Appendix A Drawings and Calculations of Global Geometry for Model0_0

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Cable-stayed bridge connected to a chained floating bridge – A case study Anntra-8@student.ltu.se

Appendix A

Anna Tranell December 20, 2016

Appendix A

Drawings and Calculations of Global Geometry for Model0_0

In Appendix A1 are drawings of the Third Nanjing Bridge, Sutong Bridge (described in § 5.5) and the

cross section from Figure 5 11 (§ 5.2.2) presented.

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Appendix A1: Drawings on example bridges

The Third Nanjing Bridge: (Virola, 2009)

Elevation and Plan

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Sutong bridge: (Bentley, 2009)

Elevation [m]

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Example of orthotropic steel box cross section (Leonhardt & Zellner, 1991)

Bibliography

Bentley. (2009). The Sutong Bridge - A structural Analysis. Retrieved May 28, 2015, from http://ftp2.bentley.com/dist/collateral/docs/bentley_structural/Bentley-Structural_the_sutong_bridge-analysis-hi-res.pdf

Leonhardt, F., & Zellner, W. (1991). Past, present and future of cable-stayed bridges. In M. Ito, Y. Fujino, T. Miyata, & Narita, Nobuyuki (Ed.), Proc. Cable-Stayed Bridges - Recent Developments and their Future, Yokahoma, Japan, 10-11

Decemeber 1991 (pp. 1-33). Yokahoma, Japan: Elsiver Science Publishers B.V.

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Appendix A2 - Calculations of global geometry

Page 1 of 3

Appendix A2 - Calculations of global geometry

Cable

Determine angle of cable plan

Surgut bridge:

≔

α_1

_{atan ⎛⎜}

=

⎝

――

146

408 ⎞

⎟⎠

19.7 3rd Nanjing Bridge:

≔

α_2

_{atan ⎛⎜}

=

⎜

⎝

――

170 ――

648

2 ⎞

⎟

⎠

27.7 Sutong Bridge:

≔

α_3

_{atan ⎛⎜}

=

⎜

⎝

――

197 ――

1088

2 ⎞

⎟

⎠

19.9 Mean value

≔

α

―――――

α_1 α_2 α_3

+

=

3

22.4 Choose: ≔

α 22.5

Spacing of cables at girder

3rd Nanjing Bridge:

_{s_1}

_≔

_―――

648 ₌

⋅

2 22

14.7 Sutong Bridge:

s_2 16

≔

Choose:

_{s 15}

_≔

gives cables

_―――

300 ₌

s

20 Girder

Required width:

_{b_min 22}

_≔

Determine hight of cross-section

Type 1:

≔

h_1

―――――

2.5 ⋅

=

⋅

2 ((

10.5 2.5))

+

b_min 2.1

to

h_2

≔

―――――

⋅

=

3.5 ⋅

2 ((

10.5 2.5))

+

b_min 3

3rd Nanjing Bridge:

≔

h_3

――

3.2 ⋅

=

32 b_min 2.2

Sutong bridge

≔

h_4

――――

4 ⋅

=

(( −

41 2 3))

⋅

b_min 2.5

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Appendix A2 - Calculations of global geometry

Page 2 of 3

Mean value:

h

≔

―――――――

h_1 h_2 h_3 h_4

+

=

4

2.4 Choose: ≔

h 2.5

Example 1

3rd Nanjing Bridge

Sutong bridge

Determine length of bottom plate

3rd Nanjing bridge:

≔

L_bottom_plate

――

21.6 ⋅

=

32 b_min 14.9

Choose:

_{L_bottom_plate 15}

_≔

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Appendix A2 - Calculations of global geometry

Page 3 of 3

Pylon

Determine hight

Requiered height below deck

_H

_B

_≔

₅₀

Extra height above top cable

_H

_T

_≔

_{tan ((α)) s 6.2}

_⋅

₌

≔

H

A

+

H

D

+

H

B

+

H

T

=

184 Choose: ≔

H 184

Width and depth

3rd Nanjing Bridge:

Based on width of deck

Based on pylon height above deck

≔

W

――

6.8 ⋅

=

32 b_min 4.7

W

≔

――

⋅

=

6.8

180 H

A

4.7 ≔

D

―

5 ⋅

=

32 b_min 3.4

D

≔

――

⋅

=

5

180 HA

3.5 Sutong bridge

≔

W_top

―――

8 ⋅

=

−

41 2 2

⋅

b_min 4.8

W_top

≔

――

⋅

=

8

197 H

A

5 ≔

W_btm

―――

16 ⋅

=

−

41 2 2

⋅

b_min 9.5

W_btm

≔

――

⋅

=

16

197 HA

10.1 Choose:

_{W 5}

_≔

and

_{D 3.5}

_≔

Requiered height above deck

_H

_A

_≔

_{tan ((α)) ((300 )) 124.3}

_⋅

₌

Requiered height at deck

_HD

_≔

_{h 1}

₊

₌

_3.5

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Appendix B

Appendix B

Definition of Geometry and Loads for Model0_0

Appendix B include the following parts;

1. Geometry and dead load

2. Variable loads

3. Stiffness at support of chained floating Bridge

4. Load combinations in ULS

5. Load combinations in SLS

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Appendix B1: Geometry and Dead Load 11.06.2015 Anna Tranell

Dead Load and Geometry

Parameters

General dimensions [m] Height Width Length Number Material fy gM0

Bridge 53 600 MPa

Girder 2.5 25 15 40 Structural Steel S355 355 1.1

Pylon 184.5 3.5 2.5 4 Concrete C45 45 1.5

Diameter Angle c/c tower

Cable 0.14 22.5 6.21 80

Dead load of Materials

Steel gsteel 78.5kN/m

3

SOFiSTiK

Hot rolled asphalt gasphalt 23.0kN/m

3 SS-EN 1991-1-1 (E ) Concrete gconcrete 25.0kN/m 3 SS-EN 1991-1-1 (E )

Girder

Components

Structural, in model (A) ID Number Length Thickness Area Load Load

L [mm] t [mm] A [mm2] G [kN/m] [kN/m2]

Top plate A1 1 23000 20 460000 36.11

Bottom plate

Middle A2 1 15000 20 300000 23.55

Side A3 2 5220 20 208806 16.39

Primary Longitudinal Stiffeners

Mid A4 3 2460 15 110700 8.69

Edge A5 2 1460 15 43800 3.44

Edge A6 2 1414 15 42426 3.33

Sum 1.17E+06 91.51 3.66

Check Cell Calculation

Input Linked Cell

Output Explanation

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Structural, not in model (B) ID Number c/c Load Length, top Length, btm Height Thickness Area Load Load

Secondary longitudinal stiffeners Gi [kN/m] L [mm] L [mm] H [mm] t [mm] A [mm

2 ] G [kN/m] [kN/m2] T (0,5 IPE 300) B1 14 0.21 37667 2.90 www.sbi.se Top stiffeners B2 44 500 250 150 250 7 203250 15.96 Bottom stiffeners B3 28 1000 250 450 250 7 193749 15.21 Sum 4.35E+05 34.06 1.36

ID Number c/c Load Wtop Htop Hbottom Thickness Area Volume Load Load Load

Gi [kN/m] [mm] [mm] [mm] t [mm] A [mm

2

] V [m3] G [kN] G [kN/m] [kN/m2]

Prim transversal stiffeners B4 3 5000

Rectangle 3 15000 2460 2460 15 110700000 1.66 130.35 8.69

Trapezoid 6 3500 2460 1460 15 4.12E+07 0.62 48.47 3.23

Secondary transversal stiffeners

T (0,5 IPE 300) B6 8 1000 0.21 22000 21524 0.47 36.47 2.43 www.sbi.se

Sum 2.75 215.28 14.35 0.57

Non-structural (C ) ID Number L t Load Load Load

[m] [mm] Gi [kN/m] G [kN/m] [kN/m

2 ]

Asphalt C1 20 150 69 Assumed thickness 150 mm on all lanes

Concrete C2 2.4 250 15

Railing C3 4 0.6 2.4

Sum 86.4 3.46

Load Load

Total dead Load g [kN/m2] G [kN/m]

Structural, in model (A) 3.66 91.5

Structural, not in model (B) 1.94 48.4

Longitudinal 1.36

Transversal 0.57

Structural dead Load 5.60 139.9

Non-structural (C ) 3.46 86.4

Total dead Load 9.05 226.3

Combination of loads

Factor Design

Dead Load gk 9.05kN/m

2

1.35 12.22

Traffic *Variable loads are defined in the following part B2 and linked to this calculation

