nemetschek frilo gmbh projekt: r2017-2 schweriner str. · pdf file1515 1515 8 15 2985 15 8...

Nemetschek Frilo GmbH

Schweriner Str. 25 Position: B8_FDB-Ref-BS

Projekt: R2017-2

09.11.2017 Seite: 101067

Tel.: 03518761411

Fax: 0351/87614-10Dresden

Position: B8_FDB-Ref-BS Spannbettbinder B8 01/2018 (Frilo prerelease)

3.75 3.75

1515 1515

8 15 2985 15 8

3030

95

75

170

19

60

146.8

23.2

170

19

60

71.8

23.2

95

19

60

71.8

23.2

95

15 3000 15

3030

10.84.3

0.61

Eigengewicht Fertigteil nicht dargestellt

System:

Double-pitch roof

Basics:Load combinatorics: NA to BS EN 1990/A1:2009-06 + EN 1990:2002/AC:2010 ULS: Structural safety checks(STR) permanent/variable design situation with equation 6.10 a,b

Design code: NA to BS EN 1992-1-1/A2:2015-07 + EN 1992-1-1:2004 /AC:2010 Prestressing for pretensioning



Projekt: R2017-2

09.11.2017 Seite: 201067

Tel.: 03518761411


System Geometry:

Total L = 30.30 m Effective L1 = 30.00 m Outstand left L0 = 0.15 m right L2 = 0.15 m Distance Ridge L3 = 15.15 m Height beam :left H1 = 95.0 cm Ridge H2 = 170.0 cm right H3 = 95.0 cm Relation eff.span to height of beam: L1/H2 = 17.65

Erection attachment, distance from the beginning resp. end of beam:Hook L8 = 3.75 m right L9 = 3.75 m

Cross-section Precast :

Layer of cross-section from top to bottomNr Width Distance Remarks

[cm] [cm]

1 60.0 0.02 60.0 15.03 19.0 23.2 Web begin4 19.0 170.0 Web end

Web height over beam length constant

Material:

Prestressing steel

Y1770S7 Strand 7 wiresdd = 4.1 mm dp = 12.3 mm Ep = 195000 N/mm2 Ap = 0.930 cm2

fp0.1k = 1520 N/mm2 fpk = 1770 N/mm2 εuk = 35.0 ‰ εud = 31.5 ‰

Partial safety factor : γs = 1.15

Coeff. prestress: charact. value rsup = 1.00 rinf = 1.00 Design value γp,max = 1.10 γp,min = 0.90

Proof of crack width Equ. diameter dpV = 7.20 mm ξ = 0.60 (Tab. 6.2)

Relaxation class 2 (strands, wires, low relaxation)σp0/fpk 10 h 200 h 1000 h 500000h

0.60 0.1 0.2 0.4 2.50.70 0.3 0.7 1.0 3.90.80 1.2 1.9 2.4 6.1

- Losses in % by 3.3.2 (6), example process

Permitted stresses: in formwork σp ≤ 1368.0 N/mm2 (0.90* fp0.1k) after anchor. release σp ≤ 1292.0 N/mm2 (0.85* fp0.1k) char. Lc σp ≤ 1327.5 N/mm2 (0.75* fp0.1k)

Transmission length ηp1 = 3.20 η1 = 1.00 α1 = 1.25 α2 = 0.19 σpm0 = 922 N/mm2 PT: fctdt = 0.81 N/mm2 fbpt = 2.58 N/mm2 lpt = 1.05 m

Dispersion_length: d = 0.91 m ldisp = 1.39 m



Projekt: R2017-2

09.11.2017 Seite: 301067

Tel.: 03518761411


Reinforcing steel:

Longitudinal StirrupB 500B B 500B

Es = 200000 N/mm2 Es = 200000 N/mm2

fyk = 500 N/mm2 fyk = 500 N/mm2

ftk = 540 N/mm2 ftk = 540 N/mm2

εuk = 50.0 ‰ εuk = 50.0 ‰εud = 45.0 ‰ εud = 45.0 ‰

Partial safety factor :γs = 1.15 γs = 1.15

permitted stresses in SLS :σs ≤ 400 N/mm2 σs ≤ 400 N/mm2 (0.80 * fyk)

Requirements durability:

top bottomattack on concrete X0 X0attack on reinforc. XC1 XC1min. concrete class C 20/25 C 20/25stirrup φ,l = 8 mmlong. reinforcement φ,m = 20 mm φ,m = 16 mmprestressed steel dp = 12.3 mm strandallowance in design Δcdev = 5 mm *2 Δcdev = 5 mm *2stirrup cmin,l = 15 mm cmin,l = 15 mmconcrete coverage cnom,l = 20 mm cnom,l = 20 mmlongitudinal bars cmin,m = 20 mm *5 cmin,m = 16 mm *5concrete coverage cnom,m = 28 mm *1 cnom,m = 28 mm *1prestressing steel : cmin,p = 19 mm *5 cmin,p = 19 mm *5concrete coverage cnom,p = 28 mm *1 cnom,p = 28 mm *1laying dist. link c,l = 20 mm c,l = 20 mmall. crack width wmax = 0.20 mm wmax = 0.20 mmdecompression not req. not req. *1:with cmin,l *2: Quality Control*5: bond decisive

Concrete:

PrecastC 50/60

fck = 50.00 N/mm2

αcc = 0.85fctk0.05 = 2.85 N/mm2

αct = 1.00γ = 25.00 kN/m3 Unit

Ecm = 37000 N/mm2

αE = 1.00 Coeff. E-moduleGcm = 14800 N/mm2

Partial safety factor : γc = 1.50

permitted stresses in SLS : char. Lc σc ≥ -30.00 N/mm2 q.perm.Lc σc ≥ -22.50 N/mm2 Removal the anchor t= t0T(sto) fcm(t) = 24.56 N/mm2 fck(t) = 16.56 N/mm2 linear creep σc ≥ -7.45 N/mm2 (k2=0.45) maximum σc ≥ -11.59 N/mm2 (k6=0.70)

Creep modulus & shrinkage strain

no heat treatment, t0T = t0CementStrenght class 42,5R;52,5ρ= 0.5 (Aging coefficient)Reference point for t0 is the start of the concreting of the precast



Projekt: R2017-2

09.11.2017 Seite: 401067

Tel.: 03518761411


Creep t0 RHDays %

Storage 1 70Utilization precast 21 50

L. Segment Part- t0 t α t0,eff βt0 ßH βc(t,t0) φRH βfcm φ(t,t0)cross-section B.9 B.5 B.8 B.7 B.3 B.4 B.1

1 Storage PcC 1.0 21.0 1 4.0 0.70 475.4 0.38 1.24 2.21 0.742 Utilization precast PcC 21.0 26000.0 1 4.0 0.70 463.7 0.61 1.47 2.21 1.39

L. A U h0 ßds(t0,ts) ßds(t,ts) ßRH εcd,0 ßas εca/10e6 εcs(t,t0)[cm2] [cm] [cm] 3.10 B.12 B.11 3.13 3.12 [‰]

1 4013.10 446.8 179.7 0.000 0.172 1.02 402.5 0.60 100.00 0.1212 4013.10 446.8 179.7 0.172 0.996 1.36 536.0 1.00 100.00 0.430

Loads:

Self weight

Beam beginning g11 = 6.47 kN/mRidge g12 = 10.03 kN/mBeam end g13 = 6.47 kN/m

Total G = 250.1 kNVolume V = 10.00 m3

Surf. A = 95.00 m2

Live loads

Units: Single load[kN] Single moment[kNm] line load[kN/m]span type gle qle Dist. a gri qri Length Fact Act. Sim. Pos.

