analisa teknis girder wika beton - Ngoro - Mojokerto.pdf

PROPOSAL TEKNIS PC I GIRDER POSTENSION NONSEGMENTAL

AnalisaTeknis Jembatan Ngrame Mojokerto PC - I Girder L – 16.6 m; H – 90 cm; CTC – 180 cm No. Job: 08004 No. Rev: 00

Innovation and Trust

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PROPOSAL TEKNIS PC I GIRDER POSTENSION NONSEGMENTAL

AnalisaTeknis Jembatan Ngrame Mojokerto PC - I Girder L – 16.6 m; H – 90 cm; CTC – 180 cm No. Job: 08004 No. Rev: 00

MENYETUJUI

(

)

Proposal ini berlaku apabila telah mendapat persetujuan dari konsultan/Owner. Proposal ini berlaku hanya untuk produk-produk Wika beton DISETUJUI : TANGGAL :

Ir. M. Zulkarnain,MM,.IPM Manajer Teknik

DIPERIKSA : TANGGAL :

Ir. Gambiro Kabag Teknik

DIBUAT : TANGGAL :

Verly Widantoro, ST. Staf Teknik

PROPOSAL TEKNIS

BALOK POST TENSION NON SEGMENTAL JEMBATAN NGRAME MOJOKERTO PROSPEKTUS Proposal teknis ini dibuat untuk konstruksi Proyek Jembatan Ngrame Mojokerto yaitu pada bagian konstruksi balok jembatan. Balok I girder dirancang menggunakan sistem post tension monolith (non segmental) yaitu merupakan balok yang terdiri dari satu segmen yang kemudian distressing atau diberi gaya prategang pada kondisi kekuatan beton balok telah mencapai kuat tekan yang ditentukan(post tensioning). Hal ini dimaksudkan agar saat balok distressing, balok telah mampu menahan gaya prategang. Sistim pabrikasi balok I girder precast memiliki keuntungan dari segi waktu pelaksanaan proyek yang lebih cepat dan terkontrolnya mutu dan kualitas produk balok sesuai spesifikasi yang direncanakan. Proposal ini dapat dilaksanakan setelah disetujui oleh konsultan atau owner. PROYEK Nama Proyek Lokasi

: Jembatan Ngrame Mojokerto : Mojokerto, Jawa Timur REFERENSI DISAIN

Referensi disain yang digunakan dalam menyusun analisa ini adalah : - Pembebanan berdasarkan Bridge Management System (BMS). - Material berdasarkan standar Japan Industrial Standard (JIS) dan American Society for Testing and Material (ASTM). SPESIFIKASI DISAIN Pelat Jembatan : - Mutu Beton - Tebal pelat Pelat Deck : - Mutu Beton - Tebal Pelat Deck Aspal : - Tebal Aspal Balok : - Post tension Girder Konfigurasi Balok - Tulangan -

Strand

= K-300 = 27 cm (termasuk Pelat dek) = K-350 = 7 cm = 5 cm = H-90cm. = L=16.6m; Ctc balok 1,85m; K-500 = D-13 fy = 400 MPa (tulangan deform). φ 10 U-24 (tulangan polos) = φ 12,7 mm (grade 270, low relaxation)

ANALISA TEKNIS Analisa yang dilakukan adalah perhitungan teknis untuk perencanaan balok I girder Pretension nonsegmental terhadap beban kerja rencana berdasarkan pembebanan Bridge Management System (BMS). Analisa teknis meliputi penentuan konfigurasi tendon dan jumlah strand yang dibutuhkan balok, penulangan balok terhadap gaya dalam yang bekerja dan analisa lendutan yang terjadi. Penggunaan konfigurasi tendon dengan konfigurasi strand pada posisi tertentu yang diberi jacking force akan mengakibatkan tegangan pada penampang balok, tegangan tersebut di check terhadap tegangan yang diijinkan pada kondisi saat transfer dan saat service balok. Pada analisa teknis juga dilakukan kontrol lendutan yang terjadi terhadap lendutan yang diijinkan baik pada saat service. KESIMPULAN Kesimpulan analisa teknis adalah sebagai berikut : PC I Girder Non Segmental Post tension L16,6m Mutu Beton : K-500 Dimensi Balok : Standar Wika Beton H=90 Rancang Jembatan : Panjang Balok 16.6m ctc185cm Jumlah Segmen : 1 Segmen (16.6m) Skiew Jembatan : 0° Strand : φ 12,7 mm (grade 270, low relaxation) Jacking Force : 75% dari Ultimate Tensile Strength (UTS) Kekuatan Beton saat jacking force : 80% dari fc’ Konfigurasi tendon & Strand Tendon

Jumlah Strand

1 2

10 12

Posisi tendon (mm) Tepi Tengah 500 200 250 100

Dari hasil analisa Teknis : φ Mn : 326.38 ton.m Mu : 276.53 ton.m Rasio φMn / Mu = 1.18 Balok mampu menahan beban rencana. Lendutan akibat gara prategang (chamber ) sebesar 2.26 cm ( ↑ ke atas) Lendutan akibat beban hidup 0.78cm < lendutan ijin syarat L/800=2.0cm (↓ ke bawah) Lendutan saat service 1.48cm < lendutan ijin syarat L/360=4.44 mm ( ↑ ke atas )

Post L16.6-I90-185 MONOLITH

RESUME OF PC I GIRDER TECHNICALLY CALCULATION 1. BEAM SPECIFICATION Span Beam Height ( H ) Distance ctc of beam ( s ) Slab thickness Beam Compressive strength Slab Compressive strength

= = = = = =

Segment Arrangement Beam Segment 1 Length (m) 5.00 Additional length at the end of beam Total length of the beam Total beam weight 2. STRESSING Nos of PC Strand = Strand configuration