-Tandem system Qk 600kN 1.35 810*

-UDL - uniformly distributed load qk 2.55kN/m

2 1.35 3.44* Wind wk 1.19kN/m 2 0.7 0.83* Sum 16.49 kN/m2 and 810.00 kN Characteristic

Concrete safety divider (attached to railings), assumed geometry 3*0.8m thickness 250 mm

Transversal members per section girder

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Cables

Estimated tension

Loaded area/cable 187.5 m2 =Width of girder*Height of girder/2

Design Only dead load of girder Design=Loaded area*Design area load+Design point load

Vertical force component 3903 kN 1697 kN Dead load=Loaded area*Dead load

Tension in cable 10 198 kN 4 436 kN Tension in cable = Vertical force component/sinus(Angle of cable)

Preliminary type

Type LC 140

Specification

Diameter f 140mm

Design load Fd 11333kN

Nominal metallic cross section A 13900mm2

Nominal axial stiffness EA 2290MN

Nominal metallic Mass m 112kg/m

Values for input in sofistik

Yield strength fy 896.9 MPa Strength

Diameter based on metallic cross section fnom 133.03 mm Cross section

Elastic modulus E 164748 N/mm2 Material properties

Density r 8058 kg/m3 Material properties

Dead load gcable 80.6 kN/m3 Material properties

Sum of whole bridge

Cable lengths Length=Distance/cosine(Angle of cable)

Number 1 2 3 4 5 6 7 8 9 10

Attachment on girder, distance 300 285 270 255 240 225 210 195 180 165

Length 324.7 308.5 292.2 276.0 259.8 243.5 227.3 211.1 194.8 178.6

Cont.

Number 11 12 13 14 15 16 17 18 19 20

Attachment on girder, distance 150 135 120 105 90 75 60 45 30 15

Length 162.4 146.1 129.9 113.7 97.4 81.2 64.9 48.7 32.5 16.2

Totals

Total length 13638 m

Dead load of cable 1.12 kN/m m*g, g=10m/s2

Total dead load 15275 kN

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Pylon

General dimensions Height

Top Htop 184.5m

Top cable Hcable 178.3m

Top of girder Hgirder 53.0m

Concrete part Hconctrete 50.0m

Ground level Hground 0m

Inclination of 1 leg Top Btm

Transversal T 1.75 19.14m

Longitudinal L 1.25 3.75m

Length of Leg Number Length

Top 2 6.21 m

Leg 4 183.5 m

Steel part 4 132.0 m

Concrete part 4 51.5 m

Estimated area in preliminary design

Loaded area 15000 m2 Width of bridge*length of bridge

Design area load 16.49kN/m2

Design point loads 810.00kN

Dead load of cables (*factor 1.35) 20621 kN

Sum, Q 268.8MN

Required area of steel, excl. dead load of

pylon Anom 0.833 m2

Required area of steel for each leg Anom/leg 0.208 m2

Factor due to moment on pylon A*nom/leg 2.00 0.417 m2

Dead load: Steel in 1 leg Gleg 4418 kN

Required area of steel, incl dead load of pylon Aleg 0.430 m2 --> 4.30E+05 mm2

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Dead Load

Steel Part Number Length Width Radius Thickness Area Load

Structural, in model L [mm] W [mm] R [mm] t [mm] A [mm2] G [kN/m] Leg 4 3500 2500 Top/bottom 2 1920 40 153600 12.06 Sides 2 3000 40 240000 18.84 Round edges 4 393 250 40 62832 4.93 Sum 4.56E+05 35.8

Transversal connector, top 3 3500 2500

Top/bottom 2 1920 40 153600 12.06

Sides 2 3000 40 240000 18.84

Round edges 4 393 250 40 62832 4.93

Sum 35.8

Connections, Calculation of lengths

Connection attached to cable nr: 1 2 3 4 5 6 7 8 9 10

Attachment on Pylon, Height 178.3 172.1 165.8 159.6 153.4 147.2 141.0 134.8 128.6 122.3

Length, L [m] 0.0 0.3 0.5 0.8 1.0 1.3 1.6 1.8 2.1 2.4

Cont.

Connection attached to cable nr: 11 12 13 14 15 16 17 18 19 20

Attachment on Pylon, Height 116.1 109.9 103.7 97.5 91.3 85.1 78.9 72.6 66.4 60.2

Length, L [mm] 2.6 2.9 3.1 3.4 3.7 3.9 4.2 4.4 4.7 5.0

Connections, sum Diameter Thickness Area Length Load

W [mm] t [mm] A [mm2] L [m] G [kN]

508 10 15645 99.3 122.00

Structural, not in model Number c/c Load Load

Secondary longitudinal stiffeners Gi [kN/m] G [kN/m]

T (0,5 IPE 600) 6 800 0.60 3.59www.sbi.se

T (0,5 IPE 600) 8 800 0.60 4.79

Secondary transversal stiffeners Gi [kN]

T (0,5 IPE 600) 1.25 800 3.88 4.85www.sbi.se

Sum 13.24

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Concrete Part

Strength concrete, fcd 25.5 MPa

Relative thickness concrete 556.9 mm

Number Length Width Radius Thickness Area Load

L [mm] W [mm] R [mm] t [mm] A [mm2] G [kN/m] Leg 4 3780 2780 560 Top/bottom 2 2780 560 3113600 77.84 Sides 2 2660 560 2979200 74.48 Round edges 4 400 560 -137345 -3.43 Sum 148.9 Transversal connector, btm 1 7000 5000 450 Top/bottom 2 5000 450 4500000 112.50 Sides 2 6100 450 5490000 137.25 Round edges 4 400 450 -137345 -3.43 Sum 246.3

Total Dead Load

Per area Per meter Per section Total

Girder

G [kN/m2] G [kN/m] G [MN] G [MN]

Structural, in model (A) 3.7 91.51 1.37 54.9

Structural, not in model (B) 1.9 48.41 0.73 29.0

Non-structural (C ) 3.5 86.40 1.30 51.8

sum 135.8

Pylon

Steel Part

Leg, in model 35.83 19.37

Leg, not in model (B) 13.24 7.16

Transversal beam, in model 30.90 0.16

Transversal beam, not in model (B) 13.24 0.07

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Appendix B2: Variable loads 11.06.2015 Anna Tranell

General dimensions

Bridge Girder Pylon, steel Pylon, conc Transversal

Length, [m] Li 600 184.5 50.0 19.1405 Cables 0.14

Height, [m] Hi 53 2.5 3.5 3.8 7 Connectors top 0.508

Width, [m] Bi 25 2.5 2.8 5 Connectors bottom 1.218

Radius, [m] Ri 0.3 0.4 0.4

Variable loads

Wind Actions According to EN 1991-1-4 Wind forces 5.3 Structural factors:

Size factor cs 1 8.2 Note 2: No dynamic response needed

Dynamic factor cd 1

Force coefficient cf

Peak velocity pressure at

reference height zb qp(ze)

Reference area Aref

Force coefficient

Girder Direction

Force coefficient, cf,i y 1.3 8.3.1 Note 2

z 0.9 8.3.3 Note 1

x 8.3.4 (1) Plated bridges, 25 % of the wind forces in x-direction

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Pylon Steel section Concrete section Transversal

Direction y x y x x

d/b= B//Wind/B_I_Wind 1.4 0.7 1.4 0.7 0.7 x=B/H, y=H/B

Force coefficient of rectangular

sections with sharp corners cf,0 1.875 2.4 1.875 2.4 2.4 7.6 fig 7.23

Ratio: r/b_l_ yr 0.10 0.07 0.1438849 0.11 0.06

Reduction factor for rounded

corners yr 0.75 0.8214286 0.6402878 0.7354497 0.8571429 7.6 fig 7.24

Effective slenderness l 70 53.8 12.6 9.3 1.9 7.13 table 7.16

Solidity ratio j 1 1 1 1 1 7.13 (3)

End-effect factor for elements with

free-end flow yl 0.92 0.8902217 0.7260385 0.6966576 0.6281953 7.13 figure 7.36

Force coefficient cf 1.29375 1.7550084 0.871638 1.229656 1.2922875 7.6 eq. 7.9

Figure 7.23 from EN 1991-1-4 section 7.6 Figure 7.24 from EN 1991-1-4 section 7.6

Cables

Force coefficient of circular

sections cf,0 1.2 7.9.2 (3) stranded cables

End-effect factor for elements with

free-end flow yl 1 7.13 figure 36, simplification

Force coefficient cf 1.2

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Reference wind velocity for

Austevoll municipality v0 [m/s] 28 NS-EN 1991-1-4:2005/NA:2009 Fylke: Hordaland

Table NA.4(901.1) Municipalities around:

Fundamental values of the basic wind velocity: Os 26 [m/s]

