desain pci girder

8/19/2019 Desain Pci Girder

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PT

WIJAYA

KARYA

BETON

Job no. : 13014 A

Rev. : 04

TECHNICAL

CALCULATION

APPROVAL

PCI GIRDER MONOLITH FOR HIGHWAY BRIDGES

PCI Girder Monolith H‐125cm ; L‐20.15m ; CTC ‐160cm ; fc' 40MPa

Approved by :

TOLL SURABAYA ‐ GRESIK

Design by :

18 Juni 2013

Suko

Technical Staff

Ir. Achmad Arifin Ignatius Harry S., S.T.

Technical Manager Chief of Technical

Consultan / Owner

Approved by : Checked by

18 Juni 2013 18 Juni 2013


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PCI Monolith H-125cm ; L-20.15m ; CTC-160cm - RSNI (Rev.04)

4. BEAM SUPPORT REACTION

Ultimate total = 1,2*(Beam+Diaphragm+Deck Slab)+1,3*Slab+2*Asphaltic+1,8*(LL+I)

Beam support react ion :

a. Dead Load = 75.90 kN

b. Additional Dead Load = 125.48 kN

c. Live Load = 250.52 kN

Ultimate support reaction = 713.78 kN

5. CONTROL OF BEAM STRESSES

Middle span position

top stress = -0.57 MPa required > -1.41 MPa

bottom stress = 17.34 MPa required < 19.20 MPa


top stress = 9.81 MPa required < 18.00 MPa

bottom stress = 1.58 MPa required > -3.16 MPa

6. CONTROL OF BEAM DEFLECTION

Deflect ion at t he middle of beam span

1. Chamber due stressing

initial = -17.68 mm

= -

2. Service Condition

1. Initial Condition

.

2. Deflection at composite DL = -8.25 mm

3. Deflection due live load = 7.48 mm,required 1) = 1.30

Cracking Capacit y requir ement :

Mcrack = 3328.03 kN.m

Mn / Mcr = 1.36

CALCULATION RESUME


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19.55 M

I. DATA

0.3 L= 19.55 M 0.3

Beam length = 20.15 m ( edge anchor to edge anchor : 19.85 m)

Beam spacing (s)=

1600 mmConcrete Slab thickness (CIP) = 200 mm

Asphalt thickness = 50 mm

Deck slab thickness = 70 mm

Cross Section

H = 1250 mm tfl-1 = 75 mm

A = 350 mm tfl-2 = 75 mm

B = 650 mm tfl-3 = 100 mm

tweb = 170 mm tfl-4 = 125 mm

II. MATERIAL

2.1 Concrete

Beam Slab

at service fc' = 40.0 28.0 [N/mm2]

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

Allowable stress

19.2 [N/mm2]Compressive

SPAN L =

Compressive strength

Allowable stress at initial ………… (SNI T-1 2-20 04 )

0.6 * fc'i =

TECHNICAL CALCULATION OF PCI MONOLITH BEAM FOR HIGHWAY BRIDGES

A

H

B

tfl-1

tfl-2

tfl-3

tfl-4

tweb

Tensile 1.4 [N/mm ]

18.0 12.6 [N/mm2]

Tensile 3.2 2.6 [N/mm2]

wc = 2500.0 2500.0 [kg/m3]

Ec = wc1.5

*0.043*sqrt(fc') = 33994.5 28441.8 [N/mm2]

Eci = wc

1.5

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

2

]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 : 132.73 [cm

2]

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

- Yield stress fy : 400 [N/mm2]

- Eff. Section area

Compressive

Steel Reinforcement

[Uncoated stress relieve seven wires strand]

- Diameter strand

- Ultimate tensile strength

- Modulus of elasticity

Prestressing Cable

0.25 * Sqrt(fc'i) =

0.45 * fc' =

0.5 * Sqrt(fc') =

Modulus of elasticity

Allowable stress at service ………. (SNI T-1 2-20 04 )

Concrete unit weight

page 1 / 15


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III. SECTION ANALYSIS

Remark :

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

Ep 2 = 28442 [N/mm2] [Slab]

n = Ep 2 / Ep 1

n = 0.84

3.1 Precast Beam

[in mm ]

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

Height Bottom Upper mm2 mm mm mm

3mm

4mm

4mm

4

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*d

2 Ix

Section Bottom Upper mm2 mm mm mm

3mm

4mm

4mm

4

2 200.0 1338.7 1338.7 267731 1320 1420.0 380178316 892437361.6 61987067626 62879504987

70.0 167.3 167.3 11713 1250 1285.0 15051514 4782906.485 1403663073 1408445980

1 1250.0 650.0 350.0 316750 0 519.3 164493750 54962557571 55744385803 1.10707E+11

Zone

Ya'

1

2

3

Yb'

COMPOSITE BEAM

1

2

3

4

5

Ya

Yb

PRECAST BEAM

Base Line

o a . . . + . +

3.3 R e s u m e

[in mm ]

Description Area (mm2) Ya (mm) Yb (mm) Ix (mm

4) Wa (mm

3) Wb (mm

3)

Precast Beam 316750 731 519.3 54962557571 75220826 105836180

Composite Beam [composite] 596194 581 938.8 174994894341 301106490 186397337

[precast] 311 562372124

IV. LOADING4.1 Dead Load

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

q1 = 0.317 x 2.50 = 0.792 [t/m'] = 7.77 [kN/m']

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

q2 = 0.334 x 2.40 = 0.802 [t/m'] = 7.86 [kN/m']

c. Deck slab q3 = Ac deck slab x s

q3 = 0.098 x 2.40 = 0.235 [t/m'] = 2.31 [kN/m']

d. Asphaltic q4 = Ac asphaltic x s

q4 = 0.080 x 2.20 = 0.176 [t/m'] = 1.73 [kN/m']

e. Diaphragm p = Vol diaph with 0.20m thickness x diaph

p = 0.294 x 2.40 = 0.706 [ton'] = 6.92 [kN']

note : from kg to N, multiply by 9.8060

Number of diaph = 4 pcs

Diaph. placement 1 2 3 4

Location 0.00 6.52 13.03 19.55

Support Va 6.92 4.62 2.31 0.00

Mid Moment 0.00 22.56 22.56 0.00

Total Diaphragma Flexural Moment at Middle Span 45.11 kN.m

eqivalen load q diaphragm q5= 0.94 [kN/m']

page 2 / 15


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V. MOMENT ANALYSIS

[in kN-meter ]

Mid Sec 1-1 Sec 2-2 Sec 3-3 Sec 4-4 Sec 5-5 Sec 6-6

span 0.00 6.28 13.28 19.55 19.55 9.78 (m)

DL Precast beam 370.98 0.00 323.42 323.42 0.00 0.00 370.98

370.98 0.00 323.42 323.42 0.00 0.00 370.98

DL Slab 375.54 0.00 327.39 327.39 0.00 0.00 375.54

ADL Asphaltic Layer 82.45 0.00 71.88 71.88 0.00 0.00 82.45

SDL Diaphragm+Deck Slab 155.30 0.00 135.39 135.39 0.00 0.00 155.30

613.29 0.00 534.66 534.66 0.00 0.00 613.29LL Distribution load 687.96 0.00 599.76 599.76 0.00 0.00 687.96

KEL 536.45 0.00 467.68 467.68 0.00 0.00 536.45

1224.42 0.00 1067.44 1067.44 0.00 0.00 1224.42

2208.69 0.00 1925.52 1925.52 0.00 0.00 2208.69

3488.59 0.00 3041.34 3041.34 0.00 0.00 3488.59


VI. SHEAR ANALYSIS

[in kN]


span 0.00 6.28 13.28 19.55 19.55 9.78 (m)

DL 0.00 75.90 27.18 -27.18 -75.90 -75.90 0.00

0.00 75.90 27.18 -27.18 -75.90 -75.90 0.00

DL 0.00 76.84 27.51 -27.51 -76.84 -76.84 0.00

ADL 0.00 16.87 6.04 -6.04 -16.87 -16.87 0.00

SDL 0.00 31.77 11.38 -11.38 -31.77 -31.77 0.00

0.00 125.48 44.93 -44.93 -125.48 -125.48 0.00

Distribution load 0.00 140.76 50.40 -50.40 -140.76 -140.76 0.00

KEL 54.88 109.76 74.53 -74.53 -109.76 -109.76 54.88

54.88 250.52 124.93 -124.93 -250.52 -250.52 54.88

54.88 451.91 197.04 -197.04 -451.91 -451.91 54.88Total (DL + LL)

Asphaltic Layer

Total (DL + LL)

Description

Subtot al

Subtot al

Subtot al

Subtot al

Type

Precast beam

Ultimate total

Slab

Diaphragm+Deck slab

Subtot al

LL

Type Description

Subtot al

. . . - . - . - . .