22

16.00 90.00 185.00 27.00 KK-

m (beam length = cm cm cm (include RC Flat) 500 300

2 6.00 = = =

3 5.00 0.3 16.60 11.20

m m ton

strand φ

12.7

mm (PC Strand 270 grade, low relaxation)

No.

number

H strand bottom (cm)

Tendon

strand

edge

mid

1

0

0

0

2

0

0

0

3

0

0

0

4

10

50

20

5

12

25

10

total

22

36.36

14.55

4 0.00

Jacking Force UTS of Strand Total Losses fc initial

5 0.00

16.60 m)

= = = =

6 0.00

75%

7 0.00

UTS

19000.00 kg/cm2 23.12% 80.0%

fc'

3. LOADING 1. Dead Load a. Precast Beam = 0.64 t/m b. Slab = 1.20 t/m Slab thickness = 27.0 cm (include RC Flat) c. Asphalt = 0.20 t/m Asphalt thickness = 5.0 cm d. Diaphragm = 0.42 ton for 1 diaphragm No. Diaphragm 3 pcs equivalent load = 0.08 t/m 2. Live Load Taken from "Bridge Management System (BMS)" D load a. Dynamic Load Allowance (DLA) = 1.4 for span length <= 50m b. Knife Edge Load (KEL) = 4.40 ton/m' c. Distribution Factor (DF) = 1.00 d. Distribution Load q= 0.80 t/m2 which : q = 0,8 t/m' For Span <= 30m q = 0,8 x (0,5 + 15/span) t/m' For Span > 30m e. Live Load Distribution load : q' = DF x q x s = 1.48 ton/m' Line Load : p' = DF x DLA x KEL x s = 11.40 ton

CALCULATION RESUME


4. BEAM SUPPORT REACTION ultimate total = 1,2*Beam + 1,3*Slab + 2*Asphalt + 1,2*Diaphragm + 2*LL ( Bridge Management System, Vol.1-Page 2-6 ) Beam support reaction : a. Dead Load = 5.15 ton b. Additional Dead Load = 11.85 ton c. Live Load = 23.24 ton Ultimate support reaction =

69.13

5. CONTROL OF BEAM STRESSES 1. Initial Condition Middle span position top stress = bottom stress = 2. Service Condition Middle span position top stress = bottom stress = 6. CONTROL OF BEAM DEFLECTION Deflection at the middle of beam span 1. Chamber due stressing initial erection final 2. Deflection due live load 3. Total deflection at service

ton

2 13.47 kg/cm 2 171.84 kg/cm

required required

> <

2 -14.88 kg/cm 2 190.21 kg/cm

2 147.80 kg/cm 2 -8.58 kg/cm

required required

< >

2 172.92 kg/cm 2 -33.06 kg/cm

= = = = =

-1.58 -2.41 -2.26 0.78 -1.48

cm cm cm cm, required < L/800 = cm, required < L/360 =

2.00 cm 4.44 cm

7. MOMENT CAPACITY OF BEAM Mult = 1,2*Beam+1,3*Slab+2*Asphalt+1,2*Diapraghm+2*LL φ Mn Ratio, φ Mn / Mu (>1)

CALCULATION RESUME

= = =

276.53 t.m 326.38 t.m 1.18


TECHNICAL CALCULATION OF SEGMENTAL PC I BEAM FOR BRIDGE SPAN (ctc) L = 16.00 M I. DATA

0.3

L=

Beam length Beam spacing (s) Concrete Slab thickness Asphalt thickness RC Flat thickness

16.00 M 16.60 185.00 27.00 5.00 7.00

= = = = =

0.3

m ( edge anchor to edge anchor : 16.3 cm cm (include RC Flat) cm A cm

m)

tfl-1 tfl-2 Cross Section

H A B tweb

= = = =

90 35 65 17

cm cm cm cm

tfl-1 tfl-2 tfl-3 tfl-4

= = = =

7.5 7.5 10 12.5

tweb

cm cm cm cm

H

tfl-3 tfl-4 B

II. MATERIAL 2.1 Concrete Beam

Slab

Compressive strength 500 300 at service * fc' = (0.76+0.2*log(σbk/150))*σbk = 432.3 246.1 at initial ( 80% ), fc'i = 345.8 196.8 Allowable stress at initial ………..(AASHTO 1992, Chapt. 9.15.2.1-Design) Compressive 0.55 * fc'I = 190.2 108.3 0.80 * Sqrt(fc'I) = Tensile 14.9 11.2 Allowable stress at service ………. (AASHTO 1992, Chapt. 9.15.2.2-Design) Compressive 0.40 * fc' = 172.9 98.4 1.59 * Sqrt(fc') = Tensile 33.1 24.9 Modulus of elasticity Ec = 313952.2 236864.0 Eci = 280807.3 Modulus rupture fr = 41.2 31.1 Note : * Pedoman Beton 1988, Chapter 3

[kg/cm2] [kg/cm2] [kg/cm2] [kg/cm2] [kg/cm2] [kg/cm2] [kg/cm2] [kg/cm2] [kg/cm2] [kg/cm2]

2.2 Prestressing Cable [Uncoated stress relieve seven wires strand] ( ASTM A 416 Grade 270 Low Relaxation or JIS G 3536 ) dia : - Diameter strand 12.7 [mm] 2 - Eff. Section area Ast : 0.9871 [cm ] 2 - Modulus of elasticity Es : 1.96E+06 [kg/cm ] 2 - Ultimate tensile strength fu : 19000 [kg/cm ] 2.3 Steel Reinforcement - Diameter - Eff. Section area - Modulus of elasticity - Yield stress

dia Ast Es fy

: 13 [mm] 2 : 1.267 [cm ] 2 : 2.10E+06 [kg/cm ] : 3900 [kg/cm2]

page 1 / 13


III. SECTION ANALYSIS 2

Remark : Ep 1 = 313952 Ep 2 = 236864

2

kg/cm kg/cm 2

5

[Girder] [Slab]

