jörg schlaich

Jörg SchlaichSchlaich Bergermann und Partner, Stuttgart

The challenge and Joy of STrucTural engineeringthurSday, OctOBer 4, 2012

inaugural edward and Mary allenlecTure in STrucTural deSign

SchOOl Of architecture + Planning

2

edward and Mary allen lecTure in STrucTural deSign

Established in 2012, the annual Edward and Mary Allen Lecture aims to bring

the world’s leading structural designers to MIT to speak about engineering

within the realm of architecture, design, and creativity and to interact closely

with students in their design work. The program includes a public lecture

in the Architecture Lecture Series as well as a workshop reviewing graduate

student structural design projects.

For the inaugural Allen Lecture on October 4, 2012, the eminent German

structural engineer, educator, and designer Jorg Schlaich visited MIT to

speak about his decades of inspired design work, including long-span roofs,

innovative bridges, and multi-story facades, as well as his more recent

efforts in solar energy. Along with Edward Allen, Schlaich also worked with

graduate students in architecture and engineering on their designs for an

enclosed skybridge over Vassar Street on the MIT campus, a project which

he had also developed conceptual designs for several years prior.

This booklet commemorates Schlaich’s visit with photographs of his lecture

and from his review of student projects, and also contains a survey of the

student structural design work.

3

Jörg Schlaich

Prof. Dr. Ing. Drs. h.c. Jorg Schlaich is a German structural engineer. He

studied architecture and civil engineering from 1953 to 1955 at Stuttgart

University before completing his studies at the Technical University of

Berlin in 1959 (Dr. Ing.). He spent 1959-60 at the Case Western Reserve

University in Cleveland, Ohio, USA (MSc.).

Jorg Schlaich was made a partner of the structural engineers, Leonhardt und

Andra and was responsible for the Olympic Stadium Roof, Munich in 1968-

72.

From 1974 to 2000 he was full professor and director of the Institute for

Concrete Structures (Institut fur Massivbau), later called the Institute for

Structural Design (Konstruktion und Entwurf) at the University of Stuttgart.

In 1980 he and his partner, Dr. Rudolph Bergermann, founded their own

firm, Schlaich Bergermann und Partner in Stuttgart.

Most of his projects, as well of that of his company with offices in Stuttgart,

Berlin, New York, Sao Paulo and Shanghai, are documented on their website

(www.sbp.de). The work of Schlaich Bergermann und Partner focuses on the

three main themes of building, surveying and solar energy.

Jorg Schlaich is also the developer of the Solar Updraft Tower for large

scale solar energy generation. He is credited with advancing the strut and

tie model for reinforced concrete with his seminal 1987 paper, “Toward a

Consistent Design of Structural Concrete” in PCI Journal.

Jörg Schlaich with Caitlin Mueller, Edward Allen, and

John Ochsendorf

5

ABOVE: Jörg Schlaich with Edward AllenLEFT: Jörg Schlaich presenting during his

public lecture

6

ABOVE: Jörg Schlaich talking to students about bridge designRIGHT: Jörg Schlaich with John Ochsendorf

9

ABOVE: Jörg Schlaich with graduate students in architecture

and engineeringLEFT: Jörg Schlaich with John

Ochsendorf and Edward Allen

10

ABOVE AND RIGHT: Jörg Schlaich reviewing student projects with Edward Allen and John Ochsendorf

14

ABOVE: Jörg Schlaich with Edward Allen and John Ochsendorf at the end of the student project reviewRIGHT: Two skybridge designs proposed by Schlaich Bergermann und Partner for the MIT campus

15

STudenT deSign worK

The following pages showcase the projects reviewed by Jorg Schlaich during his visit to MIT. The student design work comes from a second-year structural design course in the Masters of Architecture program at MIT, taught by John Ochsendorf and Andrea Love with assistance from Caitlin Mueller. Each presentation proposes a conceptual structural design developed over the course of four weeks for an enclosed skybridge connecting two existing buildings on the MIT campus across Vassar Street.

Before the review, Jorg Schlaich presented the students with two of his own designs for the same project developed several years earlier.

16

In devising a scheme for a skybridge between buildings 36 and 46 our main architectural objective was to design a visually minimal bridge that did not compete with the surrounding buildings but was still interesting in its own right. The bridge bends in plan to allow for views of the Stata Center and the envelope is cladded in folded plates of glass. After several iterations, we decided upon a cable stayed structural system anchored in both buildings.

ant bridgeSuk Lee & Susanna Pho

46.80 k208.18 kn

23.29 k103.60 kN

19.35 k86.07 kn

42.64 k189.67 kn

109.20 k485.75 kn

10.28 k45.73 kn

89.94 k400.07 kn

21.43 k95.33 kn

20.79 k92.48 kn

19.76 k87.90 kn

17.68 k78.64 kn

74 ft

h=varies

b= 8in

7.4 ft

89.94 k

a) Maximum Tension force on Tension Rods: 12.28 k or 54.62 kn Diameter = 0.5 in, Stainless Steel Rod with allowable force: 12.56k > 12.28k

b) Arequired

= F/σ = 12.28k / 15ksi = 0.82 in2 >> Diameter = 1.02 in or 25.91 mm

Stainless Steel Rods with 1.25in or 31.75 mm Diameter will be used to carry tension force>> >>

Stainless Steel Rod is used instead of tension cable to reduce the amount of possible sag

1.25 in

M NLKJIHGFEDCBAA’

1’ 1O 2 3 4 5 6 7 8 9 10 11 13 142’4’5’6’

B’C’D’E’F’

123’

B

B’

A’

O

C

C’

D’

E’

F’

D

E

F

G

H

I

J

K

L

M

N

A 1

2’

1’

3’

4’

5’

6’

2

3

4

5

6

7

8

9

10

11

12

13

14

1

Maximum Tension Member B

Maximum Tension Member A

O

3’

4’

: 7.8 k

Axial l

oad conditions

forc

e polyg

on

load condit

ions

GIRDER SIZING

cable SIZING

Bridge B

Bridge A

Material Properties:concrete deck: 40 lbs/ft2

structural glass: 35 lbs/ft2

tributary area: 5 ft or 1.52 m

Uniform Live Load: 9ft x (80 lbs/ft2 + 30 lbs/ft2) =990 lbs/ftStructure Dead Load: (1041 lbs/ft x 5ft) + ( 1090 lbs/ft x 5)

DEFLECTION ANALYSISIncreased overall depth of beam to prevent deflection.

AXIAL LOAD ANALYSISINFORMED REQUIRED DEPTH OF BEAM

Crushing:A = F/σ = 89.94 k / 3 ksi = 29.97 in2

h = 3.74 in or 95 mm

Buckling:I = ((kL)2 x P

cr )/ ( π2E)

= (((74ft x 12in))2 x 89.94 k)/(π2 x 3,000 ksi) = 2395.29 in4

bhv/12 = 2395.29 in4 (b=width=8 in)h = 15.32 in or 389.19 mm

Moment:M= wL2/16 = (3.12 k/ft)(7.4 ft)2/16 = 10.68 k-ft = 128.16 k-inS = M/σ = 128.16 k-in / 3 ksi = 42.72 in3

S = I/y = 6/h3

h = 0.52 in 13.20 mm

Point Load: (990 lbs/ft x 5 ft) + (2131 lbs/ft x 5 ft) = 15.6 k

Point Load On One Side of Structure:15.6 k / 2 = 7.8 k or 34.7 kn

DEFLEC

TION

CROSS SECTION

CABLE-DECK CONNECTION DETAIL

EXPOSED EMBEDDED STEEL PLATECustomized to act as cable

anchoring system

STEEL REINFORCEMENT

17

In devising a scheme for a skybridge between buildings 36 and 46 our main architectural objective was to design a visually minimal bridge that did not compete with the surrounding buildings but was still interesting in its own right. The bridge bends in plan to allow for views of the Stata Center and the envelope is cladded in folded plates of glass. After several iterations, we decided upon a cable stayed structural system anchored in both buildings.

ant bridgeSuk Lee & Susanna Pho

46.80 k208.18 kn

23.29 k103.60 kN

19.35 k86.07 kn

42.64 k189.67 kn

109.20 k485.75 kn

10.28 k45.73 kn

89.94 k400.07 kn

21.43 k95.33 kn

20.79 k92.48 kn

19.76 k87.90 kn

17.68 k78.64 kn

74 ft

h=varies

b= 8in

7.4 ft

89.94 k

a) Maximum Tension force on Tension Rods: 12.28 k or 54.62 kn Diameter = 0.5 in, Stainless Steel Rod with allowable force: 12.56k > 12.28k

b) Arequired

= F/σ = 12.28k / 15ksi = 0.82 in2 >> Diameter = 1.02 in or 25.91 mm

Stainless Steel Rods with 1.25in or 31.75 mm Diameter will be used to carry tension force>> >>

Stainless Steel Rod is used instead of tension cable to reduce the amount of possible sag

1.25 in

M NLKJIHGFEDCBAA’

1’ 1O 2 3 4 5 6 7 8 9 10 11 13 142’4’5’6’

B’C’D’E’F’

123’

B

B’

A’

O

C

C’

D’

E’

F’

D

E

F

G

H

I

J

K

L

M

N

A 1

2’

1’

3’

4’

5’

6’

2

3

4

5

6

7

8

9

10

11

12

13

14

1

Maximum Tension Member B

Maximum Tension Member A

O

3’

4’

: 7.8 k

Axial l

oad conditions

forc

e polyg

on

load condit

ions

GIRDER SIZING

cable SIZING

Bridge B

Bridge A

Material Properties:concrete deck: 40 lbs/ft2

structural glass: 35 lbs/ft2

tributary area: 5 ft or 1.52 m

Uniform Live Load: 9ft x (80 lbs/ft2 + 30 lbs/ft2) =990 lbs/ftStructure Dead Load: (1041 lbs/ft x 5ft) + ( 1090 lbs/ft x 5)

DEFLECTION ANALYSISIncreased overall depth of beam to prevent deflection.

AXIAL LOAD ANALYSISINFORMED REQUIRED DEPTH OF BEAM

Crushing:A = F/σ = 89.94 k / 3 ksi = 29.97 in2

h = 3.74 in or 95 mm

Buckling:I = ((kL)2 x P

cr )/ ( π2E)

= (((74ft x 12in))2 x 89.94 k)/(π2 x 3,000 ksi) = 2395.29 in4

bhv/12 = 2395.29 in4 (b=width=8 in)h = 15.32 in or 389.19 mm

Moment:M= wL2/16 = (3.12 k/ft)(7.4 ft)2/16 = 10.68 k-ft = 128.16 k-inS = M/σ = 128.16 k-in / 3 ksi = 42.72 in3

S = I/y = 6/h3

h = 0.52 in 13.20 mm

Point Load: (990 lbs/ft x 5 ft) + (2131 lbs/ft x 5 ft) = 15.6 k

Point Load On One Side of Structure:15.6 k / 2 = 7.8 k or 34.7 kn

DEFLEC

TION

CROSS SECTION

CABLE-DECK CONNECTION DETAIL

EXPOSED EMBEDDED STEEL PLATECustomized to act as cable

anchoring system

STEEL REINFORCEMENT

18

SECTION PROPERTIES / SELF WEIGHT

M =

180 kips [800.69 kN]

1.8 kips [0.026 kN/m]

force polygon

from the cable sizing table:

COMBINED STRESS

BUCKLING

1-7/8” [47.625 mm] diameter,class “A” coating throughout(breaking strength: 216.0 tons)

SIZING THE CABLE

UNIFORM LOADING

SIZING THE GIRDER/STRUT

free body diagram

187.8 kips [835.38 kN]

187.8 kips [835.38 kN]

floor dead load: 0.244 kip/ft [0.004 kN/m]floor live load: 0.800 kip/ft [0.012 kN/m]roof dead load: 0.329 kip/ft [0.005 kN/m]

roof live load: 0.300 kip/ft [0.004 kN/m]cladding: 0.124 kip/ft [0.002 kN/m]TOTAL: 1.800 kip/ft [0.026 kN/m]

LOADS

LOAD CASE 1

110 ft [33.53 m]

187. kips = 93.9 tons93.9 tons2.2 s.fx

M = C x dC = 1.89 kipsCmax = 181.89 kips

A = = 12.19 in2 [0.008 m2]

d = .75 ft

σsteel = 15 ksi

= 1.42 k·ft

distributed load on girder = (0.329 + 0.3) / 2 = 0.4645 kip/ft

assume for full unbraced length

Pcr =

7 ft [2.133 m]

0.46 kip/ft

3.25 kip/ft3.25 kip/ft

7 ft [2.133 m]

180 kips

0.46 kip/ft

.75 ft[0.23 m]

1.89 kips

assume 18 inch strut depth10 ft [3.048 m]

2 ft [0.61 m]

180 kips

wL216

Fσ

π2E(I)(k L)2

I = 1096 in4 [45,618.97cm4]

180 kips = π2(29,000 ksi)(I)(1·110 ft·12 in)2

47.6 mmfrom the hollow steel section table:

ASYMMETRICAL LOADING

1.8 kips [0.026 kN/m]

SIZING THE GIRDER

DEFLECTION

free body diagram

LOAD CASE 2 DETAIL

assume cable carries no stiffnessassume vertical struts are infinitely stiff/transfer deformations from deck to top girder

Mmax =

Mmax = 340 kip·ft [460978.1 Nm]

=wL264

(1.8 kip/ft)(1102)64

5wL4

384E∆max

Ireq ≥ 34,000 in4

Ireq ≥

5(0.09 k/in)4

384(29000 k/in2)(3.7in)≥

Length = 1320 inWeight = 1100 lb/ft = 0.09 k/inEsteel = 2900 k/in2

check via multiframe:

I = ∑Aidi2

= (2·30in2·(52in)2)+(2·2.76in2·(0in)2)+(2·20in2·(78in)2)I = 405,600 in4 ≥ 34,000 in4 :) [ 0.17 m4 ≥ 0.01 m4 ]

σ =Ms

340 kip·fts

12 in1 ft

S = 136 in3 [2000 cm3]

20 in x 8 in x 5/8 in[508 mm x 203.2 mm x 15.9 mm]

A = 30.3 in2

[0.02 m2]I = 1440 in4

[0.0006 m4]S = 144 in3

[2000 cm3]

∆max = 3.7 in

∆ = 3.46 in ≤ 3.7 in [0.087 m ≤ 0.093 m]

508

mm

203.2 mm

15.9 mm

y=0

1.8 kips [0.026 kN/m]

= x 12

x

from the hollow steel section table:

SIZING THE SECONDARY STRUT

BUCKLING

CRUSHING

A = = 0.48 m2Fσ

Pcr =π2E(I)

(k L)27,150 lbs =

I = 0.230 in4 [9.57 cm4]

π2(29 x 107 psi)(I)

(96 in)28 ft

7.15 kips

1½ in x 1½ in x 3/16 in[38.1 mm x 38.1 mm x 4.76 mm]

A = 0.84 in2

[5.42 cm2]I = 0.235 in4

[9.78 cm4]

38.1

mm

38.1 mm

4.76 mm

3550

mm

3050mm 32500 mm

30 in2

.02 m2

52 in2

.03 m2

206.58 tons [1837 kN]

20 in2

.02 m2

2.76 in2

17.81 cm2

6.35

50.8

0

6.35

203.

20

R152.40

12.5

152.40

12.50

50.8

0

6.35

38.1

0

152.40

4.76

38.10

28.54

508.

00

254.00

15.8

8

ROOF SYSTEM

FACADE SYSTEM

FLOOR SYSTEM

Component BreakdownCable Connection

Elevation

Section

1/4” Glass Roof

1/4” Glass Floor

2” Steel Diagrid Mesh


20 x 8 x 5/8 HSS

1.5 x 1.5 x 3/16 HSS

1/4” Glass Cladding

1 7/8” Steel Cable

34 lb/ft51 kg/m

150 lb/ft223 kg/m

160 lb/ft238 kg/m

110 lb/ft164 kg/m

34 lb/ft51 kg/m

7.39 lb/ft11 kg/m

34 lb/ft51 kg/m

FLOATING FOOT BRIDGE RENA YANG & YAN-PING WANG

19

SECTION PROPERTIES / SELF WEIGHT

M =

180 kips [800.69 kN]

1.8 kips [0.026 kN/m]

force polygon

from the cable sizing table:

COMBINED STRESS

BUCKLING

1-7/8” [47.625 mm] diameter,class “A” coating throughout(breaking strength: 216.0 tons)

SIZING THE CABLE

UNIFORM LOADING

SIZING THE GIRDER/STRUT

free body diagram

187.8 kips [835.38 kN]

187.8 kips [835.38 kN]

floor dead load: 0.244 kip/ft [0.004 kN/m]floor live load: 0.800 kip/ft [0.012 kN/m]roof dead load: 0.329 kip/ft [0.005 kN/m]

roof live load: 0.300 kip/ft [0.004 kN/m]cladding: 0.124 kip/ft [0.002 kN/m]TOTAL: 1.800 kip/ft [0.026 kN/m]

LOADS

LOAD CASE 1

110 ft [33.53 m]

187. kips = 93.9 tons93.9 tons2.2 s.fx

M = C x dC = 1.89 kipsCmax = 181.89 kips

A = = 12.19 in2 [0.008 m2]

d = .75 ft

σsteel = 15 ksi

= 1.42 k·ft

distributed load on girder = (0.329 + 0.3) / 2 = 0.4645 kip/ft

assume for full unbraced length

Pcr =

7 ft [2.133 m]

0.46 kip/ft

3.25 kip/ft3.25 kip/ft

7 ft [2.133 m]

180 kips

0.46 kip/ft

.75 ft[0.23 m]

1.89 kips

assume 18 inch strut depth10 ft [3.048 m]

2 ft [0.61 m]

180 kips

wL216

Fσ

π2E(I)(k L)2

I = 1096 in4 [45,618.97cm4]

180 kips = π2(29,000 ksi)(I)(1·110 ft·12 in)2

47.6 mmfrom the hollow steel section table:


1.8 kips [0.026 kN/m]

SIZING THE GIRDER

DEFLECTION

free body diagram

LOAD CASE 2 DETAIL

assume cable carries no stiffnessassume vertical struts are infinitely stiff/transfer deformations from deck to top girder

Mmax =

Mmax = 340 kip·ft [460978.1 Nm]

=wL264

(1.8 kip/ft)(1102)64

5wL4

384E∆max

Ireq ≥ 34,000 in4

Ireq ≥

5(0.09 k/in)4

384(29000 k/in2)(3.7in)≥

Length = 1320 inWeight = 1100 lb/ft = 0.09 k/inEsteel = 2900 k/in2

check via multiframe:

I = ∑Aidi2

= (2·30in2·(52in)2)+(2·2.76in2·(0in)2)+(2·20in2·(78in)2)I = 405,600 in4 ≥ 34,000 in4 :) [ 0.17 m4 ≥ 0.01 m4 ]

σ =Ms

340 kip·fts

12 in1 ft

S = 136 in3 [2000 cm3]

20 in x 8 in x 5/8 in[508 mm x 203.2 mm x 15.9 mm]

A = 30.3 in2

[0.02 m2]I = 1440 in4

[0.0006 m4]S = 144 in3

[2000 cm3]

∆max = 3.7 in

∆ = 3.46 in ≤ 3.7 in [0.087 m ≤ 0.093 m]

508

mm

203.2 mm

15.9 mm

y=0

1.8 kips [0.026 kN/m]

= x 12

x

from the hollow steel section table:

SIZING THE SECONDARY STRUT

BUCKLING

CRUSHING

A = = 0.48 m2Fσ

Pcr =π2E(I)

(k L)27,150 lbs =

I = 0.230 in4 [9.57 cm4]

π2(29 x 107 psi)(I)

(96 in)28 ft

7.15 kips

1½ in x 1½ in x 3/16 in[38.1 mm x 38.1 mm x 4.76 mm]

A = 0.84 in2

[5.42 cm2]I = 0.235 in4

[9.78 cm4]

38.1

mm

38.1 mm

4.76 mm

3550

mm

3050mm 32500 mm

30 in2

.02 m2

52 in2

.03 m2

206.58 tons [1837 kN]

20 in2

.02 m2

2.76 in2

17.81 cm2

6.35

50.8

0

6.35

203.

20

R152.40

12.5

152.40

12.50

50.8

0

6.35

38.1

0

152.40

4.76

38.10

28.54

508.