VII. PRESTRESSING CABLE

7.1 Cable Profile

[in: mm ]

ten- Nos Profile Total JF

don strand Edge Middle left right tension (kN)

0 0 0 0 0% 0% 0% 0

0 0 0 0 0% 0% 0% 0

0 0 0 0 0% 0% 0% 0

0 0 0 0 0% 0% 0% 0

1 12 600 200 75% 0% 75% 1654

2 12 300 100 75% 0% 75% 1654

total 24 450.00 150.00 75% 0% 75% 3307

Parabol ic curve (Average of Str and's posi t ion ver t i ca l ly f rom t he bot tom of beam ( Value for Y axis ) )

Y = A.x2+ B.x + C

where : A = Constanta : ( (Ymiddle + Yedge)/(L/2)2) A = 0.003046

B = Constanta : ( L x A ) B = -0.060453

C = 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 = 0.003046 X + -0.0604534 X + 0.450000

Cable tendon angle :

tg o = 0.006091 X + -0.0604534

eccentricity of tendon at middle section

Eccentricity [e] = Yb - Ys = 369.32 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)

Tension

ma e o a

page 4 / 15


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7.2 Losses of Prestress

1. Losses of Prestress (Short Term)

a. Friction

The equation for calculating the loss of prestress due to friction is :

Px = Po.e- + .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)

= friction coefficient

= Change of cable angle from tensile point to x section

k = Wobble coefficient

x = Distance from tensile point to x section

Friction and Wooble coeficient for grouting tendon in metal sheating

with Seven Wire Strand : = 0.20

When the jacking force is applied at the stressing end, the tendon will elongate. The elongation will be resisted by friction

between the strand and its sheating or duct. As the result of this friction, force will be decreased with distance from the jacking

end. The friction is comprised of two effects : curvature friction which is a function of the thendons profile, and wooble friction

which is the result of minor horizontal or vertical deviation form intended profile.

0.00

0.20

0.40

0.60

0.80

0 5 10 15 20 25

60.0%

65.0%

70.0%

75.0%

80.0%

0.00 10.00 20.00 30.00

k = 0.003

Table of calculation due to Friction

ten- Nos Profile % JF a b

don strand Edge Middle from UTS (rad) 0.00 9.925 19.85

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%

0 0 0 0 0% 0.00000 0 0.000 0.0% 0.00% 0.0%1 12 600 200 75% 0.00406 -0.0806045 0.161 75.0% 70.49% 68.4%

2 12 300 100 75% 0.00203 -0.0403023 0.081 75.0% 71.64% 69.5%

total 24 450.00 150.00 75% 0.00305 -0.0604534 0.121 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

= Loss of prestress per length

= 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 follows :

x = Sqrt ( Es . / )

effective anchorage set point position :

, . ,

retracts pulling the wedges in to the anchorage device and locks the strand in place. The lost in elongation is small . It depend on

the wedges, the jack and the jacking procedure. This lost in elongation is resisted by friction just as the initial elongation is

resisted by friction.

Prestress force (Px) = % UTS

Cable change

angle point

X (effective anchorage set)

Anchorage

set area


Cable change

angle point

Anchorage

set area

page 5 / 15


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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 set

ten- Nos draw in

don strand Mpa/mm mm X (m) Px (% UTS) X (m) Px (% UTS) 0.00 9.925 19.85

0 0 0.00000 0.00 0.00 0.00% 0.00 0.00% 0.0% 0.00% 0.0%

0 0 0.00000 0.00 0.00 0.00% 0.00 0.00% 0.0% 0.00% 0.0%

0 0 0.00000 0.00 0.00 0.00% 0.00 0.00% 0.0% 0.00% 0.0%

0 0 0.00000 0.00 0.00 0.00% 0.00 0.00% 0.0% 0.00% 0.0%

1 12 0.00616 8.00 15.83 69.26% 0.00 0.00% 63.5% 68.03% 68.4%

2 12 0.00512 8.00 17.36 70.06% 0.00 0.00% 65.1% 68.49% 69.5%

total 24 0.00564 8.00 16.60 69.66% 0.00 0.00% 64.33% 68.26% 68.98%

c. Elastic Shortening ( ES )

Elastic shortening refers to the shortening of the concrete as the postensioning force is applied.

From right sideFrom left side after anchorage set = % UTS

55.0%

60.0%

65.0%

70.0%

75.0%

80.0%

0.00 10.00 20.00 30.00

Prestress tendon section

LOSSES

OF

PRESTRESS

DUE

TO

ANCHORAGE

SET

64.33%64.33%64.33%64.33%64.33%

68.26%

69.82%69.50%68.98%

60.0%

65.0%

70.0%

75.0%

0.00 5.00 10.00 15.00 20.00 25.00

Prestress

tendon

section

AVERAGE LOSSES OF PRESTRESS

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 shortening

for member with bonded tendons :

ES = Kes . Es . f cir / Eci

where:

Kes = 0.50 for post-tensioned members when tendon are tensioned in sequential order to the same tension

ES = Elastic modulus of tendon material

Eci = Elastic modulus of the concrete at the time of prestress transfer

f cir =

Assumption Losses due ES 2.37%

Pi = Total prestressing force at release

Pi = 68.3% - 2.37% = 65.89% UTS x nos x Aps = 2905.4202 kN

f cir = Pi / A + Pi. ec2/ I + Mg.ec/I

f cir = 13.89 N/mm2

so, ES = 44.08 N/mm2, percent actual ES losses = Es/fpu 2.37% 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 60

Ksh 0.92 0.85 0.8 0.77 0.73 0.64 0.58 0.45

Ksh = 0.64

V/S = 0.08 Volume = 6.38 m3

Surface = 78.67 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 structures

that are not moist cured, Ksh is typiclly based on when the concrete was cast

page 6 / 15


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e. Creep ( CR )

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

CR = 90.40 N/mm2

percent actual CR losses = CR/fpu 4.86%

Where :

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

fcir = 13.890 N/mm2

Msd = Moment due to all superimposed permanent dead loads applied after prestressing

Msd = 613.29 kN.m

fcds = Stress in a concrete at the cgs of the tendon due to all superimposed dead load

fcds 1 = Msdl.e/I = 3.57 N/mm2

component of fcd due to load on the plain beam

fcds 2 = Madl.e/Ic = 0.37 N/mm2

component of fcd due to load on the composite beam

fcds = fcds 1 + fcds 2 = 3.94 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 = 18.38 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)

Relaxation is defined as a gradual decrease of stress in a material under constant strain. In the case of steel, relaxation is

the result of permanent alteration of the grain structure. The rate of relaxation at any point in time depends on the

stress level in the tendon at that time. Because of other prestress losses, there is a continual reduction of tendon strss;

this causes a reduction in the relaxation rate.

Over time, the compresive stress induced by postensioning causes a shortening of the concrete member. The increase in

strain due to a sustained stress is refered to as creep. Loss of prestress due to a creep is nominally propotional to the net

permanent compresive stressin the concrete. the net permanent compressive stress is the initial compressive stress in the

concrete due to the prestressing minus the tensile stress due to self weight and superimposed deadload moments

= . or p pu = .

RESUME DUE TO SHORT & LONG TERM LOSSES

Losses

Section

x (m)

0.00 75.00% 64.33% 61.96% 13.04% 60.32% 55.46% 54.48% 20.52%

0.00 75.00% 64.33% 61.96% 13.04% 60.32% 55.46% 54.48% 20.52%

0.00 75.00% 64.33% 61.96% 13.04% 60.32% 55.46% 54.48% 20.52%

0.00 75.00% 64.33% 61.96% 13.04% 60.32% 55.46% 54.48% 20.52%0.00 75.00% 64.33% 61.96% 13.04% 60.32% 55.46% 54.48% 20.52%

9.93 71.07% 68.26% 65.89% 5.18% 64.26% 59.40% 58.41% 12.65%

15.83 69.82% 69.82% 67.45% 2.37% 65.82% 60.96% 59.98% 9.85%

17.36 69.50% 69.50% 67.13% 2.37% 65.50% 60.64% 59.65% 9.85%

19.85 68.98% 68.98% 66.61% 2.37% 64.98% 60.12% 59.13% 9.85%

friction Losses equotion :

0 > x > 9.93

75.00% -+ 0.40% x

9.93 > x > 19.85

71.07% + 0.07% x x - 9.925

Long term Losses equotion :

0 > x > 0.00

54.48% #DIV/0!

0 > x > 9.93

54.48% + 0.40% x x - 0

9.925 > x > 15.83

58.41% + 0.26% x x - 9.925

15.83 > x > 17.36

59.98% -+ 0.21% x x - 15.8329534

17.36 > x > 19.85

59.65% -+ 0.21% x x - 17.3636282

II. Long Term Losses

FrictionShrinkage

(SH)

Elastic

Shortening

Steel

RelaxationAnchor set

I. Short Ter m Losses

Creep (CR)Total

Losses (%)

Total Losses

(%)

75.00% 75.00%

71.07%69.82% 69.50% 68.98%

64.33% 64.33%

68.26%69.50% 68.98%

61.96% 61.96%

65.89%

67.45% 67.13% 66.61%

60.32% 60.32%

64.26%65.82% 65.50% 64.98%

55.46% 55.46%

59.40%60.96% 60.64% 60.12%

54.48% 54.48%

58.41%59.98% 59.65% 59.13%

50.00%

65.00%

80.00%

0.00 0.00 9.93 15.83 17.36 19.85

Friction

Anchorset

Elastic Shortening (ES)

Shrinkage (SH)

Creep (CR)

Steel Relaxation (SR)

LOSSES OF PRESTRESS DIAGRAM


UTS

page 7 / 15


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7.3 Effective Stress Force

Resume Prestressed Force at middle

Cable

stress

[N/mm2] [mm

2] [kN]

9.1% 65.9% 1226 2370.72 2905.42

16.6% 58.4% 1086 2370.72 2575.64

VIII. STRESS AND DEFFLECTION ANALYSIS

Beam Segment 1 2 3 4 5 6 7 8

Length (m) 6.275 7.000 6.275 0.00 0.00 0.00 0.00 0.00

Additional length at the end of the beam = 0.30 m Total Length = 20.15 m

8.1 Stress at initial

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 6.28 13.28 19.55 19.55 9.78

Moment DL [kN.m] 370.98 0.00 323.42 323.42 0.00 0.00 370.98

Jacking Force [kN] 3307.15 3307.15 3307.15 3307.15 3307.15 3307.15 3307.15

Losses due to friction % 4% 0% 2% 4% 3% 3% 4%

Pi [kN] 3136.29 3307.15 3197.47 3144.40 3164.51 3164.51 3136.29

e (eccentricity) [m] 0.369 0.078 0.332 0.332 0.078 0.078 0.369

Pi.e [kN.m] -1158 -259 -1062 -1044 -248 -248 -1158

Moment Net. [kN.m] -787 -259 -738 -721 -248 -248 -787

Pi / A [N/mm2] 9.90 10.44 10.09 9.93 9.99 9.99 9.90

M / Wa [N/mm2

] -10.47 -3.44 -9.81 -9.58 -3.29 -3.29 -10.47 Allow.

