Download - Perhitungan Girder Pre Cast
(16153) PC I H-125cm; L-20.6m; CTC-150cm
20.00 M
I. DATA
0.3 L= 20.00 M 0.3
Beam length = 20.60 m ( edge anchor to edge anchor : 20.30 m)Beam spacing (s) = 1500.00 mmConcrete Slab thickness (CIP) = 200.00 mmAsphalt thickness = 50.00 mmDeck slab thickness = 70.00 mm
Cross SectionH = 1250 mm tfl-1 = 75 mmA = 350 mm tfl-2 = 75 mmB = 650 mm tfl-3 = 100 mm
tweb = 170 mm tfl-4 = 125 mm
II. MATERIAL
2.1 ConcreteBeam Slab
at service fc' = 40.0 25.0 [N/mm2]
at initial 80% fc' fc'i = 32.0 [N/mm2]
SPAN (ctc) L =
Compressive strength
TECHNICAL CALCULATION OF SEGMENTAL PC I BEAM FOR BRIDGE
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
4
56
Ya
Yb
PRECAST BEAM
Base Line
Cc3
Cc2
Cc1
Tps=Aps.fpsT = As.fy
Zone 2
Zone 4
COMPOSITE BEAM
dp da
b. eff
Zone 3
Cc4
Zone 1
225kN 225kN50kN
0.00
0.20
0.40
0.60
0.80
0 5 10 15 20 25
75.00% 75.00%
71.11%69.86% 69.58% 68.98%
64.44% 64.44%
68.33%69.58% 68.98%
62.14% 62.14%
66.02%67.56% 67.27% 66.68%
60.50% 60.50%
64.39%65.93% 65.64% 65.05%
55.78% 55.78%
59.67%61.21% 60.92% 60.32%
54.79% 54.79%
58.68%60.21% 59.93% 59.33%
50.00%
65.00%
80.00%
0.00 0.00 10.15 16.09 17.45 20.30
FrictionAnchor setElastic Shortening (ES)Shringkage (SH)Creep (CR)Steel Relaxation (SR)
LOSSES OF PRESTRESS DIAGRAM
Prestress tendon section
UTS
P
l
l/2 l/2
Pec
w
ee
0.002000.00
Zona 1Zona 2
Shear Steel Requirement PositionkN
beam section point
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00
Prestress tendon section
Luas A1 Luas A2
Luasan dengan asumsi X > 0.5 span
Luas A1
Luasan dengan asumsi X < 0.5 spanCable changeangle point
X (effective anchorage set)
Anchorageset area
X (effective anchorage set)
Cable changeangle point
Anchorageset area
55.0%
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00Prestress tendon section
LOSSES OF PRESTRESSDUE TO ANCHORAGE SET
64.44%64.44%64.44%64.44%64.44%
68.33%69.86%69.58%68.98%
60.0%
65.0%
70.0%
75.0%
0.00 5.00 10.00 15.00 20.00 25.00Prestress tendon section
AVERAGE LOSSES OF PRESTRESS
0.0200.0400.0600.0800.0
1000.01200.01400.01600.01800.02000.0
Zona 1
Zona 2
Zona 3
Zona 4
Vn = Vu/f
Shear Steel Requirement PositionkN
beam section point
A
H
B
tfl-1tfl-2
tfl-3tfl-4
tweb
1
Yb'
COMPOSITE BEAM
1
2
3
Yb
PRECAST BEAM
Base Line
a
dh
h'
As
As
Ah
Av
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
1
2
3
4
5
Ya
Yb
PRECAST BEAM
Base Line
1
3
Ya'
Yb''
PRECAST BEAM
Base Line
2
page 1 / 14
at initial 80% fc' fc'i = 32.0 [N/mm2]
Allowable stress
19.2 [N/mm2]
Tensile 1.4 [N/mm2]
18.0 11.3 [N/mm2]
Tensile 3.2 2.5 [N/mm2]
wc = 2500.0 2500.0 [kg/m3]
Ec = wc1.5
*0.043*sqrt(fc') = 33994.5 26875.0 [N/mm2]
Eci = wc1.5
*0.043*sqrt(fci') = 30405.6 [N/mm2]
Concrete flexural tension strength (fr)
f r = 0.7*sqrt(fc') = 4.4 [N/mm2]
2.2
( ASTM A 416 Grade 270 Low Relaxation or JIS G 3536 )dia : 12.7 [mm]
Ast : 98.78 [mm2]
Es : 1.93E+05 [N/mm2]
fu : 1860 [N/mm2]
2.3- Diameter dia : 13 [mm]
- Eff. Section area Ast : 132.7 [cm2]
- Modulus of elasticity Es : 2.10E+05 [N/mm2]
- Yield stress fy : 400 [N/mm2]
Allowable stress at service ………. (SNI T-12-2004)
- Eff. Section area
Compressive
Steel Reinforcement
[Uncoated stress relieve seven wires strand]
- Diameter strand
- Ultimate tensile strength
- Modulus of elasticity
Modulus of elasticity
Allowable stress at initial ………… (SNI T-12-2004 )
0.6 * fc'i =
Concrete unit weight
Prestressing Cable
Compressive
0.25 * Sqrt(fc'i) =
0.45 * fc' =
0.5 * Sqrt(fc') =
B
H
A
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
4
56
Ya
Yb
PRECAST BEAM
Base Line
Cc3
Cc2
Cc1
Tps=Aps.fpsT = As.fy
Zone 2
Zone 4
COMPOSITE BEAM
dp da
b. eff
Zone 3
Cc4
Zone 1
225kN 225kN50kN
0.00
0.20
0.40
0.60
0.80
0 5 10 15 20 25
75.00% 75.00%
71.11%69.86% 69.58% 68.98%
64.44% 64.44%
68.33%69.58% 68.98%
62.14% 62.14%
66.02%67.56% 67.27% 66.68%
60.50% 60.50%
64.39%65.93% 65.64% 65.05%
55.78% 55.78%
59.67%61.21% 60.92% 60.32%
54.79% 54.79%
58.68%60.21% 59.93% 59.33%
50.00%
65.00%
80.00%
0.00 0.00 10.15 16.09 17.45 20.30
FrictionAnchor setElastic Shortening (ES)Shringkage (SH)Creep (CR)Steel Relaxation (SR)
LOSSES OF PRESTRESS DIAGRAM
Prestress tendon section
UTS
P
l
l/2 l/2
Pec
w
ee
0.002000.00
Zona 1Zona 2
Shear Steel Requirement PositionkN
beam section point
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00
Prestress tendon section
Luas A1 Luas A2
Luasan dengan asumsi X > 0.5 span
Luas A1
Luasan dengan asumsi X < 0.5 spanCable changeangle point
X (effective anchorage set)
Anchorageset area
X (effective anchorage set)
Cable changeangle point
Anchorageset area
55.0%
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00Prestress tendon section
LOSSES OF PRESTRESSDUE TO ANCHORAGE SET
64.44%64.44%64.44%64.44%64.44%
68.33%69.86%69.58%68.98%
60.0%
65.0%
70.0%
75.0%
0.00 5.00 10.00 15.00 20.00 25.00Prestress tendon section
AVERAGE LOSSES OF PRESTRESS
0.0200.0400.0600.0800.0
1000.01200.01400.01600.01800.02000.0
Zona 1
Zona 2
Zona 3
Zona 4
Vn = Vu/f
Shear Steel Requirement PositionkN
beam section point
A
H
B
tfl-1tfl-2
tfl-3tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
45
Ya
Yb
PRECAST BEAM
Base Line
a
dh
h'
As
As
Ah
Av
1
2
3
4
5
Ya
Yb
PRECAST BEAM
Base Line
1
3
Ya'
Yb''
PRECAST BEAM
Base Line
2
page 1 / 14
(16153) PC I H-125cm; L-20.6m; CTC-150cm
III. SECTION ANALYSISRemark :
Ep 1 = 33994 [N/mm2] [Girder]
Ep 2 = 26875 [N/mm2] [Slab]
n = Ep 2 / Ep 1n = 0.79
3.1 Precast Beam[in mm ]
Section Width Area Level Yb Area*Yb Io Area*d2 Ix
Height Bottom Upper mm2 mm mm mm3 mm4 mm4 mm4
6 0.0 150.0 150.0 0 1250 1250.0 0 0 0 0
5 75.0 350.0 350.0 26250 1175 1212.5 31828125 12304688 12613184758 12625489445
4 75.0 170.0 350.0 19500 1100 1141.8 22265625 8775541 7556605867 7565381408
3 875.0 170.0 170.0 148750 225 662.5 98546875 9490559896 3049566872 12540126768
2 100.0 650.0 170.0 41000 125 165.2 6775000 30264228 5140086368 5170350595
1 125.0 650.0 650.0 81250 0 62.5 5078125 105794271 16955415084 17061209355
Total 1250.0 316750 519.3 164493750 9647698623 45314858949 54962557571
3.2 Composite Beam[in mm ]
Zone Height Width Area Level Yb Area*Yb Io Area*d2 Ix
Section Bottom Upper mm2 mm mm mm3 mm4 mm4 mm4
Zone
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
4
56
Ya
Yb
PRECAST BEAM
Base Line
Cc3
Cc2
Cc1
Tps=Aps.fpsT = As.fy
Zone 2
Zone 4
COMPOSITE BEAM
dp da
b. eff
Zone 3
Cc4
Zone 1
225kN 225kN50kN
0.00
0.20
0.40
0.60
0.80
0 5 10 15 20 25
75.00% 75.00%
71.11%69.86% 69.58% 68.98%
64.44% 64.44%
68.33%69.58% 68.98%
62.14% 62.14%
66.02%67.56% 67.27% 66.68%
60.50% 60.50%
64.39%65.93% 65.64% 65.05%
55.78% 55.78%
59.67%61.21% 60.92% 60.32%
54.79% 54.79%
58.68%60.21% 59.93% 59.33%
50.00%
65.00%
80.00%
0.00 0.00 10.15 16.09 17.45 20.30
FrictionAnchor setElastic Shortening (ES)Shringkage (SH)Creep (CR)Steel Relaxation (SR)
LOSSES OF PRESTRESS DIAGRAM
Prestress tendon section
UTS
P
l
l/2 l/2
Pec
w
ee
0.002000.00
Zona 1Zona 2
Shear Steel Requirement PositionkN
beam section point
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00
Prestress tendon section
Luas A1 Luas A2
Luasan dengan asumsi X > 0.5 span
Luas A1
Luasan dengan asumsi X < 0.5 spanCable changeangle point
X (effective anchorage set)
Anchorageset area
X (effective anchorage set)
Cable changeangle point
Anchorageset area
55.0%
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00Prestress tendon section
LOSSES OF PRESTRESSDUE TO ANCHORAGE SET
64.44%64.44%64.44%64.44%64.44%
68.33%69.86%69.58%68.98%
60.0%
65.0%
70.0%
75.0%
0.00 5.00 10.00 15.00 20.00 25.00Prestress tendon section
AVERAGE LOSSES OF PRESTRESS
0.0200.0400.0600.0800.0
1000.01200.01400.01600.01800.02000.0
Zona 1
Zona 2
Zona 3
Zona 4
Vn = Vu/f
Shear Steel Requirement PositionkN
beam section point
A
H
B
tfl-1tfl-2
tfl-3tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
45
Ya
Yb
PRECAST BEAM
Base Line
a
dh
h'
As
As
Ah
Av
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
1
2
3
4
5
Ya
Yb
PRECAST BEAM
Base Line
1
3
Ya'
Yb''
PRECAST BEAM
Base Line
2
page 2 / 14
Section Bottom Upper mm2 mm mm mm3 mm4 mm4 mm4
2 200.0 1185.9 1185.9 237171 1320 1420.0 336782571 790569415 61107673140 61898242555
70.0 158.1 158.1 11068 1250 1285.0 14222344 4519421.823 1536532796 1541052218
1 1250.0 650.0 350.0 316750 0 519.3 164493750 54962557571 48943588486 1.03906E+11
Total 1520.0 564989 912.4 515498665 55757646408 1.11588E+11 1.67345E+11
3.3 R e s u m e[in mm ]
Description Area (mm2) Ya (mm) Yb (mm) Ix (mm4) Wa (mm3) Wb (mm3)
Precast Beam 316750 731 519.3 54962557571 75220826 105836180
Composite Beam [composite] 564989 608 912.4 167345440830 275422726 183411337
[precast] 338 495698974
IV. LOADING4.1 Dead Load
a. Precast Beam q1 = Ac precast girder x gconc. Precast
q1 = 0.317 x 2.50 = 0.791875 [t/m'] = 7.77 [kN/m']
b. Slab q2 = Ac slab CIP x gconc. slab
q2 = 0.314 x 2.50 = 0.785 [t/m'] = 7.70 [kN/m']
c. Deck slab q3 = Ac deck slab x gs
q3 = 0.0910 x 2.50 = 0.2275 [t/m'] = 2.23 [kN/m']
d. Asphaltic q4 = Ac asphaltic x gs
q4 = 0.08 x 2.20 = 0.165 [t/m'] = 1.62 [kN/m']
e. Diaphragm p = Vol diaph with 0.15m thickness x gdiaph
p = 0.20 x 2.40 = 0.49167 [ton'] = 4.82 [kN']
note : from kg to N, multiply by 9.8060
Number of diaph = 4 pcsDiaph. placement 1 2 3 4Location 0 6.6666667 13.333333 20Support Va 4.82 3.21 1.61 0.00Mid Moment 0.00 16.07 16.07 0.00Total Diaphragma Flexural Moment at Middle Span 32.14 kN.m
eqivalen load q diaphragm q5= 0.64 [kN/m']
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
4
56
Ya
Yb
PRECAST BEAM
Base Line
Cc3
Cc2
Cc1
Tps=Aps.fpsT = As.fy
Zone 2
Zone 4
COMPOSITE BEAM
dp da
b. eff
Zone 3
Cc4
Zone 1
225kN 225kN50kN
0.00
0.20
0.40
0.60
0.80
0 5 10 15 20 25
75.00% 75.00%
71.11%69.86% 69.58% 68.98%
64.44% 64.44%
68.33%69.58% 68.98%
62.14% 62.14%
66.02%67.56% 67.27% 66.68%
60.50% 60.50%
64.39%65.93% 65.64% 65.05%
55.78% 55.78%
59.67%61.21% 60.92% 60.32%
54.79% 54.79%
58.68%60.21% 59.93% 59.33%
50.00%
65.00%
80.00%
0.00 0.00 10.15 16.09 17.45 20.30
FrictionAnchor setElastic Shortening (ES)Shringkage (SH)Creep (CR)Steel Relaxation (SR)
LOSSES OF PRESTRESS DIAGRAM
Prestress tendon section
UTS
P
l
l/2 l/2
Pec
w
ee
0.002000.00
Zona 1Zona 2
Shear Steel Requirement PositionkN
beam section point
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00
Prestress tendon section
Luas A1 Luas A2
Luasan dengan asumsi X > 0.5 span
Luas A1
Luasan dengan asumsi X < 0.5 spanCable changeangle point
X (effective anchorage set)
Anchorageset area
X (effective anchorage set)
Cable changeangle point