00

254.00

15.8

8

ROOF SYSTEM

FACADE SYSTEM

FLOOR SYSTEM

Component BreakdownCable Connection

Elevation

Section

1/4” Glass Roof

1/4” Glass Floor



20 x 8 x 5/8 HSS

1.5 x 1.5 x 3/16 HSS


1 7/8” Steel Cable

34 lb/ft51 kg/m

150 lb/ft223 kg/m

160 lb/ft238 kg/m

110 lb/ft164 kg/m

34 lb/ft51 kg/m

7.39 lb/ft11 kg/m

34 lb/ft51 kg/m

FLOATING FOOT BRIDGE RENA YANG & YAN-PING WANG

20

GLOBAL SHAPE: PRIMARY MEMBER SIZING:DESIGN APPROACH:: ASYMMETRICAL LOADING CASE: using force polygon

Final Force Polygon

Previous Iterations

(d)

(a)

(b)

(c)

(d)

a

b

c

d

e

f

g

h

i

j

k

l

m

n

o

p

q

r

s

(a)

(a)

(b)(c)

(d)

(b)

(c)

107’ = 32.1 m

edge of verticalsupport zone edge of sidewalk

10 KIPS=44.5 KN

AB

CDEFGHI

JK

L

MN

O

O’

P

Q

R

S

T

20’45’

30’=9m

horizontal force = 56.3 KIPS = 250.5 kN

10 K

IPS=

44.5

kN

1’ = 1 KIP

Fmax = 128 KIPS= 569.6 kN

113.8

KIP

S

o’

o’

a

b

c

d

e

f

g

h

i

j

k

l

m

n

o

p

q

r

s

t

LOADS:

UNIIFORM LOADING CASE (w):

people

snow

80 lbs/ft2

110 lbs/ft2

30 lbs/ft2

Live Load

steel

concrete

glass

226 lbs/ft2

336 lbs/ft2

=16.6 kN/m2

(density of steel= 490 lbs/ft3)assuming that we use 2” of steel (1/6 of a foot), » 490 lbs/ft3 • 1/6 ft = 82 lbs/ft2

(density of concrete= 150 lbs/ft3)assuming that we use 6” of cocnrete (1/2 of a foot), » 150 lbs/ft3 • 1/2 ft = 75 lbs/ft2

(density of glass= 162 lbs/ft3)assuming that we use 2 of 2” of steel (1/3 of a foot), » 162 lbs/ft3 • 1/3 ft = 54 lbs/ft2

extra

Dead Load

15 lbs/ft2

σ = P/A , where steel allowable stress = 15ksi» 15 ksi = 128 kips/A » A=8.53 in2 » b=h= 3 in = 25.4 mm

due to axial force

Live Load+ Dead Load = 336 lbs/ft2

336 lbs/ft2 • 10ft = 3360 lbs/ft = 3.36 kips/ft

3.36 kips/ft for two arches = 1.68 kips/ft for 1 arch

1.68 kips/ft • 107 ft = 179.76 kips

» 179.76 kips/19 segments = 9.46 kips/seg

Dead Load = 226 lbs/ft2

» 226 lbs/ft2 • 10ft = 2260 lbs/ft » 2.26 kips/ft

Live Load = 110 lbs/ft2

» 110 lbs/ft2 • 10ft • 107ft = 117.7 kips » 117.7 kips / 92 ft= 1.28 kips /ft

arch-in-motion Maya Taketani / Jasmine Kwak

4.463 Building Systems II

simplified diagram of design proposal

15 feet

30 feet

10 feet

92 feet

steel columns

structural glass

107 feet

concrete deck as a horizontal tie

steel cables

steel arch SECONDARY MEMBER SIZING:

MAXMIMUM MOMENT DUE TO ASYMMETRICAL LOADING:

DEFLECTION DUE TO ASYMMETRICAL LOADING

σ= F/A» 15 ksi = 10 kips / A » A=0.66 in2

» A=0.66 in2=π(r)2

» r= 0.46 in » approx. r= 1/2 in = 12.7 mm MMAX= (wLL• L

2)/32 » where wLL= 0.11 kips/ft2 •10 ft /2 arch= 0.55 k/ft » 0.55k/ft • (92ft)2/32 » MMAX= 145.5 kip•ft = 194 kN•m

T=C=M/d » T= 145.5 kip•ft•(12in/ft) / 6 in » 291 kips

σ= F/A » 15 ksi = 291 kips / A » A= 19.4 in2

» d= 4 in = 101.6 mm


Pbuckling=(π2EI)/(KL)2

» 97 kips•3= (π2•29000 k/in2•Ireq) (112 ft•12ft/in)2

» Ireq= 1836.5 in4

σ= F/A » 15 ksi = 97 kips / A » A= 6.5 in2

Steel Cables in Tension

σ= F/A» 15 ksi = 56.3 kips / A » A=3.75 in2

» I-beam S6x17.25

I-beam decking in Concrete Decking in Tension

bridge

10 feet

336 lb/ft2

336 lb/ft

bridge

336 lb/ft 168 lb/ft

10 kips / ea

due to crushing

due to buckling

Steel Column in Compression

σ= F/A» 15 ksi = 10 kips / A » A=0.67 in2 » b=0.82 in

Pcr= (π2EI)/(kL)2

» 3 •10 kips = [(π2)(29000kips/in2)(Irequired)]/ [(24.25 ft)(12in/1ft)]2 » Irequired = 8.88 in4, where I= bh3/12» for a square section column, b= 4.74 in » b=4 in. or 101.6mm and h=3 in. 76.2 mm

I= bh3/12» I= 108/12= 9 in4 Pcr= (π2EI)/(kL)2

» 3 •10 kips = [(π2)(29000kips/in2)(9 in4)]/ [L in]2

» L < 293 inches = 24 ft = 7.3 m

226 lb/ft

bridge

92 feet

110 lb/ft

bridge

226 lb/ft

110 lb/ft

1”

3”

3”

4”

6”

18”

5/8”

20”

18”

5/8”

20”

20”

5/8”

22”

3-5/8”

6”

7/16”

5”

16.8 kips each

0.9560.6050.458

0.3650.293

0.23

0.172

0.115

0.058

2.6441.449

0.9810.508

1.961

3.987 3.5762.3730.859

0.5430.411

0.3280.263

0.207

0.154

0.103

0.052

1.761.3

0.8810.456

OR

When we used HSS20X18X5/8 as sectional propertiesin Multiframe software to calculate, the highest distance of deflection was 3.987 inches as shown in the graphon the left. Therefore, we had to increase the sectional dimension in order to accomodate ∆max≤ 3.7 in, given ∆max≤ L/360 = 110 ft/360. The new max deflection is 3.576 inches as shown on the right graphand new section is HSS22X20X5/8

street perspective elevation and material

plan

peoplesnow

steel concrete

glass extra

Vassar Street is one of MIT's prominent streets located on the north edge of MIT campus. Nearby the site is Frank Gehry's Stata Center and Charles Correa's Brain and Cognitive Sciences Building. Despite many well known buildings, Vassar Street lacks a visual key urban element that brings people to this street. With these observations, this proposal attempts to achieve the following criteria: • Create a visual focal point on Vassar St. using an archway as an indicator of a grand passageway; • Maximize transparency to maintain the openness that Vassar Street currently has; • Create a comfortable and visually engaging experience for the skybridge users;

C

T

21

GLOBAL SHAPE: PRIMARY MEMBER SIZING:DESIGN APPROACH:: ASYMMETRICAL LOADING CASE: using force polygon

Final Force Polygon

Previous Iterations

(d)

(a)

(b)

(c)

(d)

a

b

c

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e

f

g

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k

l

m

n

o

p

q

r

s

(a)

(a)

(b)(c)

(d)

(b)

(c)

107’ = 32.1 m

edge of verticalsupport zone edge of sidewalk

10 KIPS=44.5 KN

AB

CDEFGHI

JK

L

MN

O

O’

P

Q

R

S

T

20’45’

30’=9m

horizontal force = 56.3 KIPS = 250.5 kN

10 K

IPS=

44.5

kN

1’ = 1 KIP

Fmax = 128 KIPS= 569.6 kN

113.8

KIP

S

o’

o’

a

b

c

d

e

f

g

h

i

j

k

l

m

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LOADS:

UNIIFORM LOADING CASE (w):

people

snow

80 lbs/ft2

110 lbs/ft2

30 lbs/ft2

Live Load

steel

concrete

glass

226 lbs/ft2

336 lbs/ft2

=16.6 kN/m2

(density of steel= 490 lbs/ft3)assuming that we use 2” of steel (1/6 of a foot), » 490 lbs/ft3 • 1/6 ft = 82 lbs/ft2

(density of concrete= 150 lbs/ft3)assuming that we use 6” of cocnrete (1/2 of a foot), » 150 lbs/ft3 • 1/2 ft = 75 lbs/ft2

(density of glass= 162 lbs/ft3)assuming that we use 2 of 2” of steel (1/3 of a foot), » 162 lbs/ft3 • 1/3 ft = 54 lbs/ft2

extra

Dead Load

15 lbs/ft2

σ = P/A , where steel allowable stress = 15ksi» 15 ksi = 128 kips/A » A=8.53 in2 » b=h= 3 in = 25.4 mm

due to axial force

Live Load+ Dead Load = 336 lbs/ft2

336 lbs/ft2 • 10ft = 3360 lbs/ft = 3.36 kips/ft

3.36 kips/ft for two arches = 1.68 kips/ft for 1 arch

1.68 kips/ft • 107 ft = 179.76 kips

» 179.76 kips/19 segments = 9.46 kips/seg

Dead Load = 226 lbs/ft2

» 226 lbs/ft2 • 10ft = 2260 lbs/ft » 2.26 kips/ft

Live Load = 110 lbs/ft2

» 110 lbs/ft2 • 10ft • 107ft = 117.7 kips » 117.7 kips / 92 ft= 1.28 kips /ft

arch-in-motion Maya Taketani / Jasmine Kwak

4.463 Building Systems II

simplified diagram of design proposal

15 feet

30 feet

10 feet

92 feet

steel columns

structural glass

107 feet

concrete deck as a horizontal tie

steel cables

steel arch SECONDARY MEMBER SIZING:

MAXMIMUM MOMENT DUE TO ASYMMETRICAL LOADING:

DEFLECTION DUE TO ASYMMETRICAL LOADING

σ= F/A» 15 ksi = 10 kips / A » A=0.66 in2

» A=0.66 in2=π(r)2

» r= 0.46 in » approx. r= 1/2 in = 12.7 mm MMAX= (wLL• L

2)/32 » where wLL= 0.11 kips/ft2 •10 ft /2 arch= 0.55 k/ft » 0.55k/ft • (92ft)2/32 » MMAX= 145.5 kip•ft = 194 kN•m


σ= F/A » 15 ksi = 291 kips / A » A= 19.4 in2

» d= 4 in = 101.6 mm


Pbuckling=(π2EI)/(KL)2

» 97 kips•3= (π2•29000 k/in2•Ireq) (112 ft•12ft/in)2

» Ireq= 1836.5 in4

σ= F/A » 15 ksi = 97 kips / A » A= 6.5 in2

Steel Cables in Tension

σ= F/A» 15 ksi = 56.3 kips / A » A=3.75 in2

» I-beam S6x17.25

I-beam decking in Concrete Decking in Tension

bridge

10 feet

336 lb/ft2

336 lb/ft

bridge

336 lb/ft 168 lb/ft

10 kips / ea

due to crushing

due to buckling

Steel Column in Compression

σ= F/A» 15 ksi = 10 kips / A » A=0.67 in2 » b=0.82 in

Pcr= (π2EI)/(kL)2

» 3 •10 kips = [(π2)(29000kips/in2)(Irequired)]/ [(24.25 ft)(12in/1ft)]2 » Irequired = 8.88 in4, where I= bh3/12» for a square section column, b= 4.74 in » b=4 in. or 101.6mm and h=3 in. 76.2 mm

I= bh3/12» I= 108/12= 9 in4 Pcr= (π2EI)/(kL)2

» 3 •10 kips = [(π2)(29000kips/in2)(9 in4)]/ [L in]2

» L < 293 inches = 24 ft = 7.3 m

226 lb/ft

bridge

92 feet

110 lb/ft

bridge

226 lb/ft

110 lb/ft

1”

3”

3”

4”

6”

18”

5/8”20

”

18”

5/8”

20”

20”

5/8”

22”

3-5/8”

6”

7/16”

5”

16.8 kips each

0.9560.6050.458

0.3650.293

0.23

0.172

0.115

0.058

2.6441.449

0.9810.508

1.961

3.987 3.5762.3730.859

0.5430.411

0.3280.263

0.207

0.154

0.103

0.052

1.761.3

0.8810.456

OR

When we used HSS20X18X5/8 as sectional propertiesin Multiframe software to calculate, the highest distance of deflection was 3.987 inches as shown in the graphon the left. Therefore, we had to increase the sectional dimension in order to accomodate ∆max≤ 3.7 in, given ∆max≤ L/360 = 110 ft/360. The new max deflection is 3.576 inches as shown on the right graphand new section is HSS22X20X5/8

street perspective elevation and material

plan

peoplesnow

steel concrete

glass extra

Vassar Street is one of MIT's prominent streets located on the north edge of MIT campus. Nearby the site is Frank Gehry's Stata Center and Charles Correa's Brain and Cognitive Sciences Building. Despite many well known buildings, Vassar Street lacks a visual key urban element that brings people to this street. With these observations, this proposal attempts to achieve the following criteria: • Create a visual focal point on Vassar St. using an archway as an indicator of a grand passageway; • Maximize transparency to maintain the openness that Vassar Street currently has; • Create a comfortable and visually engaging experience for the skybridge users;

C

T

22

ENVELOPE

Kukje Art Center by SO-IL

Primary material: steel mesh

Desired effects: varying opacity, openness, and

ENVELOPE




4.463 Skybridge Concept DesignEvelyn Ting, Jie Zhang

09/21/2012


09/21/2012

70.00

35.09

13.22

13.0

0

90.00

28.18

35.09

55.00

13.0

0

5.00

70.00

90.00

15.26

8.00

25.00

55.00

5.715.71

16.83

54.7 kips

Tributary Area = 50sf Tributary Area = 300sf

8.6 kips

5 kips

5 kips

3.1 kips

0.3 kips/ft

17.5 kips

max. moment = 1770 kip-ft

8.75

10 kips

8.75

8.758.75

17.5 kips

16.83

18.97

0.85 kips/ft

10 kips

16.83

0.55 kips/ft

18.97

16.83

65.8 kips

6m4.5m3m

UNDER UNIFORM LOAD

TRUSSES FOR LOOKOUT POINTS

For Truss 1Truss self weight = 111.09 ft x 22.37 lbs/ft + 91.45ft x 5.41lbs/ft = 2.98 kipsTributary area = 103.75sf + 103.75sf = 207 sfTotal Load = 207 sf x (45 + 110) lbs/sf + 2.98 kips = 35.1 kips Reaction force (vertical) = 35.1 kips/2 = 17.5 kips

Max. axial tension force = 18.97 kipsReq. cross sectional area = 1.26 in^2< 1.51in^2

Max. axial compression force = 16.83 kips over 35.09 ftReq. I = 10.44 in^4 < 21.7 inch^4

Structure for truss 1 is sound.

For Truss 2Truss self weight = 0.55 kips Tributary area = 61.25 sfTotal load = 61.25 sf x (45 + 110) lbs/sf + 0.55 kips = 10 kipsReaction force (vertical) = 10 kips ; (horizontal) = 3.1 kips

Member sizes are su�cient for Truss 2 with signi�cantly smaller loads

UNDER ASYMMETRICAL LOAD MULTIFRAME ANALYSIS

The trusses are braced by diagonal �oor and ceiling beams and act as rigid tubes under asymmetrial load.

MULTIFRAME ANALYSISAxial stress < 15 ksi = allowable stressThe truss structure is sound under asymmetrical load

TRUSSES FOR MAIN BRIDGE

Self-weight of one truss = 37.69 lbs/ft x 110 ft x 2 +22.37 lbs/ft x 297.14 ft + 48.86 lbs/ft x13ft x 2 = 15.23 kipsUniform Load = 15.23 kips/110 ft +0.45 kips(other systems) + 1.1 kips/ft (live loads) = 1.7 kips/ftUniform Load on each truss = Uniform load/2 = 0.85 kips/ft

BEAM ANALOG METHOD FOR VERIFYING CORD MEMBER SIZING

Max.moment = 1770 kips x ftTension/compression force in cords = 1770kipsxft /13 ft= 136.1 kips

Crushing: σ= P/AReq. area =136.1 kips / 15ksi = 9.07 in^2 < 10.4 in^2

Buckling: P = �^2E(I) / (kL)^2 , L = 10 ftI = 6.85 in^4 < 99.6 inch ^4

MULTIFRAME METHOD FOR VERIFYING DIAGONAL MEMBER SIZING

Maximum axial stress in cords = 136.24 kips (tension) / 134.56 kips (compression)Maximum axial stress in webs = 78.96 kips (tension) / 67.63 kips (compression) Maximum moment on diagonal bracing= 93.978 k x ft; required sectional modulus = 6.27 < 8.67 in^3

Multiframe results are consistent with hand calculations;Steel sections will not crush or buckle under given load; The structure is sound.

BASIC PARAMETERSTotal length = 110 ftTotal height = 13 ftTotal width = 10 ftLive load = 80lbs/sfSnow load = 30lbs/sf

CONCEPT

Allowable Stress (steel) = 15 ksiModulus of Elasticity (steel) = 29,000Allowable Stress (concrete) = 1.5 ksiModulus of Elasticity (glass) = 3,000k (�xity) = 1

This design was conceived as an intersection of two bridges. Two lookouts branch o� the bridge, sloping up and down on either side to provide views out onto the surroundings. They create speci�c views and invite visual dialogue with street tra�c, making the bridge both a circulation path and a gathering space. However, the use of glass and steel mesh attempts to bring a sense of lightness and transparency to the site.

2-in-1EVELYN TING, JIE ZHANG

SECONDARY STRUCTURE ANALYSIS

FLOOR SYSTEM (steel beam)Tributary Area A= 300 sfTotal Load = 20 lbs/sf x 300sf +80 lbs/sf x 300 sf = 30 kips

w = Total Load/ Length = 30 kips / 35 ft = 0.86 k/ftM = (wL^2)/8 = (0.77 k/ft x 35 ft x 35 ft) / 8= 131.7.9 k*ftReq. Section Modulus of beam A= M/∂ = 8.78 in^3 < 13.1 in^3

Tributary Area B= 50 sf

Req. Section Modulus of beam B= 0.42 in^3 < 0.486 in^3

DEFLECTION ANALYSIS MULTIFRAME ANALYSISMaximum de�ection = 3.687 in <3.7 in (allowed de�ection)Hand calculations are inaccurate as the application of the equation assumes a well braced truss whereas in actuality, diagonal bracings are compromised at the openings to allow circulation into lookout spaces.

FLOOR SYSTEM (composite slab)

The composite slab is rested between the main cords, and the tertiary beams e�ectively shorten the span of the slab, allowing the thickness of the slab to be reduced.

Concrete allowable stress = 1.5 ksiM = (wL^2)/8 = (0.8 k/ft x 10 ft x 10 ft) / 8= 10 k*ftT=C=m/d= 53.3 kips

A=C/1.5ksi = 35.5 sq in< actual area 180 sq in. The �oor system is sound.

Total load = Truss self weight + other structural systems dead load + Live load

Floor deck consists of 16 short diagonal beams and 1 long diagonal beam (counted under Truss self weight )

For the main bridge area of 1100 sf:Total Load (�oor beam) = 3.05 lbs/ft x 10 ft x 16 = 0.488 kips; distributed = 4.4 lbs/ftTotal Load (concrete decking) = 1.5 inch x (1/12) x 10ft x 150 lbs/cf = 187.5 lbs/ftTotal Load (metal decking) = 10 lbs/ft

Total Load (�oor) = 202 lbs/ft, or 20 lbs/sfThe ceiling system is estimated to weigh half of the �oor system = 101 lbs/ft, or 10 lbs/sfApproximate facade weight = 15 lbs/sf

Truss self-weight = 0.147 kips/ftOther systems’ self-weight = Floor + Ceiling + Facades = 45 lbs/sf

Total load = Dead Load + Live Load = 0.147 kips/ft + 0.45 kips/ft +1.1kips/ft ~1.7 kips/ft

LOAD ANALYSIS1. Main truss cord member Size = 8 x 8 x 3/8 inchWeight = 37.69 lbs/ftCross Sectional Area = 10.4 in^2S = 24.9 in^3, I = 99.6 in^4

2. Main truss web / secondary truss compression member

Size = 12 x 12 x 5/16 inchWeight = 48.86 lb/ftCross Section Area = 13.4 in^2S = 50.7 in^3, I = 304 in^4

Size = 5 x 5 x 3/8 inchWeight = 22.37 lbs/ftCross Sectional Area = 6.18 in^2S= 8.67 inch^3, I = 21.7 in^4

3. Secondary truss tension member Size = 2 x 2 x 1/4 inchWeight = 5.41 lbs/ftCross sectional area = 1.51 inch^2

4. Tertiary beamSize = 2 x 2 x 1/8 inchWeight = 3.05 lbs/ftS = 0.486 in^3

5. Floor systemComposite �oor system of 2.25 inch thickness ( max. thickness of concrete = 1.5 in, max. corrugation thickness of metal decking = 1.5in) Density of Concrete = 150 lbs/cubic feetWeight of Metal Decking = 1lbs/sf

6. Cladding material Glass for thermal insulationMetal mesh for architectural expression

PLAN CONNECTION DETAIL 1- FLOOR

ELEVATION

CONNECTION DETAIL 2- JOINT

BUILDING SYSTEMS

steel mesh envelope

glass cladding

secondary

1” �nishing0.75” concrete1.5” corrugated metal decktertiary beam bracing

welded steel connection

steel mesh5/8” gypsum board

primary truss

tertiary truss

30.00°

70.00°

10.00

8.00

25.00

10.00

110.

00

0.125

2.00

0.25

2.00

0.375

5.00

8.00

0.375

12.0

0

0.3125

0.75

” 1.00

”1.