4 Ya

n = Ep 1 / Ep 2 n= 1.33

Ya' 1

3

Yb

2

base line

Yb'

1

PRECAST BEAM

COMPOSITE BEAM

3.1 Precast Beam [ in cm ]

Zone Section

6 5 4 3 2 1 Total

Width

Area

Yb

cm

cm

cm

0.00 262.50 195.00 892.50 410.00 812.50 2572.50

90.0 82.5 75.0 22.5 12.5 0.0

90.0 86.3 79.2 48.8 16.5 6.3 36.3

0 22641 15441 43509 6775 5078 93444

0 1230 878 204996 3026 10579 220710

0 654306 358187 137805 160732 734867 2045897

Area

Level

Yb

Area*Yb

Io

Area*d

Bottom

Upper

cm

0.0 7.5 7.5 52.5 10.0 12.5 90.0

65.0 35.0 17.0 17.0 65.0 65.0

35.0 35.0 35.0 17.0 17.0 65.0

2

Area*Yb

2

Level

Height

3

Io cm

Area*d 4

cm

4

Ix cm

4

0 655537 359065 342801 163758 745446 2266607

3.2 Composite Beam [in cm ] Zone Height

2 1 Total

3.3

Width

2

3

2

4

4

cm

cm

97.0 90.0 0.0

107.0 93.5 36.3 73.4

298690 7078 93444 399212

Area (cm )

Ya (cm)

Yb (cm)

Ix (cm )

Wa (cm )

Wb (cm )

2572.50 5439.70

53.7 43.6 16.6

36.3 73.4

2266607 9078357

42228 208165 546515

62400 123702

Bottom

Upper

cm

20.0 7.0 90.0 117.0

185.0 19.0 65.0

185.0 19.0 35.0

2791.50 75.70 2572.50 5439.70

cm

cm

93050 410 2266607 2360067

Ix cm4

cm

Section

3153620 30620 3534050 6718290

3246669 31030 5800657 9078357

Resume [in cm ] 2

Description

Precast Beam Composite Beam

[composite] [precast]

4

3

3

IV. Loading 4.1 Dead Load Design Carracteristics……. Bridge Management System ( BMS ), Vol.1 Chapter 2.3.1 1. Specific Gravity of Precast Beam = 2.5 ton/m3 ( γPB ) 2. Specific Gravity of Slab = 2.4 ton/m3 ( γS ) 3. Specific Gravity of Asphalt = 2.2 t/m3 ( γasp ) 4. Specific gravity of Diaphragm = 2.4 ton/m3 ( γdiaph ) a. Precast Beam

q1 = Area x γPB x

2.5

=

0.6431

[t/m']

b. Slab

q1 = 0.2573 q2 = Hslab x s x γs q2 = 0.2700 x 1.85 q3 = tasp x s x γasp

x

2.4

=

1.1988

[t/m']

c. Asphalt

q3 = 0.05 1.85 x x p = Volume of diaph. x γdiaph

2.2

=

0.2035

[t/m']

d. Diaphragm

0.15 2.4 x q4 (q ek = p*n/span)

=

0.4234 0.0794

[ton] [t/m']

p = no. diaph.

1.68 3

x 0.7 pcs

x

=

page 2 / 13


4.2 Live Load Taken from "Bridge Management System (BMS)" D load a. Dynamic Load Allowance [DLA]

b. Knife Edge Load (KEL) c. Distribution Factor (DF) d. Distribution Load q = 0.80 t/m2

…… Vol.1, Chapter 2.3.2-Traffic Loads

DLA = 1 + 0,4 = 1.40 DLA = 1 + (0.0025*span+0.175) DLA = 1 + 0,3 = 1.30 = 4.40 = 1.00

which :

q = 0,8 t/m' q = 0,8 x (0,5 + 15/span) t/m'

e. Live load - Distribution load q' = DF x q x s x = 1.00 0.80 x 1.85 - Line load p' = DF x DLA x KEL x s 1.00 1.400 x 4.400 x x

1.85

Span <= 50 m 50 < Span < 90 m Span >= 90 m ton/m'

for

Span <= 30 m Span > 30 m

=

1.48

ton/m'

=

11.40

ton

Sec 3-3 11.00 17.69 17.69 32.97 5.60 2.18 40.75 40.70 39.17 79.87 138.31 237.64

Sec 4-4 16.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Sec 5-5 16.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Sec 6-6 8.00 20.58 20.58 38.36 6.51 2.54 47.41 47.36 45.58 92.94 160.94 276.53

V. MOMENT ANALYSIS [in ton-meter ] Type

Description

DL

Precast beam Subtotal Slab ADL Asphalt Diaphragm Subtotal LL Distribution load Line load Subtotal Total (DL + LL) Ultimate total

Mid span 20.58 20.58 38.36 6.51 2.54 47.41 47.36 45.58 92.94 160.94 276.53

Sec 1-1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Sec 2-2 5.00 17.69 17.69 32.97 5.60 2.18 40.75 40.70 39.17 79.87 138.31 237.64

(m)

Ultimate total = 1,2*Beam+1,3*Slab+2*Asphalt+1,2*Diaphragm+2*LL ( Bridge Management System, Vol.1-Page 2-6 ) Note : DL = Dead Load ADL = Additional Dead Load LL = Live Load

VI. SHEAR ANALYSIS [in ton ] Type

Description

Precast beam Subtotal Slab Asphalt ADL Diaphragm Subtotal Distribution load LL Line load Subtotal Total (DL + LL) Ultimate total DL

span

Sec 1-1 0.00

Sec 2-2 5.00

Sec 3-3 11.00

Sec 4-4 16.00

Sec 5-5 16.00

Sec 6-6 8.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 5.70 5.70 5.70 11.40