M / Wb [N/mm2] 7.44 2.45 6.97 6.81 2.34 2.34 7.44 stress

Initial Stresses top ( T ) -0.57 7.00 0.28 0.35 6.70 6.70 -0.57 -1.4

bot ( B ) 17.34 12.89 17.07 16.74 12.33 12.33 17.34 19.2

8.2 Stress at service

[N/mm2]

PCondition

Asp%UTS

effective

prestress

% Losses of

prestress

long term

short term

oa o precas , s a , ap ragm an pres ress y eam =

> Live load and asphalt by composite ( = M2 )


x - [m] Span 0.00 6.28 13.28 19.55 19.55 9.78

Moment DL [kN.m] 901.82 0.00 786.20 786.20 0.00 0.00 901.82


effective prestress P [kN] 2573.02 2402.15 2511.84 2614.77 2610.22 2610.22 2573.02

P . e [m] -950.26 -188.13 -833.95 -868.13 -204.42 -204.42 -950.26

Moment --- M1 [kN.m] -48.44 -188.13 -47.75 -81.93 -204.42 -204.42 -48.44

Moment --- M2 [kN.m] 1306.87 0.00 1139.32 1139.32 0.00 0.00 1306.87

P / A [N/mm2] 8.13 8.13 8.13 8.13 8.13 8.13 8.13

M 1 / Wa [N/mm2] -0.64 -2.50 -0.63 -1.09 -2.72 -2.72 -0.64

M 1 / Wb [N/mm2] 0.46 1.78 0.45 0.77 1.93 1.93 0.46

M 2 / Wa' [N/mm2] 2.32 0.00 2.03 2.03 0.00 0.00 2.32 Allow.

M 2 / Wb' [N/mm2] -7.01 0.00 -6.11 -6.11 0.00 0.00 -7.01 stress

Stress at Service slab ( S ) 4.34 0.00 3.78 3.78 0.00 0.00 4.34 12.6

top ( T ) 9.81 5.63 9.52 9.07 5.41 5.41 9.81 18.0

bot ( B ) 1.58 9.91 2.47 2.79 10.06 10.06 1.58 -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 condition

Wb = Modulus Section for Bottom section of Precast condition

Wa' = Modulus Section for Top section of composite Condition……. ( Chapter 3.3 - Resume )

Wb' = Modulus section for bottom section of composite condition ……. ( Chapter 3.3 - Resume )

Moment Bal =

Moment DL =

Moment Net =

[N/mm2]

page 8 / 15


13/114


8.3 Stress diagram at center span :

8. 3. 1. STRESS DIAGRAM AT INIT IAL

a. Stress at beam end section when Prestress is applied :

Pi/A = 10.44 MPa M/Wa = -3.05 MPa top = 7.39 MPa

+ =

Pi/A = 10.44 MPa M/Wb = 2.17 MPa bottom = 12.61 MPa

effective prestress = 75% UTS M = Mdl - Pi.e = -229.24 kN-m

Pi = 3307.15 kN allow comp at initial = 19.20 MPa

eccentricity (ei) = 69.32 mm allow tension initial = -1.41 MPa

Mdl = Mbeam = 0 kN-m control allow stress = meet requirement

b. Stress at beam middle section when Prestress is applied :

Pi/A = 9.89 MPa M/Wa = -10.45 MPa top = -0.56 MPa

+ =





Mdl = Mbeam = 370.98 kN-m control allow stress = meet requirement

8. 3. 2. STRESS DIAGRAM AT CONSTRUCTION

a. Stress at beam middle section when diaphragm, RC deck is install and finish fresh concreting composite slab


+ =





Mdl = Mbeam + Madl = 901.82 kN-m control allow stress = meet requirement

b. Stress at composite beam middle section due to asphaltic layer:

slab = 0.27 MPa

P/A = 9.17 MPa M1/Wa = -2.28 MPa M2/Wa'= 0.15 MPa top = 7.04 MPa

+ + =

P/A = 9.17 MPa M1/Wb = 1.62 MPa M2/Wb'= -0.44 MPa bottom = 10.35 MPa

effective prestress = 66% UTS M1 = Mdl + Pi.e = -171.20 kN-m

Pi = 2905.42 kN M2 = Masphalt = 82.45 kN-m

eccentricity (ei) = 369.32 mm allow comp at initial = 19.20 MPa

Mdl = Mbeam + Madl = 901.82 kN-m allow tension initial = -1.41 MPa

control allow stress = meet requirement

page 9 / 15


14/114


8. 3.3 . STRESS DIAGRAM AT SERVICE (at cent er of sp an)

Stress at composite beam middle section due to Live Load

slab = 4.34 MPa


+ + =



Pi = 2575.64 kN M2 = Masphalt + LL = 1306.87 kN-m

eccentricity (ei) = 369.32 mm allow comp at service = 18.00 MPa

Mdl = Mbeam + Madl = 901.82 kN-m allow tension at service = -3.16 MPa


8.4 Deflection

8.4.1 Chamber due to Prestress Load

Deflection on middle section :

pi=

-26.52 mmwhere : P = Prestress force

Eci = Modulus Elasticity of Concrete

Ixi = Section Inertia

l = length of anchor to anchor

ee =

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

Distance between c.g of strand and

c.g of concrete at end

P

l

l/2 l/2

Pec

ee

ec =

8.4.2 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 -26.52 1.80 x (1) -47.74 2.20 x (1) -58.35

2. Due to beam weight (DL) 7.77 8.84 1.85 x (1) 16.35 2.40 x (1) 21.21

-17.68 -31.39 -37.14

3. Due to ADL 3.25 3.31 3.00 x (2) 9.93

-28.08 -27.21

4. Due to Composite Overtoping 7.86 8.00 2.30 x (2) 18.40

-20.08 -8.81

5. Due to asphaltic (SDL) 1.73 0.55

-8.25

6. Due to Live Load = UDL + KEL 14.40 109.76 7.48

-0.78

Resume of deflection :

1. Deflection at service = -8.25 mm

2. Deflection due to Live Load = 7.48 mm < allow. deflection L/800 = 24.4375 mm OK

3. Total deflection with LL = -0.78 mm, chamber upward

WORKING LOAD

Loading


c.g of concrete at centre

Long time cambers and deflection

page 10 / 15


15/114


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' = 28.00 MPa

2. Beam Ctc =1600 mm …. Control Value = 0.85

3. Span length / 4 =4887.5 mm

Thus, Effectif slab width is : =1600 mm

Partial Rebar:

fy = 400 MPa

Use 0 Dia.13 mm at tension area

As = 0.00 mm2 b web = 170 mm

d = 1190.5 mm

Partial tension rebar ratio : Rebar in compresion area is neglected due calculation

t = As / (bweb x d ) t = 0.00000 c =

t = t . fy / fc t = 0.000 c =

Low Relaxation strand :

fpu = 1860 MPa

Strand stress ratio fpu / fpy = 0.9 value p = 0.28

dp = 1370.0 mm Aps = 2370.72 mm2

beff = 1600 mm

Prestress ratio :

p = Aps / (beff x dp ) p = 0.00108153

fps = fpu {1 - p / (p.fpu/fc + d/dp (t-c))) fps = 1816.0 MPa

p = p fps/fc p = 0.070

Resume of Steel Index Requirement (SNI Beton 03-2847-2002 pasal 20.8)p + d/dp (t-c) < 0.36

0.070 < 0.306 Under Reinf, Meet With Steel Index Requirement

9.2 Momen Capacity

b. eff

Tps = Aps . Fps

Tps = 4305180.91 N

strength reduction factor

= 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)

4 113.06 1600 180889.95 28.00 CIP Slab 57

3 0.00 335 0 28.00 CIP Slab 113

2 0.00 350 0 40.00 Beam 113

1 0.00 170 0 40.00 Beam 113

a = Tps / ( 0.85 x fc'' slab x beff ) a= 113.06 mm

Mn = Mn = 5654.73 kN.m

Mn = 4523.7873 kN.m

Bridge life time design for 50 year,so Transient act factor = 1

Mult = 1x 3,489kN-m Mn / Mult = 1.297 >1, Moment capacity meet with requirement

9.3 Cracking Capacity

Stress at bottom girder section due to service load (bot at service) = 1.58 MPa

Concrete flexural tension strength fr = 4.4 MPa

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

Mcr = 3328.03 kN.m

Mn / Mcr = 1.359 > 1.2 ---- Cracking Capacity requirement is achieve

0

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

Conc. Strength fc'i Cci=0.85 fc'i.Aci

N

0

4305181

Depth of Concrete Compression Block is located at zone 4

056.53

MPa

Zone 3

dp d

Cc3

Cc2

Cc1

Tps=Aps.fps

T = As.fy

c

COMPOSITE BEAM

a

Zone 2

one

Zone 1

i

Zone 3

page 11 / 15


16/114


X. SHEAR ANALYSIS

10.1 Shear calculation based on SNI 03-2847-2002

40% Ultimate Tensile Strength = 744 MPa

Effective Prestress = 1086 MPa Effective Prestress > 40% fpu

Section Properties :

