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Dong LI (DLI) Reinforcement Algorithm June 15, 2016 1 / 71 Ansys Reinforcement Algorithme Ansys APDL+ethode Capra-Maury Dong LI June 15, 2016

Concrete reinforcement Programme for Ansys

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Page 1: Concrete reinforcement Programme for Ansys

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 1 / 71

Ansys Reinforcement AlgorithmeAnsys APDL+Methode Capra-Maury

Dong LI

June 15, 2016

Page 2: Concrete reinforcement Programme for Ansys

Introduction - ANSYS F-Code

ANSYS F-Code programme is specialized in calculation of con-crete reinforcement for element coque and plate according toEuropean code 2 - Concrete structure code. It is written withAPDL according to A.Capra, J-F. Maury - Calcul automatiquedu ferraillage optimal des plaques et coques en beton arme. An-nales de l’Institut Technique du batiment et des Travaux Publics,N367,Decembre1978.It can deal with all of concrete class from fck = 12 MPa to90 MPa for the cases of membrane reinforcement, combinedmembrane and flexural reinforcement in plates and shells.

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Page 3: Concrete reinforcement Programme for Ansys

Introduction - ANSYS F-Code

y

x

Asy (0, π2 )

Asx(0, π2 )π2

y

x

Asy (0, π2 + α)

Asx(0, π2 + α)

π2 α

y

x

Asy (α, β)

Asx(α, β)αβ

-Three configurations can be dealt by F-Code- For the cases -E.T/E.C/P.T µ > µ0, F-Code memories thecorresponding element number and angle.E.T - Section completly in tensionE.C - Section completly in compressionP.T - Section partially in tension

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 3 / 71

Page 4: Concrete reinforcement Programme for Ansys

Section in flexure with axial compression-P.T:µ > µ0

A’s

As

40500

60

600300

• Concrete: fcd = 16.7MPa

• Steel: fyd = 435MPa

• ELU Forces (MN, MNm):Nx Nxy Ny

0.39 0 0.39

Mx Mxy My

0.5 0 0.5

cm2 Theory F-Code

AXS 24 24

AYS 24 24

AXI 2 2

AYI 2 2Le Projet de Beton Arme, Henry THONIER, 6eEdition,Page43, EX .4

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Page 5: Concrete reinforcement Programme for Ansys

Section Partiellement Tentue-P.T: µ > µ0

A’s

As

40500

60

600

300

• Concrete: fcd = 16.7MPa

• Steel: fyd = 435MPa

• ELU Forces (MN, MNm):Nx Nxy Ny

0.39 0 0.39

Mx Mxy My

0.5 0 -0.5

cm2 Theory F-Code

AXS 24 24

AYS 2 2

AXI 2 2

AYI 24 24

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Page 6: Concrete reinforcement Programme for Ansys

Section complete in compression-E.C

A’s

As

40520

40

600

300

• Concrete: fcd = 16.7MPa

• Steel: fyd = 435MPa

• ELU Forces (MN, MNm):Nx Nxy Ny

2.26 0 2.26

Mx Mxy My

0.13 0 0.13

cm2 Theory F-Code

AXS 0 1.67e-7

AYS 0 1.67e-7

AXI 0 1.67e-7

AYI 0 1.67e-7

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 6 / 71

Page 7: Concrete reinforcement Programme for Ansys

Analytical Solution - Detail

A’s

As

300x

E.C - A solution with As = 0

x = 0.5711mψ = 0.8095σs = 437.63MPaA′s = (N − Nc) · 1

σs= (2.26− 2.32) · 1

437.63< 0

=⇒

{A′s = 0

As = 0

ψ : Coefficient de remplissage

Le Projet de Beton Arme, Henry THONIER, 6eEdition,Page46, EX

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Page 8: Concrete reinforcement Programme for Ansys

Section completely in tension-E.T

A’s

As

40480

40

190370

300

• Concrete: fcd = 16.7MPa

• Steel: fyd = 435MPa

• ELU Forces (MN, MNm):Nx Nxy Ny

-0.321 0 -0.321

Mx Mxy My

-0.02889 0 0.02889

cm2 Theory F-Code

AXS 4.97 4.97

AYS 2.41 2.41

AXI 2.41 2.41

AYI 4.97 4.97

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 8 / 71

Page 9: Concrete reinforcement Programme for Ansys

Longitudinal reinforcement - ULS

FE Model Presentation

ULS A B/C

E 31 GPa 39 GPaρ 3.55 t/m3 3.55 t/m3

@ 3 cm 3 cmfcd 16.7e6 Pa 40e6 Pafyd 435e6 Pa 435e6 Pan 2 1.6

Uniform load applied on shell A: Q = 7KN/m2

Combination ULS: 1.35G + 1.5Q

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Page 10: Concrete reinforcement Programme for Ansys