5.15 5.15 9.59 1.63 0.64 11.85 11.84 11.40 23.24 40.23 69.13

1.93 1.93 3.60 0.61 0.24 4.45 4.44 7.83 12.27 18.65 33.05

-1.93 -1.93 -3.60 -0.61 -0.24 -4.45 -4.44 -7.83 -12.27 -18.65 -33.05

-5.15 -5.15 -9.59 -1.63 -0.64 -11.85 -11.84 -11.40 -23.24 -40.23 -69.13

-5.15 -5.15 -9.59 -1.63 -0.64 -11.85 -11.84 -11.40 -23.24 -40.23 -69.13

0.00 0.00 0.00 0.00 0.00 0.00 0.00 -5.70 -5.70 -5.70 -11.40

Mid

(m)

ultimate total = 1,2*Beam + 1,3*Slab + 2*Asphalt + 1,2*Diaphragm + 2*LL ( Bridge Management System, Vol.1-Page 2-6 )

page 3 / 13


VII. PRESTRESSING CABLE 7.1 Cable Profile [in: cm ] ten-

Nos

don

strand

edge

middle

cm

1 2 3 4 1

0 0 0 10 12 22

0.00 0.00 0.00 50.00 25.00 36.36

0.00 0.00 0.00 20.00 10.00 14.55

0.987 0.987 0.987 0.987 0.987

total

profile

Asp 2

fu

%

Jacking Force

75% 75% 75% 75% 75% 75%

0.00 0.00 0.00 140661.75 168794.10 309455.85

2

(kg)

kg/cm

19000 19000 19000 19000 19000

Parabolic curve : Y = AX Y= A= B= C=

2

+

BX +

C

Average of Strand's position vertically from the bottom of beam ( Value for Y axis ) Constanta : ( (Ymiddle + Yedge)/(L/2)2) Constanta : ( L x A ) Average of strand's position when the parabolic curve reach the Y axis X + 0.3636364 A = 0.003285 Y = 0.003285 X2 + -0.05354 B = -0.05354 tg o = 0.00657 X + -0.05354 Eccentricity [e] Yb - Ys = 21.78 cm Note : Jacking Force = Nos x Asp x Fu x (Tension Persentation) Nos = Number of Strand Yb = Distance of Neutral Axis from the bottom of non composite beam ( Chapter 3.3 - Resume ) Ys = Distance of tendon from the bottom of the beam at the middle span ( Chapter 7.1,Cable Profile-middle)

7.2 Initial Jacking Force Check for two condition at initial for mid span Top stress

σ top = Pi/Ac - Pi.e/Wa + Mbs/Wa Pi

Bottom Stress

σ bot = Pi/Ac + Pi.e/Wb - Mbs/Wb Pi Result :

at service for mid span Top stress σ top = Bottom Stress σ bot =

Pi

<=

Pe/Acp - (Pe.e-Mbp)/Wap + Mbh/Wac Pe Pe/Acp + (Pe.e-Mbp)/Wbp - Mbh/Wbc Pe Result : Pe >=

-14.88 500.82 190.21 302.53

kg/cm 2 ton kg/cm 2 ton

>= <= <= <= 302.53

ton

[3]

<= >= >= <= 197.72

172.92 161.07 -33.06 197.72 ton

kg/cm 2 ton kg/cm2 ton [6]

(

-14.88

)

-33.06

)

[1] [2]

[4] [5]

Assumption : Loss of Prestress assumption long term 23.117% (must be = 23.117% ) From eq. [3] and eq. [6], gradually stressing is not needed used prestressing cable φ 12.7" Pi = = 309456 kg Pe = 76.9% 309455.85 = 237918 kg Note : Pi = Initial Prestress Force Wa = Modulus Section for Top section of Precast Beam Mbs = Moment due to Self Weight e = eccentricity Wb = Modulus Section for Bottom section of Precast Beam Pe = Effective Prestress force Wac = Modulus Section for Top section of composite Beam Mbp = Moment due to concrete Weight (Precast Beam + Slab + Diapraghm)…(Chapt. V-Moment Analysis) Wbc = Modulus Section for Bottom section of composite Beam Wap = Modulus Section for Top section of Precast Beam Wbp = Modulus Section for Bottom section of Precast Beam Mbp = Moment due to additional Load ( Asphalt + Live Load )…… (Chapter 5-Moment Analysis) page 4 / 13


7.3 Losses of Prestress 1. Losses of Prestress (Short Term) a. Friction Friction cable and duck caused tensile at initial is not same tensile in ending section, which the deferential of tensile can be calculated as follow : -( μ *α + k *x) where : Px = Po * e ……………. ( AASHTO 1992, Chapt. 9.16.1 ) Px = Prestress force at section distance x from tensile point. Po = Jacking force ( tensile force at anchor, initial) μ = friction coefficient = 0.20 (for grouting tendon in metal sheating, 7 wire strand) α = Change of cable angle from tensile point to x section = 2 * arctg ( 0.00657 x + -0.05354 ) = 0.111 rad k = Wobble coefficient =0.003 (for grouting tendon in metal sheating, 7 wire strand) x = Distance from tensile point to x section 16.60 m If tensile of strand is taken 75% from Ultimate Tensile Stress, Po (Jacking Force) = 75% 0.9871 19000 = 14066.18 kg and value of tensile strand at end beam as follow : Px = 13089.24 kg b. Anchor slip Slip is occur after anchoring of pc strand is being held/restraint in the end of beam. Because of this friction, losses can not evenly distributed at the overall length of beam. It can calculated by formula : x = @sqrt(d*As*Es/m) where: d = draw-in, assumption = 8 mm 2 As = eff. Section area = 0.9871 cm m = loss of prestress per length m = (Po-P) / L = 0.59 kg/cm' So, x = 16.22 m Tensile force at distance 16.22 m as : P =Maximum tensile force = 13094.21 kg c. Elastic Shortening ( ES ) Losses due elastic shortening ES = (Kes*Es*fcir/Ec)*As ……………( ACI 318-95, Chapt. 18.6 ) where: Kes = 0.50 (for postensioned) As = 0.9871 cm2 fcir = concrete stress at centre gravity of prestressing force immediately after transfer 2 fcir = (fbottom-ftop) * (H-ed)/H + ftop = 146.25 kg/cm ES = 450.62 kg 2. Losses of Prestress ( Long Term ) a. Shrinkage ( SH ) SH = 8,2*e-6*Ksh*ES*(1-0,06*V/S)*(100-RH) = 198.91 kg ….. (ACI 318-95, Chapt. 18.6) Ksh = 0.68 (without moist curing) 2 V/S = 3.81 (ratio area/perimeter) Area = 2572.50 cm perimeter= 675.43 cm RH = 80.00 b. Creep