[m] [m]

1 1 10.80 4.30 1.00 10 0 1 1 0.00 0.61 1.00 9 0

Load types: 1 = uniformly distr., 2 = single load at a, 3 = single moment at a 4 = trapezoidal load from a, 5 = triangle load over L

Actions:

Act. γQ ψ0 ψ1 ψ2 Dep. Cat. Description

9 1.50 0.50 0.20 0.00 0 W Windlasten10 1.50 0.50 0.20 0.00 0 S Schnee bis NN +1000m

Tendons:

Dist(LE) > 3.5 cm axis horizontal > 3.7 cm vertical > 3.7 cm

lay. num- area Dist.LE Prestressing <--- Isolations --->No. ber Ap Yp σp(0) Count to x1 from x2 Type

[cm2] [cm] [N/mm2] [m] [m] ||

1 3 2.79 8.5 1000 0 LE2 3 2.79 12.3 1000 0 LE3 3 2.79 16.1 1000 0 LE4 3 2.79 19.9 1000 0 LE5 3 2.79 23.7 1000 0 LE6 3 2.79 27.5 1000 0 LE7 3 2.79 31.3 1000 0 LE8 1 0.93 35.1 1000 0 LE

x1 and x2 with respect to the left beginning from jointLE= parallel lower edge, UE= parallel upper edgeThe calculation of the losses due to creep, shrinkage and relaxationfollowing the method from Abelein



Projekt: R2017-2

09.11.2017 Seite: 501067

Tel.: 03518761411


Untensioned reinforcement:

Layer num- diam. area Dist.LE effective rangeNo. ber Φs,l As Ys from xA to xE Type

[mm] [cm2] [cm] [m] [m] ||

1 2 16 4.02 3.5 0.00 30.30 LE2 2 20 6.28 166.5 0.00 30.30 UE3 2 20 6.28 155.0 0.00 30.30 UE

xA and xE with respect to the left beginning from jointLE= parallel lower edge, UE= parallel upper edge

Surface reinforcement acc.to Tab. NA.J.41 (B0 < D0) :

Web (Z1/S3) AsS = 1.24 cm2/m (UwkS <= XC4) (per side)Top flange (Z3/S1) AsO = 0.00 cm2/m (UwkS <= XC4)

Settings for shear resistance check

Bearing width, distance bearing edge, effective height of the bearing lineleft bAl = 0.15 m al = 0.07 m dAl = 0.92 m right bAr = 0.15 m ar = 0.07 m dAR = 0.92 m For shear reinforcement not decisive ranges over support A and B:xaRe=0.99 m direct bearing (width of bearing/2 + eff. depth)xbLi=0.99 m direct bearing (width of bearing/2 + eff. depth)

Check the limit deformation:

Total sagging f ≤ L/ 250 Increase deflection |df| ≤ L/ 500 Cantilever left f ≤ 0.1 cm |df| ≤ 0.1 cm Span f ≤ 12.0 cm |df| ≤ 6.0 cm Cantilever right f ≤ 0.1 cm |df| ≤ 0.1 cm quasi- permanent combination and eff. char. prestressDeflection due to shrinkage consideredTension stiffening: Member rigidity, Characteristic combination

RESULTS ( summary)

Reaction forces (t = infinitely):

Units: all [kN] G:perm., Q:variable. ,V: Sum <------char. value-----> <--ULS(PT)---->

Support point G min Q max Q min V max V

A (left) 287.01 0.00 73.65 287.01 462.02B (right) 287.01 0.00 73.65 287.01 462.02

max. bending moment in erection state(char. value):

MF = = 2763.72 kNm at x = = 15.15 m

Checks are not complied with:

Checkvalue Extrem Utilisation x [m]

Resisting tens force bot η = 0.84 1.19 0.15Crack MinAs+AsDuc bottom AsMin = 6.7 cm2 1.67 15.15Incr.-deflection(Util) |df|= 6.9 cm 1.15 13.47Prc.:Compr.stress t0(sto) σc = -28.43 N/mm2 2.45 3.75Buckling installation state (Stiglat) η = 1.69 1.19

Warning

Prc.:lin. creep t0(Sto) σc =-23.91 N/mm2 x= 29.47 m σc <0.45*fck(t)= -7.45 N/mm2 _disproportional creeping by increased creep modulus considered(fk= 2.28)

Required shear reinforcement:

Column A: asw = 5.00 cm2/mColumn B: asw = 5.00 cm2/m



Projekt: R2017-2

09.11.2017 Seite: 601067

Tel.: 03518761411


Bursting reinforcement

left Laying length = 1.04 m from x = 0.00 m As = 5.6 cm2 right Laying length = 1.04 m from x = 30.30 m As = 5.6 cm2

Check of anchorage

left: Tensile force resistance in anchoring area Util = 1.19 additional reinforcement necessaryright: Tensile force resistance in anchoring area Util = 1.19 additional reinforcement necessary

Overview crit. sections

Selected basic grid: 10 Sections

Checkvalue Extrem Utilisation x [m]

Flexural capacity bottom η = 1.17 0.85 11.11Flexural capacity top η = **** **** ****Resisting tens force bot η = 0.84 1.19 0.15 !Resisting tens force top η = **** **** ****Prc.:Compr.stress t0(sto) σc = -28.43 N/mm2 2.45 3.75 !Prc.:Compr.stress Cc σc = -18.62 N/mm2 0.62 3.75Stress in prestress.steel σp,Cc = 1083.7 N/mm2 0.82 11.11Stress in rebars σs = 116.1 N/mm2 0.29 10.81Crack MinAs+AsDuc bottom AsMin = 6.7 cm2 1.67 15.15 !Crack MinAs+AsDuc top AsMin = ---- cm2 ---- ----Crack width bottom wk = 0.07 mm 0.36 9.76Crack width top wk = 0.15 mm 0.77 3.75Sagging top fo = -3.5 cm 0.29 16.83Sagging bottom fu = 7.2 cm 0.60 13.47Incr.-deflection(Util) |df|= 6.9 cm 1.15 13.47 !Prc.:Shear reinf (web) asw = 5.00 cm2/m 1.00 1.14Concrete strut capacity η = 1.33 0.75 0.83

---- Check not required**** Check not fulfilledPrc.:Precast member Add.: in-situ supplementIS : Installed state SC : State of constructionAsDuk:Ductility reinforcement

Linear creep limit, informative: Extrem Utilisation x [m]

Prc.:lin. creep t0(Sto) σc = -23.91 N/mm2 3.21 29.47Prc.:Compression quasi-permanent Lc σc = -17.37 N/mm2 0.77 29.16

Tensile stress state I, informative: Extrem Utilisation x [m]

Prc.:Tens.stress (IS) σt = 9.10 N/mm2 2.24 10.10Prc.:Tens.stress (SC) σt = 3.11 N/mm2 1.23 29.47

Internal forces ULS [kN,kNm]

Design sit. permanent/transient from prestressing ( formwork state)x Min Max Min Max Sto.tA Sto.tA Use.tE Use.tE PRE

[m] My My Qz Qz Nv Mv Nv Mv Deg

0.00 0.00 0.00 0.0 0.0 0.0 0.00 0.0 0.00 0.000.15 -0.10 -0.07 -1.3 -1.0 -363.4 -137.09 57.2 -29.46 3.020.15 -0.10 0.43 -1.3 460.8 -368.8 -139.14 54.3 -30.50 2.930.83 -3.05 306.66 -7.4 441.3 -2024.0 -801.75 -742.5 -339.86 1.611.14 -5.77 442.10 -10.2 432.4 -2044.3 -827.27 -1007.9 -477.46 2.011.38 -8.48 545.05 -12.4 425.5 -2044.3 -840.78 -1112.6 -541.72 2.051.39 -8.60 549.30 -12.5 425.2 -2044.3 -841.35 -1113.2 -542.62 2.043.37 -51.68 1334.23 -31.3 367.5 -2044.3 -952.08 -1212.9 -711.96 1.083.75 -64.27 1471.73 98.4 356.2 -2044.3 -973.19 -1233.0 -744.63 1.026.73 197.37 2400.70 75.4 266.8 -2044.3 -1137.35 -1374.5 -986.59 0.82

10.10 406.73 3125.02 46.9 162.5 -2044.3 -1320.54 -1437.0 -1198.12 0.7713.47 515.65 3492.30 15.8 54.9 -2044.3 -1501.74 -1453.0 -1364.52 0.7815.15 529.62 3538.52 -0.7 0.7 -2044.3 -1591.46 -1451.0 -1433.08 0.8116.83 515.65 3492.30 -54.9 -15.8 -2044.3 -1501.74 -1453.0 -1364.52 0.7820.20 406.75 3125.02 -162.5 -46.9 -2044.3 -1320.54 -1437.0 -1198.12 0.77



Projekt: R2017-2

09.11.2017 Seite: 701067

Tel.: 03518761411


Design sit. permanent/transient from prestressing ( formwork state)x Min Max Min Max Sto.tA Sto.tA Use.tE Use.tE PRE

[m] My My Qz Qz Nv Mv Nv Mv Deg

23.57 197.38 2400.70 -266.8 -75.4 -2044.3 -1137.35 -1374.5 -986.59 0.8226.55 -64.23 1471.73 -356.2 35.0 -2044.3 -973.19 -1233.0 -744.63 1.0226.93 -51.65 1334.23 -367.5 31.2 -2044.3 -952.08 -1212.9 -711.96 1.0828.91 -8.59 549.30 -425.2 12.5 -2044.3 -841.35 -1113.2 -542.62 2.0428.92 -8.46 545.05 -425.5 12.4 -2044.3 -840.78 -1112.6 -541.72 2.0529.16 -5.76 442.10 -432.4 10.2 -2044.3 -827.27 -1007.9 -477.46 2.0129.47 -3.04 306.66 -441.3 7.4 -2024.0 -801.75 -742.5 -339.86 1.6130.15 -0.10 0.43 -460.8 1.3 -368.8 -139.14 54.3 -30.50 2.9330.15 -0.10 -0.07 1.0 1.3 -363.4 -137.09 57.2 -29.46 3.0230.30 0.00 0.00 0.0 0.0 0.0 0.00 0.0 0.00 0.00

