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Structures Project: arbutus corridor metro stop

Date post: 10-Mar-2016
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The Arbutus Corridor in Vancouver Canada is an abandoned railway that is being transformed into a metro line.
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Page 1: Structures Project: arbutus corridor metro stop
Page 2: Structures Project: arbutus corridor metro stop

Process

The Arbutus Corridor, like a snake, slithers through the city of Vancouver. There are many parts along the corridor which are straight, but also parts where there are sharp curves. When approaching the design of the metro station I knew I wanted to make a design that was modular in both a straight formation as well as a curved formation.

The form of the shelter was inspired by the scales of a snake. When the axis they are placed on bends the shelters are able to bend with it.

The other theme of the shelter is pushing structure to the limit. The goal was to see how far and thin a steel cantilever could get under extreme snow loads.

Page 3: Structures Project: arbutus corridor metro stop
Page 4: Structures Project: arbutus corridor metro stop

3.5’3’2.75’3.75’ 7.5’

12’

Plan 1/2”=1’

Page 5: Structures Project: arbutus corridor metro stop

12’

12’

Elevation1/2”=1’

Page 6: Structures Project: arbutus corridor metro stop

20’

12’

Elevation 1/4”=1’

Page 7: Structures Project: arbutus corridor metro stop

Section1/4”=1’

Page 8: Structures Project: arbutus corridor metro stop
Page 9: Structures Project: arbutus corridor metro stop
Page 10: Structures Project: arbutus corridor metro stop

“Fatty” “Skinny”

The initial iteration resulted in a very thick, very large shelter. The results from the initial design were then imputed into the design spreadsheet. The output from the spreadsheet provided optimized member sections.

The problem with the new optimized shelter was that the max deflection was now being met in multiframe. This may be because of the geometry of the design.

HSS 20x8x5/8HSS18x6x5/8HSS 12x4x5/8HSS 10x4x5/8HSS 8x6x5/8

HSS 10x8x1/4HSS 8x6x1/4HSS 6x3x1/4HSS 5x3x1/4

Utilization30%14%11%12%13%

Utilization96%91%76%93%

Framing Process

Page 11: Structures Project: arbutus corridor metro stop

Final Combined Frame

HSS 20x8x5/8HSS 18x6x5/8HSS 10x6x5/8HSS 6x5x1/4HSS 5x3x1/4W 5x16

The utilized “skinny” frame was not holding to the de�ection it was supposed to support so the new design strategy was to combine aspects of both “Skinny” and “Fatty”. The result was a sleeker, more e�cient structure that barley met the de�ection requirements of multiframe. As far as the new utilization of the members, you are just going to have to read the rest of the booklet.

Page 12: Structures Project: arbutus corridor metro stop

Multiframe

Snow Load = (.75)25PSF

Dead Load = 15 PSF

+Self Weight

Wind Load = (.75)240 PLF

Max Actual = 1.30”Allowable = 1.33”

DeflectionThe entire structure can be treated as one cantilever therefore:

20’x12”180Allowable = = 1.33”

After many iterations mulitframe displayed a deflection that was just barely under the limit. This is pushing the structure to the limit.

LoadsBecause there is no traditional hierarchy in the structure the lateral load was applied over the entire length of the rib. The snow and dead load were applied directly between the two rib spans.

FramingHSS 20x8x5/8HSS 18x6x5/8HSS 10x6x5/8HSS 6x5x1/4HSS 5x3x1/4W 5x16

Page 13: Structures Project: arbutus corridor metro stop

Strong Axis Moment DiagramDue to the structure being a gigantic cantilever there is massive moment built up at the base of the structural ribs. The concept behind this structure was to push steel to the limits, and this massive moment is the main adversary.

Weak Axis Moment DiagramThe weak axis will mostly be resisting the lateral wind load. Therefore the moment will be much less than the strong axis moment.

MaxM=38k-ft

MaxM=6k-ft

MaxC=4.12K

MaxT=1.46K

Axial Loads DiagramThe combination of lateral winds and heavy loads creates very large outputs for the axial loads. When the wind is applied to the front rib the combined loads create a max axial load at the back for the back rib.