Ansys F-Code Results

Reinforcement orientation

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Page 11: Concrete reinforcement Programme for Ansys

Ansys F-Code Results

Shell A-Top Face-X direction-AXS cm2/m

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Page 12: Concrete reinforcement Programme for Ansys

Ansys F-Code Results

Shell A-Top Face -Y direction-AYS cm2/m

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Page 13: Concrete reinforcement Programme for Ansys

Ansys F-Code Results

Shell A-Bottom Face -X direction-AXI cm2/m

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Page 14: Concrete reinforcement Programme for Ansys

Ansys F-Code Results

Shell A-Bottom Face -Y direction-AYI cm2/m

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Page 15: Concrete reinforcement Programme for Ansys

Ansys F-Code Results

Shell C-Top Face -X direction-AXS cm2/m

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Page 16: Concrete reinforcement Programme for Ansys

Ansys F-Code Results

Shell C-Top Face -Y direction-AYS cm2/m

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Page 17: Concrete reinforcement Programme for Ansys

Ansys F-Code Results

Shell C-Bottom Face -X direction-AXS cm2/m

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Page 18: Concrete reinforcement Programme for Ansys

Ansys F-Code Results

Shell C-Bottom Face -Y direction-AYS cm2/m

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Page 19: Concrete reinforcement Programme for Ansys

Ansys F-Code Results

Shell B-Top Face -X direction-AXS cm2/m

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Page 20: Concrete reinforcement Programme for Ansys

Ansys F-Code Results

Shell B-Top Face -Y direction-AYS cm2/m

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Page 21: Concrete reinforcement Programme for Ansys

Ansys F-Code Results

Shell B-Bottom Face -X direction-AXI cm2/m*** WARNING *** INF / Case: E.T / M = -14.6687536 / N =-6427.81064 / *Enum: 152 / *Angle: -10.

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Page 22: Concrete reinforcement Programme for Ansys

Ansys F-Code Results

Shell B-Bottom Face -Y direction-AYI cm2/m*** WARNING *** INF / Case: E.T / M = -2082.09801 / N =-41171.8959 / *Enum: 140 / *Angle: -80.

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Page 23: Concrete reinforcement Programme for Ansys

Ansys F-Code Configuration 3 - α = 10 β = 110

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Page 24: Concrete reinforcement Programme for Ansys

Ansys F-Code Configuration 3 - α = 10 β = 110

Shell A-Top Face -X direction-AXS cm2/m

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Page 25: Concrete reinforcement Programme for Ansys

Longitudinal Reinforcement - ELS

As

92040

300

• Concrete: fcd = 16.7MPa

• Steel: fyd = 250MPa

• n=15

• ELS Forces(MN, MNm):Nx Nxy Ny

0 0 0

Mx Mxy My

0.235 0 0.235

cm2 Theory F-Code

AXS 0 0

AYS 0 0

AXI 11 11

AYI 11 11

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Page 26: Concrete reinforcement Programme for Ansys