Internal forces SLS

<- char. Lc-> <- freq. Lc-> <q.- perm. Lc>x Min Max Min Max Min Max

[m] My My My My My My

0.00 0.00 0.00 0.00 0.00 0.00 0.000.15 -0.07 -0.07 -0.07 -0.07 -0.07 -0.070.15 -0.07 0.32 -0.07 0.26 -0.07 0.240.83 -2.26 236.33 -2.26 198.99 -2.26 190.421.14 -4.27 340.71 -4.27 286.93 -4.27 274.591.38 -6.28 420.07 -6.28 353.81 -6.28 338.591.39 -6.37 423.35 -6.37 356.57 -6.37 341.233.37 -38.28 1028.49 -38.28 867.02 -38.28 829.943.75 -47.61 1134.52 -47.61 956.56 -47.61 915.696.73 214.01 1851.08 214.01 1562.52 214.01 1496.25

10.10 423.38 2410.09 423.38 2036.53 423.38 1950.7413.47 532.30 2693.69 532.30 2277.66 532.30 2182.1315.15 546.27 2729.40 546.27 2308.09 546.27 2211.3416.83 532.30 2693.69 532.30 2277.66 532.30 2182.1320.20 423.39 2410.09 423.39 2036.53 423.39 1950.7423.57 214.03 1851.08 214.03 1562.52 214.03 1496.2526.55 -47.58 1134.52 -47.58 956.56 -47.58 915.6926.93 -38.26 1028.49 -38.26 867.02 -38.26 829.9428.91 -6.36 423.35 -6.36 356.57 -6.36 341.2328.92 -6.27 420.07 -6.27 353.81 -6.27 338.5929.16 -4.27 340.71 -4.27 286.93 -4.27 274.5929.47 -2.25 236.33 -2.25 198.99 -2.25 190.4230.15 -0.07 0.32 -0.07 0.26 -0.07 0.2430.15 -0.07 -0.07 -0.07 -0.07 -0.07 -0.0730.30 0.00 0.00 0.00 0.00 0.00 0.00

<Flex. capacity-> <-----resisting tensile force--------->x[m] η bo η to η bo σI/σR al η to σI/σR al

=MRd/MEd =MRd/MEd =TRd/TEd [N/mm2] [cm] =TRd/TEd [N/mm2] [cm]

0.00 --- --- --- 0.00# --- --- 0.00# ---0.08 --- --- --- 0.00# --- 303.56 0.00# 43.10.15 --- --- --- 0.00# --- 209.24 0.00# 43.20.15 --- --- 0.84 0.00# 103.8 207.30 0.00# 43.20.22 62.84 --- 1.04 0.00# 104.2 110.21 0.00# 43.40.31 27.98 --- 1.27 0.00# 104.7 102.06 0.00# 43.60.32 26.37 946.57 1.29 0.00# 104.7 101.47 0.00# 43.70.61 10.11 91.70 1.87 0.00# 106.3 44.33 3.17*! 44.40.92 6.20 *** 2.34 0.00# 108.1 *** 3.01*! 150.41.22 4.64 *** 2.54 1.66# 109.7 *** 1.72# 150.21.38 4.11 *** 2.40 1.56# 110.6 *** 1.43# 146.81.39 4.08 *** 2.39 1.55# 110.7 *** 1.41# 146.61.53 3.73 *** 2.29 1.18# 111.5 *** 1.16# 143.31.84 3.12 *** 2.09 1.06# 113.2 *** 0.64# 137.33.37 1.92 *** 1.60 6.98*! 121.7 *** 0.11# 109.43.75 1.77 *** 1.55 8.40*! 123.8 *** 0.09# 102.86.73 1.29 *** 1.25 15.01*! 88.6 *** 0.02# 59.5

10.10 1.18 *** 1.17 16.76*! 70.8 *** 0.00# 67.911.15 1.17 *** 1.17 16.49*! 73.3 *** 0.00# 70.513.47 1.22 --- 1.21 14.97*! 79.1 --- 0.00# ---16.83 1.22 --- 1.21 14.97*! 79.1 --- 0.00# ---



Projekt: R2017-2

09.11.2017 Seite: 801067

Tel.: 03518761411


<Flex. capacity-> <-----resisting tensile force--------->x[m] η bo η to η bo σI/σR al η to σI/σR al

=MRd/MEd =MRd/MEd =TRd/TEd [N/mm2] [cm] =TRd/TEd [N/mm2] [cm]

20.20 1.18 *** 1.18 16.76*! 70.8 *** 0.00# 67.923.57 1.29 *** 1.25 15.01*! 88.6 *** 0.02# 59.526.55 1.77 *** 1.55 8.40*! 123.8 *** 0.09# 102.826.93 1.92 *** 1.60 6.98*! 121.7 *** 0.11# 109.428.46 3.12 *** 2.09 1.06# 113.2 *** 0.64# 137.328.77 3.73 *** 2.29 1.18# 111.5 *** 1.16# 143.328.91 4.08 *** 2.39 1.55# 110.7 *** 1.41# 146.628.92 4.11 *** 2.40 1.56# 110.6 *** 1.43# 146.829.08 4.64 *** 2.54 1.66# 109.7 *** 1.72# 150.229.38 6.20 *** 2.34 0.00# 108.1 *** 3.01*! 150.429.69 10.11 91.97 1.87 0.00# 106.3 55.14 3.17*! 44.429.98 26.37 950.37 1.29 0.00# 104.7 76.08 0.00# 43.729.99 27.98 --- 1.27 0.00# 104.7 75.32 0.00# 43.630.08 62.84 --- 1.04 0.00# 104.2 101.48 0.00# 43.430.15 --- --- 0.84 0.00# 103.8 207.92 0.00# 43.230.15 --- --- --- 0.00# --- 209.87 0.00# 43.230.22 --- --- --- 0.00# --- 304.54 0.00# 43.130.30 --- --- --- 0.00# --- --- 0.00# ---

---- Check not required**** Check not fulfilled#:Main tens.stress σI #!: σI > fctk0.05*:Edge tens. str. σR *!: σR > fctk0.05

Concrete stresses precast

x σc,1 σc,2 σc,Cc σc,Qc σt,Cc σt,SC[m] [N/mm2] [N/mm2] [N/mm2] [N/mm2] [N/mm2] [N/mm2]

0.08 -2.45 -2.45 -1.61 -1.61 0.86 0.460.15 -4.56 -4.56 -3.55 -3.55 0.98 0.780.15 -4.62 -4.62 -3.61 -3.60 0.98 0.790.69 -22.87 -19.30 -15.40 -15.40 0.77 2.610.83 -27.46 -23.91 -12.90 -12.90 0.83 3.110.92 -27.73 -23.76 -14.54 -12.52 0.52 3.011.00 -27.72 -23.41 -13.83 -12.04 0.22 2.891.14 -27.71 -22.34 -17.37 -17.37 --- 2.691.38 -27.71 -21.64 -17.09 -16.60 --- 2.351.39 -27.71 -21.62 -17.09 -16.58 --- 2.343.37 -28.23 -17.00 -18.23 -13.07 1.60 4.873.75 -28.43 -16.30 -18.62 -12.61 2.66 4.966.73 -18.50 -12.43 -16.35 -10.28 7.60 2.47

10.10 -15.14 -10.32 -14.93 -10.36 9.10 1.2213.47 -13.56 -9.63 -13.73 -9.45 7.99 1.0015.15 -13.21 -9.63 -12.34 -8.59 6.84 1.1516.83 -13.56 -9.63 -13.73 -9.45 7.99 1.0020.20 -15.14 -10.32 -14.93 -10.36 9.10 1.2223.57 -18.50 -12.43 -16.35 -10.28 7.60 2.4726.55 -28.42 -16.30 -18.62 -12.61 2.66 4.9626.93 -28.23 -17.00 -18.23 -13.07 1.60 4.8628.91 -27.71 -21.62 -17.09 -16.58 --- 2.3428.92 -27.71 -21.64 -17.09 -16.60 --- 2.3529.16 -27.71 -22.34 -17.37 -17.37 --- 2.6929.30 -27.72 -23.41 -13.83 -12.04 0.22 2.8929.38 -27.73 -23.76 -14.54 -12.52 0.52 3.0129.47 -27.46 -23.91 -12.90 -12.90 0.83 3.1129.61 -22.87 -19.30 -15.40 -15.40 0.77 2.6130.15 -4.62 -4.62 -3.61 -3.60 0.98 0.7930.15 -4.56 -4.56 -3.55 -3.55 0.98 0.7830.22 -2.45 -2.45 -1.61 -1.61 0.86 0.46