Page 14: Structures Project: arbutus corridor metro stop
Page 15: Structures Project: arbutus corridor metro stop
Page 16: Structures Project: arbutus corridor metro stop
Page 17: Structures Project: arbutus corridor metro stop
Page 18: Structures Project: arbutus corridor metro stop

Max BeamW 5x16

0.027,-0.018,0

0.027,-0.018,-0

x

y

z Beam Deflection

Page 19: Structures Project: arbutus corridor metro stop

Max Strong Axis Moment1.104 K-ft

Max Weak Axis Moment0.364 K-ft

Max Axial Force0.566 K

Page 20: Structures Project: arbutus corridor metro stop

DEP

ARTM

ENT

OF

ARC

HIT

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Uni

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462/

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igne

r:G

TF:

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an C

urle

yR

yan

Cha

mpa

gne

Mat

eria

l Pro

pert

ies:

Sect

ion

Prop

ertie

s:S

teel

Typ

e:A3

6S

ectio

n:W

5X16

F y:

36ks

iA

rea:

3.83

in2

F u:

58ks

iE

:29

000

ksi

Axi

s X-

X (S

trong

Axi

s)A

xis

Y-Y

(Wea

k A

xis)

I x:11

.3in

4I y:

3.86

in4

Sx:

5.46

in3

Sy:

1.9

in3

r x:1.

72in

r y:1

in

Mem

ber D

ata:

Mem

ber I

D:

Bea

m 1

Ax

ial P

rope

rtie

s (C

olum

n B

uckl

ing)

:U

nbra

ced

Leng

th -

X-A

xis:

10.3

42ft

Unb

race

d Le

ngth

- Y

-Axi

s:10

.342

ftK

-Con

ditio

n:a

K-C

ondi

tion:

aK

-Val

ue:

0.65

K-V

alue

:0.

65

Mem

ber L

oads

:A

xial

Com

pres

sion

P:

0.66

6ki

psM

omen

t - S

trong

Axi

s:M

x M

AX:

0.51

9ki

p-ft

Mom

ent -

Wea

k A

xis:

My

MA

X:0.

364

kip-

ft

Axia

l - T

ensi

on C

heck

[AIS

C S

pec

D1]

:U

tiliz

atio

n:f t:

N/A

ksi

F t

:22

ksi

N

/A

Axia

l - C

ompr

essi

on C

heck

[AIS

C S

pec

E2]:

Stro

ng A

xis

- X:

Wea

k A

xis

- X:

KL/

r x:46

.9

KL/

r x:80

.7<-

- Gov

erns

Cc:

126.

1

Gov

erni

ng E

ffect

ive

Sle

nder

ness

Rat

io:

KL/

r =80

.7<

Cc =

126.

1Th

eref

ore,

use

EQ

N E

2-1

[AIS

C]

Util

izat

ion:

f c:0.

17ks

i<

F c:

15.3

ksi

OK

1.1%

Flex

ure

Che

ck -

Stro

ng A

xis

[AIS

C S

pec.

F1]

:F b

x = 0

.6F y

Util

izat

ion:

f bx:

1.14

ksi

<F b

x:22

ksi

OK

5.3%

Flex

ure

Che

ck -

Wea

k Ax

is [A

ISC

Spe

c. F

2]:

F by =

0.7

5Fy

Util

izat

ion:

f by:

2.30

ksi

<F b

y:27

ksi

OK

8.5%

Cc

�2 �

2E

F y

W S

hape

sS

truct

ural

Des

ign

- Ste

el D

esig

n S

prea

dshe

etC

opyr

ight

© 2

011

by M

ark

Don

ofrio

1 of

2

Page 21: Structures Project: arbutus corridor metro stop

DEP

ARTM

ENT

OF

ARC

HIT

ECTU

RE

S cho

ol o

f Arc

hite

ctur

e an

d Al

lied

Arts

Uni

vers

ity o

f Ore

gon

Arch

itect

ure

462/

562

Don

ofrio

/Duf

fW

inte

r

Des

igne

r:G

TF:

Dyl

an C

urle

yR

yan

Cha

mpa

gne

Mem

ber I

D:

Bea

m 1

Com

bine

d St

ress

Che

ck:

Axia

l Com

pres

sion

and

Ben

ding

[AIS

C S

pec

H1]

:

F' ex:

67.9

ksi

F' ey:

22.9

ksi

Cm

x:1

Cm

y:1

AISC

EQ

N H

1-1

AISC

EQ

N H

1-2

fa/F

a:0.