Longitudinal Reinforcement - ELS

As

65050

400

• Concerte: fcd = 16.7MPa

• Steel: fyd = 250MPa

• n=15

• ELS Forces (MN, MNm):Nx Nxy Ny

0.15 0 0.15

Mx Mxy My

0.21 0 0.21

cm2 Theory F-Code

AXS 0 0

AYS 0 0

AXI 12 12

AYI 12 12

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 26 / 71

Page 27: Concrete reinforcement Programme for Ansys

Longitudinal Reinforcement - ELS

As

65050

400

• Concrete: fcd = 16.7MPa

• Steel: fyd = 250MPa

• n=15

• ELS Forces (MN, MNm):Nx Nxy Ny

0.5 0 0.5

Mx Mxy My

0.12 0 0.12

cm2 Theory F-Code

AXS 0 0

AYS 0 0

AXI 0 1.673E-7

AYI 0 1.673E-7

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 27 / 71

Page 28: Concrete reinforcement Programme for Ansys

Longitudinal Reinforcement - ELS

A’s

As

50500

50

600300

• Concrete: fcd = 16.7MPa

• Steel: fyd = 250MPa

• n=15

• ELS Forces(MN, MNm):Nx Nxy Ny

-0.42 0 -0.42

Mx Mxy My

0.06 0 0.06

cm2 Theory F-Code

AXS 3.6 3.6

AYS 3.6 3.6

AXI 13 13

AYI 13 13

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 28 / 71

Page 29: Concrete reinforcement Programme for Ansys

Longitudinal Reinforcement - ELS

FE Model Presentation

ELS A B/C

E 31 GPa 39 GPaρ 3.55 t/m3 3.55 t/m3

@ 3 cm 3 cmfcd 15e6 Pa 36e6 Pafyd 250e6 Pa 250e6 PaN 15 15

Uniform load applied on A: Q = 7KN/m2

Combination ELS: G + Q

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 29 / 71

Page 30: Concrete reinforcement Programme for Ansys

Ansys F-Code Results

Shell A-Top Face -X direction-AXS cm2/m

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Page 31: Concrete reinforcement Programme for Ansys

Ansys F-Code Results

Shell A-Top Face -Y direction-AYS cm2/m

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 31 / 71

Page 32: Concrete reinforcement Programme for Ansys

Ansys F-Code Results

Shell A-Bottom Face -X direction-AXI cm2/m

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 32 / 71

Page 33: Concrete reinforcement Programme for Ansys

Ansys F-Code Results

Shell A-Bottom Face -Y direction-AYI cm2/m

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 33 / 71

Page 34: Concrete reinforcement Programme for Ansys

Ansys F-Code Results fck > 50MPa

Shell C-Top Face -X direction-AXS cm2/m

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 34 / 71

Page 35: Concrete reinforcement Programme for Ansys

Ansys F-Code Results fck > 50MPa

Shell C-Top Face -Y direction-AYS cm2/m

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 35 / 71

Page 36: Concrete reinforcement Programme for Ansys

Ansys F-Code Results fck > 50MPa

Shell C-Bottom Face -X direction-AXI cm2/m

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 36 / 71

Page 37: Concrete reinforcement Programme for Ansys

Ansys F-Code Results fck > 50MPa

Shell C-Bottom Face -Y direction-AYI cm2/m

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 37 / 71

Page 38: Concrete reinforcement Programme for Ansys

Ansys F-Code Results fck > 50MPa

Shell B-Bottom Face -X direction-AXS cm2/m

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 38 / 71

Page 39: Concrete reinforcement Programme for Ansys

Ansys F-Code Results fck > 50MPa

Shell B-Top Face -Y direction-AYS cm2/m

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 39 / 71

Page 40: Concrete reinforcement Programme for Ansys

Ansys F-Code Results fck > 50MPa

Shell B-Bottom Face -X direction-AXI cm2/m

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 40 / 71

Page 41: Concrete reinforcement Programme for Ansys

Ansys F-Code Results fck > 50MPa

Shell B-Bottom Face -Y direction-AYI cm2/m

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 41 / 71

Page 42: Concrete reinforcement Programme for Ansys

Exemple: Reservoir

FE Model Presentation

14.64m10m

ELS Steel Concrete

E 200 GPa 0.0233 GPaρ 3.55 t/m3

Cover 3 cmfcd 23.3e6 Pafyd 153e6 Pan 15

ρwater = 1000kg/m3

Combination ELS: Gconcrete + Gwater

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 42 / 71

Page 43: Concrete reinforcement Programme for Ansys

Force presentation

Water pressure on reservoir

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 43 / 71

Page 44: Concrete reinforcement Programme for Ansys

Reinforcement orientation

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 44 / 71

Page 45: Concrete reinforcement Programme for Ansys

Top face - Vertical reinforcement cm2/m

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Page 46: Concrete reinforcement Programme for Ansys

Bottom face - Vertical reinforcement cm2/m

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Page 47: Concrete reinforcement Programme for Ansys

Top face - Horizontal reinforcement cm2/m

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Page 48: Concrete reinforcement Programme for Ansys

Bottom face - Horizontal reinforcement cm2/m

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 48 / 71

Page 49: Concrete reinforcement Programme for Ansys

Analytic solution

ELEM N11 N22 N12 M11 M22 M12

28 0.53115E+06-0.56243E+06 0.269E-06 2051.4 10225. -0.188E-07

• Horizontal direciton - X|M11/N11| = 39e − 4m 7−→ C .T

Asinf = −N11·d1z·fyd

= 16.7992 cm2/m

Assup = −N11·d2z·fyd

= 17.9165 cm2/m

• Vertical direction - Y|M22/N22| = 182e − 4m 7−→ E .Cσc ∼= N22/Ac

∼= 1.9Mpa ≤ fcdAs−inf

∼= As−sup∼= 0 cm2/m

• Elment 28 - Summarycm2/m Analytic F-CodeAXS 17.9165 17.916AYS 0 0.167e-06AXI 16.7992 16.799AYI 0 0.515e-7