---- Check not required**** Check not fulfilledσc,1 : Disproportional creeping check with early strength (sto.)σc,2 : Compressive stress check with early strength (sto./erect.)σc,Cc : Compression check Characteristic load combinationσc,Qc : Disproportional creep check quasi-perm. load combinationσt,Cc : Tensile stresses ,Installed state, Characteristic load combination (informative)σt,SC : Tensile stresses,State of construction (informative)



Projekt: R2017-2

09.11.2017 Seite: 901067

Tel.: 03518761411


Check the limit deformation:

Total sagging f ≤ L/ 250 Increase deflection |df| ≤ L/ 500 Cantilever left f ≤ 0.1 cm |df| ≤ 0.1 cm Span f ≤ 12.0 cm |df| ≤ 6.0 cm Cantilever right f ≤ 0.1 cm |df| ≤ 0.1 cm quasi- permanent combination and eff. char. prestressDeflection due to shrinkage consideredTension stiffening: Member rigidity, Characteristic combination

Storage Utilizationx ftA ftE ftA ftE |df|

[m] [cm] [cm] [cm] [cm] [cm]

0.00 0.0 0.1 0.0 -0.1 -0.13.37 -1.0 -1.8 -0.3 2.2 2.56.73 -1.6 -2.8 -0.1 4.7 4.8

10.10 -1.9 -3.3 0.2 6.4 6.213.47 -2.0 -3.5 0.3 7.2 6.916.83 -2.0 -3.5 0.3 7.2 6.920.20 -1.9 -3.3 0.2 6.4 6.223.57 -1.6 -2.8 -0.1 4.7 4.826.93 -1.0 -1.8 -0.3 2.2 2.530.30 0.0 0.1 0.0 -0.1 -0.1

|df|= ftE(service)- ftA(service)

Shear resistance

x VEd VEd,red cot Θ z asw,Web η[m] [kN] [kN] [cm] [cm] =VRd,max/VEd

0.08 0.7 ---- 1.00 68.5 2.15 610.030.22 456.5 ---- 2.50* 69.1 5.00 1.440.23 455.9 ---- 2.50* 69.1 5.00 1.450.83 420.4 ---- 2.50* 72.4 5.00 1.331.14 402.9 402.9 2.50 74.1 5.00 1.421.38 389.7 389.7 2.50 75.4 4.75 1.571.39 389.2 389.2 2.50 75.5 4.74 1.583.37 289.9 289.9 2.50 85.1 3.13 2.633.75 272.6 272.6 2.50 87.2 2.88 2.926.73 150.1 150.1 1.58 101.8 2.15 7.22

10.10 41.0 41.0 1.00 118.6 2.15 21.2313.47 73.3 73.3 1.00 134.9 2.15 30.8115.15 122.5 122.5 1.00 143.0 2.15 19.4816.83 73.3 73.3 1.00 134.9 2.15 30.8120.20 41.0 41.0 1.00 118.6 2.15 21.2423.57 150.1 150.1 1.58 101.8 2.15 7.2226.55 272.6 272.6 2.50 87.2 2.88 3.0826.93 289.9 289.9 2.50 85.1 3.13 2.6328.91 389.2 389.2 2.50 75.5 4.74 1.5828.92 389.7 389.7 2.50 75.4 4.75 1.5729.16 402.9 402.9 2.50 74.1 5.00 1.4229.47 420.4 ---- 2.50* 72.4 5.00 1.3330.08 456.5 ---- 2.50* 69.1 5.00 1.4430.22 0.7 ---- 1.00 68.5 2.15 610.03

---- Check not required**** Check not fulfilled*: Take over from last construction phase



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Internal forces

-0.07

3538.5

max MEd from external loads (PT)

0 5 10 15 20 25 30x [m]

-64.3

529.6

min MEd from external loads (PT)

-1591.5

Moment from prestressing, t= tA storage

-1433.1

1.98

Moment from prestressing, t= tE use

460.8

-75.4

max VEd from external loads (PT)

98.4

-460.8

min VEd from external loads (PT)



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Bending resitance (failure safety)

Flexural capacity bottom η = 1,17 x=11,11 m

0 5 10 15 20 25 30x [m]

Ausn

100%

Flexural capacity top η = ***** x= 0,83 m

Resisting tens force bot η = 0,84 x= 0,15 m

Resisting tens force top η = ***** x= 0,83 m

Ultimate stress precast component

Prc.:Compr.stress Cc σc =-18,62 N/mm2 x= 3,75 m

0 5 10 15 20 25 30x [m]

Ausn

100%

Prc.:Compr.stress t0(sto) σc =-28,43 N/mm2 x= 3,75 mPrc.:Tens.stress (IS) > 100% condition II, informative only

Prc.:Tens.stress (SC) > 100% condition II, informative only



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Deformation

Sagging t=tA storage -2,05 cm

0 5 10 15 20 25 30x [m]

Sagging t=tE storage -3,50 cm

Sagging t=tA utilisatio -0,34 cm

Sagging t=tE utilisa 7,19 cm

Shear force resistance (shear covering)

Prc.:Shear reinf (web) asw = 5,00 cm2/m x= 1,14 m

0 5 10 15 20 25 30x [m]

Ausn As (cm2/m)

5.0100%

Concrete strut capacity η = 1,33 x= 0,83 m



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Selected section x = 11.00 m from left support

Internal force combinations from external loadingLAc: dominant variable action (leading action)ULS-PT : permanent + transient design situation (fundam. combination)SLS-Cc : characteristic combinationSLS-Fc : frequent combinationSLS-Qc : quasi-permanent combination

maximum moment : [kNm]

ULS-PT SLS-Cc SLS-Fc SLS-Qc

Storage 1240.12 918.59 918.59 918.59Storage/Erection 649.14 468.51 468.51 468.51Utilization 3278.28 2528.41 2137.06 2047.19LAc 10 10 10 -

Minimum moment : [kNm]


Storage 918.56 918.59 918.59 918.59Storage/Erection 451.86 468.51 468.51 468.51Utilization 2047.16 2047.19 2047.19 2047.19LAc - - - -

maximum shear force:[kN]

ULS-PT

Storage 51.6Storage/Erection 52.4Utilization 129.3LAc 10

Effective Tendons ( prestressed formwork state for t = t0 (sto))

No. Area Distance Prestress tens.force ShorttimeLayer Ap f.bottom max min max min RelaxationNo. [cm2] [cm] [N/mm2] [N/mm2] [kN] [kN] [N/mm2]

1 3 2.8 8.5 999.16 999.16 278.8 278.8 -0.842 3 2.8 12.3 999.16 999.16 278.8 278.8 -0.843 3 2.8 16.1 999.16 999.16 278.8 278.8 -0.844 3 2.8 19.9 999.16 999.16 278.8 278.8 -0.845 3 2.8 23.7 999.16 999.16 278.8 278.8 -0.846 3 2.8 27.5 999.16 999.16 278.8 278.8 -0.847 3 2.8 31.3 999.16 999.16 278.8 278.8 -0.848 1 0.9 35.1 999.16 999.16 92.9 92.9 -0.84

Untensioned reinforcement

Layer Number Diameter Area LE[mm] [cm2] [cm]

1 2 16 4.0 3.52 2 20 6.3 135.23 2 20 6.3 146.7



[cm] [cm]

1 60.0 0.02 60.0 15.03 19.0 23.2 Web begin4 19.0 150.2 Web end



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Cross-section Values

brutto idealAc zu Ic Ai zi Ii

[cm2] [cm] [cm4] [cm2] [cm] [cm4]

Precast cross-section 3636.9 89.2 8019344 3797.3 88.0 8770273

Internal forces from prestress (mean values, prestressed formwork state)

Npm(0) Mpm(0) φFakCreep tB tE tB tE Prcperiod [kN] [kN] [kNm] [kNm]

Storage -2044.3 -1836.6 -1377.19 -1288.39 1.26Utilization -1836.6 -1445.6 -1288.39 -1254.32 1.00

tA=Begin, tE=End creep periodφFak: Increase factor creep modulus (non-linear creep:> 1.0)

Prestress steel relaxationStorage Utilization

Lay. Δσp,r1 Δσp,r2

No. [N/mm2] [N/mm2]

1 -1.06 -15.912 -1.07 -15.863 -1.07 -15.824 -1.08 -15.775 -1.09 -15.736 -1.09 -15.697 -1.10 -15.648 -1.11 -15.60

Prestr. steel, losses due to creeping, shrinking and relaxation:Storage Utilization