Ix = 5.496E+10 mm4 Ixcomp = 1.75E+11 mm4

Yb = 519.31728 mm Ybcomp = 938.8 mmAg = 316750 mm2

Load :

Effective prestress Pe = 2575.64 kN

Factored Load : Unfactored Load :

qult DL + ADL = 26.89 kN/m q DL + ADL = 18.88 kN/m

qult LL = 25.92 kN/m q sdl = 1.73 kN/m

Pult LL = 197.57 kN q DL + ADL = 20.60 kN/m

Concrete Shear resistance contribution (Vc)

Nominal shear strength provide by concrete

Vc = {0.05sqrt(fc') + 5 (Vu.dp/Mu)}bw.d

but nominal strength (Vc) should taken between : (1/6).sqrt(fc').bw.d < Vc < 0.4sqrt(fc').bw.d

and Vu.dp/Mu ≤ 1

where :

Mu = Maximum factored moment at section

Vu = Maximum factored shear force at section

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

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

of ultimate tensile stress

Vn = Vc + Vs where : Vn = Nominal Shear force Vu = Ultimate Shear force

Vn = Vu / Vc = Concrete shear contribution = Shear reduction factor

Vs = Shear steel contribution = 0.75

Zonafication for shear steel stirup calculation

Zone 1 Vn < 0.5 Vc No need to use stirup

Zone 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/)-Vc)

S ≤ 0.75 H

S ≤ 600mm

Zone 4 Vn < Vc+0.67 sqrt(fc') bw d Required tight stirup spacing with spacing :

S ≤ (av.fy.d) / ((Vu/)-Vc)

S ≤ 0.375 H

S ≤ 300mm

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

RSNI T-12-2005 : 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.

page 12 / 15


17/114


Shear rebar steel

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 use

m m m kN kN-m kN kN kN Zonasi mm mm

0.1 0.504 1.08 707.49 71.01 1.00 980.51 943.32 -37.19 2 600 300

0.3875 0.520 1.10 689.40 271.11 1.00 995.59 919.20 -76.39 2 600 3000.775 0.542 1.12 665.02 531.25 1.00 1015.20 886.69 -128.51 2 600 300

1.7 0.590 1.17 606.82 1107.91 0.64 701.82 809.10 107.27 3 600 300

2 0.605 1.19 587.95 1281.52 0.54 612.19 783.93 171.74 3 600 300

3 0.649 1.23 525.03 1812.74 0.36 438.72 700.04 261.32 3 500 300

4 0.687 1.27 462.12 2270.95 0.26 346.48 616.16 269.68 3 499 300

5 0.719 1.30 399.20 2656.13 0.20 286.00 532.27 246.27 3 561 300

6 0.745 1.33 336.29 2968.30 0.15 240.79 448.38 207.59 3 600 300

7 0.765 1.35 273.37 3207.44 0.11 203.75 364.50 160.75 3 600 300

8 0.779 1.36 210.46 3373.56 0.08 171.27 280.61 109.34 3 600 300

9 0.787 1.37 147.54 3466.66 0.06 141.27 196.72 55.45 2 600 300

9.775 0.789 1.37 98.78 3488.59 0.04 118.82 131.71 12.89 2 600 300

1000.0

1200.0

1400.0

1600.0

1800.0

2000.0

Zona 1

Zona 2

Shear

Steel

Requirement

PositionkN

x (m) from range nos shear

span edge (m) (row)

Shear spacing S - 75 0 0 0






Shear spacing S - 300 9.775 9.775 33

total shear rebar per half span (row) = 33

total shear rebar per span (row) = 66

Shear Rebar configuration

0.0

200.0

400.0

600.0

800.0

. Zona 3

Zona 4

Vn =Vu/f

beam section

point

page 13 / 15


18/114


10.2 Horisontal Shear

Width of contact surface area bv = 200 mm

Effective Height d = 1216 mm

= 0.75

fy = 400 MPa

Use 2 leg Dia.13 mm

Area horisontal Shear Steel Avh = 265.46 mm2

Horisontal Shear steel Spacing s = 300 mmHorisontal Shear steel ratio v = 0.442%

Shear horisontal Nominal

Vnh = (1.8 Mpa + 0.6 v. fy) . bv .d

Vnh = 696.00 KN

Requirement for shear horisontal steel :

Vult comp = 46.03 MPa

ten- Nos Anchor sheath Ult. Point Block End Bearing

don 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 38.08 EBS > Nominal compresion (not good)

2 12 215 63 1984.29 43107.75 46.03 38.08 EBS > Nominal compresion (not good)

Remark

Nominal

comp. fci

page 14 / 15


19/114


2. Stirrup and Spalling Reinforcement

Load factor = 1.2

Reduction factor () = 0.85

fy = 400 MPa

Bursting Steel

Diameter closed stirup = 13 mm

Stirup Area = 132.7 mm2

ten- Nos Anchor sheath Jacking Bursting End

don strand Heighthole Force Area Bearing sp

( ai ) (Abs) (EBS) fcc' fl p

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% 62.4

2 12 215 63 1653.5772 43107.75 38.36 64.47 7.9 3.96% 62.4

total 24

Anchor Zone Stirrup

JF Load = 3307.15 kN a1 = 430.00 mm

Ult. JF = 3968.59 kN H = 1250 mm

T bursting = 0.25 Ult.JF (1-a1/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 fy

No. Leg of stirrup = 4 leg Anchor Stirup Rebar = 3254.2 mm2

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

Spalling Rebar

Spalling Force = 2% JF

Spalling Force = 66.1 kN

EBS/0.7 (fcc'-fci)/4.1 fl / 0.5 fy



use no of stirup = 3 pcs

page 15 / 15


20/114

PT WIJAYA KARYA BETON

TECHNICAL CALCULATION


Project : TOLL SURABAYA ‐ GRESIK

Product : PCI Girder Monolith H‐125cm ; L‐20.80m ; CTC ‐160cm ; fc' 50MPa

Job no : 13014 B

Rev. No. : 04

Design Reff. : - SNI T ‐12‐2004

Perencanaan Struktur Beton Untuk Jembatan

- RSNI T ‐02‐2005

Standar Pembebanan Untuk Jembatan

- PCI : Bridge Design Manual

Gedung JW, 1st

& 2nd

floor

Jl. Jatiwaringin no. 54, Pondok Gede ‐ Bekasi

Ph: +62‐21‐8497 ‐3363 fax : +62‐21‐8497 ‐3391

www.wika‐beton.co.id


21/114

PT

WIJAYA

KARYA

BETON

Job no. : 13014 B

Rev. : 04

TECHNICAL

CALCULATION

APPROVAL



Approved by :


Design by :

18 Juni 2013

Suko

Technical Staff



Consultan / Owner


18 Juni 2013 18 Juni 2013


22/114


1. BEAM SPECIFICATION

Span = 20.20 m (beam length = 20.80 m)

Beam Height ( H ) = 1250 mm

Distance ctc of beam ( s ) = 1600 mm

Slab thickness = 200 mm

Beam Compressive strength = 50 MPaSlab Compressive strength = 28 MPa

Bridge life time = 50 years

Segment Arr angement

Beam Segment 1 2 3 4 5 6 7

Length (m) 6.600 7.000 6.600 0.00 0.00 0.00 0.00

Additional length at the end of beam = 0.30 m

Total length of the beam = 20.80 m

Total beam weight = 17.41 ton

2. STRESSING

Nos of PC Strand = 28 strand 12.7 mm (PC Strand 270 grade, low relaxation)

Strand configurationNo. number H strand bottom (mm)

Tendon strand edge mid Jacking Force = 75% UTS

0 0 0 0 UTS of Strand = 1860.00 MPa

0 0 0 0 Total Losses = 16.89% at middle

0 0 0 0 fc initial = 80.0% fc'

RESUME OF PCI GIRDER MONOLITH TECHNICALLY CALCULATION

1 4 900 300

2 12 600 200

3 12 300 100

total 28 514.29 171.43

3. LOADING

1. Dead Loada. Precast Beam = 7.77 kN/m

b. Slab = 7.86 kN/m Slab thickness = 200 mm

c. Deck Slab = 2.31 kN/m Deck slab thickness = 70 mm

d. Asphalt = 1.73 kN/m Asphalt thickness = 50 mm

e. Diaphragm = 6.92 kN for 1 diaphragm

No. Diaphragm 4 pcs equivalent load = 0.91 kN/m

2. Live Load

Taken from "Pembebanan Untuk Jembatan RSNI T-02-2005"

Moment force cause by D Loading is bigger than Truck Loading

a. Dynamic Load Allowance (DLA) = 1.40 for span length


23/114


24/114


20.20 M

I. DATA

0.3 L= 20.20 M 0.3


Beam spacing (s)=




Cross Section

H = 1250 mm tfl-1 = 75 mm

A = 350 mm tfl-2 = 75 mm

B = 650 mm tfl-3 = 100 mm

tweb = 170 mm tfl-4 = 125 mm

II. MATERIAL

2.1 Concrete

Beam Slab

at service fc' = 50.0 28.0 [N/mm2]

at initial 80% fc' fc'i = 40.0 [N/mm2]

