perhitungan girder pre cast

(16153) PC I H-125cm; L-20.6m; CTC-150cm

20.00 M

I. DATA

0.3 L= 20.00 M 0.3

Beam length = 20.60 m ( edge anchor to edge anchor : 20.30 m)Beam spacing (s) = 1500.00 mmConcrete Slab thickness (CIP) = 200.00 mmAsphalt thickness = 50.00 mmDeck slab thickness = 70.00 mm

Cross SectionH = 1250 mm tfl-1 = 75 mmA = 350 mm tfl-2 = 75 mmB = 650 mm tfl-3 = 100 mm

tweb = 170 mm tfl-4 = 125 mm

II. MATERIAL

2.1 ConcreteBeam Slab

at service fc' = 40.0 25.0 [N/mm2]

at initial 80% fc' fc'i = 32.0 [N/mm2]

SPAN (ctc) L =

Compressive strength

TECHNICAL CALCULATION OF SEGMENTAL PC I BEAM FOR BRIDGE

B

H

A

tfl-1tfl-2

tfl-3

tfl-4

tweb

Ya'

1

2

3

Yb'

COMPOSITE BEAM

1

2

3

4

56

Ya

Yb

PRECAST BEAM

Base Line

Cc3

Cc2

Cc1

Tps=Aps.fpsT = As.fy

Zone 2

Zone 4

COMPOSITE BEAM

dp da

b. eff

Zone 3

Cc4

Zone 1

225kN 225kN50kN

0.00

0.20

0.40

0.60

0.80

0 5 10 15 20 25

75.00% 75.00%

71.11%69.86% 69.58% 68.98%

64.44% 64.44%

68.33%69.58% 68.98%

62.14% 62.14%

66.02%67.56% 67.27% 66.68%

60.50% 60.50%

64.39%65.93% 65.64% 65.05%

55.78% 55.78%

59.67%61.21% 60.92% 60.32%

54.79% 54.79%

58.68%60.21% 59.93% 59.33%

50.00%

65.00%

80.00%

0.00 0.00 10.15 16.09 17.45 20.30

FrictionAnchor setElastic Shortening (ES)Shringkage (SH)Creep (CR)Steel Relaxation (SR)

LOSSES OF PRESTRESS DIAGRAM

Prestress tendon section

UTS

P

l

l/2 l/2

Pec

w

ee

0.002000.00

Zona 1Zona 2

Shear Steel Requirement PositionkN

beam section point

60.0%

65.0%

70.0%

75.0%

80.0%

0.00 10.00 20.00 30.00


Luas A1 Luas A2

Luasan dengan asumsi X > 0.5 span

Luas A1

Luasan dengan asumsi X < 0.5 spanCable changeangle point

X (effective anchorage set)

Anchorageset area


Cable changeangle point

Anchorageset area

55.0%

60.0%

65.0%

70.0%

75.0%

80.0%

0.00 10.00 20.00 30.00Prestress tendon section

LOSSES OF PRESTRESSDUE TO ANCHORAGE SET

64.44%64.44%64.44%64.44%64.44%

68.33%69.86%69.58%68.98%

60.0%

65.0%

70.0%

75.0%

0.00 5.00 10.00 15.00 20.00 25.00Prestress tendon section

AVERAGE LOSSES OF PRESTRESS

0.0200.0400.0600.0800.0

1000.01200.01400.01600.01800.02000.0

Zona 1

Zona 2

Zona 3

Zona 4

Vn = Vu/f


beam section point

A

H

B

tfl-1tfl-2

tfl-3tfl-4

tweb

1

Yb'

COMPOSITE BEAM

1

2

3

Yb

PRECAST BEAM

Base Line

a

dh

h'

As

As

Ah

Av

B

H

A

tfl-1tfl-2

tfl-3

tfl-4

tweb

1

2

3

4

5

Ya

Yb

PRECAST BEAM

Base Line

1

3

Ya'

Yb''

PRECAST BEAM

Base Line

2

page 1 / 14

at initial 80% fc' fc'i = 32.0 [N/mm2]

Allowable stress

19.2 [N/mm2]

Tensile 1.4 [N/mm2]

18.0 11.3 [N/mm2]

Tensile 3.2 2.5 [N/mm2]

wc = 2500.0 2500.0 [kg/m3]

Ec = wc1.5

*0.043*sqrt(fc') = 33994.5 26875.0 [N/mm2]

Eci = wc1.5

*0.043*sqrt(fci') = 30405.6 [N/mm2]

Concrete flexural tension strength (fr)

f r = 0.7*sqrt(fc') = 4.4 [N/mm2]

2.2

( ASTM A 416 Grade 270 Low Relaxation or JIS G 3536 )dia : 12.7 [mm]

Ast : 98.78 [mm2]

Es : 1.93E+05 [N/mm2]

fu : 1860 [N/mm2]

2.3- Diameter dia : 13 [mm]

- Eff. Section area Ast : 132.7 [cm2]

- Modulus of elasticity Es : 2.10E+05 [N/mm2]

- Yield stress fy : 400 [N/mm2]

Allowable stress at service ………. (SNI T-12-2004)

- Eff. Section area

Compressive

Steel Reinforcement

[Uncoated stress relieve seven wires strand]

- Diameter strand

- Ultimate tensile strength

- Modulus of elasticity

Modulus of elasticity

Allowable stress at initial ………… (SNI T-12-2004 )

0.6 * fc'i =

Concrete unit weight

Prestressing Cable

Compressive

0.25 * Sqrt(fc'i) =

0.45 * fc' =

0.5 * Sqrt(fc') =

B

H

A

tweb

Ya'

1

2

3

Yb'

COMPOSITE BEAM

1

2

3

4

56

Ya

Yb

PRECAST BEAM

Base Line

Cc3

Cc2

Cc1


Zone 2

Zone 4

COMPOSITE BEAM

dp da

b. eff

Zone 3

Cc4

Zone 1

225kN 225kN50kN

0.00

0.20

0.40

0.60

0.80

0 5 10 15 20 25

75.00% 75.00%

71.11%69.86% 69.58% 68.98%

64.44% 64.44%

68.33%69.58% 68.98%

62.14% 62.14%

66.02%67.56% 67.27% 66.68%

60.50% 60.50%

64.39%65.93% 65.64% 65.05%

55.78% 55.78%

59.67%61.21% 60.92% 60.32%

54.79% 54.79%

58.68%60.21% 59.93% 59.33%

50.00%

65.00%

80.00%

0.00 0.00 10.15 16.09 17.45 20.30




UTS

P

l

l/2 l/2

Pec

w

ee

0.002000.00

Zona 1Zona 2


beam section point

60.0%

65.0%

70.0%

75.0%

80.0%

0.00 10.00 20.00 30.00


Luas A1 Luas A2


Luas A1



Anchorageset area



Anchorageset area

55.0%

60.0%

65.0%

70.0%

75.0%

80.0%



64.44%64.44%64.44%64.44%64.44%

68.33%69.86%69.58%68.98%

60.0%

65.0%

70.0%

75.0%



0.0200.0400.0600.0800.0

1000.01200.01400.01600.01800.02000.0

Zona 1

Zona 2

Zona 3

Zona 4

Vn = Vu/f


beam section point

A

H

B

tfl-1tfl-2

tfl-3tfl-4

tweb

Ya'

1

2

3

Yb'

COMPOSITE BEAM

1

2

3

45

Ya

Yb

PRECAST BEAM

Base Line

a

dh

h'

As

As

Ah

Av

1

2

3

4

5

Ya

Yb

PRECAST BEAM

Base Line

1

3

Ya'

Yb''

PRECAST BEAM

Base Line

2

page 1 / 14

(16153) PC I H-125cm; L-20.6m; CTC-150cm

III. SECTION ANALYSISRemark :

Ep 1 = 33994 [N/mm2] [Girder]

Ep 2 = 26875 [N/mm2] [Slab]

n = Ep 2 / Ep 1n = 0.79

3.1 Precast Beam[in mm ]

Section Width Area Level Yb Area*Yb Io Area*d2 Ix

Height Bottom Upper mm2 mm mm mm3 mm4 mm4 mm4

6 0.0 150.0 150.0 0 1250 1250.0 0 0 0 0

5 75.0 350.0 350.0 26250 1175 1212.5 31828125 12304688 12613184758 12625489445

4 75.0 170.0 350.0 19500 1100 1141.8 22265625 8775541 7556605867 7565381408

3 875.0 170.0 170.0 148750 225 662.5 98546875 9490559896 3049566872 12540126768

2 100.0 650.0 170.0 41000 125 165.2 6775000 30264228 5140086368 5170350595

1 125.0 650.0 650.0 81250 0 62.5 5078125 105794271 16955415084 17061209355

Total 1250.0 316750 519.3 164493750 9647698623 45314858949 54962557571

3.2 Composite Beam[in mm ]

Zone Height Width Area Level Yb Area*Yb Io Area*d2 Ix

Section Bottom Upper mm2 mm mm mm3 mm4 mm4 mm4

Zone

B

H

A

tfl-1tfl-2

tfl-3

tfl-4

tweb

Ya'

1

2

3

Yb'

COMPOSITE BEAM

1

2

3

4

56

Ya

Yb

PRECAST BEAM

Base Line

Cc3

Cc2

Cc1


Zone 2

Zone 4

COMPOSITE BEAM

dp da

b. eff

Zone 3

Cc4

Zone 1

225kN 225kN50kN

0.00

0.20

0.40

0.60

0.80

0 5 10 15 20 25

75.00% 75.00%

71.11%69.86% 69.58% 68.98%

64.44% 64.44%

68.33%69.58% 68.98%

62.14% 62.14%

66.02%67.56% 67.27% 66.68%

60.50% 60.50%

64.39%65.93% 65.64% 65.05%

55.78% 55.78%

59.67%61.21% 60.92% 60.32%

54.79% 54.79%

58.68%60.21% 59.93% 59.33%

50.00%

65.00%

80.00%

0.00 0.00 10.15 16.09 17.45 20.30




UTS

P

l

l/2 l/2

Pec

w

ee

0.002000.00

Zona 1Zona 2


beam section point

60.0%

65.0%

70.0%

75.0%

80.0%

0.00 10.00 20.00 30.00


Luas A1 Luas A2


Luas A1



Anchorageset area



Anchorageset area

55.0%

60.0%

65.0%

70.0%

75.0%

80.0%



64.44%64.44%64.44%64.44%64.44%

68.33%69.86%69.58%68.98%

60.0%

65.0%

70.0%

75.0%



0.0200.0400.0600.0800.0

1000.01200.01400.01600.01800.02000.0

Zona 1

Zona 2

Zona 3

Zona 4

Vn = Vu/f


beam section point

A

H

B

tfl-1tfl-2

tfl-3tfl-4

tweb

Ya'

1

2

3

Yb'

COMPOSITE BEAM

1

2

3

45

Ya

Yb

PRECAST BEAM

Base Line

a

dh

h'

As

As

Ah

Av

B

H

A

tfl-1tfl-2

tfl-3

tfl-4

tweb

1

2

3

4

5

Ya

Yb

PRECAST BEAM

Base Line

1

3

Ya'

Yb''

PRECAST BEAM

Base Line

2

page 2 / 14

Section Bottom Upper mm2 mm mm mm3 mm4 mm4 mm4

2 200.0 1185.9 1185.9 237171 1320 1420.0 336782571 790569415 61107673140 61898242555

70.0 158.1 158.1 11068 1250 1285.0 14222344 4519421.823 1536532796 1541052218

1 1250.0 650.0 350.0 316750 0 519.3 164493750 54962557571 48943588486 1.03906E+11

Total 1520.0 564989 912.4 515498665 55757646408 1.11588E+11 1.67345E+11

3.3 R e s u m e[in mm ]

Description Area (mm2) Ya (mm) Yb (mm) Ix (mm4) Wa (mm3) Wb (mm3)