50”

2.00

”

8.00

”

elevation 1/16” scale

23

ENVELOPE




ENVELOPE





09/21/2012


09/21/2012

70.00

35.09

13.22

13.0

0

90.00

28.18

35.09

55.00

13.0

0

5.00

70.00

90.00

15.26

8.00

25.00

55.00

5.715.71

16.83

54.7 kips

Tributary Area = 50sf Tributary Area = 300sf

8.6 kips

5 kips

5 kips

3.1 kips

0.3 kips/ft

17.5 kips

max. moment = 1770 kip-ft

8.75

10 kips

8.75

8.758.75

17.5 kips

16.83

18.97

0.85 kips/ft

10 kips

16.83

0.55 kips/ft

18.97

16.83

65.8 kips

6m4.5m3m

UNDER UNIFORM LOAD

TRUSSES FOR LOOKOUT POINTS

For Truss 1Truss self weight = 111.09 ft x 22.37 lbs/ft + 91.45ft x 5.41lbs/ft = 2.98 kipsTributary area = 103.75sf + 103.75sf = 207 sfTotal Load = 207 sf x (45 + 110) lbs/sf + 2.98 kips = 35.1 kips Reaction force (vertical) = 35.1 kips/2 = 17.5 kips

Max. axial tension force = 18.97 kipsReq. cross sectional area = 1.26 in^2< 1.51in^2

Max. axial compression force = 16.83 kips over 35.09 ftReq. I = 10.44 in^4 < 21.7 inch^4

Structure for truss 1 is sound.

For Truss 2Truss self weight = 0.55 kips Tributary area = 61.25 sfTotal load = 61.25 sf x (45 + 110) lbs/sf + 0.55 kips = 10 kipsReaction force (vertical) = 10 kips ; (horizontal) = 3.1 kips

Member sizes are su�cient for Truss 2 with signi�cantly smaller loads

UNDER ASYMMETRICAL LOAD MULTIFRAME ANALYSIS

The trusses are braced by diagonal �oor and ceiling beams and act as rigid tubes under asymmetrial load.

MULTIFRAME ANALYSISAxial stress < 15 ksi = allowable stressThe truss structure is sound under asymmetrical load

TRUSSES FOR MAIN BRIDGE

Self-weight of one truss = 37.69 lbs/ft x 110 ft x 2 +22.37 lbs/ft x 297.14 ft + 48.86 lbs/ft x13ft x 2 = 15.23 kipsUniform Load = 15.23 kips/110 ft +0.45 kips(other systems) + 1.1 kips/ft (live loads) = 1.7 kips/ftUniform Load on each truss = Uniform load/2 = 0.85 kips/ft

BEAM ANALOG METHOD FOR VERIFYING CORD MEMBER SIZING

Max.moment = 1770 kips x ftTension/compression force in cords = 1770kipsxft /13 ft= 136.1 kips

Crushing: σ= P/AReq. area =136.1 kips / 15ksi = 9.07 in^2 < 10.4 in^2

Buckling: P = �^2E(I) / (kL)^2 , L = 10 ftI = 6.85 in^4 < 99.6 inch ^4

MULTIFRAME METHOD FOR VERIFYING DIAGONAL MEMBER SIZING

Maximum axial stress in cords = 136.24 kips (tension) / 134.56 kips (compression)Maximum axial stress in webs = 78.96 kips (tension) / 67.63 kips (compression) Maximum moment on diagonal bracing= 93.978 k x ft; required sectional modulus = 6.27 < 8.67 in^3

Multiframe results are consistent with hand calculations;Steel sections will not crush or buckle under given load; The structure is sound.

BASIC PARAMETERSTotal length = 110 ftTotal height = 13 ftTotal width = 10 ftLive load = 80lbs/sfSnow load = 30lbs/sf

CONCEPT

Allowable Stress (steel) = 15 ksiModulus of Elasticity (steel) = 29,000Allowable Stress (concrete) = 1.5 ksiModulus of Elasticity (glass) = 3,000k (�xity) = 1

This design was conceived as an intersection of two bridges. Two lookouts branch o� the bridge, sloping up and down on either side to provide views out onto the surroundings. They create speci�c views and invite visual dialogue with street tra�c, making the bridge both a circulation path and a gathering space. However, the use of glass and steel mesh attempts to bring a sense of lightness and transparency to the site.

2-in-1EVELYN TING, JIE ZHANG

SECONDARY STRUCTURE ANALYSIS

FLOOR SYSTEM (steel beam)Tributary Area A= 300 sfTotal Load = 20 lbs/sf x 300sf +80 lbs/sf x 300 sf = 30 kips

w = Total Load/ Length = 30 kips / 35 ft = 0.86 k/ftM = (wL^2)/8 = (0.77 k/ft x 35 ft x 35 ft) / 8= 131.7.9 k*ftReq. Section Modulus of beam A= M/∂ = 8.78 in^3 < 13.1 in^3

Tributary Area B= 50 sf

Req. Section Modulus of beam B= 0.42 in^3 < 0.486 in^3

DEFLECTION ANALYSIS MULTIFRAME ANALYSISMaximum de�ection = 3.687 in <3.7 in (allowed de�ection)Hand calculations are inaccurate as the application of the equation assumes a well braced truss whereas in actuality, diagonal bracings are compromised at the openings to allow circulation into lookout spaces.

FLOOR SYSTEM (composite slab)

The composite slab is rested between the main cords, and the tertiary beams e�ectively shorten the span of the slab, allowing the thickness of the slab to be reduced.

Concrete allowable stress = 1.5 ksiM = (wL^2)/8 = (0.8 k/ft x 10 ft x 10 ft) / 8= 10 k*ftT=C=m/d= 53.3 kips

A=C/1.5ksi = 35.5 sq in< actual area 180 sq in. The �oor system is sound.

Total load = Truss self weight + other structural systems dead load + Live load

Floor deck consists of 16 short diagonal beams and 1 long diagonal beam (counted under Truss self weight )

For the main bridge area of 1100 sf:Total Load (�oor beam) = 3.05 lbs/ft x 10 ft x 16 = 0.488 kips; distributed = 4.4 lbs/ftTotal Load (concrete decking) = 1.5 inch x (1/12) x 10ft x 150 lbs/cf = 187.5 lbs/ftTotal Load (metal decking) = 10 lbs/ft

Total Load (�oor) = 202 lbs/ft, or 20 lbs/sfThe ceiling system is estimated to weigh half of the �oor system = 101 lbs/ft, or 10 lbs/sfApproximate facade weight = 15 lbs/sf

Truss self-weight = 0.147 kips/ftOther systems’ self-weight = Floor + Ceiling + Facades = 45 lbs/sf

Total load = Dead Load + Live Load = 0.147 kips/ft + 0.45 kips/ft +1.1kips/ft ~1.7 kips/ft

LOAD ANALYSIS1. Main truss cord member Size = 8 x 8 x 3/8 inchWeight = 37.69 lbs/ftCross Sectional Area = 10.4 in^2S = 24.9 in^3, I = 99.6 in^4

2. Main truss web / secondary truss compression member

Size = 12 x 12 x 5/16 inchWeight = 48.86 lb/ftCross Section Area = 13.4 in^2S = 50.7 in^3, I = 304 in^4

Size = 5 x 5 x 3/8 inchWeight = 22.37 lbs/ftCross Sectional Area = 6.18 in^2S= 8.67 inch^3, I = 21.7 in^4

3. Secondary truss tension member Size = 2 x 2 x 1/4 inchWeight = 5.41 lbs/ftCross sectional area = 1.51 inch^2

4. Tertiary beamSize = 2 x 2 x 1/8 inchWeight = 3.05 lbs/ftS = 0.486 in^3

5. Floor systemComposite �oor system of 2.25 inch thickness ( max. thickness of concrete = 1.5 in, max. corrugation thickness of metal decking = 1.5in) Density of Concrete = 150 lbs/cubic feetWeight of Metal Decking = 1lbs/sf

6. Cladding material Glass for thermal insulationMetal mesh for architectural expression

PLAN CONNECTION DETAIL 1- FLOOR

ELEVATION

CONNECTION DETAIL 2- JOINT

BUILDING SYSTEMS

steel mesh envelope

glass cladding

secondary

1” �nishing0.75” concrete1.5” corrugated metal decktertiary beam bracing

welded steel connection

steel mesh5/8” gypsum board

primary truss

tertiary truss

30.00°

70.00°

10.00

8.00

25.00

10.00

110.

00

0.125

2.00

0.25

2.00

0.375

5.00

8.00

0.375

12.0

0

0.3125

0.75

” 1.00

”1.

50”

2.00

”

8.00

”

elevation 1/16” scale

24

1/4"=1'-0"CROSS SECTION

HSS 18x12x5/8

HSS 6x6x1/4

2-1/8” DIAMETERSTEEL CABLE

1-1/2” DIAMETER STEEL ROD

6” CONCRETE OF 3” METAL DECK

F.F.L.

+ 50'-3" A.S.L.F.F.L.

+ 49'-4" A.S.L.

+ 40'-3" A.S.L.B.O. STRUCTURE

T.O. SIDEWALK+ 20'3" A.S.L.

LONGITUDINAL SECTION1/8"=1'-0"

HSS 18x12x5/8

HSS 6x6x1/4

2-1/8” STEEL CABLE

LOCATION OF SECTION FOR AVERAGE GLOBAL MOMENT OF INERTIACALCULATION


Maximum Moment= (wL^2)/8=10153 kip-feet

w=2.5kips / linear foot

MOMENT 0

SHEAR 0

143 kips 143 kips

David Miranowski David Moses

LOADING

DEAD LOADstructural steel HSS 6x6x1/4 4122.0 lbs

HSS 6x2x1/4 7424.0 lbsHSS 6x9x1/4 5306.0 lbs

HSS 18x12x5/8 13019.0 lbs

cable length 125.0 feetweight per foot 9.5 pounds per foot

weight 1186.3 pounds

lightweight concrete volume 565.0 cubic feetweight by volume 100.0 pounds per cubic foot


skylight glass volume 174.0 cubic feetweight by volume 150.0 pounds per cubic foot


cladding allowance weight 52200.0 pounds

total distributed dead load 165.9 kips 737.8

DISTRIBUTED LIVE LOADcarried at roof weight per unit area 30.0 pounds per square foot

area 1391.0 square feetload allowance 41730.0 pounds

carried at floor weight per unit area 80.0 pounds per square footarea 1391.0 square feet

load allowance 111280.0 pounds

load allowance 111.3 kips 495.0

imperial units metric unitstotal span = 113.0 feet 34.4 meters

linear load = 2.5 kips/feet 35.8load segments = 11.0 segments

total load = 277.1 kips 1232.8load per segment = 25.2 kips 112.1

segment length = 10.3 feet 3.1 meters

kN

kN

kN/meters

kNkN

LOADING

PLAN1:192

VASSAR STREET

BRAIN AND COGNITIVE SCIENCES BUILDING BUILDING 36

ASYMETRIC LIVE LOADtotal carried by floor weight per unit area 110.0 pounds per square foot

area 565.0 square feetload allowance 62.2 kips

load length 56.5 feet ½ the total span

linear load = 1.1 kips/feet 4.9


PRIMARY STRUCTURE (LONGITUDINAL SECTION)

MAXIMUM MOMENTimperial units metric units

linear load (w) = 1.1 kips/feetload length (L) = 56.5 ft

109.7 kip*ft

T=C=M/d FORCE COUPLEimperial units metric units

Moment(M)= 109.7 kip*ftDepth(d) = 1.0 feet guess

Axial Load(T,C)= 109.7 kips

AXIAL STRESSimperial units metric units

maximum axial load(F) = 109.7 kips 488.1 (from force polygon)15.0 kips/square inch (safety factor included)

number of compression blocks = 1.0 membersrequired cross sectional area(A) = 7.3 square inches 4719.7 square mm in compression and tension blocks

actual area of tube wall = 10.1 square inches

kN

Mmax=(wL^2)/32

Maximum Moment (Mmax) =

σ=F/A

kNsteel allowable stress(σ) =

A=F/σ

DEFLECTIONCALCULATING CENTROID

3.13.1

22.087.3 in Distance between Column Center and Cable Center67.9 in location of centroid

REQUIRED MOMENT OF INERTIA

applied live load (w) = 0.1 K/inLength (L) = 1320.0 in

29000.03.7 in

required moment of inertia (I)= 33,459

AVERAGE GLOBAL MOMENT OF INERTIA

3.13.1

22.067.9 in67.9 in19.4 in

global moment of inertia (I)= 37,201

MAXIMUM ALLOWED DEFLECTION

Length (L)= 1320.0 in3.7 in

y=A3Y3/(A1+A2+A3) Area A1= in2

Area A2= in2

Area A3= in2

Y3=

y=

Ireq.d≥(5wL^4)/(384Edeltamax)

modulus of elasticitysteel (E) = K/in2

Max Deflection (∆max ) =

in4

IGLOBAL=∑Aidi2 area A1= in2

area A2= in2

area A3= in2

distance from centroid (d1)=distance from centroid (d2)=distance from centroid (d3)=

in4

∆max≤L/360Max Deflection (∆max ) =

ASYMETRICAL LOADING DEFLECTION

SECONDARY STRUCTURE - CROSS SECTION


CABLE- AXIAL STRESSimperial units metric units

maximum axial stress = 490.0 kips 2179.6 (from force polygon)number of cables = 2.0 cables

working load per cable = 245.0 kips 1089.8cable safety factor = 2.2

cable breaking strength = 269.5 tons 2397.6 Class B cable diameter 2 1/ 8 inches FORM and FORCES p. 4754.0 mm

imperial units metric unitstotal max axial load(F) = 424.0 kips 1886.0 (from force polygon)

15.0 kips/square inch (safety factor included)number of members = 1.0 members

required cross sectional area(A) = 28.3 square inches 18236.5 square mmarea per member = 28.3 square inches 18236.5 square mm HSS Steel Tube 18 x 12 x 5/8 Inch STI HSS Properties Table

457 x 305 x 16 mm

imperial units metric unitstotal max axial load(P) = 424.0 kips 1886.0 (from force polygon)

modulus of elasticity(E) = 29000.0 kips/ square inchbuckling length(L) = 123.3 inches 3131.1 mm

fixity (k) = 1.0 fixed/fixedbuckling safety factor = 3.0

moment of inertia(I) = 212.2 inches^4 88309640.3 mm^4

SECONDARY STRUCTURE (CROSS SECTION)

imperial units metric unitsmaximum axial load(F) = 22.7 kips 101.0 (from force polygon)



152 x 152 x 6 mm



fixity (k) = 1.5 fixed/pinbuckling safety factor = 3.0

moment of inertia(I) = 25.4 inches^4 10590753.2 Mm^4


15.0 kips/square inch (safety factor included)number of rods = 1.0 element

cross sectional area(A)= 1.3 square inches 838.7 square mmrod diameter = 1.3 inches 32.7 mm Steel rod diameter 1 1/ 2 Inch

38.1 mm

σ=F/A

kN

kN

kN

σ=F/ACOMPRESSION – AXIAL

STRESS


A=F/σ

P=πEI/(kL)^2COMPRESSION –

BUCKLING

kN

I=(P(kL)^2/πE)*3

σ=F/ACOMPRESSION STRUTS-

AXIAL STRESS


A=F/σ


BUCKLING

kN

I=(P(kL)^2/πE)*3

σ=F/ATENSION ROD- AXIAL

STRESS


A=F/σD=2√(A/π)









457 x 305 x 16 mm









152 x 152 x 6 mm








38.1 mm

σ=F/A

kN

kN

kN


STRESS


A=F/σ


BUCKLING

kN

I=(P(kL)^2/πE)*3


AXIAL STRESS


A=F/σ


BUCKLING

kN

I=(P(kL)^2/πE)*3


STRESS


A=F/σD=2√(A/π)

PRIMARY STRUCTURE - LONGITUDINAL SECTION

EXPLODED AXONOMETRIC


11 feet of bridge lengthsuppored by each segment

27.5 kips applied loadA B

1"=24 KIPS

b

c

a

1

22.7 KIPS (T)

26.6 KIPS (C)26.6 KIPS (C)

13.75 KIPS 13.75 KIPS

27.5 KIPS

1

C


oblique plane22.7 kips per load

o

245 KIPS

k

j

i

h

g

f

e

d

c

b

1"=48 KIPS

a

212 KIPS

KJIHGFECBA D

FAT BELLY

INTERIOR VIEW

UNDERBELLY

CROSS SECTION1:48

LONGITUDINAL SECTION1:96

M=(wL^2)/32MOMENT DIAGRAM

w=1.1 kips / foot

67.8

7 "

19.4

1 "

87.2

8 "

A1

A1, A2 3.1 sq.in

A2

=

=

A3

A3

d1, d2

d3

y

22.0 sq.in

arbitrary x axis, for finding centroid

arbitrary y axis, for finding centroid

25


HSS 18x12x5/8

HSS 6x6x1/4

2-1/8” DIAMETERSTEEL CABLE

1-1/2” DIAMETER STEEL ROD


F.F.L.

+ 50'-3" A.S.L.F.F.L.

+ 49'-4" A.S.L.

+ 40'-3" A.S.L.B.O. STRUCTURE

T.O. SIDEWALK+ 20'3" A.S.L.

LONGITUDINAL SECTION1/8"=1'-0"

HSS 18x12x5/8

HSS 6x6x1/4

2-1/8” STEEL CABLE

LOCATION OF SECTION FOR AVERAGE GLOBAL MOMENT OF INERTIACALCULATION


Maximum Moment= (wL^2)/8=10153 kip-feet


MOMENT 0

SHEAR 0

143 kips 143 kips

David Miranowski David Moses

LOADING

DEAD LOADstructural steel HSS 6x6x1/4 4122.0 lbs

HSS 6x2x1/4 7424.0 lbsHSS 6x9x1/4 5306.0 lbs

HSS 18x12x5/8 13019.0 lbs

cable length 125.0 feetweight per foot 9.5 pounds per foot


lightweight concrete volume 565.0 cubic feetweight by volume 100.0 pounds per cubic foot


skylight glass volume 174.0 cubic feetweight by volume 150.0 pounds per cubic foot


cladding allowance weight 52200.0 pounds

total distributed dead load 165.9 kips 737.8

DISTRIBUTED LIVE LOADcarried at roof weight per unit area 30.0 pounds per square foot

area 1391.0 square feetload allowance 41730.0 pounds

carried at floor weight per unit area 80.0 pounds per square footarea 1391.0 square feet

load allowance 111280.0 pounds

load allowance 111.3 kips 495.0


linear load = 2.5 kips/feet 35.8load segments = 11.0 segments

total load = 277.1 kips 1232.8load per segment = 25.2 kips 112.1

segment length = 10.3 feet 3.1 meters

kN

kN

kN/meters

kNkN

LOADING

PLAN1:192

VASSAR STREET

BRAIN AND COGNITIVE SCIENCES BUILDING BUILDING 36

ASYMETRIC LIVE LOADtotal carried by floor weight per unit area 110.0 pounds per square foot

area 565.0 square feetload allowance 62.2 kips

load length 56.5 feet ½ the total span

linear load = 1.1 kips/feet 4.9



MAXIMUM MOMENTimperial units metric units

linear load (w) = 1.1 kips/feetload length (L) = 56.5 ft

109.7 kip*ft

T=C=M/d FORCE COUPLEimperial units metric units

Moment(M)= 109.7 kip*ftDepth(d) = 1.0 feet guess

Axial Load(T,C)= 109.7 kips

AXIAL STRESSimperial units metric units

maximum axial load(F) = 109.7 kips 488.1 (from force polygon)15.0 kips/square inch (safety factor included)

number of compression blocks = 1.0 membersrequired cross sectional area(A) = 7.3 square inches 4719.7 square mm in compression and tension blocks

actual area of tube wall = 10.1 square inches

kN

Mmax=(wL^2)/32

Maximum Moment (Mmax) =

σ=F/A


A=F/σ

DEFLECTIONCALCULATING CENTROID

3.13.1

22.087.3 in Distance between Column Center and Cable Center67.9 in location of centroid

REQUIRED MOMENT OF INERTIA

applied live load (w) = 0.1 K/inLength (L) = 1320.0 in

29000.03.7 in

required moment of inertia (I)= 33,459

AVERAGE GLOBAL MOMENT OF INERTIA

3.13.1

22.067.9 in67.9 in19.4 in

global moment of inertia (I)= 37,201

MAXIMUM ALLOWED DEFLECTION

Length (L)= 1320.0 in3.7 in

y=A3Y3/(A1+A2+A3) Area A1= in2

Area A2= in2

Area A3= in2

Y3=

y=

Ireq.d≥(5wL^4)/(384Edeltamax)

modulus of elasticitysteel (E) = K/in2

Max Deflection (∆max ) =

in4

IGLOBAL=∑Aidi2 area A1= in2

area A2= in2

area A3= in2

distance from centroid (d1)=distance from centroid (d2)=distance from centroid (d3)=

in4

∆max≤L/360Max Deflection (∆max ) =

ASYMETRICAL LOADING DEFLECTION

SECONDARY STRUCTURE - CROSS SECTION









457 x 305 x 16 mm









152 x 152 x 6 mm








38.1 mm

σ=F/A

kN

kN

kN


STRESS


A=F/σ


BUCKLING

kN

I=(P(kL)^2/πE)*3


AXIAL STRESS


A=F/σ


BUCKLING

kN

I=(P(kL)^2/πE)*3


STRESS


A=F/σD=2√(A/π)









457 x 305 x 16 mm









152 x 152 x 6 mm








38.1 mm

σ=F/A

kN

kN

kN


STRESS


A=F/σ


BUCKLING

kN

I=(P(kL)^2/πE)*3


AXIAL STRESS


A=F/σ


BUCKLING

kN

I=(P(kL)^2/πE)*3


STRESS


A=F/σD=2√(A/π)

PRIMARY STRUCTURE - LONGITUDINAL SECTION

EXPLODED AXONOMETRIC


11 feet of bridge lengthsuppored by each segment

27.5 kips applied loadA B

1"=24 KIPS

b

c

a

1

22.7 KIPS (T)

26.6 KIPS (C)26.6 KIPS (C)

13.75 KIPS 13.75 KIPS

27.5 KIPS

1

C


oblique plane22.7 kips per load

o

245 KIPS

k

j

i

h

g

f

e

d

c

b

1"=48 KIPS

a

212 KIPS

KJIHGFECBA D

FAT BELLY

INTERIOR VIEW

UNDERBELLY

CROSS SECTION1:48

LONGITUDINAL SECTION1:96

M=(wL^2)/32MOMENT DIAGRAM

w=1.1 kips / foot

67.8

7 "

19.4

1 "

87.2

8 "

A1

A1, A2 3.1 sq.in

A2

=

=

A3

A3

d1, d2

d3

y

22.0 sq.in

arbitrary x axis, for finding centroid

arbitrary y axis, for finding centroid

26

BEOMKI LEE / SHIYU WEI4.463 Building Structural Systems II (Fall 2012)Professor: J.A. Ochsendorf / TA: Caitlin Mueller

Sky Illusion

Snow Load 30 lb/ft

80 lb/ft

42 lb/ft

20 lb/ft

2 lb/ft

58 lb/ft

232 lb/ft

0.4 kN/m

1.1 kN/m

0.6 kN/m

0.3 kN/m

0.03 kN/m

0.8 kN/m

3.4 kN/m

249 K 1106 kN

People Load

Steel Arch (x4)

Steel Struts (x10)


Total Distributed Load

Total Load BRIDGE AREA = 107 ft * 10 ft

12.5 K 55.6 kNPoint Loads

Deck

LOADS_

FORCE POLYGON_

MEMBER SIZING_

Shear Diagram

Maximum Moment = 1818 K*ft

12.5K55.6 kN

55.6 kN

55.6 kN

12.5K 12.5K12.5K 12.5K12.5K12.5K12.5K12.5K

606 K*ft

-606 K*ft

485 K*ft

-485 K*ft

364 K*ft

-364 K*ft

242 K*ft

-242 K*ft

121K*ft0 K*ft

-121 K*ft9.7 ft

32 m

278 kN

278 kN

107 ft K 0

62.5 K 62.5 K

Moment Diagram

T = C = M/d; Greater depth of the beam implies smaller forces on the top and bottom member, suggesting a beam shape that is thick in the middle

CONCEPT_ TransparencyTransparencyThe gray, monolithic concrete buildings on Vassar street dominate the view of the people passing through. Therefore, we strived for a design that had minimal visual impact on the site. Also, since the Stata Center already has a very strong presence on the street, a simple bridge would not interfere with the view so highly sought after by tourists and also would not clutter up an already packed street.