Allowable stress

24.0 [N/mm2]Compressive

SPAN L =

Compressive strength

Allowable stress at initial ………… (SNI T-1 2-20 04 )

0.6 * fc'i =

TECHNICAL CALCULATION OF PCI MONOLITH BEAM FOR HIGHWAY BRIDGES

A

H

B

tfl-1

tfl-2

tfl-3

tfl-4

tweb

Tensile 1.6 [N/mm ]

22.5 12.6 [N/mm2]

Tensile 3.5 2.6 [N/mm2]

wc = 2500.0 2500.0 [kg/m3]

Ec = wc1.5

*0.043*sqrt(fc') = 38007.0 28441.8 [N/mm2]

Eci = wc

1.5

*0.043*sqrt(fci') = 33994.5 [N/mm

2

]Concrete flexural tension strength (fr)

f r = 0.7*sqrt(fc') = 4.9 [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 : 132.73 [cm

2]

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

- Yield stress fy : 400 [N/mm2]

- Eff. Section area

Compressive

Steel Reinforcement

[Uncoated stress relieve seven wires strand]

- Diameter strand

- Ultimate tensile strength

- Modulus of elasticity

Prestressing Cable

0.25 * Sqrt(fc'i) =

0.45 * fc' =

0.5 * Sqrt(fc') =

Modulus of elasticity

Allowable stress at service ………. (SNI T-1 2-20 04 )

Concrete unit weight

page 1 / 15


25/114


III. SECTION ANALYSIS

Remark :

Ep 1 = 38007 [N/mm2] [Girder]

Ep 2 = 28442 [N/mm2] [Slab]

n = Ep 2 / Ep 1

n = 0.75

3.1 Precast Beam

[in mm ]

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

Height Bottom Upper mm2 mm mm mm

3mm

4mm

4mm

4

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*d

2 Ix

Section Bottom Upper mm2 mm mm mm

3mm

4mm

4mm

4

2 200.0 1197.3 1197.3 239466 1320 1420.0 340041823 798220242.5 61294439175 62092659418

70.0 149.7 149.7 10477 1250 1285.0 13462483 4277961.612 1441454078 1445732040

1 1250.0 650.0 350.0 316750 0 519.3 164493750 54962557571 49359610133 1.04322E+11

Zone

Ya'

1

2

3

Yb'

COMPOSITE BEAM

1

2

3

4

5

Ya

Yb

PRECAST BEAM

Base Line

o a . . . + . +

3.3 R e s u m e

[in mm ]

Description Area (mm2) Ya (mm) Yb (mm) Ix (mm

4) Wa (mm

3) Wb (mm

3)

Precast Beam 316750 731 519.3 54962557571 75220826 105836180

Composite Beam [composite] 566693 606 914.1 167860559162 277030629 183640372

[precast] 336 499692375

IV. LOADING4.1 Dead Load

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

q1 = 0.317 x 2.50 = 0.792 [t/m'] = 7.77 [kN/m']

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

q2 = 0.334 x 2.40 = 0.802 [t/m'] = 7.86 [kN/m']

c. Deck slab q3 = Ac deck slab x s

q3 = 0.098 x 2.40 = 0.235 [t/m'] = 2.31 [kN/m']

d. Asphaltic q4 = Ac asphaltic x s

q4 = 0.080 x 2.20 = 0.176 [t/m'] = 1.73 [kN/m']

e. Diaphragm p = Vol diaph with 0.20m thickness x diaph

p = 0.294 x 2.40 = 0.706 [ton'] = 6.92 [kN']

note : from kg to N, multiply by 9.8060

Number of diaph = 4 pcs

Diaph. placement 1 2 3 4

Location 0.00 6.73 13.47 20.20

Support Va 6.92 4.62 2.31 0.00

Mid Moment 0.00 23.31 23.31 0.00

Total Diaphragma Flexural Moment at Middle Span 46.61 kN.m

eqivalen load q diaphragm q5= 0.91 [kN/m']

page 2 / 15


26/114


4.2 Live Load


4.2.1.

"T"

Loading

(Beban

Truk)

Unit P1 P2 P3 M.max di x = 10.100 m

kN 225 225 50 DLA = 30%

1.3 1.3 1.3 Impact = 1 + DLA = 1.3

kN 292.5 292.5 65

m 6.100 10.100 15.100

kN 204.17 146.25 16.41

kNkN-m

kN-m

4.2.2. "D" Loading (Beban Lajur)


Load type :

Distribution Load Chart : Dynamics Load Factored Chart :

0.47

Impact

DF = S/3.4

Load

Item

LL + I

1192.94

M max

Va

Va

M x DF

2535.00

Distance

366.83

225kN 225kN50kN

Line Load (D load)

a. Dynamic Load Allowance [DLA] DLA = 1 + 0,4 = 1.40 Span = 90 m

b. Knife Edge Load (KEL) = 49.00 [kN/m']

c. Distribution Factor (DF) = 1.00

d. Distribution Loadq = 9.00 kN/m which : q = 9 kN/m for Span 30 m

e. Live load

Distribution load, qudl = DF x q x s

= 1.00 x 9.00 x 1.60 = 14.40 [kN/m']

KEL, PKEL = DF x DLA x KEL x s

= 1.00 x 1.40 x 49.00 x 1.60 = 109.76 [kN']

M.max at 0.5 span = 10.100 m

Va = 200.32 kN

M LL = 1 28 8. 76 k N. m

RESUME : Moment force cause by D Loading is bigger than Truck Loading

page 3 / 15


27/114


V. MOMENT ANALYSIS

[in kN-meter ]


span 0.00 6.60 13.60 20.20 20.20 10.10 (m)

DL Precast beam 396.06 0.00 348.50 348.50 0.00 0.00 396.06

396.06 0.00 348.50 348.50 0.00 0.00 396.06

DL Slab 400.92 0.00 352.78 352.78 0.00 0.00 400.92

ADL Asphaltic Layer 88.03 0.00 77.46 77.46 0.00 0.00 88.03

SDL Diaphragm+Deck Slab 164.25 0.00 144.52 144.52 0.00 0.00 164.25

653.20 0.00 574.76 574.76 0.00 0.00 653.20LL Distribution load 734.47 0.00 646.27 646.27 0.00 0.00 734.47

KEL 554.29 0.00 487.73 487.73 0.00 0.00 554.29

1288.76 0.00 1134.00 1134.00 0.00 0.00 1288.76

2338.02 0.00 2057.26 2057.26 0.00 0.00 2338.02

3689.39 0.00 3246.35 3246.35 0.00 0.00 3689.39


VI. SHEAR ANALYSIS

[in kN]


span 0.00 6.60 13.60 20.20 20.20 10.10 (m)

DL 0.00 78.43 27.18 -27.18 -78.43 -78.43 0.00

0.00 78.43 27.18 -27.18 -78.43 -78.43 0.00

DL 0.00 79.39 27.51 -27.51 -79.39 -79.39 0.00

ADL 0.00 17.43 6.04 -6.04 -17.43 -17.43 0.00

SDL 0.00 32.52 11.27 -11.27 -32.52 -32.52 0.00

0.00 129.35 44.82 -44.82 -129.35 -129.35 0.00

Distribution load 0.00 145.44 50.40 -50.40 -145.44 -145.44 0.00

KEL 54.88 109.76 73.90 -73.90 -109.76 -109.76 54.88

54.88 255.20 124.30 -124.30 -255.20 -255.20 54.88

54.88 462.97 196.30 -196.30 -462.97 -462.97 54.88Total (DL + LL)

Asphaltic Layer

Total (DL + LL)

Description

Subtot al

Subtot al

Subtot al

Subtot al

Type

Precast beam

Ultimate total

Slab

Diaphragm+Deck slab

Subtot al

LL

Type Description

Subtot al

. . . - . - . - . .


VII. PRESTRESSING CABLE

7.1 Cable Profile

[in: mm ]

ten- Nos Profile Total JF

don strand Edge Middle left right tension (kN)

0 0 0 0 0% 0% 0% 0

0 0 0 0 0% 0% 0% 0

0 0 0 0 0% 0% 0% 0

1 4 900 300 75% 0% 75% 551

2 12 600 200 75% 0% 75% 1654

3 12 300 100 75% 0% 75% 1654

total 28 514.29 171.43 75% 0% 75% 3858

Parabol ic curve (Average of Str and's posi t ion ver t i ca l ly f rom t he bot tom of beam ( Value for Y axis ) )

Y = A.x2+ B.x + C

where : A = Constanta : ( (Ymiddle + Yedge)/(L/2)2) A = 0.003263

B = Constanta : ( L x A ) B = -0.066899

C = Average of strand's position when the parabolic curve reach the Y axis


Y = 0.003263 X + -0.066899 X + 0.514286

Cable tendon angle :

tg o = 0.006527 X + -0.066899

eccentricity of tendon at middle section

Eccentricity [e] = Yb - Ys = 347.89 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)

Tension

ma e o a

page 4 / 15


28/114



7.2 Losses of Prestress

1. Losses of Prestress (Short Term)

a. Friction

The equation for calculating the loss of prestress due to friction is :

Px = Po.e- + .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)

= friction coefficient

= Change of cable angle from tensile point to x section

k = Wobble coefficient

x = Distance from tensile point to x section

Friction and Wooble coeficient for grouting tendon in metal sheating

with Seven Wire Strand : = 0.20

When the jacking force is applied at the stressing end, the tendon will elongate. The elongation will be resisted by friction

between the strand and its sheating or duct. As the result of this friction, force will be decreased with distance from the jacking

end. The friction is comprised of two effects : curvature friction which is a function of the thendons profile, and wooble friction

which is the result of minor horizontal or vertical deviation form intended profile.