Precast Beam 316750 731 519.3 54962557571 75220826 105836180

Composite Beam [composite] 564989 608 912.4 167345440830 275422726 183411337

[precast] 338 495698974

IV. LOADING4.1 Dead Load

a. Precast Beam q1 = Ac precast girder x gconc. Precast

q1 = 0.317 x 2.50 = 0.791875 [t/m'] = 7.77 [kN/m']

b. Slab q2 = Ac slab CIP x gconc. slab

q2 = 0.314 x 2.50 = 0.785 [t/m'] = 7.70 [kN/m']

c. Deck slab q3 = Ac deck slab x gs

q3 = 0.0910 x 2.50 = 0.2275 [t/m'] = 2.23 [kN/m']

d. Asphaltic q4 = Ac asphaltic x gs

q4 = 0.08 x 2.20 = 0.165 [t/m'] = 1.62 [kN/m']

e. Diaphragm p = Vol diaph with 0.15m thickness x gdiaph

p = 0.20 x 2.40 = 0.49167 [ton'] = 4.82 [kN']

note : from kg to N, multiply by 9.8060

Number of diaph = 4 pcsDiaph. placement 1 2 3 4Location 0 6.6666667 13.333333 20Support Va 4.82 3.21 1.61 0.00Mid Moment 0.00 16.07 16.07 0.00Total Diaphragma Flexural Moment at Middle Span 32.14 kN.m

eqivalen load q diaphragm q5= 0.64 [kN/m']

B

H

A

tfl-1tfl-2

tfl-3

tfl-4

tweb

Ya'

1

2

3

Yb'

COMPOSITE BEAM

1

2

3

4

56

Ya

Yb

PRECAST BEAM

Base Line

Cc3

Cc2

Cc1


Zone 2

Zone 4

COMPOSITE BEAM

dp da

b. eff

Zone 3

Cc4

Zone 1

225kN 225kN50kN

0.00

0.20

0.40

0.60

0.80

0 5 10 15 20 25

75.00% 75.00%

71.11%69.86% 69.58% 68.98%

64.44% 64.44%

68.33%69.58% 68.98%

62.14% 62.14%

66.02%67.56% 67.27% 66.68%

60.50% 60.50%

64.39%65.93% 65.64% 65.05%

55.78% 55.78%

59.67%61.21% 60.92% 60.32%

54.79% 54.79%

58.68%60.21% 59.93% 59.33%

50.00%

65.00%

80.00%

0.00 0.00 10.15 16.09 17.45 20.30




UTS

P

l

l/2 l/2

Pec

w

ee

0.002000.00

Zona 1Zona 2


beam section point

60.0%

65.0%

70.0%

75.0%

80.0%

0.00 10.00 20.00 30.00


Luas A1 Luas A2


Luas A1



Anchorageset area



Anchorageset area

55.0%

60.0%

65.0%

70.0%

75.0%

80.0%



64.44%64.44%64.44%64.44%64.44%

68.33%69.86%69.58%68.98%

60.0%

65.0%

70.0%

75.0%



0.0200.0400.0600.0800.0

1000.01200.01400.01600.01800.02000.0

Zona 1

Zona 2

Zona 3

Zona 4

Vn = Vu/f


beam section point

A

H

B

tfl-1tfl-2

tfl-3tfl-4

tweb

a

dh

h'

As

As

Ah

Av

B

H

A

tfl-1tfl-2

tfl-3

tfl-4

tweb

1

2

3

4

5

Ya

Yb

PRECAST BEAM

Base Line

1

3

Ya'

Yb''

PRECAST BEAM

Base Line

2

page 2 / 14

(16153) PC I H-125cm; L-20.6m; CTC-150cm

4.2 Live LoadTaken from "Pembebanan Untuk Jembatan RSNI T-02-2005"4.2.1. "T" Loading (Beban Truk)

Unit P1 P2 P3 M.max di x = 10.000 mkN 225 225 50 DLA = 30%

1.3 1.3 1.3 Impact = 1 + DLA = 1.3kN 292.5 292.5 65m 6.000 10.000 15.000kN 204.75 146.25 16.25kN

kN-m

kN-m

4.2.2. "D" Loading (Beban Lajur)Taken from "Pembebanan Untuk Jembatan RSNI T-02-2005"

Load type :

Distribution Load Chart : Dynamics Load Factored Chart :

Impact

367.25

DF = S/3.4

LoadItem

LL + I

1104.044

M maxVa

M x DF

2502.50

DistanceVa

0.441

B

H

A

tfl-1tfl-2

tfl-3

tfl-4

tweb

Ya'

1

2

3

Yb'

COMPOSITE BEAM

1

2

3

4

56

Ya

Yb

PRECAST BEAM

Base Line

Cc3

Cc2

Cc1


Zone 2

Zone 4

COMPOSITE BEAM

dp da

b. eff

Zone 3

Cc4

Zone 1

225kN 225kN50kN

0.00

0.20

0.40

0.60

0.80

0 5 10 15 20 25

75.00% 75.00%

71.11%69.86% 69.58% 68.98%

64.44% 64.44%

68.33%69.58% 68.98%

62.14% 62.14%

66.02%67.56% 67.27% 66.68%

60.50% 60.50%

64.39%65.93% 65.64% 65.05%

55.78% 55.78%

59.67%61.21% 60.92% 60.32%

54.79% 54.79%

58.68%60.21% 59.93% 59.33%

50.00%

65.00%

80.00%

0.00 0.00 10.15 16.09 17.45 20.30




UTS

P

l

l/2 l/2

Pec

w

ee

0.002000.00

Zona 1Zona 2


beam section point

60.0%

65.0%

70.0%

75.0%

80.0%

0.00 10.00 20.00 30.00


Luas A1 Luas A2


Luas A1



Anchorageset area



Anchorageset area

55.0%

60.0%

65.0%

70.0%

75.0%

80.0%



64.44%64.44%64.44%64.44%64.44%

68.33%69.86%69.58%68.98%

60.0%

65.0%

70.0%

75.0%



0.0200.0400.0600.0800.0

1000.01200.01400.01600.01800.02000.0

Zona 1

Zona 2

Zona 3

Zona 4

Vn = Vu/f


beam section point

A

H

B

tfl-1tfl-2

tfl-3tfl-4

tweb

Ya'

1

2

3

Yb'

COMPOSITE BEAM

1

2

3

45

Ya

Yb

PRECAST BEAM

Base Line

a

dh

h'

As

As

Ah

Av

B

H

A

tfl-1tfl-2

tfl-3

tfl-4

tweb

1

2

3

4

5

Ya

Yb

PRECAST BEAM

Base Line

1

3

Ya'

Yb''

PRECAST BEAM

Base Line

2

page 3 / 14

Line Load (D load)a. Dynamic Load Allowance [DLA] DLA = 1 + 0,4 = 1.40 Span <= 50 m

DLA = 1 + (0.0025*span+0.175) 50 < Span < 90 mDLA = 1 + 0,3 = 1.30 Span >= 90 m

b. Knife Edge Load (KEL) = 49.00 [kN/m']c. Distribution Factor (DF) = 1.00d. Distribution Load

q = 9.00 kN/m2

which : q = 9 kN/m2

for Span <= 30 mq = 9 x(0,5+15/span)kN/m

2Span > 30 m

e. Live loadDistribution load, qudl = DF x q x s

= 1.00 x 9.00 x 1.50 = 13.50 [kN/m']KEL, PKEL = DF x DLA x KEL x s

= 1.00 x 1.40 x 49.00 x 1.50 = 102.90 [kN']

M.max at 0.5 span = 10.00 mVa = 186.45 kN

M LL = 1189.5 kN.mRESUME : Moment force cause by D Loading is bigger than Truck Loading

B

H

A

tfl-1tfl-2

tfl-3

tfl-4

tweb

Ya'

1

2

3

Yb'

COMPOSITE BEAM

1

2

3

4

56

Ya

Yb

PRECAST BEAM

Base Line

Cc3

Cc2

Cc1


Zone 2

Zone 4

COMPOSITE BEAM

dp da

b. eff

Zone 3

Cc4

Zone 1

0.00

0.20

0.40

0.60

0.80

0 5 10 15 20 25

75.00% 75.00%

71.11%69.86% 69.58% 68.98%

64.44% 64.44%

68.33%69.58% 68.98%

62.14% 62.14%

66.02%67.56% 67.27% 66.68%

60.50% 60.50%

64.39%65.93% 65.64% 65.05%

55.78% 55.78%

59.67%61.21% 60.92% 60.32%

54.79% 54.79%

58.68%60.21% 59.93% 59.33%

50.00%

65.00%

80.00%

0.00 0.00 10.15 16.09 17.45 20.30




UTS

P

l

l/2 l/2

Pec

w

ee

0.002000.00

Zona 1Zona 2


beam section point

60.0%

65.0%

70.0%

75.0%

80.0%

0.00 10.00 20.00 30.00


Luas A1 Luas A2


Luas A1



Anchorageset area



Anchorageset area

55.0%

60.0%

65.0%

70.0%

75.0%

80.0%



64.44%64.44%64.44%64.44%64.44%

68.33%69.86%69.58%68.98%

60.0%

65.0%

70.0%

75.0%



0.0200.0400.0600.0800.0

1000.01200.01400.01600.01800.02000.0

Zona 1

Zona 2

Zona 3

Zona 4

Vn = Vu/f


beam section point

A

H

B

tfl-1tfl-2

tfl-3tfl-4

tweb

Ya'

1

2

3

Yb'

COMPOSITE BEAM

1

2

3

45

Ya

Yb

PRECAST BEAM

Base Line

a

dh

h'

As

As

Ah

Av

B

H

A

tfl-1tfl-2

tfl-3

tfl-4

tweb

1

2

3

4

5

Ya

Yb

PRECAST BEAM

Base Line

1

3

Ya'

Yb''

PRECAST BEAM

Base Line

2

page 3 / 14

(16153) PC I H-125cm; L-20.6m; CTC-150cm

V. MOMENT ANALYSIS[in kN-meter ]

Mid Sec 1-1 Sec 2-2 Sec 3-3 Sec 4-4 Sec 5-5 Sec 6-6span 0.00 4.70 8.20 11.80 15.30 10.00 (m)

DL Precast beam 388.26 0.00 279.20 375.68 375.68 279.20 388.26388.26 0.00 279.20 375.68 375.68 279.20 388.26

DL Slab 384.89 0.00 276.77 372.42 372.42 276.77 384.89ADL Asphaltic Layer 80.90 0.00 58.17 78.28 78.28 58.17 80.90SDL Diaphragm+Deck Slab 143.69 0.00 103.32 139.03 139.03 103.32 143.69

609.47 0.00 438.27 589.72 589.72 438.27 609.47LL Distribution load 675.00 0.00 485.39 653.13 653.13 485.39 675.00

KEL 514.50 0.00 369.98 497.83 497.83 369.98 514.501189.50 0.00 855.37 1150.96 1150.96 855.37 1189.502187.23 0.00 1572.83 2116.36 2116.36 1572.83 2187.233441.58 0.00 2474.84 3330.07 3330.07 2474.84 3441.58

Ultimate total = 1,2*(Beam+Diaphragm+Deck Slab)+1,3*Slab+2*Asphaltic+1.8*(LL+I)

VI. SHEAR ANALYSIS[in kN]

Mid Sec 1-1 Sec 2-2 Sec 3-3 Sec 4-4 Sec 5-5 Sec 6-6span 0.00 4.70 8.20 11.80 15.30 10.00 (m)

DL 0.00 77.65 41.16 13.98 -13.98 -41.16 0.000.00 77.65 41.16 13.98 -13.98 -41.16 0.00

DL 0.00 76.98 40.80 13.86 -13.86 -40.80 0.00ADL 0.00 16.18 8.58 2.91 -2.91 -8.58 0.00SDL 0.00 28.74 15.23 5.17 -5.17 -15.23 0.00

0.00 121.89 64.60 21.94 -21.94 -64.60 0.00Distribution load 0.00 135.00 71.55 24.30 -24.30 -71.55 0.00

Subtotal

Subtotal

Subtotal

LL

Subtotal

Description

Subtotal

Diaphragm+Deck slab

Type

Precast beam

Ultimate total

SlabAsphaltic Layer

Total (DL + LL)

Type Description

B

H

A

tfl-1tfl-2

tfl-3

tfl-4

tweb

Ya'

1

2

3

Yb'