01<

0.15

AISC

EQ

N H

1-3

0.01

+0.

05+

0.09

=0.

15<

1.0

OK

Sect

ion

is s

atis

fact

ory

Axia

l Ten

sion

and

Ben

ding

[AIS

C S

pec

H2]

:

AISC

EQ

N H

2-1

f a F a�

Cmxf b

x

1�

f a F' ex

� � � � � � F

bx

�C

myf b

y

1�

f a F' ey

� � � � � � � � F

by

�1.0

f a0.60

F y�

f bx

F bx

�f b

y

F by

�1.0

f a F a�

f bx

F bx

�f b

y

F by

�1.0

f a F t�

f bx

F bx

�f b

y

F by

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W S

hape

sS

truct

ural

Des

ign

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el D

esig

n S

prea

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etC

opyr

ight

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011

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ark

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ofrio

2 of

2

Page 22: Structures Project: arbutus corridor metro stop

Rib Piece 1HSS 5x3x1/4

0.065,-0.399,-0.162

0.141,-1.132,-0.072

x

y

z

Max Deflection

Page 23: Structures Project: arbutus corridor metro stop

Max Strong Axis Moment1.485 K-ft

Max Weak Axis Moment0.671 K-ft

Max Axial Force1.04 K 1.04

0.79

0

x

y

z

Page 24: Structures Project: arbutus corridor metro stop

DEP

ARTM

ENT

OF

ARC

HIT

ECTU

RE

Scho

ol o

f Arc

hite

ctur

e an

d Al

lied

Arts

Uni

vers

ity o

f Ore

gon

Arch

itect

ure

462/

562

Don

ofrio

/Duf

fW

inte

r

Des

igne

r:G

TF:

Dyl

an C

urle

yR

yan

Cha

mpa

gne

Mat

eria

l Pro

pert

ies:

Sect

ion

Prop

ertie

s:S

teel

Typ

e:A5

00 -

B (R

ect)

Sec

tion:

HSS

5X3X

1/4

F y:

46ks

iA

rea:

3.37

in2

F u:

58ks

iE

:29

000

ksi

Axi

s X-

X (S

trong

Axi

s)A

xis

Y-Y

(Wea

k A

xis)

I x:10

.7in

4I y:

4.81

in4

Sx:

4.29

in3

Sy:

3.21

in3

r x:1.

78in

r y:1.

19in

Mem

ber D

ata:

Mem

ber I

D:

Rib

Pie

ce 1

Axia

l Pro

pert

ies

(Col

umn

Buc

klin

g):

Unb

race

d Le

ngth

- X-

Axi

s:9.

12ft

Unb

race

d Le

ngth

- Y

-Axi

s:9.

12ft

K-C

ondi

tion:

eK

-Con

ditio

n:e

K-V

alue

:2.

1K

-Val

ue:

2.1

Mem

ber L

oads

:A

xial

Tens

ion

P:

1.04

kips

Mom

ent -

Stro

ng A

xis:

Mx

MA

X:1.

485

kip-

ftM

omen

t - W

eak

Axi

s:M

y M

AX:

0.67

1ki

p-ft

Axia

l - T

ensi

on C

heck

[AIS

C S

pec

D1]

:U

tiliz

atio

n:f t:

0.31

ksi

<F t

:28

ksi

OK

1.1%

Axia

l - C

ompr

essi

on C

heck

[AIS

C S

pec

E2]:

Stro

ng A

xis

- X:

Wea

k A

xis

- X:

KL/

r x:12

9.1

K

L/r x:

193.

1<-

- Gov

erns

Cc:

111.

6

Gov

erni

ng E

ffect

ive

Sle

nder

ness

Rat

io:

KL/

r =19

3.1

C

c =

111.

6Th

eref

ore,

use

EQ

N E

2-1

[AIS

C]

Util

izat

ion:

f c:N

/Aks

i

F c:

-13.

8ks

i

N/A

Flex

ure

Che

ck -

Stro

ng A

xis

[AIS

C S

pec.