Lay. Δσp,csr1(0) Δσp,csr2(0)

No. [N/mm2] [N/mm2]

1 -67.71 -76.722 -66.83 -79.153 -65.96 -81.584 -65.09 -84.015 -64.22 -86.446 -63.35 -88.867 -62.48 -91.298 -61.61 -93.72

Stress in rebars due to creeping,shringing and relaxation:Storage Utilization

Lay. Δσs,csr1(0) Δσs,csr2(0)

No. [N/mm2] [N/mm2]

1 -69.76 -62.312 -38.61 -149.893 -35.89 -157.54

Bending with Normal Force ULS

L. Creep period Cross- Tens- z MEd MRd ηsection zone [cm] [kNm] [kNm] (>1.0)

1 tB Storage P top ---- Arm of lev. Hz < 0 -918.56 ---- #12 tE Storage P bottom 123.8 3834.60 1240.12 3.093 tB Storage/Erection P top ---- Arm of lev. Hz < 0 -451.86 ---- #14 tE Storage/Erection P bottom 123.8 3834.60 649.14 5.915 tE Utilization P top 124.9 775.54 MEd < 0 n/a6 tE Utilization P bottom 123.5 3851.97 3278.28 1.17

#1: fck(t)= 0.33 * fck



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Interim results : Ultimate elongation and internal forcesL. εc εs x Ap As Zp Zs Dc Dp Ds

[‰] [‰] [cm] [cm2] [cm2] [kN] [kN] [kN] [kN] [kN]

2 3.500 21.900 20.2 20.5 4.0 2963.9 180.5 2731.8 0.0 383.54 3.500 21.900 20.2 20.5 4.0 2963.9 180.5 2731.8 0.0 383.55 3.500 9.300 40.1 0.0 12.6 0.0 551.6 1748.1 -1353.6 164.06 3.500 22.700 19.6 20.5 4.0 2968.9 180.7 2661.7 0.0 478.0

Shear Resistance

Design value shear forceL. Creep period Combination VEd,0 MEd dV due to

[kN] [kNm] [kN]

1 tB Storage QMax 51.6 1240.10 -49.6 Vccd2 tE Storage QMax 51.6 1240.10 -49.6 Vccd3 tB Storage/Erection QMax 52.4 637.90 -25.5 Vccd4 tE Storage/Erection QMax 52.4 637.90 -25.5 Vccd5 tB Utilization MMax 129.3 3278.28 -131.4 Vccd6 tE Utilization MMax 129.3 3278.28 -131.4 Vccd

Effective cross-sectionL. Cross- Tens- bw d z Ac Asl σcp VRdc

section zone [cm] [cm] [cm] [cm2] [cm2] [N/mm2] [kN]

1 P bottom 19.0 146.7 123.8 3636.9 24.5 2.21 204.12 P bottom 19.0 146.7 123.8 3636.9 24.5 4.54 351.63 P bottom 19.0 146.7 123.8 3636.9 24.5 2.21 204.14 P bottom 19.0 146.7 123.8 3636.9 24.5 4.54 351.65 P bottom 19.0 146.7 123.5 3636.9 24.5 4.54 351.66 P bottom 19.0 146.7 123.5 3636.9 24.5 3.58 311.1

Shear design ν1= 0.480L. VEd VEd,red acw cot Θ asw Note al VRd,max

[kN] [kN] [cm2/m] [cm] [kN]

1 2.0 2.0 1.250 1.000 1.24 Min 73.3 909.3 #12 2.0 2.0 1.136 1.000 2.15 Min 73.3 2138.13 26.9 26.9 1.250 1.000 1.24 Min 73.3 909.3 #14 26.9 26.9 1.136 1.000 2.15 Min 73.3 2138.15 2.1 2.1 1.136 1.000 2.15 Min 73.3 2132.96 2.1 2.1 1.107 1.000 2.15 Min 73.3 2078.4

#1: fck(t)= 0.33 * fck

Check of crack width limit in SLS

perm. crack width: wk < 0.20 mm, Frequent load combination

L. Creep period Cross- Tens- rsup max.σs sr,max εsm-εcm wk

section zone rinf [N/mm2] [mm] [‰] [mm]

1 tB Storage P top 1.00 CS completely compressed2 tE Storage P bottom 1.00 CS completely compressed3 tB Storage/Erection P top 1.00 no cracks4 tE Storage/Erection P bottom 1.00 CS completely compressed5 tE Utilization P top 1.00 CS completely compressed6 tE Utilization P bottom 1.00 119.42 191.65 0.358 0.07

Internal forces and elongationState I State II

L. Nges Mges max. σ X0I φeff εc X0II[kN] [kNm] [N/mm2] [cm] [‰] [cm]

1 -2044.3 -458.60 -2.13 190.92 -1836.6 -369.81 -8.55 202.73 -2044.3 -908.68 1.07 139.94 -1836.6 -819.88 -13.06 139.75 -1445.6 792.87 -9.43 104.36 -1445.6 882.74 5.05 100.1 2.32 -0.866 86.8

X0I: Pressure zone height in state I X0II: Pressure zone height in state II



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L. hc,ef Aceff ξ1 Ap As ρp,ef ρtot k1 k2 k3 c k4[cm] [cm2] [cm2] [cm2] [%] [%] [cm]

6 21.1 401.2 1.15 11.2 4.0 4.712 3.784 1.38 0.50 3.40 2.7 0.425

Internal forces cracking and strains (state II)State I State II


6 -1445.6 785.56 4.07 104.7


Minimum reinforcement for crack control:

L. Creep period Cross- Tens- rsup σt req. As exist. Assection zone rinf [N/mm2] [cm2] [cm2]

1 tB Storage P top 1.00 -1.58 < 4.07 not req.2 tE Storage P bottom 1.00 -8.55 < 4.07 not req.3 tB Storage/Erection P top 1.00 1.61 < 4.07 not req.4 tE Storage/Erection P bottom 1.00 -13.06 < 4.07 not req.5 tE Utilization P top 1.00 -9.19 < 4.07 not req.6 tE Utilization P bottom 1.00 8.97 <= 0 cm2

Web FlangeL. D x0IZ Ap ξ1 k kc Act As k kc Act As

[mm] [cm] [cm2] [cm2] [cm2] [cm2] [cm2]

6 16 45.5 5.6 1.15 0.65 0.28 863.7 4.3 --no flange--

x0IZ: tensile zone in state I due to cracking forces

Ductility reinforcement in precompressed tensile zone:

b fctm Zs req. As exist. As[cm3] [N/mm2] [cm] [cm2] [cm2]

19 4.07 146.7 5.9 4.0

Stress checks SLS

Concrete edge stresses in state I due to prestress, creep, shrinkage and relaxationσR Precast

L. due to top bottom[N/mm2] [N/mm2]

1 Prestr. release anchorage 4.39 -19.202 csr storage -0.08 1.443 csr utilisation 0.79 1.37

Tab. Compr stresses of concreteMEd σc Precast

L. Creep period Cross- + = Max Cc,Pk Qc,Pksection - = Min [N/mm2] [N/mm2]

1 tB Storage P -- -9.98 -9.98 #12 tE Storage P -- -8.55 -8.553 tB Storage/Erection P -- -14.50*4 tE Storage/Erection P -- -13.065 tB Utilization P +- -14.83 -10.226 tE Utilization P +- -13.31 -8.95

#1: due to σc > 0.45* fck(t) increased ceep modulus



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Tab. Steel- and Concrete tension stressMEd σp σs σt

L. Creep period Cross- + = Max Cc,Pm Cc,Pk Cc,Pksection - = Min [N/mm2] [N/mm2] [N/mm2]

1 tB Storage P -+- 956.23 < 0 ZII2 tE Storage P -+- 900.32 < 0 ZII3 tB Storage/Erection P --- 941.93 3.80 1.074 tE Storage/Erection P -+- 886.02 < 0 0.985 tB Utilization P ++- 1083.72 97.37 2.776 tE Utilization P ++- 1081.53 115.84 ZII

Pk= Prestres char. value, Pm= prestress mean value, StII: State II



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Storage 162.93 120.67 120.67 120.67Storage/Erection -4.35 -4.35 -4.35 -4.35Utilization 446.42 344.04 289.74 277.27LAc 10 10 10 -



Storage 120.65 120.67 120.67 120.67Storage/Erection -5.87 -4.35 -4.35 -4.35Utilization 277.25 277.27 277.27 277.27LAc - - - -