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 5 10 15 20 25

60.0%

65.0%

70.0%

75.0%

80.0%

0.00 10.00 20.00 30.00

k = 0.003

Table of calculation due to Friction

ten- Nos Profile % JF a b

don strand Edge Middle from UTS (rad) 0.00 10.25 20.50

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 4 900 300 75% 0.00571 -0.1170732 0.233 75.0% 69.42% 67.3%2 12 600 200 75% 0.00381 -0.0780488 0.156 75.0% 70.50% 68.4%

3 12 300 100 75% 0.00190 -0.0390244 0.078 75.0% 71.60% 69.4%

total 28 514.29 171.43 75% 0.00326 -0.066899 0.134 75.0% 70.8% 68.7%

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

= Loss of prestress per length

= 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 follows :

x = Sqrt ( Es . / )

effective anchorage set point position :

, . ,

retracts pulling the wedges in to the anchorage device and locks the strand in place. The lost in elongation is small . It depend on

the wedges, the jack and the jacking procedure. This lost in elongation is resisted by friction just as the initial elongation is

resisted by friction.

Prestress force (Px) = % UTS

Cable change

angle point


Anchorage

set area


Cable change

angle point

Anchorage

set area

page 5 / 15


29/114


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 set

ten- Nos draw in

don strand Mpa/mm mm X (m) Px (% UTS) X (m) Px (% UTS) 0.00 10.25 20.50

0 0 0.00000 0.00 0.00 0.00% 0.00 0.00% 0.0% 0.00% 0.0%

0 0 0.00000 0.00 0.00 0.00% 0.00 0.00% 0.0% 0.00% 0.0%

0 0 0.00000 0.00 0.00 0.00% 0.00 0.00% 0.0% 0.00% 0.0%

1 4 0.00697 8.00 14.88 68.47% 0.00 0.00% 61.9% 67.52% 67.3%

2 12 0.00602 8.00 16.01 69.30% 0.00 0.00% 63.6% 68.10% 68.4%

3 12 0.00505 8.00 17.49 70.07% 0.00 0.00% 65.1% 68.54% 69.4%

total 28 0.00574 8.00 16.48 69.51% 0.00 0.00% 64.02% 68.20% 68.67%

c. Elastic Shortening ( ES )

Elastic shortening refers to the shortening of the concrete as the postensioning force is applied.

From right sideFrom left side after anchorage set = % UTS

55.0%

60.0%

65.0%

70.0%

75.0%

80.0%

0.00 10.00 20.00 30.00


LOSSES

OF

PRESTRESS

DUE

TO

ANCHORAGE

SET

64.02%64.02%64.02%64.02%

68.20%

69.85%69.61%69.30%68.67%

60.0%

65.0%

70.0%

75.0%

0.00 5.00 10.00 15.00 20.00 25.00

Prestress

tendon

section

AVERAGE LOSSES OF PRESTRESS

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 shortening

for member with bonded tendons :

ES = Kes . Es . f cir / Eci

where:

Kes = 0.50 for post-tensioned members when tendon are tensioned in sequential order to the same tension

ES = Elastic modulus of tendon material

Eci = Elastic modulus of the concrete at the time of prestress transfer

f cir =

Assumption Losses due ES 2.39%

Pi = Total prestressing force at release

Pi = 68.2% - 2.39% = 65.82% UTS x nos x Aps = 3385.9865 kN

f cir = Pi / A + Pi. ec2/ I + Mg.ec/I

f cir = 15.64 N/mm2

so, ES = 44.39 N/mm2, percent actual ES losses = Es/fpu 2.39% 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 60

Ksh 0.92 0.85 0.8 0.77 0.73 0.64 0.58 0.45

Ksh = 0.64

V/S = 0.08 Volume = 6.59 m3

Surface = 81.21 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 structures

that are not moist cured, Ksh is typiclly based on when the concrete was cast

page 6 / 15


30/114


e. Creep ( CR )

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

CR = 94.83 N/mm2

percent actual CR losses = CR/fpu 5.10%

Where :

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

fcir = 15.639 N/mm2

Msd = Moment due to all superimposed permanent dead loads applied after prestressing

Msd = 653.20 kN.m

fcds = Stress in a concrete at the cgs of the tendon due to all superimposed dead load

fcds 1 = Msdl.e/I = 3.58 N/mm2

component of fcd due to load on the plain beam

fcds 2 = Madl.e/Ic = 0.39 N/mm2

component of fcd due to load on the composite beam

fcds = fcds 1 + fcds 2 = 3.97 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 = 18.26 N/mm2

percent actual RE losses = RE/fpu 0.98%

Where :

Kre = 5000.00 (for 270 grade, low relaxation strand)

J = 0.04 (for 270 grade, low relaxation strand)

Relaxation is defined as a gradual decrease of stress in a material under constant strain. In the case of steel, relaxation is

the result of permanent alteration of the grain structure. The rate of relaxation at any point in time depends on the

stress level in the tendon at that time. Because of other prestress losses, there is a continual reduction of tendon strss;

this causes a reduction in the relaxation rate.

Over time, the compresive stress induced by postensioning causes a shortening of the concrete member. The increase in

strain due to a sustained stress is refered to as creep. Loss of prestress due to a creep is nominally propotional to the net

permanent compresive stressin the concrete. the net permanent compressive stress is the initial compressive stress in the

concrete due to the prestressing minus the tensile stress due to self weight and superimposed deadload moments

= . or p pu = .

RESUME DUE TO SHORT & LONG TERM LOSSES

Losses

Section

x (m)

0.00 75.00% 64.02% 61.64% 13.36% 60.00% 54.91% 53.92% 21.08%

0.00 75.00% 64.02% 61.64% 13.36% 60.00% 54.91% 53.92% 21.08%

0.00 75.00% 64.02% 61.64% 13.36% 60.00% 54.91% 53.92% 21.08%

0.00 75.00% 64.02% 61.64% 13.36% 60.00% 54.91% 53.92% 21.08%10.25 70.82% 68.20% 65.82% 5.00% 64.19% 59.09% 58.11% 12.71%

14.88 69.85% 69.85% 67.46% 2.39% 65.83% 60.73% 59.75% 10.10%

16.01 69.61% 69.61% 67.22% 2.39% 65.59% 60.50% 59.51% 10.10%

17.49 69.30% 69.30% 66.92% 2.39% 65.29% 60.19% 59.21% 10.10%

20.50 68.67% 68.67% 66.29% 2.39% 64.66% 59.56% 58.58% 10.10%

friction Losses equotion :

0 > x > 10.25

75.00% -+ 0.41% x

10.3 > x > 20.50

70.82% + 0.05% x x - 10.25

Long term Losses equotion :

0 > x > 10.25

53.92% + 0.41% x

10.25 > x > 14.88

58.11% + 0.35% x x - 10.25

14.88 > x > 16.01

59.75% -+ 0.21% x x - 14.8798744

16.01 > x > 17.49

59.51% -+ 0.21% x x - 16.0124668

17.49 > x > 20.50

59.21% -+ 0.21% x x - 17.4863251

II. Long Term Losses

FrictionShrinkage

(SH)

Elastic

Shortening

Steel

RelaxationAnchor set

I. Short Ter m Losses

Creep (CR)Total

Losses (%)

Total Losses

(%)

75.00%

70.82%69.85% 69.61% 69.30%

68.67%

64.02%

68.20%

69.85% 69.30%68.67%

61.64%

65.82%

67.46% 67.22% 66.92%

66.29%

60.00%

64.19%65.83% 65.59% 65.29% 64.66%

54.91%

59.09%

60.73% 60.50% 60.19% 59.56%

53.92%

58.11%59.75% 59.51% 59.21% 58.58%

50.00%

65.00%

80.00%

0.00 10.25 14.88 16.01 17.49 20.50

Friction

Anchorset

ElasticShortening(ES)

Shrinkage(SH)

Creep(CR)

Steel Relaxation(SR)

LOSSES OF PRESTRESS DIAGRAM


UTS

page 7 / 15


31/114


7.3 Effective Stress Force

Resume Prestressed Force at middle

Cable

stress

[N/mm2] [mm

2] [kN]

9.2% 65.8% 1224 2765.84 3385.99

16.9% 58.1% 1081 2765.84 2989.32

VIII. STRESS AND DEFFLECTION ANALYSIS

Beam Segment 1 2 3 4 5 6 7 8

Length (m) 6.600 7.000 6.600 0.00 0.00 0.00 0.00 0.00

Additional length at the end of the beam = 0.30 m Total Length = 20.80 m

8.1 Stress at initial


x - [m] Span 0.00 6.60 13.60 20.20 20.20 10.10

Moment DL [kN.m] 396.06 0.00 348.50 348.50 0.00 0.00 396.06

Jacking Force [kN] 3858.35 3858.35 3858.35 3858.35 3858.35 3858.35 3858.35


Pi [kN] 3646.30 3858.35 3719.78 3651.01 3666.50 3666.50 3646.30

e (eccentricity) [m] 0.348 0.015 0.308 0.308 0.015 0.015 0.348

Pi.e [kN.m] -1269 -58 -1145 -1124 -55 -55 -1269

Moment Net. [kN.m] -872 -58 -797 -776 -55 -55 -872

Pi / A [N/mm2] 11.51 12.18 11.74 11.53 11.58 11.58 11.51

M / Wa [N/mm2

] -11.60 -0.77 -10.59 -10.31 -0.73 -0.73 -11.60 Allow.