Anchorageset area
55.0%
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00Prestress tendon section
LOSSES OF PRESTRESSDUE TO ANCHORAGE SET
64.44%64.44%64.44%64.44%64.44%
68.33%69.86%69.58%68.98%
60.0%
65.0%
70.0%
75.0%
0.00 5.00 10.00 15.00 20.00 25.00Prestress tendon section
AVERAGE LOSSES OF PRESTRESS
0.0200.0400.0600.0800.0
1000.01200.01400.01600.01800.02000.0
Zona 1
Zona 2
Zona 3
Zona 4
Vn = Vu/f
Shear Steel Requirement PositionkN
beam section point
A
H
B
tfl-1tfl-2
tfl-3tfl-4
tweb
a
dh
h'
As
As
Ah
Av
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
1
2
3
4
5
Ya
Yb
PRECAST BEAM
Base Line
1
3
Ya'
Yb''
PRECAST BEAM
Base Line
2
page 2 / 14
(16153) PC I H-125cm; L-20.6m; CTC-150cm
4.2 Live LoadTaken from "Pembebanan Untuk Jembatan RSNI T-02-2005"4.2.1. "T" Loading (Beban Truk)
Unit P1 P2 P3 M.max di x = 10.000 mkN 225 225 50 DLA = 30%
1.3 1.3 1.3 Impact = 1 + DLA = 1.3kN 292.5 292.5 65m 6.000 10.000 15.000kN 204.75 146.25 16.25kN
kN-m
kN-m
4.2.2. "D" Loading (Beban Lajur)Taken from "Pembebanan Untuk Jembatan RSNI T-02-2005"
Load type :
Distribution Load Chart : Dynamics Load Factored Chart :
Impact
367.25
DF = S/3.4
LoadItem
LL + I
1104.044
M maxVa
M x DF
2502.50
DistanceVa
0.441
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
4
56
Ya
Yb
PRECAST BEAM
Base Line
Cc3
Cc2
Cc1
Tps=Aps.fpsT = As.fy
Zone 2
Zone 4
COMPOSITE BEAM
dp da
b. eff
Zone 3
Cc4
Zone 1
225kN 225kN50kN
0.00
0.20
0.40
0.60
0.80
0 5 10 15 20 25
75.00% 75.00%
71.11%69.86% 69.58% 68.98%
64.44% 64.44%
68.33%69.58% 68.98%
62.14% 62.14%
66.02%67.56% 67.27% 66.68%
60.50% 60.50%
64.39%65.93% 65.64% 65.05%
55.78% 55.78%
59.67%61.21% 60.92% 60.32%
54.79% 54.79%
58.68%60.21% 59.93% 59.33%
50.00%
65.00%
80.00%
0.00 0.00 10.15 16.09 17.45 20.30
FrictionAnchor setElastic Shortening (ES)Shringkage (SH)Creep (CR)Steel Relaxation (SR)
LOSSES OF PRESTRESS DIAGRAM
Prestress tendon section
UTS
P
l
l/2 l/2
Pec
w
ee
0.002000.00
Zona 1Zona 2
Shear Steel Requirement PositionkN
beam section point
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00
Prestress tendon section
Luas A1 Luas A2
Luasan dengan asumsi X > 0.5 span
Luas A1
Luasan dengan asumsi X < 0.5 spanCable changeangle point
X (effective anchorage set)
Anchorageset area
X (effective anchorage set)
Cable changeangle point
Anchorageset area
55.0%
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00Prestress tendon section
LOSSES OF PRESTRESSDUE TO ANCHORAGE SET
64.44%64.44%64.44%64.44%64.44%
68.33%69.86%69.58%68.98%
60.0%
65.0%
70.0%
75.0%
0.00 5.00 10.00 15.00 20.00 25.00Prestress tendon section
AVERAGE LOSSES OF PRESTRESS
0.0200.0400.0600.0800.0
1000.01200.01400.01600.01800.02000.0
Zona 1
Zona 2
Zona 3
Zona 4
Vn = Vu/f
Shear Steel Requirement PositionkN
beam section point
A
H
B
tfl-1tfl-2
tfl-3tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
45
Ya
Yb
PRECAST BEAM
Base Line
a
dh
h'
As
As
Ah
Av
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
1
2
3
4
5
Ya
Yb
PRECAST BEAM
Base Line
1
3
Ya'
Yb''
PRECAST BEAM
Base Line
2
page 3 / 14
Line Load (D load)a. Dynamic Load Allowance [DLA] DLA = 1 + 0,4 = 1.40 Span <= 50 m
DLA = 1 + (0.0025*span+0.175) 50 < Span < 90 mDLA = 1 + 0,3 = 1.30 Span >= 90 m
b. Knife Edge Load (KEL) = 49.00 [kN/m']c. Distribution Factor (DF) = 1.00d. Distribution Load
q = 9.00 kN/m2
which : q = 9 kN/m2
for Span <= 30 mq = 9 x(0,5+15/span)kN/m
2Span > 30 m
e. Live loadDistribution load, qudl = DF x q x s
= 1.00 x 9.00 x 1.50 = 13.50 [kN/m']KEL, PKEL = DF x DLA x KEL x s
= 1.00 x 1.40 x 49.00 x 1.50 = 102.90 [kN']
M.max at 0.5 span = 10.00 mVa = 186.45 kN
M LL = 1189.5 kN.mRESUME : Moment force cause by D Loading is bigger than Truck Loading
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
4
56
Ya
Yb
PRECAST BEAM
Base Line
Cc3
Cc2
Cc1
Tps=Aps.fpsT = As.fy
Zone 2
Zone 4
COMPOSITE BEAM
dp da
b. eff
Zone 3
Cc4
Zone 1
0.00
0.20
0.40
0.60
0.80
0 5 10 15 20 25
75.00% 75.00%
71.11%69.86% 69.58% 68.98%
64.44% 64.44%
68.33%69.58% 68.98%
62.14% 62.14%
66.02%67.56% 67.27% 66.68%
60.50% 60.50%
64.39%65.93% 65.64% 65.05%
55.78% 55.78%
59.67%61.21% 60.92% 60.32%
54.79% 54.79%
58.68%60.21% 59.93% 59.33%
50.00%
65.00%
80.00%
0.00 0.00 10.15 16.09 17.45 20.30
FrictionAnchor setElastic Shortening (ES)Shringkage (SH)Creep (CR)Steel Relaxation (SR)
LOSSES OF PRESTRESS DIAGRAM
Prestress tendon section
UTS
P
l
l/2 l/2
Pec
w
ee
0.002000.00
Zona 1Zona 2
Shear Steel Requirement PositionkN
beam section point
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00
Prestress tendon section
Luas A1 Luas A2
Luasan dengan asumsi X > 0.5 span
Luas A1
Luasan dengan asumsi X < 0.5 spanCable changeangle point
X (effective anchorage set)
Anchorageset area
X (effective anchorage set)
Cable changeangle point
Anchorageset area
55.0%
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00Prestress tendon section
LOSSES OF PRESTRESSDUE TO ANCHORAGE SET
64.44%64.44%64.44%64.44%64.44%
68.33%69.86%69.58%68.98%
60.0%
65.0%
70.0%
75.0%
0.00 5.00 10.00 15.00 20.00 25.00Prestress tendon section
AVERAGE LOSSES OF PRESTRESS
0.0200.0400.0600.0800.0
1000.01200.01400.01600.01800.02000.0
Zona 1
Zona 2
Zona 3
Zona 4
Vn = Vu/f
Shear Steel Requirement PositionkN
beam section point
A
H
B
tfl-1tfl-2
tfl-3tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
45
Ya
Yb
PRECAST BEAM
Base Line
a
dh
h'
As
As
Ah
Av
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
1
2
3
4
5
Ya
Yb
PRECAST BEAM
Base Line
1
3
Ya'
Yb''
PRECAST BEAM
Base Line
2
page 3 / 14
(16153) PC I H-125cm; L-20.6m; CTC-150cm
V. MOMENT ANALYSIS[in kN-meter ]
Mid Sec 1-1 Sec 2-2 Sec 3-3 Sec 4-4 Sec 5-5 Sec 6-6span 0.00 4.70 8.20 11.80 15.30 10.00 (m)
DL Precast beam 388.26 0.00 279.20 375.68 375.68 279.20 388.26388.26 0.00 279.20 375.68 375.68 279.20 388.26
DL Slab 384.89 0.00 276.77 372.42 372.42 276.77 384.89ADL Asphaltic Layer 80.90 0.00 58.17 78.28 78.28 58.17 80.90SDL Diaphragm+Deck Slab 143.69 0.00 103.32 139.03 139.03 103.32 143.69
609.47 0.00 438.27 589.72 589.72 438.27 609.47LL Distribution load 675.00 0.00 485.39 653.13 653.13 485.39 675.00
KEL 514.50 0.00 369.98 497.83 497.83 369.98 514.501189.50 0.00 855.37 1150.96 1150.96 855.37 1189.502187.23 0.00 1572.83 2116.36 2116.36 1572.83 2187.233441.58 0.00 2474.84 3330.07 3330.07 2474.84 3441.58
Ultimate total = 1,2*(Beam+Diaphragm+Deck Slab)+1,3*Slab+2*Asphaltic+1.8*(LL+I)
VI. SHEAR ANALYSIS[in kN]
Mid Sec 1-1 Sec 2-2 Sec 3-3 Sec 4-4 Sec 5-5 Sec 6-6span 0.00 4.70 8.20 11.80 15.30 10.00 (m)
DL 0.00 77.65 41.16 13.98 -13.98 -41.16 0.000.00 77.65 41.16 13.98 -13.98 -41.16 0.00
DL 0.00 76.98 40.80 13.86 -13.86 -40.80 0.00ADL 0.00 16.18 8.58 2.91 -2.91 -8.58 0.00SDL 0.00 28.74 15.23 5.17 -5.17 -15.23 0.00
0.00 121.89 64.60 21.94 -21.94 -64.60 0.00Distribution load 0.00 135.00 71.55 24.30 -24.30 -71.55 0.00
Subtotal
Subtotal
Subtotal
LL
Subtotal
Description
Subtotal
Diaphragm+Deck slab
Type
Precast beam
Ultimate total
SlabAsphaltic Layer
Total (DL + LL)
Type Description
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
4
56
Ya
Yb
PRECAST BEAM
Base Line
Cc3
Cc2
Cc1
Tps=Aps.fpsT = As.fy
Zone 2
Zone 4
COMPOSITE BEAM
dp da
b. eff
Zone 3
Cc4
Zone 1
225kN 225kN50kN
0.00
0.20
0.40
0 5 10 15 20 25
75.00% 75.00%
71.11%69.86% 69.58% 68.98%
64.44% 64.44%
68.33%69.58% 68.98%
62.14% 62.14%
66.02%67.56% 67.27% 66.68%
60.50% 60.50%
64.39%65.93% 65.64% 65.05%
55.78% 55.78%
59.67%61.21% 60.92% 60.32%
54.79% 54.79%
58.68%60.21% 59.93% 59.33%
50.00%
65.00%
80.00%
0.00 0.00 10.15 16.09 17.45 20.30
FrictionAnchor setElastic Shortening (ES)Shringkage (SH)Creep (CR)Steel Relaxation (SR)
LOSSES OF PRESTRESS DIAGRAM
Prestress tendon section
UTS
P
l
l/2 l/2
Pec
w
ee
0.002000.00
Zona 1Zona 2
Shear Steel Requirement PositionkN
beam section point
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00
Prestress tendon section
Luas A1 Luas A2
Luasan dengan asumsi X > 0.5 span
Luas A1
Luasan dengan asumsi X < 0.5 spanCable changeangle point
X (effective anchorage set)
Anchorageset area
X (effective anchorage set)
Cable changeangle point
Anchorageset area
55.0%
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00Prestress tendon section
LOSSES OF PRESTRESSDUE TO ANCHORAGE SET
64.44%64.44%64.44%64.44%64.44%
68.33%69.86%69.58%68.98%
60.0%
65.0%
70.0%
75.0%
0.00 5.00 10.00 15.00 20.00 25.00Prestress tendon section
AVERAGE LOSSES OF PRESTRESS
0.0200.0400.0600.0800.0
1000.01200.01400.01600.01800.02000.0
Zona 1
Zona 2
Zona 3
Zona 4
Vn = Vu/f
Shear Steel Requirement PositionkN
beam section point
A
H
B
tfl-1tfl-2
tfl-3tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
45
Ya
Yb
PRECAST BEAM
Base Line
a
dh
h'
As
As
Ah
Av
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
1
2
3
4
5
Ya
Yb
PRECAST BEAM
Base Line
1
3
Ya'
Yb''
PRECAST BEAM
Base Line
2
page 4 / 14
Distribution load 0.00 135.00 71.55 24.30 -24.30 -71.55 0.00KEL 51.45 102.90 78.72 60.71 -60.71 -78.72 51.45
51.45 237.90 150.27 85.01 -85.01 -150.27 51.4551.45 437.45 256.03 120.93 -120.93 -256.03 51.4592.61 688.32 408.33 199.84 -199.84 -408.33 92.61
Ultimate total = 1,2*(Beam+Diaphragm+Deck Slab)+1,3*Slab+2*Asphaltic+1.8*(LL+I)
VII. PRESTRESSING CABLE7.1 Cable Profile
[in: mm ]ten- Nos Profile Total JF
don strand Edge Middle left right tension (kN)
0 0 0 0 0% 0% 0% 00 0 0 0 0% 0% 0% 00 0 0 0 0% 0% 0% 00 0 0 0 0% 0% 0% 01 12 600 220 75% 0% 75% 16542 12 300 100 75% 0% 75% 1654
total 24 450.00 160.00 75% 0% 75% 3307
Parabolic curve (Average of Strand's position vertically from the bottom of beam ( Value for Y axis ))
Y = A.x2+ B.x + C
where : A = Constanta : ( (Ymiddle + Yedge)/(L/2)2) A = 0.002815
B = Constanta : ( L x A ) B = -0.057143C = Average of strand's position when the parabolic curve reach the Y axis
Average of Strand's position vertically from the bottom of beam ( Value for Y axis )Y = 0.002815 X
2 + -0.057143 X + 0.450000
Cable tendon angle :
tg αo = 0.005630 X + -0.057143
eccentricity of tendon at middle sectionEccentricity [e] = Yb - Ys = 359.32 mm
Yb = Distance of Neutral Axis from the bottom of non composite beam ( Chapter 3.3 - Resume )Ys = Distance of tendon from the bottom of the beam at the middle span ( Chapter 7.1, Cable Profile-middle)
Ultimate totalTotal (DL + LL)
LL
Subtotal
Tension
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
4
56
Ya
Yb
PRECAST BEAM
Base Line
Cc3
Cc2
Cc1
Tps=Aps.fpsT = As.fy
Zone 2
Zone 4
COMPOSITE BEAM
dp da
b. eff
Zone 3
Cc4
Zone 1
225kN 225kN50kN
0.00
0.20
0.40
0.60
0.80
