PT WIJAYA PT WIJAYA KARYA BETON
TECHNICAL CALCULATION PCI GIRDER PCI GIRDER MONOLITH MONOLITH FOR FOR HIGHWAY HIGHWAY BRIDGES BRIDGES Project Product Job no Rev. No.
: : : :
TOLL SURABAYA ‐ GRESIK PCI Girder Monolith Girder Monolith H‐125cm ; 125cm ; L‐20.15m ; 20.15m ; CTC ‐160cm ; 160cm ; fc' fc' 40MPa 40MPa 13014 A 04
Design Reff.
:
- SNI T ‐12‐2004
Perencanaan Struktur Beton Struktur Beton Untuk Jembatan Jembatan - RSNI T ‐02‐2005 Standar Pembebanan Standar Pembebanan Untuk Jembatan Jembatan - PCI : Bridge Design Manual
Gedung JW, 1
st
nd
& 2 floor
Jl. Jatiwaring Jl. Jatiwaringin in no. 54, Pondok Gede ‐ Bekasi Ph: +62‐21‐8497 ‐3363 fax : fax : +62‐21‐8497 ‐3391 www.wika‐beton.co.id
PT WIJAYA PT WIJAYA KARYA BETON
TECHNICAL CALCULATION APPROVAL APPROVAL PCI GIRDER PCI GIRDER MONOLITH MONOLITH FOR FOR HIGHWAY HIGHWAY BRIDGES BRIDGES TOLL SURABAYA ‐ GRESIK PCI Girder Monolith Girder Monolith H‐125cm ; 125cm ; L‐20.15m ; 20.15m ; CTC ‐160cm ; 160cm ; fc' fc' 40MPa 40MPa Job no. : 1301 3014 A Rev. : 04
Approved by Approved by ::
Consultan / Consultan / Owner Owner
Approved by Approved by :: 18 Juni 18 Juni 2 2013
Checked by 18 Juni 2013 Juni 2013
Design by : by : 18 Juni 18 Juni 2013 2013
Ir. Achmad Ir. Achmad Arifin Arifin Technical M Technical Manager
Ignatius Harry S., Harry S., S.T. Chief of Technical o f Technical
Suko Technical Staff Technical Staff
PT WIJAYA PT WIJAYA KARYA BETON
TECHNICAL CALCULATION APPROVAL APPROVAL PCI GIRDER PCI GIRDER MONOLITH MONOLITH FOR FOR HIGHWAY HIGHWAY BRIDGES BRIDGES TOLL SURABAYA ‐ GRESIK PCI Girder Monolith Girder Monolith H‐125cm ; 125cm ; L‐20.15m ; 20.15m ; CTC ‐160cm ; 160cm ; fc' fc' 40MPa 40MPa Job no. : 1301 3014 A Rev. : 04
Approved by Approved by ::
Consultan / Consultan / Owner Owner
Approved by Approved by :: 18 Juni 18 Juni 2 2013
Checked by 18 Juni 2013 Juni 2013
Design by : by : 18 Juni 18 Juni 2013 2013
Ir. Achmad Ir. Achmad Arifin Arifin Technical M Technical Manager
Ignatius Harry S., Harry S., S.T. Chief of Technical o f Technical
Suko Technical Staff Technical Staff
PCI Monolith H-125cm ; L-20.15m ; CTC-160cm - RSNI (Rev.04)
RESUME OF PCI GIRDER MONOLITH TECHNICALLY CALCULATION 1. BEAM SPECIFICATION
Span Beam Height ( H )
=
19.55 m (beam length
=
1250 mm
Distance ctc of beam ( s )
=
1600 mm
Slab thickness
=
200 mm
Beam Compressive strength
=
40 MPa
Slab Compressive strength
=
28 MPa
Bridge life time
=
50 years
=
20.15 m)
Segment egment Arr angement
Beam Segment Length (m)
1
2
3
4
5
6
7
6.275
7.000
6.275
0.00
0.00
0.00
0.00
Additional length at the end of beam
=
0.30
m
Total length of the beam
=
20.15
m
Total beam weight
=
16.90
ton
12.7 12.7
mm (PC (PC Str Stran and d 270 270 grad grade, e, low low rel relax axat atio ion) n)
2. STRESSING
Nos of PC Strand
=
strand
24
Strand configuration No.