( CR ) CR = Kcr*(Es/Ec)*(fcir-fcds)

……… ( ACI 318-95, Chapt.18.6 )

Where :

Kcr = fcir = fcds = fcds = Msd = Ig = CR =

1.60 (for postensioned member) stress at center point prestress force, initial condition stress at center point prestress force, permanent dead load. 2 Msd (e) / Ig fcds = 45.56 kg/cm Moment due to all superimposed permanent dead loads applied after prestressing Moment of inertia of gross concrete section at the cross section considered. 992.79 kg

page 5 / 13


c. Steel Relaxation ( RE ) RE = [ Kre - J*(SH+CR+ES) ] *C

…………… ( ACI 318-95, Chapt. 18.6 )

where :

Kre = J = C =

5000 0.04 0.57

RE =

162.91

(for 270 grade, low relaxation strand) (for 270 grade, low relaxation strand) (to refer fpi/fpu, fpi=stress after friction and anchor slip) fpi = 12620 kg fpi/fpu = 0.66

kg GRAPHICS OF LOSS OF PRESTRESS STAGE

1. Due Friction 14066

13089 2. Due Slip (chek effect of prestress losses at mid span, wheather of not) 14066 13094 12122 12620 13578 16.22

m

8.30

m

13089

3. Due Elastic Shortening 14066 13094 12122

13089 12620

11672

12169 8.30

13578 12644 13127

12639

m

4. Long Term Losses 14066 13094 12122

13089 12620 12169

11672

13578 12644 13127

10814

12639

11772 11284

10317

16.22 m 8.30 m Stress force at X =

8 22 - Initial = 22 - Service = 22 Total losses for long term - Jacking Force =

m (mid span) total : x 14066.18 x 12619.69 x 10814.46 23.12 %

= = =

309455.9 kg 277633.3 kg 237918.2 kg

( ( (

75.00% ) 67.29% ) 57.66% )

page 6 / 13


7.4 Effective Stress Force Effective Prestress = Initial prestress - losses stress Resume Prestressed Force Asp

Condition

2

Tranfer Service

Cable

P

stress

% tensile

2

[cm ]

[ton]

[kg/cm ]

21.72 21.72

277.63 237.92

12785 10956

67.3% 57.7%

IIX. STRESS AND DEFFLECTION ANALYSIS Beam Segment Length (m)

1

2

3

5.00

6.00

5.00

Additional length at the end of the beam =

0.30

4

5

6

m

7

Total Length =

8

16.60

m

8.1 Stress at initial Description

Moment DL Pi e (eccentricity) Pi.e Moment Net. Pi / A M / Wa M / Wb Initial Stresses [kg/cm2]

Middle

SEC 1-1

SEC 2-2

SEC 3-3

SEC 4-4

SEC 5-5

x - [m]

Span

0.00

5.00

11.00

16.00

16.00

8.00

[ton.m]

20.58 277.63 0.22 -60.46 -39.88 107.92 -94.45 63.92 13.47 171.84

0.00 277.63 0.01 -2.10 -2.10 107.92 -4.97 3.36 102.95 111.29

17.69 277.63 0.19 -52.26 -34.57 107.92 -81.87 55.40 26.05 163.33

17.69 277.63 0.19 -52.26 -34.57 107.92 -81.87 55.40 26.05 163.33

0.00 277.63 0.01 -2.10 -2.10 107.92 -4.97 3.36 102.95 111.29

0.00 277.63 0.01 -2.10 -2.10 107.92 -4.97 3.36 102.95 111.29

20.58 277.63 0.22 -60.46 -39.88 107.92 -94.45 63.92 13.47 171.84

[ton] [m] [ton.m] [ton.m] [kg/cm2] 2

[kg/cm ] 2

[kg/cm ] top ( σT ) bottom ( σB )

8.2 Stress at service > Load of precast, slab, diaphragm and prestress by PC Beam > Live load and asphalt by composite Description Middle SEC 1-1 SEC 2-2 x - [m] Span 0.00 5.00 Moment DL + ADL [t-m] 67.99 0.00 58.43 P [t] 237.92 237.92 237.92 P.e [t-m] -51.82 -1.80 -44.78 [t-m] Moment --- M1 16.18 -1.80 13.65 [t-m] Moment --- M2 92.94 0.00 79.87 P/A 92.49 92.49 92.49 [kg/cm2] 2 M 1 / Wa 38.31 -4.26 32.33 [kg/cm ] M 1 / Wb -25.93 2.88 -21.88 [kg/cm2] M 2 / Wa' 17.01 0.00 14.62 [kg/cm2] 2 M 2 / Wb' -75.14 0.00 -64.57 [kg/cm ] Stress at Service slab ( σS ) 44.65 0.00 38.37 [kg/cm2] top ( σT ) 147.80 88.22 139.43 bottom ( σB ) -8.58 95.37 6.04 Note :