ULS-PT

Storage 158.5Storage/Erection -10.3Utilization 432.1LAc 10



1 3 2.8 8.5 999.16 913.66 278.8 254.9 -0.842 3 2.8 12.3 999.16 913.66 278.8 254.9 -0.843 3 2.8 16.1 999.16 913.66 278.8 254.9 -0.844 3 2.8 19.9 999.16 913.66 278.8 254.9 -0.845 3 2.8 23.7 999.16 913.66 278.8 254.9 -0.846 3 2.8 27.5 999.16 913.66 278.8 254.9 -0.847 3 2.8 31.3 999.16 913.66 278.8 254.9 -0.848 1 0.9 35.1 999.16 913.66 92.9 85.0 -0.84



1 2 16 4.0 3.52 2 20 6.3 85.73 2 20 6.3 97.2



[cm] [cm]

1 60.0 0.02 60.0 15.03 19.0 23.2 Web begin4 19.0 100.7 Web end



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[cm2] [cm] [cm4] [cm2] [cm] [cm4]








No. [N/mm2] [N/mm2]

1 -0.78 -8.352 -0.81 -8.663 -0.83 -8.964 -0.85 -9.285 -0.88 -9.616 -0.90 -9.957 -0.93 -10.308 -0.95 -10.65



No. [N/mm2] [N/mm2]

1 -174.80 -168.662 -167.86 -165.793 -160.91 -162.934 -153.97 -160.085 -147.02 -157.236 -140.08 -154.407 -133.13 -151.578 -126.19 -148.75



No. [N/mm2] [N/mm2]

1 -188.04 -170.322 -33.56 -101.393 -11.94 -91.75



1 tB Storage P top ---- Arm of lev. Hz < 0 -120.65 ---- #12 tE Storage P bottom 74.4 2208.47 162.93 13.553 tB Storage/Erection P top ---- Arm of lev. Hz < 0 5.87 ---- #14 tE Storage/Erection P bottom 74.4 2208.47 MEd < 0 n/a5 tB Utilization P top 75.6 504.87 MEd < 0 n/a6 tE Utilization P bottom 74.2 2195.10 446.42 4.92

#1: fck(t)= 0.33 * fck



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2 3.500 13.900 19.6 20.5 4.0 2823.6 178.0 2656.3 0.0 369.74 3.500 13.900 19.6 20.5 4.0 2823.6 178.0 2656.3 0.0 369.75 3.500 5.100 39.6 0.0 12.6 0.0 548.5 1723.8 -1353.3 164.06 3.500 14.700 18.7 20.5 4.0 2822.4 178.0 2553.9 0.0 425.9

Shear Resistance


[kN] [kNm] [kN]

1 tB Storage QMax 158.5 162.91 -10.8 Vccd2 tE Storage QMax 158.5 162.91 -10.8 Vccd3 tB Storage/Erection QMax -10.3 -5.87 0.0 -------4 tE Storage/Erection QMax -10.3 -5.87 0.0 -------5 tB Utilization QMax 432.1 446.40 -29.8 Vccd6 tE Utilization QMax 432.1 446.40 -29.8 Vccd



1 P bottom 19.0 97.2 74.4 2696.3 24.5 2.21 151.42 P bottom 19.0 97.2 74.4 2696.3 24.5 4.97 268.03 P top 19.0 91.4 82.3 2696.3 12.6 2.21 127.64 P top 19.0 91.4 82.3 2696.3 12.6 4.97 230.75 P bottom 19.0 97.2 74.2 2696.3 24.5 5.43 280.96 P bottom 19.0 97.2 74.2 2696.3 24.5 3.39 224.3



1 147.7 147.7 0.955 3.692 1.24 Min 137.3 210.5 #12 147.7 147.7 1.149 2.125 2.15 Min 79.0 1000.63 10.3 10.3 0.955 1.000 1.24 Min 45.7 461.8 #14 10.3 10.3 1.149 1.000 2.15 Min 45.7 1437.45 402.4 402.4 1.163 2.500 4.99 Var 92.8 904.66 402.4 402.4 1.102 2.500 4.99 Var 92.8 857.0

#1: fck(t)= 0.33 * fck





1 tB Storage P top 1.00 no cracks2 tE Storage P bottom 1.00 CS completely compressed3 tB Storage/Erection P top 1.00 59.04 420.27 0.177 0.074 tE Storage/Erection P bottom 1.00 CS completely compressed5 tB Utilization P top 1.00 CS completely compressed6 tE Utilization P bottom 1.00 CS completely compressed



1 -2044.3 -707.16 2.67 89.92 -1488.4 -485.80 -15.62 91.63 -2044.3 -832.18 4.41 85.6 0.00 -0.749 69.74 -1488.4 -610.82 -18.30 85.45 -1627.7 -385.96 -0.33 103.26 -1016.2 -192.22 -7.68 113.8




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3 10.3 619.6 1.29 0.0 6.3 1.014 1.014 0.80 0.50 3.40 2.5 0.425



1 -2044.3 -807.84 4.07 86.33 -2044.3 -807.84 4.07 86.3




1 tB Storage P top 1.00 4.62 <= 0 cm22 tE Storage P bottom 1.00 -15.62 < 4.07 not req.3 tB Storage/Erection P top 1.00 6.36 <= 0 cm24 tE Storage/Erection P bottom 1.00 -18.30 < 4.07 not req.5 tB Utilization P top 1.00 1.81 < 4.07 not req.6 tE Utilization P bottom 1.00 -6.51 < 4.07 not req.


[mm] [cm] [cm2] [cm2] [cm2] [cm2] [cm2]

1 20 14.4 0.0 0.00 0.65 0.00 272.9 -nan(ind) 0.97 0.52 484.8 4.53 20 14.4 0.0 0.00 0.65 0.00 272.9 -nan(ind) 0.97 0.52 484.8 4.5




19 4.07 97.2 3.9 4.0

Stress checks SLS



1 Prestr. release anchorage 4.35 -24.902 csr storage -0.83 4.993 csr utilisation -0.08 4.73



1 tB Storage P -- -22.31* -22.31 #12 tE Storage P -- -17.33 -17.333 tB Storage/Erection P -- -27.71*4 tE Storage/Erection P -- -15.705 tB Utilization P -- -13.97 -13.976 tE Utilization P -- -9.24 -9.24




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1 tB Storage P --- 927.47 9.75 2.67*2 tE Storage P -+- 731.36 < 0 1.843 tB Storage/Erection P --- 940.41 59.04 ZII4 tE Storage/Erection P --- 690.99 52.54 ZII5 tB Utilization P ++- 827.61 < 0 ZII6 tE Utilization P ++- 609.42 < 0 ZII




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ULS-PT

Storage 133.8Storage/Erection 134.5Utilization 356.2LAc 10



1 3 2.8 8.5 999.16 999.16 278.8 278.8 -0.842 3 2.8 12.3 999.16 999.16 278.8 278.8 -0.843 3 2.8 16.1 999.16 999.16 278.8 278.8 -0.844 3 2.8 19.9 999.16 999.16 278.8 278.8 -0.845 3 2.8 23.7 999.16 999.16 278.8 278.8 -0.846 3 2.8 27.5 999.16 999.16 278.8 278.8 -0.847 3 2.8 31.3 999.16 999.16 278.8 278.8 -0.848 1 0.9 35.1 999.16 999.16 92.9 92.9 -0.84



1 2 16 4.0 3.52 2 20 6.3 98.63 2 20 6.3 110.1



[cm] [cm]

1 60.0 0.02 60.0 15.03 19.0 23.2 Web begin4 19.0 113.6 Web end



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[cm2] [cm] [cm4] [cm2] [cm] [cm4]








No. [N/mm2] [N/mm2]

1 -0.89 -11.152 -0.91 -11.293 -0.92 -11.444 -0.94 -11.585 -0.95 -11.736 -0.97 -11.887 -0.99 -12.038 -1.00 -12.18



No. [N/mm2] [N/mm2]

1 -140.31 -112.892 -136.24 -113.913 -132.17 -114.944 -128.11 -115.965 -124.04 -116.986 -119.97 -118.017 -115.91 -119.048 -111.84 -120.06



No. [N/mm2] [N/mm2]

1 -148.68 -105.412 -44.01 -128.693 -31.35 -131.51



1 tB Storage P top ---- Arm of lev. Hz < 0 -402.45 ---- #12 tE Storage P bottom 87.4 2614.28 543.37 4.813 tB Storage/Erection P top ---- Arm of lev. Hz < 0 64.27 ---- #14 tE Storage/Erection P bottom 87.4 2614.28 MEd < 0 n/a5 tE Utilization P top 89.6 594.41 MEd < 0 n/a6 tE Utilization P bottom 87.2 2611.08 1471.73 1.77