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 49 / 71

Page 50: Concrete reinforcement Programme for Ansys

Exemple: CNIT - Paris Ladefense

CNIT Double Shin Shell - Complex Structure

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 50 / 71

Page 51: Concrete reinforcement Programme for Ansys

Ansys F-Code Exemple:CNIT Paris.Ladefense

Exemple - Reinforcement zone ELS/Under dead load

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Page 52: Concrete reinforcement Programme for Ansys

Ansys F-Code Exemple:CNIT Paris.La Defense

Exemple - Reinforcement Orientation

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 52 / 71

Page 53: Concrete reinforcement Programme for Ansys

Ansys F-Code Exemple:CNIT Paris.La defense

Exemple - Reinforcement -AXI m2/m - Top face

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 53 / 71

Page 54: Concrete reinforcement Programme for Ansys

Ansys F-Code Exemple:CNIT Paris.La defense

Exemple - Reinforcement -AYI m2/m - Top face

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 54 / 71

Page 55: Concrete reinforcement Programme for Ansys

Ansys F-Code-Coque A-Element Number

Coque A-Element Number

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Page 56: Concrete reinforcement Programme for Ansys

Coque A-ULS-Forces N/Moment NmELEM N11 N22 N12 M11 M22 M12

1 -9440.1 -19013. 38344. 3018.8 739.45 2366.6

2 -18615. -9051.5 48166. 2320.0 4742.2 5963.0

3 -21251. -12213. 52340. 2974.2 12420. 7719.0

4 -21976. -17532. 53138. 4386.1 21926. 8313.0

5 -21480. -23054. 51695. 6106.1 31869. 8216.0

6 -20130. -28055. 48761. 7901.1 41438. 7743.4

7 -18039. -32356. 44819. 9651.3 50232. 7118.4

8 -15347. -36145. 40186. 11315. 58141. 6504.2

9 -12456. -40229. 34898. 12894. 65258. 6013.3

10 -9896.7 -46393. 28666. 14367. 71719. 5708.6

11 -6279.8 -52525. 15828. 14648. 77001. 5206.9

12 2936.0 -4100.0 -12261. 8824.7 80021. 2934.0

13 -22811. -22235. 48785. 10972. 2790.8 4202.1

14 -26446. -13749. 50815. 6781.7 4758.6 10134.

15 -26659. -13652. 52470. 4275.7 8587.4 13497.

16 -25192. -16587. 52062. 3195.9 13711. 14853.

17 -22894. -20419. 49835. 3121.8 19517. 14865.

18 -20013. -24247. 46276. 3702.6 25485. 14090.

19 -16632. -27761. 41778. 4693.8 31244. 12945.

20 -12711. -30982. 36610. 5928.2 36554. 11728.

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 56 / 71

Page 57: Concrete reinforcement Programme for Ansys

Coque A-ULS-Forces/MomentELEM N11 N22 N12 M11 M22 M12

21 -7881.9 -34250. 30628. 7244.6 41234. 10617.

22 -1361.2 -37173. 22236. 8268.0 45119. 9596.3

23 6176.8 -34492. 7693.0 7809.6 48283. 8443.8

24 1472.1 -1408.9 -5729.3 2639.5 51201. 7901.7

25 -33007. -19962. 53026. 21132. 4629.5 5410.3

26 -33837. -14717. 51307. 12878. 4631.5 12544.

27 -32330. -13513. 50821. 6844.7 5880.7 16682.

28 -29333. -14782. 49326. 2968.6 8049.6 18506.

29 -25530. -17181. 46466. 857.52 10843. 18700.

30 -21240. -19933. 42447. 63.298 13976. 17866.

31 -16583. -22644. 37508. 201.25 17186. 16474.

32 -11522. -25092. 31741. 957.66 20236. 14864.

33 -5976.4 -26898. 24845. 2020.8 22931. 13258.

34 -403.50 -26397. 15897. 2897.3 25154. 11791.

35 2673.5 -19128. 5122.1 2794.5 27004. 10663.

36 1372.5 -3659.6 -567.73 1046.9 28676. 10410.

37 -43796. -15607. 53051. 32673. 6804.6 6087.9

38 -41705. -13252. 49800. 19899. 5170.6 13879.

39 -38455. -11977. 47689. 10166. 4477.2 18343.

40 -34004. -12199. 45137. 3430.6 4483.7 20344.

41 -28793. -13481. 41702. -759.36 5056.0 20630.

