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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
Middle span position
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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PCI Monolith H-125cm ; L-20.15m ; CTC-160cm - RSNI (Rev.04)
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
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PCI Monolith H-125cm ; L-20.15m ; CTC-160cm - RSNI (Rev.04)
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']
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PCI Monolith H-125cm ; L-20.15m ; CTC-160cm - RSNI (Rev.04)
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
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 6-6
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
. . . - . - . - . .
Ultimate total = 1,2*(Beam+Diaphragm+Deck Slab)+1,3*Slab+2*Asphaltic+1,8*(LL+I)
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
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PCI Monolith H-125cm ; L-20.15m ; CTC-160cm - RSNI (Rev.04)
Average of Strand's position vertically from the bottom of beam ( Value for Y axis )
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
X (effective anchorage set)
Cable change
angle point
Anchorage
set area
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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
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PCI Monolith H-125cm ; L-20.15m ; CTC-160cm - RSNI (Rev.04)
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
Prestress tendon section
UTS
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PCI Monolith H-125cm ; L-20.15m ; CTC-160cm - RSNI (Rev.04)
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 )
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] 901.82 0.00 786.20 786.20 0.00 0.00 901.82
Losses due to friction % 17% 21% 18% 16% 16% 16% 17%
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]
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PCI Monolith H-125cm ; L-20.15m ; CTC-160cm - RSNI (Rev.04)
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
+ =
Pi/A = 9.89 MPa M/Wb = 7.43 MPa bottom = 17.32 MPa
effective prestress = 71% UTS M = Mdl - Pi.e = -786.3 kN-m
Pi = 3133.66 kN allow comp at initial = 19.20 MPa
eccentricity (ei) = 369.32 mm allow tension initial = -1.41 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
Pi/A = 9.17 MPa M/Wa = -2.28 MPa top = 6.90 MPa
+ =
Pi/A = 9.17 MPa M/Wb = 1.62 MPa bottom = 10.79 MPa
effective prestress = 66% UTS M = Mdl - Pi.e = -171.20 kN-m
Pi = 2905.42 kN allow comp at initial = 19.20 MPa
eccentricity (ei) = 369.32 mm allow tension initial = -1.41 MPa
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
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PCI Monolith H-125cm ; L-20.15m ; CTC-160cm - RSNI (Rev.04)
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
P/A = 8.13 MPa M1/Wa = -0.66 MPa M2/Wa'= 2.32 MPa top = 9.80 MPa
+ + =
P/A = 8.13 MPa M1/Wb = 0.47 MPa M2/Wb'= -7.01 MPa bottom = 1.59 MPa
effective prestress = 58% UTS M1 = Mdl + Pi.e = -49.41 kN-m
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
control allow stress = meet requirement
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
Distance between c.g of strand and
c.g of concrete at centre
Long time cambers and deflection
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PCI Monolith H-125cm ; L-20.15m ; CTC-160cm - RSNI (Rev.04)
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
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PCI Monolith H-125cm ; L-20.15m ; CTC-160cm - RSNI (Rev.04)
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.
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PCI Monolith H-125cm ; L-20.15m ; CTC-160cm - RSNI (Rev.04)
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 - 100 0 0 0
Shear spacing S - 125 0 0 0
Shear spacing S - 150 0 0 0
Shear spacing S - 200 0 0 0
Shear spacing S - 250 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
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PCI Monolith H-125cm ; L-20.15m ; CTC-160cm - RSNI (Rev.04)
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
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PCI Monolith H-125cm ; L-20.15m ; CTC-160cm - RSNI (Rev.04)
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
Diameter closed stirup = 13 mm
Stirup Area = 132.7 mm2
use no of stirup = 3 pcs
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PT WIJAYA KARYA BETON
TECHNICAL CALCULATION
PCI GIRDER MONOLITH FOR HIGHWAY BRIDGES
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
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PT
WIJAYA
KARYA
BETON
Job no. : 13014 B
Rev. : 04
TECHNICAL
CALCULATION
APPROVAL
PCI GIRDER MONOLITH FOR HIGHWAY BRIDGES
PCI Girder Monolith H‐125cm ; L‐20.80m ; CTC ‐160cm ; fc' 50MPa
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-20.80m ; CTC-160cm - RSNI (Rev.04)
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
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PCI Monolith H-125cm ; L-20.80m ; CTC-160cm - RSNI (Rev.04)
20.20 M
I. DATA
0.3 L= 20.20 M 0.3
Beam length = 20.80 m ( edge anchor to edge anchor : 20.50 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' = 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
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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']
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PCI Monolith H-125cm ; L-20.80m ; CTC-160cm - RSNI (Rev.04)
4.2 Live Load
Taken from "Pembebanan Untuk Jembatan RSNI T-02-2005"
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)
Taken from "Pembebanan Untuk Jembatan RSNI T-02-2005"
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
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PCI Monolith H-125cm ; L-20.80m ; CTC-160cm - RSNI (Rev.04)
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 6.60 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
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 6-6
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
. . . - . - . - . .