Increased with open sea factor 1,3

vb,0 [m/s] 36.4 NS-EN 1991-1-4:2005/NA:2009 Austevoll 28 [m/s]

Traffic simultaneous with wind,

incl. traffic vb,0* [m/s] 23 8.1 (4) Tysnes 26 [m/s]

Basic wind velocity, section 4.2 (2)

Constants:

Directional factor cdir 1

Season factor cseason 1

Basic wind velocity Excl. T vb [m/s] 36.4

Incl. T vb* [m/s] 23.0

Peak velocity pressure, section 4.5 Constants:

Air density r [kg/m3_] _1.25 _{4.1 Note 2}

Orography factor c0(z) [-] 1.0 4.3.1 (1)

Turbulence factor kl [-] 1.0 4.4 Note 2

Roughness length zo [m] 0.003 4.3.2 table 4.1 terrain category 0: sea or costal area exposed to the open sea

Roughness length for terrain

category II z0,II [m] 0.05

4.3.2 table 4.1 terrain category II

Terrain factor kr [-] 0.156 4.2.3 eq. 4.5

Formulas:

Girder Incl. T Excl. T

Reference height zb [m] 53 53

Turbulence intensity Iv(z) [-] 0.102 0.102 4.4 Note 2

Terrain roughness factor cr(z) [-] 1.526 1.526 4.2.3

Mean wind velocity vm(z) [m/s] 35.1 55.5 4.3.1 (1)

Peak velocity pressure at reference

height zb qp(ze) [N/m 2_]

1321 3308 4.5 Note 1 Peak velocity pressure at reference height zb

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Pylon

Should be divided into horizontal strips 7.2.2 (1)

Strips

Reference height zb [m] 20.00 50.00 78.85 109.92 147.20 184.48

Turbulence intensity Iv [-] 0.114 0.103 0.098 0.095 0.093 0.091

Terrain roughness factor cr(z) [-] 1.37 1.52 1.59 1.64 1.69 1.72

Incl. T vm(z)* [m/s] 31.6 34.9 36.5 37.7 38.8 39.6 Excl. T vm(z) [m/s] 50.0 55.2 57.8 59.7 61.3 62.6 Incl. T qp(ze)* [N/m 2_] 1120 1308 1407 1481 1548 1600 Excl. T qp(ze) [N/m 2_] 2806 3277 3524 3710 3876 4008

Mean wind velocity

Peak velocity pressure at reference height zb 0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 160.00 180.00 200.00 0 500 1000 1500 2000 2500 3000 3500 4000 4500 R efe re n ce h ei gh t, zb [m]

Peak velocity pressure, qp(ze) [N/m]

Approximation of Peak Velocity Pressure

qp(ze) Real qp(ze) qp(ze)* Real qp(ze)*

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Cable and pylon connectors Bottom Top cables and connectors

Number [-] All 1 2 3 4 5 6 7 8 9 10

Reference height zb [m] 53.0 178.26407 172.05087 165.83766 159.62446 153.41125 147.19805 140.98485 134.77164 128.55844 122.34524

Turbulence intensity Iv [-] 0.102 0.091 0.091 0.092 0.092 0.092 0.093 0.093 0.093 0.094 0.094

Terrain roughness factor cr(z) [-] 1.53 1.72 1.71 1.70 1.70 1.69 1.69 1.68 1.67 1.66 1.66

Incl. T vm(z)* [m/s] 35.1 39.4 39.3 39.2 39.1 38.9 38.8 38.6 38.4 38.3 38.1 Excl. T vm(z) [m/s] 55.5 62.4 62.2 62.0 61.8 61.6 61.3 61.1 60.8 60.6 60.3 Incl. T qp(ze)* [N/m 2_] 1321 1592 1584 1575 1566 1557 1548 1538 1527 1517 1505 Excl. T qp(ze) [N/m 2_] 3308 3988 3967 3945 3923 3900 3876 3852 3826 3799 3770

Continuing top Transversal connectors

Number [-] 11 12 13 14 15 16 17 18 19 20 Top 1 Top 2 Top 3 Btm

Reference height zb [m] 116.13203 109.91883 103.70563 97.492424 91.279221 85.066017 78.852814 72.63961 66.426407 60.213203 153.4 134.8 116.1 50.0

Turbulence intensity Iv [-] 0.095 0.095 0.096 0.096 0.097 0.098 0.098 0.099 0.100 0.101 0.092 0.093 0.095 0.103

Terrain roughness factor cr(z) [-] 1.65 1.64 1.63 1.62 1.61 1.60 1.59 1.58 1.56 1.55 1.69 1.67 1.65 1.52

Incl. T vm(z)* [m/s] 37.9 37.7 37.5 37.3 37.0 36.8 36.5 36.2 35.9 35.6 38.9 38.4 37.9 34.9 Excl. T vm(z) [m/s] 60.0 59.7 59.4 59.0 58.6 58.2 57.8 57.3 56.8 56.3 61.6 60.8 60.0 55.2 Incl. T qp(ze)* [N/m 2 ] 1494 1481 1468 1454 1440 1424 1407 1389 1370 1348 1557 1527 1494 1308 Excl. T qp(ze) [N/m 2 ] 3741 3710 3677 3642 3605 3566 3524 3479 3430 3377 3900 3826 3741 3277

Mean wind velocity

Peak velocity pressure at reference height zb

Mean wind velocity

0 20 40 60 80 100 120 140 160 180 200 0 500 1000 1500 2000 2500 3000 3500 4000 4500 Re fe re n ce h ei gh t, zb [m]

Peak velocity pressure, qp(ze) [N/m2]

Approx. of Peak Velocity Pressure Cable no: 1

qp(ze)* Real qp(ze)* qp(ze) Real qp(ze)

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Reference area

Direction

Girder y Aref [m

2_/m]

3.7 8.3.1 (4) Aref=H+1.2 (open parapet and safety barrier) z Aref [m 2_/m] 25 8.3.3 (2) Tower Direction y Aref [m 2_/m] 2.5 7.6 (2) x Aref [m 2_/m] 3.5

Beam Pylon-Girder Aref [m

2

/m] 7 7.6 (2)

Connectors Top Aref [m

2_/m] 0.508 7.9.2 (4) Btm Aref [m 2 /m] 1.218 Cables Aref [m 2_/m] 0.14 7.9.2 (4) Wind force, Fw

Girder Direction Incl. T Excl. T

Beam elements y [kN/m] 6.35 15.91

x [kN/m] 1.59 3.98

z [kN/m] 29.72 74.44

Direction Incl. T Excl. T Area elements y [kN/m2_]

2.54 6.37

x [N/m2] 0.06 0.16

z [kN/m2] 1.19 2.98

Pylon Concrete Steel Transversal

Direction Height [m] 20 50 50 79 110 147.20 184 153.4 134.8 116.1 50.0 Incl. T [kN/m] 2.44 2.85 4.23 4.55 4.79 5.01 5.18 Excl. T [kN/m] 6.11 7.14 10.60 11.40 12.00 12.54 12.96 Incl. T [kN/m] 4.82 5.63 8.04 8.64 9.10 9.51 9.83 19.13 18.76 18.35 11.84 Excl. T [kN/m] 12.08 14.10 20.13 21.65 22.79 23.81 24.62 47.92 47.00 45.96 29.65 Connectors Height [m] 178.3 172.1 165.8 159.6 153.4 147.2 141.0 134.8 128.6 122.3 Incl. T [kN/m] 1.0 1.0 1.0 1.0 0.9 0.9 0.9 0.9 0.9 0.9 Excl. T [kN/m] 2.4 2.4 2.4 2.4 2.4 2.4 2.3 2.3 2.3 2.3 Cont.… Height [m] 116.1 109.9 103.7 97.5 91.3 85.1 78.9 72.6 66.4 60.2 Incl. T [kN/m] 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.8 0.8 0.8 Excl. T [kN/m] 2.3 2.3 2.2 2.2 2.2 2.2 2.1 2.1 2.1 2.1

Cable Bottom Top

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Traffic

According to EN 1991-2

Number of lanes, b>6m --> n=Integer(b/wl) 4.2.3 table 4.1

Width of notional lane wl 3m

n= 7

Load model 1

According to NS-EN 1991-2:2003/NA:2010 section 4.3.2

Coefficients Axle loads, tandem system Uniformly distributed load, UDL

aQi 1i: 1,2,…,n Q1k 300 kN q1k 9[kN/m 2 ] aq1 0.6 Q2k 200 kN qik 2.5[kN/m 2_] i: 2,…,n aqi 1i: 2,…,n Q3k 100 kN

e FTS TTS fUDL FUDL TUDL

[m] [kN] [kNm] [kN/m2_] _[kN/m] _[kNm/m] Lane 1 9.5 300 2850 5.4 16.2 153.9 Lane 2 6.5 200 1300 2.5 7.5 48.75 Lane 3 3.5 100 350 2.5 7.5 26.25 Lane 4 0.5 2.5 7.5 3.75 Lane 5 -2.5 2.5 7.5 -18.75 Lane 6 -5.5 2.5 7.5 -41.25 Lane 7 -8.5 2.5 7.5 -63.75 Residual -9 2.5 2.5 -22.5 Traffic 1 F T

