.8mm d n/a Piece 32.00 A - C 615.60 304.80 0.001486 600.00 26.592 Length (mm) Width (mm) Thickness (mm) Notch (m3) Density (kg/m3) 304.80 32.00 600.00 17.498 304.8mm C - l= D 304.80 304.80 n/a304.80 600.00 17.498 304.80 32.00 n/a 600.

304.80 32.00 0.001486 A - B 32.00600.00 26.592 E - F 615.60 304.80 600.00 26.592 0.001486 A - C 32.00 615.60 0.001486304.80 32.00 600. gth (mm) Width (mm) Thickness (mm) Notch (m3) Density (kg/m3) Weight (N) C - D 304.80 304.80 32.00 BODY DIAGRAM|1:5 n/a 600.

4 POS 3 |FREE 304.80 32.00 ARCH 365 304.80 | ANALYSIS 4 BO E - F n/a 615.60 600.00 304.80 17.498 32.00 0.001486 POS 3 |FREE600.

615.60 600.00 26.592 Thickness (mm) 304.80 Notch (m3) 32.00 Density0.001486 (kg/m3) Weight (N) 304.80 304.80 32.00 n/a| ANALYSIS 600.00 17.498 ARCH 365 4 17.498 0 32.00 n/a 600.00 moment connections 615.60 304.80 32.00 0.001486 600.00 26.592

0 32.00 0.001486 oment connections 0 n/a | ANALYSIS 4 32.00 roviding lateral tabilityFREE-BODY 0 32.00 0.001486 DIAGRAM: [P5][P6] VERTICAL

600.00 lateral 26.592 providing 600.00 17.498 stability 600.00 26.592 106

Piece A - B A - C

POS f 3 |FREE BODY DIAGRAM|1:5 c

l= 304.8mm

d

POS 3 |FREE BODY DIAGRAM|1:5

Length (mm) Width (mm) Thickness (mm) Notch (m3) Density (kg/m 304.80 304.80 32.00 n/a 6 615.60 304.80 32.00 0.001486 6

ANALYSIS IV: BEAMS & COLUMNS

RE =1361.32N

RE =1361.32N

A - C (Buckling Resistance) Vixi (mm ) 16.00 A - C 425.4746577 fa 16.00 Piece F21780.96 xiP(mm) = i (N) 3 22206.43466 26.592 a VDead ixi (mm )

Pdead = R1 =

3

16.00 Live fCR 1361.3 = 9753.6 mm! 425.4746577 fa 1387.9 11800 MPa 16.00 21780.96 = fC(Ash) =4 22206.43466 bh" = 832307.2 mm A = 12 fCRE ==

π2EI 2 Pl A 7.6 a

PD+R1 = 1387.9 N A - C (Buckling Resistance)

Vixi (mm3) 16.00

425.4746577

16.00

fa 21780.96 = 22206.43466

P a

f

π2EI

MPa

26.592 N 1361.3 N

=

Pdead = R1 = fCR P =D+R1 =

CR 9753.6 mm!

2 l2A π EI 11800 MPa A - C (Buckling (Ash) Resistance) 2 f4 = 7.6 MPa l "A I 26.592 = bh = 832307.2 mmC(Ash) Pdead = N A = 9753.6 mm!

26.224 MPa fC(Ash) = 7.6 MPa 12 R1 = N E(Ash) = 11800 MPa A 1361.3 = 9753.6 mm!

PD+R1 = E(Ash) 1387.9 N11800 I = bh" = = MPa = 26.224 MPa MPa x 1089025 mm4 12 I = bh" = 832307.2 mm4 0.108 (304.8MPa mm x 32 mm) 12 fCR = = 26.224 MPa π2 x 11800 MPa x 1089025 mm4 = 0.1422964 = 0.142 MPa 2 (679.60 mm) x MPa (304.8 mm x 32 mm) = 26.224 Pa x 1089025 mm4 mm ce (304.8 mm x 32 mm) ance fa = 1026.7 N = 0.1422964 = 0.142 MPa r has sufficient buckling 304.8 resistance mm x 32 mm = 0.1422964 = 0.142 MPa ber has sufficient crushing resistance mm Fa << fCR, therefore this member has sufficient buckling resistance Fa << fC(Ash) , therefore this member has sufficient crushing resistance has sufficient buckling resistance N) = 0.427 MPa er has sufficient crushing resistance 32 mm

fv = 3 x (1387.9 N) = 0.427 MPa ber has sufficient shear 2resistance ) = 0.427 MPax 152.4 mm x 32 mm 2 mm Fv(Ash) >> fv, therefore this member has sufficient shear resistance

er has sufficient shear resistance

ARCH 365 | ANALYSIS 4

fa

=

ffCRa ==

P a

26.592 N 1361.3 N π2 x 11800 MPa 1387.9 N (679.60 mm)2 x (3

π2 1026.7 x 11800N MPa x

π2EI 304.8 mmmm) x 232 (679.60 x mm (30 l2A fa = P fC(Ash) = 4 7.6 MPa 832307.2 Fa << mm fCR,a therefore this member ha fCR