Ultimate total = 1,2*(Beam+Diaphragm+Deck Slab)+1,3*Slab+2*Asphaltic+1,8*(LL+I)
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
Average of Strand's position vertically from the bottom of beam ( Value for 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
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PCI Monolith H-125cm ; L-20.80m ; CTC-160cm - RSNI (Rev.04)
Average of Strand's position vertically from the bottom of beam ( Value for Y axis )
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
X (effective anchorage set)
Anchorage
set area
X (effective anchorage set)
Cable change
angle point
Anchorage
set area
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PCI Monolith H-125cm ; L-20.80m ; CTC-160cm - RSNI (Rev.04)
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
Prestress tendon section
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
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PCI Monolith H-125cm ; L-20.80m ; CTC-160cm - RSNI (Rev.04)
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
Prestress tendon section
UTS
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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
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 6.60 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
Losses due to friction % 4% 0% 3% 4% 4% 4% 4%
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 )
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 6.60 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
Losses due to friction % 17% 21% 18% 16% 16% 16% 17%
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]
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PCI Monolith H-125cm ; L-20.80m ; CTC-160cm - RSNI (Rev.04)
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 = 12.18 MPa M/Wa = -0.26 MPa top = 11.92 MPa
+ =
Pi/A = 12.18 MPa M/Wb = 0.18 MPa bottom = 12.36 MPa
effective prestress = 75% UTS M = Mdl - Pi.e = -19.41 kN-m
Pi = 3858.35 kN allow comp at initial = 24.00 MPa
eccentricity (ei) = 5.03 mm allow tension initial = -1.58 MPa
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
+ =
Pi/A = 11.50 MPa M/Wb = 8.23 MPa bottom = 19.73 MPa
effective prestress = 71% UTS M = Mdl - Pi.e = -871.4 kN-m
Pi = 3643.15 kN allow comp at initial = 24.00 MPa
eccentricity (ei) = 347.89 mm allow tension initial = -1.58 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
Pi/A = 10.69 MPa M/Wa = -2.88 MPa top = 7.81 MPa
+ =
Pi/A = 10.69 MPa M/Wb = 2.05 MPa bottom = 12.74 MPa
effective prestress = 66% UTS M = Mdl - Pi.e = -216.71 kN-m
Pi = 3385.99 kN allow comp at initial = 24.00 MPa
eccentricity (ei) = 347.89 mm allow tension initial = -1.58 MPa
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
P/A = 10.69 MPa M1/Wa = -2.88 MPa M2/Wa'= 0.18 MPa top = 7.98 MPa
+ + =
P/A = 10.69 MPa M1/Wb = 2.05 MPa M2/Wb'= -0.48 MPa bottom = 12.26 MPa
effective prestress = 66% UTS M1 = Mdl + Pi.e = -216.71 kN-m
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
control allow stress = meet requirement
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PCI Monolith H-125cm ; L-20.80m ; CTC-160cm - RSNI (Rev.04)
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
P/A = 9.44 MPa M1/Wa = -1.05 MPa M2/Wa'= 2.76 MPa top = 11.15 MPa
+ + =
P/A = 9.44 MPa M1/Wb = 0.74 MPa M2/Wb'= -7.50 MPa bottom = 2.68 MPa
effective prestress = 58% UTS M1 = Mdl + Pi.e = -78.72 kN-m
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
control allow stress = meet requirement
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=
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 -26.87 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
Distance between c.g of strand and
c.g of concrete at centre
Long time cambers and deflection
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PCI Monolith H-125cm ; L-20.80m ; CTC-160cm - RSNI (Rev.04)
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
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PCI Monolith H-125cm ; L-20.80m ; CTC-160cm - RSNI (Rev.04)
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.
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PCI Monolith H-125cm ; L-20.80m ; CTC-160cm - RSNI (Rev.04)
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 - 75 0 0 0
Shear spacing S - 100 0 0 0
Shear spacing S - 125 0 0 0
Shear spacing S - 150 0 0 0
Shear spacing S - 200 0 0 0
Shear spacing S - 250 0 0 0
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
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PCI Monolith H-125cm ; L-20.80m ; CTC-160cm - RSNI (Rev.04)
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
2 12 215 63 1984.29 43107.75 46.03 47.60 EBS < Nominal Compresion
3 12 215 63 1984.29 43107.75 46.03 47.60 EBS < Nominal Compresion
Remark
Nominal
comp. fci
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PCI Monolith H-125cm ; L-20.80m ; CTC-160cm - RSNI (Rev.04)
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
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
Diameter closed stirup = 13 mm
Stirup Area = 132.7 mm2
use no of stirup = 3 pcs
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PT WIJAYA KARYA BETON
TECHNICAL CALCULATION
PCI GIRDER MONOLITH FOR HIGHWAY BRIDGES
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
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PT
WIJAYA
KARYA
BETON
Job no. : 13014 C
Rev. : 04
TECHNICAL
CALCULATION
APPROVAL
PCI GIRDER MONOLITH FOR HIGHWAY BRIDGES
PCI Girder Monolith H‐125cm ; L‐21.75m ; CTC ‐160cm ; fc' 60MPa
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-21.75m ; CTC-160cm - RSNI (Rev.04)
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
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
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PCI Monolith H-125cm ; L-21.75m ; 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 = 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
Middle span position
top stress = 0.66 MPa required > -1.73 MPa
bottom stress = 24.05 MPa required < 28.80 MPa
Middle span position
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
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PCI Monolith H-125cm ; L-21.75m ; CTC-160cm - RSNI (Rev.04)
21.15 M
I. DATA
0.3 L= 21.15 M 0.3
Beam length = 21.75 m ( edge anchor to edge anchor : 21.45 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 = 17