M / Wb [N/mm2] 8.24 0.55 7.53 7.33 0.52 0.52 8.24 stress

Initial Stresses top ( T ) -0.09 11.41 1.15 1.21 10.84 10.84 -0.09 -1.6

bot ( B ) 19.75 12.73 19.27 18.86 12.09 12.09 19.75 24.0

8.2 Stress at service

[N/mm2]

PCondition

Asp%UTS

effective

prestress

% Losses of

prestress

long term

short term

oa o precas , s a , ap ragm an pres ress y eam =

> Live load and asphalt by composite ( = M2 )


x - [m] Span 0.00 6.60 13.60 20.20 20.20 10.10

Moment DL [kN.m] 961.23 0.00 845.80 845.80 0.00 0.00 961.23


effective prestress P [kN] 2986.17 2774.12 2912.68 3050.49 3016.60 3016.60 2986.17

P . e [m] -1038.85 -41.59 -896.85 -939.28 -45.23 -45.23 -1038.85

Moment --- M1 [kN.m] -77.62 -41.59 -51.05 -93.48 -45.23 -45.23 -77.62

Moment --- M2 [kN.m] 1376.79 0.00 1211.45 1211.45 0.00 0.00 1376.79

P / A [N/mm2] 9.44 9.44 9.44 9.44 9.44 9.44 9.44

M 1 / Wa [N/mm2] -1.03 -0.55 -0.68 -1.24 -0.60 -0.60 -1.03

M 1 / Wb [N/mm2] 0.73 0.39 0.48 0.88 0.43 0.43 0.73

M 2 / Wa' [N/mm2] 2.76 0.00 2.42 2.42 0.00 0.00 2.76 Allow.

M 2 / Wb' [N/mm2] -7.50 0.00 -6.60 -6.60 0.00 0.00 -7.50 stress

Stress at Service slab ( S ) 4.97 0.00 4.37 4.37 0.00 0.00 4.97 12.6

top ( T ) 11.16 8.88 11.18 10.62 8.84 8.84 11.16 22.5

bot ( B ) 2.67 9.83 3.32 3.72 9.86 9.86 2.67 -3.5

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 condition

Wb = Modulus Section for Bottom section of Precast condition

Wa' = Modulus Section for Top section of composite Condition……. ( Chapter 3.3 - Resume )

Wb' = Modulus section for bottom section of composite condition ……. ( Chapter 3.3 - Resume )

Moment Bal =

Moment DL =

Moment Net =

[N/mm2]

page 8 / 15


32/114


8.3 Stress diagram at center span :

8. 3. 1. STRESS DIAGRAM AT INIT IAL

a. Stress at beam end section when Prestress is applied :


+ =





Mdl = Mbeam = 0 kN-m control allow stress = meet requirement

b. Stress at beam middle section when Prestress is applied :

Pi/A = 11.50 MPa M/Wa = -11.58 MPa top = -0.08 MPa

+ =





Mdl = Mbeam = 396.06 kN-m control allow stress = meet requirement

8. 3. 2. STRESS DIAGRAM AT CONSTRUCTION

a. Stress at beam middle section when diaphragm, RC deck is install and finish fresh concreting composite slab


+ =





Mdl = Mbeam + Madl = 961.23 kN-m control allow stress = meet requirement

b. Stress at composite beam middle section due to asphaltic layer:

slab = 0.32 MPa


+ + =



Pi = 3385.99 kN M2 = Masphalt = 88.03 kN-m

eccentricity (ei) = 347.89 mm allow comp at initial = 24.00 MPa

Mdl = Mbeam + Madl = 961.23 kN-m allow tension initial = -1.58 MPa


page 9 / 15


33/114


8. 3.3 . STRESS DIAGRAM AT SERVICE (at cent er of sp an)

Stress at composite beam middle section due to Live Load

slab = 4.97 MPa


+ + =



Pi = 2989.32 kN M2 = Masphalt + LL = 1376.79 kN-m

eccentricity (ei) = 347.89 mm allow comp at service = 22.50 MPa

Mdl = Mbeam + Madl = 961.23 kN-m allow tension at service = -3.54 MPa


8.4 Deflection

8.4.1 Chamber due to Prestress Load

Deflection on middle section :

pi=

-26.87 mmwhere : P = Prestress force

Eci = Modulus Elasticity of Concrete

Ixi = Section Inertia

l = length of anchor to anchor

ee =

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


c.g of concrete at end

P

l

l/2 l/2

Pec

ee

ec =

8.4.2 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 -26.87 1.80 x (1) -48.37 2.20 x (1) -59.12

2. Due to beam weight (DL) 7.77 9.01 1.85 x (1) 16.67 2.40 x (1) 21.62

-17.86 -31.71 -37.50

3. Due to ADL 3.22 3.34 3.00 x (2) 10.03

-28.36 -27.47

4. Due to Composite Overtoping 7.86 8.16 2.30 x (2) 18.76

-20.21 -8.71

5. due to asphaltic (SDL) 1.73 0.59

-8.12

6. due to Live Load = UDL + KEL 14.40 109.76 7.85

-0.28

Resume of deflection :

1. Deflection at service = -8.12 mm

2. Deflection due to Live Load = 7.85 mm < allow. deflection L/800 = 25.25 mm OK

3. Total deflection with LL = -0.28 mm, chamber upward

WORKING LOAD

Loading


c.g of concrete at centre

Long time cambers and deflection

page 10 / 15


34/114


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' = 28.00 MPa

2. Beam Ctc =1600 mm …. Control Value = 0.85

3. Span length / 4 =5050 mm

Thus, Effectif slab width is : =1600 mm

Partial Rebar:

fy = 400 MPa

Use 0 Dia.13 mm at tension area

As = 0.00 mm2 b web = 170 mm

d = 1190.5 mm

Partial tension rebar ratio : Rebar in compresion area is neglected due calculation

t = As / (bweb x d ) t = 0.00000 c =

t = t . fy / fc t = 0.000 c =

Low Relaxation strand :

fpu = 1860 MPa

Strand stress ratio fpu / fpy = 0.9 value p = 0.28

dp = 1348.6 mm Aps = 2765.84 mm2

beff = 1600 mm

Prestress ratio :

p = Aps / (beff x dp ) p = 0.00128184

fps = fpu {1 - p / (p.fpu/fc + d/dp (t-c))) fps = 1807.8 MPa

p = p fps/fc p = 0.083

Resume of Steel Index Requirement (SNI Beton 03-2847-2002 pasal 20.8)p + d/dp (t-c) < 0.36

0.083 < 0.306 Under Reinf, Meet With Steel Index Requirement

9.2 Momen Capacity

b. eff

Tps = Aps . Fps

Tps = 5000162.13 N

strength reduction factor

= 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)

4 131.31 1600 210090.85 28.00 CIP Slab 66

3 0.00 335 0 28.00 CIP Slab 131

2 0.00 350 0 50.00 Beam 131

1 0.00 170 0 50.00 Beam 131

a = Tps / ( 0.85 x fc'' slab x beff ) a= 131.31 mm

Mn = Mn = 6414.80 kN.m

Mn = 5131.8386 kN.m

Bridge life time design for 50 year,so Transient act factor = 1

Mult = 1x 3,689kN-m Mn / Mult = 1.391 >1, Moment capacity meet with requirement

9.3 Cracking Capacity

Stress at bottom girder section due to service load (bot at service) = 2.67 MPa

Concrete flexural tension strength fr = 4.9 MPa

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

Mcr = 3737.99 kN.m

Mn / Mcr = 1.373 > 1.2 ---- Cracking Capacity requirement is achieve

0

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

Conc. Strength fc'i Cci=0.85 fc'i.Aci

N

0

5000162

Depth of Concrete Compression Block is located at zone 4

065.65

MPa

Zone 3

dp d

Cc3

Cc2

Cc1

Tps=Aps.fps

T = As.fy

c

COMPOSITE BEAM

a

Zone 2

one

Zone 1

i

Zone 3

page 11 / 15


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X. SHEAR ANALYSIS

10.1 Shear calculation based on SNI 03-2847-2002

40% Ultimate Tensile Strength = 744 MPa

Effective Prestress = 1081 MPa Effective Prestress > 40% fpu

Section Properties :

Ix = 5.496E+10 mm4 Ixcomp = 1.679E+11 mm4

Yb = 519.31728 mm Ybcomp = 914.1 mmAg = 316750 mm2

Load :

Effective prestress Pe = 2989.32 kN

Factored Load : Unfactored Load :

qult DL + ADL = 26.85 kN/m q DL + ADL = 18.85 kN/m

qult LL = 25.92 kN/m q sdl = 1.73 kN/m

Pult LL = 197.57 kN q DL + ADL = 20.57 kN/m

Concrete Shear resistance contribution (Vc)

Nominal shear strength provide by concrete

Vc = {0.05sqrt(fc') + 5 (Vu.dp/Mu)}bw.d

but nominal strength (Vc) should taken between : (1/6).sqrt(fc').bw.d < Vc < 0.4sqrt(fc').bw.d

and Vu.dp/Mu ≤ 1

where :