1/4 inch = 1 kipForce in vertical strut = 9.7K = 46kN

= Checking for Uneven Loading Conditions

ω = 30lb/ft + 80 lb/ft = 110 lb/ft = 0.11 k/ftM = �L2 / 32M = [(0.11k/ft)(107.2ft)2]/32 = 474 k*inσ�= 15 ksi = M/S σ = 15ksi = 474 k*in/SS = 31.6 in3 = 517 cm3

= Check for Buckling over L/2

L/2 = 53.6 ftE = 29,000 ksiP = � 2EI/(kL)k = 1 (pin-pin condition)158K = � 2(29,000ksi)I / (1(53.6ft))Ireq

= 228in4 = 9490 cm4 --> 684in4 = 28470 cm4 (safety factor)

= Checking for Max Allowable Stress

Largest force = 158KStress = force/area15 ksi = 158K / areaArea

req = 158K / 15ksi =10.5in2 = 67.7 cm2

Choose 16”x12”x3/8” Rectangular HSS 40.6cm x 30.5cm x 0.9cmS

x = 87.7in3 S

y = 75.3in3

Ix = 702 in4 I

y = 452 in4

12.5K

9.7 ft

3 m

1

62.5K 62.5K

2 3 4 5 6 7 8 109 11

KA B C D E F I J

L

G H

12.5K 12.5K 12.5K

12.5K

12.5K

12.5K

12.5K

12.5K

12.5K

12.5K12.5K

12.5K

12.5K

12.5K12.5K12.5K 12.5K 12.5K12.5K

= Check for Max Allowable Stress

Largest force = 9.7 K15 ksi = 9.7 K/Area

req

Areareq

= 9.7 K/15ksi = 0.65 in2

Choose member 4”x3”x3/16” 10.2cm x 7.6cmx 0.5cmIx = 4.9 in4

Iy

= 3.2 in4

= Check for Buckling

E = 29,000 ksiP = � 2EI/(kL)2

9.7 K = � 2(29,000ksi)I/(1(144in))2

Ireq

= 0.97 in4 = 40.4 cm4 --> 2.91in4 = 121 cm4 (safety factor)


Largest Force = 164.3KArea

req = 164.3K / 15ksi = 10.9 in2

Choose 7”x7”x1/2” Square HSS 17.8cm x 17.8cm x 1.3cm

J

K

G

H

I

F

E

D

C

B

A158K703K

164K 730K

12

3

4

56

789

10

11

PRIMARY COMPRESSION MEMBER SIZING

PRIMARY TENSION MEMBER SIZING

SECONDARY COMPRESSION MEMBER SIZING

Exploded Axon

Render ViewInterior Render View Render View

Render View

9 ft


Steel Structure for Cladding

Concrete Deck

Tension Cable

Primary Tension Member

Secondary Compression Member

Primary Compression Member

Cross Section

Elevation0m 6m

0m 1.5m

Site Plan

Building 46

Building 36 Stata Center

Vassar Street

Connection Detail

PARALLEL AXIS THEOREM_

I = I + A d 2 I = 2*[702 in4 + 18.7 in2 *(23.1 in)2] + 2*[80.5 in4 + 11.6 in2 *(33.6 in)2 ] I = 47713.9 in4

i

i

i

DEFLECTION OF STRUCTURE_

allowed

= L/360 < 3.7 in

max = (5ωL4) / 384*EI

max

= (5*(0.09 K)(1320in)4) / (384*(29000 K/in2)(47713.9 in4))

max = 2.57 in

A1= 18.7 in2

I1

= 702 in4

d1= 23.1 in

A2= 18.7 in2

I2

= 702 in4

d2= 23.1 in

A3= 11.6 in2

I3

= 80.5 in4

d3= 33.6 in

A4= 11.6 in2

I4

= 80.5 in4

d4= 33.6 in

23.1 in

33.6 in

Axis

27

BEOMKI LEE / SHIYU WEI4.463 Building Structural Systems II (Fall 2012)Professor: J.A. Ochsendorf / TA: Caitlin Mueller

Sky Illusion

Snow Load 30 lb/ft

80 lb/ft

42 lb/ft

20 lb/ft

2 lb/ft

58 lb/ft

232 lb/ft

0.4 kN/m

1.1 kN/m

0.6 kN/m

0.3 kN/m

0.03 kN/m

0.8 kN/m

3.4 kN/m

249 K 1106 kN

People Load

Steel Arch (x4)

Steel Struts (x10)


Total Distributed Load

Total Load BRIDGE AREA = 107 ft * 10 ft

12.5 K 55.6 kNPoint Loads

Deck

LOADS_

FORCE POLYGON_

MEMBER SIZING_

Shear Diagram

Maximum Moment = 1818 K*ft

12.5K55.6 kN

55.6 kN

55.6 kN

12.5K 12.5K12.5K 12.5K12.5K12.5K12.5K12.5K

606 K*ft

-606 K*ft

485 K*ft

-485 K*ft

364 K*ft

-364 K*ft

242 K*ft

-242 K*ft

121K*ft0 K*ft

-121 K*ft9.7 ft

32 m

278 kN

278 kN

107 ft K 0

62.5 K 62.5 K

Moment Diagram

T = C = M/d; Greater depth of the beam implies smaller forces on the top and bottom member, suggesting a beam shape that is thick in the middle

CONCEPT_ TransparencyTransparencyThe gray, monolithic concrete buildings on Vassar street dominate the view of the people passing through. Therefore, we strived for a design that had minimal visual impact on the site. Also, since the Stata Center already has a very strong presence on the street, a simple bridge would not interfere with the view so highly sought after by tourists and also would not clutter up an already packed street.

1/4 inch = 1 kipForce in vertical strut = 9.7K = 46kN

= Checking for Uneven Loading Conditions

ω = 30lb/ft + 80 lb/ft = 110 lb/ft = 0.11 k/ftM = �L2 / 32M = [(0.11k/ft)(107.2ft)2]/32 = 474 k*inσ�= 15 ksi = M/S σ = 15ksi = 474 k*in/SS = 31.6 in3 = 517 cm3

= Check for Buckling over L/2

L/2 = 53.6 ftE = 29,000 ksiP = � 2EI/(kL)k = 1 (pin-pin condition)158K = � 2(29,000ksi)I / (1(53.6ft))Ireq

= 228in4 = 9490 cm4 --> 684in4 = 28470 cm4 (safety factor)


Largest force = 158KStress = force/area15 ksi = 158K / areaArea

req = 158K / 15ksi =10.5in2 = 67.7 cm2

Choose 16”x12”x3/8” Rectangular HSS 40.6cm x 30.5cm x 0.9cmS

x = 87.7in3 S

y = 75.3in3

Ix = 702 in4 I

y = 452 in4

12.5K

9.7 ft

3 m

1

62.5K 62.5K

2 3 4 5 6 7 8 109 11

KA B C D E F I J

L

G H

12.5K 12.5K 12.5K

12.5K

12.5K

12.5K

12.5K

12.5K

12.5K

12.5K12.5K

12.5K

12.5K

12.5K12.5K12.5K 12.5K 12.5K12.5K

= Check for Max Allowable Stress

Largest force = 9.7 K15 ksi = 9.7 K/Area

req

Areareq

= 9.7 K/15ksi = 0.65 in2

Choose member 4”x3”x3/16” 10.2cm x 7.6cmx 0.5cmIx = 4.9 in4

Iy

= 3.2 in4

= Check for Buckling

E = 29,000 ksiP = � 2EI/(kL)2

9.7 K = � 2(29,000ksi)I/(1(144in))2

Ireq

= 0.97 in4 = 40.4 cm4 --> 2.91in4 = 121 cm4 (safety factor)


Largest Force = 164.3KArea

req = 164.3K / 15ksi = 10.9 in2

Choose 7”x7”x1/2” Square HSS 17.8cm x 17.8cm x 1.3cm

J

K

G

H

I

F

E

D

C

B

A158K703K

164K 730K

12

3

4

56

789

10

11

PRIMARY COMPRESSION MEMBER SIZING

PRIMARY TENSION MEMBER SIZING

SECONDARY COMPRESSION MEMBER SIZING

Exploded Axon

Render ViewInterior Render View Render View

Render View

9 ft


Steel Structure for Cladding

Concrete Deck

Tension Cable

Primary Tension Member

Secondary Compression Member

Primary Compression Member

Cross Section

Elevation0m 6m

0m 1.5m

Site Plan

Building 46

Building 36 Stata Center

Vassar Street

Connection Detail

PARALLEL AXIS THEOREM_

I = I + A d 2 I = 2*[702 in4 + 18.7 in2 *(23.1 in)2] + 2*[80.5 in4 + 11.6 in2 *(33.6 in)2 ] I = 47713.9 in4

i

i

i

DEFLECTION OF STRUCTURE_

allowed

= L/360 < 3.7 in

max = (5ωL4) / 384*EI

max

= (5*(0.09 K)(1320in)4) / (384*(29000 K/in2)(47713.9 in4))

max = 2.57 in

A1= 18.7 in2

I1

= 702 in4

d1= 23.1 in

A2= 18.7 in2

I2

= 702 in4

d2= 23.1 in

A3= 11.6 in2

I3

= 80.5 in4

d3= 33.6 in

A4= 11.6 in2

I4

= 80.5 in4

d4= 33.6 in

23.1 in

33.6 in

Axis

28

H

11.79k

Z

E

68.95k

A

68.95k

11.79k

B

Mmax = wL^2 / 8 = (2k/ft)(15ft)^2 / 8 = 56.25 k-ft = 675 k-inσ = My/I = M/SSreq’d = 45 in^3

If solid and rectangular, then bh^2/6 = 45;Can use W12x35 (flange 12.5" deep / 6.56" wide)

G

B

Q

Q

15.0

1

68.95k23.58k

11.79k

11.79k

3.66k

6k

Bottom tied arches support deck and transfersload to bottom chord of truss.

Max internal force 7.46k so 0.5 sq in cross section neededHorizontal force 1.4k need tie of 0.1 sq in steel

Asymmetrical loading:Moment in arch: Mmax = wL^2 / 32= (80 psf)(18.33ft)(15ft)^2 / 32 = 10311 lb-ft = 123.7k-in15ksi = M/SSreq’d = 8.25 in^3

Max internal force 13.4k so 0.9 sq inHorizontal force 6k need tie of 0.4 sq in steel

Asymmetrical loading:Moment in arch: Mmax = wL^2 / 32= (130psf)(18.33ft)(15ft)^2 / 32 = 16755 lb-ft = 201k-inσ = My/I = M/SSreq’d = 13.4 in^3

3.66k

30.64k30.64k

U

F

116.07k

a

3.66k

Dominant Loads:

Top Chord C-T / D-U: 301.94k C 20 sq in or 10 sq in each sideBottom Chord K-V: 281.47k T 18.75 sq in or 9.4 sq each sideVertical G-Z: 173.85k C 11.6 sq in or 5.8 sq in each sideDiagonal Y-Z: 208.41k T 13.9 sq in or 6.9 sq in each side

Buckling check:Top chord C-T: Pcr = π^2 EI / (kL)^2 safety factor 3 * 301.94k = π^2 (30000 ksi) I / (0.5 * 220.33in)^2 Ireq = 37.1 in^4

Vertical G-Z: Pcr = π^2 EI / (kL)^2 safety factor 3 * 173.85k = π^2 (30000 ksi) I / (0.5 * 180in)^2 Ireq = 14.3 in^4

Top Chord C-T / D-U: 296.23k C 19.75 sq in or 10 sq in each sideBottom Chord K-V: 281.47k T 18.75 sq in or 9.4 sq each sideVertical G-Z: 173.85k C 11.6 sq in or 5.8 sq in each sideDiagonal Y-Z: 208.41k T 13.9 sq in or 6.9 sq in each side

Top Chord C-T / D-U: 301.94k C 20 sq in or 10 sq in each sideBottom Chord K-V: 268.39k T 17.9 sq in or 9 sq each sideVertical O-I,/ G-Z: 155.94k C 10.4 sq in or 5.2 sq in each sideDiagonal O-P / Y-Z: 194.79k T 13 sq in or 6.5 sq in each side

6k6k

X

23.58k

44.79k

24.16k11.79k

R1 + R2 = 346.5k

Moment equilibirum around a: (18.33*23.58k) + (18.33*2*23.58) + ... + (18.33*6*68.95k) = (18.33*6*R2)R2 = 218.64k, R1 = 127.86k

E

I

YR

C DE

2k/ft

F

S V

T UW

N

D

110.0018.33

J

TY

173.85k

R1 = 127.86k

b

AD

O

C

C

O

DB EA

WR

R2 = 218.64k

24.0

1

6k

23.58k

44.79k44.79k

6k

V

24.16k24.16k

6k Dead load distributed evenly, live load on half.

Dead load and live load distributed evenly.

Z

ML

P

O KJ

H

B

GS

I

For 18.33' segment (distance between truss joints), supporting roof load on top and pedestrian load on bottom.

Distributed load for 18' span

A

Approaching the center, the arch supports become shallow like beams.

18.85k

18.85k18.85k 18.85k 18.85k

18.85k

18.85k

30.64k30.64k

X

9.00

30.64k

123.76k 123.76k

NM

L

3.66k

P

C

O

3.66k

K

68.95k

24.16k

3.66k

D

E

1k = 25"

A

WUT

S

Q

P

F

EM

D

I

BA

N, O

K

J

G

H, ZX

Y

C

LE

F

D

A

B

H, Z

G

CK

M

I

N, O

B

J

L

A

U

X

C

Q

S

V

W

E

P, YR

R

T

B

C

VD

Assumed dead load:20 psf steel deck and horizontal supports25 psf 2" concrete topping20 psf steel truss35 psf cladding100 psf total

Assumed live load:80 psf pedestrian30 psf snow/rain

Total distributed load 210 psf

...split so that top chords take 80 psf and bottom 130 psf

x

y

4.75"

Sample Section: Truss element C-T in compression

1.5"

1"

Aa = 9 sq in Ya = 3.25" AaYa = 29.25in^3Ab = 8 sq in Yb = 6.75" AbYb = 54in^3 total 83.25in^3 / 17in^2 = 4.90" to centroid

Ia = (1.5)(6)^3 / 12 = 27 d = 3.25 - 4.90 = -1.65 Ad = (9)(-1.65)^2 = 24.5Ib = (8)(1)^3 / 12 = 0.67 d = 6.75 - 4.90 = 1.75 Ad = (8)(1.85)^2 = 27.38Iy = 79.55 in^4

Ix = (6)(1.5)^3 / 12 + (1)(8)^3 / 12 = 44.35 in^4

6"

8"

Estimate deflection: Allowed 3.7" deflection minimum3.7" = 5wL^4 / (384*E*I)LL = 110lb/sqft; 0.09k/inI req'd > 5(0.09k/in)(1320in)^4 / 384(30000k/sqin)(3.7in)I req'd > 32000 in^4

Taking just the abstracted four chords of the truss (two top, two bottom):

I = Σ Aidi^2 = 4 * 10 sqin * (90 in)^2 = 324000 in^4, an order of magnitude above what is necessary

90 in

10 sq in ea

29

H

11.79k

Z

E

68.95k

A

68.95k

11.79k

B

Mmax = wL^2 / 8 = (2k/ft)(15ft)^2 / 8 = 56.25 k-ft = 675 k-inσ = My/I = M/SSreq’d = 45 in^3

If solid and rectangular, then bh^2/6 = 45;Can use W12x35 (flange 12.5" deep / 6.56" wide)

G

B

Q

Q

15.0

1

68.95k23.58k

11.79k

11.79k

3.66k

6k

Bottom tied arches support deck and transfersload to bottom chord of truss.

Max internal force 7.46k so 0.5 sq in cross section neededHorizontal force 1.4k need tie of 0.1 sq in steel

Asymmetrical loading:Moment in arch: Mmax = wL^2 / 32= (80 psf)(18.33ft)(15ft)^2 / 32 = 10311 lb-ft = 123.7k-in15ksi = M/SSreq’d = 8.25 in^3

Max internal force 13.4k so 0.9 sq inHorizontal force 6k need tie of 0.4 sq in steel

Asymmetrical loading:Moment in arch: Mmax = wL^2 / 32= (130psf)(18.33ft)(15ft)^2 / 32 = 16755 lb-ft = 201k-inσ = My/I = M/SSreq’d = 13.4 in^3

3.66k

30.64k30.64k

U

F

116.07k

a

3.66k

Dominant Loads:

Top Chord C-T / D-U: 301.94k C 20 sq in or 10 sq in each sideBottom Chord K-V: 281.47k T 18.75 sq in or 9.4 sq each sideVertical G-Z: 173.85k C 11.6 sq in or 5.8 sq in each sideDiagonal Y-Z: 208.41k T 13.9 sq in or 6.9 sq in each side

Buckling check:Top chord C-T: Pcr = π^2 EI / (kL)^2 safety factor 3 * 301.94k = π^2 (30000 ksi) I / (0.5 * 220.33in)^2 Ireq = 37.1 in^4

Vertical G-Z: Pcr = π^2 EI / (kL)^2 safety factor 3 * 173.85k = π^2 (30000 ksi) I / (0.5 * 180in)^2 Ireq = 14.3 in^4

Top Chord C-T / D-U: 296.23k C 19.75 sq in or 10 sq in each sideBottom Chord K-V: 281.47k T 18.75 sq in or 9.4 sq each sideVertical G-Z: 173.85k C 11.6 sq in or 5.8 sq in each sideDiagonal Y-Z: 208.41k T 13.9 sq in or 6.9 sq in each side

Top Chord C-T / D-U: 301.94k C 20 sq in or 10 sq in each sideBottom Chord K-V: 268.39k T 17.9 sq in or 9 sq each sideVertical O-I,/ G-Z: 155.94k C 10.4 sq in or 5.2 sq in each sideDiagonal O-P / Y-Z: 194.79k T 13 sq in or 6.5 sq in each side

6k6k

X

23.58k

44.79k

24.16k11.79k

R1 + R2 = 346.5k

Moment equilibirum around a: (18.33*23.58k) + (18.33*2*23.58) + ... + (18.33*6*68.95k) = (18.33*6*R2)R2 = 218.64k, R1 = 127.86k

E

I

YR

C DE

2k/ft

F

S V

T UW

N

D

110.0018.33

J

TY

173.85k

R1 = 127.86k

b

AD

O

C

C

O

DB EA

WR

R2 = 218.64k

24.0

1

6k

23.58k

44.79k44.79k

6k

V

24.16k24.16k

6k Dead load distributed evenly, live load on half.

Dead load and live load distributed evenly.