0 5 10 15 20 25
75.00% 75.00%
71.11%69.86% 69.58% 68.98%
64.44% 64.44%
68.33%69.58% 68.98%
62.14% 62.14%
66.02%67.56% 67.27% 66.68%
60.50% 60.50%
64.39%65.93% 65.64% 65.05%
55.78% 55.78%
59.67%61.21% 60.92% 60.32%
54.79% 54.79%
58.68%60.21% 59.93% 59.33%
50.00%
65.00%
80.00%
0.00 0.00 10.15 16.09 17.45 20.30
FrictionAnchor setElastic Shortening (ES)Shringkage (SH)Creep (CR)Steel Relaxation (SR)
LOSSES OF PRESTRESS DIAGRAM
Prestress tendon section
UTS
P
l
l/2 l/2
Pec
w
ee
0.002000.00
Zona 1Zona 2
Shear Steel Requirement PositionkN
beam section point
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00
Prestress tendon section
Luas A1 Luas A2
Luasan dengan asumsi X > 0.5 span
Luas A1
Luasan dengan asumsi X < 0.5 spanCable changeangle point
X (effective anchorage set)
Anchorageset area
X (effective anchorage set)
Cable changeangle point
Anchorageset area
55.0%
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00Prestress tendon section
LOSSES OF PRESTRESSDUE TO ANCHORAGE SET
64.44%64.44%64.44%64.44%64.44%
68.33%69.86%69.58%68.98%
60.0%
65.0%
70.0%
75.0%
0.00 5.00 10.00 15.00 20.00 25.00Prestress tendon section
AVERAGE LOSSES OF PRESTRESS
0.0200.0400.0600.0800.0
1000.01200.01400.01600.01800.02000.0
Zona 1
Zona 2
Zona 3
Zona 4
Vn = Vu/f
Shear Steel Requirement PositionkN
beam section point
A
H
B
tfl-1tfl-2
tfl-3tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
45
Ya
Yb
PRECAST BEAM
Base Line
a
dh
h'
As
As
Ah
Av
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
1
2
3
4
5
Ya
Yb
PRECAST BEAM
Base Line
1
3
Ya'
Yb''
PRECAST BEAM
Base Line
2
page 4 / 14
(16153) PC I H-125cm; L-20.6m; CTC-150cm
Average of Strand's position vertically from the bottom of beam ( Value for Y axis )
7.2 Losses of Prestress1. Losses of Prestress (Short Term)a. Friction
The equation for calculating the loss of prestress due to friction is :Px = Po.e
-( µ .α + k.x)( AASHTO 1992, Chapt. 9.16.1 )
Where :Px = Prestress force at section distance x from tensile point.Po = Jacking force ( tensile force at anchor, initial)
µ = friction coefficientα = Change of cable angle from tensile point to x sectionk = Wobble coefficientx = Distance from tensile point to x section
When the jacking force is applied at the stressing end, the tendon will elongate. The elongation will be resisted by frictionbetween the strand and its sheating or duct. As the result of this friction, force will be decreased with distance from the jackingend. The friction is comprised of two effects : curvature friction which is a function of the thendons profile, and wooble frictionwhich is the result of minor horizontal or vertical deviation form intended profile.
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
4
56
Ya
Yb
PRECAST BEAM
Base Line
Cc3
Cc2
Cc1
Tps=Aps.fpsT = As.fy
Zone 2
Zone 4
COMPOSITE BEAM
dp da
b. eff
Zone 3
Cc4
Zone 1
225kN 225kN50kN
0.00
0.20
0.40
0.60
0.80
0 5 10 15 20 25
75.00% 75.00%
71.11%69.86% 69.58% 68.98%
64.44% 64.44%
68.33%69.58% 68.98%
62.14% 62.14%
66.02%67.56% 67.27% 66.68%
60.50% 60.50%
64.39%65.93% 65.64% 65.05%
55.78% 55.78%
59.67%61.21% 60.92% 60.32%
54.79% 54.79%
58.68%60.21% 59.93% 59.33%
50.00%
65.00%
80.00%
0.00 0.00 10.15 16.09 17.45 20.30
FrictionAnchor setElastic Shortening (ES)Shringkage (SH)Creep (CR)Steel Relaxation (SR)
LOSSES OF PRESTRESS DIAGRAM
Prestress tendon section
UTS
P
l
l/2 l/2
Pec
w
ee
0.002000.00
Zona 1Zona 2
Shear Steel Requirement PositionkN
beam section point
65.0%
70.0%
75.0%
80.0%
Luas A1 Luas A2
Luasan dengan asumsi X > 0.5 span
Luas A1
Luasan dengan asumsi X < 0.5 span
55.0%
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00Prestress tendon section
LOSSES OF PRESTRESSDUE TO ANCHORAGE SET
64.44%64.44%64.44%64.44%64.44%
68.33%69.86%69.58%68.98%
60.0%
65.0%
70.0%
75.0%
0.00 5.00 10.00 15.00 20.00 25.00Prestress tendon section
AVERAGE LOSSES OF PRESTRESS
0.0200.0400.0600.0800.0
1000.01200.01400.01600.01800.02000.0
Zona 1
Zona 2
Zona 3
Zona 4
Vn = Vu/f
Shear Steel Requirement PositionkN
beam section point
A
H
B
tfl-1tfl-2
tfl-3tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
45
Ya
Yb
PRECAST BEAM
Base Line
a
dh
h'
As
As
Ah
Av
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
1
2
3
4
5
Ya
Yb
PRECAST BEAM
Base Line
1
3
Ya'
Yb''
PRECAST BEAM
Base Line
2
page 5 / 14
x = Distance from tensile point to x section
Friction and Wooble coeficient for grouting tendon in metal sheatingwith Seven Wire Strand : µ = 0.20
k = 0.003
Table of calculation due to Frictionten- Nos Profile % JF a b αdon strand Edge Middle from UTS (rad) 0.00 10.15 20.300 0 0 0 0% 0.00000 0 0.000 0.0% 0.00% 0.0%0 0 0 0 0% 0.00000 0 0.000 0.0% 0.00% 0.0%0 0 0 0 0% 0.00000 0 0.000 0.0% 0.00% 0.0%0 0 0 0 0% 0.00000 0 0.000 0.0% 0.00% 0.0%1 12 600 220 75% 0.00369 -0.0748768 0.149 75.0% 70.61% 68.5%2 12 300 100 75% 0.00194 -0.0394089 0.079 75.0% 71.61% 69.5%
total 24 450.00 160.00 75% 0.00281 -0.0571429 0.114 75.0% 71.1% 69.0%
b. Anchor set
Exact calculation is typical done as an iterative process as follows :1. Calculated loss of prestress per length with assuming a linear variation in prestress at start to end of tendon
β = Loss of prestress per lengthβ = Fpu . (P at JF - P at end of tendon) / distance JF to end of tendon
2. Assuming drawn-in (∆).
3. The length, x, over which anchorage set is effective is determined as followos :x = Sqrt ( Es . ∆ / β )
effective anchorage set point position :
Tendons are typically anchored with two piece, conical wedges. When the tension applied by the jack is released, the strandretracts pulling the wedges in to the anchorage device and locks the strand in place. The lost in elongation is small . It depend onthe wedges, the jack and the jacking procedure. This lost in elongation is resisted by friction just as the initial elongation isresisted by friction.
Prestress force (Px) = % UTS
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
4
56
Ya
Yb
PRECAST BEAM
Base Line
Cc3
Cc2
Cc1
Tps=Aps.fpsT = As.fy
Zone 2
Zone 4
COMPOSITE BEAM
dp da
b. eff
Zone 3
Cc4
Zone 1
225kN 225kN50kN
75.00% 75.00%
71.11%69.86% 69.58% 68.98%
64.44% 64.44%
68.33%69.58% 68.98%
62.14% 62.14%
66.02%67.56% 67.27% 66.68%
60.50% 60.50%
64.39%65.93% 65.64% 65.05%
55.78% 55.78%
59.67%61.21% 60.92% 60.32%
54.79% 54.79%
58.68%60.21% 59.93% 59.33%
50.00%
65.00%
80.00%
0.00 0.00 10.15 16.09 17.45 20.30
FrictionAnchor setElastic Shortening (ES)Shringkage (SH)Creep (CR)Steel Relaxation (SR)
LOSSES OF PRESTRESS DIAGRAM
Prestress tendon section
UTS
P
l
l/2 l/2
Pec
w
ee
0.002000.00
Zona 1Zona 2
Shear Steel Requirement PositionkN
beam section point
60.0%
65.0%
0.00 10.00 20.00 30.00
Prestress tendon section
Luas A1 Luas A2
Luasan dengan asumsi X > 0.5 span
Luas A1
Luasan dengan asumsi X < 0.5 spanCable changeangle point
X (effective anchorage set)
Anchorageset area
X (effective anchorage set)
Cable changeangle point
Anchorageset area
55.0%
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00Prestress tendon section
LOSSES OF PRESTRESSDUE TO ANCHORAGE SET
64.44%64.44%64.44%64.44%64.44%
68.33%69.86%69.58%68.98%
60.0%
65.0%
70.0%
75.0%
0.00 5.00 10.00 15.00 20.00 25.00Prestress tendon section
AVERAGE LOSSES OF PRESTRESS
0.0200.0400.0600.0800.0
1000.01200.01400.01600.01800.02000.0
Zona 1
Zona 2
Zona 3
Zona 4
Vn = Vu/f
Shear Steel Requirement PositionkN
beam section point
A
H
B
tfl-1tfl-2
tfl-3tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
45
Ya
Yb
PRECAST BEAM
Base Line
a
dh
h'
As
As
Ah
Av
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
1
2
3
4
5
Ya
Yb
PRECAST BEAM
Base Line
1
3
Ya'
Yb''
PRECAST BEAM
Base Line
2
page 5 / 14
(16153) PC I H-125cm; L-20.6m; CTC-150cm
4 Check Assuming drawn-in (∆). The displacement of jacking end of tendon should be equal with assumption∆ = Anchorage set area x Ult. Tensile Stress / Modulus Elasticity of PC Strand∆ = Aset . Fpu / Es∆ = equal with assumption (trial)
Table of calculation due anchor setten- Nos β draw in ∆
don strand Mpa/mm mm X (m) Px (% UTS) X (m) Px (% UTS) 0.00 10.15 20.300 0.0 0.00000 0.00 0.00 0.00% 0.00 0.00% 0.0% 0.00% 0.0%0 0.0 0.00000 8.00 0.00 0.00% 0.00 0.00% 0.0% 0.00% 0.0%0 0.0 0.00000 8.00 0.00 0.00% 0.00 0.00% 0.0% 0.00% 0.0%0 0.0 0.00000 8.00 0.00 0.00% 0.00 0.00% 0.0% 0.00% 0.0%1 12.0 0.00596 8.00 16.09 69.37% 0.00 0.00% 63.7% 68.13% 68.5%2 12.0 0.00507 8.00 17.45 70.07% 0.00 0.00% 65.1% 68.52% 69.5%
total 24 0.00552 8.00 16.77 69.72% 0.00 0.00% 64.44% 68.33% 68.98%
From left side From right side after anchorage set = % UTS
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
4
56
Ya
Yb
PRECAST BEAM
Base Line
Cc3
Cc2
Cc1
Tps=Aps.fpsT = As.fy
Zone 2
Zone 4
COMPOSITE BEAM
dp da
b. eff
Zone 3
Cc4
Zone 1
225kN 225kN50kN
0.00
0.20
0.40
0.60
0.80
0 5 10 15 20 25
75.00% 75.00%
71.11%69.86% 69.58% 68.98%
64.44% 64.44%
68.33%69.58% 68.98%
62.14% 62.14%
66.02%67.56% 67.27% 66.68%
60.50% 60.50%
64.39%65.93% 65.64% 65.05%
55.78% 55.78%
59.67%61.21% 60.92% 60.32%
54.79% 54.79%
58.68%60.21% 59.93% 59.33%
50.00%
65.00%
80.00%
0.00 0.00 10.15 16.09 17.45 20.30
FrictionAnchor setElastic Shortening (ES)Shringkage (SH)Creep (CR)Steel Relaxation (SR)
LOSSES OF PRESTRESS DIAGRAM
Prestress tendon section
UTS
P
l
l/2 l/2
Pec
w
ee
0.002000.00
Zona 1Zona 2
Shear Steel Requirement PositionkN
beam section point
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00
Prestress tendon section
Luas A1 Luas A2
Luasan dengan asumsi X > 0.5 span
Luas A1
Luasan dengan asumsi X < 0.5 spanCable changeangle point
X (effective anchorage set)
Anchorageset area
X (effective anchorage set)
Cable changeangle point
Anchorageset area
55.0%
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00
LOSSES OF PRESTRESSDUE TO ANCHORAGE SET
64.44%64.44%64.44%64.44%64.44%
68.33%69.86%69.58%68.98%
60.0%
65.0%
70.0%
75.0%
0.00 5.00 10.00 15.00 20.00 25.00
AVERAGE LOSSES OF PRESTRESS
0.0200.0400.0600.0800.0
1000.01200.01400.01600.01800.02000.0
Zona 1
Zona 2
Zona 3
Zona 4
Vn = Vu/f
Shear Steel Requirement PositionkN
beam section point
A
H
B
tfl-1tfl-2
tfl-3tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
45
Ya
Yb
PRECAST BEAM
Base Line
a
dh
h'
As
As
Ah
Av
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
1
2
3
4
5
Ya
Yb
PRECAST BEAM
Base Line
1
3
Ya'
Yb''
PRECAST BEAM
Base Line
2
page 6 / 14