COMPOSITE BEAM

1

2

3

4

56

Ya

Yb

PRECAST BEAM

Base Line

Cc3

Cc2

Cc1


Zone 2

Zone 4

COMPOSITE BEAM

dp da

b. eff

Zone 3

Cc4

Zone 1

225kN 225kN50kN

0.00

0.20

0.40

0 5 10 15 20 25

75.00% 75.00%

71.11%69.86% 69.58% 68.98%

64.44% 64.44%

68.33%69.58% 68.98%

62.14% 62.14%

66.02%67.56% 67.27% 66.68%

60.50% 60.50%

64.39%65.93% 65.64% 65.05%

55.78% 55.78%

59.67%61.21% 60.92% 60.32%

54.79% 54.79%

58.68%60.21% 59.93% 59.33%

50.00%

65.00%

80.00%

0.00 0.00 10.15 16.09 17.45 20.30




UTS

P

l

l/2 l/2

Pec

w

ee

0.002000.00

Zona 1Zona 2


beam section point

60.0%

65.0%

70.0%

75.0%

80.0%

0.00 10.00 20.00 30.00


Luas A1 Luas A2


Luas A1



Anchorageset area



Anchorageset area

55.0%

60.0%

65.0%

70.0%

75.0%

80.0%



64.44%64.44%64.44%64.44%64.44%

68.33%69.86%69.58%68.98%

60.0%

65.0%

70.0%

75.0%



0.0200.0400.0600.0800.0

1000.01200.01400.01600.01800.02000.0

Zona 1

Zona 2

Zona 3

Zona 4

Vn = Vu/f


beam section point

A

H

B

tfl-1tfl-2

tfl-3tfl-4

tweb

Ya'

1

2

3

Yb'

COMPOSITE BEAM

1

2

3

45

Ya

Yb

PRECAST BEAM

Base Line

a

dh

h'

As

As

Ah

Av

B

H

A

tfl-1tfl-2

tfl-3

tfl-4

tweb

1

2

3

4

5

Ya

Yb

PRECAST BEAM

Base Line

1

3

Ya'

Yb''

PRECAST BEAM

Base Line

2

page 4 / 14

Distribution load 0.00 135.00 71.55 24.30 -24.30 -71.55 0.00KEL 51.45 102.90 78.72 60.71 -60.71 -78.72 51.45

51.45 237.90 150.27 85.01 -85.01 -150.27 51.4551.45 437.45 256.03 120.93 -120.93 -256.03 51.4592.61 688.32 408.33 199.84 -199.84 -408.33 92.61

Ultimate total = 1,2*(Beam+Diaphragm+Deck Slab)+1,3*Slab+2*Asphaltic+1.8*(LL+I)

VII. PRESTRESSING CABLE7.1 Cable Profile

[in: mm ]ten- Nos Profile Total JF

don strand Edge Middle left right tension (kN)

0 0 0 0 0% 0% 0% 00 0 0 0 0% 0% 0% 00 0 0 0 0% 0% 0% 00 0 0 0 0% 0% 0% 01 12 600 220 75% 0% 75% 16542 12 300 100 75% 0% 75% 1654

total 24 450.00 160.00 75% 0% 75% 3307

Parabolic curve (Average of Strand's position vertically from the bottom of beam ( Value for Y axis ))

Y = A.x2+ B.x + C

where : A = Constanta : ( (Ymiddle + Yedge)/(L/2)2) A = 0.002815

B = Constanta : ( L x A ) B = -0.057143C = Average of strand's position when the parabolic curve reach the Y axis

Average of Strand's position vertically from the bottom of beam ( Value for Y axis )Y = 0.002815 X

2 + -0.057143 X + 0.450000

Cable tendon angle :

tg αo = 0.005630 X + -0.057143

eccentricity of tendon at middle sectionEccentricity [e] = Yb - Ys = 359.32 mm

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)

Ultimate totalTotal (DL + LL)

LL

Subtotal

Tension

B

H

A

tfl-1tfl-2

tfl-3

tfl-4

tweb

Ya'

1

2

3

Yb'

COMPOSITE BEAM

1

2

3

4

56

Ya

Yb

PRECAST BEAM

Base Line

Cc3

Cc2

Cc1


Zone 2

Zone 4

COMPOSITE BEAM

dp da

b. eff

Zone 3

Cc4

Zone 1

225kN 225kN50kN

0.00

0.20

0.40

0.60

0.80

0 5 10 15 20 25

75.00% 75.00%

71.11%69.86% 69.58% 68.98%

64.44% 64.44%

68.33%69.58% 68.98%

62.14% 62.14%

66.02%67.56% 67.27% 66.68%

60.50% 60.50%

64.39%65.93% 65.64% 65.05%

55.78% 55.78%

59.67%61.21% 60.92% 60.32%

54.79% 54.79%

58.68%60.21% 59.93% 59.33%

50.00%

65.00%

80.00%

0.00 0.00 10.15 16.09 17.45 20.30




UTS

P

l

l/2 l/2

Pec

w

ee

0.002000.00

Zona 1Zona 2


beam section point

60.0%

65.0%

70.0%

75.0%

80.0%

0.00 10.00 20.00 30.00


Luas A1 Luas A2


Luas A1



Anchorageset area



Anchorageset area

55.0%

60.0%

65.0%

70.0%

75.0%

80.0%



64.44%64.44%64.44%64.44%64.44%

68.33%69.86%69.58%68.98%

60.0%

65.0%

70.0%

75.0%



0.0200.0400.0600.0800.0

1000.01200.01400.01600.01800.02000.0

Zona 1

Zona 2

Zona 3

Zona 4

Vn = Vu/f


beam section point

A

H

B

tfl-1tfl-2

tfl-3tfl-4

tweb

Ya'

1

2

3

Yb'

COMPOSITE BEAM

1

2

3

45

Ya

Yb

PRECAST BEAM

Base Line

a

dh

h'

As

As

Ah

Av

B

H

A

tfl-1tfl-2

tfl-3

tfl-4

tweb

1

2

3

4

5

Ya

Yb

PRECAST BEAM

Base Line

1

3

Ya'

Yb''

PRECAST BEAM

Base Line

2

page 4 / 14

(16153) PC I H-125cm; L-20.6m; CTC-150cm

Average of Strand's position vertically from the bottom of beam ( Value for Y axis )

7.2 Losses of Prestress1. Losses of Prestress (Short Term)a. Friction

The equation for calculating the loss of prestress due to friction is :Px = Po.e

-( µ .α + k.x)( AASHTO 1992, Chapt. 9.16.1 )

Where :Px = Prestress force at section distance x from tensile point.Po = Jacking force ( tensile force at anchor, initial)

µ = friction coefficientα = Change of cable angle from tensile point to x sectionk = Wobble coefficientx = Distance from tensile point to x section

When the jacking force is applied at the stressing end, the tendon will elongate. The elongation will be resisted by frictionbetween the strand and its sheating or duct. As the result of this friction, force will be decreased with distance from the jackingend. The friction is comprised of two effects : curvature friction which is a function of the thendons profile, and wooble frictionwhich is the result of minor horizontal or vertical deviation form intended profile.

B

H

A

tfl-1tfl-2

tfl-3

tfl-4

tweb

Ya'

1

2

3

Yb'

COMPOSITE BEAM

1

2

3

4

56

Ya

Yb

PRECAST BEAM

Base Line

Cc3

Cc2

Cc1


Zone 2

Zone 4

COMPOSITE BEAM

dp da

b. eff

Zone 3

Cc4

Zone 1

225kN 225kN50kN

0.00

0.20

0.40

0.60

0.80

0 5 10 15 20 25

75.00% 75.00%

71.11%69.86% 69.58% 68.98%

64.44% 64.44%

68.33%69.58% 68.98%

62.14% 62.14%

66.02%67.56% 67.27% 66.68%

60.50% 60.50%

64.39%65.93% 65.64% 65.05%

55.78% 55.78%

59.67%61.21% 60.92% 60.32%

54.79% 54.79%

58.68%60.21% 59.93% 59.33%

50.00%

65.00%

80.00%

0.00 0.00 10.15 16.09 17.45 20.30




UTS

P

l

l/2 l/2

Pec

w

ee

0.002000.00

Zona 1Zona 2


beam section point

65.0%

70.0%

75.0%

80.0%

Luas A1 Luas A2


Luas A1

Luasan dengan asumsi X < 0.5 span

55.0%

60.0%

65.0%

70.0%

75.0%

80.0%



64.44%64.44%64.44%64.44%64.44%

68.33%69.86%69.58%68.98%

60.0%

65.0%

70.0%

75.0%



0.0200.0400.0600.0800.0

1000.01200.01400.01600.01800.02000.0

Zona 1

Zona 2

Zona 3

Zona 4

Vn = Vu/f


beam section point

A

H

B

tfl-1tfl-2

tfl-3tfl-4

tweb

Ya'

1

2

3

Yb'

COMPOSITE BEAM

1

2

3

45

Ya

Yb

PRECAST BEAM

Base Line

a

dh

h'

As

As

Ah

Av

B

H

A

tfl-1tfl-2

tfl-3

tfl-4

tweb

1

2

3

4

5

Ya

Yb

PRECAST BEAM

Base Line

1

3

Ya'

Yb''

PRECAST BEAM

Base Line

2

page 5 / 14

x = Distance from tensile point to x section

Friction and Wooble coeficient for grouting tendon in metal sheatingwith Seven Wire Strand : µ = 0.20

k = 0.003

Table of calculation due to Frictionten- Nos Profile % JF a b αdon strand Edge Middle from UTS (rad) 0.00 10.15 20.300 0 0 0 0% 0.00000 0 0.000 0.0% 0.00% 0.0%0 0 0 0 0% 0.00000 0 0.000 0.0% 0.00% 0.0%0 0 0 0 0% 0.00000 0 0.000 0.0% 0.00% 0.0%0 0 0 0 0% 0.00000 0 0.000 0.0% 0.00% 0.0%1 12 600 220 75% 0.00369 -0.0748768 0.149 75.0% 70.61% 68.5%2 12 300 100 75% 0.00194 -0.0394089 0.079 75.0% 71.61% 69.5%

total 24 450.00 160.00 75% 0.00281 -0.0571429 0.114 75.0% 71.1% 69.0%

b. Anchor set

Exact calculation is typical done as an iterative process as follows :1. Calculated loss of prestress per length with assuming a linear variation in prestress at start to end of tendon

β = Loss of prestress per lengthβ = Fpu . (P at JF - P at end of tendon) / distance JF to end of tendon

2. Assuming drawn-in (∆).

3. The length, x, over which anchorage set is effective is determined as followos :x = Sqrt ( Es . ∆ / β )

effective anchorage set point position :

Tendons are typically anchored with two piece, conical wedges. When the tension applied by the jack is released, the strandretracts pulling the wedges in to the anchorage device and locks the strand in place. The lost in elongation is small . It depend onthe wedges, the jack and the jacking procedure. This lost in elongation is resisted by friction just as the initial elongation isresisted by friction.

