Bridge Design v1 En

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BRIDGE GENERAL DATA

LONGITUDINAL DIRECTION

Span Length Ltab = 19510 mm Support Back length a = 400 mm Between Pannel - Beam bi = 50 mm

GIRDER DIMENSIONS

PRECAST GIRDER BEAM

19410 18710 400 400 Ldeck =19510 a = a = Lcalc = Lbeam = Bi = 50

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Cover pp = 25 mm y6 = 100 mm y5 = 125 mm y4 = 0 mm y3 = 300 mm y2 = 75 mm y1 = 150 mm x1 = 750 mm x2 = 750 mm x3 = 200 mm x4 = 0 mm MATERIAL DATA Relative humidity RH = 60.0 % Unit weight of concrete Gc = 24.0 kN/m3

15.11 0. 00 0. 00 -5.56 -1 4. 42 -14.42 15 .1 1

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Esteel = 200000.0 Mpa

DECK REINFORCEMENT DESIGN

h = 200 mm b = 1100 mm

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Cover = 25 mm

Bar radius = 12 mm

Bar spacing = 200 mm

ELASTOMERIC BEARING DESIGN

┏━━━━━━ ━━━━━━ ━━━━┓ 63 6┃━━━━━━ s. plate ━━━━┃ 5┃━━━━━━ s. plate ━━━━┃ 4┃━━━━━━ s. plate ━━━━┃ 3┃━━━━━━ s. plate ━━━━┃ 2┃━━━━━━ s. plate ━━━━┃ 1┃━━━━━━ s. plate ━━━━┃ ┗━━━━━ ━━━━━━━━━ ━━━━┛ 0 300

Number of steel reinforcement layers Nst = 6 #

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Elastomer internal layer thickness hri = 8 mm

Steel reinforcement thickness hs = 3 mm

GIRDER DESIGN TOP 0 mm 1 #N/A #N/A #N/A #N/A 2 7 120 ● ● ● ● ● ● ● 1 10 60 ● ● ● ● ● ● ● ● ● ● BOTTOM 17 mm

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PROJECT NAME………: YAVUZ SELiM BULVARI ALTGECiT iNSAATI

LOCATION…..……....: BEYLiKDUZU-ISTANBUL

REGULATION……...: AASHTO LRFD 2007 TURAN BABACAN

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DECK SLAB

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TOP & BOTTOM :

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GIRDER CONTROLS

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0.90 0.77 1.22 0.14

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PROJECT NAME………: YAVUZ SELiM BULVARI ALTGECiT iNSAATI LOCATION…..……....: BEYLiKDUZU-ISTANBUL REGULATION……...: AASHTO LRFD 2007 UNITS DATA……...: US SI 1.00 1 in. 25,4 mm 25.4 1.00 1 in.2 645,2 mm2 645.2 1.00 1 ft. 0,305 m 0.305 1.00 1 ft.2 0,093 m2 0.093 1.00 1 psi 0,006895 MPa 0.007 1.00 1 ksi 6,895 MPa 6.9 1.00 1 kip 4,448 kN 4.4 1.00 1 k-ft 1,356 kN-m 1.356 1.00 1 lb 0,004448 kN 0.004 1.00 1 kip 1000 lb 1000.0 1.00 1 Kn 1000 N 1000.0 1.00 1 lb/ft 0,01459 kN/m 0.015 SI US 1.00 1 mm 0,0394 in. 0.039 1.00 1 mm2 0,002 in.2 0.002 1.00 1 m 3,279 ft. 3.3 1.00 1 m2 10,753 ft.2 10.8 1.00 1 MPa 145,035 psi 145.0 1.00 1 MPa 0,145 ksi 0.145 1.00 1 kN 0,225 kip 0.225 1.00 1 kN-m 0,737 k-ft 0.737 1.00 1 kN 224,82 lb 224.8 1.00 1 lb 0,001 kip 0.001 1.00 1 N 0,001 kN 0.001 1.00 1 kN/m 68,54 lb/ft 68.5 PRECAST SECTION

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Beam heigth hb = 750 mm Beam Area Abeam = 342500 mm2 Moment of inertia I = 23173044657.3 mm4 Distance from centroid top fiber Yt = 383.698296837 mm Distance from centroid bottom fiber Yb = 366.301703163 mm Section modulus top fiber St = 60393921.0791 mm3 Section modulus bottom fiber Sb = 63262181.0307 mm3

Description Area yb A.yb Istrong

(in2) (in) (in3) (in4) (in4) (in4)

Beam 530.88 14.42 7655.94 29449.31 55673.46 85122.77

Pavement and barrier weight Wbarr = 4.76 kN/m Unit weight of asphalt wearing surface Gw = 22.0 kN/m3

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Concrete Strength at 28-days f'c = 25.0 Mpa Reinforcement Steel Yield Strength fy = 420.0 Mpa

hc > 17,5 cm OK

Mu =1.25Mc + 1.5Ma + 1.75Mq'

Mu = 39.10 kN.m

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Mr = 43.324585 kN.m Mr > Mu ; OK

TOP & BOTTOM : 6 θ 12 / 20

BEARING CONTROLS

Check Nst (14.7.6.1) :

hc ≤ 0.70 hri OK Check Compressive Stress (14.7.5.3.2) :

σs ≤ 1,66 G.S OK

σs ≤ 11 OK

σL ≤ 0,66 G.S OK Shear deformation? -NO- (14.7.5.3.2-4) :

σs ≤ 2 G.S OK

σs ≤ 12 OK

σL ≤ G.S OK Check Compressive Deflection (14.7.5.3.3) :

δLi ≤ 0.07 hri OK Check Shear Deformation (14.7.5.3.4) :

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Lch ≤ σs OK Wch ≤ σs OK Check Stability (14.7.6.3.6) : ht ≤ minLW OK Check Reinforcement (14.7.6.3.7) : hsi ≤ hmax OK hsii ≤ hmax OK GIRDER CONTROLS 3,5 ≤ S ≤ 16 OK 0.78 ≤ 2,18 OK 4,5 ≤ ts ≤ 12 OK 0.21 ≤ -0,42 OK 20 ≤ L ≤ 240 OK 0.23 ≤ 0,93 OK Nb ≥ 4 OK > 135,1 OK 10.000 ≤ Kg ≤ 7.000.000 OK ≤ 7,87 OK ≤ 1,82 OK ≤ 7,87 OK 159.7862692 < 195 OK > 1488,1 OK 2.480148823 > 1,82 OK ≤ 0.42 OK > 1272 OK ft-top 0.623√f'ci > 1526 OK (ksi) -1.38 OK -0.693355261 OK dv ≥ 0.72h ≥ 26 OK -0.536785557 OK dv ≥ 0.9dc ≥ 30 OK 0.228172358 OK 292.86 279.80 Mu>Vudv OK 0.23681525 OK 325.13 276.87 Mu>Vudv OK fb-bot. 0.6f'ci 419.18 268.13 Mu>Vudv OK (ksi) 2.93 542.93 256.03 Mu>Vudv OK 2.932219167 OK exex1 0.10 -0.140 OK 2.782748217 OK Vu > 0.5 ø (Vc + Vp ) > 26 OK 2.052472921 OK stirrup s ≤ smax OK 2.044221891 OK stirrup 0,182> 0,064 OK 0.137270125 OK stirrup 0,053< 0,182 OK 0.783200943 OK stirrup ≤ 0.25 f'c bv dv OK 0.900458393 OK body 1,75 > 0,15 OK 1.218936488 OK body Avf ≥ 0.05 bv / fy OK 0.205121893 OK body Vn ≤ 0.2 f'c Acv OK Check Rotation or Combined Compression

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≤ 2,2 OK body Vn ≤ 0.8 Acv OK ≤ 1,95 OK long.reinf. 157.62 276.641 OK ≤ 2,93 OK stirr.end 1,402 > 1,323 OK ≤ 1,63 OK L/800 > Σ∆ 0.92 0.246 OK

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PROJECT NAME………: YAVUZ SELiM BULVARI ALTGECiT iNSAATI LOCATION…..……....: BEYLiKDUZU-ISTANBUL

REGULATION……...: AASHTO LRFD 2007 TRANSVERSE DIRECTION

Number of beam Nb =

The average height of the pavement Hk = The average width of the pavement Bk = Between Beam - Beam S = Wearing surface heigth tw = Deck heigth ts = Haunch heigth th = Haunch width thw = COMPOSITE SECTION 14100 1100 80 2000 300 15.53 15.53 7. 66 7. 66

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Akomp = 5.63E+05 mm2 hc = 9.50E+02 mm Ic = 5.52E+10 mm4 ybc = 5.55E+02 mm ytg = 1.95E+02 mm ytc = 3.95E+02 mm Sbc = 9.93E+07 mm3 Stg = 2.84E+08 mm3 Stc = 1.58E+08 mm3 Description Area yb (in2) (in) Beam 530.88 14.42 Haunch 0.00 29.53 Deck 341.00 33.46 Total 871.88 0.00 PRECAST GIRDER

Precast beam Concrete Strength at 28 days f'c = Concrete Strength at release(0.8f'c) f'ci =

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DEBONDING

ROW STRAND SHEATH

2 7 1

1 10 3

BOTTOM 17 4

With regards to strand debonding, the AASHTO-LRFD specifications provide the following general guidelines.

•Not more than 40% of the strands at any one horizontal row will be debonded. •Not more than 25% of the total strands can be debonded.

•The exterior strands of each horizontal row shall be fully bonded. •Symmetric debonding about member centerline is required.

•Not more than 40% of the debonded strands, or four strands, whichever is greater, have the debonding terminated at any section.

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YAVUZ SELiM BULVARI ALTGECiT iNSAATI BEYLiKDUZU-ISTANBUL AASHTO LRFD 2007 11 # 300 mm 2000 mm 1100 mm 80 mm 200 mm 0 mm 0 mm 0 250 1100 15.53 15.53 7. 66 7. 66

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871.88 in2 37.40 in 132527 in4 21.87 in 7.66 in 15.53 in 6059.95 in3 17305.25 in3 9653.32 in3 A.yb Istrong

(in3) (in4) (in4) (in4)

7655.94 29449.31 55673.46 85122.77 0.00 0.00 0.00 0.00 11411.44 45847.22 1557.26 47404.48 19067.38 0.00 0.00 132527.26 40.0 Mpa 32.0 Mpa A(ycb-yb)2 _Istr+ADy2

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LENGTH CHECK

1478 OK

2956 OK

mm OK

With regards to strand debonding, the AASHTO-LRFD specifications provide the following general guidelines.

•Not more than 40% of the strands at any one horizontal row will be debonded. •Not more than 25% of the total strands can be debonded.

•The exterior strands of each horizontal row shall be fully bonded. •Symmetric debonding about member centerline is required.

•Not more than 40% of the debonded strands, or four strands, whichever is greater, have •Shear investigation shall be made in the regard to the reduced horizontal force.

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PROJECT NAME………: YAVUZ SELiM BULVARI ALTGECiT iNSAATI LOCATION…..……....: BEYLiKDUZU-ISTANBUL REGULATION……...: AASHTO LRFD 2007 IMPACT FACTOR IMPACT ( IM) = 0.27 TRUCK LOAD PARAMETRE HS20 H30-S24 H20 H30 UNIT P1 35.6 30.0 35.6 30.0 kN P2 142.3 120.0 142.3 120.0 kN P3 142.3 120.0 0.0 0.0 kN X1 4250.0 4250.0 4250.0 4250.0 mm X2 4250.0 4250.0 0.0 0.0 mm TRUCK[H30-S24] P+%50 X-%50 P1 = 30.00 kN P2 = 120.00 kN P3 = 120.00 kN X1 = 4250 mm X2 = 4250 mm TANDEM LOAD Pta = 110.00 kN Xta = 4250 mm LANES LOAD Qlanes = 10.00 kN/m

Note : [*] Kiriş ringde çalışıyor.dingil araları %50 azaltıldı. Dingil yükleri %50 arttırıldı.