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 57 / 71

Page 58: Concrete reinforcement Programme for Ansys

Coque A-ULS-Forces/MomentELEM N11 N22 N12 M11 M22 M12

42 -23228. -15277. 37366. -2977.9 6054.1 19794.

43 -17538. -17161. 32206. -3747.2 7306.6 18287.

44 -11853. -18726. 26244. -3502.4 8623.5 16451.

45 -6420.7 -19286. 19398. -2632.2 9834.3 14553.

46 -1982.6 -17495. 11802. -1547.8 10831. 12855.

47 287.79 -11545. 4659.2 -696.32 11587. 11686.

48 128.70 -2000.8 590.03 -184.04 12012. 11174.

49 -55547. -10950. 49675. 45044. 9329.5 6511.9

50 -50914. -10437. 46102. 27358. 6402.9 14576.

51 -45487. -9182.2 42813. 13801. 4184.3 19006.

52 -39070. -8889.5 39359. 4287.2 2568.2 20966.

53 -32201. -9462.4 35540. -1880.6 1554.0 21260.

54 -25345. -10520. 31165. -5467.2 1065.1 20436.

55 -18773. -11683. 26161. -7130.8 968.13 18892.

56 -12699. -12549. 20554. -7389.7 1099.2 16944.

57 -7409.2 -12518. 14486. -6650.2 1292.2 14873.

58 -3366.5 -10761. 8428.5 -5232.1 1397.3 12977.

59 -1000.5 -6578.0 3421.4 -3348.4 1275.1 11585.

60 -95.874 -206.88 630.77 -1033.0 750.75 10687.

61 -70143. -7345.1 43663. 58005. 12162. 6935.6

62 -62487. -6539.9 39744. 34674. 7942.5 14848.

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 58 / 71

Page 59: Concrete reinforcement Programme for Ansys

Coque A-ULS-Forces/MomentELEM N11 N22 N12 M11 M22 M12

63 -53410. -5394.0 35224. 17349. 4407.8 18961.

64 -44042. -5208.0 31430. 5301.8 1711.2 20790.

65 -35045. -5498.8 27764. -2637.7 -233.31 21075.

66 -26746. -6068.2 23848. -7468.0 -1534.1 20278.

67 -19300. -6698.9 19501. -9966.4 -2357.2 18737.

68 -12879. -7127.8 14756. -10708. -2865.2 16735.

69 -7665.6 -6983.2 9836.5 -10093. -3226.3 14526.

70 -3829.4 -5815.7 5238.9 -8350.6 -3629.0 12385.

71 -1404.6 -3251.4 1732.5 -5555.8 -4309.1 10609.

72 -220.88 912.40 82.578 -1730.5 -5514.2 9249.5

73 -91432. -6022.0 32923. 70955. 14329. 7225.6

74 -76855. -614.07 27511. 41330. 8376.3 14490.

75 -60440. -1662.1 23382. 20562. 4017.0 18387.

76 -47579. -1976.6 20760. 6337.1 1134.4 20181.

77 -36240. -2230.3 18134. -3136.0 -812.83 20457.

78 -26353. -2476.7 15327. -9059.5 -2145.5 19663.

79 -17960. -2743.8 12227. -12307. -3045.3 18118.

80 -11197. -2919.7 8869.7 -13507. -3655.2 16076.

81 -6151.6 -2848.3 5444.6 -13060. -4109.6 13746.

82 -2793.5 -2332.9 2342.9 -11131. -4583.3 11322.

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 59 / 71

Page 60: Concrete reinforcement Programme for Ansys

Coque A-ULS-Forces/Moment

ELEM N11 N22 N12 M11 M22 M12

83 -911.59 -1159.1 143.07 -7644.4 -5372.6 9008.6

84 -128.61 905.98 -464.60 -2365.8 -6900.4 7038.8

85 -0.10275E+06 -2176.1 7378.2 82355. 9818.9 5638.3

86 -79689. -542.20 7556.8 46976. 3267.0 13798.

87 -63652. 127.39 8179.5 23357. 1552.8 17605.

88 -48183. -328.53 7428.0 7216.6 340.67 19098.

89 -34620. -327.36 6525.9 -3552.3 -407.07 19149.

90 -22942. -388.74 5455.2 -10376. -917.62 18227.

91 -13423. -429.73 4263.9 -14245. -1263.7 16640.

92 -6269.0 -462.43 2957.4 -15847. -1500.2 14602.

93 -1619.9 -454.52 1614.0 -15611. -1671.2 12267.