Prestress force (Px) = % UTS

B

H

A

tfl-1tfl-2

tfl-3

tfl-4

tweb

Ya'

1

2

3

Yb'

COMPOSITE BEAM

1

2

3

4

56

Ya

Yb

PRECAST BEAM

Base Line

Cc3

Cc2

Cc1


Zone 2

Zone 4

COMPOSITE BEAM

dp da

b. eff

Zone 3

Cc4

Zone 1

225kN 225kN50kN

75.00% 75.00%

71.11%69.86% 69.58% 68.98%

64.44% 64.44%

68.33%69.58% 68.98%

62.14% 62.14%

66.02%67.56% 67.27% 66.68%

60.50% 60.50%

64.39%65.93% 65.64% 65.05%

55.78% 55.78%

59.67%61.21% 60.92% 60.32%

54.79% 54.79%

58.68%60.21% 59.93% 59.33%

50.00%

65.00%

80.00%

0.00 0.00 10.15 16.09 17.45 20.30




UTS

P

l

l/2 l/2

Pec

w

ee

0.002000.00

Zona 1Zona 2


beam section point

60.0%

65.0%

0.00 10.00 20.00 30.00


Luas A1 Luas A2


Luas A1



Anchorageset area



Anchorageset area

55.0%

60.0%

65.0%

70.0%

75.0%

80.0%



64.44%64.44%64.44%64.44%64.44%

68.33%69.86%69.58%68.98%

60.0%

65.0%

70.0%

75.0%



0.0200.0400.0600.0800.0

1000.01200.01400.01600.01800.02000.0

Zona 1

Zona 2

Zona 3

Zona 4

Vn = Vu/f


beam section point

A

H

B

tfl-1tfl-2

tfl-3tfl-4

tweb

Ya'

1

2

3

Yb'

COMPOSITE BEAM

1

2

3

45

Ya

Yb

PRECAST BEAM

Base Line

a

dh

h'

As

As

Ah

Av

B

H

A

tfl-1tfl-2

tfl-3

tfl-4

tweb

1

2

3

4

5

Ya

Yb

PRECAST BEAM

Base Line

1

3

Ya'

Yb''

PRECAST BEAM

Base Line

2

page 5 / 14

(16153) PC I H-125cm; L-20.6m; CTC-150cm

4 Check Assuming drawn-in (∆). The displacement of jacking end of tendon should be equal with assumption∆ = Anchorage set area x Ult. Tensile Stress / Modulus Elasticity of PC Strand∆ = Aset . Fpu / Es∆ = equal with assumption (trial)

Table of calculation due anchor setten- Nos β draw in ∆

don strand Mpa/mm mm X (m) Px (% UTS) X (m) Px (% UTS) 0.00 10.15 20.300 0.0 0.00000 0.00 0.00 0.00% 0.00 0.00% 0.0% 0.00% 0.0%0 0.0 0.00000 8.00 0.00 0.00% 0.00 0.00% 0.0% 0.00% 0.0%0 0.0 0.00000 8.00 0.00 0.00% 0.00 0.00% 0.0% 0.00% 0.0%0 0.0 0.00000 8.00 0.00 0.00% 0.00 0.00% 0.0% 0.00% 0.0%1 12.0 0.00596 8.00 16.09 69.37% 0.00 0.00% 63.7% 68.13% 68.5%2 12.0 0.00507 8.00 17.45 70.07% 0.00 0.00% 65.1% 68.52% 69.5%

total 24 0.00552 8.00 16.77 69.72% 0.00 0.00% 64.44% 68.33% 68.98%

From left side From right side after anchorage set = % UTS

B

H

A

tfl-1tfl-2

tfl-3

tfl-4

tweb

Ya'

1

2

3

Yb'

COMPOSITE BEAM

1

2

3

4

56

Ya

Yb

PRECAST BEAM

Base Line

Cc3

Cc2

Cc1


Zone 2

Zone 4

COMPOSITE BEAM

dp da

b. eff

Zone 3

Cc4

Zone 1

225kN 225kN50kN

0.00

0.20

0.40

0.60

0.80

0 5 10 15 20 25

75.00% 75.00%

71.11%69.86% 69.58% 68.98%

64.44% 64.44%

68.33%69.58% 68.98%

62.14% 62.14%

66.02%67.56% 67.27% 66.68%

60.50% 60.50%

64.39%65.93% 65.64% 65.05%

55.78% 55.78%

59.67%61.21% 60.92% 60.32%

54.79% 54.79%

58.68%60.21% 59.93% 59.33%

50.00%

65.00%

80.00%

0.00 0.00 10.15 16.09 17.45 20.30




UTS

P

l

l/2 l/2

Pec

w

ee

0.002000.00

Zona 1Zona 2


beam section point

60.0%

65.0%

70.0%

75.0%

80.0%

0.00 10.00 20.00 30.00


Luas A1 Luas A2


Luas A1



Anchorageset area



Anchorageset area

55.0%

60.0%

65.0%

70.0%

75.0%

80.0%

0.00 10.00 20.00 30.00


64.44%64.44%64.44%64.44%64.44%

68.33%69.86%69.58%68.98%

60.0%

65.0%

70.0%

75.0%

0.00 5.00 10.00 15.00 20.00 25.00


0.0200.0400.0600.0800.0

1000.01200.01400.01600.01800.02000.0

Zona 1

Zona 2

Zona 3

Zona 4

Vn = Vu/f


beam section point

A

H

B

tfl-1tfl-2

tfl-3tfl-4

tweb

Ya'

1

2

3

Yb'

COMPOSITE BEAM

1

2

3

45

Ya

Yb

PRECAST BEAM

Base Line

a

dh

h'

As

As

Ah

Av

B

H

A

tfl-1tfl-2

tfl-3

tfl-4

tweb

1

2

3

4

5

Ya

Yb

PRECAST BEAM

Base Line

1

3

Ya'

Yb''

PRECAST BEAM

Base Line

2

page 6 / 14

c. Elastic Shortening ( ES )Elastic shortening refers to the shortening of the concrete as the postensioning force is applied.As the concrete shorterns, the tendon length also shortens, resulting in a loss of prestress.The following simplified equation to estimate the appropriate amount of prestress loss to attribute to elastic shorteningfor member with bonded tendons :ES = Kes . Es . fcir / Eci

where:Kes = 0.50 for post-tensioned members when tendon are tensioned in sequential order to the same tensionES = Elastic modulus of tendon materialEci = Elastic modulus of the concrete at the time of prestress transferfcir =

Assumption Losses due ES 2.30%

Pi = Total prestressing force at releasePi = 68.3% - 2.30% = 66.02% UTS x nos x Aps = 2911.3893 kN

fcir = Pi / A + Pi. ec2/ I + Mg.ec/I

fcir = 13.49 N/mm2

so, ES = 42.82 N/mm2, percent actual ES losses = Es/fpu 2.30% equal with losses assumption

2. Losses of Prestress ( Long Term )d. Shrinkage ( SH )

SH = 8,2*e-6*Ksh*ES*(1-0,06*V/S)*(100-RH) (ACI 318-95, Chapt. 18.6)

SH = 30.33 N/mm2 percent actual SH losses = SH/fpu 1.63%

Where :The factor Ksh account for the shringkage that will have taken place before the prestressing applied.for postensioning members, Ksh is taken from the following table :

Days 1 3 5 7 10 20 30 60Ksh 0.92 0.85 0.8 0.77 0.73 0.64 0.58 0.45

Ksh = 0.64

V/S = 0.08 Volume = 6.53 m3

Surface = 80.43 m2

RH = 70.00

concrete stress at the centre of gravity of prestressing tendons due to prestressing force at transfer and the self weight ofthe member at the section of maximum positive moment

"days" is the number of days between the end of moist curing and the application of prestress.In a structuresthat are not moist cured, Ksh is typiclly based on when the concrete was cast

B

H

A

tfl-1tfl-2

tfl-3

tfl-4

tweb

Ya'

1

2

3

Yb'

COMPOSITE BEAM

1

2

3

4

56

Ya

Yb

PRECAST BEAM

Base Line

Cc3

Cc2

Cc1


Zone 2

Zone 4

COMPOSITE BEAM

dp da

b. eff

Zone 3

Cc4

Zone 1

225kN 225kN50kN

0.00

0.20

0.40

0.60

0.80

0 5 10 15 20 25

75.00% 75.00%

71.11%69.86% 69.58% 68.98%

64.44% 64.44%

68.33%69.58% 68.98%

62.14% 62.14%

66.02%67.56% 67.27% 66.68%

60.50% 60.50%

64.39%65.93% 65.64% 65.05%

55.78% 55.78%

59.67%61.21% 60.92% 60.32%

54.79% 54.79%

58.68%60.21% 59.93% 59.33%

50.00%

65.00%

80.00%

0.00 0.00 10.15 16.09 17.45 20.30




UTS

P

l

l/2 l/2

Pec

w

ee

0.002000.00

Zona 1Zona 2


beam section point

60.0%

65.0%

70.0%

75.0%

80.0%

0.00 10.00 20.00 30.00


Luas A1 Luas A2


Luas A1

Luasan dengan asumsi X < 0.5 span



0.0200.0400.0600.0800.0

1000.01200.01400.01600.01800.02000.0

Zona 1

Zona 2

Zona 3

Zona 4

Vn = Vu/f


beam section point

A

H

B

tfl-1tfl-2

tfl-3tfl-4

tweb

Ya'

1

2

3

Yb'

COMPOSITE BEAM

1

2

3

45

Ya

Yb

PRECAST BEAM

Base Line

a

dh

h'

As

As

Ah

Av

B

H

A

tfl-1tfl-2

tfl-3

tfl-4

tweb

1

2

3

4

5

Ya

Yb

PRECAST BEAM

Base Line

1

3

Ya'

Yb''

PRECAST BEAM

Base Line

2

page 6 / 14

(16153) PC I H-125cm; L-20.6m; CTC-150cm

e. Creep ( CR )

CR = Kcr*(Es/Ec)*(fcir-fcds) (ACI 318-95, Chapt. 18.6)

CR = 87.87 N/mm2

percent actual CR losses = CR/fpu 4.72%Where :

Kcr = 1.60 (for postensioned member)fcir = stress at center point prestress force, initial condition

fcir = 13.492 N/mm2

Msd = Moment due to all superimposed permanent dead loads applied after prestressingMsd = 609.47 kN.mfcds = Stress in a concrete at the cgs of the tendon due to all superimposed dead load

fcds 1 = Msdl.e/I = 3.46 N/mm2

component of fcd due to load on the plain beam

fcds 2 = Madl.e/Ic = 0.36 N/mm2

component of fcd due to load on the composite beam

fcds = fcds 1 + fcds 2 = 3.82 N/mm2

f. Steel Relaxation ( RE )

The equation for prestress loss due to relaxation of tendons is :RE = [ Kre - J*(SH+CR+ES) ] *C (ACI 318-95, Chapt. 18.6)

RE = 18.48 N/mm2

percent actual RE losses = RE/fpu 0.99%

Over time, the compresive stress induced by postensioning causes a shortening of the concrete member. The increase instrain due to a sustained stress is refered to as creep. Loss of prestress due to a creep is nominally propotional to the netpermanent compresive stressin the concrete. the net permanent compressive stress is the initial compressive stress in theconcrete due to the prestressing minus the tensile stress due to self weight and superimposed deadload moments

Relaxation is defined as a gradual decrease of stress in a material under constant strain. In the case of steel, relaxation isthe result of permanent alteration of the grain structure. The rate of relaxation at any point in time depends on the stresslevel in the tendon at that time. Because of other prestress losses, there is a continual reduction of tendon strss; thiscauses a reduction in the relaxation rate.

B

H

A

tfl-1tfl-2

tfl-3

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Ya'

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COMPOSITE BEAM

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56

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Base Line

Cc3

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Zone 2

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COMPOSITE BEAM

dp da

b. eff

Zone 3

Cc4

Zone 1

225kN 225kN50kN

0.00

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0 5 10 15 20 25

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l

l/2 l/2

Pec

w

ee

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Zona 1Zona 2


beam section point

60.0%

65.0%

70.0%

75.0%

80.0%

0.00 10.00 20.00 30.00


Luas A1 Luas A2


Luas A1



Anchorageset area



Anchorageset area

55.0%

60.0%

65.0%

70.0%

75.0%

80.0%



64.44%64.44%64.44%64.44%64.44%

68.33%69.86%69.58%68.98%

60.0%

65.0%

70.0%

75.0%



0.0200.0400.0600.0800.0

1000.01200.01400.01600.01800.02000.0

Zona 1

Zona 2

Zona 3

Zona 4

Vn = Vu/f


beam section point

A

H

B

tfl-1tfl-2

tfl-3tfl-4

tweb

Ya'

1

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Yb'

COMPOSITE BEAM

1

2

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45

Ya

Yb

PRECAST BEAM

Base Line

a

dh

h'

As

As

Ah

Av

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A

tfl-1tfl-2

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tfl-4

tweb

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page 7 / 14

RE = 18.48 N/mm2

percent actual RE losses = RE/fpu 0.99%Where :

Kre = 5000.00 (for 270 grade, low relaxation strand)J = 0.04 (for 270 grade, low relaxation strand)C = 0.66 for fpi/fpu = 0.683

RESUME DUE TO SHORT & LONG TERM LOSSESLossesSectionx (m)0.00 75.00% 64.44% 62.14% 12.86% 60.50% 55.78% 54.79% 20.21%0.00 75.00% 64.44% 62.14% 12.86% 60.50% 55.78% 54.79% 20.21%0.00 75.00% 64.44% 62.14% 12.86% 60.50% 55.78% 54.79% 20.21%0.00 75.00% 64.44% 62.14% 12.86% 60.50% 55.78% 54.79% 20.21%0.00 75.00% 64.44% 62.14% 12.86% 60.50% 55.78% 54.79% 20.21%10.15 71.11% 68.33% 66.02% 5.09% 64.39% 59.67% 58.68% 12.43%16.09 69.86% 69.86% 67.56% 2.30% 65.93% 61.21% 60.21% 9.65%17.45 69.58% 69.58% 67.27% 2.30% 65.64% 60.92% 59.93% 9.65%20.30 68.98% 68.98% 66.68% 2.30% 65.05% 60.32% 59.33% 9.65%

friction Losses equotion :0 > x > 10.1575.00% -+ 0.38% x

10.2 > x > 20.3071.11% + 0.06% x x - 10.15

Long term Losses equotion :0 > x > 0.0054.79% #DIV/0!0 > x > 10.1554.79% + 0.38% x x - 0