ELASTOMERIC BEARING

10,00 110,00 110,00

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Pad length (bridge longitudinal direction) Lm = 300 mm Pad width (bridge transverse direction) Wm = 300 mm

STRANDS

in mm

0.5 12.7 0.6 15.24 0.7 17.78

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Strand diameter Cap = 14.2 mm Ultimate Stress fpu = 1863 Mpa Modulus of Elasticity Estr = 195000 Mpa

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Top face of the beam(compression) As'

⑤ 6 Ø16

Bottom face of the beam(tension) As

⑥ 7 Ø16

Shear reinforcement in the body Asg

⑦ 2x5 Ø12

Stirrups in the middle of the beam Ase

④③②① Ø8 /150

Stirrups at the beam Ase'

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[*] Kiriş ringde çalışıyor.dingil araları %50 azaltıldı. Dingil yükleri %50 arttırıldı.

10,00 110,00

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PROJECT NAME………: YAVUZ SELiM BULVARI ALTGECiT iNSAATI LOCATION…..……....: BEYLiKDUZU-ISTANBUL

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165.0 Mpa

Elastomer hardness Hshore = 50.0 Constant amplitude fatigue threshold for Category A DFt =

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Shear modulus of elastomer { (0,68 - 0,93) SELECT } G = 0.7 Mpa Steel reinforcement yield strength fy = 240.0 Mpa

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PROJECT NAME………: YAVUZ SELiM BULVARI ALTGECiT iNSAATI LOCATION…...……....: BEYLiKDUZU-ISTANBUL

REGULATION……...: CONCRETE DECK DESIGN AASHTO LRFD 2007

INPUT DATA:

Effective span length L = 18.71 m

Deck Thickness hc > 17,5 cm OK hc = 20.0 cm

Asphalt Thickness ha = 8.0 cm

Girder spacing ( S.9.7.2.3.) S = 110.0 cm

Truck type TT = [H30-S24] P+%50 X-%50

Lanes numbers SS = 3.0

Reinforcement strength fy = 420 Mpa

Concrete 28-day compressive strength: f'c = 25 Mpa

Beton elastisite modülü Eci = 19400 Mpa

Concrete density: 24 kN/m3

Wearing surface density: 21.99 kN/m3

Cover All edges are the same; pp = 2.5 cm

Bar Radius Top + Bottom; D = 12 mm

γc = γa =

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Bar spacing Top + Bottom; si = 20 cm

CALCULATIONS AND CHECKS Dead load effects: (S.3.4.1-2)

Dtab = 5.28 kN/m

Deck Moment Mc = Dtab S^2 / 10 Mc = 0.70 kN.m

Dbw = 3.02 kN/m

Wearing sur. + Barr. Ma = Dba. S^2 / 10 Ma = 0.40 kN.m

Live load effects (S.3.6.1.1.2-1)

Lanes factor SS = 3 için ; m = 0.85

Truck load Dy = Kam.yük * m Dy = 120 kN

Live load moment Mq =(s+0,6)*Dy/12 Mq = 17 kN.m

impact factor θ = 1.26

Live load factored moment Mq' = 21.49792 kN.m

Mu =1.25Mc + 1.5Ma + 1.75Mq' Mu = 39.10369 kN.m

Bending calculations : (S.5.7.3.2.1)

The pressure coefficient of the depth region 0.85

Moment safety factor 0.9

Concrete tensile stress fr = 3.125 Mpa

Section Length constant 1 m ; b = 110 cm

Sectional Elevation Account ds = hc-pp ds = 17.5 cm

Bar numbers Da = int(b/si)+1 Da = 6 Adet

Bar Numbers / Radius(mm) / spacing(cm) 6 θ 12 / 20

Total bar area As = 6.78584 cm2

Depth of stress block a=As.Fy/0.85.f'c.b a = 1.219274 cm

Flexural strength Mn = As.fy.(ds-a/2) Mn = 48.13843 kN.m

Flexural strength of Coefficients Mr = ɸ.Mn Mr = 43.32458 kN.m

θ = 1+ 15/(L+375) Mq'= θ .Mq β1 = ɸ = fr = 0,625√f'c As = Da.π.D^2/4

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PROJECT NAME………: YAVUZ SELiM BULVARI ALTGECiT iNSAATI LOCATION…...……...: BEYLiKDUZU-ISTANBUL

REGULATION…..…...: PK-750/750/750 AASHTO LRFD 2007

1_ DIMENSIONS

1.1_ LONGITIDUAL PROFILE (SPAN)

Span Length Ltab = 19510 mm 64.01 ft Support Back length a = 400 mm 15.75 in Between Pannel - Beam bi = 50 mm 1.97 in Pad length (bridge longitudinal direction) Lm = 300 mm 11.81 in

L-2*a/12 Calculation Length Lcalc = 18710 mm 61.38 ft

L-2*bi/12 Girder Length Lbeam = 19410 mm 63.68 ft

1.2_ TRANSVERSE PROFILE

Number of beam Nb = 11 adet

Total deck width B = 14100 mm 46.26 ft The average height of the pavement Hk = 300 mm 0.98 ft The average width of the pavement Bk = 2000 mm 6.56 ft Between Beam - Beam S = 1100 mm 3.61 ft Wearing surface heigth tw = 80 mm 3.15 in Deck heigth ts = 200 mm 7.87 in Haunch heigth th = 0 mm 0.00 in Haunch width thw = 0 mm 0.00 in

1.3_ PRECAST BEAM SECTION

Cover pp = 25 mm 1.00 in y6 = 100 mm 3.94 in y5 = 125 mm 4.92 in y4 = 0 mm 0.00 in y3 = 300 mm 11.81 in y2 = 75 mm 2.95 in y1 = 150 mm 5.91 in x1 = 750 mm 29.53 in x2 = 750 mm 29.53 in x3 = 200 mm 7.87 in x4 = 0 mm 0.00 in 14100 0 250 1100 80 2000 300 50 300

PRECAST GIRDER BEAM

18710 18710 400 400 Ldeck = a = Lcalc= a = Lbeam =

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2_ MATERIAL DATA

Relative humidity RH = 60.00 %

2.1_ CONCRETE

Unit weight of concrete Gc = 24.0 kN/m3 152.9 pcf

2.1.1_ PRECAST BEAM

f'c = 40.0 Mpa 5800.0 psi

0.8 fc' f'ci = 32.0 Mpa 4640.0 psi

fb = 0.038 Mpa 0.458 psi

gcd^1,5*33*(fuci)^0,5/1000 Ebeam = 21948.5 Mpa 4248.5 ksi

karea/12/12*gcd Gbeam = 8.2 m.de kN 563.6 ft.de lb

2.1.2_ DECK SLAB

f'c = 25.0 Mpa 3625.0 psi

Ebeam = 19400.0 Mpa 3755.2 ksi

2.2_ STEEL

2.2.1_ REINFORCEMENT STEEL

[LRFD Art. 5.4.3.2] fy = 420.0 Mpa 60900 psi

[LRFD Art. 5.4.3.2] Esteel = 200000.0 Mpa 29000 ksi

Top face of the beam(compression) As' = 6 Ø16 1206 mm2 1.87 in2 Bottom face of the beam(tension) As = 7 Ø16 1407 mm2 2.18 in2 Shear reinforcement in the bodyı Asg = 2x5 Ø12 1131 mm2 1.75 in2 Stirrups in the middle of the beam Ase = Ø8 /150 385 mm2/m 0.18 in2/ft

Stirrups at the beam Ase = Ø12 /70 226 mm2 0.35 in2

[LRFD Eq. 5.4.2.4-1] 2.2.2_ PRESTRESSED STEEL

Strand Diameter Cap = 14.2 mm 0.561 in

[LRFD Table 5.4.4.1-1] Area of one strand Astr.1 = 123.9 mm2 0.192 in2

fpu = 1863 Mpa 270196 psi

[LRFD Art. 5.4.4.2] Estrand = 195000 Mpa 28275 ksi

0,9*fpu fpy = 1676.7 Mpa 243176.2 psi

[LRFD Table 5.9.3-1] 0,75*fpu fpi = 1677.1 Mpa 202646.8 psi

0,8*fpy fpe = 1677.1 Mpa 194541.0 psi

2.3_ WEARING SURFACE, PAVEMENT, BARRIERS

Pavement and barrier weight Wbarr = 4.76 kN/m 326.0 lb /ft Unit weight of asphalt wearing surface Gw = 22.0 kN/m3 140.0 pcf

[*] Kiriş ringde çalışıyor.dingil araları %50 azaltıldı. Dingil yükleri %50 arttırıldı.

IMPACT ( IM) = 0.26 [H30-S24] P+%50 X-%50 US Fatigue P1 = 30.00 kN P1 = 6.7 6.7 kip P2 = 120.00 kN P2 = 27.0 27.0 kip P3 = 120.00 kN P3 = 27.0 27.0 kip X1 = 4250 mm X1 = 14.1 14.1 ft

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X2 = 4250 mm X2 = 14.1 28.2 ft IM = 0.26 0.15

3_ STRAND PATTERN= [ 0,6']; [Grade 270 KSI] ; [LOW RELAXATION] ; [SEVEN WIRE] -- PRESTRESSED STRANDS

TOP 0 mm in. KOT

1 0 0 0.00 29.53 2 0 0 0.00 29.53 3 0 0 0.00 29.53 4 0 0 0.00 29.53 5 0 0 0.00 29.53 6 0 0 0.00 29.53 0.0 STRAND PATTERN ROW NUMBERS 6 0 0 0.00 0.00 5 0 0 0.00 0.00 4 0 0 0.00 0.00 3 0 0 0.00 0.00 2 7 120 4.72 7.00 ● ● ● ● ● ● ● 1 10 60 2.36 10.00 ● ● ● ● ● ● ● ● ● ● BOTTOM 17 in. 17 4_ KILIF DÜZENİ

ROW STRAND NUMBER OF SHEATH LENGTH AASHTO

NUMBERS NUMBERS SHEATH mm ft CONTROLS

6 0 0 5 0 0 4 0 0 3 0 0 2 7 1 1478 9.82 % 14.3 14.3 ≤ 40 OK 1 10 3 2956 9.82 % 30.0 30 ≤ 40 OK BOTTOM 17 4 % 23.5 23,5 ≤ 25 OK

CALCULATION SHEATH LENGTH

0.16L = 9.82 ft Min[0.16 L; 0.5L(1-(1-Mcr/Mu)^0.5)] = 19.01 ft Ltrans+K[fpe-2/3*fpei)scap = 8.46 ft L/2 STRAND PATTERN

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● ● ● ● ● ● ●

● ● ● ● ● ● ● ● ● ● SELECT SHEATH LENGTH min(1;2;3) = 2546 mm

CALCULATION CROSS-SECTION PROPERTIES BEAM

X1 29.5275590551 X2 29.5275590551 X3 7.874015748 X4 0 Y1 5.905511811 Y2 2.9527559055 Y3 11.811023622 Y4 0 Y5 4.9212598425 Y6 3.937007874

A(in2) yb (in) A*yb Ix A*(yb-yb')^2 A1 174.375348751 2.952755906 514.8878408 506.7793709 22935.26189 A2 31.9688139376 6.88976378 220.2575763 15.48492522 1813.413163 A3 23.2500465001 7.381889764 171.6292803 16.8926457 1152.125251 A4 93.0001860004 14.76377953 1373.034242 1081.129325 10.90648565 A5 0 20.66929134 0 0 0 A6 0 20.66929134 0 0 0 A7 53.2813565627 23.95013123 1276.095482 71.68946862 4837.846586 A8 38.7500775002 23.12992126 896.2862414 78.20669303 2938.790989 A9 116.2502325 27.55905512 3203.746565 150.1568506 20064.77883 Σ 7655.94 1.92E+03 5.38E+04 XX --> A 531 in2