F1]

:F b

x = 0

.6F y

Util

izat

ion:

f bx:

4.15

ksi

<F b

x:28

ksi

OK

15.1

%

Flex

ure

Che

ck -

Wea

k Ax

is [A

ISC

Spe

c. F

2]:

F by =

0.7

5Fy

Util

izat

ion:

f by:

2.51

ksi

<F b

y:35

ksi

OK

7.3%

Cc

22E

F y

HSS

Rec

tang

ular

Stru

ctur

al D

esig

n - S

teel

Des

ign

Spr

eads

heet

Cop

yrig

ht ©

201

1 by

Mar

k D

onof

rio1

of 2

Page 25: Structures Project: arbutus corridor metro stop

DEP

ARTM

ENT

OF

ARC

HIT

ECTU

RE

S cho

ol o

f Arc

hite

ctur

e an

d Al

lied

Arts

Uni

vers

ity o

f Ore

gon

Arch

itect

ure

462/

562

Don

ofrio

/Duf

fW

inte

r

Des

igne

r:G

TF:

Dyl

an C

urle

yR

yan

Cha

mpa

gne

Mem

ber I

D:

Rib

Pie

ce 1

Com

bine

d St

ress

Che

ck:

Axia

l Com

pres

sion

and

Ben

ding

[AIS

C S

pec

H1]

:

F' ex:

9.0

ksi

F' ey:

4.0

ksi

Cm

x:1

Cm

y:1

AISC

EQ

N H

1-1

AISC

EQ

N H

1-2

AISC

EQ

N H

1-3

Axia

l Ten

sion

and

Ben

ding

[AIS

C S

pec

H2]

:

AISC

EQ

N H

2-1

0.01

+0.

15+

0.07

=0.

23<

1.0

OK

Sect

ion

is s

atis

fact

ory

f a F a�

Cmxf b

x

1�

f a F' ex

� � � � � � F

bx

�C

myf b

y

1�

f a F' ey

� � � � � � � � F

by

�1.0

f a0.60

F y�

f bx

F bx

�f b

y

F by

�1.0

f a F a�

f bx

F bx

�f b

y

F by

�1.0

f a F t�

f bx

F bx

�f b

y

F by

�1.0

HSS

Rec

tang

ular

Stru

ctur

al D

esig

n - S

teel

Des

ign

Spr

eads

heet

Cop

yrig

ht ©

201

1 by

Mar

k D

onof

rio2

of 2

Page 26: Structures Project: arbutus corridor metro stop

Rib Piece 2HSS 10x6x5/8

Page 27: Structures Project: arbutus corridor metro stop

Max Strong Axis Moment12.762 K-ft

Max Weak Axis Moment1.624K-ft

Max Axial Force1.652 K

Page 28: Structures Project: arbutus corridor metro stop

DEP

ARTM

ENT

OF

ARC

HIT

ECTU

RE

Scho

ol o

f Arc

hite

ctur

e an

d Al

lied

Arts

Uni

vers

ity o

f Ore

gon

Arch

itect

ure

462/

562

Don

ofrio

/Duf

fW

inte

r

Des

igne

r:G

TF:

Dyl

an C

urle

yR

yan

Cha

mpa

gne

Mat

eria

l Pro

pert

ies:

Sect

ion

Prop

ertie

s:S

teel

Typ

e:A5

00 -

B (R

ect)

Sec

tion:

HSS

10X6

X5/8

F y:

46ks

iA

rea:

16.4

in2

F u:

58ks

iE

:29

000

ksi

Axi

s X-

X (S

trong

Axi

s)A

xis

Y-Y

(Wea

k A

xis)

I x:20

1in

4I y:

89.4

in4

Sx:

40.2

in3

Sy:

29.8

in3

r x:3.

5in

r y:2.

34in

Mem

ber D

ata:

Mem

ber I

D:

Rib

Pie

ce 2

Axia

l Pro

pert

ies

(Col

umn

Buc

klin

g):

Unb

race

d Le

ngth

- X-

Axi

s:4.

6ft

Unb

race

d Le

ngth

- Y

-Axi

s:2.

3ft

K-C

ondi

tion:

eK

-Con

ditio

n:e

K-V

alue

:2.

1K

-Val

ue:

2.1

Mem

ber L

oads

:A

xial

Tens

ion

P:

1.65

kips

Mom

ent -

Stro

ng A

xis:

Mx

MA

X:12

.7ki

p-ft

Mom

ent -

Wea

k A

xis:

My

MA

X:1.