94 607.58 -371.78 394.18 -13707. -1841.1 9739.6

95 887.46 -169.61 -425.60 -9940.6 -2082.7 7050.8

96 241.63 241.77 -406.11 -3502.0 -3011.9 4129.5

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Page 61: Concrete reinforcement Programme for Ansys

Coque A-ELS-Forces N/Moment NmELEM N11 N22 N12 M11 M22 M12

1 -6507.9 -13141. 26484. 2095.8 517.41 1649.9

2 -12795. -6158.1 33263. 1614.0 3306.3 4148.0

3 -14588. -8323.3 36168. 2070.3 8649.2 5367.4

4 -15088. -12020. 36737. 3053.0 15263. 5779.2

5 -14757. -15870. 35752. 4249.9 22181. 5711.0

6 -13840. -19360. 33731. 5498.9 28839. 5381.9

7 -12410. -22363. 31010. 6716.6 34957. 4947.1

8 -10563. -25007. 27808. 7874.2 40460. 4519.8

9 -8580.6 -27858. 24151. 8972.3 45411. 4178.5

10 -6830.2 -32157. 19842. 9997.5 49907. 3966.7

11 -4344.7 -36444. 10945. 10192. 53582. 3617.9

12 2043.2 -2814.5 -8548.0 6140.3 55683. 2036.9

13 -15683. -15311. 33686. 7620.3 1940.1 2928.8

14 -18209. -9426.2 35079. 4712.2 3311.7 7051.6

15 -18362. -9346.0 36250. 2972.1 5977.6 9388.0

16 -17350. -11387. 35996. 2222.7 9543.6 10329.

17 -15764. -14060. 34475. 2172.3 13584. 10337.

18 -13779. -16734. 32024. 2577.1 17737. 9797.2

19 -11450. -19188. 28920. 3267.2 21745. 9000.8

20 -8748.2 -21438. 25348. 4126.3 25439. 8154.3

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 61 / 71

Page 62: Concrete reinforcement Programme for Ansys

Coque A-ELS-Forces N/Moment NmELEM N11 N22 N12 M11 M22 M12 21 -5416.4 -23723. 21209. 5042.2 28696. 7381.2

22 -907.77 -25772. 15398. 5754.0 31399. 6671.4

23 4312.1 -23936. 5310.4 5434.7 33601. 5869.9

24 1026.1 -976.11 -3997.0 1836.8 35632. 5493.2

25 -22720. -13709. 36631. 14682. 3217.2 3769.2

26 -23316. -10108. 35439. 8947.9 3220.3 8729.1

27 -22293. -9277.2 35120. 4755.7 4091.3 11605.

28 -20233. -10161. 34109. 2062.2 5602.1 12872.

29 -17609. -11836. 32150. 595.58 7546.8 13006.

30 -14647. -13758. 29383. 44.406 9727.8 12425.

31 -11431. -15653. 25974. 141.27 11962. 11456.

32 -7936.1 -17365. 21986. 668.03 14085. 10336.

33 -4103.2 -18632. 17213. 1407.9 15961. 9218.8

34 -250.02 -18301. 11012. 2017.5 17508. 8198.7

35 1871.7 -13274. 3539.4 1945.5 18795. 7414.4

36 956.40 -2560.8 -400.84 728.79 19959. 7238.7

37 -30207. -10696. 36660. 22707. 4729.2 4240.0

38 -28777. -9103.2 34419. 13829. 3593.7 9657.9

39 -26548. -8232.7 32971. 7062.8 3112.9 12761.

40 -23483. -8394.7 31222. 2381.4 3119.1 14151.

41 -19886. -9291.8 28861. -530.77 3518.8 14349.

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 62 / 71

Page 63: Concrete reinforcement Programme for Ansys

Coque A-ELS-Forces N/Moment NmELEM N11 N22 N12 M11 M22 M12

42 -16042. -10547. 25873. -2072.3 4214.5 13767.

43 -12109. -11864. 22309. -2606.2 5086.9 12718.

44 -8177.9 -12960. 18186. -2435.1 6004.1 11441.

45 -4421.9 -13360. 13447. -1829.4 6847.2 10121.

46 -1354.4 -12130. 8183.4 -1075.1 7541.0 8939.6

47 209.93 -8016.3 3230.8 -483.17 8068.0 8126.6

48 90.993 -1415.6 409.32 -127.63 8364.3 7770.9

49 -38379. -7491.0 34334. 31311. 6484.9 4534.5

50 -35186. -7165.9 31877. 19014. 4450.1 10143.

51 -31444. -6312.1 29612. 9589.6 2908.0 13223.