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
=
16.59%
at middle
0
0
0
0
fc initial
=
80.0%
fc'
0
0
0
0
1
12
600
200
2
12
300
100
total
24
450.00
150.00
3. LOADING 1. Dead Load
a. 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. A Assphalt
=
1.73
kN/m
Asphalt thickness =
50
mm
e. Di D iaphragm
=
6.92
kN
4
pcs
No. Diaphragm
for 1 diaphragm equivalent load =
0.94
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)
=
b. Kn Knife Edge Load (KEL)
=
c. Di D istribution Factor (DF)
=
1.40 for span length <= 50m 49.00 kN/m 1.00
d. Distribu Distribution tion Load q=
9.00 kN/m2
9.00 kN/m2
For Span <= 30m
9.00 x(0,5+15/span)kN/m2
For Span > 30m
e. Live Live Load Load Distribution load : Line Load
:
q' = DF x q x s p' = DF x DLA x KEL x s
CALCULATION RESUME
= =
14.40 kN k N/m 109.76 kN
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 1. Initial Condition
Middle span position top stress =
-0.57 MPa
required
>
-1.41 MPa
bottom stress =
17.34 MPa
required
<
19.20 MPa
top stress =
9.81 MPa
required
<
18.00 MPa
bottom stress =
1.58 MPa
required
>
-3.16 MPa
2. Service Condition
Middle span position
6. CONTROL OF BEAM DEFLECTION
De f l e c t i o n a t t h e m i d d l e of b e a m sp a n
1. Chamber due stressing initial
=
-17.68
mm
=
-
2. Deflection at composite DL
=
-8.25
mm
3. Deflection due live load
=
7.48
mm,required
4. Total deflection at service
=
-0.78
mm
. = 24.44 mm
7. MOMENT AND CRACKING CAPACITY OF BEAM
Moment Capacit y requir ement :
Mult = 1,2*(Beam+Diaphragm+Deck Slab)+1,3*Slab+2*Asphaltic+1,8*(LL+I) Mn
=
3488.59 kN.m
=
4523.79 kN.m
Ratio, Mn / Mu (>1)
=
Cracking Capacit y requir ement :
Mcrack Mn / Mcr
= =
3328.03 kN.m 1.36
CALCULATION RESUME
1.30
PCI Monolith H-125cm ; L-20.15m ; CTC-160cm - RSNI (Rev.04)
TECHNICAL CALCULATION OF PCI MONOLITH BEAM FOR HIGHWAY BRIDGES SPAN L = 19.55 M I. DATA
0.3
L=
19.55 M
0.3
20.15 m
Beam length
=
Beam spacing (s)
=
1600 mm
( edge anchor to e dge an ch or :
Concrete Slab thickness (CIP)
=
200 mm
Asphalt thickness
=
50 mm
Deck slab thickness
=
70 mm
19.85
m)
A
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
tfl-1 tfl-2 tweb
H
tfl-3 tfl-4
II. MATERIAL B
2.1 Concrete Beam
Slab
fc' =
40.0
28.0
fc'i =
32.0
[N/mm ]
0.6 * fc'i =
19.2
[N/mm ]
Tensile 0.25 * Sqrt(fc'i) = Allowable stress at service ………. ( SNI T-1 2-20 04 )
1.4
[N/mm ]
Compressive strength at service at initial
80% fc'
2
[N/mm ] 2
Allowable stress Allowable stress at initial ………… ( SNI T-1 2-20 04 ) Compressive
2
2
0.45 * fc' =
18.0
12.6
[N/mm ]
0.5 * Sqrt(fc') =
3.2
2.6
[N/mm ]
wc =
2500.0
2500.0
[kg/m ]
*0.043*sqrt(fc') =
33994.5
28441.8
[N/mm ]
*0.043*sqrt(fci') =
30405.6
[N/mm ]
f r = 0.7*sqrt(fc') =
4.4
[N/mm ]
Compressive Tensile
2
Modulus of elasticity Concrete unit weight Ec = wc Eci = wc
1.5
1.5
3
2 2
Concrete flexural tension strength (fr) 2
2.2 Prestressing Cable [Uncoated stress relieve seven wires strand] ( ASTM A 416 Grade 270 Low Relaxation or JIS G 3536 ) - Diameter strand
dia
:
12.7
[mm]
- Eff. Section area
Ast
:
98.78
[mm ]
- Modulus of elasticity
Es
: 1.93E+05
[N/mm ]
- Ultimate tensile strength
fu
:
1860
[N/mm ]
- Diameter
dia
:
13
[mm]
- Eff. Section area
Ast
:
132.73
[cm ]
- Modulus of elasticity
Es
: 2.10E+05
[N/mm ]
- Yield stress
fy
:
[N/mm ]
2
2 2
2.3 Steel Reinforcement
400
2
2 2
page 1 / 15
PCI Monolith H-125cm ; L-20.15m ; CTC-160cm - RSNI (Rev.04)
III. SECTION ANALYSIS Remark : Ep 1 = Ep 2 =
2
33994
[N/mm ] [Girder]
28442
[N/mm ] [Slab]
3
2
2
5
Ya'
4 Ya
n = Ep 2 / Ep 1 n=
3
0.84
1
2
Yb
Yb'
1
Base Line
PRECAST BEAM
COMPOSITE BEAM
3.1 Precast Beam [in mm ] Zone
Section
Width
Area
Level
2
Yb
Area*Yb 3
2
Io
Ix
Area*d 4
4
4
Height
Bottom
Upper
mm
mm
mm
mm
mm
mm
mm
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
519.3
1644 93750
96476 98623
45314 85894 9
54 96255 7571
Level
Yb
Area*Yb
Io
Area*d
mm
mm
mm
mm
mm
mm
62 87950 4987
316750
3.2 Composite Beam [in mm ] Zone
2 1
Height
Width
Area 2
3
2
4
Ix
4
4
Section
Bottom
Upper
mm
200.0
1338.7
1338.7
267731
1320
1420.0
3801 78316
89243 7361. 6
6 1987 06762 6
70.0
167.3
167.3
11713
1250
1285.0
15051514
4782906.485
1403663073
1408445980
1250.0
650.0
350.0
316750
0
519.3
1644 93750
549 62557 571
5574 43858 03
1. 107 07E +1 1
.
o a
.
.
+
.
+
3.3 R e s u m e [in mm ] 2
Description
Area (mm )
Precast Beam Composite Beam
[composite]
Ya (mm)
Yb (mm)
4
Ix (mm )
3
Wa (mm )
3
Wb (mm )
316750
731
519.3
54962557571
75220826
105836180
596194
581
938.8
1749 94894 341
301 1064 90
1863 97337
[precast]
311
562372124
IV. LOADING 4.1 Dead Load a. Precast Beam
q1 = Ac precast girder x q1 =
b. Slab
0.080 x
[t/m'] =
7.77
[kN/m']
0.802
[t/m'] =
7.86
[kN/m']
0.235
[t/m'] =
2.31
[kN/m']
0.176
[t/m'] =
1.73
[kN/m']
6.92
[kN']
s
2.40 =
q4 = Ac asphaltic x q4 =
e. Diaphragm
0.098 x
0.792
conc. slab
2.40 =
q3 = Ac deck slab x q3 =
d. Asphaltic
0.334 x
conc. Precast
2.50 =
q2 = Ac slab CIP x q2 =
c. Deck slab
0.317 x
s
2.20 =
p
= Vol diaph with 0.20m thickness x
p
=
0.294 x
2.40 =
0.706 note :
Number of diaph = Diaph. placement Location
4
diaph
[ton'] =
from kg to N, multiply by 9.8060
pcs
1
2
3
4
0.00
6.52
13.03
19.55 0.00
Support Va
6.92
4.62
2.31
Mid Moment
0.00
22.56
22.56
Total Diaphragma Flexural Moment at Middle Span eqivalen load q diaphragm
q5=
0.00 45.11
kN.m
0.94
[kN/m']
page 2 / 15
PCI Monolith H-125cm ; L-20.15m ; 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 Item P1 kN Load 225 Impact 1.3 LL + I 292.5 kN Distance 5.775 m Va 206.10 kN Va kN M max kN-m DF = S/3.4 M x DF kN-m
P2 225 1.3 292.5 9.775 146.25
P3 50 1.3 65 14.775 15.88
M.max di x = 9.775 m DLA = 30% Impact = 1 + DLA = 1.3
368.22 2429.38 0.47 1143.24
50kN
225kN
225kN
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 :
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) DLA = 1 + 0,3
50 < Span < 90 m
=
1.30
b. Knife Edge Load (KEL)
=
49.00
c. Distribution Factor (DF)
=
1.00
Span >= 90 m
[kN/m']
d. Distribution Load q =
9.00 kN/m
q = 9 kN/m q = 9 x(0,5+15/span)kN/m
which :
for
Span <= 30 m Span > 30 m
e. Live load Distribution load, qudl = DF x q x s = 1.00 x 9.00 KEL, PKEL = DF x DLA x KEL x s =
1.00
M.max at 0.5 span = Va = M LL =
x
1.40
x x
1.60 49.00
x
1.60
=
14.40
[kN/m']
=
109.76
[kN']
9.775 m 195.64 kN 1 22 4. 42 k N. m
RESUME : Moment force cause by D Loading is bigger than Truck Loading