Maximum vertical loads UDL 63.7 [kN/m] 86.4 [kNm/m]

TS 600 [kN] 4500 [kNm]

Traffic 2

Maximum torque UDL 38.7 [kN/m] 232.65 [kNm/m]

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Temperature

According to EN 1991-1-5:2003/NA:2008

Air temperature

Maximum shade air temp Tmax 34°C Figure NA.A1

Minimum shade air temp Tmin -25°C Figure NA.A2

Initial temp. when restrained T0 10°C NA.A. 1

Bridge deck 6.1.1

Assessed by 6.1.3 Uniform temperature load 6.1.4 Temperature difference components

Uniform temperature component

Max uniform temp component Te,max 50 °C NA.6.1 Tmax+16 Min uniform temp component Te,min -28 °C NA.6.1 Tmin -3

Range of uniform bridge temperature component

Maximum contraction range TN,con 38 °C 6.1.3.3 (6.1)

Maximum expansion range TN,exp 40 °C 6.1.3.3 (6.2)

For bearings and expansion joints

Maximum contraction range DT 58 °C 6.1.3.3 Note 2

Maximum expansion range DT 60 °C

Temperature difference components

Vertical linear component ksur 6.1.4.1 Table 6.2, 150 mm surface

Top warmer than bottom TM,heat 18 0.7 12.6 °C 6.1.4.1 Table 6.1

Bottom warmer than top TM,cool 13 1.2 15.6 °C 6.1.4.1 Table 6.1

Horizontal components 5°C 6.1.4.3

Simultaneity of uniform temperature difference components

Numerical values N 0.35 6.1.5 Note 1

M 0.75

Differences in the uniform temperature component between different structural elements, 6.1.6

Between structural elements DT 15°C Stay cables and deck/tower DT 20°C

Considered in addition to the effects resulting from a uniform temperature component in all elements

Type 1

𝑚𝑜𝑠𝑡 𝑎𝑑𝑣𝑒𝑟𝑠𝑒 𝑜𝑓 𝑇𝑀,ℎ𝑒𝑎𝑡𝑜𝑟 𝑇𝑀,𝑐𝑜𝑜𝑙 +𝑁∗ 𝑇𝑁,𝑒𝑥𝑝(𝑜𝑟 𝑇𝑁,𝑐𝑜𝑛)

𝑀∗ 𝑇𝑀,ℎ𝑒𝑎𝑡 𝑜𝑟 𝑇𝑀,𝑐𝑜𝑜𝑙 + 𝑇𝑁,𝑒𝑥𝑝(𝑜𝑟 𝑇𝑁,𝑐𝑜𝑛)

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Appendix B4: Load combinations ULS 19.12.2016 Anna Tranell Ac Co Pa γsup γinf γac ψ0 ψ1 ψ2 ψ1' G 2 G 1.35 1.00 1.00 1.00 1.00 1.00 1.00 AC Action P 1 P 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Co Combination R 2 P 1.00 0.50 0.75 0.75 0.75 0.75 0.75 Pa Partition W 6 Q 1.60 0.00 1.00 0.70 0.60 0.50 0.80 γsup γunfavourable

L 6 Q 1.35 0.00 1.00 0.70 0.70 0.50 0.80 γinf γfavourable X Action included

Z 3 Q 1.60 0.00 1.00 0.70 0.60 0.50 0.80 γac γaccidental O Dominate action

T 4 Q 1.20 0.00 1.00 0.70 0.60 0.50 0.80 Combination of actions No G P R W L Z T G P R W L Z T Total A X X X 2 1 2 1 1 1 1 4 B:1 X X X O 2 1 2 6 1 1 1 24 B:2 X X X O X 2 1 2 6 1 1 4 96 B:3 X X X X O 2 1 2 6 1 1 4 96 B:4 X X X O 2 1 2 1 1 1 4 16 C:1 X X X O 1 1 2 1 6 1 1 12 C:2 X X X O X 1 1 2 1 6 3 1 36 C:3 X X X O X X 1 1 2 1 6 3 4 144 C:4 X X X X O 1 1 2 1 6 3 1 36 C:5 X X X X O X 1 1 2 1 6 3 4 144 C:6 X X X X X O 1 1 2 1 6 3 4 144 C:7 X X X X O 1 1 2 1 6 1 4 48

*Assume that for combinations with traffic G is always unfavourable Sum 800

G P R W1 W2 W3 W4 W5 W6 L1 L2 L4 L5 L6 L7 Z1 Z2 Z3 T2 T10 T11 T12 100 4 5 101 102 103 104 105 106 201 202 204 205 206 207 301 302 303 402 410 411 412 A 1001 1.35 1.00 1.00 A 1002 1.00 1.00 1.00 A 1003 1.35 1.00 0.50 A 1004 1.00 1.00 0.50 B:1 1005 1.35 1.00 1.00 1.60 B:1 1006 1.00 1.00 1.00 1.60 B:1 1007 1.35 1.00 0.50 1.60 B:1 1008 1.00 1.00 0.50 1.60 B:1 1009 1.35 1.00 1.00 1.60 B:1 1010 1.00 1.00 1.00 1.60 B:1 1011 1.35 1.00 0.50 1.60 B:1 1012 1.00 1.00 0.50 1.60 B:1 1013 1.35 1.00 1.00 1.60 B:1 1014 1.00 1.00 1.00 1.60 B:1 1015 1.35 1.00 0.50 1.60 B:1 1016 1.00 1.00 0.50 1.60 B:1 1017 1.35 1.00 1.00 1.60 B:1 1018 1.00 1.00 1.00 1.60 B:1 1019 1.35 1.00 0.50 1.60 B:1 1020 1.00 1.00 0.50 1.60 B:1 1021 1.35 1.00 1.00 1.60 B:1 1022 1.00 1.00 1.00 1.60 B:1 1023 1.35 1.00 0.50 1.60 B:1 1024 1.00 1.00 0.50 1.60 B:1 1025 1.35 1.00 1.00 1.60 B:1 1026 1.00 1.00 1.00 1.60 B:1 1027 1.35 1.00 0.50 1.60 B:1 1028 1.00 1.00 0.50 1.60 B:2 1029 1.35 1.00 1.00 1.60 0.84 B:2 1030 1.00 1.00 1.00 1.60 0.84 B:2 1031 1.35 1.00 0.50 1.60 0.84 B:2 1032 1.00 1.00 0.50 1.60 0.84 B:2 1033 1.35 1.00 1.00 1.60 0.84 B:2 1034 1.00 1.00 1.00 1.60 0.84 B:2 1035 1.35 1.00 0.50 1.60 0.84 B:2 1036 1.00 1.00 0.50 1.60 0.84 ULS Comb.

Ultimate limit state

Dominate Action: Z Dominate Action: T Additional wind incl, traffic Temperature loading Description

B: Combinations without traffic

C: Combinations with traffic* Dominate Action: L

Dead load Prestressing Wind loading

Reaction from floating bridge Traffic load

A: No variable loads

𝛾𝐺,𝑗,𝑠𝑢𝑝𝐺𝑘𝑗,𝑠𝑢𝑝+ 𝛾𝐺,𝑗,𝑖𝑛𝑓𝐺𝑘𝑗,𝑖𝑛𝑓 + 𝛾𝑝𝑃 + 𝛾𝑄,1𝑄𝑘,1+ 𝛾𝑄,𝑖𝜓0,𝑖𝑄𝑘,𝑖

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Appendix B5: Load combinations SLS (Rare) 19.12.2016 Anna Tranell AC Co Pa γsup γinf γac ψ0 ψ1 ψ2 ψ1' G 1 G 1.35 1.00 1.00 1.00 1.00 1.00 1.00AC Action γ= 1 P 1 P 1.00 1.00 1.00 1.00 1.00 1.00 1.00Co Combination R 1 P 1.00 0.50 0.75 0.75 0.75 0.75 0.75Pa Partition W 6 Q 1.60 0.00 1.00 0.70 0.60 0.50 0.80γsup γunfavourable