#1: fck(t)= 0.33 * fck



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2 3.500 16.300 19.5 20.5 4.0 2869.3 178.8 2645.3 0.0 375.54 3.500 16.300 19.5 20.5 4.0 2869.3 178.8 2645.3 0.0 375.55 3.500 7.100 36.3 0.0 12.6 0.0 549.7 1583.8 -1196.6 164.16 3.500 17.100 18.7 20.5 4.0 2871.5 178.9 2555.0 0.0 452.3

Shear Resistance


[kN] [kNm] [kN]

1 tB Storage QMax 133.8 543.35 -30.8 Vccd2 tE Storage QMax 133.8 543.35 -30.8 Vccd3 tB Storage/Erection QMax 134.5 -64.27 0.0 -------4 tE Storage/Erection QMax 134.5 -64.27 0.0 -------5 tB Utilization QMax 356.2 1471.72 -83.6 Vccd6 tE Utilization QMax 356.2 1471.72 -83.6 Vccd






1 103.0 103.0 1.083 2.191 1.24 Min 95.8 420.5 #12 103.0 103.0 1.154 1.261 2.15 Min 55.1 1493.13 134.5 134.5 1.083 2.664 1.24 Min 125.0 393.3 #14 134.5 134.5 1.154 1.533 2.15 Min 72.0 1507.15 272.6 272.6 1.154 3.347 2.15 Min 145.9 838.66 272.6 272.6 1.113 2.500 2.88 Var 108.9 1017.1

#1: fck(t)= 0.33 * fck





1 tB Storage P top 1.00 CS completely compressed2 tE Storage P bottom 1.00 CS completely compressed3 tB Storage/Erection P top 1.00 90.77 565.24 0.272 0.154 tE Storage/Erection P bottom 1.00 CS completely compressed5 tE Utilization P top 1.00 CS completely compressed6 tE Utilization P bottom 1.00 CS completely compressed



1 -2044.3 -570.72 -0.13 114.52 -1676.6 -423.20 -12.61 119.43 -2044.3 -1020.80 4.96 94.1 0.00 -0.768 69.24 -1676.6 -873.28 -20.27 93.05 -1233.0 171.06 -5.91 138.56 -1233.0 211.93 -0.37 120.6




Projekt: R2017-2

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Tel.: 03518761411



3 14.8 887.5 1.29 0.0 6.3 0.708 0.708 0.80 0.50 3.40 2.5 0.425



3 -1676.6 -837.17 4.07 94.1




1 tB Storage P top 1.00 1.06 < 4.07 not req.2 tE Storage P bottom 1.00 -12.61 < 4.07 not req.3 tB Storage/Erection P top 1.00 4.48 <= 0 cm24 tE Storage/Erection P bottom 1.00 -20.27 < 4.07 not req.5 tE Utilization P top 1.00 -5.00 < 4.07 not req.6 tE Utilization P bottom 1.00 2.66 < 4.07 not req.


[mm] [cm] [cm2] [cm2] [cm2] [cm2] [cm2]

3 20 19.5 0.0 0.00 0.65 0.00 370.3 -nan(ind) 0.97 0.64 657.9 9.2




19 4.07 110.1 4.4 4.0

Stress checks SLS






1 tB Storage P -- -16.30* -16.30 #12 tE Storage P -- -12.61 -12.613 tB Storage/Erection P -- -28.43*4 tE Storage/Erection P -- -18.625 tB Utilization P +- -8.90 -6.436 tE Utilization P +- -8.39 -5.91




Projekt: R2017-2

09.11.2017 Seite: 2701067

Tel.: 03518761411




1 tB Storage P -+- 939.58 < 0 ZII2 tE Storage P -+- 840.41 < 0 ZII3 tB Storage/Erection P --- 939.36 90.77 ZII4 tE Storage/Erection P --- 775.87 94.17 ZII5 tB Utilization P ++- 872.28 < 0 ZII6 tE Utilization P +++ 763.28 < 0 2.66




Projekt: R2017-2

09.11.2017 Seite: 2801067

Tel.: 03518761411











ULS-PT

Storage 166.7Storage/Erection -2.0Utilization 458.5LAc 10



1 3 2.8 8.5 274.35 182.90 76.5 51.0 -0.002 3 2.8 12.3 274.35 182.90 76.5 51.0 -0.003 3 2.8 16.1 274.35 182.90 76.5 51.0 -0.004 3 2.8 19.9 274.35 182.90 76.5 51.0 -0.005 3 2.8 23.7 274.35 182.90 76.5 51.0 -0.006 3 2.8 27.5 274.35 182.90 76.5 51.0 -0.007 3 2.8 31.3 274.35 182.90 76.5 51.0 -0.008 1 0.9 35.1 274.35 182.90 25.5 17.0 -0.00



1 2 16 4.0 3.52 2 20 6.3 81.13 2 20 6.3 92.6



[cm] [cm]

1 60.0 0.02 60.0 15.03 19.0 23.2 Web begin4 19.0 96.1 Web end



Projekt: R2017-2

09.11.2017 Seite: 2901067

Tel.: 03518761411




[cm2] [cm] [cm4] [cm2] [cm] [cm4]



Npm(0) Mpm(0)

Creep tB tE tB tEperiod [kN] [kN] [kNm] [kNm]

Storage -561.3 -291.0 -213.02 -121.04Utilization -436.6 -49.0 -181.56 -69.53

tA=Begin, tE=End creep period



No. [N/mm2] [N/mm2]

1 -0.01 -0.612 -0.01 -0.623 -0.01 -0.634 -0.01 -0.635 -0.01 -0.646 -0.01 -0.657 -0.01 -0.668 -0.01 -0.67



No. [N/mm2] [N/mm2]

1 -41.09 -108.722 -40.20 -107.393 -39.30 -106.064 -38.40 -104.735 -37.50 -103.396 -36.61 -102.067 -35.71 -100.738 -34.81 -99.40



No. [N/mm2] [N/mm2]

1 -43.35 -112.822 -24.54 -84.743 -21.75 -80.58



1 tB Storage P top 73.1 446.23 MEd < 0 n/a #12 tE Storage P bottom 69.0 2035.23 13.29 153.083 tB Storage/Erection P top 73.1 446.23 0.23 1916.60 #14 tE Storage/Erection P bottom 69.0 2035.23 MEd < 0 n/a5 tB Utilization P top 61.4 541.22 MEd < 0 n/a6 tE Utilization P bottom 69.1 2020.00 36.70 55.04

#1: fck(t)= 0.33 * fck



Projekt: R2017-2

09.11.2017 Seite: 3001067

Tel.: 03518761411




1 3.500 5.900 34.5 0.9 12.6 24.1 549.2 497.9 -88.5 171.32 3.500 13.500 19.1 20.5 4.0 2771.3 178.1 2600.0 0.0 355.83 3.500 5.900 34.5 0.9 12.6 24.1 549.2 497.9 -88.5 171.34 3.500 13.500 19.1 20.5 4.0 2771.3 178.1 2600.0 0.0 355.85 3.500 12.300 20.5 9.3 12.6 438.5 554.6 894.3 -76.9 163.76 3.500 14.300 18.2 20.5 4.0 2774.0 178.2 2495.0 0.0 399.8

Shear Resistance


[kN] [kNm] [kN]

1 tB Storage QMax 166.7 13.27 -1.0 Vccd2 tE Storage QMax 166.7 13.27 -1.0 Vccd3 tB Storage/Erection QMax -2.0 -0.23 0.0 -------4 tE Storage/Erection QMax -2.0 -0.23 0.0 -------5 tB Utilization QMax 458.5 36.68 -2.6 Vccd6 tE Utilization QMax 458.5 36.68 -2.6 Vccd




Shear design ν1= 0.480Check VRd,s not requ.,asw und CotΘ from the last contruction phaseL. VEd VEd,red acw cot Θ asw Note al VRd,max


1 165.8 165.8 1.175 3.700 1.24 Var 86.3 240.2 #12 165.8 165.8 1.030 2.129 2.15 Var 86.3 832.03 2.0 2.0 1.175 1.000 1.24 Min 43.4 504.9 #14 2.0 2.0 1.030 1.000 2.15 Min 43.4 1144.75 455.9 455.9 1.045 2.500 5.00 Var 86.4 757.66 455.9 455.9 1.005 2.500 5.00 Var 86.4 728.5

#1: fck(t)= 0.33 * fck





1 tB Storage P top 1.00 no cracks2 tE Storage P bottom 1.00 CS completely compressed3 tB Storage/Erection P top 1.00 no cracks4 tE Storage/Erection P bottom 1.00 CS completely compressed5 tB Utilization P top 1.00 no cracks6 tE Utilization P bottom 1.00 CS completely compressed



Projekt: R2017-2

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Tel.: 03518761411




1 -561.3 -203.19 1.03 83.42 -291.0 -111.21 -3.66 82.13 -561.3 -213.19 1.18 82.34 -291.0 -121.21 -3.89 80.25 -436.6 -158.81 0.81 83.36 -49.0 -45.74 -1.25 68.2








1 tB Storage P top 1.00 2.01 < 4.07 not req.2 tE Storage P bottom 1.00 -3.66 < 4.07 not req.3 tB Storage/Erection P top 1.00 2.16 < 4.07 not req.4 tE Storage/Erection P bottom 1.00 -3.89 < 4.07 not req.5 tB Utilization P top 1.00 2.21 < 4.07 not req.6 tE Utilization P bottom 1.00 -1.14 < 4.07 not req.