10.15 > x > 16.0958.68% + 0.26% x x - 10.15

16.09 > x > 17.4560.21% -+ 0.21% x x - 16.0892968

17.45 > x > 20.3059.93% -+ 0.21% x x - 17.4494923

SteelRelaxation

(SR)

Anchor set

II. Long Term Losses

Friction Creep (CR)Shringkage

(SH)Elastic

Shortening(ES)

TotalLosses (%)

I. Short Term LossesTotal Losses

(%)

B

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Base Line

Cc3

Cc2

Cc1


Zone 2

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COMPOSITE BEAM

dp da

b. eff

Zone 3

Cc4

Zone 1

225kN 225kN50kN

0.00

0.20

0.40

0.60

0.80

0 5 10 15 20 25

75.00% 75.00%

71.11%69.86% 69.58% 68.98%

64.44% 64.44%

68.33%69.58% 68.98%

62.14% 62.14%

66.02%67.56% 67.27% 66.68%

60.50% 60.50%

64.39%65.93% 65.64% 65.05%

55.78% 55.78%

59.67%61.21% 60.92% 60.32%

54.79% 54.79%

58.68%60.21% 59.93% 59.33%

50.00%

65.00%

80.00%

0.00 0.00 10.15 16.09 17.45 20.30




UTS

P

l

l/2 l/2

Pec

w

ee

0.002000.00

Zona 1Zona 2


beam section point

60.0%

65.0%

70.0%

75.0%

80.0%

0.00 10.00 20.00 30.00


Luas A1 Luas A2


Luas A1



Anchorageset area



Anchorageset area

55.0%

60.0%

65.0%

70.0%

75.0%

80.0%



64.44%64.44%64.44%64.44%64.44%

68.33%69.86%69.58%68.98%

60.0%

65.0%

70.0%

75.0%



0.0200.0400.0600.0800.0

1000.01200.01400.01600.01800.02000.0

Zona 1

Zona 2

Zona 3

Zona 4

Vn = Vu/f


beam section point

A

H

B

tfl-1tfl-2

tfl-3tfl-4

tweb

Ya'

1

2

3

Yb'

COMPOSITE BEAM

1

2

3

45

Ya

Yb

PRECAST BEAM

Base Line

a

dh

h'

As

As

Ah

Av

B

H

A

tfl-1tfl-2

tfl-3

tfl-4

tweb

1

2

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PRECAST BEAM

Base Line

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Base Line

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page 7 / 14

(16153) PC I H-125cm; L-20.6m; CTC-150cm

7.3 Effective Stress Force

Resume Prestressed Force at middleCable

stress

[kN/mm2] [mm2] [kN]

9.0% 66.0% 1228 2370.72 2911.3916.3% 58.7% 1091 2370.72 2587.37

VIII. STRESS AND DEFFLECTION ANALYSISBeam Segment 1 2 3 4 5 6 7 8

Length (m) 4.70 3.50 3.60 3.50 4.70 0.00 0.00 0.00Additional length at the end of the beam = 0.30 m Total Length = 20.60 m

8.1 Stress at initialDescription Middle SEC 1-1 SEC 2-2 SEC 3-3 SEC 4-4 SEC 5-5 SEC 6-6

x - [m] Span 0.00 4.70 8.20 11.80 15.30 10.00

Moment DL [kN.m] 388.26 0.00 279.20 375.68 375.68 279.20 388.26Jacking Force [kN] 3307.15 3307.15 3307.15 3307.15 3307.15 3307.15 3307.15Losses due to friction % 4% 0% 2% 3% 4% 4% 4%Pi [kN] 3180.43 3307.15 3247.59 3203.24 3182.03 3189.45 3180.43e (eccentricity) [m] 0.359 0.078 0.280 0.350 0.350 0.280 0.359Pi.e [kN.m] -1143 -257 -910 -1122 -1114 -894 -1143Moment Net. [kN.m] -755 -257 -631 -746 -739 -615 -755

Pi / A [N/mm2] 10.04 10.44 10.25 10.11 10.05 10.07 10.04

M / Wa [N/mm2] -10.03 -3.42 -8.39 -9.92 -9.82 -8.17 -10.03 Allow.

M / Wb [N/mm2] 7.13 2.43 5.96 7.05 6.98 5.81 7.13 stress

Initial Stresses top ( σT ) 0.01 7.02 1.87 0.19 0.23 1.90 0.01 -1.4

% Losses ofprestress

ConditionP%UTS

effectiveprestress

long term

Asp

short term

B

H

A

tfl-1tfl-2

tfl-3

tfl-4

tweb

Ya'

1

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COMPOSITE BEAM

1

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56

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PRECAST BEAM

Base Line

Cc3

Cc2

Cc1


Zone 2

Zone 4

COMPOSITE BEAM

dp da

b. eff

Zone 3

Cc4

Zone 1

225kN 225kN50kN

0.00

0.20

0.40

0.60

0.80

0 5 10 15 20 25

75.00% 75.00%

71.11%69.86% 69.58% 68.98%

64.44% 64.44%

68.33%69.58% 68.98%

62.14% 62.14%

66.02%67.56% 67.27% 66.68%

60.50% 60.50%

64.39%65.93% 65.64% 65.05%

55.78% 55.78%

59.67%61.21% 60.92% 60.32%

54.79% 54.79%

58.68%60.21% 59.93% 59.33%

50.00%

65.00%

80.00%

0.00 0.00 10.15 16.09 17.45 20.30




UTS

P

l

l/2 l/2

Pec

w

ee

0.002000.00

Zona 1Zona 2


beam section point

60.0%

65.0%

70.0%

75.0%

80.0%

0.00 10.00 20.00 30.00


Luas A1 Luas A2


Luas A1



Anchorageset area



Anchorageset area

55.0%

60.0%

65.0%

70.0%

75.0%

80.0%



64.44%64.44%64.44%64.44%64.44%

68.33%69.86%69.58%68.98%

60.0%

65.0%

70.0%

75.0%



0.0200.0400.0600.0800.0

1000.01200.01400.01600.01800.02000.0

Zona 1

Zona 2

Zona 3

Zona 4

Vn = Vu/f


beam section point

A

H

B

tfl-1tfl-2

tfl-3tfl-4

tweb

Ya'

1

2

3

Yb'

COMPOSITE BEAM

1

2

3

45

Ya

Yb

PRECAST BEAM

Base Line

a

dh

h'

As

As

Ah

Av

B

H

A

tfl-1tfl-2

tfl-3

tfl-4

tweb

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2

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PRECAST BEAM

Base Line

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PRECAST BEAM

Base Line

2

page 8 / 14

Initial Stresses top ( σT ) 0.01 7.02 1.87 0.19 0.23 1.90 0.01 -1.4

bot ( σB ) 17.17 12.87 16.21 17.16 17.03 15.88 17.17 19.2

8.2 Stress at service> Load of precast, slab, diaphragm and prestress by PC Beam ( = M1 )> Live load and asphalt by composite ( = M2 )Description Middle SEC 1-1 SEC 2-2 SEC 3-3 SEC 4-4 SEC 5-5 SEC 6-6

x - [m] Span 0.00 4.70 8.20 11.80 15.30 10.00Moment DL [kN.m] 916.83 0.00 659.29 887.12 887.12 659.29 916.83Total Losses % 16% 20% 18% 17% 16% 15% 16%effective prestress P [kN] 2584.83 2415.87 2495.28 2554.42 2606.18 2646.09 2584.83P . e [m] -928.77 -188.02 -699.29 -894.55 -912.68 -741.56 -928.77Moment --- M1 [kN.m] -11.95 -188.02 -40.00 -7.43 -25.55 -82.27 -11.95Moment --- M2 [kN.m] 1270.40 0.00 913.54 1229.24 1229.24 913.54 1270.40

P / A [N/mm2] 8.17 8.17 8.17 8.17 8.17 8.17 8.17

M 1 / Wa [N/mm2] -0.16 -2.50 -0.53 -0.10 -0.34 -1.09 -0.16

M 1 / Wb [N/mm2] 0.11 1.78 0.38 0.07 0.24 0.78 0.11

M 2 / Wa' [N/mm2] 2.56 0.00 1.84 2.48 2.48 1.84 2.56 Allow.

M 2 / Wb' [N/mm2] -6.93 0.00 -4.98 -6.70 -6.70 -4.98 -6.93 stress

Stress at Service slab ( σS ) 4.61 0.00 3.32 4.46 4.46 3.32 4.61 11.3

top ( σT ) 10.57 5.67 9.48 10.55 10.31 8.92 10.57 18.0

bot ( σB ) 1.35 9.94 3.57 1.54 1.71 3.96 1.35 -3.2

Note : 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 )

Pi = Initial Prestress ( at transfer condition - chapt. 7.4. Effective Stress Force )P = Prestress at service condition….. ( Chapter 7.4 -effective Stress Force )M = Moment Net.A = Total Area of Precast Beam ( Chapter 3.1 - Precast Beam)

Wa = Modulus Section for Top section of Precast conditionWb = Modulus Section for Bottom section of Precast conditionWa' = Modulus Section for Top section of composit Condition……. ( Chapter 3.3 - Resume )Wb' = Modulus section for bottom section of composite condition ……. ( Chapter 3.3 - Resume )

Moment Bal =Moment DL =

Moment Net =

[kg/cm2]

B

H

A

tfl-1tfl-2

tfl-3

tfl-4

tweb

Ya'

1

2

3

Yb'

COMPOSITE BEAM

1

2

3

4

56

Ya

Yb

PRECAST BEAM

Base Line

Cc3

Cc2

Cc1


Zone 2

Zone 4

COMPOSITE BEAM

dp da

b. eff

Zone 3

Cc4

Zone 1

225kN 225kN50kN

0.00

0.20

0.40

0.60

0.80

0 5 10 15 20 25

75.00% 75.00%

71.11%69.86% 69.58% 68.98%

64.44% 64.44%

68.33%69.58% 68.98%

62.14% 62.14%

66.02%67.56% 67.27% 66.68%

60.50% 60.50%

64.39%65.93% 65.64% 65.05%

59.67%61.21% 60.92% 60.32%

58.68%60.21% 59.93% 59.33%

65.00%

80.00%


LOSSES OF PRESTRESS DIAGRAMUTS

P

l

l/2 l/2

Pec

w

ee

0.002000.00

Zona 1Zona 2


beam section point

60.0%

65.0%

70.0%

75.0%

80.0%

0.00 10.00 20.00 30.00


Luas A1 Luas A2


Luas A1



Anchorageset area



Anchorageset area

55.0%

60.0%

65.0%

70.0%

75.0%

80.0%



64.44%64.44%64.44%64.44%64.44%

68.33%69.86%69.58%68.98%

60.0%

65.0%

70.0%

75.0%



0.0200.0400.0600.0800.0

1000.01200.01400.01600.01800.02000.0

Zona 1

Zona 2

Zona 3

Zona 4

Vn = Vu/f


beam section point

A

H

B

tfl-1tfl-2

tfl-3tfl-4

tweb

Ya'

1

2

3

Yb'

COMPOSITE BEAM

1

2

3

45

Ya

Yb

PRECAST BEAM

Base Line

a

dh

h'

As

As

Ah

Av

B

H

A

tfl-1tfl-2

tfl-3

tfl-4

tweb

1

2

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page 8 / 14

(16153) PC I H-125cm; L-20.6m; CTC-150cm

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

Pi/A = 10.04 MPa M/Wa = -10.03 MPa stop = 0.01 MPa

+ =

Pi/A = 10.04 MPa M/Wb = 7.13 MPa sbottom = 17.17 MPa

2. STRESS DIAGRAM AT SERVICE

sslab = 4.61 MPa

P/A = 8.17 MPa M1/Wa = -0.16 MPa M2/Wa'= 2.56 MPa stop = 10.57 MPa

+ +

P/A = 8.17 MPa M1/Wb = 0.11 MPa M2/Wb'= -6.93 MPa sbottom = 1.35 MPa

8.3 Deflection8.3.1 Chamber due to Prestress Load

Deflection on middle section :