Z

ML

P

O KJ

H

B

GS

I

For 18.33' segment (distance between truss joints), supporting roof load on top and pedestrian load on bottom.

Distributed load for 18' span

A

Approaching the center, the arch supports become shallow like beams.

18.85k

18.85k18.85k 18.85k 18.85k

18.85k

18.85k

30.64k30.64k

X

9.00

30.64k

123.76k 123.76k

NM

L

3.66k

P

C

O

3.66k

K

68.95k

24.16k

3.66k

D

E

1k = 25"

A

WUT

S

Q

P

F

EM

D

I

BA

N, O

K

J

G

H, ZX

Y

C

LE

F

D

A

B

H, Z

G

CK

M

I

N, O

B

J

L

A

U

X

C

Q

S

V

W

E

P, YR

R

T

B

C

VD

Assumed dead load:20 psf steel deck and horizontal supports25 psf 2" concrete topping20 psf steel truss35 psf cladding100 psf total

Assumed live load:80 psf pedestrian30 psf snow/rain

Total distributed load 210 psf

...split so that top chords take 80 psf and bottom 130 psf

x

y

4.75"

Sample Section: Truss element C-T in compression

1.5"

1"

Aa = 9 sq in Ya = 3.25" AaYa = 29.25in^3Ab = 8 sq in Yb = 6.75" AbYb = 54in^3 total 83.25in^3 / 17in^2 = 4.90" to centroid

Ia = (1.5)(6)^3 / 12 = 27 d = 3.25 - 4.90 = -1.65 Ad = (9)(-1.65)^2 = 24.5Ib = (8)(1)^3 / 12 = 0.67 d = 6.75 - 4.90 = 1.75 Ad = (8)(1.85)^2 = 27.38Iy = 79.55 in^4

Ix = (6)(1.5)^3 / 12 + (1)(8)^3 / 12 = 44.35 in^4

6"

8"

Estimate deflection: Allowed 3.7" deflection minimum3.7" = 5wL^4 / (384*E*I)LL = 110lb/sqft; 0.09k/inI req'd > 5(0.09k/in)(1320in)^4 / 384(30000k/sqin)(3.7in)I req'd > 32000 in^4

Taking just the abstracted four chords of the truss (two top, two bottom):

I = Σ Aidi^2 = 4 * 10 sqin * (90 in)^2 = 324000 in^4, an order of magnitude above what is necessary

90 in

10 sq in ea

30

60 cm2 Hollow Steel Arch Tension Tie

5 cm Thick Reinforced Concrete Deck

22 mm Diameter Steel Cable

25.4 cm Diameter 22mm Thick Hollow Steel Arch

20 cm deep I-BeamsCompression Flange: 18 cm2

Tension Flagne: 20 cm2

Duoble-Pane Low-E Glass

Insulated Panels

NETWORK NODE Precast Concrete Deck (Local Bending)

Deck Hangers (Tension)

Lattice Members (Bending)

Arch Sized by Evenly Distributed Loads (Compression)

Local Moment

Load in tributary area Compression/Tension Concrete Thickness

WL2

8

(45872N +18933N) / 3.929m = 16494 N/m

T=C=MD

(3.9m)2(16494 N/m)

31.8 kN-m 637 kN=5 cm

= 31.8 kN-m8

σFA

= AFσ

= = = =637 kN

.06 m2 .06 m2

3.05 m2.24 cmx100

9308 kN/m2

Steel thickness

σFA

= AFσ

= = = =637 kN

.006 m2 .006 m2

3.05 m 2 mm steel bottom

x1000103421 kN/m2

Tension in CableCross sectional cable area

AFσ

= = =39 kN

x10000 cm2/m2 = 103421 kN/m2

11.9 m2 (46 kN +19 kN)

= 38.7 kN .0003 m2 3.75 cm2 = 1.1cmradius

Tributary vertical load on deck

resultant angular forcecos(33.23o)

2

Loads Moment as a �xed beam Force in tension and compression of �anges

Cross sectional area of tension and compression �anges

WL2

16

= .0017 m2 186 kN103421 kN/m2

= 37.2 kN-m(2.55 kN/m) (15.3 m)2

1637.2 kN-m

= 186 kN20 cm

Lattice member max tributary area (measured with Rhino model) = 17.8 m2

Length of lattice member= 15.3 m17.8 m2 (1.4kN + 0.7 kN) = 39 kN39 kN / 15.3m = 2.55 kN/m

Total tributary load of member:Linear load of Lattice member:

AFσ

= = = x10000 = 68.67 cm2 cross section710 kN

.007 m2103421 kN/m2

Total deck load in plane of one arch: (Tension hanger load) x 7

Total vertical roof load and arch self weigth on one arch: ((32.1 kN x 14 roof ) + (17.6kN x 14 arch) / 2 = 348 kNAngle of Vertical load to plane of arch: 33.23o

(38.7 kN)(7) = 271 kN= = 417 kNcos(33.23o) resultant angular

force

Total vertical loads

Total Planar loads =

Force along each point = 688 kN / 7 = 98.3 kN

271kN + 417 kN = 688 kN

348 kN98 kN

98 kN

98 kN

98 kN

98 kN

98 kN

710 kN

Required Cross sectional Area

98 kN98 kN98 kN98 kN98 kN98 kN98 kN

CALCULATIONS

Roof Load(32.1 kN)

Lattice Reaction(32.6 kN)

Arch Reaction(98.3 kN)

Arch Self Weight

(17.6 kN)

Deck Load(38.7 kN)

5 cm concrete top

< 2x

A = π r2 3.75 cm2 = π r2 r

T = C =MD

98 kN

x10000 =

75.6 kN103421 kN/m2

Total Vertical Load on Individual Arch: 348 kNPoint loads on arch (at lattice points):Lattice Component of vertical force:

Additonal Tension Resulting from Oblique Angles in Plan:

Area to be added to Tension Flange:

348 kN / 7 = 49.8 kN

cos(64.4o)32.6 kN

tan(33.2o) 49.8kN = 32.6 kN

= 75.6 kN

= 0.0003 m2 = 3.15 cm2

Addiontal area for tension �ange (from arch interaction)

Total Tension Flange area: 21.15 cm2 cross sectiontension �ange

20cm

8cm

22.5 mm

26.5 mm

Arch Tension Tie

σFA

= AFσ

= = =621kN

103421kN/m2

Global moment under full asymmetrical loading(derived in Multiframe and compared with hand calculations - not shown)

Multiframe ResultsMoment of Inertia

Under even loading conditions Under asymmetrical loading conditions

Neutral Axis Finding

98 kN

621 kN

98 kN

98 kN

98 kN

98 kN

98 kN

98 kN

710 kN

Arch Sized by Assymetrical Load (Global Bending)

Arch/Total Bridge Deflection (Compression + Bending)

Horizontal component of forces = Cross sectional Area

Member sizing based on sectional Modulus Formula for hollow tube

Desired Outer radius:

Wall Thickness: .022 m

.011 m 11 mm Max De�ection: 59mm

Max Moment: 399 kN-m

621 kN

.006 m2

= 60 cm2

20 cm

20 cm

1 cm

π πr1 = =

4Sr2+πr24 4(399kN-m) 0.25m +π (0.25m)4

4

S =π(r2

4-r14)

4r2

4

25.4 cm

23.2 cminner radius

σMS

= σM

S

I = ΣI1 + ΣA1d12 (.001m4)+(4.14E-05m4)+(2(.066m2(.532))+(2(.013m2(2.642)) = .228m4

Max De�ection

max = = =5wL4

384EI

= =

Required Sectional modulus399 kN-m

.003 m3

103421 kN/m2241 kN-m

352 kN-m

304 kN-m 98.5 kN-M

265 kN-M399 kN-M

300 kN-M

-39 mm

-59 mm

-50 mm -17 mm 21 mm

42 mm

32 mm

5(38495)314

384(1.99E+11).228

3.17

8 m

0.53 mTop Axis

Bottom Axis

Neutral Axis

22 mm

25.4 cm

18 cm2

cross sectioncompression �ange

31

60 cm2 Hollow Steel Arch Tension Tie

5 cm Thick Reinforced Concrete Deck

22 mm Diameter Steel Cable

25.4 cm Diameter 22mm Thick Hollow Steel Arch

20 cm deep I-BeamsCompression Flange: 18 cm2

Tension Flagne: 20 cm2

Duoble-Pane Low-E Glass

Insulated Panels

NETWORK NODE Precast Concrete Deck (Local Bending)

Deck Hangers (Tension)

Lattice Members (Bending)

Arch Sized by Evenly Distributed Loads (Compression)

Local Moment

Load in tributary area Compression/Tension Concrete Thickness

WL2

8

(45872N +18933N) / 3.929m = 16494 N/m

T=C=MD

(3.9m)2(16494 N/m)

31.8 kN-m 637 kN=5 cm

= 31.8 kN-m8

σFA

= AFσ

= = = =637 kN

.06 m2 .06 m2

3.05 m2.24 cmx100

9308 kN/m2

Steel thickness

σFA

= AFσ

= = = =637 kN

.006 m2 .006 m2

3.05 m 2 mm steel bottom

x1000103421 kN/m2

Tension in CableCross sectional cable area

AFσ

= = =39 kN

x10000 cm2/m2 = 103421 kN/m2

11.9 m2 (46 kN +19 kN)

= 38.7 kN .0003 m2 3.75 cm2 = 1.1cmradius

Tributary vertical load on deck

resultant angular forcecos(33.23o)

2

Loads Moment as a �xed beam Force in tension and compression of �anges

Cross sectional area of tension and compression �anges

WL2

16

= .0017 m2 186 kN103421 kN/m2

= 37.2 kN-m(2.55 kN/m) (15.3 m)2

1637.2 kN-m

= 186 kN20 cm

Lattice member max tributary area (measured with Rhino model) = 17.8 m2

Length of lattice member= 15.3 m17.8 m2 (1.4kN + 0.7 kN) = 39 kN39 kN / 15.3m = 2.55 kN/m

Total tributary load of member:Linear load of Lattice member:

AFσ

= = = x10000 = 68.67 cm2 cross section710 kN

.007 m2103421 kN/m2

Total deck load in plane of one arch: (Tension hanger load) x 7

Total vertical roof load and arch self weigth on one arch: ((32.1 kN x 14 roof ) + (17.6kN x 14 arch) / 2 = 348 kNAngle of Vertical load to plane of arch: 33.23o

(38.7 kN)(7) = 271 kN= = 417 kNcos(33.23o) resultant angular

force

Total vertical loads

Total Planar loads =

Force along each point = 688 kN / 7 = 98.3 kN

271kN + 417 kN = 688 kN

348 kN98 kN

98 kN

98 kN

98 kN

98 kN

98 kN

710 kN

Required Cross sectional Area

98 kN98 kN98 kN98 kN98 kN98 kN98 kN

CALCULATIONS

Roof Load(32.1 kN)

Lattice Reaction(32.6 kN)

Arch Reaction(98.3 kN)

Arch Self Weight

(17.6 kN)

Deck Load(38.7 kN)

5 cm concrete top

< 2x

A = π r2 3.75 cm2 = π r2 r

T = C =MD

98 kN

x10000 =

75.6 kN103421 kN/m2

Total Vertical Load on Individual Arch: 348 kNPoint loads on arch (at lattice points):Lattice Component of vertical force:

Additonal Tension Resulting from Oblique Angles in Plan:

Area to be added to Tension Flange:

348 kN / 7 = 49.8 kN

cos(64.4o)32.6 kN

tan(33.2o) 49.8kN = 32.6 kN

= 75.6 kN

= 0.0003 m2 = 3.15 cm2

Addiontal area for tension �ange (from arch interaction)

Total Tension Flange area: 21.15 cm2 cross sectiontension �ange

20cm

8cm

22.5 mm

26.5 mm

Arch Tension Tie

σFA

= AFσ

= = =621kN

103421kN/m2

Global moment under full asymmetrical loading(derived in Multiframe and compared with hand calculations - not shown)

Multiframe ResultsMoment of Inertia

Under even loading conditions Under asymmetrical loading conditions

Neutral Axis Finding

98 kN

621 kN

98 kN

98 kN

98 kN

98 kN

98 kN

98 kN

710 kN

Arch Sized by Assymetrical Load (Global Bending)

Arch/Total Bridge Deflection (Compression + Bending)

Horizontal component of forces = Cross sectional Area

Member sizing based on sectional Modulus Formula for hollow tube

Desired Outer radius:

Wall Thickness: .022 m

.011 m 11 mm Max De�ection: 59mm

Max Moment: 399 kN-m

621 kN

.006 m2

= 60 cm2

20 cm

20 cm

1 cm

π πr1 = =

4Sr2+πr24 4(399kN-m) 0.25m +π (0.25m)4

4

S =π(r2

4-r14)

4r2

4

25.4 cm

23.2 cminner radius

σMS

= σM

S

I = ΣI1 + ΣA1d12 (.001m4)+(4.14E-05m4)+(2(.066m2(.532))+(2(.013m2(2.642)) = .228m4

Max De�ection

max = = =5wL4

384EI

= =

Required Sectional modulus399 kN-m

.003 m3

103421 kN/m2241 kN-m

352 kN-m

304 kN-m 98.5 kN-M

265 kN-M399 kN-M

300 kN-M

-39 mm

-59 mm

-50 mm -17 mm 21 mm

42 mm

32 mm

5(38495)314

384(1.99E+11).228

3.17

8 m

0.53 mTop Axis

Bottom Axis

Neutral Axis

22 mm

25.4 cm

18 cm2

cross sectioncompression �ange

32

SECONDARY

A required = 4 in2 Buckling

DC

3 x 1 1/2 x 1/4

A required = 7.3 in2

L = 5' (fixed to deck)

26.6 kips 63.42 kips

SIZING MEMBERS

ARCH AND FIN SYSTEM

I required = 21.13 in4

87.0 kips

25.67 kips

80.9 kips20.1 kips

21.2 kips

A required = 5 in2

56.9 kips

Crushing

Mullion / FinsCOMPRESSION STRUT

L = 37'Buckling I required = 150 in4

12.5 x 0.250

B

63.42 kips

56.9 kips

A

50'40' 25'

Crushing

G

F

37.5 kips37.5 kips

75 kips

E

D

PRIMARY COMP. MEMBER (C1)

80.6 kips

C

A

B

D

E

O

N

M

L

K

J

F

G

H

4 k4 k4 k4 k4 k4 k4 k4 k4 k4 k4 k4 k4 k4 k

C

B

39.6 kips41 kips


TENSION CABLE (T1)

A

26.6 kips

B C D

12.5 x 0.625

6.0 x 0.312


40’12192mm

29’37’

78’

8840mm

23780mm

11280mm

10’3050mm

25’7620mm

50’15240mm

L = 50.7'Buckling I required = 377.7 in4


PRIMARY TENSION MEMBER (T2)

MAXIMUM DEFLECTION

COMPRESSION STRUT (C2)

A E F G H I J K L M

87.0 kips21.3 kips

N O

21.2 kips

I

Buckling


DL + Live Load

DL + Snow Load


CABLE 2

M

J

A

Vd

K

L

RIGID MOMENT FRAME

S required = 8.3 in3


M max = 125 kips.ft

Point load = 5ft x 1.6 kips/ft / 2 = 4 kips

M max = 406.3 kips.ft

DL + Snow Load = 0.4 kips/ft

DL + Live Load = 1.3 kips/ft

H

1.6 kips/ft

Snow Load = 300lb/ft = 0.3 kips/ft

DETAIL A

W6x8.5 Beam and girdersCast steel tube Y-column

1.5” Double Glazed Frosted Glass1”x9” Steel strap

1.5” Double Glazed Clear Vision Glass

DETAIL A

DETAIL B

DETAIL B

CABLE 1SIZING MEMBERS

CABLE AND FIN SYSTEM

REACTION ON BUILDING 46 Top Level

25.7 kips

20.1 kips

C

REACTION ON BUILDING 46 3rd level

60.8 kips

DA E F G H

87.0 kips

87.0 kips

80.9 kips

H

G

87.5 kips

87.0 kips

25.7 kips

39.6 kips

F

J

K

L

87.0 kips

21.3 kips

41 kips

M

N

O

I

21.3 kips

63.4 kips

82.9 kips

37.5 kips

63.4 kips

21.3 kips

J K L M

4 k 4 k 4 k 4 k 4 k

Vc

Hc

Vb

4 k 4 k 4 k 4 k 4 k 4 k 4 k

T1

T1

C1

C1

T2

C2

C2108.9 kips

T2

SIZING MEMBERS

ARCH AND CABLE


Hb

ARCH 1

F

CABLE 2


FRAME 1

PRIMARY

PRIMARY MEMBERS

DEFLECTION ANALYSIS

S required = 27.1 in3W10X12W10X22S required = 8.3 in3

FRAME 2

C

A

B

C

D

E

F

G

80.9 kips

63.4 kips

61.1 kips

37.5 kips

26.6 kips

37.5 kips

61.1 kips

G H I J K L M N

56.9 kips

63.42 kips

4 k 4 k 4 k 4 k 4 k 4 k 4 k 4 k

O

Va

LOADS

26.6 kips63.42 kips

49.4 kips

61 kips

DL = .445 kips/ft = 0.5 kips/ft

Total Weight of Glass = 0.325kips/ft

79.2 kips


TENSION CABLE

REACTION ON BUILDING 36

ARCH 1

B C D

Total Weight of Steel = 0.12 kips/ft

BC

A

ARCH 2

35.7 kips


A E F G H

4 k 4 k 4 k 4 k 4 k 4 k 4 k 4 k 4 k 4 k

87.0 kips25.67 kips

B

B


TRIBUTARY AREA

Width of Deck = 10ft

THE HANDSHAKEBARRY BEAGEN + TRYGVE WASTVEDT

LL = 800lb/ft = 0.8kips/ft


Total Load = 1.6kips/ft10’

387 kN

359.9 kN89.4 kN

94.3 kN

118.3 kN282.1 kN

253.1 kN

550.9 kN.m

169.5 kN.m282.1 kN

253.1 kN

387 kN

359.9 kN

182.4 kN387 kN

94.7 kN

484.4 kN

368.8 kN94.7 kN

282 kN

166.8 kN

34.5 cm2

182.4 kN 176.1 kN

358.5 kN

176.1 kN

389.2 kN 114.3 kN

387 kN

118.3 kN

282 kN 166.8 kN

271.8 kN

15.4 cm227.3 cm2 11.4 cm2

31.8 cm x 0.6 cm

35.5 cm2

31.8 cm x 1.6 cm

152 mm x 7.9 mm

114.2 kN

37.4 cm227.3 cm2

37.4 cm211 cm2

270.5kN

158.8 kN

23.4 kN/m4.4 kN/m11.7 kN/m

3.1 m

1.8 kN/m4.7 kN/m

7.3 kN/m

17.9 kN

Column Side = -0.86 in

Cable Side = -3.3 in

33

SECONDARY

A required = 4 in2 Buckling

DC

3 x 1 1/2 x 1/4


L = 5' (fixed to deck)

26.6 kips 63.42 kips

SIZING MEMBERS

ARCH AND FIN SYSTEM


87.0 kips

25.67 kips

80.9 kips20.1 kips

21.2 kips

A required = 5 in2

56.9 kips

Crushing

Mullion / FinsCOMPRESSION STRUT

L = 37'Buckling I required = 150 in4

12.5 x 0.250

B

63.42 kips

56.9 kips

A

50'40' 25'

Crushing

G

F

37.5 kips37.5 kips

75 kips

E

D

PRIMARY COMP. MEMBER (C1)

80.6 kips

C

A

B

D

E

O

N

M

L

K

J

F

G

H

4 k4 k4 k4 k4 k4 k4 k4 k4 k4 k4 k4 k4 k4 k

C

B

39.6 kips41 kips


TENSION CABLE (T1)

A

26.6 kips

B C D

12.5 x 0.625

6.0 x 0.312


40’12192mm

29’37’

78’

8840mm

23780mm

11280mm

10’3050mm

25’7620mm

50’15240mm

L = 50.7'Buckling I required = 377.7 in4


PRIMARY TENSION MEMBER (T2)

MAXIMUM DEFLECTION

COMPRESSION STRUT (C2)