STRONG AXES yb' 14 in

IXX 55673 in4 A yl A*yl Iy A*(yl-yl')^2 A1 174.375348751 14.76377953 2574.439204 12669.48427 0 A2 15.9844069688 7.217847769 115.3730162 104.0931084 910.1694935 A3 15.9844069688 22.30971129 356.6075046 104.0931084 910.1694935 A4 23.2500465001 14.76377953 343.2585605 120.1254805 0 A5 93.0001860004 14.76377953 1373.034242 480.501922 0 A6 0 10.82677165 0 0 0 A7 0 18.7007874 0 0 0 A8 0 14.76377953 0 0 0 A9 26.6406782814 7.217847769 192.2883603 173.488514 1516.949156 A10 26.6406782814 22.30971129 594.3458409 173.488514 1516.949156 A11 38.7500775002 14.76377953 572.0976009 200.2091342 0 A12 116.2502325 14.76377953 1716.292803 8446.322848 0 Σ 7837.74 2.25E+04 4.85E+03 YY --> A 531 in2

WEAK AXES yl' 15 in

IXX

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IYY 27326 in4

CALCULATIONS AND CONTROLS Precast section

Distance from centroid to the extreme bottom fiber yb = 3.66E+02 mm 14.4 in hb-yb distance from centroid to the extreme top fiber yt = 3.84E+02 mm 15.1 in

TOPLA(G45:G50) Beam Heigth hb = 7.50E+02 mm 29.5 in

Area of Beam Abeam = 3.43E+05 mm2 530.9 in2 Moment of inertia I = 2.32E+10 mm4 55673.5 in4 I/yb Section modulus for the extreme bottom fiber Sb = 6.33E+07 mm3 3860.5 in3 I/yt Section modulus for the extreme top fiber St = 6.04E+07 mm3 3685.5 in3

Composite section

Description alan yb A.yb Istrong

(in2) (in) (in3) (in4) (in4) (in4)

Beam 530.88 14.42 7.66E+03 2.94E+04 5.57E+04 8.51E+04 Haunch 0.00 29.53 0.00E+00 0.00E+00 0.00E+00 0.00E+00 Slab 341.00 33.46 1.14E+04 4.58E+04 1.56E+03 4.74E+04

total 871.88 1.91E+04 1.33E+05

[LRFD Art. 4.6.2.6.1] Edsm/Ekrs n = 0.88 0.88

ck*12/4 1* = 4.68E+03 mm 184.15 in

S*12 2* = 1.10E+03 mm 43.31 in

12*ts+xii/2 3* = 2.78E+03 mm 109.25 in

[TxDOT Pg. #7-85] n*min(1*;2*;3*) ekkg = 9.72E+02 mm 38.28 in

ts*ekkg ekka = 1.94E+05 mm2 301.40 in2

Akomp = 5.63E+05 mm2 871.88 in2

ts+th+hb hc = 9.50E+02 mm 37.40 in A(ycb-yb)2 _Istr+ADy2 15.11 0. 00 0. 00 -5.56 -1 4. 42 -14.42 15.11

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Ic = 5.52E+10 mm4 132527 in4

ΣArea*yb/ΣArea ybc = 5.55E+02 mm 21.87 in

D-ybc ytg = 1.95E+02 mm 7.66 in

hc-ybc ytc = 3.95E+02 mm 15.53 in

Ic/ybc Sbc = 9.93E+07 mm3 6059.95 in3

Ic/ytg Stg = 2.84E+08 mm3 17305.25 in3

Ic/(ytc*nc) Stc = 1.58E+08 mm3 9653.32 in3

SHEAR FORCES AND BENDING MOMENTS DEAD LOAD [ DC ]

[LRFD Art. 3.3.2]

Dtab 0.36 kip/ft Gcd/1000*(ts/12*S+th/12*thw)

Dbeam 0.56 kips/ft Gkiris/1000+DA

DEAD LOAD [ DW ] [LRFD Art. 4.6.2.2.1]

Dbarr 0.06 kips/ft/krs2*Wbarr/1000/Nb

Dwear 0.15 kip/ft/krs Gw/1000*tw/12*(B-2*tbarr)/Nb

Dbw 0.21 kip/ft/krs DBarr+Dwear

no factored shear and moments

HD 27.62 ft Lhesap/2-Lhesap/20

BEAM WEIGHT SLAB WEIGHT total DC

x x/L V M V M V M

ft. kips k-ft kips k-ft kips k-ft

0.00 0.000 17.30 0.00 11.11 0.00 28.41 0.00 3.13 0.051 15.53 51.39 9.98 33.01 25.51 84.40 3.50 0.057 15.33 57.07 9.84 36.66 25.17 93.73 4.60 0.100 14.70 73.66 9.44 47.31 24.15 120.97 6.14 0.200 13.84 95.56 8.89 61.38 22.73 156.94 12.28 0.300 10.38 169.88 6.67 109.12 17.04 279.00 18.42 0.400 6.92 222.97 4.44 143.22 11.36 366.19 24.55 0.425 3.46 254.82 2.22 163.68 5.68 418.51 27.62 0.450 1.73 262.79 1.11 168.80 2.84 431.59 30.69 0.500 0.00 265.44 0.00 170.50 0.00 435.95 17.30 265.44 11.11 170.50 28.41 435.95

BARRIER WEIGHT W.SURF. WEIGHT total DW

x x/L V M V M V M

ft. kips k-ft kips k-ft kips k-ft

0.00 0.000 1.82 0.00 4.54 0.00 6.36 0.00 3.13 0.051 1.63 5.40 4.08 13.49 5.71 18.90 3.50 0.057 1.61 6.00 4.02 14.98 5.64 20.99 4.60 0.100 1.55 7.75 3.86 19.34 5.41 27.09 6.14 0.200 1.46 10.05 3.63 25.09 5.09 35.14 12.28 0.300 1.09 17.87 2.72 44.60 3.82 62.47 18.42 0.400 0.73 23.45 1.82 58.54 2.54 81.99 24.55 0.425 0.36 26.80 0.91 66.90 1.27 93.70 27.62 0.450 0.18 27.64 0.45 68.99 0.64 96.63 30.69 0.500 0.00 27.92 0.00 69.69 0.00 97.60 1.82 27.92 4.54 69.69 6.36 97.60 DC +DW x x/L V M ft. kips k-ft 0.00 0.000 34.77 0.00 w

(50)

3.13 0.051 31.22 103.29 3.50 0.057 30.80 114.72 4.60 0.100 29.55 148.06 6.14 0.200 27.81 192.08 12.28 0.300 20.86 341.47 18.42 0.400 13.91 448.18 V= w (0.5 L-x) 24.55 0.425 6.95 512.21 M=0.5 w x (L-x) 27.62 0.450 3.48 528.21 30.69 0.500 0.00 533.55 34.77 533.55 LIVE LOADS [ LL ] [LRFD Art. 3.6.1.2.1] n 1.13 Ekrs/Edsm eg 19.04 in ts/2+yt

Kg 280798 in4 n*(I+karea*C120^2) [LRFD Art. 3.6.1.1.1]

NL 3.00 şerit tamsayı((B-2*tbarr)/12) S= 3,6089238 ft 3,5 ≤ S ≤ 16 OK ts= 7,874015 in 4,5 ≤ ts ≤ 12 OK L= 64,009186 ft 20 ≤ L ≤ 240 OK Nb= 11 OK Kg= 280798 10.000 ≤ Kg ≤ 7.000.000 OK

Factor of bendıng moment [LRFD Table 5.4.4.1-1]

DFM 0.30 0.06 + (S/14)^0.4 (S/L)^0.3 (Kg/(12Lts^3))^0.1 DFM 0.38 NL > 1 0.075 + (S/9,5)^0.6 (S/L)^0.2 (Kg/(12Lts^3))^0.1

DFM 0.38 şerit/krs

Factor of shear force. [LRFD Table 4.6.2.2.3a-1]

DFS 0.49 0.2 + (S/12) - (S/35)^2 DFS 0.50 NL > 1 0.36 + (S/25) DFS 0.49 şerit/krs IMPACT IM(aashto) 0.27 50/(ck+125) ≤ 0,3 IM(Lrfd) 0.33 [LRFD Table 3.6.2.1-1] Truck load [H30-S24] P+ P+%50 X-%50 [H30-S24] P+%50 X-%50 US Fatigue P1 = 30 kN P1 = 6.74 6.74 kip P2 = 120 kN P2 = 26.98 26.98 kip P3 = 120 kN P3 = 26.98 26.98 kip X1 = 4250 mm X1 = 14.12 14.12 ft X2 = 4250 mm X2 = 14.12 28.24 ft IMPACT ( IM) = 0.265 IM = 0.26 0.15 Tandem load Nb ≥ 4 NL = 1 NL = 1 L 24,73 24,73 14,12

(51)

Pta = 110.00 kN 24.73 kip Xta = 4250 mm 14.12 ft Lanes load Qlanes = 10.00 kN/m 0.69 kip/ft LOADING RESULT TRUCK LOAD TRUCK TRUCK + IM x x/L V M ft. kips k-ft kips k-ft 0.00 0.000 51.39 0.00 31.85 0.00 3.13 0.051 48.30 140.88 29.93 67.84 3.50 0.057 47.93 156.32 29.71 75.28 4.60 0.100 46.84 201.21 29.03 96.90 6.14 0.200 45.32 260.00 28.09 125.21 12.28 0.300 39.25 453.75 24.33 218.51 18.42 0.400 33.18 601.55 20.57 289.69 24.55 0.425 27.11 684.76 16.80 329.76 27.62 0.450 24.08 698.42 14.92 336.34 30.69 0.500 21.04 693.45 13.04 333.95 max value 51.39 698.42 31.85 336.34 TANDEM LOAD FACTORED UNFOCTORED x x/L ft. kips k-ft kips k-ft 0.00 0.000 43.77 0.00 21.45 0.00 3.13 0.051 43.77 77.42 21.45 29.48 3.50 0.057 43.77 86.53 21.45 32.95 4.60 0.100 43.77 113.85 21.45 43.36 6.14 0.200 43.77 151.81 21.45 57.81 12.28 0.300 -5.69 303.61 -2.79 115.62 18.42 0.400 -5.69 455.42 -2.79 173.43 24.55 0.425 -5.69 607.22 -2.79 231.24 27.62 0.450 -5.69 683.12 -2.79 260.14 30.69 0.500 -5.69 759.03 -2.79 289.05 max value 43.77 759.03 21.45 289.05

LANES LOAD FATIGUE TRUCK TRUCK+IM x x/L V M M Mf VLT MLT Vlta Mlta 0,69 27,0 27,0 6,7 14,1 14,1 61,38 MOTION DIRECTION

(52)

ft. kips k-ft k-ft k-ft 0.00 0.000 10.31 0.00 0.00 0.00 3.13 0.051 9.29 23.80 121.45 34.73 3.50 0.057 9.17 26.43 134.60 38.49 4.60 0.100 8.82 34.12 172.64 49.37 6.14 0.200 8.35 44.26 221.91 63.45 12.28 0.300 6.60 78.68 377.57 107.97 18.42 0.400 5.05 103.27 487.27 139.34 24.55 0.425 3.71 118.02 532.39 152.24 27.62 0.450 3.12 121.71 527.01 150.70 30.69 0.500 2.58 122.94 502.99 143.83 max value 10.31 122.94 532.39 152.24

Service load stressed at Midspan 265.44 k-ft 170.50 k-ft 97.60 k-ft 336.34 k-ft 122.94 k-ft 2.28 kip/in2 (Mg+Ms)12/Sb+[Msdl+0.8 (Mlt+Mll)]12/Sbc

Allowable Stress Limit

Fbb 0.46 kip/in2 0,19(fuc/1000)^0,5 [LRFD Art. 5.9.4.2b]

Required Number of Strands (GHS)

fpb 1.82 kip/in2 fb-fbb

yb 14.42 in

ybs= the distance from center of gravity of the strand at midspan to the bottom of the beam

ybs 2.36 in

12.06 in yb-ybsi

363.14 kips fpb*karea*Sb/(Sb+karea*ec)

lossy 20.00 %

lossk 40.53 kip/in2 (lossy/100)*(fpi/1000)

loss 31.13 kips Sarea*(fpi/1000- lossk)