624

kip-

ft

Axia

l - T

ensi

on C

heck

[AIS

C S

pec

D1]

:U

tiliz

atio

n:f t:

0.10

ksi

<F t

:28

ksi

OK

0.4%

Axia

l - C

ompr

essi

on C

heck

[AIS

C S

pec

E2]:

Stro

ng A

xis

- X:

Wea

k A

xis

- X:

KL/

r x:33

.1<-

- Gov

erns

KL/

r x:24

.8

Cc:

111.

6

Gov

erni

ng E

ffect

ive

Sle

nder

ness

Rat

io:

KL/

r =33

.1

Cc =

111.

6Th

eref

ore,

use

EQ

N E

2-1

[AIS

C]

Util

izat

ion:

f c:N

/Aks

i

F c:

24.8

ksi

N

/A

Flex

ure

Che

ck -

Stro

ng A

xis

[AIS

C S

pec.

F1]

:F b

x = 0

.6F y

Util

izat

ion:

f bx:

3.79

ksi

<F b

x:28

ksi

OK

13.7

%

Flex

ure

Che

ck -

Wea

k Ax

is [A

ISC

Spe

c. F

2]:

F by =

0.7

5Fy

Util

izat

ion:

f by:

0.65

ksi

<F b

y:35

ksi

OK

1.9%

Cc

22E

F y

HSS

Rec

tang

ular

Stru

ctur

al D

esig

n - S

teel

Des

ign

Spr

eads

heet

Cop

yrig

ht ©

201

1 by

Mar

k D

onof

rio1

of 2

Page 29: Structures Project: arbutus corridor metro stop

DEP

ARTM

ENT

OF

ARC

HIT

ECTU

RE

S cho

ol o

f Arc

hite

ctur

e an

d Al

lied

Arts

Uni

vers

ity o

f Ore

gon

Arch

itect

ure

462/

562

Don

ofrio

/Duf

fW

inte

r

Des

igne

r:G

TF:

Dyl

an C

urle

yR

yan

Cha

mpa

gne

Mem

ber I

D:

Rib

Pie

ce 2

Com

bine

d St

ress

Che

ck:

Axia

l Com

pres

sion

and

Ben

ding

[AIS

C S

pec

H1]

:

F' ex:

136.

1ks

iF' ey

:24

3.4

ksi

Cm

x:1

Cm

y:1

AISC

EQ

N H

1-1

AISC

EQ

N H

1-2

AISC

EQ

N H

1-3

Axia

l Ten

sion

and

Ben

ding

[AIS

C S

pec

H2]

:

AISC

EQ

N H

2-1

0.00

+0.

14+

0.02

=0.

16<

1.0

OK

Sect

ion

is s

atis

fact

ory

f a F a�

Cmxf b

x

1�

f a F' ex

� � � � � � F

bx

�C

myf b

y

1�

f a F' ey

� � � � � � � � F

by

�1.0

f a0.60

F y�

f bx

F bx

�f b

y

F by

�1.0

f a F a�

f bx

F bx

�f b

y

F by

�1.0

f a F t�

f bx

F bx

�f b

y

F by

�1.0

HSS

Rec

tang

ular

Stru

ctur

al D

esig

n - S

teel

Des

ign

Spr

eads

heet

Cop

yrig

ht ©

201

1 by

Mar

k D

onof

rio2

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Page 30: Structures Project: arbutus corridor metro stop

Rib Piece 3HSS 20x8x5/8

Page 31: Structures Project: arbutus corridor metro stop

Max Strong Axis Moment38.869 K-ft

Max Weak Axis Moment6.558K-ft

Max Axial Force2.594 K

38.869

29.547

x

y

z

Page 32: Structures Project: arbutus corridor metro stop

DEP

ARTM

ENT

OF

ARC

HIT

ECTU

RE

Scho

ol o

f Arc

hite

ctur

e an

d Al

lied

Arts

Uni

vers

ity o

f Ore

gon

Arch

itect

ure

462/

562

Don

ofrio

/Duf

fW

inte

r

Des

igne

r:G

TF:

Dyl

an C

urle

yR

yan

Cha

mpa

gne

Mat

eria

l Pro

pert

ies:

Sect

ion

Prop

ertie

s:S

teel

Typ

e:A5

00 -

B (R

ect)

Sec

tion:

HSS

20X8

X5/8

F y:

46ks

iA

rea:

30.3

in2

F u:

58ks

iE

:29

000

ksi

Axi

s X-

X (S

trong

Axi

s)A

xis

Y-Y

(Wea

k A

xis)

I x:14

40in

4I y:

338

in4

Sx:

144

in3

Sy:

84.6

in3

r x:6.