L 6 Q 1.35 0.00 1.00 0.70 0.70 0.50 0.80γinf γfavourable X Action included

Z 3 Q 1.60 0.00 1.00 0.70 0.60 0.50 0.80γac γaccidental O Dominate action

T 4 Q 1.20 0.00 1.00 0.70 0.60 0.50 0.80 Combination of actions No G P R W L Z T G P R W L Z T Total A X X X 1 1 1 1 1 1 1 1 B:1 X X X O 1 1 1 6 1 1 1 6 B:2 X X X O X 1 1 1 6 1 1 4 24 B:3 X X X X O 1 1 1 6 1 1 4 24 B:4 X X X O 1 1 1 1 1 1 4 4 C:1 X X X O 1 1 1 1 6 1 1 6 C:2 X X X O X 1 1 1 1 6 3 1 18 C:4 X X X O X X 1 1 1 1 6 3 4 72 C:4 X X X X O 1 1 1 1 6 3 1 18 C:5 X X X X O X 1 1 1 1 6 3 4 72 C:6 X X X X X O 1 1 1 1 6 3 4 72 C:7 X X X X O 1 1 1 1 6 1 4 24 Sum 341 G P R W1 W2 W3 W4 W5 W6 L1 L2 L4 L5 L6 L7 Z1 Z2 Z3 T2 T3 T4 T6 100 4 5 101 102 103 104 105 106 201 202 204 205 206 207 301 302 303 402 410 411 412 A 2001 1.00 1.00 0.75 B:1 2002 1.00 1.00 0.75 1.00 B:1 2003 1.00 1.00 0.75 1.00 B:1 2004 1.00 1.00 0.75 1.00 B:1 2005 1.00 1.00 0.75 1.00 B:1 2006 1.00 1.00 0.75 1.00 B:1 2007 1.00 1.00 0.75 1.00 B:2 2008 1.00 1.00 0.75 1.00 0.70 B:2 2009 1.00 1.00 0.75 1.00 0.70 B:2 2010 1.00 1.00 0.75 1.00 0.70 B:2 2011 1.00 1.00 0.75 1.00 0.70 B:2 2012 1.00 1.00 0.75 1.00 0.70 B:2 2013 1.00 1.00 0.75 1.00 0.70 B:2 2014 1.00 1.00 0.75 1.00 0.70 B:2 2015 1.00 1.00 0.75 1.00 0.70 B:2 2016 1.00 1.00 0.75 1.00 0.70 B:2 2017 1.00 1.00 0.75 1.00 0.70 B:2 2018 1.00 1.00 0.75 1.00 0.70 B:2 2019 1.00 1.00 0.75 1.00 0.70 B:2 2020 1.00 1.00 0.75 1.00 0.70 B:2 2021 1.00 1.00 0.75 1.00 0.70 B:2 2022 1.00 1.00 0.75 1.00 0.70 B:2 2023 1.00 1.00 0.75 1.00 0.70 B:2 2024 1.00 1.00 0.75 1.00 0.70 B:2 2025 1.00 1.00 0.75 1.00 0.70 B:2 2026 1.00 1.00 0.75 1.00 0.70 B:2 2027 1.00 1.00 0.75 1.00 0.70 B:2 2028 1.00 1.00 0.75 1.00 0.70 B:2 2029 1.00 1.00 0.75 1.00 0.70 B:2 2030 1.00 1.00 0.75 1.00 0.70 B:2 2031 1.00 1.00 0.75 1.00 0.70 SLS1 Com Description Dead load Prestressing

Reaction from floating bridge Wind loading

Traffic load

Additional wind incl, traffic Temperature loading

Serviceability Limit State, Rare

Dominate Action: Z Dominate Action: T C: Combinations with traffic Dominate Action: L

B: Combinations without traffic 𝐺𝑘𝑗,𝑠𝑢𝑝+ 𝐺𝑘𝑗,𝑖𝑛𝑓 + 𝑃 + 𝑄𝑘,1+ 𝜓0,𝑖𝑄𝑘,𝑖

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Appendix B5: Load combinations SLS (Ferequent) 19.12.2016 Anna Tranell AC Co Pa γsup γinf γac ψ0 ψ1 ψ2 ψ1' G 1 G 1.35 1.00 1.00 1.00 1.00 1.00 1.00AC Action γ= 1 P 1 P 1.00 1.00 1.00 1.00 1.00 1.00 1.00Co Combination R 1 P 1.00 0.50 0.75 0.75 0.75 0.75 0.75Pa Partition W 6 Q 1.60 0.00 1.00 0.70 0.60 0.50 0.80γsup γunfavourable L 6 Q 1.35 0.00 1.00 0.70 0.70 0.50 0.80γinf γfavourable X Z 3 Q 1.60 0.00 1.00 0.70 0.60 0.50 0.80γac γaccidental O T 4 Q 1.20 0.00 1.00 0.70 0.60 0.50 0.80 Combination of actions No G P R W L Z T G P R W L Z T Total A X X X 1 1 1 1 1 1 1 1 B:1 X X X O 1 1 1 6 1 1 1 6 B:2 X X X O X 1 1 1 6 1 1 4 24 B:3 X X X X O 1 1 1 6 1 1 4 24 B:4 X X X O 1 1 1 1 1 1 4 4 C:1 X X X O 1 1 1 1 6 1 1 6 C:2 X X X O X 1 1 1 1 6 3 1 18 C:4 X X X O X X 1 1 1 1 6 3 4 72 C:4 X X X X O 1 1 1 1 6 3 1 18 C:5 X X X X O X 1 1 1 1 6 3 4 72 C:6 X X X X X O 1 1 1 1 6 3 4 72 C:7 X X X X O 1 1 1 1 6 1 4 24 Sum 341 G P R W1 W2 W3 W4 W5 W6 L1 L2 L4 L5 L6 L7 Z1 Z2 Z3 T2 T3 T4 T6 100 4 5 101 102 103 104 105 106 201 202 204 205 206 207 301 302 303 402 410 411 412 A 3001 1.00 1.00 0.75 B:1 3002 1.00 1.00 0.75 0.60 B:1 3003 1.00 1.00 0.75 0.60 B:1 3004 1.00 1.00 0.75 0.60 B:1 3005 1.00 1.00 0.75 0.60 B:1 3006 1.00 1.00 0.75 0.60 B:1 3007 1.00 1.00 0.75 0.60 B:2 3008 1.00 1.00 0.75 0.60 0.50 B:2 3009 1.00 1.00 0.75 0.60 0.50 B:2 3010 1.00 1.00 0.75 0.60 0.50 B:2 3011 1.00 1.00 0.75 0.60 0.50 B:2 3012 1.00 1.00 0.75 0.60 0.50 B:2 3013 1.00 1.00 0.75 0.60 0.50 B:2 3014 1.00 1.00 0.75 0.60 0.50 B:2 3015 1.00 1.00 0.75 0.60 0.50 B:2 3016 1.00 1.00 0.75 0.60 0.50 B:2 3017 1.00 1.00 0.75 0.60 0.50 B:2 3018 1.00 1.00 0.75 0.60 0.50 B:2 3019 1.00 1.00 0.75 0.60 0.50 B:2 3020 1.00 1.00 0.75 0.60 0.50 B:2 3021 1.00 1.00 0.75 0.60 0.50 B:2 3022 1.00 1.00 0.75 0.60 0.50 B:2 3023 1.00 1.00 0.75 0.60 0.50 B:2 3024 1.00 1.00 0.75 0.60 0.50 B:2 3025 1.00 1.00 0.75 0.60 0.50 B:2 3026 1.00 1.00 0.75 0.60 0.50 B:2 3027 1.00 1.00 0.75 0.60 0.50 B:2 3028 1.00 1.00 0.75 0.60 0.50 B:2 3029 1.00 1.00 0.75 0.60 0.50 B:2 3030 1.00 1.00 0.75 0.60 0.50 B:2 3031 1.00 1.00 0.75 0.60 0.50 Action included Dominate action Dominate Action: Z Dominate Action: T SLS2 Com Traffic load

Additional wind incl, traffic Temperature loading

B: Combinations without traffic

C: Combinations with traffic Dominate Action: L Wind loading

Serviceability Limit State, Frequent

Description

Dead load Prestressing

Reaction from floating bridge

𝐺𝑘𝑗,𝑠𝑢𝑝+ 𝐺𝑘𝑗,𝑖𝑛𝑓 + 𝑃 + 𝜓1,1𝑄𝑘,1+ 𝜓2,𝑖𝑄𝑘,𝑖

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Appendix C

Appendix C

SOFiSTiK Model0_0, First design attempt

First design attempt SOFiSTiK Model0_0 is the result of step 1 in (§ 6.1) and is further developed in

step 2 (§ 6.2).