=

fa =

1026.7 N

π2EI fCR Fa =<< fC(Ash) , therefore this member fV = 15 MPa 304.8 mm x 32 mm l2A fC(Ash) = 7.6 MPa

Fa << fCR, therefore this member ha fv = 3 x (1387.9 N) Fa << f C(Ash), therefore this member f = 15 MPa2 x 152.4 mm x 32 m V

Fv(Ash) f>> fv, therefore this member 3 x (1387.9 N) v = 2 x 152.4 mm x 32 m Fv(Ash) >> fv, therefore this member

POS 3 | A-C | CRUSHING RESISTANCE

POS 3 POS 3 | A-C | CRUSHING RESISTANCE

CRUSHING RESISTANCE: [P5][P6] VERTICAL - EF 107

ANALYSIS V: JOINTS

108

ANALYSIS V: JOINTS

ANALYSIS V: JOINTS The final analysis, and most important for the Parker Brothers’ chair, examines the joints. All 6 pieces share the same finger joint, but in the case of [P3] and [P4], when used as a stool, the shorter member is purely cantilevered with no additional support. The finger joints on these pieces are subject to the greatest bending moment, and will be examined to see if the wood can withstand these loads. The other joint examined is the dado joint connecting the internal members of [P2],[P5] and [P6]. For this scenario, a person is assumed to have “flipped” these pieces and is sitting in the middle of the member. Again, the joint will be examined to see if the wood can withstand these loads.

109

ANALYSIS V: JOINTS

l= 8

P1 = P2 = self weight + weight of person 2 = (26.6N) + 1000N 2 = 513.3N 5 kN/m over 200 mm = 1.6244 kN/m over 615.6 mm therefore Wt = wp + wc = 1.6244 kN/m + 0.043197 kN/m = 1.66760 kN/m Mmax = 1.6676 kN/m x (0.6156m)2 12 = 52.663 Nm =

Wt (1/3)D = 26.332 Nm / (0.016mm/3) = 4.937 kN

F1 = F/2 = 2.469 kN

W

wp = P / 2L = 513.3 N / 2(8mm) = 32.08125 kN/m W1net = W1 + Wp = 649.331 kN/m W2net = W2 - Wp = 585.169 kN/m

F1 = 0.5 x L x w1 w1 = 2 x F1 / L = 2 x 2.469kN / 8 mm = 617.25 kN/m w1 = w2 = 617.25 kN/m

l= 16mm

F

I = BH3 12 = 304.8mm x (16mm)3 12 = 0.104x106mm4

Fb = MC I = 52663 Nmm x 8 mm 0.104x106mm4 = 4.0495 MPa

Fb = 4.05 MPa < 8.3 MPa (allowable for ash) therefore okay in bending Fv = 3V 2A = 3(513.3N) 2(16mm x 304.8mm) = 0.158MPa (Fv allowable = 15.0MPa) therefore okay in shear ARCH 365 | ANALYSIS 5 JOINT ANALYSIS: DADO JOINT [P5][P6] 110

11

ANALYSIS V: JOINTS

l= 8 mm

5.6 mm .043197 kN/m

1.6676 kN/m

W2 = 617.25 kN/m

+ Wp = 649.331 kN/m - Wp = 585.169 kN/m

l= 16mm

2L .3 N / 2(8mm) 08125 kN/m

Wp W1 = 617.25 kN/m

8mm x (16mm)3 12 4x106mm4

P1

ash)

11.66mm 5.83mm

JOINT 2 | DADO JOINT JOINT ANALYSIS: DADO JOINT [P5][P6] 111

ANALYSIS V: JOINTS

ARCH 365 | ANALYSIS 5

JOINT 1 | FINGER JOINT

Finger Joint (Piece 3/4) All 6 pieces share this type of finger joint. However, in the case of pieces 3 and 4, the joint when set up as a bar stool is purely cantilevered with no additional support within the member. Therefore the finger joints for these pieces are subject to the greatest bending moments.

Mmax VR

= =

207.467 Nm 1017.498 N

No. of fingers = Lfinger =

16 19.05

IFinger mm

=

bh3 12

=

416154 mm4

Assume glue has greater shear and bending resistance than the wood it binds, therefore if wood resistance is sufficient, glue resistance will exceed requirements.