Mu = Maximum factored moment at section

Vu = Maximum factored shear force at section

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

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

of ultimate tensile stress

Vn = Vc + Vs where : Vn = Nominal Shear force Vu = Ultimate Shear force

Vn = Vu / Vc = Concrete shear contribution = Shear reduction factor

Vs = Shear steel contribution = 0.75

Zonafication for shear steel stirup calculation

Zone 1 Vn < 0.5 Vc No need to use stirup

Zone 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/)-Vc)

S ≤ 0.75 H

S ≤ 600mm

Zone 4 Vn < Vc+0.67 sqrt(fc') bw d Required tight stirup spacing with spacing :

S ≤ (av.fy.d) / ((Vu/)-Vc)

S ≤ 0.375 H

S ≤ 300mm

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

RSNI T-12-2005 : 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.

page 12 / 15


36/114


Shear rebar steel

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 use

m m m kN kN-m kN kN kN Zonasi mm mm

0.1 0.416 1.02 724.32 72.70 1.00 930.34 965.76 35.42 2 600 300

0.3875 0.435 1.04 706.33 277.67 1.00 947.17 941.78 -5.39 2 600 3000.775 0.459 1.06 682.09 544.47 1.00 969.08 909.46 -59.62 2 600 300

1.7 0.512 1.12 624.23 1137.45 0.61 650.60 832.31 181.71 3 600 300

2 0.529 1.13 605.47 1316.48 0.52 571.31 807.29 235.98 3 510 300

3 0.578 1.18 542.91 1866.22 0.34 417.85 723.88 306.03 3 411 300

4 0.621 1.23 480.36 2343.62 0.25 336.11 640.48 304.37 3 428 300

5 0.658 1.26 417.81 2748.69 0.19 282.28 557.08 274.80 3 488 300

6 0.688 1.29 355.25 3081.43 0.15 241.77 473.67 231.90 3 592 300

7 0.711 1.32 292.70 3341.83 0.12 208.34 390.27 181.92 3 600 300

8 0.728 1.33 230.15 3529.90 0.09 178.84 306.86 128.02 3 600 300

9 0.739 1.34 167.59 3645.63 0.06 151.47 223.46 71.99 2 600 300

10 0.743 1.35 105.04 3689.03 0.04 125.07 140.05 14.99 2 600 300

10.100 0.743 1.35 98.78 3689.39 0.04 122.44 131.71 9.27 2 600 300

1400.0

1600.0

1800.0

2000.0

Zona1

Shear

Steel

Requirement

PositionkN

x (m) from range nos shear

span edge (m) (row)







Shear spacing S - 300 10.1 10.1 34

total shear rebar per half span (row) = 34

total shear rebar per span (row) = 68

Shear Rebar configuration

0.0

200.0

400.0

600.0

800.0

1000.0

1200.0 Zona2

Zona3

Zona4

Vn= Vu/f

beam section

point

page 13 / 15


37/114


10.2 Horisontal Shear

Width of contact surface area bv = 200 mm

Effective Height d = 1216 mm

= 0.75

fy = 400 MPa

Use 2 leg Dia.13 mm

Area horisontal Shear Steel Avh = 265.46 mm2

Horisontal Shear steel Spacing s = 300 mmHorisontal Shear steel ratio v = 0.442%

Shear horisontal Nominal

Vnh = (1.8 Mpa + 0.6 v. fy) . bv .d

Vnh = 696.00 KN

Requirement for shear horisontal steel :

Vult comp = 46.03 MPa

ten- Nos Anchor sheath Ult. Point Block End Bearing

don strand Height hole Load Area Stress

( ai ) (Pu) (A) (EBS=Pu/A)

mm kN mm2 Mpa Mpa

0 0

0 0

0 0

1 4 165 51 661.43 25182.18 26.27 47.60 EBS < Nominal Compresion



Remark

Nominal

comp. fci

page 14 / 15


38/114


2. Stirrup and Spalling Reinforcement

Load factor = 1.2

Reduction factor () = 0.85

fy = 400 MPa

Bursting Steel



ten- Nos Anchor sheath Jacking Bursting End

don strand Heighthole Force Area Bearing sp

( ai ) (Abs) (EBS) fcc' fl p

mm kN mm2 Mpa Mpa Mpa (mm)

0 0

0 0

0 0

1 4 165 51 551.1924 25182.18 21.89 36.79 -0.8 -0.39% -821.2

2 12 215 63 1653.5772 43107.75 38.36 64.47 6.0 2.98% 82.8

3 12 215 63 1653.5772 43107.75 38.36 64.47 6.0 2.98% 82.8

total 28

Anchor Zone Stirrup

JF Load = 3858.35 kN a1 = 595.00 mm

Ult. JF = 4630.02 kN H = 1250 mm

T bursting = 0.25 Ult.JF (1-a1/H) d bursting = 0.5(h-2e)

T bursting = 606.53212 kN d bursting = 630.031571 mm

Diameter closed stirup = 13 mm Anchor Stirup Rebar = T bursting / 0.5 fy

No. Leg of stirrup = 4 leg Anchor Stirup Rebar = 3032.7 mm2

Stirup Area = 530.9 mm2 use no of stirup = 6 pcs

Spalling Rebar

Spalling Force = 2% JF

Spalling Force = 77.2 kN

EBS/0.7 (fcc'-fci)/4.1 fl / 0.5 fy



use no of stirup = 3 pcs

page 15 / 15


39/114

PT WIJAYA KARYA BETON

TECHNICAL CALCULATION


Project : TOLL SURABAYA ‐ GRESIK

Product : PCI Girder Monolith H‐125cm ; L‐21.75m ; CTC ‐160cm ; fc' 60MPa

Job no : 13014 C

Rev. No. : 04

Design Reff. : - SNI T ‐12‐2004

Perencanaan Struktur Beton Untuk Jembatan

- RSNI T ‐02‐2005

Standar Pembebanan Untuk Jembatan

- PCI : Bridge Design Manual

Gedung JW, 1st

& 2nd

floor

Jl. Jatiwaringin no. 54, Pondok Gede ‐ Bekasi

Ph: +62‐21‐8497 ‐3363 fax : +62‐21‐8497 ‐3391

www.wika‐beton.co.id


40/114

PT

WIJAYA

KARYA

BETON

Job no. : 13014 C

Rev. : 04

TECHNICAL

CALCULATION

APPROVAL



Approved by :


Design by :

18 Juni 2013

Suko

Technical Staff



Consultan / Owner


18 Juni 2013 18 Juni 2013


41/114


1. BEAM SPECIFICATION

Span = 21.15 m (beam length = 21.75 m)

Beam Height ( H ) = 1250 mm

Distance ctc of beam ( s ) = 1600 mm

Slab thickness = 200 mm

Beam Compressive strength = 60 MPaSlab Compressive strength = 28 MPa

Bridge life time = 50 years

Segment Arr angement

Beam Segment 1 2 3 4 5 6 7

Length (m) 7.075 7.000 7.075 0.00 0.00 0.00 0.00

Additional length at the end of beam = 0.30 m

Total length of the beam = 21.75 m

Total beam weight = 18.17 ton

2. STRESSING

Nos of PC Strand = 35 strand 12.7 mm (PC Strand 270 grade, low relaxation)

Strand configurationNo. number H strand bottom (mm)

Tendon strand edge mid Jacking Force = 75% UTS

0 0 0 0 UTS of Strand = 1860.00 MPa

0 0 0 0 Total Losses = 17.89% at middle

0 0 0 0 fc initial = 80.0% fc'

RESUME OF PCI GIRDER MONOLITH TECHNICALLY CALCULATION

1 11 900 300

2 12 600 200

3 12 300 100

total 35 591.43 197.14

3. LOADING

1. Dead Loada. Precast Beam = 7.77 kN/m

b. Slab = 7.86 kN/m Slab thickness = 200 mm

c. Deck Slab = 2.31 kN/m Deck slab thickness = 70 mm

d. Asphalt = 1.73 kN/m Asphalt thickness = 50 mm

e. Diaphragm = 6.92 kN for 1 diaphragm

No. Diaphragm 4 pcs equivalent load = 0.87 kN/m

2. Live Load


Moment force cause by D Loading is bigger than Truck Loading

a. Dynamic Load Allowance (DLA) = 1.40 for span length


42/114


4. BEAM SUPPORT REACTION


Beam support react ion :

a. Dead Load = 82.12 kN

b. Additional Dead Load = 135.00 kN

c. Live Load = 262.04 kN

Ultimate support reaction = 755.12 kN

5. CONTROL OF BEAM STRESSES


top stress = 0.66 MPa required > -1.73 MPa

bottom stress = 24.05 MPa required < 28.80 MPa


top stress = 13.11 MPa required < 27.00 MPa

bottom stress = 4.65 MPa required > -3.87 MPa

6. CONTROL OF BEAM DEFLECTION

Deflect ion at t he middle of beam span

1. Chamber due stressing

initial = -19.65 mm

= -

2. Service Condition

1. Initial Condition

.

2. Deflection at composite DL = -9.15 mm

3. Deflection due live load = 8.76 mm,required 1) = 1.54

Cracking Capacit y requir ement :

Mcrack = 4360.35 kN.m

Mn / Mcr = 1.41

CALCULATION RESUME


43/114


21.15 M

I. DATA

0.3 L= 21.15 M 0.3


Beam spacing (s)=




Cross Section

H = 1250 mm tfl-1 = 75 mm

A = 350 mm tfl-2 = 75 mm

B = 650 mm tfl-3 = 100 mm

tweb = 17

desain pci girder

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