page 3 / 15
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
Precast beam
370.98
0.00
323.42
323.42
0.00
0.00
370.98
Subtot al
370.98
0.00
323.42
323.42
0.00
0.00
370.98
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
613.29
Type
Description
DL DL
Subtot al
LL
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
Subtot al
1224.42
0.00
1067.44
1067.44
0.00
0.00
1224.42
Total (DL + LL)
2208.69
0.00
1925.52
1925.52
0.00
0.00
2208.69
Ultimate total
3488.59
0.00
3041.34
3041.34
0.00
0.00
3488.59
Sec 4-4 19.55 -75.90 -75.90 -76.84 -16.87 -31.77 -125.48 -140.76 -109.76 -250.52
Sec 5-5 19.55 -75.90 -75.90 -76.84 -16.87 -31.77 -125.48 -140.76 -109.76 -250.52
Sec 6-6 9.78 0.00 0.00 0.00 0.00 0.00 0.00 0.00 54.88 54.88 54.88
(m)
Ultimate total = 1,2*(Beam+Diaphragm+Deck Slab)+1,3*Slab+2*Asphaltic+1,8*(LL+I) VI. SHEAR ANALYSIS [in kN] Mid
Subtot al
span 0.00 0.00 0.00 0.00 0.00 0.00 0.00 54.88 54.88
Sec 1-1 0.00 75.90 75.90 76.84 16.87 31.77 125.48 140.76 109.76 250.52
Sec 2-2 6.28 27.18 27.18 27.51 6.04 11.38 44.93 50.40 74.53 124.93
Total (DL + LL)
54.88
451.91
197.04
.
.
.
Type
Description
DL
Precast beam
DL
Slab
Subtot al
ADL
Asphaltic Layer
SDL
Diaphragm+Deck slab Subtot al
Distribution load
LL
KEL
ma e o a
Sec 3-3 13.28 -27.18 -27.18 -27.51 -6.04 -11.38 -44.93 -50.40 -74.53 -124.93 -197.04
-451.91
-451.91
-
-
-
.
.
.
(m)
.
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 ] Tension
ten-
Nos
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
total
Profile
12
300
100
75%
0%
75%
1654
24
450.00
150.00
75%
0%
75%
3307
Pa r a b o l i c c u r v e ( Av e r a g e of St r a n d ' s p o si t i o n v e r t i c a l l y f r o m t h e b o t t o m o f b e a m ( V a l ue f o r Y a x i s ) ) 2
Y = A.x + B.x + C 2
where :
A = Constanta : ( (Ymiddle + Yedge)/(L/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 ) X + Y = 0.003046 -0.0604534 X + 0.450000 Cable tendon angle : o
tg =
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)
page 4 / 15
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 ) 0.80 0.60 0.40 0.20 0.00 0
5
10
15
20
25
7.2 Losses of Prestress 1. Losses of Prestress (Short Term) a. Friction 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. The equation for calculating the loss of prestress due to friction is : - + .x Po.e Px = ( AASHTO 1992, Chapt. 9.16.1 ) Where :
80.0%
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
75.0% 70.0%
k = Wobble coefficient x = Distance from tensile point to x section
65.0% 60.0%
Friction and Wooble coeficient for grouting tendon in metal sheating = 0.20 with Seven Wire Strand :
0.00
10.00
20.00
30.00
k = 0.003
Table of calculation due to Friction strand
Edge
Middle
from UTS
0
0
0
0
0%
0.00000
0
0
0
0
0
0%
0.00000
0
0%
0.00000
0
0
% JF
b
Nos
don
0
Profile
a
ten-
Prestress force (Px) = % UTS
0.00
9.925
19.85
0.000
0.0%
0.00%
0.0%
0
0.000
0.0%
0.00%
0.0%
0
0.000
0.0%
0.00%
0.0%
(rad)
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
, . , 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 e longation is resisted by friction just as the initial elongation is resisted by friction. 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 : Cable change angle point