c. Elastic Shortening ( ES )Elastic shortening refers to the shortening of the concrete as the postensioning force is applied.As the concrete shorterns, the tendon length also shortens, resulting in a loss of prestress.The following simplified equation to estimate the appropriate amount of prestress loss to attribute to elastic shorteningfor member with bonded tendons :ES = Kes . Es . fcir / Eci
where:Kes = 0.50 for post-tensioned members when tendon are tensioned in sequential order to the same tensionES = Elastic modulus of tendon materialEci = Elastic modulus of the concrete at the time of prestress transferfcir =
Assumption Losses due ES 2.30%
Pi = Total prestressing force at releasePi = 68.3% - 2.30% = 66.02% UTS x nos x Aps = 2911.3893 kN
fcir = Pi / A + Pi. ec2/ I + Mg.ec/I
fcir = 13.49 N/mm2
so, ES = 42.82 N/mm2, percent actual ES losses = Es/fpu 2.30% equal with losses assumption
2. Losses of Prestress ( Long Term )d. Shrinkage ( SH )
SH = 8,2*e-6*Ksh*ES*(1-0,06*V/S)*(100-RH) (ACI 318-95, Chapt. 18.6)
SH = 30.33 N/mm2 percent actual SH losses = SH/fpu 1.63%
Where :The factor Ksh account for the shringkage that will have taken place before the prestressing applied.for postensioning members, Ksh is taken from the following table :
Days 1 3 5 7 10 20 30 60Ksh 0.92 0.85 0.8 0.77 0.73 0.64 0.58 0.45
Ksh = 0.64
V/S = 0.08 Volume = 6.53 m3
Surface = 80.43 m2
RH = 70.00
concrete stress at the centre of gravity of prestressing tendons due to prestressing force at transfer and the self weight ofthe member at the section of maximum positive moment
"days" is the number of days between the end of moist curing and the application of prestress.In a structuresthat are not moist cured, Ksh is typiclly based on when the concrete was cast
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
4
56
Ya
Yb
PRECAST BEAM
Base Line
Cc3
Cc2
Cc1
Tps=Aps.fpsT = As.fy
Zone 2
Zone 4
COMPOSITE BEAM
dp da
b. eff
Zone 3
Cc4
Zone 1
225kN 225kN50kN
0.00
0.20
0.40
0.60
0.80
0 5 10 15 20 25
75.00% 75.00%
71.11%69.86% 69.58% 68.98%
64.44% 64.44%
68.33%69.58% 68.98%
62.14% 62.14%
66.02%67.56% 67.27% 66.68%
60.50% 60.50%
64.39%65.93% 65.64% 65.05%
55.78% 55.78%
59.67%61.21% 60.92% 60.32%
54.79% 54.79%
58.68%60.21% 59.93% 59.33%
50.00%
65.00%
80.00%
0.00 0.00 10.15 16.09 17.45 20.30
FrictionAnchor setElastic Shortening (ES)Shringkage (SH)Creep (CR)Steel Relaxation (SR)
LOSSES OF PRESTRESS DIAGRAM
Prestress tendon section
UTS
P
l
l/2 l/2
Pec
w
ee
0.002000.00
Zona 1Zona 2
Shear Steel Requirement PositionkN
beam section point
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00
Prestress tendon section
Luas A1 Luas A2
Luasan dengan asumsi X > 0.5 span
Luas A1
Luasan dengan asumsi X < 0.5 span
0.00 10.00 20.00 30.00Prestress tendon section
0.00 5.00 10.00 15.00 20.00 25.00Prestress tendon section
0.0200.0400.0600.0800.0
1000.01200.01400.01600.01800.02000.0
Zona 1
Zona 2
Zona 3
Zona 4
Vn = Vu/f
Shear Steel Requirement PositionkN
beam section point
A
H
B
tfl-1tfl-2
tfl-3tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
45
Ya
Yb
PRECAST BEAM
Base Line
a
dh
h'
As
As
Ah
Av
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
1
2
3
4
5
Ya
Yb
PRECAST BEAM
Base Line
1
3
Ya'
Yb''
PRECAST BEAM
Base Line
2
page 6 / 14
(16153) PC I H-125cm; L-20.6m; CTC-150cm
e. Creep ( CR )
CR = Kcr*(Es/Ec)*(fcir-fcds) (ACI 318-95, Chapt. 18.6)
CR = 87.87 N/mm2
percent actual CR losses = CR/fpu 4.72%Where :
Kcr = 1.60 (for postensioned member)fcir = stress at center point prestress force, initial condition
fcir = 13.492 N/mm2
Msd = Moment due to all superimposed permanent dead loads applied after prestressingMsd = 609.47 kN.mfcds = Stress in a concrete at the cgs of the tendon due to all superimposed dead load
fcds 1 = Msdl.e/I = 3.46 N/mm2
component of fcd due to load on the plain beam
fcds 2 = Madl.e/Ic = 0.36 N/mm2
component of fcd due to load on the composite beam
fcds = fcds 1 + fcds 2 = 3.82 N/mm2
f. Steel Relaxation ( RE )
The equation for prestress loss due to relaxation of tendons is :RE = [ Kre - J*(SH+CR+ES) ] *C (ACI 318-95, Chapt. 18.6)
RE = 18.48 N/mm2
percent actual RE losses = RE/fpu 0.99%
Over time, the compresive stress induced by postensioning causes a shortening of the concrete member. The increase instrain due to a sustained stress is refered to as creep. Loss of prestress due to a creep is nominally propotional to the netpermanent compresive stressin the concrete. the net permanent compressive stress is the initial compressive stress in theconcrete due to the prestressing minus the tensile stress due to self weight and superimposed deadload moments
Relaxation is defined as a gradual decrease of stress in a material under constant strain. In the case of steel, relaxation isthe result of permanent alteration of the grain structure. The rate of relaxation at any point in time depends on the stresslevel in the tendon at that time. Because of other prestress losses, there is a continual reduction of tendon strss; thiscauses a reduction in the relaxation rate.
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
4
56
Ya
Yb
PRECAST BEAM
Base Line
Cc3
Cc2
Cc1
Tps=Aps.fpsT = As.fy
Zone 2
Zone 4
COMPOSITE BEAM
dp da
b. eff
Zone 3
Cc4
Zone 1
225kN 225kN50kN
0.00
0.20
0.40
0.60
0.80
0 5 10 15 20 25
P
l
l/2 l/2
Pec
w
ee
0.002000.00
Zona 1Zona 2
Shear Steel Requirement PositionkN
beam section point
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00
Prestress tendon section
Luas A1 Luas A2
Luasan dengan asumsi X > 0.5 span
Luas A1
Luasan dengan asumsi X < 0.5 spanCable changeangle point
X (effective anchorage set)
Anchorageset area
X (effective anchorage set)
Cable changeangle point
Anchorageset area
55.0%
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00Prestress tendon section
LOSSES OF PRESTRESSDUE TO ANCHORAGE SET
64.44%64.44%64.44%64.44%64.44%
68.33%69.86%69.58%68.98%
60.0%
65.0%
70.0%
75.0%
0.00 5.00 10.00 15.00 20.00 25.00Prestress tendon section
AVERAGE LOSSES OF PRESTRESS
0.0200.0400.0600.0800.0
1000.01200.01400.01600.01800.02000.0
Zona 1
Zona 2
Zona 3
Zona 4
Vn = Vu/f
Shear Steel Requirement PositionkN
beam section point
A
H
B
tfl-1tfl-2
tfl-3tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
45
Ya
Yb
PRECAST BEAM
Base Line
a
dh
h'
As
As
Ah
Av
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
1
2
3
4
5
Ya
Yb
PRECAST BEAM
Base Line
1
3
Ya'
Yb''
PRECAST BEAM
Base Line
2
page 7 / 14
RE = 18.48 N/mm2
percent actual RE losses = RE/fpu 0.99%Where :
Kre = 5000.00 (for 270 grade, low relaxation strand)J = 0.04 (for 270 grade, low relaxation strand)C = 0.66 for fpi/fpu = 0.683
RESUME DUE TO SHORT & LONG TERM LOSSESLossesSectionx (m)0.00 75.00% 64.44% 62.14% 12.86% 60.50% 55.78% 54.79% 20.21%0.00 75.00% 64.44% 62.14% 12.86% 60.50% 55.78% 54.79% 20.21%0.00 75.00% 64.44% 62.14% 12.86% 60.50% 55.78% 54.79% 20.21%0.00 75.00% 64.44% 62.14% 12.86% 60.50% 55.78% 54.79% 20.21%0.00 75.00% 64.44% 62.14% 12.86% 60.50% 55.78% 54.79% 20.21%10.15 71.11% 68.33% 66.02% 5.09% 64.39% 59.67% 58.68% 12.43%16.09 69.86% 69.86% 67.56% 2.30% 65.93% 61.21% 60.21% 9.65%17.45 69.58% 69.58% 67.27% 2.30% 65.64% 60.92% 59.93% 9.65%20.30 68.98% 68.98% 66.68% 2.30% 65.05% 60.32% 59.33% 9.65%
friction Losses equotion :0 > x > 10.1575.00% -+ 0.38% x
10.2 > x > 20.3071.11% + 0.06% x x - 10.15
Long term Losses equotion :0 > x > 0.0054.79% #DIV/0!0 > x > 10.1554.79% + 0.38% x x - 0
10.15 > x > 16.0958.68% + 0.26% x x - 10.15
16.09 > x > 17.4560.21% -+ 0.21% x x - 16.0892968
17.45 > x > 20.3059.93% -+ 0.21% x x - 17.4494923
SteelRelaxation
(SR)
Anchor set
II. Long Term Losses
Friction Creep (CR)Shringkage
(SH)Elastic
Shortening(ES)
TotalLosses (%)
I. Short Term LossesTotal Losses
(%)
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
4
56
Ya
Yb
PRECAST BEAM
Base Line
Cc3
Cc2
Cc1
Tps=Aps.fpsT = As.fy
Zone 2
Zone 4
COMPOSITE BEAM
dp da
b. eff
Zone 3
Cc4
Zone 1
225kN 225kN50kN
0.00
0.20
0.40
0.60
0.80
0 5 10 15 20 25
75.00% 75.00%
71.11%69.86% 69.58% 68.98%
64.44% 64.44%
68.33%69.58% 68.98%
62.14% 62.14%
66.02%67.56% 67.27% 66.68%
60.50% 60.50%
64.39%65.93% 65.64% 65.05%
55.78% 55.78%
59.67%61.21% 60.92% 60.32%
54.79% 54.79%
58.68%60.21% 59.93% 59.33%
50.00%
65.00%
80.00%
0.00 0.00 10.15 16.09 17.45 20.30
FrictionAnchor setElastic Shortening (ES)Shringkage (SH)Creep (CR)Steel Relaxation (SR)
LOSSES OF PRESTRESS DIAGRAM
Prestress tendon section
UTS
P
l
l/2 l/2
Pec
w
ee
0.002000.00
Zona 1Zona 2
Shear Steel Requirement PositionkN
beam section point
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00
Prestress tendon section
Luas A1 Luas A2
Luasan dengan asumsi X > 0.5 span
Luas A1
Luasan dengan asumsi X < 0.5 spanCable changeangle point
X (effective anchorage set)
Anchorageset area
X (effective anchorage set)
Cable changeangle point
Anchorageset area
55.0%
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00Prestress tendon section
LOSSES OF PRESTRESSDUE TO ANCHORAGE SET
64.44%64.44%64.44%64.44%64.44%
68.33%69.86%69.58%68.98%
60.0%
65.0%
70.0%
75.0%
0.00 5.00 10.00 15.00 20.00 25.00Prestress tendon section
AVERAGE LOSSES OF PRESTRESS
0.0200.0400.0600.0800.0
1000.01200.01400.01600.01800.02000.0
Zona 1
Zona 2
Zona 3
Zona 4
Vn = Vu/f
Shear Steel Requirement PositionkN
beam section point
A
H
B
tfl-1tfl-2
tfl-3tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
45
Ya
Yb
PRECAST BEAM
Base Line
a
dh
h'
As
As
Ah
Av
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
1
2
3
4
5
Ya
Yb
PRECAST BEAM
Base Line
1
3
Ya'
Yb''
PRECAST BEAM
Base Line
2
page 7 / 14
(16153) PC I H-125cm; L-20.6m; CTC-150cm
7.3 Effective Stress Force
Resume Prestressed Force at middleCable
stress
[kN/mm2] [mm2] [kN]
9.0% 66.0% 1228 2370.72 2911.3916.3% 58.7% 1091 2370.72 2587.37
VIII. STRESS AND DEFFLECTION ANALYSISBeam Segment 1 2 3 4 5 6 7 8
Length (m) 4.70 3.50 3.60 3.50 4.70 0.00 0.00 0.00Additional length at the end of the beam = 0.30 m Total Length = 20.60 m
8.1 Stress at initialDescription Middle SEC 1-1 SEC 2-2 SEC 3-3 SEC 4-4 SEC 5-5 SEC 6-6
x - [m] Span 0.00 4.70 8.20 11.80 15.30 10.00
Moment DL [kN.m] 388.26 0.00 279.20 375.68 375.68 279.20 388.26Jacking Force [kN] 3307.15 3307.15 3307.15 3307.15 3307.15 3307.15 3307.15Losses due to friction % 4% 0% 2% 3% 4% 4% 4%Pi [kN] 3180.43 3307.15 3247.59 3203.24 3182.03 3189.45 3180.43e (eccentricity) [m] 0.359 0.078 0.280 0.350 0.350 0.280 0.359Pi.e [kN.m] -1143 -257 -910 -1122 -1114 -894 -1143Moment Net. [kN.m] -755 -257 -631 -746 -739 -615 -755
Pi / A [N/mm2] 10.04 10.44 10.25 10.11 10.05 10.07 10.04
M / Wa [N/mm2] -10.03 -3.42 -8.39 -9.92 -9.82 -8.17 -10.03 Allow.