Figure 6 1: Schematics of Part 1: Step 1

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Multiconsult * Nedre Skojen v ei 2 * 0213 Oslo

SOFiSTiK 2016-5 TEMPLATE - GENERAL PRE- AND POSTPROCESSING TOOL (V 12.02)

Appendix C 1 2016-09-19 Model0_0 - First design attempt

1 Model and geometry

S O F iS T iK A G www. so fis tik .d e Introduction

This is the report of Model0_0 - first design attempt

Contents

1. Model and geometry 1.1 Materials 1.2 Cross Sections 1.3 Structure 1.4 Single loads 1.5 Intermediate combinations 2. Prestress 3. Preliminary design

3.1 Evaluation of Intermediate Combinations (IC) 3.1.1 Displacement and Support Reaction of IC 3.2 Design (based on IC)

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SOFiSTiK 2016-6 AQUA - GENERAL CROSS SECTIONS (V 17.06)

1.1 Materials S O F iS T iK A G www. so fis tik .d e Table of Contents

1. Model and geometry 1 Model and Geometry

Introduction ... 1 General dimensions ... 1 Contents ... 1 1.1 Materials

1.1 Materials

Default design code is NS EuroNorm EN 1992-2:2005 (NA:2010) Betongkonstruksjoner (Norge) V 6 Mat 1 Cables ... 6 Mat 20 Girder t<40mm ... 6 Mat 30 Pylon t<40mm ... 6 Mat 35 Pylon C45 ... 6 Mat 36 B 500 B (EN 1992) ... 6 Mat 37 C45 g=0 ... 7 Mat 40 Connector t<40mm ... 7 Spring Material 1 Spring - Anchor ... 7 Force-displacement law P ... 7 Force-displacement law P ... 7 1.2 Cross sections

1.2 Cross Sections

Cross sections 1,20,30,40,46, Cross section properties (steel) ... 8 Cross sections 5,35,45, Cross section properties (concrete) ... 8 Cross sections 5,35,45, Cross sections Reinforcement per layer Minimum reinforcement ... 8 Cross section overview Cross section No. 1 Cable LC 125 ... 8 Cross section overview Cross section No. 40 Connector 1 ... 8 Thinwalled cross section element Thickness [mm] Cross section No. 20 Girder 1 Cross sectio 9 Cross section overview Cross section No. 50 Girder 1, with stiffeners ... 9 Thinwalled cross section element Thickness [mm] Cross section No. 30 Pylon Cross section o 9 Thinwalled cross section element Thickness [mm] Cross section No. 46 Connector top Cross s 9 Cross section overview Cross section No. 5 Column leg Single reinforcement Layer number Cr 10 Cross section overview Cross section No. 35 Pylon btm Single reinforcement Layer number Cr 10 Cross section overview Cross section No. 45 Connector btm Single reinforcement Layer numbe 10 1.3 Structure

Interactive Graphics

Cross sections Structure ... 11 Cross sections ... 12 Contour of Cross section Structure ... 13 Numbers of cross section Numbers of cross section ... 14 1.4 Single loads

1.4 Single loads

Table 6-2 Loads ... 15 1.4 Single loads

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1.1 Materials S O F iS T iK A G www. so fis tik .d e Interactive Graphics

All loads (in components) LC: 23 All loads (in components) LC: 23 All loads (in components 23 All loads (in components) LC: 31 All loads (in components) LC: 32 All loads (in components 24 All loads (in components) LC: 34 All loads (in components) LC: 35 All loads (in components 25 All loads (in components) LC: 37 ... 26 All loads (in components) LC: 41 All loads (in components) LC: 42 ... 27 All loads (in components) LC: 43 All loads (in components) LC: 44 ... 28 All loads (in components) LC: 45 All loads (in components) LC: 46 ... 29 1.5 Intermediate Combinations

1.5 Intermediate Combination

Load Case 100 ((H) ) Self-weight structural ... 30 Load Case 121 ((H) ) SDL ... 30 Load Case 160 ((H) ) SW and T from F.B ... 30 Load Case 161 ((H) ) SW+P and T from FB ... 30 Load Case 101 ((H) ) Wind: Y and Z ... 31 Load Case 102 ((H) ) Wind: Y and -Z ... 31 Load Case 103 ((H) ) Wind: X and Z ... 31 Load Case 104 ((H) ) Wind: -X and Z ... 31 Load Case 105 ((H) ) Wind: X and -Z ... 31 Load Case 106 ((H) ) Wind: -X and -Z ... 31 Load Case 201 ((H) ) Traffic: UDL max V +TS1 ... 31 Load Case 202 ((H) ) Traffic: UDL max V +TS2 ... 31 Load Case 203 ((H) ) Traffic: UDL max V +TS3 ... 31 Load Case 204 ((H) ) Traffic: UDL max T +TS1 ... 31 Load Case 205 ((H) ) Traffic: UDL max T +TS2 ... 31 Load Case 206 ((H) ) Traffic: UDL max T +TS3 ... 31 Load Case 207 ((H) ) Traffic: UDL max V/2 +TS2 ... 32 Load Case 301 ((H) ) Traffic: UDL max V/2 +TS3 ... 32 Load Case 302 ((H) ) WIND*: Y and Z ... 32 Load Case 303 ((H) ) Wind*: X and Z ... 32 Load Case 401 ((H) ) Wind*: -X and Z ... 32 Load Case 402 ((H) ) Temp: Contr+Gradient (warm cable ... 32 Load Case 403 ((H) ) Temp: Contr+Gradient (warm cable ... 32 Load Case 404 ((H) ) Temp: Contr+Gradient (cool cable ... 32 Load Case 405 ((H) ) Temp: Contr+Gradient (cool cable ... 32 Load Case 406 ((H) ) Temp: Contr+Gradient (warm cable ... 32 Load Case 407 ((H) ) Temp: Contr+Gradient (warm cable ... 32 Load Case 408 ((H) ) Temp: Contr+Gradient (cool cable ... 32 Load Case 409 ((H) ) Temp: Contr+Gradient (cool cable ... 33 Load Case 410 ((H) ) Temp: Expan+Gradient (warm cable ... 33 Load Case 411 ((H) ) Temp: Expan+Gradient (warm cable ... 33 Load Case 412 ((H) ) Temp: Expan+Gradient (cool cable ... 33 Load Case 413 ((H) ) Temp: Expan+Gradient (cool cable ... 33 Load Case 414 ((H) ) Temp: Expan+Gradient (warm cable ... 33 Load Case 415 ((H) ) Temp: Expan+Gradient (warm cable ... 33 Load Case 416 ((H) ) Temp: Expan+Gradient (cool cable ... 33 2 Prestress

Cable Elements , Normal force Nx LC: 160 Nodal displacement vector LC: 160 Cable Elements 34 3 Preliminary design

3 Preliminary design

Introduction ... 35 3.1 Evaluation of Intermediate Combinations (IC)

3.1 Evaluation of IC: Combinations of Wind

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1.1 Materials S O F iS T iK A G www. so fis tik .d e

3.1 Evaluation of IC: Combinations of Wind

LC: 9101-9106, Table 2: Max/min Results for Girder Groups 21,22 ... 36 LC: 9101-9106, Table 3: Max/min Results for Cable ... 36 LC: 9101-9106, Table 4: Max/min Results for Pylon btm (Concrete) Groups 30,31 ... 36 LC: 9101-9106, Table 5: Max/min Results for Pylon top (Steel) ... 37 3.1 Evaluation of IC: Combinations of Traffic

Introduction ... 38 LC: 9201-9207, Table 1: Max/min Displacement ... 38 LC: 9201-9207, Table 2: Max/min Results for Girder Groups 21,22 ... 38 LC: 9201-9207, Table 3: Max/min Results for Cable ... 38 LC: 9201-9207, Table 4: Max/min Results for Pylon btm (Concrete) Groups 30,31 ... 38 LC: 9201-9207, Table 5: Max/min Results for Pylon top (Steel) ... 39 3.1 Evaluation of IC: Combinations of Wind with Traffic

Introduction ... 40 LC: 9301-9303, Table 1: Max/min Displacement ... 40 LC: 9301-9303, Table 2: Max/min Results for Girder Groups 21,22 ... 40 LC: 9301-9303, Table 3: Max/min Results for Cable ... 40 LC: 9301-9303, Table 4: Max/min Results for Pylon btm (Concrete) Groups 30,31 ... 40 LC: 9301-9303, Table 5: Max/min Results for Pylon top (Steel) ... 41 3.1 Evaluation of IC: Combinations of Temperature

Introduction ... 42 LC: 9401-9416, Table 1: Max/min Displacement ... 42 LC: 9401-9416, Table 2: Max/min Results for Girder Groups 21,22 ... 42 LC: 9401-9416, Table 3: Max/min Results for Cable ... 42 LC: 9401-9416, Table 4: Max/min Results for Pylon btm (Concrete) Groups 30,31 ... 43 LC: 9401-9416, Table 5: Max/min Results for Pylon top (Steel) ... 43 3.1.1 Displacement and support reactions of IC