[mm] [cm] [cm2] [cm2] [cm2] [cm2] [cm2]




19 4.07 92.6 3.7 4.0

Stress checks SLS






1 tB Storage P -- -6.79 -6.792 tE Storage P -- -5.60 -5.603 tB Storage/Erection P -- -7.024 tE Storage/Erection P -- -5.845 tB Utilization P -- -5.30 -5.306 tE Utilization P -- -2.18 -2.18



Projekt: R2017-2

09.11.2017 Seite: 3201067

Tel.: 03518761411




1 tB Storage P --- 253.62 4.04 1.032 tE Storage P -+- 131.29 < 0 1.013 tB Storage/Erection P --- 253.12 4.78 1.184 tE Storage/Erection P -+- 130.79 < 0 1.165 tB Utilization P ++- 223.65 < 0 0.816 tE Utilization P ++- 43.53 < 0 0.96


Lateral buckling (Stiglat)

Safety in installed state η = 1.69 < 2.00Design buckling moment: Mkipp = 4657.51 kNmexisting moment : MEd = 2763.72 kNm without prestressCombination of characteristic values

Interim values acc. to 'Beton- und Stahlbetonbau' 1985, H. 9,10,11 Ecm = 37000 N/mm2 Gcm = 14800 N/mm2 It, Iy averaged It = 208188 cm4 Iy = 394505 cm4 acc.to Rafla Ix = 11379011 cm4 Ak = 4664.5 MN2cm4 (It 60% as C.II) hc = 1.58 m β1 = 0.000 β2 = 0.003 k1 = 3.540 k2 = 1.000 k3 = 0.920 Mk = 7415.48 kNm Wxo = 123859 cm3 x = 10.10 m σB = 52.87 N/mm2 σT = 33.21 N/mm2 λV = 83.1 (σT acc. eq.62calculated !)

a potentially nessecary reinforcement for torsion is not determined in the program

Erection with spreader

Lateral buckling safety η = 4.29 > 2.50Design buckling moment: Mkipp = 2343.70 kNmexisting moment : MEd = 546.27 kNm without prestress

Interim values acc. to 'Beton- und Stahlbetonbau' 1985, H. 9,10,11 β4 = 0.000 δ = 0.000 γ = 1.000 f = 0.331 m Ak = 4664.5 MN2cm4 p = 0.752 j(α) = 0.095 α = 1.478 qkl = 47.76 kN/m Wxo = 148769 cm3 Mk = 2700.05 kNm x = 16.83 m σB = 18.15 N/mm2 σT = 15.75 N/mm2 λV = 141.8

Anchorage by bond ( over the left bearing)

lpt2 = 1.26 m Distance first bending crack lr = 3.37 m fctd(t) = 0.81 N/mm2 t= release anchorage fbpt = 2.58 N/mm2 ηP2 = 1.20 fbpd = 2.28 N/mm2

x Zp Zs TEd η= Util[m] [kN] [kN] [kN] (Zp+Zs)/TEd

0.15 378.4 178.1 664.0 0.84 1.190.31 776.3 178.0 752.1 1.27 0.790.61 1527.5 177.9 910.0 1.87 0.530.92 2303.8 178.0 1058.5 2.34 0.431.22 2826.6 178.0 1185.0 2.54 0.391.53 2830.2 178.0 1315.7 2.29 0.441.84 2842.1 178.3 1446.4 2.09 0.48

Zp: resisting tensile force by the prestressed steelZs: resisting tensile force by the rebarsTEd: tensile force to be anchored

No. Dist.LE XA σp Eq. lbpd xk ΣZp ΣZs TEd add. AsLay. [cm] [m] [N/mm2] [m] [cm2] [kN] [kN] [kN] [cm2]

1 8.5 0.00 583.29 8.21 2.24 Anchorage range uncracked (PT)2 12.3 0.00 596.66 8.21 2.23 Anchorage range uncracked (PT)3 16.1 0.00 610.01 8.21 2.21 Anchorage range uncracked (PT)4 19.9 0.00 623.36 8.21 2.20 Anchorage range uncracked (PT)5 23.7 0.00 636.71 8.21 2.19 Anchorage range uncracked (PT)



Projekt: R2017-2

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Tel.: 03518761411



6 27.5 0.00 650.04 8.21 2.17 Anchorage range uncracked (PT)7 31.3 0.00 663.37 8.21 2.43 Anchorage range uncracked (PT)8 35.1 0.00 676.68 8.21 2.42 Anchorage range uncracked (PT)

XA: Beginning of the anchoring area of the steel layer (dist. from the corresp. binder side)Eq. 8.21.1: Anchorage area uncracked, σp acc.to fig. 8.17DE (b)Eq. 8.21.1: Anchorage area cracked, σp acc.to fig. 8.17DE (b)xk: decisive section in the anchoring area of the layer (distance from the beginning of the binder)add. As: Additional sagging reinforcement required for anchorage

Anchorage by bond ( over the right bearing)

lpt2 = 1.26 m Distance first bending crack lr = 3.37 m fctd(t) = 0.81 N/mm2 t= release anchorage fbpt = 2.58 N/mm2 ηP2 = 1.20 fbpd = 2.28 N/mm2

x Zp Zs TEd η= Util[m] [kN] [kN] [kN] (Zp+Zs)/TEd

28.46 2842.1 178.3 1446.4 2.09 0.4828.77 2830.2 178.0 1315.7 2.29 0.4429.08 2826.6 178.0 1185.0 2.54 0.3929.38 2303.8 178.0 1058.5 2.34 0.4329.69 1527.5 177.9 910.0 1.87 0.5329.99 776.3 178.0 752.1 1.27 0.7930.15 378.4 178.1 664.0 0.84 1.19

Zp: resisting tensile force by the prestressed steelZs: resisting tensile force by the rebarsTEd: tensile force to be anchored


1 8.5 0.00 583.29 8.21 2.24 Anchorage range uncracked (PT)2 12.3 0.00 596.66 8.21 2.23 Anchorage range uncracked (PT)3 16.1 0.00 610.01 8.21 2.21 Anchorage range uncracked (PT)4 19.9 0.00 623.36 8.21 2.20 Anchorage range uncracked (PT)5 23.7 0.00 636.71 8.21 2.19 Anchorage range uncracked (PT)6 27.5 0.00 650.04 8.21 2.17 Anchorage range uncracked (PT)7 31.3 0.00 663.37 8.21 2.43 Anchorage range uncracked (PT)8 35.1 0.00 676.68 8.21 2.42 Anchorage range uncracked (PT)

XA: Beginning of the anchoring area of the steel layer (dist. from the corresp. binder side)Eq. 8.21.1: Anchorage area uncracked, σp acc.to fig. 8.17DE (b)Eq. 8.21.1: Anchorage area cracked, σp acc.to fig. 8.17DE (b)xk: decisive section in the anchoring area of the layer (distance from the beginning of the binder)add. As: Additional sagging reinforcement required for anchorage

Bursting Reinforcement at beginning of beam

γp,unfav = 1.20 ldisp = 1.39 m

Initiation zone Section over the last effective position of tension. member No. from to Dist.LE Nc Np Tp Factor req. As

[m] [m] [cm] [kN] [kN] [kN] Interpolation [cm2]

1 0.00 1.39 36.1 -1342.9 1841.0 498.2 0.406 5.6

The bursting reinforcement must be arranged in zone of reduced dispersion length.red. dispersion length indented wire w.o. strand 3/4*l disp=1.04 m

Burstring Reinforcement at end of beam

γp,unfav = 1.20 ldisp = 1.39 m

Initiation zone Section over the last effective position of tension. member No. from to Dist.LE Nc Np Tp Factor req. As

[m] [m] [cm] [kN] [kN] [kN] Interpolation [cm2]

1 30.30 28.91 36.1 -1342.9 1841.0 498.2 0.406 5.6



Projekt: R2017-2

09.11.2017 Seite: 3401067

Tel.: 03518761411


The bursting reinforcement must be arranged in zone of reduced dispersion length.red. dispersion length indented wire w.o. strand 3/4*l disp=1.04 m

nemetschek frilo gmbh projekt: r2017-2 schweriner str. · pdf file1515 1515 8 15 2985 15 8...

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