A E F G H I J K L M

87.0 kips21.3 kips

N O

21.2 kips

I

Buckling


DL + Live Load

DL + Snow Load


CABLE 2

M

J

A

Vd

K

L

RIGID MOMENT FRAME



M max = 125 kips.ft

Point load = 5ft x 1.6 kips/ft / 2 = 4 kips

M max = 406.3 kips.ft

DL + Snow Load = 0.4 kips/ft

DL + Live Load = 1.3 kips/ft

H

1.6 kips/ft

Snow Load = 300lb/ft = 0.3 kips/ft

DETAIL A

W6x8.5 Beam and girdersCast steel tube Y-column

1.5” Double Glazed Frosted Glass1”x9” Steel strap

1.5” Double Glazed Clear Vision Glass

DETAIL A

DETAIL B

DETAIL B

CABLE 1SIZING MEMBERS

CABLE AND FIN SYSTEM

REACTION ON BUILDING 46 Top Level

25.7 kips

20.1 kips

C

REACTION ON BUILDING 46 3rd level

60.8 kips

DA E F G H

87.0 kips

87.0 kips

80.9 kips

H

G

87.5 kips

87.0 kips

25.7 kips

39.6 kips

F

J

K

L

87.0 kips

21.3 kips

41 kips

M

N

O

I

21.3 kips

63.4 kips

82.9 kips

37.5 kips

63.4 kips

21.3 kips

J K L M

4 k 4 k 4 k 4 k 4 k

Vc

Hc

Vb

4 k 4 k 4 k 4 k 4 k 4 k 4 k

T1

T1

C1

C1

T2

C2

C2108.9 kips

T2

SIZING MEMBERS

ARCH AND CABLE


Hb

ARCH 1

F

CABLE 2


FRAME 1

PRIMARY

PRIMARY MEMBERS

DEFLECTION ANALYSIS

S required = 27.1 in3W10X12W10X22S required = 8.3 in3

FRAME 2

C

A

B

C

D

E

F

G

80.9 kips

63.4 kips

61.1 kips

37.5 kips

26.6 kips

37.5 kips

61.1 kips

G H I J K L M N

56.9 kips

63.42 kips

4 k 4 k 4 k 4 k 4 k 4 k 4 k 4 k

O

Va

LOADS

26.6 kips63.42 kips

49.4 kips

61 kips

DL = .445 kips/ft = 0.5 kips/ft

Total Weight of Glass = 0.325kips/ft

79.2 kips


TENSION CABLE

REACTION ON BUILDING 36

ARCH 1

B C D

Total Weight of Steel = 0.12 kips/ft

BC

A

ARCH 2

35.7 kips


A E F G H

4 k 4 k 4 k 4 k 4 k 4 k 4 k 4 k 4 k 4 k

87.0 kips25.67 kips

B

B


TRIBUTARY AREA

Width of Deck = 10ft

THE HANDSHAKEBARRY BEAGEN + TRYGVE WASTVEDT

LL = 800lb/ft = 0.8kips/ft


Total Load = 1.6kips/ft10’

387 kN

359.9 kN89.4 kN

94.3 kN

118.3 kN282.1 kN

253.1 kN

550.9 kN.m

169.5 kN.m282.1 kN

253.1 kN

387 kN

359.9 kN

182.4 kN387 kN

94.7 kN

484.4 kN

368.8 kN94.7 kN

282 kN

166.8 kN

34.5 cm2

182.4 kN 176.1 kN

358.5 kN

176.1 kN

389.2 kN 114.3 kN

387 kN

118.3 kN

282 kN 166.8 kN

271.8 kN

15.4 cm227.3 cm2 11.4 cm2

31.8 cm x 0.6 cm

35.5 cm2

31.8 cm x 1.6 cm

152 mm x 7.9 mm

114.2 kN

37.4 cm227.3 cm2

37.4 cm211 cm2

270.5kN

158.8 kN

23.4 kN/m4.4 kN/m11.7 kN/m

3.1 m

1.8 kN/m4.7 kN/m

7.3 kN/m

17.9 kN

Column Side = -0.86 in

Cable Side = -3.3 in

34

Frame development

offset determined by need to reconcile center of gravity in relation to the possible torsion of the connec-tion between the arch and the deck

Fmax = 165 kips

o = F/A

o = 15 ksiF= 340 kips

o = 165 kips/A

A= 165 kips/ 15ksi

A= 11 in^2

rectangular section with A > 22.7 :14” x 12” x 1/2”

14”

12”

1/2”

x

y

I x = 678 in^4Iy = 536 in ^4

Sx = 96.9Sy = 89.3

Rectangular Arch Beam sized as follows

Checking for Buckling

since the arch is not being completely stabilized by the connection to the deck it is necessary for us to check for buckling at two areas.The most conservative span is halfway along the arch above the deck. Because the force is highest on the left side of the arch we assume that buckling will occur over the first half. A less con-serative span is the distance between the plates that connect the arch to the deck.

conservative estimate check Pcr = [pi^2(EI)]/kL^2

E = 29000ksiI = Ix = 678 in^4

L = 75’

Pcr = [pi^2(29000ksi*678 in^4)]/75ft(12inch/ft)^2

Pcr = 239.6 kips

less conservative estimate check

working backward we get the actual buckling length

Because this length occurs in between our two estimates it is safe to assume that the member size chosen will be adequate to prevent buckling along the arch.

Pcr = [pi^2(EI)]/kL^2

E = 29000ksiI = Ix = 678 in^4

L = 11’


Pcr = 11137 kips

L = sqrt[ [pi^2(EI)]/(Pcr * 3)]L = 436 in or about 36 ft

Calculating Dead load

9’

15’

8x10.5

assuming 11 identical panels @ 5.1ft^2

Panel size:2 @ 110ft x 8ft x .25in1 @ 110ft x 10ft x .25in

Floor size:110ft x 8ft x .5ft

.1’

Dead Load steel = 35519lbs

Dead Load glass = 10335lbs

Frame Load

2k2k2k2k2k2k2k4k

load greater on arch because deck not supported on the left side10k

Bending and asymmetrical loadBy finding the maximum bending moment we can increase the size of the arch in order to stiffen it for asymmetrical loading

DeformationUsing a computer model of our arch and loads mentioned above in the deformation was calculated.The input for the beam size was the minimum dimension of 12” x 14“

Mmax =wl^2/32

w = live load (estimate to be about 110 psf or 1.1 ksf)

Mmax = [1.1 ksf(90ft)^2]/32Mmax = 278 kf

o = Mmax/Sxo = 15 ksi

90ft

Sx = Mmax/ oSx = 278kf(12in/ft)/15 ksiSx = 222.4 in^3

The rectangular section that has a section modulus of at least 223 and keeps the width and thickness of the current beam is 12” x 20” x 1/2”

b

B

hH

S = [BH^2/6] - (bh^3)/(6H)S = [12in*24in^2/6] - (11in*23in^3/(24in*6)S= 222.5in^3

The beam section is large enough because the two Section modulus values are equal

14”

24”

Steel = .28 lbs/in^3

20,000 lbs = 20 kips

20 kips/11 = 1.8 kips

Floor Dead load: 66147lbs/ (880) = 75psf80ft^2 x 75psf = 6000lbs

Roof Dead load: 2851lbs/(880) = 3.25psf80ft^2 x 3.25ps =260 lbs

Wall Dead Load: 3742lbs/(880) = 4.25psf100ft^2 x (4.25psf +4.25psf) = 850lbs

Steel Dead load 35519lbs/(165ft^2) = 215 psf15ft^2 x 215psf = 3229lbs

Live load Roof = 30psf

Live load Floor 80psf80ft^2 x (30psf + 80psf) = 8,800lbs

Total Load = 20,000 lbs

Wall and Roof Load

Floor Load

Calculating Point Loads

Concrete = .087 lbs/in^3Dead load Concrete = 66147 lbs

Glass = .09 lbs/in^3

157.9kN

45.9kN

294.3kN

3.59kN/m^2

.15kN/m^2

.20kN/m^2

10.29kN/m^2

3.83kN/m^2

1.43kN/m^2

89kN

8kN

734kN

279mm

.35mm x .3m x .025m

1065kN

49539kN

10.9m

5.6m^3

5.6m^3

110ft

28ft

52ft

Iguana Bridge

frame attachment to concrete deck

10’

1’

6”

Stata center

Building 46

DMAX = 1.442”

DMAX = 1.368”

DMAX = 0.930”

DMAX = 0.313”

DMAX = 0.988”

DMAX = 1.397”

Dmax = 1.483”

DMAX = 1.144”

Our arch is properly sized because 1.483” is lower than the allowable 3.5” for deformation of this arch

Chris Martin & Robert White

35

Frame development

offset determined by need to reconcile center of gravity in relation to the possible torsion of the connec-tion between the arch and the deck

Fmax = 165 kips

o = F/A

o = 15 ksiF= 340 kips

o = 165 kips/A

A= 165 kips/ 15ksi

A= 11 in^2

rectangular section with A > 22.7 :14” x 12” x 1/2”

14”

12”

1/2”

x

y

I x = 678 in^4Iy = 536 in ^4

Sx = 96.9Sy = 89.3

Rectangular Arch Beam sized as follows

Checking for Buckling

since the arch is not being completely stabilized by the connection to the deck it is necessary for us to check for buckling at two areas.The most conservative span is halfway along the arch above the deck. Because the force is highest on the left side of the arch we assume that buckling will occur over the first half. A less con-serative span is the distance between the plates that connect the arch to the deck.

conservative estimate check Pcr = [pi^2(EI)]/kL^2

E = 29000ksiI = Ix = 678 in^4

L = 75’


Pcr = 239.6 kips

less conservative estimate check

working backward we get the actual buckling length

Because this length occurs in between our two estimates it is safe to assume that the member size chosen will be adequate to prevent buckling along the arch.

Pcr = [pi^2(EI)]/kL^2

E = 29000ksiI = Ix = 678 in^4

L = 11’


Pcr = 11137 kips

L = sqrt[ [pi^2(EI)]/(Pcr * 3)]L = 436 in or about 36 ft

Calculating Dead load

9’

15’

8x10.5

assuming 11 identical panels @ 5.1ft^2

Panel size:2 @ 110ft x 8ft x .25in1 @ 110ft x 10ft x .25in

Floor size:110ft x 8ft x .5ft

.1’

Dead Load steel = 35519lbs

Dead Load glass = 10335lbs

Frame Load

2k2k2k2k2k2k2k4k

load greater on arch because deck not supported on the left side10k

Bending and asymmetrical loadBy finding the maximum bending moment we can increase the size of the arch in order to stiffen it for asymmetrical loading

DeformationUsing a computer model of our arch and loads mentioned above in the deformation was calculated.The input for the beam size was the minimum dimension of 12” x 14“

Mmax =wl^2/32

w = live load (estimate to be about 110 psf or 1.1 ksf)

Mmax = [1.1 ksf(90ft)^2]/32Mmax = 278 kf

o = Mmax/Sxo = 15 ksi

90ft

Sx = Mmax/ oSx = 278kf(12in/ft)/15 ksiSx = 222.4 in^3

The rectangular section that has a section modulus of at least 223 and keeps the width and thickness of the current beam is 12” x 20” x 1/2”

b

B

hH

S = [BH^2/6] - (bh^3)/(6H)S = [12in*24in^2/6] - (11in*23in^3/(24in*6)S= 222.5in^3

The beam section is large enough because the two Section modulus values are equal

14”

24”

Steel = .28 lbs/in^3

20,000 lbs = 20 kips

20 kips/11 = 1.8 kips

Floor Dead load: 66147lbs/ (880) = 75psf80ft^2 x 75psf = 6000lbs

Roof Dead load: 2851lbs/(880) = 3.25psf80ft^2 x 3.25ps =260 lbs

Wall Dead Load: 3742lbs/(880) = 4.25psf100ft^2 x (4.25psf +4.25psf) = 850lbs

Steel Dead load 35519lbs/(165ft^2) = 215 psf15ft^2 x 215psf = 3229lbs

Live load Roof = 30psf

Live load Floor 80psf80ft^2 x (30psf + 80psf) = 8,800lbs

Total Load = 20,000 lbs

Wall and Roof Load

Floor Load

Calculating Point Loads

Concrete = .087 lbs/in^3Dead load Concrete = 66147 lbs

Glass = .09 lbs/in^3

157.9kN

45.9kN

294.3kN

3.59kN/m^2

.15kN/m^2

.20kN/m^2

10.29kN/m^2

3.83kN/m^2

1.43kN/m^2

89kN

8kN

734kN

279mm

.35mm x .3m x .025m

1065kN

49539kN

10.9m

5.6m^3

5.6m^3

110ft

28ft

52ft

Iguana Bridge

frame attachment to concrete deck

10’

1’

6”

Stata center

Building 46

DMAX = 1.442”

DMAX = 1.368”

DMAX = 0.930”

DMAX = 0.313”

DMAX = 0.988”

DMAX = 1.397”

Dmax = 1.483”

DMAX = 1.144”

Our arch is properly sized because 1.483” is lower than the allowable 3.5” for deformation of this arch

Chris Martin & Robert White

36

custom glazing (planar slices)

top �ange (steel)

web (carbon composite)

bottom �ange (steel/aluminum)

Steel and insulated glass web; steel is perforated

Depth and frequency of curvature varies along elevation

BOTTOM FLANGE (STEEL/ALUMINUM CLADDING)

WEB (CARBON COMPOSITE SHELLS WITH FOAM CORE)

TOP FLANGE (STEEL)*This revision will allow us to add thermal performance to the envelope, lighten structure by using less steel, and make the previously uninhabitable spaces accessible. NOTE: Carbon Composite is not used in our calculations as of yet.

GLAZING (PLANAR WEB SLICES)

Buckling in Top FlangeI = (bh3/12)outer - (bh3/12)innerbo = 1.25ft, bi = 1.19ft, ho = 3.5ft, hi = 3.44ftI = ((3.5*12)(1.25*12)3/12) - ((3.44*12)(1.19*12)3/12)I = 1748in4

Pcr = π2EI/(kL2)Pcr = π2(29,000ksi)(1748i4)/(1*118ft(12)2)Pcr = 249kPsafety = 166k (Safety factor increased due to support from web)T=163k OKShear: For this calculation, both beams are considered simultaneously since the corrugations are asymmetrical. Divide bridge into four chunks of 29.5 ft or 354 inches. For the outermost part (with most shear:Stress = V/Av = must be under 15ksiAv = (5/6)(teq)(h)h = 112inTeq = (length of corrugation)(width)/length of chunkTeq = (117.75in)(.125in)/(354in)Teq= .50inAv = (5/6)(.50in)(112in)V from shear diagram – average shear over length measuredV = 84kStress = 84/(5/6)(.50in)(112in)Stress = 1.80ksi OK

Asymmetrical Loading:Assume a live load of 3.85k distributed over one half of the beam or L/2.Assume a dead load of 565k distributed over the entire beam.

Reactions:∑F = 0∑M = 0W1 = Live Load over ½ beamW2 = Dead Load over entire beamVB + VA = W1(L) + W2(L/2) VB(L) =( (W1*L)/2)(L/4) + (W2*L)(L/2) VB= (.39)(118)/(8) + (.56)(118)/2VB = 5.75 + 33.04VB = 39kVA= (.56)(118) + (.39)(59) - 39VA= 50kHA= 0k

Area under shear diagram: 1317k*fMax. M = 1317k*f

THE CORRIGATOR TYLER CRAIN & CLAUDIA BODECROSS SECTION 1/2” = 1’

1:24

PERFORATED WEB

1:96PLAN 1/8” = 1’

NEED FROM RHINO:- FINAL RENDERS(2)- PLAN(MAKE2D)- CROSS SECTION(MAKE2D)- EXPLODED AXON(MAKE2D OR RENDER)-LAYERS- QUICK AXON RENDERS FOR DIAGRAMS- ELEVATION(MAKE2D/RENDER) FOR STRUCTURAL DIAG

The inspiration for this bridge is a Guy Nordenson pedestrian bridge in New Haven, CT which utilizes a curved, perforated steel sheet as support for the handrail

Aluminum Framing

Glass Roof

Top Flange (Box Girder)

Interior Flooring

Corrugated Aluminum Decking

Tributary Steel Support Ribs (spanning ribs)

Bottom Flange (steel)

Aluminum Cladding and Insulation Cavity

EXPLODED ISOMETRIC 1/16” = 1’1:192

1’-6

”

0.13

0.10

DESIGN REVISIONS FOR FUTURE






ADDITIONAL CALCULATIONS

ASSUMPTIONS AND LOADS

MAXIMUM MOMENT


FLANGE FORCES

COMPRESSION CHORD BUCKLING

Average width = 9ftWidth of center glass roof = 4ft Allowable stress of steel = 15ksiWeight of steel = 490pcfE steel = 29,000k/128,998 kNL = Length = 118ft/36md = depth = 9.875ftdepth of web = 9ft

Live Load = 110psf/537kg/m^2Dead Load = 166psf Top Flange = 51psf or 54420lbs Bottom Flange = 17psf or 18727lbs Steel Web = 74psf or 78553lbs Cladding/Glass = 23psf Glass Facade = 12psf or 12744lbs Glass Roof = 1.33psf or 1416lbs Flange Cladding = 10psfW = Total Load per linear ft = 2.49k/ft Reactions = Fy,A = 147k, Fy,A = 147k, Fx,A = 0

Find the maximum moment of the beam using WL2/8:M=WL2/8M = (2.49(118)2)/8M= 4326k*ft

Assume a live load of 58k (= 1k/linear ft)distributed over one half of the beam or L/2. Assume a dead load of 177k (= 1.5 k/linear ft) distributed over the entire beam.

Reactions:∑F = 0, ∑M = 0W1 = Live Load over ½ beamW2 = Dead Load over entire beamVB + VA = W1(L) + W2(L/2) VB(L) =( (W1*L)/2)(L/4) + (W2*L)(L/2) VB= (1)(118)/(8) + (1.5)(118)/2VB = 14.75 + 88.5VB = 103kVA= (1.5)(118) + (1)(118/2) - 103VA= 133kHA= 0k

Area under shear diagram: 3537.8k*fMax. M = 3537.8k*f

Find the stresses in the flanges by using T=C=M/d:T=C=M/dT=C=4326/9.875T=C=438k

Verify that the compression chord will not crush under the flange forces:The top flange is made of 2 connected boxes each with a depth of 1.5ft, average width of 2.5 ft, and a wall thickness of 0.85in. For the purposes of calculating axial stress, only the continuous cross-sectional area is used.A = cross-sectional area = 54 sq/inStress = Force/AreaStress = 438/54Stress = 8.1ksi OK

Verify that the tension chord can carry the necessary tension:The bottom flange is a steel box. It has an average depth of 8” and a wall thickness of .4”.A = cross-sectional area = 47 sq/inStress = Force/AreaStress = 438/47Stress = 9.4ksi OK

Buckling in Top FlangeFind the moment of inertia of a box by subtracting the I(inside wall) from I(outside wall) of each box:I = (bh3/12)outer - (bh3/12)innerb(outer) = 1.5ft, b(inner) = 1.43ft, h(outer) = 2.5ft, h(inner)= 2.43ftI = ((2.5*12)(1.5*12)3/12) - ((2.43*12)(1.43*12)3/12)I = 2327in4 for each sideI total= 4654in4

Use the buckling equation to find the point of failure in buckling:Pcr = π2EI/(kL2)Pcr = π2(29,000ksi)(4654i4)/(1*118ft(12)2)Pcr = 664k

Reduce by a safety factor. Because this chord is being supported on one side by the web, the safety factor is increased from 1/3 the critical value to 2/3 the critical value.Pcr = 664kPsafety = 442k, C=438k OK

SHEAR CALCULATION FOR WEBSDivide bridge into four chunks of 29.5 ft or 354 inches. For the outermost part (with most shear):

Stress = V/Av = must be under 15ksiAv = (5/6)(teq)(h)h = 108in (height of web)Teq = (length of corrugation)(width)/length of chunkTeq = (720in)(.125in)/(354in)Teq= .25in (effective cross sectional area)Av = (5/6)(.25in)(108in)V from shear diagram – max. shear over length measuredV = 147kStress = 147/(5/6)(.25in)(108in)Stress = 6.42ksi OK

DEFLECTION CALCULATIONAmax = (5wL^4)/(384EI) --> I = (5wl^4)/(384E*Amax)w= 110psf = .08k/in, L = 118’ or , Ama x = 118/360 = .33 or 4”

Imin = [(5)(.08)(1416^4)]/[(384)(29,000)(4)]Imin= 37861 in^4

To calculat e I of entire structure: use parallel axis theorem for simply supported beam: I = ∑I + ∑Ad^2

I = ∑I + ∑Ad^2I(1) = I(2) = (54in^2)(34in)^2I(3) = (47in^2)(85in)^2I(total) = 395571 in^4Deflection for actual I = 0.38 inch

COMPRESSION = UPPER DECK

TENSION = LOWER DECK

V

SYMMETRICAL LOADING

d2d1

A1 A2

A3d3

CALCULATIONS

STEEL SUPPORT FOR GLASS ROOF (BEYOND) @ 48” O.C

INSULATED GLASS ROOF DRAINS TO GUTTER

SLOPED RIGID INSULATION

VARIES4’-0”1.22mVARIES

1’-6

”46

cm8” 23

cm8” 23

cm9’

-0”

2.74

cm

18” DEEP BOX FLANGE W/ WALL THICK-NESS OF 0.85IN, VARIABLE WIDTH

PERFORATED, CORRUGATED STEEL WEB

(2) LAYERS INSULATED GLASS

CLADDING WITH SPACE FOR INSULATION AND ELECTRICAL WIRING

8” DEEP STL BOX WITH INTER-NAL CROSS SUPPORTS

37

custom glazing (planar slices)

top �ange (steel)

web (carbon composite)

bottom �ange (steel/aluminum)

Steel and insulated glass web; steel is perforated

Depth and frequency of curvature varies along elevation

BOTTOM FLANGE (STEEL/ALUMINUM CLADDING)

WEB (CARBON COMPOSITE SHELLS WITH FOAM CORE)

TOP FLANGE (STEEL)*This revision will allow us to add thermal performance to the envelope, lighten structure by using less steel, and make the previously uninhabitable spaces accessible. NOTE: Carbon Composite is not used in our calculations as of yet.