GHS 12 # Karea 530.88 in2 Sb 3860.50 in3 Mf Mg Ms MSDL MLT MLL fb ec* Ppei

(53)

eh 0.00 in ybsend 3.33 in ybs 3.33 in HS 17 # ec 11.09 in eci 11.09 in

Ppe* 529.15 Kips HS*loss

fb* 2.52 kip/in2 ppu/karea+ecu*ppu/Sb ≤ 1,82 OK

PRESTRESSED LOSSES [LRFD Eq. 5.9.5.1-1]

% or kip/i Viok 8.00 % Mg 265.44 k-ft Ms 170.50 k-ft Msdl 97.60 k-ft ec 11.09 in I 55673.46 in4 Ic 132527.26 in4 ybc 21.87 in ybs 20.04 in fb.reqd 1.82 kip/in2

1.ITERATION 2.ITERATION 3.ITERATION

Ekrs 4248.55 Ekrs 3700.17 Ekrs 4339.15

Viok 0.00 Viok 6.89 Viok 7.67

Pi 661.43 Pi 615.83 Pi 610.67 fcgp 2.07 fcgp 1.89 fcgp 1.86 13.79 14.41 12.15 8.00 8.00 8.00 0.42 0.42 0.42 21.90 19.66 19.40 2.55 2.61 2.90

Viok* 7.43 NO Viok* 7.75 NO Viok* 6.71 NO

Pi* 612.26 Pi* 610.15 Pi* 617.06

fcgp* 1.87 fcgp* 1.86 fcgp* 1.89

12.45 14.41 12.32

19.48 19.38 19.72

2.86 2.63 2.86

Viok** 6.85 NO Viok** 7.76 OK Viok** 6.78 NO

Pi** 616.14 Pi** 610.12 Pi** 616.56

fcgp** 1.89 fcgp** 1.86 fcgp** 1.89

12.56 14.23 12.30

19.67 19.38 19.69

2.83 2.65 2.86

Viok*** 6.89 NO Viok*** 7.67 NO Viok*** 6.78 OK

13.97 15.55 13.74

Pi*** 615.83 Pi*** 610.67 Pi*** 616.60

43.06 44.26 42.86

21.25 % 21.84 % 21.15 %

∆fpT ∆fpES + ∆fpSR + ∆fpCR + ∆fpR2

∆fpES ∆fpES ∆fpES

∆fpSR ∆fpSR ∆fpSR

∆fcdp ∆fcdp ∆fcdp

∆fpCR ∆fpCR ∆fpCR

∆fpR2 ∆fpR2 ∆fpR2

∆fpES* ∆fpES* ∆fpES*

∆fpCR* ∆fpCR* ∆fpCR*

∆fpR2* ∆fpR2* ∆fpR2*

∆fpES** ∆fpES** ∆fpES**

∆fpCR ∆fpCR ∆fpCR

∆fpR2 ∆fpR2 ∆fpR2

∆fpi ∆fpi ∆fpi

Σ∆fpT Σ∆fpT Σ∆fpT

(54)

fpe* 159.59 < 195 OK fpe* 158.39 < 195 OK fpe* 159.79 < 195 OK

Ppe* 520.88 Ppe* 516.98 Ppe* 521.54

fb* 2.48 > 1,82 OK fb* 2.46 > 1,82 OK fb* 2.48 > 1,82 OK ft.srvI.MP 0.90 1502.36ft.EP+PR 0.91 2012.9ft.EP+PR 0.90 2001.5 ft.tr.srvI.MP 1.22 2033.15ft.½EP+½PR+T 0.77 1928.4ft.½EP+½PR+T 0.77 1922.0 ft.srvI.HDP 0.16 271.93ft.EP+PR+TR 1.22 2040.5ft.EP+PR+TR 1.22 2031.9 ft.tr.srvI.HDP 2.11 3519.50fbf.SIII 0.18 923.0fbf.SIII 0.20 1155.1

fti.HDP fti.HDP 0.17 281.6fti.HDP 0.16 270.5

fbi.HDP fbi.HDP 2.09 3478.6fbi.HDP 2.12 3525.6

fti.END fti.END -0.69 -1144.5fti.END -0.69 -1155.6

FBi.END FBi.END 2.90 4840.0FBi.END 2.93 4887.0319

MİN 271.9 MİN -1144.5 MİN -1155.6

MAX 3519.5 MAX 4840.0 MAX 4887.0

f'ci.reqd.min -1155.59 kip/in1

f'ci.reqd.max 4887.03 kip/in2

Ekrs.reqd 4360.17 kip/in2

PRESTRESSED LOSSES [LRFD Art. 5.9.5.2.3a] Elastic Shortening Pi 616.60 Kips HS*Sarea*(1-viok/100)*fpi/1000 I 55673.46 in4 Mg 265.44 k-ft ec 11.09 in 530.88 in2 fcgp 1.89 kip/in2 Pi/karea+Pi*ec^2/I-Mg*ec/I*12 Estr 28275.00 kip/in2 Ekrs 4360.17 kip/in2 12.25 kip/in2 Estr/Ekrs*fcgp Shrinkage [LRFD Eq. 5.9.5.4.2-1] RH 60.00 % 8.00 kip/in2 17-0,15*RH

Creep of Concrete [LRFD Eq. 5.9.5.4.3-1]

Ms 170.50 k-ft MSDL 97.60 k-ft ybc 21.87 in ybs* 20.04 in loss-ec I 55673.46 in4 Ic 132527.26 in4 0.42 kip/in2 Ms*12*ec/I+Msdl*12*(ybc-ybsu)/Ic 19.69 kip/in2 12*fcgp-7*Dfctp

Relaxation after Transfer [LRFD Eq. 5.9.5.1-1]

Ms 170.50 k-ft MSDL 97.60 k-ft ybc 21.87 in fpi 202646.85 lbf/in2 HS 17 # Mg 265.44 k-ft 2.862 kip/in2 0,3*(20-0,4*DfpES-0,2*(DfpSR+DfpCR)) Karea 530.88 in2 ∆fpES Karea ∆fpES ∆fpSR ∆fpSR ∆fpCR ∆fcdp ∆fpCR ∆fpR2 ∆fpR2

(55)

Ekrs 4360.17 ksi

Estr 28275.00 ksi

ec 11.09 in

0.42 ksi

8.00 ksi

Σ∆fp Total Losses at Service Loads [LRFD Eq. 5.9.5.1-1]

IPLoss 6.78 % (DfpES+0,5*DfpR2_)*100/fpi 42.80 kip/in2

21.12 % DfpTksi*100/fpi

fpe 159.786 kip/in2

Ppe 521.73 kips HS*Sarea*fpei

STRESS SUMMARY [LRFD Art. 5.9.4]

f 'ci.güncel 4887.03 lbf/in2

0.6f'ci 2.9322 kip/in2

0.0948√f'ci 6.63 √

Stresses at Beam End

≤ 0.60f'ci.reqd.

ec 11.09 in

eci 11.09 in

616.60 kips

top fti -0.693 kip/in2 Pii/karea-Pii*eci/St ≤ 2,9322 OK

bottom fbi 2.9322 kip/in2 Pii/karea+Pii*eci/St ≤ 2,9322 OK

[LRFD Art. 5.8.2.3]

Stresses at Transfer Length Section

≤ 0.60f'ci.reqd. Ltran 2.80 ft Scap*60/12

Mtran 48.09 k-ft 0,5*Gkiris*Ltran*(Lk-C553)/1000

et 11.09 in ec-(ec-eci)*(Lharp-Ltran)/Lharp

top ft -0.537 kip/in2 Pii/karea-et*Pii/St+Mtran*12/St ≤ 2,9322 OK

bottom fb 2.7827 kip/in2 Pii/karea-et*Pii/St+Mtran*12/St ≤ 2,9322 OK

Stresses at Harp points

≤ 0.60f'ci.reqd. eharb 11.09 in ec

Lharb 27.62 ft 0,45*Lhesap

Lharb* 28.77 ft Lharp+(Lbeam-Lhesap)/2

Mharp 283.02 k-ft 0,5*Gkiris*Lharppo*(Lbeam-C566)/1000

top ft 0.228 kip/in2 Pii/karea-eharp*Pii/St+C567*12/St ≤ 2,9322 OK

∆fctp

∆fpSR

∆fpT ∆fpES + ∆fpSR + ∆fpCR + ∆fpR2

∆fpT%

(56)

bottom fb 2.0525 kip/in2 Pii/karea+eharp*Pii/Sb-Mharp*12/Sb ≤ 2,9322 OK

Stresses at Midspan

≤ 0.60f'ci.reqd.

ec 11.09 in

Morta 285.6758 k-ft 0,5*Gkiris*(Lbeam/2)^2/1000

top ft 0.237 kip/in2 Pii/karea-ec*Pii/St+Morta*12/St ≤ 2,9322 OK

bottom fb 2.0442 kip/in2 Pii/karea+ec*Pii/Sb-Morta*12/Sb ≤ 2,9322 OK

control x ft-top 0.623√f'ci fb-bot. 0.6f'ci point (ft) (ksi) -1.377 (ksi) 2.932

Beam.end 0.00 -0.693 OK 2.932 OK

Ltransfer 2.80 -0.537 OK 2.783 OK

Harp.Point 27.62 0.228 OK 2.052 OK

MidSpan 30.69 0.237 OK 2.044 OK

Concrete Stresses at Service Loads Allowable Stress Limits

[LRFD Art. 5.9.4.2]

(f'c.güncel =f'ci.güncel)

f 'c.güncel 4887.03 lbf/in2 precast beam

f 'c 3625 lbf/in2 slab

compression

Due to (Effective prestress + permanent loads) for load combination service I 0.45f'c 2.20 kip/in2 precast beam

0.45f'c 1.63 kip/in2 slab

Due to ½(effective prestress + permanent loads) + transient loads for load comb. Service I 0.4f'c 1.95 kip/in2 precast beam

Due to permanent and transient loads for load combination Service I 0.6f'c 2.93 kip/in2 precast beam

0.6f'c 2.18 kip/in2 slab

tension

For components with bonded prestressing tendons for load combination Service III: -0,19√f'c -0.420 kip/in2 precast beam

Stresses at Midspan

Concrete stresses at top fiber of the beam:

The compressive stresses are checked for two cases

1. Effective prestress + permanent loads, Service I ≤ 0.45f'ci.reqd.

ft 0.90 kip/in2 precast beam ≤ 2,2 OK

2. ½(Effective prestress + permanent loads) + transient loads, Service I: ≤ 0.40f'ci.reqd.