Moment DL = Moment Bal = Moment Net = Pi = P= M= A= Wa = Wb = Wa' = Wb' =

SEC 3-3 11.00 58.43 237.92 -44.78 13.65 79.87 92.49 32.33 -21.88 14.62 -64.57 38.37 139.43 6.04

( = M1 ) ( = M2 ) SEC 4-4 SEC 5-5 16.00 16.00 0.00 0.00 237.92 237.92 -1.80 -1.80 -1.80 -1.80 0.00 0.00 92.49 92.49 -4.26 -4.26 2.88 2.88 0.00 0.00 0.00 0.00 0.00 0.00 88.22 88.22 95.37 95.37

SEC 6-6

SEC 6-6 8.00 67.99 237.92 -51.82 16.18 92.94 92.49 38.31 -25.93 17.01 -75.14 44.65 147.80 -8.58

Allow. stress

-14.9 190.2

Allow. stress

98.4 172.9 -33.1

Moment due to dead load ( Chapter V - Moment Analysis ) Moment due to uniform load in balance condition ( Chapter 7.4 - Effective Stress Force ) ( Moment DL + Moment Bal ) Initial Prestress ( at transfer condition - chapt. 7.4. Effective Stress Force ) Prestress at service condition….. ( Chapter 7.4 -effective Stress Force ) Moment Net. Total Area of Precast Beam ( Chapter 3.1 - Precast Beam) Modulus Section for Top section of Precast condition Modulus Section for Bottom section of Precast condition Modulus Section for Top section of composit Condition……. ( Chapter 3.3 - Resume ) Modulus section for bottom section of composite condition ……. ( Chapter 3.3 - Resume ) page 7 / 13


Stress - strain diagram at center span : 1. STRESS - STRAIN DIAGRAM AT INITIAL

σ top =

M/Wa = -94.45 kg/cm2

Pi/A = 107.92 kg/cm2

13.47

kg/cm2

+ +

-

-

= -

Pi/A = 107.92 kg/cm2

M/Wb =

63.92

kg/cm2

σ bottom =

171.84 kg/cm2

2. STRESS - STRAIN DIAGRAM AT SERVICE 2 M2/Wa' = 17.01 kg/cm 2

Pi/A = 92.49 kg/cm

2

M1/Wa = 38.31 kg/cm

σ slab = 44.65

-

-

-

2

kg/cm σ top = 147.80 kg/cm2

-

+

+

= +

+

+ 2

σ bottom =

2

Pi/A = 92.49 kg/cm2 M1/Wb = -25.93 kg/cm

M2/Wb' = -75.14 kg/cm

-8.58 kg/cm2

8.3 Deflection l

Note : P = Prestress force e' = Distance between c.g of strand at end and

P

c.g of strand at lowest point.

P

l = length of anchor to anchor

e'

w = Equivalent loading for prestress force Ix = Inertia of beam Ex = Modulus of Elasticity

l/ 2

l/ 2 w=

8 . P . e' l2

Reference : PCI Design Handbook : Part 11.1.4 page no. 11-12

w Condition

at initial at aDL (total) at service (total) due to Live Load

q (t/m)

p (ton)

w (t/m)

0.64 1.48 3.60 1.48

0.00 0.00 11.40 11.40

-1.82

4

-1.56

3

deflection = (5q*L /384EI) + (pL /48EI) No.

due load

1 2

prestress wd

3

w ad

4

w LL

based : PCI handbook 4.6.5 Long-Time Chamber Deflection (1) release multiplier (2) erect. multiplier (3) final descibtion Allowable L/800 (cm) (cm) (cm) (cm) (cm) (cm) -2.45 1.8 x (1) -4.40 2.45 x (1) -5.99 ( - ) up 0.86 1.85 x (1) 1.55 2.7 x (1) 2.40 (+ ) down -1.58

-2.85 0.44 -2.41

3 x (2)

-3.59 1.33 -2.26 0.78

2.00

-1.48 page 8 / 13


IX. MOMENT CAPACITY….. PCI Design Handbook, Chapt. 4.2.1-Strength Design First Analysis There are two thickness flens which t-slab and t-flens of beam. slab (t1) = 20.00 cm bslab = 185.00 cm tflens (t2) = 7.50 cm bflens = 35.00 cm Aps = 21.72 cm2 fps = 0,9 * fu kg/cm 2 = 17100 kg/cm 2

must <=

337

cm

φ = 0.9

So There is analyzed as T beam or square beam. To analysis as T Beam : C3 C2 C1 d

T

T C1 C2 C3 a

= = = = =

Aps * fps = 371347 kg 0.85*fc'beam*tweb*(a-tslab-tflens) 0.85*fc'beam*A*tflens = 96454 kg 0.85*fc'slab*bslab*tslab = 1044717 kg ((T-C2-C3)/(0.85*fc'*tweb))+tslab+tflens = -88.7 cm -- Check, if a < (tslab+tflens), so must analyse as T beam or square beam. (tslab+tflens) = 34.5 cm C1 = -769824 kg d = (H+tslab-ed) = 102.45 cm Mn = C1(d-(a-tslab-tflens)/2)+C2(d-tslab-tflens/2)+C3(d-tslab/2) = -264.60 ton.m φ Mn = -238.14 ton.m Analysed as T beam, for a < (tslab+tflens) or at flens of beam : a = ((T-C3)/(0.85*fc'*A))+tslab = -25.4 cm -- Check, if a < (tslab), so must analyse as square beam. (tslab) = 27 cm C2 = 0.85*fc'beam*A*(a-tslab) = -673370 kg Mn = C2(d-tslab-((a-tslab)/2))+C3(d-tslab/2) = 244.95 ton.m φ Mn = 220.45 ton.m Analysed as square beam, for a < tslab a = Aps*fps/(0.85*fc'slab*bslab) Mn = T*(d-a/2) = 362.64 ton.m φ Mn = 326.38 ton.m

=

9.6

Momen Ultimate Calculation(Mu) Ultimate Moment = 1,2*Beam+1,3*Slab+2*Asphalt+1,2*Diaphragm+2*LL ( Bridge Design Manual, Vol.1-Page 2-6 ) Ratio (φMn / Mu), (>1) = Cracking Moment: Mcr = Requirement = (initial) (service)