GLAZING (PLANAR WEB SLICES)






THE CORRIGATOR TYLER CRAIN & CLAUDIA BODECROSS SECTION 1/2” = 1’

1:24

PERFORATED WEB

1:96PLAN 1/8” = 1’

NEED FROM RHINO:- FINAL RENDERS(2)- PLAN(MAKE2D)- CROSS SECTION(MAKE2D)- EXPLODED AXON(MAKE2D OR RENDER)-LAYERS- QUICK AXON RENDERS FOR DIAGRAMS- ELEVATION(MAKE2D/RENDER) FOR STRUCTURAL DIAG

The inspiration for this bridge is a Guy Nordenson pedestrian bridge in New Haven, CT which utilizes a curved, perforated steel sheet as support for the handrail

Aluminum Framing

Glass Roof

Top Flange (Box Girder)

Interior Flooring

Corrugated Aluminum Decking

Tributary Steel Support Ribs (spanning ribs)

Bottom Flange (steel)

Aluminum Cladding and Insulation Cavity

EXPLODED ISOMETRIC 1/16” = 1’1:192

1’-6

”

0.13

0.10

DESIGN REVISIONS FOR FUTURE






ADDITIONAL CALCULATIONS

ASSUMPTIONS AND LOADS

MAXIMUM MOMENT


FLANGE FORCES

COMPRESSION CHORD BUCKLING

Average width = 9ftWidth of center glass roof = 4ft Allowable stress of steel = 15ksiWeight of steel = 490pcfE steel = 29,000k/128,998 kNL = Length = 118ft/36md = depth = 9.875ftdepth of web = 9ft

Live Load = 110psf/537kg/m^2Dead Load = 166psf Top Flange = 51psf or 54420lbs Bottom Flange = 17psf or 18727lbs Steel Web = 74psf or 78553lbs Cladding/Glass = 23psf Glass Facade = 12psf or 12744lbs Glass Roof = 1.33psf or 1416lbs Flange Cladding = 10psfW = Total Load per linear ft = 2.49k/ft Reactions = Fy,A = 147k, Fy,A = 147k, Fx,A = 0

Find the maximum moment of the beam using WL2/8:M=WL2/8M = (2.49(118)2)/8M= 4326k*ft

Assume a live load of 58k (= 1k/linear ft)distributed over one half of the beam or L/2. Assume a dead load of 177k (= 1.5 k/linear ft) distributed over the entire beam.

Reactions:∑F = 0, ∑M = 0W1 = Live Load over ½ beamW2 = Dead Load over entire beamVB + VA = W1(L) + W2(L/2) VB(L) =( (W1*L)/2)(L/4) + (W2*L)(L/2) VB= (1)(118)/(8) + (1.5)(118)/2VB = 14.75 + 88.5VB = 103kVA= (1.5)(118) + (1)(118/2) - 103VA= 133kHA= 0k

Area under shear diagram: 3537.8k*fMax. M = 3537.8k*f

Find the stresses in the flanges by using T=C=M/d:T=C=M/dT=C=4326/9.875T=C=438k

Verify that the compression chord will not crush under the flange forces:The top flange is made of 2 connected boxes each with a depth of 1.5ft, average width of 2.5 ft, and a wall thickness of 0.85in. For the purposes of calculating axial stress, only the continuous cross-sectional area is used.A = cross-sectional area = 54 sq/inStress = Force/AreaStress = 438/54Stress = 8.1ksi OK

Verify that the tension chord can carry the necessary tension:The bottom flange is a steel box. It has an average depth of 8” and a wall thickness of .4”.A = cross-sectional area = 47 sq/inStress = Force/AreaStress = 438/47Stress = 9.4ksi OK

Buckling in Top FlangeFind the moment of inertia of a box by subtracting the I(inside wall) from I(outside wall) of each box:I = (bh3/12)outer - (bh3/12)innerb(outer) = 1.5ft, b(inner) = 1.43ft, h(outer) = 2.5ft, h(inner)= 2.43ftI = ((2.5*12)(1.5*12)3/12) - ((2.43*12)(1.43*12)3/12)I = 2327in4 for each sideI total= 4654in4

Use the buckling equation to find the point of failure in buckling:Pcr = π2EI/(kL2)Pcr = π2(29,000ksi)(4654i4)/(1*118ft(12)2)Pcr = 664k

Reduce by a safety factor. Because this chord is being supported on one side by the web, the safety factor is increased from 1/3 the critical value to 2/3 the critical value.Pcr = 664kPsafety = 442k, C=438k OK

SHEAR CALCULATION FOR WEBSDivide bridge into four chunks of 29.5 ft or 354 inches. For the outermost part (with most shear):

Stress = V/Av = must be under 15ksiAv = (5/6)(teq)(h)h = 108in (height of web)Teq = (length of corrugation)(width)/length of chunkTeq = (720in)(.125in)/(354in)Teq= .25in (effective cross sectional area)Av = (5/6)(.25in)(108in)V from shear diagram – max. shear over length measuredV = 147kStress = 147/(5/6)(.25in)(108in)Stress = 6.42ksi OK

DEFLECTION CALCULATIONAmax = (5wL^4)/(384EI) --> I = (5wl^4)/(384E*Amax)w= 110psf = .08k/in, L = 118’ or , Ama x = 118/360 = .33 or 4”

Imin = [(5)(.08)(1416^4)]/[(384)(29,000)(4)]Imin= 37861 in^4

To calculat e I of entire structure: use parallel axis theorem for simply supported beam: I = ∑I + ∑Ad^2

I = ∑I + ∑Ad^2I(1) = I(2) = (54in^2)(34in)^2I(3) = (47in^2)(85in)^2I(total) = 395571 in^4Deflection for actual I = 0.38 inch

COMPRESSION = UPPER DECK

TENSION = LOWER DECK

V

SYMMETRICAL LOADING

d2d1

A1 A2

A3d3

CALCULATIONS

STEEL SUPPORT FOR GLASS ROOF (BEYOND) @ 48” O.C

INSULATED GLASS ROOF DRAINS TO GUTTER

SLOPED RIGID INSULATION

VARIES4’-0”1.22mVARIES

1’-6

”46

cm8” 23

cm8” 23

cm9’

-0”

2.74

cm

18” DEEP BOX FLANGE W/ WALL THICK-NESS OF 0.85IN, VARIABLE WIDTH

PERFORATED, CORRUGATED STEEL WEB

(2) LAYERS INSULATED GLASS

CLADDING WITH SPACE FOR INSULATION AND ELECTRICAL WIRING

8” DEEP STL BOX WITH INTER-NAL CROSS SUPPORTS

38

C

B

J

L

I

E

L

B

F

D

G

K

G

D

B

C

K

A

L

I

E

H

J

F

E

G

H

D JH IE F

F G K

L

C I

C

B JD

KA

A

A

H 60.9 kN

Floor Tributary Area

w = 300 lbs/ft

3

Snow Load: 30 psf -> 300 lbs/ft

60.9 kN

59.2 kN69.8 kN

60.9 kN

69.8 kN 69.8 kN69.8 kN

69.8 kN

365 kN

69.8 kN

Bottom

69.8 kN69.8 kN 69.8 kN

DL: Concretew = 750 lbs/ft

Total: w = 1550 lbs/ft

LL: Peoplew = 800 lbs/ft

Tributary Area = 3m x 3m

445 kN 303 kN

Assymetric Maximum Stress: 13.6 ksi < 15 ksi OK

Roof Uniform Load

60.9 kN

2

24.9 kN

69.8 kN

69.8 kN

Additional Stress = 4.4 ksi

Uniform Load Stress: 9.36 ksi

60.9 kN Floor Beam SizingMmax = 232.5 kips * in

σ,steel = 15 ksi

Section Modulus = 15.5 in

W10X17 S = 16.2 in.

3

3

274 kN

Floor Uniform Load

35.1 kN

No.6 (US) BarsAs = 1700 mmSteel Ratio = 0.006

69.8 kN 69.8 kN 69.8 kN

Assymetric Maximum Stress: 18.3 ksi > 15 ksi too much

Top

60.9 kN


60.9 kN

30.8 kN

60.9 kN

69.8 kN

30.8 kN

274 kN

60.9 kN60.9 kN 60.9 kN

Column Sizing

Concrete Strength: 3 ksiSteel Rebar Strength: 40 ksi


Load from Roof = 365 kNLoad from Floor = 445 kN

810 kN Through Column

2

Force Polygon

60.9 kN60.9 kN51.6 kN

Roof Tributary Area

60.9 kN

287 kN

21.4 kN

60.9 kN

30.8 kN

60.9 kN60.9 kN

Force Polygon

69.8 kN

314 kN

Mmax = 76 kips/ft

69.8 kN

35.1 kN

Mmax = 203 kips/ft

Maximum Force Based On Force Polygon

Floor: 406 kNRoof: 406 kN


w = 800 lbs/ft


Surface Area: 5000 mm

Primary Member Sizing

314 kN

k = 0.5 fixed-fixedE = 29,000 ksi

Pcr = 5700 kN >> 406 kNNo chance of buckling

Buckling Check

152mm x 102mm x 13mm

Buckling Check

2Surface Area: 5000 mm

2

3


New Primary Member Sizing



People Load: 80 psf -> 800 lbs/ft


Assymetric Loading Floor



Current Member: 152mm x 102mm x 13mmSx = 185000 mm





35.1 kN

2

3

Try 203mm x 152mm x 16mm

Surface Area = 9000 mm Sx = 467000 mm


Assymetric Loading Roof

Mmax = 474 kips * in


33Use 230mm x 178mm x 13mmSx = 33 in > 31.6 in OK

Each strut carries 35 kN

3

Worst case scenario: 35kN

Equal horizontal forces allowforces to negate each other at their connection points

DL: Concrete, Glassw = 500 lbs/ft + 540 lbs/ft


LL: Snoww = 300 lbs/ft


Roof Beam SizingMmax = 201 kips * in

σ,steel = 15 ksi


W10X15 S = 13.8 in.

3

3

Floor and Roof Strut Sizing

Secondary Member Sizing



2

3



A

A

B

B

PROCESS DIAGRAMSPROCESS DIAGRAMS SECTION DIAGRAM CALCULATIONS

DL: Concrete = 50 lbs/ft Beam = 150 lbs Glass = 536 lbs/ftLL: Snow = 30 lbs/ft

Total Weight (every 3.0m x 3.0m area)= 50*100 + 150 + 536*10 + 30*100= 60.9 kN

178 mm

102 mm

178

mm

13 m

m

127 mm

325 kN

610 mm

406 kN

400 kN

14 m

3.0 m2.1 m

3.0 m

3.0 m2.1 m

3.0 m

406 mm

152 mm

152

mm

230

mm

13 m

m

203

mm

152

mm

13 m

m

102 mm

13 m

m16

mm

102mm

254m

m27

5 m

m

102mm

2

2

2

2

ReducedTributaryArea

ReducedTributaryAreaReduced

TributaryArea




DL: Concrete = 75 lbs/ft Beam = 170 lbsLL: People = 80 lbs/ft

Total Weight (every 3.0m x 3.0m area)= 75*100 + 170 + 80*100= 69.8 kN

SECTION B-B

7.5

m5.

4 m

3.5

m

0.4

m0.

4 m

1.2

m

SECTION A-A

7.0

m6.

0 m

0.4

m3.

5 m

0.4

m1.

8 m

Dual-Restrained Arch Skybridge Andrew Sang Sean T. Tang

39

C

B

J

L

I

E

L

B

F

D

G

K

G

D

B

C

K

A

L

I

E

H

J

F

E

G

H

D JH IE F

F G K

L

C I

C

B JD

KA

A

A

H 60.9 kN

Floor Tributary Area

w = 300 lbs/ft

3

Snow Load: 30 psf -> 300 lbs/ft

60.9 kN

59.2 kN69.8 kN

60.9 kN

69.8 kN 69.8 kN69.8 kN

69.8 kN

365 kN

69.8 kN

Bottom

69.8 kN69.8 kN 69.8 kN

DL: Concretew = 750 lbs/ft


LL: Peoplew = 800 lbs/ft


445 kN 303 kN


Roof Uniform Load

60.9 kN

2

24.9 kN

69.8 kN

69.8 kN



60.9 kN Floor Beam SizingMmax = 232.5 kips * in

σ,steel = 15 ksi


W10X17 S = 16.2 in.

3

3

274 kN

Floor Uniform Load

35.1 kN


69.8 kN 69.8 kN 69.8 kN


Top

60.9 kN


60.9 kN

30.8 kN

60.9 kN

69.8 kN

30.8 kN

274 kN

60.9 kN60.9 kN 60.9 kN

Column Sizing

Concrete Strength: 3 ksiSteel Rebar Strength: 40 ksi


Load from Roof = 365 kNLoad from Floor = 445 kN

810 kN Through Column

2

Force Polygon

60.9 kN60.9 kN51.6 kN

Roof Tributary Area

60.9 kN

287 kN

21.4 kN

60.9 kN

30.8 kN

60.9 kN60.9 kN

Force Polygon

69.8 kN

314 kN

Mmax = 76 kips/ft

69.8 kN

35.1 kN

Mmax = 203 kips/ft




w = 800 lbs/ft


Surface Area: 5000 mm


314 kN



Buckling Check


Buckling Check

2Surface Area: 5000 mm

2

3





People Load: 80 psf -> 800 lbs/ft


Assymetric Loading Floor








35.1 kN

2

3




Assymetric Loading Roof

Mmax = 474 kips * in


33Use 230mm x 178mm x 13mmSx = 33 in > 31.6 in OK

Each strut carries 35 kN

3

Worst case scenario: 35kN

Equal horizontal forces allowforces to negate each other at their connection points

DL: Concrete, Glassw = 500 lbs/ft + 540 lbs/ft


LL: Snoww = 300 lbs/ft


Roof Beam SizingMmax = 201 kips * in

σ,steel = 15 ksi


W10X15 S = 13.8 in.

3

3

Floor and Roof Strut Sizing

Secondary Member Sizing



2

3



A

A

B

B

PROCESS DIAGRAMSPROCESS DIAGRAMS SECTION DIAGRAM CALCULATIONS

DL: Concrete = 50 lbs/ft Beam = 150 lbs Glass = 536 lbs/ftLL: Snow = 30 lbs/ft

Total Weight (every 3.0m x 3.0m area)= 50*100 + 150 + 536*10 + 30*100= 60.9 kN

178 mm

102 mm

178

mm

13 m

m

127 mm

325 kN

610 mm

406 kN

400 kN

14 m

3.0 m2.1 m

3.0 m

3.0 m2.1 m

3.0 m

406 mm

152 mm

152

mm

230

mm

13 m

m

203

mm

152

mm

13 m

m

102 mm

13 m

m16

mm

102mm

254m

m27

5 m

m 102mm

2

2

2

2


ReducedTributaryAreaReduced

TributaryArea




DL: Concrete = 75 lbs/ft Beam = 170 lbsLL: People = 80 lbs/ft

Total Weight (every 3.0m x 3.0m area)= 75*100 + 170 + 80*100= 69.8 kN

SECTION B-B

7.5

m5.

4 m

3.5

m

0.4

m0.

4 m

1.2

m

SECTION A-A

7.0

m6.

0 m

0.4

m3.

5 m

0.4

m1.

8 m

Dual-Restrained Arch Skybridge Andrew Sang Sean T. Tang

40

virendeel bridge dicle uzunyayla & sayjel patel

DL + LL = 3.2 kip/ft

84 kip84 kip

Mmax = 2200 kip*ft

BEAMANALYSIS

MULTIFRAME ANALYSIS

PARAMETRICLOGIC

Moment (z) kN*m

Shear (V) kN

Axial Loads (P) kN

De�ection (mm)

CONCEPT

Fabrication

13731212 3732540912984 1681 693551 2088873


66 C

2 C

66 T 63 T

63 C

12 C 9 C 4 C

62 T

62 C

25 T

1 C

9 C

9 T 3 T

3 C

2 C

25 C

17 T

3 C

17 C

13 C

40 C23 C52 C 44 C54 C

23 T9 T40 T

9 C

52 T

34 C

54 T

2 C1 C2 C 8 C 4 C 3 C

34 T44 T

2 C

3 3333 33

1. Loadsa. Dead Loads

A Cross Sectional Area of Top Beam 20 Ft 2 from geometryB Cross Sectional Area of Bottom Beam 16 Ft 2 "C Bridge Length 105 Ft "D Total Beam Volume 33,600 Ft 3 D = A*B*CE Percentage Steel 30.00% estimateF Volume Steel 10080 Ft 3 F = D*EG Density of Steel 22 lb/ft3 givenH Total Mass of Steel (Total Deadload) 222 Kips H = F * G / 1000I W DL 2.11 Kips / ft J = I*C

b. Live LoadsJ Live Load Typical Pedestrian Bridge 110 lbs/ft2 gIvenK Bridge Width 10 Ft from geometryL LL Total 116 Kips L = (K * C)*J / 1000M W LL 1.10 Kips / Ft M = L / C

1.49 KN / m // Metricc. Find W

N W 3.21 Kips / ft N = M + IO W/2 (split between right and left side) 1.605 Kips / ft O = N / 2

d. Find P 2.18 KN / m // MetricP Uniform Load (W)' 1605.0 lbs/ft P = O*1000Q Total Load 168.5 Kips P = O*CR Number of Segments 15 from geometryS P / NumSegments 11.2 Kips S = Q / R

50 KN // Metric2. Primary Elementsa. Find Max Allowable Bending Stress

T Reaction Force 84.3 Kips T = Q / 2U Max Bending Moment 2,211,891 Lb*ft U = P *C^2/8 (w L^2/8)V Allowable Bending Stress 19800 ơ

b. Find Section Modulus RequiredW Section Modulus (S req'd) 112 in^3 W = U /V Mmax / I (steel

c.Find moment of Inertia required usingdeflection formula

X Max Allowable De�ection 3.5 inches T = Q / 360 * 12 L / 360Y Modulus of Elasticity Steel 30,000,000 psi E constant Mod for SteelZ I Total (Required) 41,805 in^4 I = 5wL^4/384ED

d. Select Steel Section, check moment ofinertia and STop HSS a Height 20 in

b Width 12 inc Thickness 1/2 ind Section Modulus 117 in^3 > S req'de Iy 705 in^4

Bottom HSS d Height 20 ine Width 12 inf Thickness 1/2 ing Section Modulus 117 in^3 > S req'dh Iy 705 in^4

Check I req'dg Atop 240 in^2 g = a*bh Abottom 240 in^2 h = d*ei Height of Section 120 inj Dtop 60 ink Dbottom 60 inl Itotal 1,729,410 in^2 l = (g + h) + g*j^2+ h*k^2

Check A req'd Axial Force 55.0 KN (M.F)13.75 KIP

Allowable Bending Stress 15 KSIArea Required 0.9 in^2 p = m / o (A = P / ơ)

3. Secondary Elements - (Multi Framefind area Req'd

m Axial Force (vertical elements) 10.0 KN multi framen " 2.25 KIP // metricso Allowable Bending Stress 15 KSIp Area Required 0.2 in^2 p = m / o (A = P / ơ)

Choose Sectionq Height 8.0 inr Width 8.0 ins Thickness 0.625 in

(t > a) t Area 18 in^2u I 125 in^4v s 31 in^3

Check Buckling (x > n)w member length 120.0 inx Max Axial Force 2.6 KIPs p = m / o (F = pi^2 * E* I^2 / (KL)^2) buckling governs

4. Asymetrical Loading

Secondary Elements - check max axial forcefind area Req'd

m Axial Force (vertical elements) KNn " KIPo Allowable Bending Stress 15 KSIp Area Required in^2

Choose Sectionq Height inr Width ins Thickness 0.625 in

(t > a) t Area in^2u I in^4v s in^3

Check Buckling (x > n)w member length 120.0 inx Max Axial Force KIPs

In most extreme case, member ( Fc = 23 kN)requires 16 " x 16" HSS, governed bybuckling)

13.03.25

0.2

9.09.0

2118240

3.7

Massing

32.0 m

3.2 m

prefabricated vertical elements are built with welded steel plates

Custom plate steel sections serve as a deck and ceiling

Secondary ribs

ceiling and deck are perforated toreduce the weight of the structure

30 cm

30 cm

2

4

4

4

0

3

0 2

0

28

15

13

8

8

4

8

5

5

15

159

8

8

5

6

7

8 9

10

6

5

6

8

4

8

9 0

0

15

15

13

12

5

2

31

1

2 1

6 9 5

4

6

2

9

11 8

8 5 7

30

1115 6

8 5

7 0

09 8

55 C

0 C

55 T 58 T

58 C

8 C 5 C 5 C5 C

48 T

48 C

9 C

28 C16 C 38 C

16 T6 T 28 T

6 C

38 T

1 C1 C

852.4

41

virendeel bridge dicle uzunyayla & sayjel patel

DL + LL = 3.2 kip/ft

84 kip84 kip

Mmax = 2200 kip*ft

BEAMANALYSIS

MULTIFRAME ANALYSIS

PARAMETRICLOGIC

Moment (z) kN*m

Shear (V) kN

Axial Loads (P) kN

De�ection (mm)

CONCEPT

Fabrication

13731212 3732540912984 1681 693551 2088873


66 C

2 C

66 T 63 T

63 C

12 C 9 C 4 C

62 T

62 C

25 T

1 C

9 C

9 T 3 T

3 C

2 C

25 C

17 T

3 C

17 C

13 C

40 C23 C52 C 44 C54 C

23 T9 T40 T

9 C

52 T

34 C

54 T

2 C1 C2 C 8 C 4 C 3 C

34 T44 T

2 C

3 3333 33

1. Loadsa. Dead Loads

A Cross Sectional Area of Top Beam 20 Ft 2 from geometryB Cross Sectional Area of Bottom Beam 16 Ft 2 "C Bridge Length 105 Ft "D Total Beam Volume 33,600 Ft 3 D = A*B*CE Percentage Steel 30.00% estimateF Volume Steel 10080 Ft 3 F = D*EG Density of Steel 22 lb/ft3 givenH Total Mass of Steel (Total Deadload) 222 Kips H = F * G / 1000I W DL 2.11 Kips / ft J = I*C

b. Live LoadsJ Live Load Typical Pedestrian Bridge 110 lbs/ft2 gIvenK Bridge Width 10 Ft from geometryL LL Total 116 Kips L = (K * C)*J / 1000M W LL 1.10 Kips / Ft M = L / C