V = 1017.498 N = w = VFinger

L/2 x w 152.4 mm x w 6.676 N/mm

= wLfinger = 6.740 N/mm x 19.05 mm = 127.1873092 N

fv

=

3V 2A

=

Fv(Ash)

=

15

MPa

3 (128.3892N) 2 (19.05 mm x 35 mm)

0.31296 MPa = = ########

313

kPa

Fv(Ash) >> fv, therefore joint has sufficient shear resistance Mfinger

= =

Mmax No. of fingers 12.9667 Nm

fb

=

Fb(Ash) =

Mc I

=

19308.3 Nmm x 17.5 mm 544513 mm4

0.49853 MPa = ########

8.3 MPa

Fb(Ash) >> fb, therefore joint has sufficient bending resistance

ARCH 365 | ANALYSIS 5

JOINT 1 | FINGER JOINT

JOINT ANALYSIS: FINGER JOINT 112

ANALYSIS V: JOINTS

fig 2. the fingers joints each carry a distributed load

of 6.7396 N/mm as the chair handles self weight and human loads.

fig 1. 16 finger joints serve as the primary joint system for the chair. load is equally distributed through these fingers.

ARCH 365 | ANALYSIS 5

JOINT 1 | FINGER JOINT

JOINT ANALYSIS: FINGER JOINT 113

APPENDIX A : PRECEDENTS

114

APPENDIX A : PRECEDENTS

APPENDIX A: PRECEDENTS

115

APPENDIX A : PRECEDENTS

WOODEN PUZZLE 116

APPENDIX A : PRECEDENTS

WOODEN PUZZLE 117

APPENDIX B : MATERIAL & COST

118

APPENDIX B : MATERIAL & COST

APPENDIX B: MATERIAL & COST

119

APPENDIX B : MATERIAL & COST

Piece 1 Length (mm) Width (mm) Height (mm) Thickness (mm) Volume (m3) Void Length Width Height Volume

(mm) (mm) (mm) (m3)

Net Volume

679.60 304.80 304.80 32.00 0.06

Piece 2 Length (mm) Width (mm) Height (mm) Thickness (mm) Volume (m3)

615.60 304.80 240.80 0.05

Void Length Width Height Volume

0.02

Black Walnut Density (kg/m3) Mass (kg)

Net Volume White Ash Density (kg/m3)

550.00

9.87

Net Mass (kg) =

52.96

(mm) (mm) (mm) (m3)

Mass (kg) or

12.50 13.75 $10.95 $170.14

Board Feet of White Ash +10% Waste Price per Board Foot Cost + 13% HST

= = = =

72.73 80.00 $4.12 $372.16

Miscellaneous =

$6.78

Total Cost =

$549.08

(mm (mm (mm (m3

0.02

Net Volume

600.00

White Ash Density (k

116.51 lbs = = = =

120

615.60 304.80 240.80 0.05

Void Length Width Height Volume

10.77

Board Feet of Black Walnut +10% Waste Price per Board Foot Cost + 13% HST

MATERIAL

679.60 304.80 304.80 32.00 0.06

Piece 3/4 Length (mm Width (mm) Height (mm Thickness Volume (m3

Mass (kg)

Width (mm) Height (mm) Thickness (mm) Volume (m3) Void Length Width Height Volume

304.80 304.80 32.00 0.06 & COST APPENDIX B : MATERIAL

(mm) (mm) (mm) (m3)

615.60 304.80 240.80 0.05

Net Volume

0.02

Black Walnut Density (kg/m3) Mass (kg)

Width Height Thickn Volume

Void Length Width Height Volume

615.60 304.80 240.80 0.05

Void Length Width Height Volume

0.02

Net Vo

600.00

White Densit

10.77

Mass (

(mm) (mm) (mm) (m3)

White Ash Density (kg/m3)

550.00

52.96

304.80 304.80 32.00 0.06

Net Volume

9.87

Net Mass (kg) =

Width (mm) Height (mm) Thickness (mm) Volume (m3)

Mass (kg) or

116.51 lbs

Board Feet of Black Walnut +10% Waste Price per Board Foot Cost + 13% HST

= = = =

12.50 13.75 $10.95 $170.14

Board Feet of White Ash +10% Waste Price per Board Foot Cost + 13% HST

= = = =

72.73 80.00 $4.12 $372.16

Miscellaneous =

$6.78

Total Cost =

ARCH 365 | ANALYSIS 1

COST 121

$549.08

122

123

124