M / Wb [N/mm2] 7.13 2.43 5.96 7.05 6.98 5.81 7.13 stress
Initial Stresses top ( σT ) 0.01 7.02 1.87 0.19 0.23 1.90 0.01 -1.4
% Losses ofprestress
ConditionP%UTS
effectiveprestress
long term
Asp
short term
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
4
56
Ya
Yb
PRECAST BEAM
Base Line
Cc3
Cc2
Cc1
Tps=Aps.fpsT = As.fy
Zone 2
Zone 4
COMPOSITE BEAM
dp da
b. eff
Zone 3
Cc4
Zone 1
225kN 225kN50kN
0.00
0.20
0.40
0.60
0.80
0 5 10 15 20 25
75.00% 75.00%
71.11%69.86% 69.58% 68.98%
64.44% 64.44%
68.33%69.58% 68.98%
62.14% 62.14%
66.02%67.56% 67.27% 66.68%
60.50% 60.50%
64.39%65.93% 65.64% 65.05%
55.78% 55.78%
59.67%61.21% 60.92% 60.32%
54.79% 54.79%
58.68%60.21% 59.93% 59.33%
50.00%
65.00%
80.00%
0.00 0.00 10.15 16.09 17.45 20.30
FrictionAnchor setElastic Shortening (ES)Shringkage (SH)Creep (CR)Steel Relaxation (SR)
LOSSES OF PRESTRESS DIAGRAM
Prestress tendon section
UTS
P
l
l/2 l/2
Pec
w
ee
0.002000.00
Zona 1Zona 2
Shear Steel Requirement PositionkN
beam section point
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00
Prestress tendon section
Luas A1 Luas A2
Luasan dengan asumsi X > 0.5 span
Luas A1
Luasan dengan asumsi X < 0.5 spanCable changeangle point
X (effective anchorage set)
Anchorageset area
X (effective anchorage set)
Cable changeangle point
Anchorageset area
55.0%
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00Prestress tendon section
LOSSES OF PRESTRESSDUE TO ANCHORAGE SET
64.44%64.44%64.44%64.44%64.44%
68.33%69.86%69.58%68.98%
60.0%
65.0%
70.0%
75.0%
0.00 5.00 10.00 15.00 20.00 25.00Prestress tendon section
AVERAGE LOSSES OF PRESTRESS
0.0200.0400.0600.0800.0
1000.01200.01400.01600.01800.02000.0
Zona 1
Zona 2
Zona 3
Zona 4
Vn = Vu/f
Shear Steel Requirement PositionkN
beam section point
A
H
B
tfl-1tfl-2
tfl-3tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
45
Ya
Yb
PRECAST BEAM
Base Line
a
dh
h'
As
As
Ah
Av
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
1
2
3
4
5
Ya
Yb
PRECAST BEAM
Base Line
1
3
Ya'
Yb''
PRECAST BEAM
Base Line
2
page 8 / 14
Initial Stresses top ( σT ) 0.01 7.02 1.87 0.19 0.23 1.90 0.01 -1.4
bot ( σB ) 17.17 12.87 16.21 17.16 17.03 15.88 17.17 19.2
8.2 Stress at service> Load of precast, slab, diaphragm and prestress by PC Beam ( = M1 )> Live load and asphalt by composite ( = M2 )Description Middle SEC 1-1 SEC 2-2 SEC 3-3 SEC 4-4 SEC 5-5 SEC 6-6
x - [m] Span 0.00 4.70 8.20 11.80 15.30 10.00Moment DL [kN.m] 916.83 0.00 659.29 887.12 887.12 659.29 916.83Total Losses % 16% 20% 18% 17% 16% 15% 16%effective prestress P [kN] 2584.83 2415.87 2495.28 2554.42 2606.18 2646.09 2584.83P . e [m] -928.77 -188.02 -699.29 -894.55 -912.68 -741.56 -928.77Moment --- M1 [kN.m] -11.95 -188.02 -40.00 -7.43 -25.55 -82.27 -11.95Moment --- M2 [kN.m] 1270.40 0.00 913.54 1229.24 1229.24 913.54 1270.40
P / A [N/mm2] 8.17 8.17 8.17 8.17 8.17 8.17 8.17
M 1 / Wa [N/mm2] -0.16 -2.50 -0.53 -0.10 -0.34 -1.09 -0.16
M 1 / Wb [N/mm2] 0.11 1.78 0.38 0.07 0.24 0.78 0.11
M 2 / Wa' [N/mm2] 2.56 0.00 1.84 2.48 2.48 1.84 2.56 Allow.
M 2 / Wb' [N/mm2] -6.93 0.00 -4.98 -6.70 -6.70 -4.98 -6.93 stress
Stress at Service slab ( σS ) 4.61 0.00 3.32 4.46 4.46 3.32 4.61 11.3
top ( σT ) 10.57 5.67 9.48 10.55 10.31 8.92 10.57 18.0
bot ( σB ) 1.35 9.94 3.57 1.54 1.71 3.96 1.35 -3.2
Note : Moment due to dead load ( Chapter V - Moment Analysis )Moment due to uniform load in balance condition ( Chapter 7.4 - Effective Stress Force )( Moment DL + Moment Bal )
Pi = Initial Prestress ( at transfer condition - chapt. 7.4. Effective Stress Force )P = Prestress at service condition….. ( Chapter 7.4 -effective Stress Force )M = Moment Net.A = Total Area of Precast Beam ( Chapter 3.1 - Precast Beam)
Wa = Modulus Section for Top section of Precast conditionWb = Modulus Section for Bottom section of Precast conditionWa' = Modulus Section for Top section of composit Condition……. ( Chapter 3.3 - Resume )Wb' = Modulus section for bottom section of composite condition ……. ( Chapter 3.3 - Resume )
Moment Bal =Moment DL =
Moment Net =
[kg/cm2]
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
4
56
Ya
Yb
PRECAST BEAM
Base Line
Cc3
Cc2
Cc1
Tps=Aps.fpsT = As.fy
Zone 2
Zone 4
COMPOSITE BEAM
dp da
b. eff
Zone 3
Cc4
Zone 1
225kN 225kN50kN
0.00
0.20
0.40
0.60
0.80
0 5 10 15 20 25
75.00% 75.00%
71.11%69.86% 69.58% 68.98%
64.44% 64.44%
68.33%69.58% 68.98%
62.14% 62.14%
66.02%67.56% 67.27% 66.68%
60.50% 60.50%
64.39%65.93% 65.64% 65.05%
59.67%61.21% 60.92% 60.32%
58.68%60.21% 59.93% 59.33%
65.00%
80.00%
FrictionAnchor setElastic Shortening (ES)Shringkage (SH)Creep (CR)Steel Relaxation (SR)
LOSSES OF PRESTRESS DIAGRAMUTS
P
l
l/2 l/2
Pec
w
ee
0.002000.00
Zona 1Zona 2
Shear Steel Requirement PositionkN
beam section point
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00
Prestress tendon section
Luas A1 Luas A2
Luasan dengan asumsi X > 0.5 span
Luas A1
Luasan dengan asumsi X < 0.5 spanCable changeangle point
X (effective anchorage set)
Anchorageset area
X (effective anchorage set)
Cable changeangle point
Anchorageset area
55.0%
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00Prestress tendon section
LOSSES OF PRESTRESSDUE TO ANCHORAGE SET
64.44%64.44%64.44%64.44%64.44%
68.33%69.86%69.58%68.98%
60.0%
65.0%
70.0%
75.0%
0.00 5.00 10.00 15.00 20.00 25.00Prestress tendon section
AVERAGE LOSSES OF PRESTRESS
0.0200.0400.0600.0800.0
1000.01200.01400.01600.01800.02000.0
Zona 1
Zona 2
Zona 3
Zona 4
Vn = Vu/f
Shear Steel Requirement PositionkN
beam section point
A
H
B
tfl-1tfl-2
tfl-3tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
45
Ya
Yb
PRECAST BEAM
Base Line
a
dh
h'
As
As
Ah
Av
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
1
2
3
4
5
Ya
Yb
PRECAST BEAM
Base Line
1
3
Ya'
Yb''
PRECAST BEAM
Base Line
2
page 8 / 14
(16153) PC I H-125cm; L-20.6m; CTC-150cm
Stress diagram at center span :1. STRESS DIAGRAM AT INITIAL
Pi/A = 10.04 MPa M/Wa = -10.03 MPa stop = 0.01 MPa
+ =
Pi/A = 10.04 MPa M/Wb = 7.13 MPa sbottom = 17.17 MPa
2. STRESS DIAGRAM AT SERVICE
sslab = 4.61 MPa
P/A = 8.17 MPa M1/Wa = -0.16 MPa M2/Wa'= 2.56 MPa stop = 10.57 MPa
+ +
P/A = 8.17 MPa M1/Wb = 0.11 MPa M2/Wb'= -6.93 MPa sbottom = 1.35 MPa
8.3 Deflection8.3.1 Chamber due to Prestress Load
Deflection on middle section :
∆pi= -27.09 mm
[ee+(5/6)(ec-ee)] x (P. l2/8 Ec Ix)∆pi=
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
4
56
Ya
Yb
PRECAST BEAM
Base Line
Cc3
Cc2
Cc1
Tps=Aps.fpsT = As.fy
Zone 2
Zone 4
COMPOSITE BEAM
dp da
b. eff
Zone 3
Cc4
Zone 1
225kN 225kN50kN
0.00
0.20
0.40
0.60
0.80
0 5 10 15 20 25
75.00% 75.00%
71.11%69.86% 69.58% 68.98%
64.44% 64.44%
68.33%69.58% 68.98%
62.14% 62.14%
66.02%67.56% 67.27% 66.68%
60.50% 60.50%
64.39%65.93% 65.64% 65.05%
55.78% 55.78%
59.67%61.21% 60.92% 60.32%
54.79% 54.79%
58.68%60.21% 59.93% 59.33%
50.00%
65.00%
80.00%
0.00 0.00 10.15 16.09 17.45 20.30
FrictionAnchor setElastic Shortening (ES)Shringkage (SH)Creep (CR)Steel Relaxation (SR)
LOSSES OF PRESTRESS DIAGRAM
Prestress tendon section
UTS
P
l
Pec
ee
0.002000.00
Zona 1Zona 2
Shear Steel Requirement PositionkN
beam section point
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00
Prestress tendon section
Luas A1 Luas A2
Luasan dengan asumsi X > 0.5 span
Luas A1
Luasan dengan asumsi X < 0.5 spanCable changeangle point
X (effective anchorage set)
Anchorageset area
X (effective anchorage set)
Cable changeangle point
Anchorageset area
55.0%
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00Prestress tendon section
LOSSES OF PRESTRESSDUE TO ANCHORAGE SET
64.44%64.44%64.44%64.44%64.44%
68.33%69.86%69.58%68.98%
60.0%
65.0%
70.0%
75.0%
0.00 5.00 10.00 15.00 20.00 25.00Prestress tendon section
AVERAGE LOSSES OF PRESTRESS
0.0200.0400.0600.0800.0
1000.01200.01400.01600.01800.02000.0
Zona 1
Zona 2
Zona 3
Zona 4
Vn = Vu/f
Shear Steel Requirement PositionkN
beam section point
A
H
B
tfl-1tfl-2
tfl-3tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
45
Ya
Yb
PRECAST BEAM
Base Line
a
dh
h'
As
As
Ah
Av
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
1
2
3
4
5
Ya
Yb
PRECAST BEAM
Base Line
1
3
Ya'
Yb''
PRECAST BEAM
Base Line
2
page 9 / 14
∆pi= -27.09 mmwhere : P = Prestress force
Eci = Modulus Elasticity of ConcreteIxi = Section Inertia
l = length of anchor to anchoree =
ec =
8.3.2 Deflection at initial, erection and service condition (based : PCI handbook 4.6.5 Long-Time Chamber Deflection)Deflection (∆) on simple span structure : where : q = Uniform Load
∆q= (5/384)*q*L4/Ec Ix) P = Point Load
∆p= P.l3/48 Ec Ix l = Beam Span
Deflection calculation table : Estimating long-time cambers and deflections
q (kN/m) P (kN) Release(1)
multipliers Erection(2)
multipliers Service(3)
1. Due to Prestress force -27.09 1.80 x (1) -48.76 2.20 x (1) -59.602. Due to beam weight (DL) 7.77 9.68 1.85 x (1) 17.91 2.40 x (1) 23.23
-17.41 -30.85 -36.363. Due to ADL 2.87 3.20 3.00 x (2) 9.61
-27.65 -26.754. Due to Composite overtoping 7.70 8.58 2.30 x (2) 19.74
-19.06 -7.014. due to asphaltic (SDL) 1.62 0.59
-6.425. due to Live Load = UDL + KEL 13.50 102.90 7.96
1.54Resume of deflection :
1. Deflection at service = -6.42 mm2. Deflection due to Live Load = 7.96 mm < allow. deflection L/800 = 25 mm OK3. Total deflection with LL = 1.54 mm, deflection downward
Distance between c.g of strand andc.g of concrete at end
Distance between c.g of strand andc.g of concrete at centre
Long time cambers and deflectionWORKING LOAD Loading
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
4
56
Ya
Yb
PRECAST BEAM
Base Line
Cc3
Cc2
Cc1
Tps=Aps.fpsT = As.fy
Zone 2
Zone 4
COMPOSITE BEAM
dp da
b. eff
Zone 3
Cc4
Zone 1
225kN 225kN50kN
0.00
0.20
0.40
0.60
0.80
0 5 10 15 20 25
75.00% 75.00%
71.11%69.86% 69.58% 68.98%
64.44% 64.44%
68.33%69.58% 68.98%
62.14% 62.14%
66.02%67.56% 67.27% 66.68%
60.50% 60.50%
64.39%65.93% 65.64% 65.05%
55.78% 55.78%
59.67%61.21% 60.92% 60.32%
54.79% 54.79%
58.68%60.21% 59.93% 59.33%
50.00%
65.00%
80.00%
0.00 0.00 10.15 16.09 17.45 20.30
FrictionAnchor setElastic Shortening (ES)Shringkage (SH)Creep (CR)Steel Relaxation (SR)
LOSSES OF PRESTRESS DIAGRAM
Prestress tendon section
UTS
P
l/2 l/2
Pec
w
ee
0.002000.00
Zona 1Zona 2
Shear Steel Requirement PositionkN
beam section point
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00
Prestress tendon section
Luas A1 Luas A2
Luasan dengan asumsi X > 0.5 span
Luas A1
Luasan dengan asumsi X < 0.5 spanCable changeangle point
X (effective anchorage set)
Anchorageset area
X (effective anchorage set)
Cable changeangle point
Anchorageset area
55.0%
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00Prestress tendon section