(57)

Stresses at the top of the deck

1. Under permanent loads, Service I ≤ 0.45f'ci.reqd.

ftc 0.137 kip/in2 slab ≤ 1,63 OK

2. Under permanent and transient loads, Service I ≤ 0.60f'ci.reqd.

ftc 0.783 kip/in2 slab ≤ 2,18 OK

Concrete stresses at bottom fiber of the beam, Service III: ≤ -0,19√f'c.reqd. fb 0.205 kip/in2 precast beam ≤ -0,42 OK

FATIGUE

ft 0.93 kip/in2

ffat 0.23 kip/in2 ≤ 0,93 OK

MIDSPAN SLAB TOP LIFT BEAM TOP LIFT BEAM BOT. Permanent total load Permanent total load service III

(ft) (ksi) (ksi) (ksi) (ksi) (ksi)

30.69 0.14 0.78 0.90 1.22 0.21

OK OK OK OK OK

STRENGTH LIMIT STATE [LRFD Table 3.4.1-1 snd 2] service I Q = 1.00 ( DC+DW ) + 1.00 ( LL+IM )

service III Q = 1.00 ( DC+DW ) + 0.80 ( LL+IM )

strength I max. Q = 1.25 ( DC ) + 1.50 ( DW ) + 1.75 ( LL+IM )

min. Q = 0.90 ( DC ) + 0.65 ( DW ) + 1.75 ( LL+IM ) fatigue Q = 0.75 ( LL+IM ) Mu 1.25[DC] + 1.5[DW] + 1.75[LL+IM] 1.25[DC] Mg 265.44 k-ft Ms 170.50 k-ft Mbarr 27.92 k-ft 1.5[DW] Mw 69.69 k-ft 1.75[LL+IM] Mll 122.94 k-ft Mlt 336.34 k-ft Mu 1488.10 k-ft

fpu 270.20 kip/in2 fpu/1000

fpe 159.79 kip/in2 fpe>0,5fpu > 135,1 OK

k 0.28 2*(1,04-fpy/fpu) [LRFD Eq. 5.7.3.1.1-1]

[LRFD Table C5.7.3.1.1-1]

dp 34.07 in hc-ybs

β1 0.85 [LRFD Art. 5.7.2.2]

Aps 3.26 in2 HS*Sarea

As 2.18 in2

As' 1.87 in2

b 43.31 in S*12

f'c 3.63 kip/in2 fcu/1000

fy 60.90 kip/in2 fy/1000

fy' 60.90 kip/in2 fy/1001 c = (Aps*fpu+As*fy-Asu*fyu)/(0,85*bti*fcu*b_+k*Aps*fpu/db)

c 7.47 in c < ts ≤ 7,87 OK

a 6.35 in β1*c a < ts ≤ 7,87 OK

(58)

Nominal flexural resistance: [LRFD Art. 5.7.3.2.3]

Mn 2131.15 kip-ft Aps*fps*(dp-a/2)/12 [LRFD Eq. 5.7.3.2.2-1]

ø 1.00 resistance factor [LRFD Art. 5.5.4.2.1]

Mr 2131.15 kip-ft Mr > Mu > 1488,1 OK LIMITS OF REINFORCEMENT MAX [LRFD Art. 5.7.3.3.1] c/dc ≤ 0.42 [LRFD Eq. 5.7.3.3.1-1] dc 29.49 in (Aps*fps*dp+As*fy*1)/(Aps*fps+As*fy) [LRFD Eq. 5.7.3.3.1-2] c/dc 0.25 c/dc ≤ 0.42 ≤ 0.42 OK MIN [LRFD Art. 5.7.3.3.2] Check at midspan:

fr 0.53 kip/in2 0,24*(fuci_/1000)^0,5 [LRFD Art. 5.4.2.6]

Ppe 521.73 kips

ec 11.09 in

fpe 2.48 kip/in2 Ppe/karea+Ppe*ec/Sb

Md-nc 435.95 kip-ft Mg+Ms

Mcr 1272.49 kip-ft (fr+fpe_)*Sbc/12-Mdnc*(Sbc/Sb-1) [LRFD Eq. 5.7.3.3.2-1]

Scfr 3215.16 kip-ft Sbc*fr Scfr > Mcr > 1272 OK

Mu* 1881.82 kip-ft (1+HIM)*Mu Mu* > 1.2Mcr > 1526 OK

Mr 2131.15 kip-ft Mr > 1.2Mcr > 1526 OK

SHEAR DESIGN

barrier wea.surf. beam slab truck truck lanes weight weight weight weight load IM load

x x/L Mbarr Mw Mg Ms M MLT MLL ft. k-ft k-ft k-ft k-ft k-ft k-ft k-ft 0.00 0.000 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3.13 0.051 5.40 13.49 51.39 33.01 140.88 67.84 23.80 3.50 0.057 6.00 14.98 57.07 36.66 156.32 75.28 26.43 4.60 0.100 7.75 19.34 73.66 47.31 201.21 96.90 34.12 6.14 0.200 10.05 25.09 95.56 61.38 260.00 125.21 44.26 12.28 0.300 17.87 44.60 169.88 109.12 453.75 218.51 78.68 18.42 0.400 23.45 58.54 222.97 143.22 601.55 289.69 103.27 24.55 0.425 26.80 66.90 254.82 163.68 684.76 329.76 118.02 27.62 0.450 27.64 68.99 262.79 168.80 698.42 336.34 121.71 30.69 0.500 27.92 69.69 265.44 170.50 693.45 333.95 122.94 x/L 0 0,051L 0,057L 0,1L 0,2L Mg 0.00 51.39 57.07 73.66 95.56 Ms 0.00 33.01 36.66 47.31 61.38 Mbarr 0.00 5.40 6.00 7.75 10.05

(59)

Mw 0.00 13.49 14.98 19.34 25.09 Mlt 0.00 67.84 75.28 96.90 125.21 Mll 0.00 23.80 26.43 34.12 44.26

Q 0.00 292.86 325.13 419.18 542.93

x x/L Vbarr Vw Vg Vs V

ft. kips kips kips kips kips kips kips

0.00 0.000 1.82 4.54 17.30 11.11 51.39 31.85 10.31 3.13 0.051 1.63 4.08 15.53 9.98 48.30 29.93 9.29 3.50 0.057 1.61 4.02 15.33 9.84 47.93 29.71 9.17 4.60 0.100 1.55 3.86 14.70 9.44 46.84 29.03 8.82 6.14 0.200 1.46 3.63 13.84 8.89 45.32 28.09 8.35 12.28 0.300 1.09 2.72 10.38 6.67 39.25 24.33 6.60 18.42 0.400 0.73 1.82 6.92 4.44 33.18 20.57 5.05 24.55 0.425 0.36 0.91 3.46 2.22 27.11 16.80 3.71 27.62 0.450 0.18 0.45 1.73 1.11 24.08 14.92 3.12 30.69 0.500 0.00 0.00 0.00 0.00 21.04 13.04 2.58 x/L 0 0,051L 0,057L 0,1L 0,2L Vg 17.30 15.53 15.33 14.70 13.84 Vs 11.11 9.98 9.84 9.44 8.89 Vbarr 1.82 1.63 1.61 1.55 1.46 Vw 4.54 4.08 4.02 3.86 3.63 Vlt 31.85 29.93 29.71 29.03 28.09 Vll 10.31 9.29 9.17 8.82 8.35 Q 118.38 108.68 107.55 104.15 99.45

Critical section near the supports is the greater of: [LRFD Art. 5.8.3.2]

bv 7.87 in a 6.35 in 0.72h 26.93 in [LRFD Art. 5.8.2.9] dc 34.07 in hc-ybsend [LRFD Art. 5.7.3.3.1] 0.9dc 30.66 in dv 30.89 in dc-0,5*a dv ≥ 0.72h ≥ 26 OK dv ≥ 0.9dc ≥ 30 OK Vc = 0.0316 β √ f'c bv dv [LRFD Eq. 5.8.3.3.-3]

Ash 3.26 in2 (HS-hhs)*Sarea

fpo 202.65 kip/in2 yht 0.00 in ybsend 3.33 in hb 29.53 in Lbeam/2-(Lhesap*0,5-Lhesap*0,45) HDe 28.77 ft ATAN((hb-yht-ybsend)/12/HDe) ψ 0.0757 rad Ppe/HS*hhs*SİN(kisi) Vp 0.00 kips Ppe/HS*hhs*SİN(kisi) Nu 0.00 kips Ac 307.09 in2 xi*yi+(xi+xiii)/2*yii+xiii*(hc/2-yi-yii) φ 0.90 Lem 11.81 in Ec 4360.17 kip/in2 VLT VLL

(60)

0,051L 0,057L 0,1L 0,2L [LRFD Table. 5.8.3.4.2-1] Ø 23.000 19.573 19.779 20.058 0.5dv.cotØ 36.391 43.445 42.956 42.307 kpo 42.296 49.350 48.861 48.213 Mu 292.863 325.132 419.180 542.933 Vu 108.680 107.545 104.148 99.449 εx -0.001 -0.001 -0.001 -0.001 εx -0.00014 -0.00013 -0.00012 -0.00011 Uu 0.496 0.491 0.476 0.454 0.102 -0.140 OK εx -0.140 -0.128 -0.118 -0.105 Uu/f'c 0.102 0.101 0.097 0.093 β 3.509 3.515 3.487 3.524 Vu dv 279.796 276.874 268.128 256.030 Mu ≥ Vu dv OK OK OK OK [LRFD Eq. 5.8.2.4.2-1]

LineerEnterpolation calc. detail 'Ø ve β table' see

x/L 0,1L minβ 3.49 Vc 59.26 kips 0,0316*Betta*(fuci_/1000)^0,5*bv*dv [LRFD Art. 5.8.2.4-1] Vu 104.15 kips Vu > 0.5 ø (Vc + Vp ) > 26 OK Ø ve β table [LRFD Table. 5.8.3.4.2-1] Ø ex < 1,0 Uu/f'c -0.2 -0.1 -0.05 0 0.125 0.25 0.5 1 0.075 22.20 20.40 21.00 21.80 24.30 26.60 30.50 36.40 0.1 18.10 20.40 21.40 22.50 24.90 27.10 30.80 36.70 0.125 19.90 21.90 22.80 23.70 25.90 27.90 31.40 37.00 0.15 21.60 23.30 24.20 25.00 26.90 28.80 32.10 37.30 0.175 23.20 24.70 25.50 26.20 28.00 29.70 32.70 36.80 0.2 24.70 26.10 26.70 27.40 29.00 30.60 32.80 36.10 0.225 26.10 27.30 27.90 28.50 30.00 30.80 32.30 35.70 0.25 27.50 28.60 29.10 29.70 30.60 31.30 32.80 35.80 β ex < 1,0 Uu/f'c -0.2 -0.1 -0.05 0 0.125 0.25 0.5 1 0.075 6.32 4.75 4.10 3.75 3.24 2.94 2.59 2.23 0.1 3.79 3.38 3.24 3.14 2.91 2.75 2.50 2.18 0.125 3.18 2.99 2.94 2.87 2.74 2.62 2.42 2.13 0.15 2.88 2.79 2.78 2.72 2.60 2.52 2.36 2.08 0.175 2.73 2.66 2.65 2.60 2.52 2.44 2.28 1.96 0.2 2.63 2.59 2.52 2.51 2.43 2.37 2.14 1.79 0.225 2.53 2.45 2.42 2.40 2.34 2.14 1.86 1.64 0.25 2.39 2.39 2.33 2.33 2.12 1.93 1.70 1.50 Lineer Enterpolation Y2 = [ (X2-X1) (Y3-Y1) / (X3-X1) ] + Y1

interpolation β 1 Ø 2

(61)

2 0.100 3.790 3.546 3.380 18.100 20.400 0.102 3.515 18.214 19.573 20.495 3 0.125 3.180 3.067 2.990 19.900 21.900 interpolation β 1 Ø 2 0,1L -0.200 -0.128 -0.100 -0.200 -0.128 -0.100 2 0.100 3.790 3.497 3.380 18.100 20.400 0.101 3.487 18.137 19.779 20.431 3 0.125 3.180 3.044 2.990 19.900 21.900 interpolation β 1 Ø 2 0,2L -0.200 -0.118 -0.100 -0.200 -0.118 -0.100 1 0.075 6.320 5.038 4.750 22.200 20.400 0.097 3.524 18.536 20.058 20.400 2 0.100 3.180 3.343 3.380 18.100 20.400 STIRRUP CALCULATION Vu/ø ≤ Vc + Vs + Vp [LRFD Eq. 5.8.3.3-1] Vs 56.46 kips Vu/ffi-Vc-Vp

Vs = Av fy dv (cotØ+cotα) sinα / s [LRFD Eq. 5.8.3.3-4]

α 90.00 drc cot α 0.00 sin α 1.00 Ø 19.78 drc cot Ø 2.78 stirrup s = 150 mm spacing s = 5.906 in Av 0.064 in2/ft s_*Vs/(fy/1000*dv*(cotO+cotA)*sinA)

spacing control [LRFD Art. 5.8.2.7]