∆pi= -27.09 mm

[ee+(5/6)(ec-ee)] x (P. l2/8 Ec Ix)∆pi=

B

H

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Base Line

Cc3

Cc2

Cc1


Zone 2

Zone 4

COMPOSITE BEAM

dp da

b. eff

Zone 3

Cc4

Zone 1

225kN 225kN50kN

0.00

0.20

0.40

0.60

0.80

0 5 10 15 20 25

75.00% 75.00%

71.11%69.86% 69.58% 68.98%

64.44% 64.44%

68.33%69.58% 68.98%

62.14% 62.14%

66.02%67.56% 67.27% 66.68%

60.50% 60.50%

64.39%65.93% 65.64% 65.05%

55.78% 55.78%

59.67%61.21% 60.92% 60.32%

54.79% 54.79%

58.68%60.21% 59.93% 59.33%

50.00%

65.00%

80.00%

0.00 0.00 10.15 16.09 17.45 20.30




UTS

P

l

Pec

ee

0.002000.00

Zona 1Zona 2


beam section point

60.0%

65.0%

70.0%

75.0%

80.0%

0.00 10.00 20.00 30.00


Luas A1 Luas A2


Luas A1



Anchorageset area



Anchorageset area

55.0%

60.0%

65.0%

70.0%

75.0%

80.0%



64.44%64.44%64.44%64.44%64.44%

68.33%69.86%69.58%68.98%

60.0%

65.0%

70.0%

75.0%



0.0200.0400.0600.0800.0

1000.01200.01400.01600.01800.02000.0

Zona 1

Zona 2

Zona 3

Zona 4

Vn = Vu/f


beam section point

A

H

B

tfl-1tfl-2

tfl-3tfl-4

tweb

Ya'

1

2

3

Yb'

COMPOSITE BEAM

1

2

3

45

Ya

Yb

PRECAST BEAM

Base Line

a

dh

h'

As

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page 9 / 14

∆pi= -27.09 mmwhere : P = Prestress force

Eci = Modulus Elasticity of ConcreteIxi = Section Inertia

l = length of anchor to anchoree =

ec =

8.3.2 Deflection at initial, erection and service condition (based : PCI handbook 4.6.5 Long-Time Chamber Deflection)Deflection (∆) on simple span structure : where : q = Uniform Load

∆q= (5/384)*q*L4/Ec Ix) P = Point Load

∆p= P.l3/48 Ec Ix l = Beam Span

Deflection calculation table : Estimating long-time cambers and deflections

q (kN/m) P (kN) Release(1)

multipliers Erection(2)

multipliers Service(3)

1. Due to Prestress force -27.09 1.80 x (1) -48.76 2.20 x (1) -59.602. Due to beam weight (DL) 7.77 9.68 1.85 x (1) 17.91 2.40 x (1) 23.23

-17.41 -30.85 -36.363. Due to ADL 2.87 3.20 3.00 x (2) 9.61

-27.65 -26.754. Due to Composite overtoping 7.70 8.58 2.30 x (2) 19.74

-19.06 -7.014. due to asphaltic (SDL) 1.62 0.59

-6.425. due to Live Load = UDL + KEL 13.50 102.90 7.96

1.54Resume of deflection :

1. Deflection at service = -6.42 mm2. Deflection due to Live Load = 7.96 mm < allow. deflection L/800 = 25 mm OK3. Total deflection with LL = 1.54 mm, deflection downward

Distance between c.g of strand andc.g of concrete at end

Distance between c.g of strand andc.g of concrete at centre

Long time cambers and deflectionWORKING LOAD Loading

B

H

A

tfl-1tfl-2

tfl-3

tfl-4

tweb

Ya'

1

2

3

Yb'

COMPOSITE BEAM

1

2

3

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56

Ya

Yb

PRECAST BEAM

Base Line

Cc3

Cc2

Cc1


Zone 2

Zone 4

COMPOSITE BEAM

dp da

b. eff

Zone 3

Cc4

Zone 1

225kN 225kN50kN

0.00

0.20

0.40

0.60

0.80

0 5 10 15 20 25

75.00% 75.00%

71.11%69.86% 69.58% 68.98%

64.44% 64.44%

68.33%69.58% 68.98%

62.14% 62.14%

66.02%67.56% 67.27% 66.68%

60.50% 60.50%

64.39%65.93% 65.64% 65.05%

55.78% 55.78%

59.67%61.21% 60.92% 60.32%

54.79% 54.79%

58.68%60.21% 59.93% 59.33%

50.00%

65.00%

80.00%

0.00 0.00 10.15 16.09 17.45 20.30




UTS

P

l/2 l/2

Pec

w

ee

0.002000.00

Zona 1Zona 2


beam section point

60.0%

65.0%

70.0%

75.0%

80.0%

0.00 10.00 20.00 30.00


Luas A1 Luas A2


Luas A1



Anchorageset area



Anchorageset area

55.0%

60.0%

65.0%

70.0%

75.0%

80.0%



64.44%64.44%64.44%64.44%64.44%

68.33%69.86%69.58%68.98%

60.0%

65.0%

70.0%

75.0%



0.0200.0400.0600.0800.0

1000.01200.01400.01600.01800.02000.0

Zona 1

Zona 2

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Vn = Vu/f


beam section point

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page 9 / 14

(16153) PC I H-125cm; L-20.6m; CTC-150cm

IX. FLEXURAL STRENGTH AND DUCTILITY

9.1 Steel Index Requirement (SNI Beton 03-2847-2002 pasal 20.8)Effectif slab width, is minimum length from :1. Girder web thickness + 16 Slab thickness =3370 mm for slab with fc' = 25.00 MPa2. Beam Ctc =1500 mm …. Control β Value = 0.853. Span length / 4 =5000 mm

Thus, Effectif slab width is : =1500 mm

Partial Rebar:fy = 400 MPaUse 3 Dia.10 mm at tension area

As = 235.62 mm2 b web = 170 mm

d = 1192.0 mmPartial tension rebar ratio : Rebar in compresion area is neglected due calculationρt = As / (bweb x d ) ρt = 0.00116 ρc = 0ωt = ρt . fy / fc ωt = 0.019 ωc = 0

Low Relaxation strand :fpu = 1860 MPaStrand stress ratio fpu / fpy = 0.9 value γp = 0.28

dp = 1360.0 mm Aps = 2370.72 mm2

beff = 1500 mm

Prestress ratio :ρp = Aps / (beff x dp ) ρp = 0.00116212

fps = fpu {1 - γp / β (ρp.fpu/fc + d/dp (ωt-ωc))) fps = 1797.0 MPaωp = ρp fps/fc ωp = 0.08353459Resume of Steel Index Requirement (SNI Beton 03-2847-2002 pasal 20.8)

ωp + d/dp (ωt-ωc) < 0.36 β

0.0998404 < 0.306 Under Reinf, Meet With Steel Index Requirement

B

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225kN 225kN50kN

0.00

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0 5 10 15 20 25

75.00% 75.00%

71.11%69.86% 69.58% 68.98%

64.44% 64.44%

68.33%69.58% 68.98%

62.14% 62.14%

66.02%67.56% 67.27% 66.68%

60.50% 60.50%

64.39%65.93% 65.64% 65.05%

55.78% 55.78%

59.67%61.21% 60.92% 60.32%

54.79% 54.79%

58.68%60.21% 59.93% 59.33%

50.00%

65.00%

80.00%

0.00 0.00 10.15 16.09 17.45 20.30




UTS

P

l

l/2 l/2

Pec

w

ee

0.002000.00

Zona 1Zona 2


beam section point

60.0%

65.0%

70.0%

75.0%

80.0%

0.00 10.00 20.00 30.00


Luas A1 Luas A2


Luas A1



Anchorageset area



Anchorageset area

55.0%

60.0%

65.0%

70.0%

75.0%

80.0%



64.44%64.44%64.44%64.44%64.44%

68.33%69.86%69.58%68.98%

60.0%

65.0%

70.0%

75.0%



0.0200.0400.0600.0800.0

1000.01200.01400.01600.01800.02000.0

Zona 1

Zona 2

Zona 3

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Vn = Vu/f


beam section point

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page 10 / 14

0.0998404 < 0.306 Under Reinf, Meet With Steel Index Requirement

9.2 Momen Capacity

Tps = Aps . FpsTps = 4260264 N

strength reduction factorφ = 0.8

Location of Depth of Concrete Compression Block (a) :Zone hi wi Aci=hi.wi Comp (i) Compresion

(mm) (mm) (mm2) Point (mm) Point (mm)4 133.65534 1500 200483.01 25.00 CIP Slab 673 0.0 335 0 25.00 CIP Slab 1342 0 350 0 40.00 Beam 1341 0 170 0 40.00 Beam 134

a = Tps / ( 0.85 x fc'' slab x beff ) a= 133.66 mmMn = Mn = 5615.30 kN.m

φ Mn = 4492.2404 kN.mBridge life time design for 50 year,so Transient act factor = 1

Mult = 1x 3,442kN-m φ Mn / Mult = 1.305 >1, Moment capacity meet with requirement

9.3 Cracking Capacity

Stress at bottom girder section due to service load (σbot at service) = 1.35 MPaConcrete flexural tension strength fr = 4.4 MPa

Crack Moment, Mcr = (σbot at service + fr ) Wb.comp + Momen (DL+ADL+LL+I)

Mcr = 3247.72 kN.mφMn / Mcr = 1.383 > 1.2 ---- Cracking Capacity requirement is achieve

Cci=0.85 fc'i.Aci

N

00

MPa

66.83

(Tps (dp - comp. point) + As.fy (d - comp. point)

0

Conc. Strength fc'i

Depth of Concrete Compression Block is located at zone 4

4260264

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COMPOSITE BEAM

dp da

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Zone 3

Cc4

Zone 1

225kN 225kN50kN

0.00

0.20

0.40

0.60

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0 5 10 15 20 25

75.00% 75.00%

71.11%69.86% 69.58% 68.98%

64.44% 64.44%

68.33%69.58% 68.98%

62.14% 62.14%

66.02%67.56% 67.27% 66.68%

60.50% 60.50%

64.39%65.93% 65.64% 65.05%

55.78% 55.78%

59.67%61.21% 60.92% 60.32%

54.79% 54.79%

58.68%60.21% 59.93% 59.33%

50.00%

65.00%

80.00%

0.00 0.00 10.15 16.09 17.45 20.30




UTS

P

l

l/2 l/2

Pec

w

ee

0.002000.00

Zona 1Zona 2


beam section point

60.0%

65.0%

70.0%

75.0%

80.0%

0.00 10.00 20.00 30.00


Luas A1 Luas A2


Luas A1



Anchorageset area



Anchorageset area

55.0%

60.0%

65.0%

70.0%

75.0%

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64.44%64.44%64.44%64.44%64.44%

68.33%69.86%69.58%68.98%

60.0%

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0.0200.0400.0600.0800.0

1000.01200.01400.01600.01800.02000.0

Zona 1

Zona 2

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Vn = Vu/f


beam section point

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page 10 / 14

(16153) PC I H-125cm; L-20.6m; CTC-150cm

X. SHEAR ANALYSIS10.1 Shear calculation based on SNI 03-2847-2002

40% Ultimate Tensile Strength = 744 MPaEffective Prestress = 1091 MPa Effective Prestress > 40% fpu

Section Properties :Ix = 5.496E+10 mm4 Ixcomp = 1.673E+11 mm4

Yb = 519.31728 mm Ybcomp = 912.4 mm

Ag = 316750 mm2

Load :Effective prestress Pe = 2587.37 kNFactored Load : Unfactored Load :

qult DL + ADL = 26.0096 kN/m q DL + ADL = 18.3365 kN/mqult LL = 24.3000 kN/m q sdl = 1.6180 kN/mPult LL = 185.2200 kN q DL + ADL = 19.9545 kN/m

Concrete Shear resistance contribution (Vc)Nominal shear strength provide by concrete

Vc = {0.05sqrt(fc') + 5 (Vu.dp/Mu)}bw.dbut nominal strength (Vc) should taken between : (1/6).sqrt(fc').bw.d < Vc < 0.4sqrt(fc').bw.dand Vu.dp/Mu ≤ 1

where :Mu = Maximum factored moment at sectionVu = Maximum factored shear force at sectiond = distance from extreme compresion fiber to centroid of prestress tendon.