LOSSES OF PRESTRESSDUE TO ANCHORAGE SET
64.44%64.44%64.44%64.44%64.44%
68.33%69.86%69.58%68.98%
60.0%
65.0%
70.0%
75.0%
0.00 5.00 10.00 15.00 20.00 25.00Prestress tendon section
AVERAGE LOSSES OF PRESTRESS
0.0200.0400.0600.0800.0
1000.01200.01400.01600.01800.02000.0
Zona 1
Zona 2
Zona 3
Zona 4
Vn = Vu/f
Shear Steel Requirement PositionkN
beam section point
A
H
B
tfl-1tfl-2
tfl-3tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
45
Ya
Yb
PRECAST BEAM
Base Line
a
dh
h'
As
As
Ah
Av
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
1
2
3
4
5
Ya
Yb
PRECAST BEAM
Base Line
1
3
Ya'
Yb''
PRECAST BEAM
Base Line
2
page 9 / 14
(16153) PC I H-125cm; L-20.6m; CTC-150cm
IX. FLEXURAL STRENGTH AND DUCTILITY
9.1 Steel Index Requirement (SNI Beton 03-2847-2002 pasal 20.8)Effectif slab width, is minimum length from :1. Girder web thickness + 16 Slab thickness =3370 mm for slab with fc' = 25.00 MPa2. Beam Ctc =1500 mm …. Control β Value = 0.853. Span length / 4 =5000 mm
Thus, Effectif slab width is : =1500 mm
Partial Rebar:fy = 400 MPaUse 3 Dia.10 mm at tension area
As = 235.62 mm2 b web = 170 mm
d = 1192.0 mmPartial tension rebar ratio : Rebar in compresion area is neglected due calculationρt = As / (bweb x d ) ρt = 0.00116 ρc = 0ωt = ρt . fy / fc ωt = 0.019 ωc = 0
Low Relaxation strand :fpu = 1860 MPaStrand stress ratio fpu / fpy = 0.9 value γp = 0.28
dp = 1360.0 mm Aps = 2370.72 mm2
beff = 1500 mm
Prestress ratio :ρp = Aps / (beff x dp ) ρp = 0.00116212
fps = fpu {1 - γp / β (ρp.fpu/fc + d/dp (ωt-ωc))) fps = 1797.0 MPaωp = ρp fps/fc ωp = 0.08353459Resume of Steel Index Requirement (SNI Beton 03-2847-2002 pasal 20.8)
ωp + d/dp (ωt-ωc) < 0.36 β
0.0998404 < 0.306 Under Reinf, Meet With Steel Index Requirement
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
4
56
Ya
Yb
PRECAST BEAM
Base Line
225kN 225kN50kN
0.00
0.20
0.40
0.60
0.80
0 5 10 15 20 25
75.00% 75.00%
71.11%69.86% 69.58% 68.98%
64.44% 64.44%
68.33%69.58% 68.98%
62.14% 62.14%
66.02%67.56% 67.27% 66.68%
60.50% 60.50%
64.39%65.93% 65.64% 65.05%
55.78% 55.78%
59.67%61.21% 60.92% 60.32%
54.79% 54.79%
58.68%60.21% 59.93% 59.33%
50.00%
65.00%
80.00%
0.00 0.00 10.15 16.09 17.45 20.30
FrictionAnchor setElastic Shortening (ES)Shringkage (SH)Creep (CR)Steel Relaxation (SR)
LOSSES OF PRESTRESS DIAGRAM
Prestress tendon section
UTS
P
l
l/2 l/2
Pec
w
ee
0.002000.00
Zona 1Zona 2
Shear Steel Requirement PositionkN
beam section point
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00
Prestress tendon section
Luas A1 Luas A2
Luasan dengan asumsi X > 0.5 span
Luas A1
Luasan dengan asumsi X < 0.5 spanCable changeangle point
X (effective anchorage set)
Anchorageset area
X (effective anchorage set)
Cable changeangle point
Anchorageset area
55.0%
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00Prestress tendon section
LOSSES OF PRESTRESSDUE TO ANCHORAGE SET
64.44%64.44%64.44%64.44%64.44%
68.33%69.86%69.58%68.98%
60.0%
65.0%
70.0%
75.0%
0.00 5.00 10.00 15.00 20.00 25.00Prestress tendon section
AVERAGE LOSSES OF PRESTRESS
0.0200.0400.0600.0800.0
1000.01200.01400.01600.01800.02000.0
Zona 1
Zona 2
Zona 3
Zona 4
Vn = Vu/f
Shear Steel Requirement PositionkN
beam section point
A
H
B
tfl-1tfl-2
tfl-3tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
45
Ya
Yb
PRECAST BEAM
Base Line
a
dh
h'
As
As
Ah
Av
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
1
2
3
4
5
Ya
Yb
PRECAST BEAM
Base Line
1
3
Ya'
Yb''
PRECAST BEAM
Base Line
2
page 10 / 14
0.0998404 < 0.306 Under Reinf, Meet With Steel Index Requirement
9.2 Momen Capacity
Tps = Aps . FpsTps = 4260264 N
strength reduction factorφ = 0.8
Location of Depth of Concrete Compression Block (a) :Zone hi wi Aci=hi.wi Comp (i) Compresion
(mm) (mm) (mm2) Point (mm) Point (mm)4 133.65534 1500 200483.01 25.00 CIP Slab 673 0.0 335 0 25.00 CIP Slab 1342 0 350 0 40.00 Beam 1341 0 170 0 40.00 Beam 134
a = Tps / ( 0.85 x fc'' slab x beff ) a= 133.66 mmMn = Mn = 5615.30 kN.m
φ Mn = 4492.2404 kN.mBridge life time design for 50 year,so Transient act factor = 1
Mult = 1x 3,442kN-m φ Mn / Mult = 1.305 >1, Moment capacity meet with requirement
9.3 Cracking Capacity
Stress at bottom girder section due to service load (σbot at service) = 1.35 MPaConcrete flexural tension strength fr = 4.4 MPa
Crack Moment, Mcr = (σbot at service + fr ) Wb.comp + Momen (DL+ADL+LL+I)
Mcr = 3247.72 kN.mφMn / Mcr = 1.383 > 1.2 ---- Cracking Capacity requirement is achieve
Cci=0.85 fc'i.Aci
N
00
MPa
66.83
(Tps (dp - comp. point) + As.fy (d - comp. point)
0
Conc. Strength fc'i
Depth of Concrete Compression Block is located at zone 4
4260264
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
4
56
Ya
Yb
PRECAST BEAM
Base Line
Cc3
Cc2
Cc1
Tps=Aps.fpsT = As.fy
Zone 2
Zone 4
COMPOSITE BEAM
dp da
b. eff
Zone 3
Cc4
Zone 1
225kN 225kN50kN
0.00
0.20
0.40
0.60
0.80
0 5 10 15 20 25
75.00% 75.00%
71.11%69.86% 69.58% 68.98%
64.44% 64.44%
68.33%69.58% 68.98%
62.14% 62.14%
66.02%67.56% 67.27% 66.68%
60.50% 60.50%
64.39%65.93% 65.64% 65.05%
55.78% 55.78%
59.67%61.21% 60.92% 60.32%
54.79% 54.79%
58.68%60.21% 59.93% 59.33%
50.00%
65.00%
80.00%
0.00 0.00 10.15 16.09 17.45 20.30
FrictionAnchor setElastic Shortening (ES)Shringkage (SH)Creep (CR)Steel Relaxation (SR)
LOSSES OF PRESTRESS DIAGRAM
Prestress tendon section
UTS
P
l
l/2 l/2
Pec
w
ee
0.002000.00
Zona 1Zona 2
Shear Steel Requirement PositionkN
beam section point
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00
Prestress tendon section
Luas A1 Luas A2
Luasan dengan asumsi X > 0.5 span
Luas A1
Luasan dengan asumsi X < 0.5 spanCable changeangle point
X (effective anchorage set)
Anchorageset area
X (effective anchorage set)
Cable changeangle point
Anchorageset area
55.0%
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00Prestress tendon section
LOSSES OF PRESTRESSDUE TO ANCHORAGE SET
64.44%64.44%64.44%64.44%64.44%
68.33%69.86%69.58%68.98%
60.0%
65.0%
70.0%
75.0%
0.00 5.00 10.00 15.00 20.00 25.00Prestress tendon section
AVERAGE LOSSES OF PRESTRESS
0.0200.0400.0600.0800.0
1000.01200.01400.01600.01800.02000.0
Zona 1
Zona 2
Zona 3
Zona 4
Vn = Vu/f
Shear Steel Requirement PositionkN
beam section point
A
H
B
tfl-1tfl-2
tfl-3tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
45
Ya
Yb
PRECAST BEAM
Base Line
a
dh
h'
As
As
Ah
Av
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
1
2
3
4
5
Ya
Yb
PRECAST BEAM
Base Line
1
3
Ya'
Yb''
PRECAST BEAM
Base Line
2
page 10 / 14
(16153) PC I H-125cm; L-20.6m; CTC-150cm
X. SHEAR ANALYSIS10.1 Shear calculation based on SNI 03-2847-2002
40% Ultimate Tensile Strength = 744 MPaEffective Prestress = 1091 MPa Effective Prestress > 40% fpu
Section Properties :Ix = 5.496E+10 mm4 Ixcomp = 1.673E+11 mm4
Yb = 519.31728 mm Ybcomp = 912.4 mm
Ag = 316750 mm2
Load :Effective prestress Pe = 2587.37 kNFactored Load : Unfactored Load :
qult DL + ADL = 26.0096 kN/m q DL + ADL = 18.3365 kN/mqult LL = 24.3000 kN/m q sdl = 1.6180 kN/mPult LL = 185.2200 kN q DL + ADL = 19.9545 kN/m
Concrete Shear resistance contribution (Vc)Nominal shear strength provide by concrete
Vc = {0.05sqrt(fc') + 5 (Vu.dp/Mu)}bw.dbut nominal strength (Vc) should taken between : (1/6).sqrt(fc').bw.d < Vc < 0.4sqrt(fc').bw.dand Vu.dp/Mu ≤ 1
where :Mu = Maximum factored moment at sectionVu = Maximum factored shear force at sectiond = distance from extreme compresion fiber to centroid of prestress tendon.
Alternatif solution to calculated shear on prestress element is use for structure element which have effective prestress above 40%of ultimate tensile stress
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
4
56
Ya
Yb
PRECAST BEAM
Base Line
Cc3
Cc2
Cc1
Tps=Aps.fpsT = As.fy
Zone 2
Zone 4
COMPOSITE BEAM
dp da
b. eff
Zone 3
Cc4
Zone 1
225kN 225kN50kN
0.00
0.20
0.40
0.60
0.80
0 5 10 15 20 25
75.00% 75.00%
71.11%69.86% 69.58% 68.98%
64.44% 64.44%
68.33%69.58% 68.98%
62.14% 62.14%
66.02%67.56% 67.27% 66.68%
60.50% 60.50%
64.39%65.93% 65.64% 65.05%
55.78% 55.78%
59.67%61.21% 60.92% 60.32%
54.79% 54.79%
58.68%60.21% 59.93% 59.33%
50.00%
65.00%
80.00%
0.00 0.00 10.15 16.09 17.45 20.30
FrictionAnchor setElastic Shortening (ES)Shringkage (SH)Creep (CR)Steel Relaxation (SR)
LOSSES OF PRESTRESS DIAGRAM
Prestress tendon section
UTS
P
l
l/2 l/2
Pec
w
ee
0.002000.00
Zona 1Zona 2
Shear Steel Requirement PositionkN
beam section point
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00
Prestress tendon section
Luas A1 Luas A2
Luasan dengan asumsi X > 0.5 span
Luas A1
Luasan dengan asumsi X < 0.5 spanCable changeangle point
X (effective anchorage set)
Anchorageset area
X (effective anchorage set)
Cable changeangle point
Anchorageset area
55.0%
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00Prestress tendon section
LOSSES OF PRESTRESSDUE TO ANCHORAGE SET
64.44%64.44%64.44%64.44%64.44%
68.33%69.86%69.58%68.98%
60.0%
65.0%
70.0%
75.0%
0.00 5.00 10.00 15.00 20.00 25.00Prestress tendon section
AVERAGE LOSSES OF PRESTRESS
0.0200.0400.0600.0800.0
1000.01200.01400.01600.01800.02000.0
Zona 1
Zona 2
Zona 3
Zona 4
Vn = Vu/f
Shear Steel Requirement PositionkN
beam section point
A
H
B
tfl-1tfl-2
tfl-3tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
45
Ya
Yb
PRECAST BEAM
Base Line
a
dh
h'
As
As
Ah
Av
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
1
2
3
4
5
Ya
Yb
PRECAST BEAM
Base Line
1
3
Ya'
Yb''
PRECAST BEAM
Base Line
2
page 11 / 14
d = distance from extreme compresion fiber to centroid of prestress tendon.But d need not to take n less than 0.8 hcomposite
bw = width of shear section
Vn = Vc + Vs where : Vn = Nominal Shear force Vu = Ultimate Shear forceVn = Vu / φ Vc = Concrete shear contribution φ = Shear reduction factor
Vs = Shear steel contribution φ = 0.75
Zonafication for shear steel stirup calculationZone 1 Vn < 0.5 Vc No need to use stirupZone 2 Vn < Vc+[0.35 or (75/1200) sqrt(fc')] bw d Required stirup spacing with minimum spacing :
S ≤ 0.75 H S ≤ (av.fy) / (0.35 bw)
S ≤ 600mm S ≤ (av.fy/fpu) (80/Aps) d sqrt(bw/d)
Zone 3 Vn < Vc+0.33 sqrt(fc') bw d Required stirup spacing with spacing :S ≤ (av.fy.d) / ((Vu/φ)-Vc)
S ≤ 0.75 H
S ≤ 600mmZone 4 Vn < Vc+0.67 sqrt(fc') bw d Required tight stirup spacing with spacing :
S ≤ (av.fy.d) / ((Vu/φ)-Vc)
S ≤ 0.375 H
S ≤ 300mmZone 5 Vn > Vc+0.67 sqrt(fc') bw d Section to small, change beam section
Shear rebar steel
SNI 03-2847-2002 Pasal 11.1 : Shear force on beam is hold a part by concrete and the rest of force is hold by shear steel.Concrete contribution (vc), is define as shear force when diagonal cracking appear.