Cable change angle point Anchorage set area
X (effective anchorage set)
Anchorage set area
X (effective anchorage set)
page 5 / 15
PCI Monolith H-125cm ; L-20.15m ; 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 draw in tenNos
From left side
From right side
after anchorage set = % UTS
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%
AVERAGE LOSSES OF PRESTRESS
LOSSES OF PRESTRESS DUE TO ANCHORAGE SET
75.0%
80.0% 75.0%
70.0% 70.0%
69.82% 69.50% 68.98%
68.26%
65.0%
65.0%
60.0% 55.0%
64.33%
60.0% 0.00
10.00
20.00
30.00
0.00
5.00
Prestress tendon section
10.00
15.00
20.00
25.00
Prestress tendon section
c. Elastic Shortening ( ES ) Elastic shortening refers to the shortening of the concrete as the postensioning force is applied. As the concrete shorterns, the ten don 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 = concrete stress at the centre of gravity of prestressing tendons due to prestressing force at transfer and the self weight of the member at the section of maximum positive moment 2.37%
Assumption Losses due ES Pi = Pi =
Total prestressing force at release 68 .3% - 2. 37% = 65.89% UTS x nos x Aps =
2905.4202 kN
2
f cir = Pi / A + Pi. ec / I + Mg.ec/I f cir = so,
13.89 N/mm2 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) SH
=
(ACI 318-95, Chapt. 18.6) 1.63% percent actual SH losses = SH/fpu
30.33 N/mm2
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
"days" is the number of days between the end of moist curing and t he application of prestress.In a structures that are not moist cured, Ksh is typiclly based on when the concrete was cast Ksh =
0.64
V/S =
0.08
RH
=
Volume =
3
6.38 m
Surface =
2
78.67 m
70.00
page 6 / 15
PCI Monolith H-125cm ; L-20.15m ; CTC-160cm - RSNI (Rev.04)
e. Creep ( CR )
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 cree p. Loss of prestress due to a creep is nominally propotional to the net permanent compresive stressin the concrete. the n et permanent compressive stress is the initial compressive stress in the concrete due to the prestressing minus th e tensile stress due to self weight and superimposed deadload moments CR CR
= Kcr*(Es/Ec)*(fcir-fcds)
90.40 N/mm
=
(ACI 318-95, Chapt. 18.6)
2
percent actual CR losses = CR/fpu
4.86%
Where :
Kcr =
1.60 (for posten sion ed member)
fcir = stress at center point prestress force, initial condition fcir =
13.890 N/mm
2
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 = fcds 2 = Madl.e/Ic =
3.57 N/mm
2
0.37 N/mm
2
component of fcd due to load on the plain beam component of fcd due to load on the composite beam
3.94 N/mm
fcds = fcds 1 + fcds 2 =
2
f. Steel Relaxation ( RE ) 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 ten don at that time. Because of other prestress losses, there is a continual reduction of tendon strss; this causes a reduction in the r elaxation rate. The equation for prestress loss due to relaxation of tendons is : RE = [ Kre - J*(SH+CR+ES) ] *C
18.38 N/mm
RE =
(ACI 318-95, Chapt. 18.6)
2
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) .
=
or p
pu =
.