= =

cm

276.53

ton.m

1.18 ( Fr + Peff / A + Peff * e / Wb ) * Wb φMn > 1.2 * Mcr 1.2 * Mcr φMn 180.9417 ton.m < 191.8638 260.576 ton.m < 326.3782

ton.m (Ok!) ton.m (Ok!) page 9 / 13


X. SHEAR ANALYSIS 10.1Shear calculation by rebar φ =

WEB SHEAR

bw =

Description Vu = 1.3[Vdl+5/3Vll] Mu = 1.3[Mdl+5/3Mll] dp > 0.80 h [Vu*dp]/>1 Vc min Vc Vc max Vc taken Vu/φ Vs = Vu/φ - Vc --STIRRU, nos stirrup Dia. fy Av S Smax Smax Smax S using S

x - [m] [ton] [t-m] [cm] [kg] [kg] [kg] [kg] [kg] [kg]

[mm] [kg/cm2] [cm2] [mm] [mm] [mm] [mm] 1565 [mm] [mm]

0.85 17 Sec 4-4 16.00 69.13 0.00 54.43

bwu=

Mid Sec 1-1 Sec 2-2 Sec 3-3 Sec 5-5 span 0.00 5.00 11.00 16.00 11.40 69.13 33.05 33.05 69.13 276.53 0.00 237.64 237.64 0.00 75.45 54.43 72.50 72.50 54.43 0.03 3.76E+100 0.10 0.10 3.76E+100 3.76E+100 14135.03 20993.5 13581.2 13581.2 10196.9 10196.9 199715.46 3.5E+107 6.1E+05 6.13E+05 1.7E+107 1.71E+107 35470.92 52681.9 34081.2 34081.2 25588.3 25588.3 35470.92 52681.9 34081.2 34081.2 25588.3 25588.3 13407.06 81331.3 38878.6 38878.6 81331.3 81331.3 0.000 28649.4 4797.4 4797.4 55742.9 55742.9 2 4 2 2 13 13 13 13 3900 3900 3900 3900 2.65 5.31 2.65 2.65 7.8E+16 393.4061 1564.547 1.6E+03 15816.62 38551.21 15503.7 15503.7 450.00 450.00 450.00 450.00 15816.62 1183.21 1218.01 1218.01 450.00

2 2 13 13 3900 3900 2.65 2.65 1.0E+02 101 13433.8 13433.79 450.00 450.00 1218.01 1218.01

393.41 450.00 450.00 101.10 150 200 300

Reference (ACI) : Vc min = 0.53*sqrt(f'c)*bw*dp …….. (1) Vc = (0.16*sqrt(f'c)+49*vu*dp/Mu)*bw*dp …..(2) Vc max = 1.33*sqrt(f'c)*bw*dp …….(3)

S S min

= = = =

101.10

35 Sec 6-6 8.00 11.40 276.53 75.45 0.03 14135.0 199715.5 35470.9 35470.9 13407.1 0.0 2 13 3900 2.65 7.8E+16 15816.62 450.00 15816.62 450.00

10*Av*fy*dp/Vs 10*Av*80*fy*dp/(Aps*fps*sqrt(dp/bw) d/2 atau 24 in (=60.96 cm) 10*Av*fy/(50*bw) ……if only Vu/φ > Vc/2

Note : Formula (1),(2) and (3) are adapted from the ACI formula for Shear Design Conversion Factor From Psi to Kg/cm 2 is 0.0703 ( 1 Psi = 0.0703 kg/cm 2 ) ACI standard states : Vc min = 2x(fc')^0.5………… ( Psi ) Vc min = 2x(0.0703x fc')^0.5 …….. ( kg/cm2 ) 10.2Shear Connector Slab K- 300 Distance ctc beam (be) = Thickness of slab = Height of compression stress (a) =

2

f'c = 246.06 kg/cm 1.85 m 27.00 cm 9.60 cm (see moment capacity section)

Hu = 3.7E+05 kg Avf total of 1/2 span = 112.02 cm2 Average stirrup space = 196.69 mm Number of stirrup for 1/2 span = 43 pcs.

( = 0.85*f'c*be*(minimum value between tslab or a)) ( = Hu/(0.85*fy*μ) , with μ =1)

page 10 / 13


XI. END BLOCK DESIGN

Centre of gravity sheat at end beam = a = 22 cm b = 35 cm Bursting steel calculation 0.75 Tensile assumption = 75%, P = [Pi max] = Fx = Fy = F prefer = 25.00 As = 25.00 / ( 0.87 x Number of bursting steel needed

36.36

cm

12 0.9871 3/8 P (1 - a/b) = 3/8 P (1 - a/h) = ton 3900 ) = 4 D13

19000 = 23.51 ton 25.00 ton 7.37 cm

168794.1 kg

2

XII. SEGMENT'S JOINT CONTROL

200 100

Ya'[c] Ya

φ 225

Y'b[c] 36.3

Yb

73.4

100 275

27.00 cm 0.00 cm

Check top point = Check bottom point = Keterangan x [m]

Ya = Yb =

Middle Span

Vn = Vdl + Vll

[ton]

tg φ Vp = P tg φ

[ton]

Vs = Vn - Vp

[ton]