Nodal displacement vector LC: 4 ; Nodes , Support force in global X LC: 4 ; Nodes , Suppor Nodal displacement vector LC: 100 ; Nodes , Support force in global X LC: 100 ; Nodes , Su Nodal displacement vector LC: 9101 ; Nodes , Support force in global X LC: 9101 ; Nodes , Nodal displacement vector LC: 9103 ; Nodes , Support force in global X LC: 9103 ; Nodes , Nodal displacement vector LC: 9105 ; Nodes , Support force in global X LC: 9105 ; Nodes , Nodal displacement vector LC: 9201 ; Nodes , Support force in global X LC: 9201 ; Nodes , Nodal displacement vector LC: 9203 ; Nodes , Support force in global X LC: 9203 ; Nodes , Nodal displacement vector LC: 9205 ; Nodes , Support force in global X LC: 9205 ; Nodes , Nodal displacement vector LC: 9207 ; Nodes , Support force in global X LC: 9207 ; Nodes , Nodal displacement vector LC: 9301 ; Nodes , Support force in global X LC: 9301 ; Nodes , Nodal displacement vector LC: 9303 ; Nodes , Support force in global X LC: 9303 ; Nodes , Nodal displacement vector LC: 9401 ; Nodes , Support force in global X LC: 9401 ; Nodes , Nodal displacement vector LC: 9403 ; Nodes , Support force in global X LC: 9403 ; Nodes , Nodal displacement vector LC: 9405 ; Nodes , Support force in global X LC: 9405 ; Nodes , Nodal displacement vector LC: 9407 ; Nodes , Support force in global X LC: 9407 ; Nodes , Nodal displacement vector LC: 9409 ; Nodes , Support force in global X LC: 9409 ; Nodes , Nodal displacement vector LC: 9411 ; Nodes , Support force in global X LC: 9411 ; Nodes , Nodal displacement vector LC: 9413 ; Nodes , Support force in global X LC: 9413 ; Nodes , Nodal displacement vector LC: 9415 ; Nodes , Support force in global X LC: 9415 ; Nodes , 3.2 Design Steel - Deck and Pylon 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62

3.2 Design Steel - Deck and Pylon (Beams)

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3.2 Design Steel - Rest of steel cross sections

3.2 Design Steel - Rest of steel cross sections (Trusses)

Default design code is EuroNorm EN 1993-1-1:2005 Steel Structures (Norge) V 2016 ... 64 Elastic Stress Check ... 64 Combinations of Load Cases ... 64 Maximum Stresses and Checked Limits ... 64 Maximum Utilisation Level ... 64 3.2 Design Steel - Rest of steel cross sections (Cables)

Default design code is EuroNorm EN 1993-1-1:2005 Steel Structures (Norge) V 2016 ... 65 Elastic Stress Check ... 65 Combinations of Load Cases ... 65 Maximum Stresses and Checked Limits ... 65 Maximum Utilisation Level ... 65 3.2 Design ULS - Concrete beams

3.2 Design ULS - Concrete beams

Default design code is NS EuroNorm EN 1992-2:2005 (NA:2010) Betongkonstruksjoner (Norge) V 66 Longitudinal Reinforcements - Design case No. 1 ... 66 Maximum Utilisation Level ... 66 3.2.1 Design results (of IC)

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Default design code is NS EuroNorm EN 1992-2:2005 (NA:2010) Betongkonstruksjoner (Norge) V 2016 Konstruksjon og Pålitelighetsklasse: B (vegbruer)

Snow load zone : 1 Mat 1 Cables

Young's modulus E 164748 [N/mm2] Safetyfactor 1.10 [-] ...

Poisson's ratio μ 0.30 [-] Yield stress fy 896.80 [MPa] ...

Shear modulus G 63365 [N/mm2] Compressive yield fyc 896.80 [MPa] ...

Compression modulus K 137290 [N/mm2] Tensile strength ft 896.80 [MPa] ...

Weight γ 80.6 [kN/m3] Compressive strength fc 896.80 [MPa] ...

Density ρ 8058.00 [kg/m3] Ultimate strain 100.00 [o/oo] ...

Elongation coefficient α 1.20E-05 [1/K] relative bond coeff. 0.00 [-] ...

max. thickness t-max 50.00 [mm] EN 1992 bond coeff. k1 0.00 [-] ...

Hardening modulus Eh 0.00 [MPa] ...

Proportional limit fp 960.00 [MPa] ...

Dynamic allowance σ-dyn 0.00 [MPa] ...

Mat 20 Girder t<40mm

Mat 30 Pylon t<40mm

Mat 35 Pylon C45

Poisson's ratio μ 0.20 [-] Strength fc 38.25 [MPa] ...

Shear modulus G 15118 [N/mm2] Nominal strength fck 45.00 [MPa] ...

Compression modulus K 20157 [N/mm2] Tensile strength fctm 3.80 [MPa] ...

Weight γ 25.0 [kN/m3] Tensile strength fctk,05 2.66 [MPa] ...

Density ρ 2350.00 [kg/m3] Tensile strength fctk,95 4.93 [MPa] ...

Elongation coefficient α 1.00E-05 [1/K] Bond strength fbd 3.39 [MPa] ...

Service strength fcm 53.00 [MPa] ...

Fatigue strength fcd,fat 20.91 [MPa] ...

Tensile strength fctd 1.51 [MPa] ...

Tensile failure energy Gf 0.05 [N/mm] ...

Mat 36 B 500 B (EN 1992)

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1.1 Materials S O F iS T iK A G www. so fis tik .d e Mat 36 B 500 B (EN 1992)

Mat 37 C45 g=0

Poisson's ratio μ 0.20 [-] Strength fc 38.25 [MPa] ...

Shear modulus G 15118 [N/mm2] Nominal strength fck 45.00 [MPa] ...

Compression modulus K 20157 [N/mm2] Tensile strength fctm 3.80 [MPa] ...

Weight γ 0.0 [kN/m3] Tensile strength fctk,05 2.66 [MPa] ...

Density ρ 2350.00 [kg/m3] Tensile strength fctk,95 4.93 [MPa] ...

Elongation coefficient α 1.00E-05 [1/K] Bond strength fbd 3.39 [MPa] ...

Service strength fcm 53.00 [MPa] ...

Fatigue strength fcd,fat 20.91 [MPa] ...

Tensile strength fctd 1.51 [MPa] ...

Tensile failure energy Gf 0.05 [N/mm] ...

Mat 40 Connector t<40mm

Spring Material 1 Spring - Anchor

Connection type: Standard spring work law(s)

Material type: Elastoplastic, anisotropic hardening Force-displacement law P

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SOFiSTiK 2016-6 RESULTS - OUTPUT FOR FINITE ELEMENTS (V 14.06)

1.2 Cross Sections

-General properties; Cable (no1) and Longitudinal connector (no46)

S O F iS T iK A G www. so fis tik .d e

Cross sections 1,20,30,40,46, Cross section properties (steel)

NR Text MNo zc zsc A Ay Az It Iy Iz EM GM gam/m [mm] [mm] [m2] [m2] [m2] [m4] [m4] [m4] [N/mm2] [N/mm2] [kN/m] 1 Cable LC 125 1 0.0 0.0 0.0139 0.0125 0.0125 0.000 0.000 0.000 164748 63365 1.12 20 Girder 1 20 1128.2 1414.3 1.1695 0.8326 0.1328 4.780 1.370 61.617 210000 80769 91.80 30 Pylon 30 1750.0 1750.0 0.4612 0.1548 0.2495 1.045 0.837 0.510 210000 80769 36.21 40 Connector 1 20 0.0 0.0 0.0156 0.0078 0.0078 0.001 0.000 0.000 210000 80769 1.23 46 Connector top 30 1750.0 1750.0 0.2306 0.0774 0.1247 0.522 0.419 0.255 210000 80769 18.10

NR cross section number Az Sheardeformation area Z Text Cross section description It Torsional moment of inertia MNo Materialnumber of sections Iy Moments of inertia y-y zc z-Ordinate Center of gravity Iz Moments of inertia z-z zsc z-Ordinate of Shear-Center EM Elasticity Modulus A Area GM Shear Modulus Ay Sheardeformation area Y gam/m Dead weight per m

Cross sections 5,35,45, Cross section properties (concrete)