0.125f'c 0.61 kip/in2 Vu 0.10 kip/in2 if Vu < 0.125 f'c then; [LRFD Eq. 5.8.2.7-1] smax min[ 0.8dv ; 24] 0.8dv 24.72 in smax 24.00 in

(62)

if Vu ≥ 0.125 f'c then; [LRFD Eq. 5.8.2.7-2] smax min[ 0.4dv ; 12] 0.4dv 12.36 in smax 12.00 in Vu < 0.125 f'c [LRFD Eq. 5.8.2.7-1] smax 24.00 in s 5.906 in s ≤ smax OK Av.seç 0.182 in2/ft 2*Pİ()*C924^2/4 0,182> 0,064 OK Vs 161.27 kips Av_*fy/1000*dv*cotO/s_

min. shear reinforcement control [LRFD Art. 5.8.2.5]

Avmin = 0.0316√ f'c bv s /fy [LRFD Eq. 5.8.2.5-1]

Avmin 0.05 0,053< 0,182 OK

max. shear reinforcement control

Vu/ø ≤ Vn = Vc + Vs + Vp ==> Vc + Vs ≤ 0.25 f'c bv dv

Vn = 0.25 f'c bv dv [LRFD Eq. 5.8.3.3-2]

0.25 f'c bv dv 297.20 kips

Vc + Vs 115.72 kips ≤ 0.25 f'c bv dv OK

factored shear force [LRFD Art. 5.8.4]

Vh=Vu/dv [LRFD Eq. C5.8.4.1-1] 0,1L point strength I STIRRUP CALCULATION 0,1L kips Vbarr 1.55 Vw 3.86 VLT 29.03 VLL 8.82 Vu 73.97 1,25*Vbarr+1,5*Vw+1,75*(VLT+VLL) Vh 2.39 kips/in

required min. Stresses Vn = Vu/ø

Vn 2.66 kip/in

Contribution of Reinforcement to Nominal Shear Resistance

Vn = c Acv + μ [Avf fy +Pc ] [LRFD Eq. 5.8.4.1-1]

(63)

μ 0.600 bvt 29.53 in Acv 29.53 in2 Pc 0.00 fy 60.90 kip/in2 Avf 0.15 in2/ft

Avf' 1.75 in2/ft existing => 2x5 Ø12 1,75 > 0,15 OK

minAvf [LRFD Eq. 5.8.4.1-4]

0.05bv /fy 0.29 in2/ft Avf ≥ 0.05 bv / fy OK

Vnp 7.55 kips/in

0,2f'c Acv 21.41 kips/in Vn ≤ 0.2 f'c Acv OK

0.8 Acv 23.62 kips/in Vn ≤ 0.8 Acv OK

ADDITIONAL LONGITUDINAL REINFORCEMENT REQUIREMENT

x x/L Mbarr Mw Mg Ms M MLT MLL

ft. k-ft k-ft k-ft k-ft k-ft k-ft k-ft

0.49 0.000 0.89 2.22 8.44 5.42 23.29 11.21 3.91 barrier wea.surf. beam slab truck truck lanes weight weight weight weight load IM load

x x/L Vbarr Vw Vg Vs V

ft. kips kips kips kips kips kips kips

0.49 0.000 1.79 4.47 17.02 10.93 50.91 31.55 10.15 x/L 0.49 x/L 0.49 Vg 17.02 Mg 8.44 Vs 10.93 Ms 5.42 Vbarr 1.79 Mbarr 0.89 Vw 4.47 Mw 2.22 Vlt 31.55 Mlt 11.21 VLT VLL

(64)

Vll 10.15 Mll 3.91

Q 116.85 Q 48.24

1,25*(Vg+Vs+Vbarr)+1,5*Vw+1,75*(Vlt+Vll) 1,25*(Mg+Ms+Mbarr)+1,5*Mw+1,75*(Mlt+Mll)

As fy + Aps fps ≥ Mu / [dv ø] + 0.5 Nu/ø +[Vu/ø -0.5 Vs -Vp) cot Ø [LRFD Art. 5.8.3.5]

Lbearing 11.81 in end of beam 0.49 ft cot Ø 2.78 ø 0.90 Nu 0.00 Mu 48.24 kip-ft Vu 116.85 kips Vs 161.27 kips Vp 0.00 kips dv 30.89 in eh 0.00 in ybsend 3.33 in As 2.18 in2 fy 60.90 kip/in2 Ltransfer 2.80 ft

right 157.62 kips Mu / [dv ø] + 0.5 Nu/ø +[Vu/ø -0.5 Vs -Vp) cot Ø

left 276.64 kips 0+SHS*Sarea*fpei*(eh+ybsend*cotO)/(Ltransfer*12) OK

PRETENSIONED ANCHORAGE ZONE [LRFD Art. 5.10.10]

min. Vertical reinforcement [LRFD Art. 5.10.10.1]

fs 20.00 kip/in2

fpi 661.43 kips

Pr = %4 fpi 26.46 kips Pr = fs.As ≥ 0.04 fpi

Asea 1.32 in2/ft

mesafe 9.35 in hc/4

s' 2.76 in

Asea' 1.40 in2/ft 1,402 > 1,323 OK

REINFORCEMENT DRAWING

Top face of the beam(compression) As'

⑤ 6 Ø16

Bottom face of the beam(tension) As

⑥ 7 Ø16

Shear reinforcement in the body Asg

(65)

Stirrups in the middle of the beam Ase Stirrups at the beam Ase'

④③②① ④③②①

Ø12 /70 Ø8 /150

DEFLECTION AND CAMBER

DIPLACEMENT CAMBER CALCULATION ↑

Pi 616.60 kips Ec 4248.55 kip/in2 ec 11.09 in ybs 3.33 in a 28.77 ft L 61.38 ft I 55673.46 in4 ∆cam 1.40 in ↑ Ppe/Ekrsg/I*(ec*(Lbeam*12)^2/8-(ec-ybs)*(Lharppo*12)^2/6) DEFLECTIONS CALCULATION ↓

Deflection due to wearing surface weight at midspan + Deflection due to barrier weight at midspan

(66)

Eci 4360.17 kip/in2

Ic 132527.26 in4

L 61.38 ft

∆bw 0.115 in ↓ 5*(Dbw/12)*(Lhesap*12)^4/(384*Ekrsg*Ic)

Deflection at midspan due to slab weight

Gtab 0.36 kips/ft

Eci 4360.17 kip/in2

I 55673.46 in4

L 61.38 ft

∆tab 0.476 in ↓ 5*(Dtab/12)*(Lhesap*12)^4/(384*Ekrsg*I)

Deflection due to beam weight at midspan Gbeam 0.564 kips/ft

Eci 4360.17 kip/in2

Ic 55673.46 in4

L 61.38 ft

∆beam 0.742 in ↓ 5*(Dwear/12)*(Lhesap*12)^4/(384*Ekrsg*I)

Deflection due to lanes load at midspan

DFM 0.381 NL/Nb

0.26 kip/ft/beam

0.144 in ↓ 5*(DFM*Qlanes/12)*(Lhesap*12)^4/(384*Ekrsg*I)

Deflection due to truck + IM load at midspan MLT 336.34 0.316 in ↓ 5*(Dwear/12)*(Lhesap*12)^4/(384*Ekrsg*I) ∆cam -35.6mm -1.40 in ↑ ∆bw 2.9mm 0.11 in ↓ ∆tab 12.1mm 0.48 in ↓ ∆beam 18.8mm 0.74 in ↓ ∆lanes* 3.7mm 0.14 in ↓ ∆arac* 8.0mm 0.32 in ↓ Σ∆ 6.2mm 0.25 in ↓ (*) max. L/800 23.39 0.92 ↓ L/800 > Σ∆ OK UNITS US SI 0 SI US 1 in. 25,4 mm <=> 1 mm 0,0394 in. 1 in.2 645,2 mm2 <=> 1 mm2 0,002 in.2 1 ft. 0,305 m <=> 1 m 3,279 ft. 1 ft.2 0,093 m2 <=> 1 m2 10,753 ft.2 1 psi 0,006895 MPa <=> 1 MPa 145,035 psi 1 ksi 6,895 MPa <=> 1 MPa 0,145 ksi 1 kip 4,448 kN <=> 1 kN 0,225 kip

Llsehim

∆lanes

(67)

1 ft-kip 1,356 kN-m <=> 1 kN-m 0,737 ft-kip 1 lb 0,004448 kN <=> 1 kN 224,82 lb 1 kip 1000 lb <=> 1 lb 0,001 kip 1 Kn 1000 N <=> 1 N 0,001 kN 1 lb/ft 0,01459 kN/m <=> 1 kN/m 68,54 lb/ft

(68)

PROJECT NAME………: YAVUZ SELiM BULVARI ALTGECiT iNSAATI LOCATION…...……....: BEYLiKDUZU-ISTANBUL

REGULATION……...: ELASTOMERIC BEARING DESIGN AASHTO LRFD 2007

METHOD B

System and material input data :

Expandable span length Ls = 18710 mm

Constant amplitude fatigue threshold for Category A 165 Mpa

Elastomer hardness: Hshore = 50

Shear modulus of elastomer { (0,68 - 0,93) SELECT } G = 0.7 Mpa

Steel reinforcement yield strength: fy = 240 Mpa

Pad length (bridge longitudinal direction): Lpad = 300 mm

Pad width (bridge transverse direction): Wpad = 300 mm

Elastomer cover thickness: hc = 2.5 mm

Elastomer internal layer thickness: hri = 8 mm

Number of steel reinforcement layers: Nst = 6

Steel reinforcement thickness: hs = 3 mm

(69)

System and material output data :

Elastomer creep deflection at 25 years divided by the instantaneous deflection: Cd = 0.25

Number of elastomer internal layers Nel = 5

total elastomer thickness hrt = 45 mm

Total steel plate heigth hst = 18 mm

Total bearing heigth ht = 63 mm

Bearing surface area Area = 90000 mm2

Check Nst (14.7.6.1) :

Nst = 6 Nst > 2 ise;

hc = 2.5

0.70 hri = 5.6 hc ≤ 0.70 hri OK

Compute Shape Factor (14.7.5.1-1) :

Sint = 9.375 Si = L.W / (2.hri.(L+W))

Scov = 30 Si = L.W / (2.hc.(L+W))

S = 9.375 S=min(Sint,Scov)

Check Compressive Stress (14.7.5.3.2) :

DLs = 106 kN DL reaction/girder

LLs = 111 kN LL reaction /girder

σs = 2.411111 MPa σs = (DLs+LLs) /Area

σL = 1.233333 MPa σL = LLs / Area

Shear deformation? -YES- (14.7.5.3.2-2) :

1.66 G.S = 10.89375 Mpa σs ≤ 1,66 G.S OK

0.66 G.S = 4.33125 Mpa σs ≤ 11 OK

σL ≤ 0,66 G.S OK

Shear deformation? -NO- (14.7.5.3.2-4) :

G.S = 6.5625 Mpa σs ≤ 2 G.S OK

2G.S = 13.125 Mpa σs ≤ 12 OK

σL ≤ G.S OK

Check Compressive Deflection (14.7.5.3.3) :

εi = 0.02662 durometer 50 60 70

δLi = 0.212963 mm C 0.013966 0.01513 0.011639

δLt = 1.197919 mm x 0.288213 0.262921 0.284806

δcr = 0.006655 mm 0.02662 0.012879 0.009775

1.204574 mm

0.07 hri = 0.56 mm δLi ≤ 0.07 hri OK

εi = Cs^x Σδ =

(70)

Check Shear Deformation (14.7.5.3.4) :

1.17E-05

tset = 20

γTU = 1.2

Δco = 4.37814 mm Δco = α . tset . Ls

Δs = 5.253768 mm

2.Δs = 10.50754 mm 2. Δco ≤ hrt OK

Ls = 18710 mm

θsx = 0.003 rad. Construction Tolerance

θsz = 0.003 rad. σs = 2.411111 MPa Nel = 5 G.S = 6.5625 Mpa n = 6 Lch = 0.5 GS (Lpad/hri)^2 (θsx/n) Lch = 2.360366 Mpa Lch ≤ σs OK Wch = 0.5 GS (Wpad/hri)^2 (θsz/n) Wch = 2.360366 Mpa Wch ≤ σs OK Check Stability (14.7.6.3.6) : ht = 63 mm minLW=min(Lpad/3 , Wpad/3) minLW = 100 mm ht ≤ minLW OK Check Reinforcement (14.7.6.3.7) : hmax = 8 mm

hsi = 0.241111 mm hsi =3 hri σs / fy

hsi ≤ hmax OK

hsii = 0.119596 mm hsii =2 hri σL / Aft

hsii ≤ hmax OK

α = /°C

°C

Δs = Δco . γTU

Check Rotation or Combined Compression and Rotation (14.7.5.3.5) :

(71)

(72)

ACI Engineering Page 72 12/01/2017

Metrication Conversion Guide for 318M and 318S

Note:

Based on IEEE/ASTM SI 10-2002 document

1a. LENGTH

1 in. = 25.40 mm

Rules:

2. Orange shading: equivalence number for ACI 318M document.

in.-lb Units [in.]