89in

r y:3.

34in

Mem

ber D

ata:

Mem

ber I

D:

Rib

Pie

ce 2

Axia

l Pro

pert

ies

(Col

umn

Buc

klin

g):

Unb

race

d Le

ngth

- X-

Axi

s:4

ftU

nbra

ced

Leng

th -

Y-A

xis:

4ft

K-C

ondi

tion:

eK

-Con

ditio

n:e

K-V

alue

:2.

1K

-Val

ue:

2.1

Mem

ber L

oads

:A

xial

Com

pres

sion

P:

2.59

4ki

psM

omen

t - S

trong

Axi

s:M

x M

AX:

38.8

69ki

p-ft

Mom

ent -

Wea

k A

xis:

My

MA

X:6.

58ki

p-ft

Axia

l - T

ensi

on C

heck

[AIS

C S

pec

D1]

:U

tiliz

atio

n:f t:

N/A

ksi

F t

:28

ksi

N

/A

Axia

l - C

ompr

essi

on C

heck

[AIS

C S

pec

E2]:

Stro

ng A

xis

- X:

Wea

k A

xis

- X:

KL/

r x:14

.6

KL/

r x:30

.2<-

- Gov

erns

Cc:

111.

6

Gov

erni

ng E

ffect

ive

Sle

nder

ness

Rat

io:

KL/

r =30

.2<

Cc =

111.

6Th

eref

ore,

use

EQ

N E

2-1

[AIS

C]

Util

izat

ion:

f c:0.

09ks

i<

F c:

25.1

ksi

OK

0.3%

Flex

ure

Che

ck -

Stro

ng A

xis

[AIS

C S

pec.

F1]

:F b

x = 0

.6F y

Util

izat

ion:

f bx:

3.24

ksi

<F b

x:28

ksi

OK

11.7

%

Flex

ure

Che

ck -

Wea

k Ax

is [A

ISC

Spe

c. F

2]:

F by =

0.7

5Fy

Util

izat

ion:

f by:

0.93

ksi

<F b

y:35

ksi

OK

2.7%

Cc

22E

F y

HSS

Rec

tang

ular

Stru

ctur

al D

esig

n - S

teel

Des

ign

Spr

eads

heet

Cop

yrig

ht ©

201

1 by

Mar

k D

onof

rio1

of 2

Page 33: Structures Project: arbutus corridor metro stop

DEP

ARTM

ENT

OF

ARC

HIT

ECTU

RE

S cho

ol o

f Arc

hite

ctur

e an

d Al

lied

Arts

Uni

vers

ity o

f Ore

gon

Arch

itect

ure

462/

562

Don

ofrio

/Duf

fW

inte

r

Des

igne

r:G

TF:

Dyl

an C

urle

yR

yan

Cha

mpa

gne

Mem

ber I

D:

Rib

Pie

ce 2

Com

bine

d St

ress

Che

ck:

Axia

l Com

pres

sion

and

Ben

ding

[AIS

C S

pec

H1]

:

F' ex:

697.

7ks

iF' ey

:16

4.0

ksi

Cm

x:1

Cm

y:1

AISC

EQ

N H

1-1

AISC

EQ

N H

1-2

fa/F

a:0.

00<

0.15

AISC

EQ

N H

1-3

0.00

+0.

12+

0.03

=0.

15<

1.0

OK

Sect

ion

is s

atis

fact

ory

Axia

l Ten

sion

and

Ben

ding

[AIS

C S

pec

H2]

:

AISC

EQ

N H

2-1

f a F a�

Cmxf b

x

1�

f a F' ex

� � � � � � F

bx

�C

myf b

y

1�

f a F' ey

� � � � � � � � F

by

�1.0

f a0.60

F y�

f bx

F bx

�f b

y

F by

�1.0

f a F a�

f bx

F bx

�f b

y

F by

�1.0

f a F t�

f bx

F bx

�f b

y

F by

�1.0

HSS

Rec

tang

ular

Stru

ctur

al D

esig

n - S

teel

Des

ign

Spr

eads

heet

Cop

yrig

ht ©

201

1 by

Mar

k D

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rio2

of 2


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