52 -27014. -6119.1 27234. 2975.3 1785.2 14585.

53 -22267. -6524.0 24604. -1312.2 1080.9 14788.

54 -17527. -7264.3 21586. -3805.0 742.09 14214.

55 -12982. -8078.1 18130. -4960.7 675.66 13140.

56 -8779.1 -8685.4 14251. -5139.8 767.77 11785.

57 -5119.1 -8672.0 10050. -4624.8 902.77 10343.

58 -2322.9 -7462.0 5852.3 -3638.3 976.53 9024.6

59 -688.60 -4571.2 2380.2 -2328.2 892.09 8056.5

60 -65.574 -167.98 441.48 -718.29 527.84 7432.5

61 -48537. -5023.2 30185. 40325. 8454.8 4829.0

62 -43246. -4479.2 27488. 24102. 5520.7 10332.

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 63 / 71

Page 64: Concrete reinforcement Programme for Ansys

Coque A-ELS-Forces N/Moment NmELEM N11 N22 N12 M11 M22 M12

63 -36967. -3700.6 24368. 12056. 3063.0 13192.

64 -30488. -3582.9 21753. 3679.5 1188.4 14463.

65 -24263. -3791.3 19226. -1840.2 -163.26 14660.

66 -18521. -4190.9 16524. -5197.8 -1067.2 14105.

67 -13367. -4632.4 13520. -6933.9 -1638.9 13033.

68 -8920.9 -4933.8 10238. -7448.9 -1991.6 11639.

69 -5310.0 -4838.0 6831.4 -7019.9 -2242.2 10103.

70 -2652.8 -4033.6 3645.2 -5807.8 -2521.8 8613.3

71 -973.22 -2262.1 1212.6 -3863.9 -2994.4 7378.2

72 -153.10 616.55 62.690 -1203.5 -3832.3 6432.9

73 -63345. -4134.7 22755. 49332. 9962.0 5030.8

74 -53248. -383.95 19016. 28730. 5823.0 10083.

75 -41874. -1129.8 16171. 14289. 2791.7 12793.

76 -32973. -1357.2 14370. 4398.3 787.35 14040.

77 -25125. -1537.6 12561. -2187.9 -566.51 14230.

78 -18278. -1710.7 10624. -6305.6 -1492.9 13677.

79 -12463. -1897.6 8481.7 -8562.9 -2118.3 12602.

80 -7775.0 -2021.2 6158.8 -9396.2 -2542.2 11181.

81 -4275.1 -1973.5 3786.9 -9084.2 -2857.8 9560.3

82 -1944.0 -1618.5 1636.9 -7742.1 -3187.0 7874.4

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 64 / 71

Page 65: Concrete reinforcement Programme for Ansys

Coque A-ELS-Forces N/Moment Nm

ELEM N11 N22 N12 M11 M22 M12

83 -635.80 -807.75 109.42 -5316.8 -3735.8 6265.4

84 -89.911 621.11 -317.62 -1645.4 -4798.2 4895.5

85 -71140. -1478.6 5038.2 57259. 6826.5 3927.5

86 -55213. -367.79 5200.6 32657. 2271.3 9601.4

87 -44141. 94.083 5654.4 16232. 1079.2 12248.

88 -33438. -225.71 5142.1 5009.1 236.34 13286.

89 -24046. -225.54 4521.9 -2478.3 -283.59 13320.

90 -15952. -268.57 3782.9 -7221.9 -638.56 12678.

91 -9349.6 -297.23 2959.5 -9911.4 -879.12 11574.

92 -4382.9 -320.15 2055.4 -11024. -1043.5 10156.

93 -1150.1 -314.94 1124.9 -10859. -1162.4 8532.3

94 404.74 -257.99 279.21 -9534.0 -1280.4 6773.9

95 608.24 -118.39 -290.54 -6914.0 -1448.4 4903.8

96 166.37 166.47 -280.04 -2435.7 -2094.6 2872.1

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 65 / 71

Page 66: Concrete reinforcement Programme for Ansys

Ansys F-Code-Coque B-Element Number

Coque B-Element Number

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 66 / 71

Page 67: Concrete reinforcement Programme for Ansys

Coque B-ULS-Forces N/Moment Nm

ELEM N11 N22 N12 M11 M22 M12

129 -8845.3 -89675. 9548.0 5411.8 86498. 7637.9

130 -24539. -89792. 12690. 12755. 81465. 8843.3

131 -22042. -74713. 27332. 14362. 75161. 8906.3

132 -23184. -65862. 37639. 13671. 68487. 9320.9

133 -25888. -60397. 43564. 12349. 61193. 9846.3

134 -28365. -54831. 47467. 10736. 53051. 10372.