1/4 6.35 6.4 6 3/8 9.53 9.5 10 1/2 12.70 13 13 5/8 15.88 16 16 3/4 19.05 19 20 7/8 22.23 22 22 1 25.40 25 25 1 1/4 31.75 32 30 1 1/2 38.10 38 40 1 3/4 44.45 44 45 2 50.80 51 50 2 1/2 63.50 64 65 3 76.20 76 75 3 1/2 88.90 89 90 4 101.60 100 100 5 127.00 130 125 5 1/2 139.70 140 140 6 152.40 150 150 7 177.80 180 175 7 1/2 190.50 190 190 8 203.20 200 200 9 228.60 230 230 9 3/4 247.65 250 245 10 254.00 250 250 11 279.40 280 280 12 304.80 300 300 12.5 317.50 320 315 14 355.60 360 350 16 406.40 410 400 18 457.20 460 450 20 508.00 510 500 24 609.60 610 600 25 635.00 640 635 30 762.00 760 750

The values stated in either inch-pound or SI units are to be regarded separately as standard. The values stated in each system are not exact equivalents; therefore, each system must be used independently of the other, without combining values in any way.

1. Convert in. to mm using the factor 25.40 and round to two significant digits. 3. Change to m, when conversion reaches 1000 mm.

Example 1: 1/2 in. = 0.5 x 25.40 = 12.70 à use 13 mm Conversion to SI

(73)

(74)

1a. LENGTH CONTINUED

in.-lb Units [in.]

48 1.22 1.2 1.2 50 1.27 1.3 1.3 54 1.37 1.4 1.4 60 1.52 1.5 1.5 72 1.83 1.8 1.8 120 3.05 3.0 3.0 144 3.66 3.7 3.7 1,200 30.48 30 30 1,800 45.72 46 46

1b. CRACK WIDTH

1 in. = 25.40 mm

Rule:

in.-lb Units [in.]

0.012 0.3048 0.30 0.30 0.016 0.4064 0.41 0.41

1c. AGGREGATE SIZE

ASTM E 11 4 4 in. 100 mm 100 mm 3.5 3-1/2 in. 90 mm 90 mm 3 3 in. 75 mm 75 mm 2.5 2-1/2 in. 63 mm 63 mm 2 2 in. 50 mm 50 mm 1.5 1-1/2 in. 37.5 mm 37.5 mm 1 1 in. 25.0 mm 25.0 mm 0.875 7/8 in. 22.4 mm 22.4 mm 0.750 3/4 in. 19.0 mm 19.0 mm 0.625 5/8 in. 16.0 mm 16.0 mm 0.500 1/2 in. 12.5 mm 12.5 mm 0.375 3/8 in. 9.5 mm 9.5 mm 0.250 1/4 in. 6.3 mm 6.3 mm 0.187 No. 4 4.75 mm 4.75 mm 0.132 No. 6 3.35 mm 3.35 mm 0.0937 No. 8 2.36 mm 2.36 mm 0.0787 No. 10 2.00 mm 2.00 mm 0.0469 No. 16 1.18 mm 1.18 mm 0.0331 No. 20 0.0234 No. 30 0.0165 No. 40 0.0117 No. 50 0.0070 No. 80 0.0059 No. 100 0.0029 No. 200 Conversion to SI

Units [m] Equivalent SI Units [m] ACI 318M Units [m]

Convert in. to mm using the factor 25.40 and round to 2 significant digits. Example : 0.013 in. = 0.013 x 25.40 = 0.3302 à use 0.33 mm

Conversion to SI

Units [mm] Equivalent SI Units [mm] ACI 318M Units [mm]

ACI 318M Units [mm] Approx. Size

in.-lb Units [in.] Nomenclature in.-lb Units

Size and Nomenclature are the Same

SI Units 850 mm 850 mm 600 mm 600 mm 425 mm 425 mm 300 mm 300 mm 180 mm 180 mm 150 mm 150 mm 75 mm 75 mm

(75)

1d. AREA

0.09290

Rule:

5,000 464.50 460 460

1e. AREA PER UNIT LENGTH

2117

Rule: 0.10 211.70 210 210

1f. VOLUME

0.7646 Rule: 50 38.23 38 38 150 114.69 110 110

1g. LOADS

1 lb = 0.004448 kN Rule: in.-lb Units [lb] 3,000 13.34 13 13 9,000 40.03 40 40 10,000 44.48 44 44 16,000 71.17 71 71

1h. LOADS PER UNIT LENGTH

1 lb / ft = 0.01459 kN / m

Rule: 200 2.918 2.9 3.0 300 4.377 4.4 4.4 1,500 21.885 22 22 3,000 43.770 44 44 1 ft2 = _m2

Convert ft2_{to m}2_{using the factor 0.09290 and round to 2 significant digits.}

Therefore 5,000 ft2_{= 5,000 x 0.09290 = 464.5 à use 460 m}2

in.-lb Units [ft2_] Conversion to SI

Units [m2_] Equivalent SI Units [m2_] ACI 318M Units [m2_] 1 in.2 _{/ ft =} _mm2 _{/ m}

Convert in2_{/ft to mm}2_{/m using the factor 2117 and round to 2 significant digits.}

Therefore : 0.10 in.2_{/ft = 0.10 x 2117 = 211.7 à use 210 mm}2_/m

in.-lb Units [in.2_/ft]

Conversion to SI Units [mm2_/m] Equivalent SI Units [mm2_/m] ACI 318M Units [mm2_/m] 1 yd3₌ _m3

Convert yd3_{to m}3_{using the factor 0.7646 and round to 2 significant digits.}

Example : 50 yd3_{= 50 x 0.7646 = 38.23 à use 38 m}3

in.-lb Units [yd3_] Conversion to SI

Units [m3_]

Equivalent in SI Units [m3_]

ACI 318M Units [m3_]

Convert lb to kN using the factor 0.004448 and round to 2 significant digits. Example : 16,000 lb = 16,000 x 0.004448 = 71.17 à use 71 kN

Conversion to SI

Units [kN] Equivalent SI Units [kN] ACI 318M Units [kN]

Convert lb/ft to kN/m using the factor 0.01459 and round to 2 significant digits. Example : 1,500 lb/ft = 1,500 x 0.01459 = 21.89 à use 22 kN/m

(76)

1i. AREA LOADS

1 psf = 0.04788

Rule:

in.-lb Units [psf]

100 4.7880 4.8 4.8

2. TEMPERATURE

Degree F = (F-32)/1.8 = Degree C Rule: 35 1.6667 2 2 40 4.4444 4 4 50 10.0000 10 10 60 15.5556 16 16 90 32.2222 32 32 95 35.0000 35 35 100 37.7778 38 38 200 93.3333 93 93 300 148.8889 150 150 400 204.4444 200 200 600 315.5556 320 320 1,500 815.5556 820 820

3. CONCRETE UNIT WEIGHT

16.02

Rule: in.-lb Units [pcf] 70 1121.40 1120 1120 90 1441.80 1440 1440 105 1682.10 1680 1680 110 1762.20 1760 1760 115 1842.30 1840 1840 120 1922.40 1920 1920 140 2242.80 2240 2240 144 2306.88 2310 2310 145 2322.90 2320 2320 150 2403.00 2400 2400 kN/m2

Convert psf to kN/m2_{using the factor 0.04788 and round to 2 significant digits.}

Therefore : 100 psf = 100 x 0.04788 = 4.788 à use 4.8 kN/m2 Conversion to SI Units [kN/m2_] Equivalent SI Units [kN/m2_] ACI 318M Units [kN/m2_]

To convert °F to °C use the conversion above and round to the nearest degree. Except for temperatures above 212 deg F, for which the conversion is rounded to 2 significant figures).

Example: 35 °F = (35 – 32)/1.8 = 1.67 à use 2 °C

According to ACI style manual, the degree symbol should be used with temperature, °F and °C.

in.-lb Units [°F] Conversion to SI _{Units [°}_C_] Equivalent SI _{Units [°}_C_] ACI 318M Units _[°C]

1 lb/ft3₌ _kg/m3

Convert the unit weight in lb/ft3_{to kg/m}3 _{using the factor 16.02 and round to three (3) significant}

digits. (Show to the nearest 5 kg/m3_{for values in the 'ones' digit.)}

Example: 144 x 16.02 = 2307 à use 2310 kg/m3

Conversion to SI Units [kg/m3_]

Equivalent SI

(77)

155 2483.10 2480 2480

NOTE:

(78)

4a. CONCRETE STRESS

1000 psi = 6.895 MPa

Rule:

in.-lb Units [psi]

50 0.3448 0.34 0.35 70 0.4827 0.48 0.5 80 0.5516 0.55 0.55 100 0.6895 0.69 0.7 125 0.8619 0.86 0.9 150 1.0343 1.0 1.0 200 1.3790 1.4 1.4 225 1.5514 1.6 1.6 250 1.7238 1.7 1.7 260 1.7927 1.8 1.8 300 2.0685 2.1 2.1 400 2.7580 2.8 2.8 500 3.4475 3.4 3.5 700 4.8265 4.8 5.0 800 5.5160 5.5 5.5 1,000 6.8950 6.9 7.0 1,200 8.2740 8.3 8.3 2,000 13.7900 14 14 2,500 17.2375 17 17 3,000 20.6850 21 21 3,500 24.1325 24 24 4,000 27.5800 28 28 4,440 30.6138 31 31 4,500 31.0275 31 31 5,000 34.4750 35 35 6,000 41.3700 40 40 8,000 55.1600 55 55 10,000 68.9500 70 70 11,000 75.8450 75 75 12,000 82.7400 85 85 15,000 103.4250 105 105

4b. MODULUS OF ELASTICITY

1000 psi = 6.895 MPa

Rule:

in.-lb Units [psi]

29,000,000 199955 200000 200 000

Convert psi to MPa using the factor 0.006895 and round to two (2) significant digits (except for concrete stress levels 5000 psi and above round to the nearest 5 MPa - see shaded equivalents below).

Example 1: 4440 psi = 4.44 x 6.894757 = 30.61 à use 31 MPa Example 2: 12,000 psi = 12 x 6.894757 = 82.737 à use 85 MPa

Conversion to SI

Units [MPa] Equivalent SI Units [MPa] ACI 318M Units [MPa]

Convert psi to MPa using the factor 0.006895 and round to 2 significant digits.