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
4
56
Ya
Yb
PRECAST BEAM
Base Line
Cc3
Cc2
Cc1
Tps=Aps.fpsT = As.fy
Zone 2
Zone 4
COMPOSITE BEAM
dp da
b. eff
Zone 3
Cc4
Zone 1
225kN 225kN50kN
0.00
0.20
0.40
0.60
0.80
0 5 10 15 20 25
75.00% 75.00%
71.11%69.86% 69.58% 68.98%
64.44% 64.44%
68.33%69.58% 68.98%
62.14% 62.14%
66.02%67.56% 67.27% 66.68%
60.50% 60.50%
64.39%65.93% 65.64% 65.05%
55.78% 55.78%
59.67%61.21% 60.92% 60.32%
54.79% 54.79%
58.68%60.21% 59.93% 59.33%
50.00%
65.00%
80.00%
0.00 0.00 10.15 16.09 17.45 20.30
FrictionAnchor setElastic Shortening (ES)Shringkage (SH)Creep (CR)Steel Relaxation (SR)
LOSSES OF PRESTRESS DIAGRAM
Prestress tendon section
UTS
P
l
l/2 l/2
Pec
w
ee
0.002000.00
Zona 1Zona 2
Shear Steel Requirement PositionkN
beam section point
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00
Prestress tendon section
Luas A1 Luas A2
Luasan dengan asumsi X > 0.5 span
Luas A1
Luasan dengan asumsi X < 0.5 spanCable changeangle point
X (effective anchorage set)
Anchorageset area
X (effective anchorage set)
Cable changeangle point
Anchorageset area
55.0%
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00Prestress tendon section
LOSSES OF PRESTRESSDUE TO ANCHORAGE SET
64.44%64.44%64.44%64.44%64.44%
68.33%69.86%69.58%68.98%
60.0%
65.0%
70.0%
75.0%
0.00 5.00 10.00 15.00 20.00 25.00Prestress tendon section
AVERAGE LOSSES OF PRESTRESS
0.0200.0400.0600.0800.0
1000.01200.01400.01600.01800.02000.0
Zona 1
Zona 2
Zona 3
Zona 4
Vn = Vu/f
Shear Steel Requirement PositionkN
beam section point
A
H
B
tfl-1tfl-2
tfl-3tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
45
Ya
Yb
PRECAST BEAM
Base Line
a
dh
h'
As
As
Ah
Av
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
1
2
3
4
5
Ya
Yb
PRECAST BEAM
Base Line
1
3
Ya'
Yb''
PRECAST BEAM
Base Line
2
page 11 / 14
(16153) PC I H-125cm; L-20.6m; CTC-150cm
fy = 400 MPa shear width :Use 2 leg Dia.13 mm bw = 170 mm
Av = 265.46 mm2 bw-e = 650 mm
Shear steel requirement calculation table :dist. ecomp d=dp>0.8H Vu Mu dp(Vu/Mu) Vc Vn Vs Shear Use Space usem m m kN kN-m kN kN kN Zonasi mm mm
0.1 0.460 1.07 682.36 68.49 1.00 964.43 909.81 -54.62 2 600 3000.39 0.476 1.08 665.23 261.55 1.00 979.14 886.98 -92.17 2 600 3000.78 0.497 1.10 642.15 512.77 1.00 998.31 856.20 -142.11 2 600 3001.7 0.544 1.15 587.05 1070.68 0.63 680.21 782.73 102.52 3 600 3002 0.558 1.17 569.17 1238.97 0.54 593.65 758.90 165.25 3 600 3003 0.602 1.21 509.60 1755.21 0.35 426.37 679.47 253.11 3 508 3004 0.641 1.25 450.03 2202.61 0.26 337.72 600.04 262.33 3 505 3005 0.673 1.28 390.46 2581.18 0.19 279.84 520.62 240.78 3 565 300
5.5 0.688 1.30 360.68 2744.66 0.17 256.99 480.90 223.91 3 600 3006.5 0.712 1.32 301.11 3019.99 0.13 218.45 401.48 183.03 3 600 3007.5 0.730 1.34 241.54 3226.48 0.10 185.83 322.05 136.22 3 600 3008.5 0.743 1.35 181.97 3364.14 0.07 156.52 242.62 86.10 3 600 3009.5 0.751 1.36 122.40 3432.98 0.05 128.92 163.19 34.28 2 600 30010 0.752 1.36 92.61 3441.58 0.04 115.39 123.48 8.09 2 600 300
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
4
56
Ya
Yb
PRECAST BEAM
Base Line
Cc3
Cc2
Cc1
Tps=Aps.fpsT = As.fy
Zone 2
Zone 4
COMPOSITE BEAM
dp da
b. eff
Zone 3
Cc4
Zone 1
225kN 225kN50kN
0.00
0.20
0.40
0.60
0.80
0 5 10 15 20 25
75.00% 75.00%
71.11%69.86% 69.58% 68.98%
64.44% 64.44%
68.33%69.58% 68.98%
62.14% 62.14%
66.02%67.56% 67.27% 66.68%
60.50% 60.50%
64.39%65.93% 65.64% 65.05%
55.78% 55.78%
59.67%61.21% 60.92% 60.32%
54.79% 54.79%
58.68%60.21% 59.93% 59.33%
50.00%
65.00%
80.00%
0.00 0.00 10.15 16.09 17.45 20.30
FrictionAnchor setElastic Shortening (ES)Shringkage (SH)Creep (CR)Steel Relaxation (SR)
LOSSES OF PRESTRESS DIAGRAM
Prestress tendon section
UTS
P
l
l/2 l/2
Pec
w
ee
0.002000.00
Zona 1Zona 2
Shear Steel Requirement PositionkN
beam section point
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00
Prestress tendon section
Luas A1 Luas A2
Luasan dengan asumsi X > 0.5 span
Luas A1
Luasan dengan asumsi X < 0.5 spanCable changeangle point
X (effective anchorage set)
Anchorageset area
X (effective anchorage set)
Cable changeangle point
Anchorageset area
55.0%
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00Prestress tendon section
LOSSES OF PRESTRESSDUE TO ANCHORAGE SET
64.44%64.44%64.44%64.44%64.44%
68.33%69.86%69.58%68.98%
60.0%
65.0%
70.0%
75.0%
0.00 5.00 10.00 15.00 20.00 25.00Prestress tendon section
AVERAGE LOSSES OF PRESTRESS
Shear Steel Requirement PositionkN
A
H
B
tfl-1tfl-2
tfl-3tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
45
Ya
Yb
PRECAST BEAM
Base Line
a
dh
h'
As
As
Ah
Av
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
1
2
3
4
5
Ya
Yb
PRECAST BEAM
Base Line
1
3
Ya'
Yb''
PRECAST BEAM
Base Line
2
page 12 / 14
x (m) from range nos shearspan edge (m) (row)
Shear spacing S - 75 0 0 0Shear spacing S - 100 0 0 0Shear spacing S - 125 0 0 0Shear spacing S - 150 0 0 0Shear spacing S - 200 0 0 0Shear spacing S - 250 0 0 0Shear spacing S - 300 10 10 33
total shear rebar per half span (row) = 33total shear rebar per span (row) = 66
10.2 Horisontal Shear
Shear Rebar configuration
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
4
56
Ya
Yb
PRECAST BEAM
Base Line
Cc3
Cc2
Cc1
Tps=Aps.fpsT = As.fy
Zone 2
Zone 4
COMPOSITE BEAM
dp da
b. eff
Zone 3
Cc4
Zone 1
225kN 225kN50kN
0.00
0.20
0.40
0.60
0.80
0 5 10 15 20 25
75.00% 75.00%
71.11%69.86% 69.58% 68.98%
64.44% 64.44%
68.33%69.58% 68.98%
62.14% 62.14%
66.02%67.56% 67.27% 66.68%
60.50% 60.50%
64.39%65.93% 65.64% 65.05%
55.78% 55.78%
59.67%61.21% 60.92% 60.32%
54.79% 54.79%
58.68%60.21% 59.93% 59.33%
50.00%
65.00%
80.00%
0.00 0.00 10.15 16.09 17.45 20.30
FrictionAnchor setElastic Shortening (ES)Shringkage (SH)Creep (CR)Steel Relaxation (SR)
LOSSES OF PRESTRESS DIAGRAM
Prestress tendon section
UTS
P
l
l/2 l/2
Pec
w
ee
0.002000.00
Zona 1Zona 2
Shear Steel Requirement PositionkN
beam section point
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00
Prestress tendon section
Luas A1 Luas A2
Luasan dengan asumsi X > 0.5 span
Luas A1
Luasan dengan asumsi X < 0.5 spanCable changeangle point
X (effective anchorage set)
Anchorageset area
X (effective anchorage set)
Cable changeangle point
Anchorageset area
55.0%
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00Prestress tendon section
LOSSES OF PRESTRESSDUE TO ANCHORAGE SET
64.44%64.44%64.44%64.44%64.44%
68.33%69.86%69.58%68.98%
60.0%
65.0%
70.0%
75.0%
0.00 5.00 10.00 15.00 20.00 25.00Prestress tendon section
AVERAGE LOSSES OF PRESTRESS
0.0200.0400.0600.0800.0
1000.01200.01400.01600.01800.02000.0
Zona 1
Zona 2
Zona 3
Zona 4
Vn = Vu/f
Shear Steel Requirement PositionkN
beam section point
A
H
B
tfl-1tfl-2
tfl-3tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
45
Ya
Yb
PRECAST BEAM
Base Line
a
dh
h'
As
As
Ah
Av
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
1
2
3
4
5
Ya
Yb
PRECAST BEAM
Base Line
1
3
Ya'
Yb''
PRECAST BEAM
Base Line
2
page 12 / 14
(16153) PC I H-125cm; L-20.6m; CTC-150cm
Width of contact surface area bv = 200 mmEffective Height d = 1216 mm
φ = 0.75fy = 400 MPaUse 2 leg Dia.13 mm
Area horisontal Shear Steel Avh = 265.46 mm2Horisontal Shear steel Spacing s = 300 mmHorisontal Shear steel ratio ρv = 0.442%Shear horisontal Nominal
Vnh = (1.8 Mpa + 0.6 ρv. fy) . bv .d
Vnh = 696.00 KNRequirement for shear horisontal steel :Vult < fVnh < 350 bv.d
Vult = Ultimate shear due to superimposed DL + LLVult = 378.26 kNφVnh = 522.00 kN RESUME:
3.5 bv d = 851.20 kN Shear horisontal : OKMinimal Use :
bys = 200 mm Spacing = 1540.04 mm or 4 tweb = 680 mmAvh = 50 by.s / fy Max. Spacing = 300.00 mmAvh = 172.375 mm2/m min no. Spacing = 67 @ 2D13 for shear horisontal / span
Resume = additional shear horizontal requiredXI. END BLOCK DESIGN
Block Anchor dimensiontype a b dia hole Block Area
(mm) (mm) (mm) A (mm2) A1 (mm
2) A2 (mm
2) sqrt(A2/A1)
7 165 165 51 25182.18 27225 1625000 7.73
Concrete Area
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
4
56
Ya
Yb
PRECAST BEAM
Base Line
Cc3
Cc2
Cc1
Tps=Aps.fpsT = As.fy
Zone 2
Zone 4
COMPOSITE BEAM
dp da
b. eff
Zone 3
Cc4
Zone 1
225kN 225kN50kN
0.00
0.20
0.40
0.60
0.80
0 5 10 15 20 25
75.00% 75.00%
71.11%69.86% 69.58% 68.98%
64.44% 64.44%
68.33%69.58% 68.98%
62.14% 62.14%
66.02%67.56% 67.27% 66.68%
60.50% 60.50%
64.39%65.93% 65.64% 65.05%
55.78% 55.78%
59.67%61.21% 60.92% 60.32%
54.79% 54.79%
58.68%60.21% 59.93% 59.33%
50.00%
65.00%
80.00%
0.00 0.00 10.15 16.09 17.45 20.30
FrictionAnchor setElastic Shortening (ES)Shringkage (SH)Creep (CR)Steel Relaxation (SR)
LOSSES OF PRESTRESS DIAGRAM
Prestress tendon section
UTS
P
l
l/2 l/2
Pec
w
ee
0.002000.00
Zona 1Zona 2
Shear Steel Requirement PositionkN
beam section point
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00
Prestress tendon section
Luas A1 Luas A2
Luasan dengan asumsi X > 0.5 span
Luas A1
Luasan dengan asumsi X < 0.5 spanCable changeangle point
X (effective anchorage set)
Anchorageset area
X (effective anchorage set)
Cable changeangle point
Anchorageset area
55.0%
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00Prestress tendon section
LOSSES OF PRESTRESSDUE TO ANCHORAGE SET
64.44%64.44%64.44%64.44%64.44%
68.33%69.86%69.58%68.98%
60.0%
65.0%
70.0%
75.0%
0.00 5.00 10.00 15.00 20.00 25.00Prestress tendon section
AVERAGE LOSSES OF PRESTRESS