1.49 KN / m // Metricc. Find W

N W 3.21 Kips / ft N = M + IO W/2 (split between right and left side) 1.605 Kips / ft O = N / 2

d. Find P 2.18 KN / m // MetricP Uniform Load (W)' 1605.0 lbs/ft P = O*1000Q Total Load 168.5 Kips P = O*CR Number of Segments 15 from geometryS P / NumSegments 11.2 Kips S = Q / R

50 KN // Metric2. Primary Elementsa. Find Max Allowable Bending Stress

T Reaction Force 84.3 Kips T = Q / 2U Max Bending Moment 2,211,891 Lb*ft U = P *C^2/8 (w L^2/8)V Allowable Bending Stress 19800 ơ

b. Find Section Modulus RequiredW Section Modulus (S req'd) 112 in^3 W = U /V Mmax / I (steel

c.Find moment of Inertia required usingdeflection formula

X Max Allowable De�ection 3.5 inches T = Q / 360 * 12 L / 360Y Modulus of Elasticity Steel 30,000,000 psi E constant Mod for SteelZ I Total (Required) 41,805 in^4 I = 5wL^4/384ED

d. Select Steel Section, check moment ofinertia and STop HSS a Height 20 in

b Width 12 inc Thickness 1/2 ind Section Modulus 117 in^3 > S req'de Iy 705 in^4

Bottom HSS d Height 20 ine Width 12 inf Thickness 1/2 ing Section Modulus 117 in^3 > S req'dh Iy 705 in^4

Check I req'dg Atop 240 in^2 g = a*bh Abottom 240 in^2 h = d*ei Height of Section 120 inj Dtop 60 ink Dbottom 60 inl Itotal 1,729,410 in^2 l = (g + h) + g*j^2+ h*k^2

Check A req'd Axial Force 55.0 KN (M.F)13.75 KIP

Allowable Bending Stress 15 KSIArea Required 0.9 in^2 p = m / o (A = P / ơ)

3. Secondary Elements - (Multi Framefind area Req'd

m Axial Force (vertical elements) 10.0 KN multi framen " 2.25 KIP // metricso Allowable Bending Stress 15 KSIp Area Required 0.2 in^2 p = m / o (A = P / ơ)

Choose Sectionq Height 8.0 inr Width 8.0 ins Thickness 0.625 in

(t > a) t Area 18 in^2u I 125 in^4v s 31 in^3

Check Buckling (x > n)w member length 120.0 inx Max Axial Force 2.6 KIPs p = m / o (F = pi^2 * E* I^2 / (KL)^2) buckling governs

4. Asymetrical Loading

Secondary Elements - check max axial forcefind area Req'd

m Axial Force (vertical elements) KNn " KIPo Allowable Bending Stress 15 KSIp Area Required in^2

Choose Sectionq Height inr Width ins Thickness 0.625 in

(t > a) t Area in^2u I in^4v s in^3

Check Buckling (x > n)w member length 120.0 inx Max Axial Force KIPs

In most extreme case, member ( Fc = 23 kN)requires 16 " x 16" HSS, governed bybuckling)

13.03.25

0.2

9.09.0

2118240

3.7

Massing

32.0 m

3.2 m

prefabricated vertical elements are built with welded steel plates

Custom plate steel sections serve as a deck and ceiling

Secondary ribs

ceiling and deck are perforated toreduce the weight of the structure

30 cm

30 cm

2

4

4

4

0

3

0 2

0

28

15

13

8

8

4

8

5

5

15

159

8

8

5

6

7

8 9

10

6

5

6

8

4

8

9 0

0

15

15

13

12

5

2

31

1

2 1

6 9 5

4

6

2

9

11 8

8 5 7

30

1115 6

8 5

7 0

09 8

55 C

0 C

55 T 58 T

58 C

8 C 5 C 5 C5 C

48 T

48 C

9 C

28 C16 C 38 C

16 T6 T 28 T

6 C

38 T

1 C1 C

852.4

42

Bldg 36

cable anchored to �oor platecable cable

roof

20*

deck3’

10’

15’

cable anchored to �oor plate

Bldg 46

Deck

Roof

Cable

Closing line

(30’)

A B C D E F G H I J K L

a

b

c

d

e

f

g

h

i

j

k

l

29.4 k

29.4 k29.4 k29.4 k29.4 k29.4 k29.4 k29.4 k29.4 k29.4 k29.4 k29.4 k

point load

245.7 kMaximum Force

Force Polygon

9.7ft

o

2.96 m

130.86 kN

1092.93 kN

9.14 m

θ=20o

ah

θ=20o

PPh

Bldg 36


roof

20*

deck3’

10’

15’


Bldg 46

Deck

Roof

Cable

Closing line

(30’)


a

b

c

d

e

f

g

h

i

j

k

l

29.4 k

29.4 k29.4 k29.4 k29.4 k29.4 k29.4 k29.4 k29.4 k29.4 k29.4 k29.4 k

point load


Force Polygon

9.7ft

o

2.96 m

130.86 kN

1092.93 kN

9.14 m

ESTIMATED LOADSFloor Dead Load: 3.11 kN/m2 (65 psf)Floor Live Load: 3.83 kN/m2 (80 psf)Roof Dead Load: 1.44 kN/m2 (30 psf)Roof Live Load: 2.15 kN/m2 (45 psf)Cladding Load: 0.48 kN/m2 (10 psf)

CONCEPTThe Vassar Skybridge will allow for visibility down the street and by its slanted geometry it will allow for people on the bridge to lean over and see the street life below.

DESIGN ASSUMPTIONSBridge length: 32.54 m (106.75 ft)Bridge Width: 3.05 m (10 ft)Bridge Height: 4.57 m (15 ft)

ALLOWABLE STRESSES (σ)Steel: 103 N/mm2 (15 ksi)

POINT LOADS

Tributary Area - Floor(65 psf+80 psf )(10 ft)(9.7 ft)=14.065 kips

Tributary Area - Roof(30 psf+45 psf )(10 ft)(9.7 ft)=10.67 kips

Tributary Area - Cladding(10 psf)(15 ft)(9.7 ft)(2)=2.91 kips

Vertical Point Loads (P)27.645 kips =122.97 kN

Point Loads for Cable (Ph)Ph =P/cos(20o)=29.419 kips=130.86 kN

Maximum Force in Cable (Pm)Pm =245.7 kips=1092.93 kN

Gross Required Area for 2 Cables (Ag)σ=Pm/AgAg= Pm/ σ=245.7 kips/15 ksi=16.4 in2

Required Area for 1 Cable (A)A= 1/2 Ag=8.2 in2=5290.31 mm2

A= πr2

r=1.41 in=35.81 mm

SIZING THE CABLES

Required Area for Secondary Cables (As)As= Ph/ σ= πrs

2

rs=0.79 in= 20.06 mm

DISTRIBUTED LOADS

w=(80 psf+45 psf)(10 ft) =1250 plf=21161.155 N/m

SIZING THE TRUSSES

Maximum Moment in Truss(Mmax)Mmax=wL2/32Mmax=(1250 plf)(106.75 ft)2/32=516.36 klbft=1110.50 kNm

Maximum Tension and Compression Forces in Truss(T/C)T=C=Mmax/dT=C=516.36 klbft/3 ft=172.12 kips=765.63 kN

Gross Required Area for 2 Trusses (Ag)σ=T/AgAg= T/ σ=172.12 kips/15 ksi=11.47 in2

Required Area for 1 Truss (A)A= 1/2 Ag=5.74 in2=3703.22 mm2

A= πr2

r=1.35 in=34.29 mmRequired Area for Secondary Cables (As)As= 1/2 A= πrs

2

rs=0.95 in= 24.13 mm

Maximum Moment in Truss(Mmax) Mmax=wL2/64r=0.95 in= 24.13 mmrs=0.68 in= 17.27 mm

Vassar Skybridge

d=0.91m (3 ft)

T=607.23 kN (136.51 kips)

C=607.23 kN (136.51 kips)

Mmax=555.25 kNm (409.53 klbft)

Structural Design[4.463]Building Structural Systems IIProfessor: John Ochsendorf Andrea LoveTA: Caitlin Tobin Mueller

Laura Renee Schmitz Enid Xuezhu Tian

32.54 m

4.57m

9.14m

3.05m

0.91m

r=35.81mm

rs=20.06 mm

PLAN

SECTION A

SECTION B

Primary Cable Section

Secondary Cable Section

Primary Truss Member Section

Secondary member

MODULUS OF ELASTICITY (E)Steel: 29000 ksi

DEFLECTION

d1=1.5 ft

d2=1.5 ft

y’ y

A3

A4

A1

A2

d3

d4

Dimensions and Sectional Properties of Round HSS

for hollow steel tube, d=6.625 in

Δmax= 5wL4/384EI L=106.75 ft/2=53.375 ft We calculated for the deflection of half of the bridge for asymmetrical loadingΔmax ≤ L/360=53.375 ft/360=640.5 in/360=1.779 inwLL=(80 psf)(10 ft)+(45psf)(19.5 ft)=1677.5 plf =1.6775 k/ft=0.139 k/inE=29000 k/in2

I ≥5 wLLL4/384E Δmax= 5(0.139 k/in)(640.5 in)4/384(29000 k/in2)(1.779 in)=5094.1 in4

I= ΣIi=ΣAidi2

A1=A2=A3=A4= 5.74 in2

d1=d2=d3=d4=1.5 ft=18 in

I=4(5.74 in2)(18 in)2=7439.04 in4

7439.04 in4> 5094.1 in4

43

Bldg 36


roof

20*

deck3’

10’

15’


Bldg 46

Deck

Roof

Cable

Closing line

(30’)


a

b

c

d

e

f

g

h

i

j

k

l

29.4 k

29.4 k29.4 k29.4 k29.4 k29.4 k29.4 k29.4 k29.4 k29.4 k29.4 k29.4 k

point load


Force Polygon

9.7ft

o

2.96 m

130.86 kN

1092.93 kN

9.14 m

θ=20o

ah

θ=20o

PPh

Bldg 36


roof

20*

deck3’

10’

15’


Bldg 46

Deck

Roof

Cable

Closing line

(30’)


a

b

c

d

e

f

g

h

i

j

k

l

29.4 k

29.4 k29.4 k29.4 k29.4 k29.4 k29.4 k29.4 k29.4 k29.4 k29.4 k29.4 k

point load


Force Polygon

9.7ft

o

2.96 m

130.86 kN

1092.93 kN

9.14 m

ESTIMATED LOADSFloor Dead Load: 3.11 kN/m2 (65 psf)Floor Live Load: 3.83 kN/m2 (80 psf)Roof Dead Load: 1.44 kN/m2 (30 psf)Roof Live Load: 2.15 kN/m2 (45 psf)Cladding Load: 0.48 kN/m2 (10 psf)

CONCEPTThe Vassar Skybridge will allow for visibility down the street and by its slanted geometry it will allow for people on the bridge to lean over and see the street life below.

DESIGN ASSUMPTIONSBridge length: 32.54 m (106.75 ft)Bridge Width: 3.05 m (10 ft)Bridge Height: 4.57 m (15 ft)

ALLOWABLE STRESSES (σ)Steel: 103 N/mm2 (15 ksi)

POINT LOADS

Tributary Area - Floor(65 psf+80 psf )(10 ft)(9.7 ft)=14.065 kips

Tributary Area - Roof(30 psf+45 psf )(10 ft)(9.7 ft)=10.67 kips

Tributary Area - Cladding(10 psf)(15 ft)(9.7 ft)(2)=2.91 kips

Vertical Point Loads (P)27.645 kips =122.97 kN

Point Loads for Cable (Ph)Ph =P/cos(20o)=29.419 kips=130.86 kN

Maximum Force in Cable (Pm)Pm =245.7 kips=1092.93 kN

Gross Required Area for 2 Cables (Ag)σ=Pm/AgAg= Pm/ σ=245.7 kips/15 ksi=16.4 in2

Required Area for 1 Cable (A)A= 1/2 Ag=8.2 in2=5290.31 mm2

A= πr2

r=1.41 in=35.81 mm

SIZING THE CABLES

Required Area for Secondary Cables (As)As= Ph/ σ= πrs

2

rs=0.79 in= 20.06 mm

DISTRIBUTED LOADS

w=(80 psf+45 psf)(10 ft) =1250 plf=21161.155 N/m

SIZING THE TRUSSES

Maximum Moment in Truss(Mmax)Mmax=wL2/32Mmax=(1250 plf)(106.75 ft)2/32=516.36 klbft=1110.50 kNm

Maximum Tension and Compression Forces in Truss(T/C)T=C=Mmax/dT=C=516.36 klbft/3 ft=172.12 kips=765.63 kN

Gross Required Area for 2 Trusses (Ag)σ=T/AgAg= T/ σ=172.12 kips/15 ksi=11.47 in2

Required Area for 1 Truss (A)A= 1/2 Ag=5.74 in2=3703.22 mm2

A= πr2

r=1.35 in=34.29 mmRequired Area for Secondary Cables (As)As= 1/2 A= πrs

2

rs=0.95 in= 24.13 mm

Maximum Moment in Truss(Mmax) Mmax=wL2/64r=0.95 in= 24.13 mmrs=0.68 in= 17.27 mm

Vassar Skybridge

d=0.91m (3 ft)

T=607.23 kN (136.51 kips)

C=607.23 kN (136.51 kips)

Mmax=555.25 kNm (409.53 klbft)

Structural Design[4.463]Building Structural Systems IIProfessor: John Ochsendorf Andrea LoveTA: Caitlin Tobin Mueller

Laura Renee Schmitz Enid Xuezhu Tian

32.54 m

4.57m

9.14m

3.05m

0.91m

r=35.81mm

rs=20.06 mm

PLAN

SECTION A

SECTION B

Primary Cable Section

Secondary Cable Section

Primary Truss Member Section

Secondary member

MODULUS OF ELASTICITY (E)Steel: 29000 ksi

DEFLECTION

d1=1.5 ft

d2=1.5 ft

y’ y

A3

A4

A1

A2

d3

d4

Dimensions and Sectional Properties of Round HSS

for hollow steel tube, d=6.625 in

Δmax= 5wL4/384EI L=106.75 ft/2=53.375 ft We calculated for the deflection of half of the bridge for asymmetrical loadingΔmax ≤ L/360=53.375 ft/360=640.5 in/360=1.779 inwLL=(80 psf)(10 ft)+(45psf)(19.5 ft)=1677.5 plf =1.6775 k/ft=0.139 k/inE=29000 k/in2

I ≥5 wLLL4/384E Δmax= 5(0.139 k/in)(640.5 in)4/384(29000 k/in2)(1.779 in)=5094.1 in4

I= ΣIi=ΣAidi2

A1=A2=A3=A4= 5.74 in2

d1=d2=d3=d4=1.5 ft=18 in

I=4(5.74 in2)(18 in)2=7439.04 in4

7439.04 in4> 5094.1 in4

44

Load Calculations:

ωds 957.6 Pa:= Beam Depth: d 1.4 m:=Superimposed Dead Load on Deck:

ωll 4.8 103× Pa:= Beam Length: L 34.1 m:=Live Load on Deck:

Deck Width: w 3 m:=

Factored_Load 1.2ωds 1.6 ωll⋅+ 8.8 103× Pa⋅=:= Momentmax

Factored_Load w⋅ L2⋅

83.8 106

× N m⋅⋅=:=

TensionmaxMomentmax

d2.7 106

× N⋅=:= CompressionmaxTensionmax

21.4 106

× N⋅=:=

Size Tension Member:

Material Strength Reduction: ϕt 0.9:= Material Yeild Strength: Fy 3.4 108× Pa:=

AgTensionmax

Fy80.9 cm2

⋅=:=

HSS 12.750 x 0.375 gross area = 87.1 cm2

Pipe Diameter: 32.4 cm

Pipe Thickness: 1 cm

Size Compression Members:

Material Strength Reduction: ϕc 0.9:=Effective Length Factor: K 0.7:=Member Radius: r 32.4 cm:=Material Young's Modulus: E 2 1011

× Pa:=Length of Compression Member: Lc 5.2 m:=

Feπ

2 E⋅

K L⋅r

23.6 108

× Pa⋅=:= AgcCompressionmax

Fe37.8 cm2

⋅=:=




Vassar Street Skywalk

•  A unique feature of MIT’s campus is its system of interconnected buildings which allow students and faculty to travel across campus indoors.

•  The Brain and Sciences Complex was completed in 2005, and has no connection to this interconnected network. This requires students and faculty to cross Vassar Street if they wish to go to buildings on the main campus.

•  MIT would like to connect the recently built Brain and Cognitive Sciences Building to the Main Campus via a Skywalk over Vassar Street

Schematic Plan

Load Path

Prepared By: Emidio Piermarini – PM Tzoni Tzonev – SE Congyi Qian – AIA

Project Background Calculations

17' - 0"

A B

A BK = 0.7

ISOMETRIC VIEW PLAN VIEW

ELEVATION VIEW

TYP. SECTION

4'-9"(1.5 m)

10'-0"(3 m)

BLDG 46COG. SCI.

BLDG 36

34° TYP.

10'-0"(3 m)

112'-0"(34 m)

17'-6", TYP. SPAN(5.3 m)

33°

45

Load Calculations:

ωds 957.6 Pa:= Beam Depth: d 1.4 m:=Superimposed Dead Load on Deck:

ωll 4.8 103× Pa:= Beam Length: L 34.1 m:=Live Load on Deck:

Deck Width: w 3 m:=

Factored_Load 1.2ωds 1.6 ωll⋅+ 8.8 103× Pa⋅=:= Momentmax

Factored_Load w⋅ L2⋅

83.8 106

× N m⋅⋅=:=

TensionmaxMomentmax

d2.7 106

× N⋅=:= CompressionmaxTensionmax

21.4 106

× N⋅=:=

Size Tension Member:

Material Strength Reduction: ϕt 0.9:= Material Yeild Strength: Fy 3.4 108× Pa:=

AgTensionmax

Fy80.9 cm2

⋅=:=




Size Compression Members:

Material Strength Reduction: ϕc 0.9:=Effective Length Factor: K 0.7:=Member Radius: r 32.4 cm:=Material Young's Modulus: E 2 1011

× Pa:=Length of Compression Member: Lc 5.2 m:=

Feπ

2 E⋅

K L⋅r

23.6 108

× Pa⋅=:= AgcCompressionmax

Fe37.8 cm2

⋅=:=




Vassar Street Skywalk

•  A unique feature of MIT’s campus is its system of interconnected buildings which allow students and faculty to travel across campus indoors.

•  The Brain and Sciences Complex was completed in 2005, and has no connection to this interconnected network. This requires students and faculty to cross Vassar Street if they wish to go to buildings on the main campus.

•  MIT would like to connect the recently built Brain and Cognitive Sciences Building to the Main Campus via a Skywalk over Vassar Street

Schematic Plan

Load Path

Prepared By: Emidio Piermarini – PM Tzoni Tzonev – SE Congyi Qian – AIA

Project Background Calculations

17' - 0"

A B

A BK = 0.7

ISOMETRIC VIEW PLAN VIEW

ELEVATION VIEW

TYP. SECTION

4'-9"(1.5 m)

10'-0"(3 m)

BLDG 46COG. SCI.

BLDG 36

34° TYP.

10'-0"(3 m)

112'-0"(34 m)

17'-6", TYP. SPAN(5.3 m)

33°

46

9.14 m max.

2.74 mmin.

STRUCTUREPRECEDENTS

CONNECTION DETAIL PRECENTS

SCHLAICH BERGERMANN UND PARTNERRipshorst Bridge


BIRDS PORTCHMOUTH RUSSUMPlashet School Footbridge

ELEVATION 1:100

PLAN 1:200SECTION 1:200

VCATHERINE DE WOLFTYLER STEVERMER

BRIDGE

LOADS

PRIMARY STRUCTURE SIZING

SECONDARY STRUCTURE SIZING

1.52 m typ.

6.2 m

6.2 m

33 m

DEFLECTION

y

47

9.14 m max.

2.74 mmin.

STRUCTUREPRECEDENTS

CONNECTION DETAIL PRECENTS



BIRDS PORTCHMOUTH RUSSUMPlashet School Footbridge

ELEVATION 1:100

PLAN 1:200SECTION 1:200

VCATHERINE DE WOLFTYLER STEVERMER

BRIDGE

LOADS

PRIMARY STRUCTURE SIZING

SECONDARY STRUCTURE SIZING

1.52 m typ.

6.2 m

6.2 m

33 m

DEFLECTION

y

School of archiTecTure + Planning

Design by Caitlin Mueller, 2013Photos by Ana Vargas and Caitlin Mueller, 2012

“The experience of having Jorg Schlaich in our class was particularly great: not only was he was able to pinpoint the flaws in the structural logic, but he also gave very good advice in the program and aesthetics of the design, which I appreciated very much as an architect. It was really great to learn from him; thanks very much!”

– Shiyu Wei, Master of Architecture Student

jörg schlaich

Documents