Therefore : 29,000,000 psi = 29,000,000 x 6.895 / 1000 = 199,995 à use 200,000 MPa

Conversion to SI

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5. EMPIRICAL EQUATIONS FOR CONCRETE WITH MULTIPLIERS OF

1/12.043 or 0.08304

Rule:

Conversion of commonly used multipliers of :

in.-lb Units 0.1 0.0083 0.0083 0.0083 0.6 0.0498 0.050 0.050 0.75 0.0623 0.062 0.062 1 0.0830 0.083 0.083 1.25 0.1038 0.10 0.10 1.33 0.1104 0.11 0.11 1.7 0.1412 0.14 0.14 1.9 0.1578 0.16 0.16 2 0.1661 0.17 0.17 2.66 0.2209 0.22 0.22 3 0.2491 0.25 0.25 3.3 0.2740 0.27 0.27 3.5 0.2906 0.29 0.29 4 0.3322 0.33 0.33 5 0.4152 0.42 0.42 6 0.4982 0.50 0.50 6.7 0.5564 0.56 0.56 7 0.5813 0.58 0.58 7.5 0.6228 0.62 0.62 8 0.6643 0.66 0.66 10 0.8304 0.83 0.83 12 0.9965 1.0 1.0 15 1.2456 1.2 1.2 16 1.3286 1.3 1.3 20 1.6608 1.7 1.7 25 2.0760 2.1 2.1 33 2.7403 2.7 2.7 40 3.3216 3.3 3.3 50 4.1520 4.2 4.2 65 5.3976 5.4 5.4 100 8.3040 8.3 8.3 160 13.2864 13 13 57000 4733.2800 4700 4700

To convert the multipliers of use the factor 1/12.043 (or 0.08304) and round to two (2) significant digits. Show constants or multipliers in front of equation.

Conversion to SI

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Not included: A 53 - 02, A 307 - 04, A 500 - 03, A 501 - 01 A 185 - 02 and A 497 - 02 refer to A 82

A 185 - 02 and A 497 - 02 refer to A 82

A 775 - 01 and A 934 - 03 refer to A 615, A 706, and A 996 A 884 - 02 refers to A 82, A 185, A 496, and A 497

in.-lb Units [ksi] SI Units [MPa] ASTM A 36/ A 36M - 03 Plate, Bar Summary

36 250 and Shapes 36 250

ASTM A 82 - 02 WWR 40

56 385 42 290

65 450 46 315

70 485 50

ASTM A 242/ A 242M - 03 Plate, Bar 55 380

42 290 and Shapes 56 385 46 315 60 50 70 485 ASTM A 416/ A 416M - 02 Strand 75 520 250 1725 150 1035 270 1860 235 1620 ASTM A 421/ A 421M - 02 Strand 240 1655 235 1620 250 1725 240 1655 270 1860 250 1725

ASTM A 496 - 02 WWR 1. ASTM is in the process of

70 485 changing to 280.

ASTM A 572/ A 572M - 03 Plate, Bar 2. Steel plate uses 345 and concrete 42 290 and Shapes reinforcement uses 350: Use 350.

50 3. Steel plate uses 415 and concrete

55 380 reinforcement uses 420: Use 420.

60

65 450

ASTM A 588/ A 588M - 03 Plate, Bar 42 290 and Shapes 46 315 50 ASTM A 615/ A 615M - 03 Rebar 40 280 60 420 75 520 ASTM A 706/ A 706M - 03 Rebar 60 420 ASTM A 722/ A 722M - 98 Rebar 150 1035 ASTM A 767/ A 767M - 00 Rebar 40 50 350 60 420

6a. STEEL GRADES IN REFERENCED ASTMs FOR REINFORCING BARS, WELDED WIRE

REINFORCEMENT, STEEL STRANDS, AND STRUCTURAL STEEL PLATES & SHAPES

Conversion of reinforcing steel grades per ASTMs listed in the 318: (Minimum yield strengths)

in.-lb Units

[ksi] SI Units [MPa]

280(300)1

350(345)2

420(415)3

345 4

415 4 _4._Red_{values shall not be used.}

345 4

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75 520

ASTM A 992/ A 992M - 03 Plate, Bar

50 and Shapes 65 450 ASTM A 996/ A 996M - 03 Rebar 40 280 50 350 60 420 345 4

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6b. STEEL STRESSES NOT REFERENCED IN ASTMs

1000 psi = 6.895 MPa

significant digits (except for 5000 psi and above round up to the nearest 5 MPa) 3,000 20.69 21 21 10,000 68.95 70 70 18,000 124.11 125 125 20,000 137.90 140 140 30,000 206.85 205 210 52,000 358.54 360 360 80,000 551.60 550 550 100,000 689.50 690 700 125,000 861.88 860 860 275,000 1896.13 1895 1900 Rule: Convert psi to MPa using the factor 0.006895; round to 2

Example: 80,000 psi = 80000 x 0.006895 = 551.6 à use 550 MPa

in.-lb Units

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7a. REINFORCING BAR SIZE

in.-lbs Units (SI) Units

ACI 318M No. 3 No. 10 No. 10 No. 4 No. 13 No. 13 No. 5 No. 16 No. 16 No. 6 No. 19 No. 19 No. 7 No. 22 No. 22 No. 8 No. 25 No. 25 No. 9 No. 29 No. 29 No. 10 No. 32 No. 32 No. 11 No. 36 No. 36 No. 14 No. 43 No. 43 No. 18 No. 57 No. 57

7b. STEEL STRAND SIZE*

in.-lbs Units [in.] SI Units [mm]

ASTM Designated Strand No. 0.250 6.4 6 6 0.313 7.9 8 8 0.375 9.5 9 9 0.438 11.1 11 11 0.500 12.7 13 13 0.600 15.2 15 15

**7c. REINFORCING BAR SIZE* (HIGH-STRENGTH)**

in.-lbs SI Units

ACI 318M

in.-lbs SI Units

Units [in.] [mm] Units [in.] [mm]

Type I (Plain) Bar Type II (Deformed) Bar

--- --- --- 5/8 15 3/4 19 19 3/4 20 7/8 22 22 --- ---1 25 25 1 26 1-1/8 29 29 --- ---1-1/4 32 32 1-1/4 32 1-3/8 35 35 1-3/8 36 1-3/4 46 2-1/2 65

Conversion of reinforcing steel bar sizes per ASTM:

ASTM A 615/ A 615M–03

Conversion of steel strand sizes per ASTM:

ACI 318M ASTM A 416/ A 416M–02

Conversion of steel strand sizes per ASTM:

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*Where ACI 318 gives limits on general 'Tendon' sizes, an exact conversion of shall be made. (Example; 5/8" tendon will be converted to 16 mm)

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8. STEEL WIRE REINFORCEMENT

in.-lb Units SI Units

Size Diameter [in.] Size Calculated Calculated

Diameter [mm] W 0.5 0.080 0.005 2.03 3.23 MW 5 2.50 5.00 D 1 0.113 0.01 2.87 6.45 W 1.2 0.124 0.012 3.15 7.74 W 1.4 0.134 0.014 3.40 9.08 MW 10 3.60 10.00 W 2 or D 2 0.160 : 0.159 0.02 4.06 12.90 MW 15 4.40 15.00 W 2.5 0.178 0.025 4.52 16.13 W 2.9 0.192 0.029 4.88 18.70 D 3 0.195 0.03 4.95 19.35 MW 20 5.00 20.00 W 3.5 0.211 0.035 5.36 22.58 MW 25 or MD 25 5.60 25 W 4 or D 4 0.226 : 0.225 0.04 5.74 25.81 W 4.5 0.239 0.045 6.07 29.03 MW 30 or MD 30 6.20 30 W 5 or D 5 0.252 : 0.250 0.05 6.40 32.26 MW 35 or MD 35 6.70 35 W 5.5 0.265 0.055 6.73 35.48 W 6 or D 6 0.276 0.06 7.01 38.71 MW 40 or MD 40 7.10 40 D 7 0.299 0.07 MW 45 or MD 45 7.60 45 MW 50 or MD 50 8.00 50 W 8 or D 8 0.319 0.08 8.10 51.61 MW 55 or MD 55 8.40 55 D 9 0.338 0.09 8.59 58.96 MW 60 or MD 60 8.70 60 W 10 or D 10 0.357 : 0.356 0.10 9.07 64.52 MW 65 or MD 65 9.10 65 MW 70 or MD 70 9.40 70 D 11 0.374 0.11 9.50 70.97 W 12 or D 12 0.391 : 0.390 0.12 9.93 77.42 MW 80 or MD 80 10.10 80 D 13 0.406 0.13 10.31 83.87 MW 90 or MD 90 10.70 90 W 14 or D 14 0.422 0.14 10.72 90.32 D 15 0.437 0.15 11.10 96.77 MW 100 or MD 100 11.30 100 W 16 or D 16 0.451 0.16 11.46 103.25 D 17 0.465 0.17 11.81 109.68 W 18 or D 18 0.479 : 0.478 0.18 12.17 116.13 MW 120 or MD 120 12.40 120 D 19 0.491 0.19 12.47 122.58 W 20 or D 20 0.505 : 0.504 0.20 12.83 129.03 MW 130 or MD 130 12.90 130 D 21 0.517 0.21 13.13 135.48 W 22 or D 22 0.529 0.22 13.44 141.90 D 23 0.541 0.23 13.74 148.39

ASTM does not have a direct SI equivalent (ASTM sizes and dimensions not shaded); Table below shows in.-lb unit sizes with calculated SI dimensions and suggested SI sizes (shaded). Use the nearest SI size as appropriate.

ASTM A 82–02 (W, MW) and ASTM A 496-02 (D, MD) Area [in.2_]

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ACI Engineering Page 86 12/01/2017 W 24 or D 24 0.533 : 0.553 0.24 14.05 154.80 D 25 0.564 0.25 14.33 161.29 W 26 or D 26 0.575 0.26 14.61 167.70 D 27 0.586 0.27 14.88 174.19 W 28 or D 28 0.597 0.28 15.16 180.60 D 29 0.608 0.29 15.44 187.10 W 30 or D 30 0.618 0.3 15.70 193.50 W 31 or D 31 0.628 0.31 MW 200 or MD 200 15.95 200 W 45 or D 45 0.757 0.45 MW 290 or MD 290 19.22 290

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Metrication Conversion Guide for 318M and 318S

2. Orange shading: equivalence number for ACI 318M document.

The values stated in either inch-pound or SI units are to be regarded separately as standard. The values stated in each system are not exact equivalents; therefore, each system must be used independently of the other, without combining

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ACI Engineering Page 88 12/01/2017 and round to 2 significant digits.

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and round to 2 significant digits.

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ACI Engineering Page 92 12/01/2017 and round to two (2) significant digits (except for

concrete stress levels 5000 psi and above round to the nearest 5 MPa - see shaded equivalents

and round to 2 significant digits.

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ACI Engineering Page 94 12/01/2017 Nearest 5 MPa 250 280 290 315 350 380 385 420 485 520 1035 1620 1655 1725 1860

2. Steel plate uses 345 and concrete 3. Steel plate uses 415 and concrete

6a. STEEL GRADES IN REFERENCED ASTMs FOR REINFORCING BARS, WELDED WIRE

REINFORCEMENT, STEEL STRANDS, AND STRUCTURAL STEEL PLATES & SHAPES

(Minimum yield strengths)

ACI 318M Units [MPa]

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ACI Engineering Page 95 12/01/2017 ACI 318M 15 20 ---26 ---32 36 46 65

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ACI Engineering Page 96 12/01/2017 SI Units MW 5 MW 5 MW 10 MW 15 MW 15 MW 20 MW 25 MW25 or MD25 MW 30 MW 30 or MD 30 MW 35 MW 40 or MD 40 MD 45 MW 50 or MD 50 MD 60 MW 65 or MD 65 MD 70 MW 80 or MD 80 MD 80 MW 90 or MD 90 MD 100 MW 100 or MD 100 MD 100 MW 120 or MD 120 MD 120 MW 130 or MD 130 MD 130

ASTM does not have a direct SI equivalent (ASTM sizes and dimensions not shaded); Table below shows in.-lb unit sizes with calculated SI dimensions and suggested SI sizes (shaded). Use the nearest SI size as appropriate.

ACI 318 M - Suggested Size

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MW 200 or MD 200 MW 290 or MD 290

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