0.0200.0400.0600.0800.0
1000.01200.01400.01600.01800.02000.0
Zona 1
Zona 2
Zona 3
Zona 4
Vn = Vu/f
Shear Steel Requirement PositionkN
beam section point
A
H
B
tfl-1tfl-2
tfl-3tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
45
Ya
Yb
PRECAST BEAM
Base Line
a
dh
h'
As
As
Ah
Av
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
1
2
3
4
5
Ya
Yb
PRECAST BEAM
Base Line
1
3
Ya'
Yb''
PRECAST BEAM
Base Line
2
page 13 / 14
7 165 165 51 25182.18 27225 1625000 7.7312 215 215 63 43107.75 46225 1950000 6.4919 265 265 84 64683.23 70225 2275000 5.69
SNI 03-2847-2002 Pasal 11.3.2 (Anchorage Zone)Maximum strand = 12
Anchor Block type = 12 StrandLoad factor = 1.2
Reduction factor (φ) = 0.91. End BearingUltimate Point LoadPu = min (1.2 x nStrand x Astrand x %JF x fpu , nstrand x Astrand x 96% x fpu)Pu = 1984.3 kN
End Bearing stress : Nominal concrete comp. :σ comp = Pu / A fci = 32.00 Mpaσ comp = 46.03 MPa min(2, sqrt(A2/A1)) = 2.0
Nominal fci = φ x 0.7 x fci x min(2,sqrt (A2/A1))
Nominal fci = 40.32 > σcomp = 46.03 MPa
ten- Nos Anchor sheath Ult. Point Block End Bearingdon strand Height hole Load Area Stress
( ai ) (Pu) (A) (EBS=Pu/A)mm kN mm2 Mpa Mpa
0 0
0 0
0 0
0 0
1 12 215 63 1984.29 43107.75 46.03 40.32 EBS > Nominal compresion (not good)2 12 215 63 1984.29 43107.75 46.03 40.32 EBS > Nominal compresion (not good)
Remark
Nominalcomp. fci
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
4
56
Ya
Yb
PRECAST BEAM
Base Line
Cc3
Cc2
Cc1
Tps=Aps.fpsT = As.fy
Zone 2
Zone 4
COMPOSITE BEAM
dp da
b. eff
Zone 3
Cc4
Zone 1
225kN 225kN50kN
0.00
0.20
0.40
0.60
0.80
0 5 10 15 20 25
75.00% 75.00%
71.11%69.86% 69.58% 68.98%
64.44% 64.44%
68.33%69.58% 68.98%
62.14% 62.14%
66.02%67.56% 67.27% 66.68%
60.50% 60.50%
64.39%65.93% 65.64% 65.05%
55.78% 55.78%
59.67%61.21% 60.92% 60.32%
54.79% 54.79%
58.68%60.21% 59.93% 59.33%
50.00%
65.00%
80.00%
0.00 0.00 10.15 16.09 17.45 20.30
FrictionAnchor setElastic Shortening (ES)Shringkage (SH)Creep (CR)Steel Relaxation (SR)
LOSSES OF PRESTRESS DIAGRAM
Prestress tendon section
UTS
P
l
l/2 l/2
Pec
w
ee
0.002000.00
Zona 1Zona 2
Shear Steel Requirement PositionkN
beam section point
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00
Prestress tendon section
Luas A1 Luas A2
Luasan dengan asumsi X > 0.5 span
Luas A1
Luasan dengan asumsi X < 0.5 spanCable changeangle point
X (effective anchorage set)
Anchorageset area
X (effective anchorage set)
Cable changeangle point
Anchorageset area
55.0%
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00Prestress tendon section
LOSSES OF PRESTRESSDUE TO ANCHORAGE SET
64.44%64.44%64.44%64.44%64.44%
68.33%69.86%69.58%68.98%
60.0%
65.0%
70.0%
75.0%
0.00 5.00 10.00 15.00 20.00 25.00Prestress tendon section
AVERAGE LOSSES OF PRESTRESS
0.0200.0400.0600.0800.0
1000.01200.01400.01600.01800.02000.0
Zona 1
Zona 2
Zona 3
Zona 4
Vn = Vu/f
Shear Steel Requirement PositionkN
beam section point
A
H
B
tfl-1tfl-2
tfl-3tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
45
Ya
Yb
PRECAST BEAM
Base Line
a
dh
h'
As
As
Ah
Av
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
1
2
3
4
5
Ya
Yb
PRECAST BEAM
Base Line
1
3
Ya'
Yb''
PRECAST BEAM
Base Line
2
page 13 / 14
(16153) PC I H-125cm; L-20.6m; CTC-150cm
2. Stirrup and Spaling ReinforcementLoad factor = 1.2
Reduction factor (φ) = 0.85fy = 400 MPa
Bursting SteelDiameter closed stirup = 13 mm
Stirup Area = 132.7 mm2ten- Nos Anchor sheath Jacking Bursting Enddon strand Height hole Force Area Bearing sp
( ai ) (Abs) (EBS) fcc' fl ρp
mm kN mm2 Mpa Mpa Mpa (mm)0 0
0 0
0 0
0 0
1 12 215 63 1653.5772 43107.75 38.36 64.47 7.9 3.96% 62.42 12 215 63 1653.5772 43107.75 38.36 64.47 7.9 3.96% 62.4
total 24
Anchor Zone StirupJF Load = 3307.15 kN Σ a1 = 430.00 mm
Ult. JF = 3968.59 kN H = 1250 mm
T bursting = 0.25 Σ Ult.JF (1-Σa1/H) d bursting = 0.5(h-2e)T bursting = 650.84799 kN d bursting = 694.317285 mm
Diameter closed stirup = 13 mm Anchor Stirup Rebar = T bursting / 0.5 fyNo. Leg of stirrup = 4 leg Anchor Stirup Rebar = 3254.2 mm2
Stirup Area = 530.9 mm2 use no of stirup = 7 pcs
Spalling Rebar
EBS/0.7 φ (fcc'-fci)/4.1 fl / 0.5 fy
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
4
56
Ya
Yb
PRECAST BEAM
Base Line
Cc3
Cc2
Cc1
Tps=Aps.fpsT = As.fy
Zone 2
Zone 4
COMPOSITE BEAM
dp da
b. eff
Zone 3
Cc4
Zone 1
225kN 225kN50kN
0.00
0.20
0.40
0.60
0.80
0 5 10 15 20 25
75.00% 75.00%
71.11%69.86% 69.58% 68.98%
64.44% 64.44%
68.33%69.58% 68.98%
62.14% 62.14%
66.02%67.56% 67.27% 66.68%
60.50% 60.50%
64.39%65.93% 65.64% 65.05%
55.78% 55.78%
59.67%61.21% 60.92% 60.32%
54.79% 54.79%
58.68%60.21% 59.93% 59.33%
50.00%
65.00%
80.00%
0.00 0.00 10.15 16.09 17.45 20.30
FrictionAnchor setElastic Shortening (ES)Shringkage (SH)Creep (CR)Steel Relaxation (SR)
LOSSES OF PRESTRESS DIAGRAM
Prestress tendon section
UTS
P
l
l/2 l/2
Pec
w
ee
0.002000.00
Zona 1Zona 2
Shear Steel Requirement PositionkN
beam section point
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00
Prestress tendon section
Luas A1 Luas A2
Luasan dengan asumsi X > 0.5 span
Luas A1
Luasan dengan asumsi X < 0.5 spanCable changeangle point
X (effective anchorage set)
Anchorageset area
X (effective anchorage set)
Cable changeangle point
Anchorageset area
55.0%
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00Prestress tendon section
LOSSES OF PRESTRESSDUE TO ANCHORAGE SET
64.44%64.44%64.44%64.44%64.44%
68.33%69.86%69.58%68.98%
60.0%
65.0%
70.0%
75.0%
0.00 5.00 10.00 15.00 20.00 25.00Prestress tendon section
AVERAGE LOSSES OF PRESTRESS
0.0200.0400.0600.0800.0
1000.01200.01400.01600.01800.02000.0
Zona 1
Zona 2
Zona 3
Zona 4
Vn = Vu/f
Shear Steel Requirement PositionkN
beam section point
A
H
B
tfl-1tfl-2
tfl-3tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
45
Ya
Yb
PRECAST BEAM
Base Line
a
dh
h'
As
As
Ah
Av
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
1
2
3
4
5
Ya
Yb
PRECAST BEAM
Base Line
1
3
Ya'
Yb''
PRECAST BEAM
Base Line
2
page 14 / 14
Spalling RebarSpalling Force = 2% JFSpalling Force = 66.1 kN
Diameter closed stirup = 13 mmStirup Area = 132.7 mm2
use no of stirup = 3 pcs
XII. SHEAR KEY ANALYSIS (FOR SEGMENTAL BEAM ONLY)
item Unit SEC 2-2 SEC 3-3 SEC 4-4 SEC 5-5 the shear load is transferred through the joint by frictionx (m) 4.7 8.2 11.8 15.3 and by the direct shear capacity of the steel shear pin
at initial stage (Only Beam SW) Shear transfer by joint friction :σtop (Mpa) 1.87 0.19 0.23 1.90 Vj = μ ⋅σ n ⋅ Ajointσbot (Mpa) 16.21 17.16 17.03 15.88 φ Vj = φ . μ ⋅σ n ⋅ Ajoint
σn (Mpa) 9.04 8.68 8.63 8.89 With : φ = 0.5Ajoint (mm) 212500 212500 212500 212500 μ = 0.65 friction coefficientφ Vj (kN) 624.3 599.3 595.7 613.8 σn = compressive stress in the joint in MPaVult (kN) 49.4 16.8 16.8 49.4 Ajoint = Area under compression
φ Vj / Vult 12.6 35.7 35.5 12.4at Service stage (all DL and Live Load) Shear transfer by steel shear pin :σtop (Mpa) 9.48 10.55 10.31 8.92 Vpin = 0.6 Apin . fupin
σbot (Mpa) 3.57 1.54 1.71 3.96 φ Vpin = φ 0.6 Apin . fupin
σn (Mpa) 6.52 6.04 6.01 6.44 With : φ = 0.8Ajoint (mm) 212500 212500 212500 212500 Apin = Steel shear pinφ Vj (kN) 450.5 417.3 414.9 444.9 fu pin = Ultimate Tensile strengthVult (kN) 408.3 199.8 199.8 408.3
φ Vj / Vult 1.1 2.1 2.1 1.1 Shear steel pin capacity :Shear steel Pin Requirement Dia Apin fu φ Vpin
Exceed Shear - - - - 28 615.8 400 118.22Min. Shear pin Min.2 Min.2 Min.2 Min.2Steel shear pin 236.4 236.4 236.4 236.4Add. shear pin - - - -Total. shear pin 2 Dia.28 2 Dia.28 2 Dia.28 2 Dia.28
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
4
56
Ya
Yb
PRECAST BEAM
Base Line
Cc3
Cc2
Cc1
Tps=Aps.fpsT = As.fy
Zone 2
Zone 4
COMPOSITE BEAM
dp da
b. eff
Zone 3
Cc4
Zone 1
225kN 225kN50kN
0.00
0.20
0.40
0.60
0.80
0 5 10 15 20 25
75.00% 75.00%
71.11%69.86% 69.58% 68.98%
64.44% 64.44%
68.33%69.58% 68.98%
62.14% 62.14%
66.02%67.56% 67.27% 66.68%
60.50% 60.50%
64.39%65.93% 65.64% 65.05%
55.78% 55.78%
59.67%61.21% 60.92% 60.32%
54.79% 54.79%
58.68%60.21% 59.93% 59.33%
50.00%
65.00%
80.00%
0.00 0.00 10.15 16.09 17.45 20.30
FrictionAnchor setElastic Shortening (ES)Shringkage (SH)Creep (CR)Steel Relaxation (SR)
LOSSES OF PRESTRESS DIAGRAM
Prestress tendon section
UTS
P
l
l/2 l/2
Pec
w
ee
0.002000.00
Zona 1Zona 2
Shear Steel Requirement PositionkN
beam section point
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00
Prestress tendon section
Luas A1 Luas A2
Luasan dengan asumsi X > 0.5 span
Luas A1
Luasan dengan asumsi X < 0.5 spanCable changeangle point
X (effective anchorage set)
Anchorageset area
X (effective anchorage set)
Cable changeangle point
Anchorageset area
55.0%
60.0%
65.0%
70.0%
75.0%
80.0%
0.00 10.00 20.00 30.00Prestress tendon section
LOSSES OF PRESTRESSDUE TO ANCHORAGE SET
64.44%64.44%64.44%64.44%64.44%
68.33%69.86%69.58%68.98%
60.0%
65.0%
70.0%
75.0%
0.00 5.00 10.00 15.00 20.00 25.00Prestress tendon section
AVERAGE LOSSES OF PRESTRESS
0.0200.0400.0600.0800.0
1000.01200.01400.01600.01800.02000.0
Zona 1
Zona 2
Zona 3
Zona 4
Vn = Vu/f
Shear Steel Requirement PositionkN
beam section point
A
H
B
tfl-1tfl-2
tfl-3tfl-4
tweb
Ya'
1
2
3
Yb'
COMPOSITE BEAM
1
2
3
45
Ya
Yb
PRECAST BEAM
Base Line
a
dh
h'
As
As
Ah
Av
B
H
A
tfl-1tfl-2
tfl-3
tfl-4
tweb
1
2
3
4
5
Ya
Yb
PRECAST BEAM
Base Line
1
3
Ya'
Yb''
PRECAST BEAM
Base Line
2
page 14 / 14