135 -29579. -47658. 50203. 8875.9 43931. 10809.

136 -29188. -37890. 51778. 6762.9 33910. 11063.

137 -26937. -24769. 51522. 4441.4 23354. 10992.

138 -22116. -7822.3 47911. 2094.2 13061. 10409.

139 -12743. 12963. 38542. 52.143 4364.7 9040.8

140 2650.2 36081. 17834. -967.97 21.893 6110.9

141 -2716.4 -0.10211E+06 14981. 2600.4 62339. 4095.2

142 -5032.3 -0.11021E+06 23760. 8380.9 58422. 6080.5

143 -16782. -91608. 31549. 10417. 54108. 6498.4

144 -20897. -78337. 39351. 10290. 49388. 6685.5

145 -21605. -69816. 44411. 9339.6 44035. 6826.0

146 -20719. -62618. 47340. 8081.7 38047. 6911.6

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 67 / 71

Page 68: Concrete reinforcement Programme for Ansys

Coque B-ELS-Forces N/Moment NmELEM N11 N22 N12 M11 M22 M12

129 -6145.0 -62449. 6612.7 3769.4 60205. 5300.3

130 -17042. -62562. 8729.5 8882.3 56707. 6134.5

131 -15270. -52080. 18877. 10000. 52324. 6177.3

132 -16028. -45926. 26023. 9519.2 47682. 6464.9

133 -17873. -42125. 30125. 8599.9 42609. 6829.8

134 -19561. -38254. 32820. 7478.3 36946. 7194.9

135 -20371. -33266. 34703. 6185.4 30603. 7499.5

136 -20067. -26475. 35782. 4717.0 23633. 7677.2

137 -18474. -17359. 35598. 3103.9 16289. 7630.1

138 -15113. -5593.1 33106. 1472.1 9125.1 7229.1

139 -8631.1 8826.3 26660. 45.607 3066.5 6283.4

140 1994.1 24892. 12367. -693.83 24.688 4247.1

141 -1884.3 -71246. 10374. 1811.3 43388. 2832.3

142 -3476.9 -76943. 16410. 5836.3 40666. 4212.0

143 -11639. -64032. 21788. 7252.8 37669. 4501.4

144 -14491. -54812. 27190. 7165.3 34390. 4630.6

145 -14971. -48887. 30690. 6505.6 30672. 4727.7

146 -14342. -43879. 32708. 5632.2 26511. 4786.8

147 -12941. -38081. 33742. 4617.3 21971. 4811.5

148 -10776. -30298. 33881. 3454.3 17166. 4808.8

149 -7911.8 -19432. 32693. 2149.0 12305. 4785.8

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 68 / 71

Page 69: Concrete reinforcement Programme for Ansys

Ansys F-Code-Reservoir Element Number

Element Number

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 69 / 71

Page 70: Concrete reinforcement Programme for Ansys

Ansys F-Code-Reservoir Element Number

Element Number

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 70 / 71

Page 71: Concrete reinforcement Programme for Ansys

ELS-Forces N/Moment Nm

ELEM N11 N22 N12 M11 M22 M12

25 0.53115E+06-0.56243E+06 0.617E-07 2051.4 10225. -0.433E-08

26 0.53115E+06-0.56243E+06 0.126E-06 2051.4 10225. -0.139E-07

27 0.53115E+06-0.56243E+06 0.201E-06 2051.4 10225. -0.178E-07

28 0.53115E+06-0.56243E+06 0.269E-06 2051.4 10225. -0.188E-07

29 0.53115E+06-0.56243E+06 0.126E-06 2051.4 10225. -0.174E-07

30 0.53115E+06-0.56243E+06-0.848E-06 2051.4 10225. -0.148E-07

31 0.53115E+06-0.56243E+06 0.153E-05 2051.4 10225. 0.590E-08

32 0.53115E+06-0.56243E+06-0.106E-05 2051.4 10225. 0.560E-10

33 0.53115E+06-0.56243E+06-0.547E-06 2051.4 10225. 0.191E-07

34 0.53115E+06-0.56243E+06-0.191E-06 2051.4 10225. 0.217E-07

35 0.53115E+06-0.56243E+06 0.306E-05 2051.4 10225. 0.499E-07

36 0.53115E+06-0.56243E+06-0.615E-05 2051.4 10225. -0.348E-07

Dong LI (DLI) Reinforcement Algorithm June 15, 2016 71 / 71