SEC 1-1 0.00

33.68 cm 8.82 cm SEC 2-2 5.00

Ya' = Yb' =

SEC 3-3 11.00

SEC 4-4 16.00

-3.39 cm 45.89 cm SEC 5-5 16.00

SEC 6-6 8.00

5.70 0.000 0.00 5.70

40.23 -0.053 12.50 27.73

18.65 -0.020 4.69 13.96

18.65 0.020 4.69 13.96

40.23 0.053 12.50 27.73

40.23 0.053 12.50 27.73

5.70 0.000 0.00 5.70

0.79 67.99 92.94 -51.82 116.18 81.49

3.84 0.00 0.00 -1.80 89.81 93.19

1.93 58.43 79.87 -44.78 112.47 83.13

1.93 58.43 79.87 -44.78 112.47 83.13

3.84 0.00 0.00 -1.80 89.81 93.19

3.84 0.00 0.00 -1.80 89.81 93.19

0.79 67.99 92.94 -51.82 116.18 Allow. 81.49 stress

116.18 -0.01

89.98 -0.16

112.50 -0.03

112.50 -0.03

89.98 -0.16

89.98 -0.16

116.18 172.9 -0.01 -33.1

81.50 -0.01

93.34 -0.16

83.18 -0.04

83.18 -0.04

93.34 -0.16

93.34 -0.16

81.50 172.9 -0.01 -33.1

Joint's shear stress V =Vs/(Concrete Area)

2

[kg/cm ]

M(dl+adl) resissted by precast

[t-m]

M(ll) resissted by composite [t-m]

P.e

[t-m]

Top stress

[kg/cm2]

Bottom stress

[kg/cm2]

Top point σ max

[kg/cm2]

σ min

[kg/cm2]

Bottom Point σ max

[kg/cm2]

σ min

[kg/cm2]

Calculation : Top stress = P/A + Mdl/Wa + Mll/Wa' Bottom Stress = P/A + Mdl/Wb + Mll/Wb' P max = Teg./2 + [ (teg./2)^2 + V^2 ]^(1/2) P min = Teg./2 - [ (teg./2)^2 + V^2 ]^(1/2) page 11 / 13


Note : P= A= Mdl = Mll = Wa =

effective Prestress Force Area of Precast beam Moment due to dead load Moment due to live load Section Modulus for top section

Wb = teg. = V= Vn = Vp = s=

Section Modulus for bottom section Stress due to moment Stress due to shear force Shear force due to dead load and live load Shear force due to Prestress force Stresses due to shear force and moment

XIII. SHEAR KEY DESIGN A'B

Ae

h'

h

AB

A'e

Av

Av' H

Calculation of Shear Key Reinforcement

(ton) (mm) (mm) (mm) (mm) (kg/cm2) (kg/cm2)

Sec 2-2 5.00 18.65 100 50 425 300 3900 1950

Sec 3-3 11.00 -18.65 100 50 425 300 3900 1950

Sec 4-4 16.00 -40.23 100 50 425 300 3900 1950

Sec 5-5 16.00 -40.23 100 50 425 300 3900 1950

( mm2 )

265.46

265.46

265.46

265.46

( mm2 )

140.64

-140.64

-303.43

-303.43

0.53

0.53

1.14

1.14

2 35.16

2 -35.16

2 -75.86

2 -75.86

Number of stell Needed

0.13

0.13

0.29

0.29

Number of steel Used

2

2

2

2

478.18

-478.18

-1031.65

-1031.65


1.80

1.80

3.89

3.89


2

2

4

4

199.24

-199.24

-429.86

-429.86

0.75 2 49.81 0.19 2 478.18

0.75 2 -49.81 0.19 2 -478.18

1.62 2 -107.46 0.40 2 -1031.65

1.62 2 -107.46 0.40 2 -1031.65


1.80

1.80

3.89

3.89


2

2

4

4

Description x [m] S ( DL + LL ) H a h h' fy σsa Steel of reinforcement 2D - 13 Area Male Section Ae Number of stell Needed Number of steel Used AB

Av

( mm2 )

2

( mm )

Female section A'e

( mm2 )

Number of stell Needed Number of steel Used A'B

( mm2 )

Number of stell Needed Number of steel Used Av'

( mm2 )

page 12 / 13


Formula for Shear Key Design according to Japan Road Association :

Ae = AB = Av =

Sxa 0.8 x h x σsa

A'e =

Ae 4 S 2 x σsa

Sxa 0.8 x h' x σsa

AB =

A'e 4

Av' =

Av

Ae, A'e = Area of reinforcement AB, A'B = Area of stirrup reinforcement Av, A'v = Area of stirrup reinforcement

S = Total Vertical Load σsa = Allowable stress for reinforcement a=H/2

XIV. LIFTING CONTROL Lifting at stock yard : Lifting at instalation :

Beam Segment Length (m) a b Precast beam weight Segment beam weight Dynamic load factor Force at lifitng point Safety Factor No. legs for lifting point MDL middle Wx σbotom fr' conc.at stock yard fr' conc.at instalation Stress control

fc at lifting = 50% fc' = frupture = 0.8 sqrt(fc at lifting) = fc at install = 80% fc' = frupture = 0.8 sqrt(fc at instal) = 2 3 5.30 6.00 5.30 1.10 1.24 1.10 3.11 3.52 3.11 0.6431 0.6431 0.6431 3.4 3.9 3.4 1.4 1.4 1.4 2.4 2.7 2.4 2 2 2 1 1 1 5.44E+04 6.97E+04 5.44E+04 6.24E+04 6.24E+04 6.24E+04 0.87 1.12 0.87

2

216.1439 [kg/cm ] 2 11.76147 [kg/cm ] 2 345.8303 [kg/cm ] 14.87721

1

11.76 14.88 OK

11.76 14.88 OK

a

0.00

0.00

0.00

0.00

m m t/m ton ton leg kg.cm cm3 kg/cm2 kg/cm2 kg/cm2

11.76 14.88 OK b

Unit

a

Lifting Point

Lifitng beam design Strand lifting beam = Ast = UTS = Allowed tension = Tension strength =

φ 12,7 0.987 19000 75% 14.06

mm

Beam Weight =

cm2

Dynamic Load Factor = Force at lifitng point = SF = No legs for lifting point =

kg/cm2

UTS ton for 1 leg of strand

12.2038 ton 1.4 8.54266 ton 2 3 legs

page 13 / 13

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