Alternatif solution to calculated shear on prestress element is use for structure element which have effective prestress above 40%of ultimate tensile stress

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Zone 2

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COMPOSITE BEAM

dp da

b. eff

Zone 3

Cc4

Zone 1

225kN 225kN50kN

0.00

0.20

0.40

0.60

0.80

0 5 10 15 20 25

75.00% 75.00%

71.11%69.86% 69.58% 68.98%

64.44% 64.44%

68.33%69.58% 68.98%

62.14% 62.14%

66.02%67.56% 67.27% 66.68%

60.50% 60.50%

64.39%65.93% 65.64% 65.05%

55.78% 55.78%

59.67%61.21% 60.92% 60.32%

54.79% 54.79%

58.68%60.21% 59.93% 59.33%

50.00%

65.00%

80.00%

0.00 0.00 10.15 16.09 17.45 20.30




UTS

P

l

l/2 l/2

Pec

w

ee

0.002000.00

Zona 1Zona 2


beam section point

60.0%

65.0%

70.0%

75.0%

80.0%

0.00 10.00 20.00 30.00


Luas A1 Luas A2


Luas A1



Anchorageset area



Anchorageset area

55.0%

60.0%

65.0%

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75.0%

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64.44%64.44%64.44%64.44%64.44%

68.33%69.86%69.58%68.98%

60.0%

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0.0200.0400.0600.0800.0

1000.01200.01400.01600.01800.02000.0

Zona 1

Zona 2

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Vn = Vu/f


beam section point

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a

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page 11 / 14

d = distance from extreme compresion fiber to centroid of prestress tendon.But d need not to take n less than 0.8 hcomposite

bw = width of shear section

Vn = Vc + Vs where : Vn = Nominal Shear force Vu = Ultimate Shear forceVn = Vu / φ Vc = Concrete shear contribution φ = Shear reduction factor

Vs = Shear steel contribution φ = 0.75

Zonafication for shear steel stirup calculationZone 1 Vn < 0.5 Vc No need to use stirupZone 2 Vn < Vc+[0.35 or (75/1200) sqrt(fc')] bw d Required stirup spacing with minimum spacing :

S ≤ 0.75 H S ≤ (av.fy) / (0.35 bw)

S ≤ 600mm S ≤ (av.fy/fpu) (80/Aps) d sqrt(bw/d)

Zone 3 Vn < Vc+0.33 sqrt(fc') bw d Required stirup spacing with spacing :S ≤ (av.fy.d) / ((Vu/φ)-Vc)

S ≤ 0.75 H

S ≤ 600mmZone 4 Vn < Vc+0.67 sqrt(fc') bw d Required tight stirup spacing with spacing :

S ≤ (av.fy.d) / ((Vu/φ)-Vc)

S ≤ 0.375 H

S ≤ 300mmZone 5 Vn > Vc+0.67 sqrt(fc') bw d Section to small, change beam section

Shear rebar steel

SNI 03-2847-2002 Pasal 11.1 : Shear force on beam is hold a part by concrete and the rest of force is hold by shear steel.Concrete contribution (vc), is define as shear force when diagonal cracking appear.

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COMPOSITE BEAM

dp da

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Zone 3

Cc4

Zone 1

225kN 225kN50kN

0.00

0.20

0.40

0.60

0.80

0 5 10 15 20 25

75.00% 75.00%

71.11%69.86% 69.58% 68.98%

64.44% 64.44%

68.33%69.58% 68.98%

62.14% 62.14%

66.02%67.56% 67.27% 66.68%

60.50% 60.50%

64.39%65.93% 65.64% 65.05%

55.78% 55.78%

59.67%61.21% 60.92% 60.32%

54.79% 54.79%

58.68%60.21% 59.93% 59.33%

50.00%

65.00%

80.00%

0.00 0.00 10.15 16.09 17.45 20.30




UTS

P

l

l/2 l/2

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w

ee

0.002000.00

Zona 1Zona 2


beam section point

60.0%

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75.0%

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0.00 10.00 20.00 30.00


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Luas A1



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Anchorageset area

55.0%

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65.0%

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64.44%64.44%64.44%64.44%64.44%

68.33%69.86%69.58%68.98%

60.0%

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0.0200.0400.0600.0800.0

1000.01200.01400.01600.01800.02000.0

Zona 1

Zona 2

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Zona 4

Vn = Vu/f


beam section point

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tfl-1tfl-2

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page 11 / 14

(16153) PC I H-125cm; L-20.6m; CTC-150cm

fy = 400 MPa shear width :Use 2 leg Dia.13 mm bw = 170 mm

Av = 265.46 mm2 bw-e = 650 mm

Shear steel requirement calculation table :dist. ecomp d=dp>0.8H Vu Mu dp(Vu/Mu) Vc Vn Vs Shear Use Space usem m m kN kN-m kN kN kN Zonasi mm mm

0.1 0.460 1.07 682.36 68.49 1.00 964.43 909.81 -54.62 2 600 3000.39 0.476 1.08 665.23 261.55 1.00 979.14 886.98 -92.17 2 600 3000.78 0.497 1.10 642.15 512.77 1.00 998.31 856.20 -142.11 2 600 3001.7 0.544 1.15 587.05 1070.68 0.63 680.21 782.73 102.52 3 600 3002 0.558 1.17 569.17 1238.97 0.54 593.65 758.90 165.25 3 600 3003 0.602 1.21 509.60 1755.21 0.35 426.37 679.47 253.11 3 508 3004 0.641 1.25 450.03 2202.61 0.26 337.72 600.04 262.33 3 505 3005 0.673 1.28 390.46 2581.18 0.19 279.84 520.62 240.78 3 565 300

5.5 0.688 1.30 360.68 2744.66 0.17 256.99 480.90 223.91 3 600 3006.5 0.712 1.32 301.11 3019.99 0.13 218.45 401.48 183.03 3 600 3007.5 0.730 1.34 241.54 3226.48 0.10 185.83 322.05 136.22 3 600 3008.5 0.743 1.35 181.97 3364.14 0.07 156.52 242.62 86.10 3 600 3009.5 0.751 1.36 122.40 3432.98 0.05 128.92 163.19 34.28 2 600 30010 0.752 1.36 92.61 3441.58 0.04 115.39 123.48 8.09 2 600 300

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Zone 3

Cc4

Zone 1

225kN 225kN50kN

0.00

0.20

0.40

0.60

0.80

0 5 10 15 20 25

75.00% 75.00%

71.11%69.86% 69.58% 68.98%

64.44% 64.44%

68.33%69.58% 68.98%

62.14% 62.14%

66.02%67.56% 67.27% 66.68%

60.50% 60.50%

64.39%65.93% 65.64% 65.05%

55.78% 55.78%

59.67%61.21% 60.92% 60.32%

54.79% 54.79%

58.68%60.21% 59.93% 59.33%

50.00%

65.00%

80.00%

0.00 0.00 10.15 16.09 17.45 20.30




UTS

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l/2 l/2

Pec

w

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0.002000.00

Zona 1Zona 2


beam section point

60.0%

65.0%

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80.0%

0.00 10.00 20.00 30.00


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Luas A1



Anchorageset area



Anchorageset area

55.0%

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65.0%

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64.44%64.44%64.44%64.44%64.44%

68.33%69.86%69.58%68.98%

60.0%

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page 12 / 14

x (m) from range nos shearspan edge (m) (row)

Shear spacing S - 75 0 0 0Shear spacing S - 100 0 0 0Shear spacing S - 125 0 0 0Shear spacing S - 150 0 0 0Shear spacing S - 200 0 0 0Shear spacing S - 250 0 0 0Shear spacing S - 300 10 10 33

total shear rebar per half span (row) = 33total shear rebar per span (row) = 66

10.2 Horisontal Shear

Shear Rebar configuration

B

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Cc3

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COMPOSITE BEAM

dp da

b. eff

Zone 3

Cc4

Zone 1

225kN 225kN50kN

0.00

0.20

0.40

0.60

0.80

0 5 10 15 20 25

75.00% 75.00%

71.11%69.86% 69.58% 68.98%

64.44% 64.44%

68.33%69.58% 68.98%

62.14% 62.14%

66.02%67.56% 67.27% 66.68%

60.50% 60.50%

64.39%65.93% 65.64% 65.05%

55.78% 55.78%

59.67%61.21% 60.92% 60.32%

54.79% 54.79%

58.68%60.21% 59.93% 59.33%

50.00%

65.00%

80.00%

0.00 0.00 10.15 16.09 17.45 20.30




UTS

P

l

l/2 l/2

Pec

w

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0.002000.00

Zona 1Zona 2


beam section point

60.0%

65.0%

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75.0%

80.0%

0.00 10.00 20.00 30.00


Luas A1 Luas A2


Luas A1



Anchorageset area



Anchorageset area

55.0%

60.0%

65.0%

70.0%

75.0%

80.0%



64.44%64.44%64.44%64.44%64.44%

68.33%69.86%69.58%68.98%

60.0%

65.0%

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75.0%



0.0200.0400.0600.0800.0

1000.01200.01400.01600.01800.02000.0

Zona 1

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beam section point

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page 12 / 14

(16153) PC I H-125cm; L-20.6m; CTC-150cm

Width of contact surface area bv = 200 mmEffective Height d = 1216 mm

φ = 0.75fy = 400 MPaUse 2 leg Dia.13 mm

Area horisontal Shear Steel Avh = 265.46 mm2Horisontal Shear steel Spacing s = 300 mmHorisontal Shear steel ratio ρv = 0.442%Shear horisontal Nominal

Vnh = (1.8 Mpa + 0.6 ρv. fy) . bv .d

Vnh = 696.00 KNRequirement for shear horisontal steel :Vult < fVnh < 350 bv.d

Vult = Ultimate shear due to superimposed DL + LLVult = 378.26 kNφVnh = 522.00 kN RESUME:

3.5 bv d = 851.20 kN Shear horisontal : OKMinimal Use :

bys = 200 mm Spacing = 1540.04 mm or 4 tweb = 680 mmAvh = 50 by.s / fy Max. Spacing = 300.00 mmAvh = 172.375 mm2/m min no. Spacing = 67 @ 2D13 for shear horisontal / span

Resume = additional shear horizontal requiredXI. END BLOCK DESIGN

Block Anchor dimensiontype a b dia hole Block Area

(mm) (mm) (mm) A (mm2) A1 (mm

2) A2 (mm

2) sqrt(A2/A1)

7 165 165 51 25182.18 27225 1625000 7.73

Concrete Area

B

H

A

tfl-1tfl-2

tfl-3

tfl-4

tweb

Ya'

1

2

3

Yb'

COMPOSITE BEAM

1

2

3

4

56

Ya

Yb

PRECAST BEAM

Base Line

Cc3

Cc2

Cc1


Zone 2

Zone 4

COMPOSITE BEAM

dp da

b. eff

Zone 3

Cc4

Zone 1

225kN 225kN50kN

0.00

0.20

0.40

0.60

0.80

0 5 10 15 20 25

75.00% 75.00%

71.11%69.86% 69.58% 68.98%

64.44% 64.44%

68.33%69.58% 68.98%

62.14% 62.14%

66.02%67.56% 67.27% 66.68%

60.50% 60.50%

64.39%65.93% 65.64% 65.05%

55.78% 55.78%

59.67%61.21% 60.92% 60.32%

54.79% 54.79%

58.68%60.21% 59.93% 59.33%

50.00%

65.00%

80.00%

0.00 0.00 10.15 16.09 17.45 20.30




UTS

P

l

l/2 l/2

Pec

w

ee

0.002000.00

Zona 1Zona 2


beam section point

60.0%

65.0%

70.0%

75.0%

80.0%

0.00 10.00 20.00 30.00


Luas A1 Luas A2


Luas A1



Anchorageset area



Anchorageset area

55.0%

60.0%

65.0%

70.0%

75.0%

80.0%



64.44%64.44%64.44%64.44%64.44%

68.33%69.86%69.58%68.98%

60.0%

65.0%

70.0%

75.0%



0.0200.0400.0600.0800.0

1000.01200.01400.01600.01800.02000.0

Zona 1

Zona 2

Zona 3

Zona 4

Vn = Vu/f


beam section point

A

H

B

tfl-1tfl-2

tfl-3tfl-4

tweb

Ya'

1

2

3

Yb'