NR Text MNo MRf zc A It Iy Iz EM GM gam/m [mm] [m2] [m4] [m4] [m4] [N/mm2] [N/mm2] [kN/m] 5 Column leg 37 36 -60.0 5.9529 11.754 9.455 5.517 36283 15118 0.00 35 Pylon btm 35 36 -60.0 5.9529 11.754 9.455 5.517 36283 15118 148.82 45 Connector btm 35 36 3500.0 12.0457 88.600 75.557 43.482 36283 15118 301.14

NR cross section number It Torsional moment of inertia Text Cross section description Iy Moments of inertia y-y MNo Materialnumber of sections Iz Moments of inertia z-z MRf Materialnumber of Reinforcement EM Elasticity Modulus zc z-Ordinate Center of gravity GM Shear Modulus A Area gam/m Dead weight per m

Cross sections 5,35,45, Cross sections Reinforcement per layer Minimum reinforcement Sect MinLay1 MinLay2 MinLay3 MinLay4

[cm2] [cm2] [cm2] [cm2] 5 76.82 76.82 117.04 117.04 35 76.82 76.82 117.04 117.04 45 166.11 166.11 246.55 246.55

Sect Cross Section

MinLay1 Minimum reinforcement Layer 1 MinLay2 Minimum reinforcement Layer 2 MinLay3 Minimum reinforcement Layer 3 MinLay4 Minimum reinforcement Layer 4

M 1 : 10 X Y Z Y 300. 200. 100. 0. -100. -200. -300. mm Z 100. 0. -100.

Cross section overview Cross section No. 1 Cable LC 125 M 1 : 20 X Y Z Y 600. 400. 200. 0. -200. -400. -600. mm Z 200. 0. -200.

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1.2 Cross sections (steel)

-Girder no20 (no50 with stiffeners)

-Pylon no30 and Transversal connector (no46)

S O F iS T iK A G www. so fis tik .d e M 1 : 200 X Y Z Y -15000. -10000. -5000. 0. 5000. 10000. 15000. mm Z 0.

Thinwalled cross section element Thickness [mm] Cross section No. 20 Girder 1 Cross section overview Cross section No. 20 Girder 1

0 2 5 1 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 5 1 0 2 0 2 5 1 0 2 5 1 15 15 M 1 : 200 X Y Z Y -15000. -10000. -5000. 0. 5000. 10000. 15000. mm Z 0.

Cross section overview Cross section No. 50 Girder 1, with stiffeners

M 1 : 100 X Y Z Y -6000. -4000. -2000. 0. 2000. 4000. 6000. mm Z 2000.

Thinwalled cross section element Thickness [mm] Cross section No. 30 Pylon Cross section overview Cross section No. 30 Pylon

0 4 ₄₀ 0 4 0 4 0 4 0 4 0 4 0 4 M 1 : 100 X Y Z Y -6000. -4000. -2000. 0. 2000. 4000. 6000. mm Z 2000.

Thinwalled cross section element Thickness [mm] Cross section No. 46 Connector top Cross section overview Cross section No. 46 Connector top

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1.2 Cross sections (concrete)

-Column (no5), Pylon btm (no35) and Transversal connector btm (no45)

S O F iS T iK A G www. so fis tik .d e M 1 : 100 X Y Z Y 3000. 2000. 1000. 0. -1000. -2000. mm Z 4000. 3000. 2000. 1000. 0. -1000. -2000. -3000. -4000.

Cross section overview Cross section No. 5 Column leg Single reinforcement Layer number

Cross section No. 5 Column leg

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 5 5 5 5 M 1 : 100 X Y Z Y 3000. 2000. 1000. 0. -1000. -2000. mm Z 4000. 3000. 2000. 1000. 0. -1000. -2000. -3000. -4000.

Cross section overview Cross section No. 35 Pylon btm Single reinforcement Layer number

Cross section No. 35 Pylon btm

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 5 5 5 5 M 1 : 100 X Y Z Y 3000. 2000. 1000. 0. -1000. -2000. mm Z 8000. 7000. 6000. 5000. 4000. 3000. 2000. 1000. 0. -1000.

Cross section overview Cross section No. 45 Connector btm Single reinforcement Layer number

Cross section No. 45 Connector btm

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SOFiSTiK 2016-6 WINGRAF - GRAPHICS FOR FINITE ELEMENTS (V 18.06)

1.3 Definition of Structure General Structure S O F iS T iK A G www. so fis tik .d e M 1 : 3007 XY Z X * 0.502 Y * 0.906 Z * 0.962

Cross sections, Beam Elements, Truss Elements, Cable Elements

m -200.00 -150.00 -100.00 -50.00 0.00 50.00 100.00 150.00 200.00 -50. 00 0. 00 50. 00 100. 00 150. 00 M 1 : 3001 XY Z X * 0.502 Y * 0.906 Z * 0.962

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1.3 Definition of Structure General Structure: Pylon

S O F iS T iK A G www. so fis tik .d e M 1 : 892 X Y Z X * 0.895 Y * 0.566 Z * 0.938

Sector of system Group 30...36 40...43 50 Cross sections, Beam Elements, Truss Elements

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1.3 Definition of Structure General Structure: Girder

S O F iS T iK A G www. so fis tik .d e M 1 : 668 XY Z X * 0.502 Y * 0.906 Z * 0.962 Sector of system

Contour of Cross section, Beam Elements, Truss Elements, Cable Elements

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1.3 Definition of Structure Numbers of cross section

S O F iS T iK A G www. so fis tik .d e M 1 : 3323 X Y Z X * 0.840 Y * 0.710 Z * 0.889 35 35 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 5 1 1 1 1 1 1 1 1 1 1 1

Sector of system Group 0 1 20...22 100...119

Numbers of cross section, Beam Elements(Max=35), Cable Elements(Max=1)

1 5 20 35 m -250.00 -200.00 -150.00 -100.00 -50.00 0.00 50.00 100.00 150.00 200.00 -50. 00 0. 00 50. 00 100. 00 150. 00 M 1 : 2070 XY Z X * 0.708 Y * 0.818 Z * 0.911 46 46 46 45 45 40 40 40 40 40 40 40 35 35 35 35 ₃₅ 35

Sector of system Group 30...36 40...43 50...53

Numbers of cross section, Beam Elements(Max=45), Truss Elements(Max=46)

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SOFiSTiK 2016-5 TEMPLATE - GENERAL PRE- AND POSTPROCESSING TOOL (V 12.02)

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1.4 Single Loads

Dead load: Type B and C

S O F iS T iK A G www. so fis tik .d e M 1 : 3798 XY Z X * 0.682 Y * 0.802 Z * 0.944 48 .4 48 .4 48 .4 48 .4 48 .4 48 .4 48 .4 48 .4 48 .4 48 .4 48 .4 48 .4 48 .4 48 .4 48 .4 48 .4 48 .4 48 .4 48 .4 13.2 13 .2 Total construction

All loads (in components), Loadcase 2 (B) SW str. not in model , (1 cm 3D = unit) Trussing load (force) in global Z (Unit=100.0 kN/m,Min=-13.2

-48. 4 -13. 2 m -300.00 -250.00 -200.00 -150.00 -100.00 -50.00 0.00 50.00 100.00 150.00 200.00 250.00 -50. 00 0. 00 50. 00 100. 00 150. 00 200. 00 M 1 : 3388 XY Z X * 0.682 Y * 0.802 Z * 0.944 86 .4 86 .4 86 .4 86 .4 86 .4 86 .4 86 .4 86 .4 86 .4 86 .4 86 .4 86 .4 86 .4 86 .4 86 .4 86 .4 86 .4 86 .4 86 .4 86 .4 86 .4 Total construction

All loads (in components), Loadcase 3 (B) SW str. not in model , (1 cm 3D =

unit) Beam line load (force) in global Z (Unit=200.0 kN/m ) (Min=-86.4)

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1.4 Single Loads

Prestress and reactrion from floating bridge

S O F iS T iK A G www. so fis tik .d e M 1 : 3438 XY Z X * 0.682 Y * 0.802 Z * 0.944 450₀ 45₀₀ 450₀ 45₀₀ 45 00 4500 4500 4500 4500 4500 4500 Total construction

All loads (in components), Loadcase 4 Prestress Cables , (1 cm 3D = unit) Cable load (prestress) (Unit=10000. kN ) (Max=4500.)

4500. 0 m -250.00 -200.00 -150.00 -100.00 -50.00 0.00 50.00 100.00 150.00 200.00 250.00 -50. 00 0. 00 50. 00 100. 00 150. 00 200. 00 M 1 : 3388 XY Z X * 0.682 Y * 0.802 Z * 0.944 1.6150_E5 Total construction

All loads (in components), Loadcase 5 Reaction from FB , (1 cm 3D = unit) Nodal load (force) in global X (Unit= 5.0000e+05 kN ) (Max= 1.6150e+05)