COMPOSITE BEAM

1

2

3

45

Ya

Yb

PRECAST BEAM

Base Line

a

dh

h'

As

As

Ah

Av

B

H

A

tfl-1tfl-2

tfl-3

tfl-4

tweb

1

2

3

4

5

Ya

Yb

PRECAST BEAM

Base Line

1

3

Ya'

Yb''

PRECAST BEAM

Base Line

2

page 13 / 14

7 165 165 51 25182.18 27225 1625000 7.7312 215 215 63 43107.75 46225 1950000 6.4919 265 265 84 64683.23 70225 2275000 5.69

SNI 03-2847-2002 Pasal 11.3.2 (Anchorage Zone)Maximum strand = 12

Anchor Block type = 12 StrandLoad factor = 1.2

Reduction factor (φ) = 0.91. End BearingUltimate Point LoadPu = min (1.2 x nStrand x Astrand x %JF x fpu , nstrand x Astrand x 96% x fpu)Pu = 1984.3 kN

End Bearing stress : Nominal concrete comp. :σ comp = Pu / A fci = 32.00 Mpaσ comp = 46.03 MPa min(2, sqrt(A2/A1)) = 2.0

Nominal fci = φ x 0.7 x fci x min(2,sqrt (A2/A1))

Nominal fci = 40.32 > σcomp = 46.03 MPa

ten- Nos Anchor sheath Ult. Point Block End Bearingdon strand Height hole Load Area Stress

( ai ) (Pu) (A) (EBS=Pu/A)mm kN mm2 Mpa Mpa

0 0

0 0

0 0

0 0

1 12 215 63 1984.29 43107.75 46.03 40.32 EBS > Nominal compresion (not good)2 12 215 63 1984.29 43107.75 46.03 40.32 EBS > Nominal compresion (not good)

Remark

Nominalcomp. fci

B

H

A

tfl-1tfl-2

tfl-3

tfl-4

tweb

Ya'

1

2

3

Yb'

COMPOSITE BEAM

1

2

3

4

56

Ya

Yb

PRECAST BEAM

Base Line

Cc3

Cc2

Cc1


Zone 2

Zone 4

COMPOSITE BEAM

dp da

b. eff

Zone 3

Cc4

Zone 1

225kN 225kN50kN

0.00

0.20

0.40

0.60

0.80

0 5 10 15 20 25

75.00% 75.00%

71.11%69.86% 69.58% 68.98%

64.44% 64.44%

68.33%69.58% 68.98%

62.14% 62.14%

66.02%67.56% 67.27% 66.68%

60.50% 60.50%

64.39%65.93% 65.64% 65.05%

55.78% 55.78%

59.67%61.21% 60.92% 60.32%

54.79% 54.79%

58.68%60.21% 59.93% 59.33%

50.00%

65.00%

80.00%

0.00 0.00 10.15 16.09 17.45 20.30




UTS

P

l

l/2 l/2

Pec

w

ee

0.002000.00

Zona 1Zona 2


beam section point

60.0%

65.0%

70.0%

75.0%

80.0%

0.00 10.00 20.00 30.00


Luas A1 Luas A2


Luas A1



Anchorageset area



Anchorageset area

55.0%

60.0%

65.0%

70.0%

75.0%

80.0%



64.44%64.44%64.44%64.44%64.44%

68.33%69.86%69.58%68.98%

60.0%

65.0%

70.0%

75.0%



0.0200.0400.0600.0800.0

1000.01200.01400.01600.01800.02000.0

Zona 1

Zona 2

Zona 3

Zona 4

Vn = Vu/f


beam section point

A

H

B

tfl-1tfl-2

tfl-3tfl-4

tweb

Ya'

1

2

3

Yb'

COMPOSITE BEAM

1

2

3

45

Ya

Yb

PRECAST BEAM

Base Line

a

dh

h'

As

As

Ah

Av

B

H

A

tfl-1tfl-2

tfl-3

tfl-4

tweb

1

2

3

4

5

Ya

Yb

PRECAST BEAM

Base Line

1

3

Ya'

Yb''

PRECAST BEAM

Base Line

2

page 13 / 14

(16153) PC I H-125cm; L-20.6m; CTC-150cm

2. Stirrup and Spaling ReinforcementLoad factor = 1.2

Reduction factor (φ) = 0.85fy = 400 MPa

Bursting SteelDiameter closed stirup = 13 mm

Stirup Area = 132.7 mm2ten- Nos Anchor sheath Jacking Bursting Enddon strand Height hole Force Area Bearing sp

( ai ) (Abs) (EBS) fcc' fl ρp

mm kN mm2 Mpa Mpa Mpa (mm)0 0

0 0

0 0

0 0

1 12 215 63 1653.5772 43107.75 38.36 64.47 7.9 3.96% 62.42 12 215 63 1653.5772 43107.75 38.36 64.47 7.9 3.96% 62.4

total 24

Anchor Zone StirupJF Load = 3307.15 kN Σ a1 = 430.00 mm

Ult. JF = 3968.59 kN H = 1250 mm

T bursting = 0.25 Σ Ult.JF (1-Σa1/H) d bursting = 0.5(h-2e)T bursting = 650.84799 kN d bursting = 694.317285 mm

Diameter closed stirup = 13 mm Anchor Stirup Rebar = T bursting / 0.5 fyNo. Leg of stirrup = 4 leg Anchor Stirup Rebar = 3254.2 mm2

Stirup Area = 530.9 mm2 use no of stirup = 7 pcs

Spalling Rebar

EBS/0.7 φ (fcc'-fci)/4.1 fl / 0.5 fy

B

H

A

tfl-1tfl-2

tfl-3

tfl-4

tweb

Ya'

1

2

3

Yb'

COMPOSITE BEAM

1

2

3

4

56

Ya

Yb

PRECAST BEAM

Base Line

Cc3

Cc2

Cc1


Zone 2

Zone 4

COMPOSITE BEAM

dp da

b. eff

Zone 3

Cc4

Zone 1

225kN 225kN50kN

0.00

0.20

0.40

0.60

0.80

0 5 10 15 20 25

75.00% 75.00%

71.11%69.86% 69.58% 68.98%

64.44% 64.44%

68.33%69.58% 68.98%

62.14% 62.14%

66.02%67.56% 67.27% 66.68%

60.50% 60.50%

64.39%65.93% 65.64% 65.05%

55.78% 55.78%

59.67%61.21% 60.92% 60.32%

54.79% 54.79%

58.68%60.21% 59.93% 59.33%

50.00%

65.00%

80.00%

0.00 0.00 10.15 16.09 17.45 20.30




UTS

P

l

l/2 l/2

Pec

w

ee

0.002000.00

Zona 1Zona 2


beam section point

60.0%

65.0%

70.0%

75.0%

80.0%

0.00 10.00 20.00 30.00


Luas A1 Luas A2


Luas A1



Anchorageset area



Anchorageset area

55.0%

60.0%

65.0%

70.0%

75.0%

80.0%



64.44%64.44%64.44%64.44%64.44%

68.33%69.86%69.58%68.98%

60.0%

65.0%

70.0%

75.0%



0.0200.0400.0600.0800.0

1000.01200.01400.01600.01800.02000.0

Zona 1

Zona 2

Zona 3

Zona 4

Vn = Vu/f


beam section point

A

H

B

tfl-1tfl-2

tfl-3tfl-4

tweb

Ya'

1

2

3

Yb'

COMPOSITE BEAM

1

2

3

45

Ya

Yb

PRECAST BEAM

Base Line

a

dh

h'

As

As

Ah

Av

B

H

A

tfl-1tfl-2

tfl-3

tfl-4

tweb

1

2

3

4

5

Ya

Yb

PRECAST BEAM

Base Line

1

3

Ya'

Yb''

PRECAST BEAM

Base Line

2

page 14 / 14

Spalling RebarSpalling Force = 2% JFSpalling Force = 66.1 kN

Diameter closed stirup = 13 mmStirup Area = 132.7 mm2

use no of stirup = 3 pcs

XII. SHEAR KEY ANALYSIS (FOR SEGMENTAL BEAM ONLY)

item Unit SEC 2-2 SEC 3-3 SEC 4-4 SEC 5-5 the shear load is transferred through the joint by frictionx (m) 4.7 8.2 11.8 15.3 and by the direct shear capacity of the steel shear pin

at initial stage (Only Beam SW) Shear transfer by joint friction :σtop (Mpa) 1.87 0.19 0.23 1.90 Vj = μ ⋅σ n ⋅ Ajointσbot (Mpa) 16.21 17.16 17.03 15.88 φ Vj = φ . μ ⋅σ n ⋅ Ajoint

σn (Mpa) 9.04 8.68 8.63 8.89 With : φ = 0.5Ajoint (mm) 212500 212500 212500 212500 μ = 0.65 friction coefficientφ Vj (kN) 624.3 599.3 595.7 613.8 σn = compressive stress in the joint in MPaVult (kN) 49.4 16.8 16.8 49.4 Ajoint = Area under compression

φ Vj / Vult 12.6 35.7 35.5 12.4at Service stage (all DL and Live Load) Shear transfer by steel shear pin :σtop (Mpa) 9.48 10.55 10.31 8.92 Vpin = 0.6 Apin . fupin

σbot (Mpa) 3.57 1.54 1.71 3.96 φ Vpin = φ 0.6 Apin . fupin

σn (Mpa) 6.52 6.04 6.01 6.44 With : φ = 0.8Ajoint (mm) 212500 212500 212500 212500 Apin = Steel shear pinφ Vj (kN) 450.5 417.3 414.9 444.9 fu pin = Ultimate Tensile strengthVult (kN) 408.3 199.8 199.8 408.3

φ Vj / Vult 1.1 2.1 2.1 1.1 Shear steel pin capacity :Shear steel Pin Requirement Dia Apin fu φ Vpin

Exceed Shear - - - - 28 615.8 400 118.22Min. Shear pin Min.2 Min.2 Min.2 Min.2Steel shear pin 236.4 236.4 236.4 236.4Add. shear pin - - - -Total. shear pin 2 Dia.28 2 Dia.28 2 Dia.28 2 Dia.28

B

H

A

tfl-1tfl-2

tfl-3

tfl-4

tweb

Ya'

1

2

3

Yb'

COMPOSITE BEAM

1

2

3

4

56

Ya

Yb

PRECAST BEAM

Base Line

Cc3

Cc2

Cc1


Zone 2

Zone 4

COMPOSITE BEAM

dp da

b. eff

Zone 3

Cc4

Zone 1

225kN 225kN50kN

0.00

0.20

0.40

0.60

0.80

0 5 10 15 20 25

75.00% 75.00%

71.11%69.86% 69.58% 68.98%

64.44% 64.44%

68.33%69.58% 68.98%

62.14% 62.14%

66.02%67.56% 67.27% 66.68%

60.50% 60.50%

64.39%65.93% 65.64% 65.05%

55.78% 55.78%

59.67%61.21% 60.92% 60.32%

54.79% 54.79%

58.68%60.21% 59.93% 59.33%

50.00%

65.00%

80.00%

0.00 0.00 10.15 16.09 17.45 20.30




UTS

P

l

l/2 l/2

Pec

w

ee

0.002000.00

Zona 1Zona 2


beam section point

60.0%

65.0%

70.0%

75.0%

80.0%

0.00 10.00 20.00 30.00


Luas A1 Luas A2


Luas A1



Anchorageset area



Anchorageset area

55.0%

60.0%

65.0%

70.0%

75.0%

80.0%



64.44%64.44%64.44%64.44%64.44%

68.33%69.86%69.58%68.98%

60.0%

65.0%

70.0%

75.0%



0.0200.0400.0600.0800.0

1000.01200.01400.01600.01800.02000.0

Zona 1

Zona 2

Zona 3

Zona 4

Vn = Vu/f


beam section point

A

H

B

tfl-1tfl-2

tfl-3tfl-4

tweb

Ya'

1

2

3

Yb'

COMPOSITE BEAM

1

2

3

45

Ya

Yb

PRECAST BEAM

Base Line

a

dh

h'

As

As

Ah

Av

B

H

A

tfl-1tfl-2

tfl-3

tfl-4

tweb

1

2

3

4

5

Ya

Yb

PRECAST BEAM

Base Line

1

3

Ya'

Yb''

PRECAST BEAM

Base Line

2

page 14 / 14

perhitungan girder pre cast

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