RESUME DUE TO SHORT & LONG TERM LOSSES Losses
I. Short Ter m Losses
Section
Elastic Total Anchor set Shortening Losses (%)
x (m)
Friction
II. Long Term Losses
Shrinkage (SH)
Creep (CR)
Steel Total Losses Relaxation (%)
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 : UTS
Friction
LOSSES OF PRESTRESS DIAGRAM
0 > x > 9.93
Anchorset Elastic Shortening (ES)
80.00%
75.00% -+ 0.40% x
Shrinkage (SH)
9.93 > x > 19.85
Creep (CR) Steel Relaxation (SR)
75.00%
75.00% 71.07% 68.26%
65.00%
64.33%
64.33%
61.96% 60.32%
61.96% 60.32%
55.46% 54.48%
65.89% 64.26%
69.82% 69.50% 68.98% 67.45% 67.13% 66.61% 65.82% 65.50% 64.98%
71.07% + 0.07% x
x - 9.925
Long term Losses equotion : 0 > x > 0.00 54.48% #DIV/0! 0 > x > 9.93
59.40% 58.41%
60.96% 60.64% 59.98% 59.65% 60.12% 59.13%
54.48% + 0.40% x
x-0
9.925 > x > 15.83
55.46% 54.48%
58.41% + 0.26% x
x - 9.925
15.83 > x > 17.36 59.98% -+ 0.21% x
50.00% 0.00
0.00
9.93
15.83
Prestress tendon section
17.36
19.85
x - 15.8329534
17.36 > x > 19.85 59.65% -+ 0.21% x
x - 17.3636282
page 7 / 15
PCI Monolith H-125cm ; L-20.15m ; CTC-160cm - RSNI (Rev.04)
7.3 Effective Stress Force Resume Prestressed Force at middle % Losses of prestress
Condition
Cable
%UTS effective prestress
[N/mm ]
[mm ]
[kN]
Asp
stress 2
P
2
short term
9.1%
65.9%
1226
2370.72
2905.42
long term
16.6%
58.4%
1086
2370.72
2575.64
VIII. STRESS AND DEFFLECTION ANALYSIS Beam Segment Length (m)
1
2
3
4
5
6
6.275
7.000
6.275
0.00
0.00
0.00
Additional length at the end of the beam =
0.30
m
7
0.00 Total Length =
8
0.00 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
x - [m]
Span
0.00
6.28
13.28
19.55
19.55
9.78
[kN.m]
370.98
0.00
323.42
323.42
0.00
0.00
370.98
[kN]
3307.15
3307.15
3307.15
3307.15
3307.15
3307.15
3307.15
%
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
2
9.90
10.44
10.09
9.93
9.99
9.99
9.90
2
-10.47
-3.44
-9.81
-9.58
-3.29
-3.29
-10.47
Allow.
Moment DL Jacking Force Losses due to friction
Pi / A
[N/mm ]
M / Wa
[N/mm ] 2
M / Wb Initial Stresses 2
[N/mm ]
SEC 6-6
[N/mm ]
7.44
2.45
6.97
6.81
2.34
2.34
7.44
stress
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 oa o precas , s a ,
ap ragm an pres ress y
eam
=
> Live load and asphalt by composite Description Moment DL
SEC 1-1
SEC 2-2
SEC 3-3
SEC 4-4
SEC 5-5
x - [m]
Span
0.00
6.28
13.28
19.55
19.55
SEC 6-6 9.78
[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 -950.26
P.e
[m]
-950.26
-188.13
-833.95
-868.13
-204.42
-204.42
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
2
8.13
8.13
8.13
8.13
8.13
8.13
8.13
2
-0.64
-2.50
-0.63
-1.09
-2.72
-2.72
-0.64
2
0.46
1.78
0.45
0.77
1.93
1.93
0.46
2
2.32
0.00
2.03
2.03
0.00
0.00
2.32
Allow.
2
stress
P/A
[N/mm ]
M 1 / Wa
[N/mm ]
M 1 / Wb
[N/mm ]
M 2 / Wa'
[N/mm ]
M 2 / Wb' Stress at Service 2
[N/mm ]
Note :
( = M2 ) Middle
[N/mm ]
-7.01
0.00
-6.11
-6.11
0.00
0.00
-7.01
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
Moment DL = Moment due to dead load ( Chapter V - Moment Analysis ) Moment Bal = Moment due to uniform load in balance condition ( Chapter 7.4 - Effective Stress Force ) Moment Net = ( 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 )
page 8 / 15
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 =
+
Pi/A = 10.44 MPa
7.39 MPa
=
M/Wb = 2.17 MPa
effective prestress =
75% UTS
Pi = eccentricity (ei) =
3307.15 69.32
Mdl = Mbeam =
bottom
= 12.61 MPa
M = Mdl - Pi.e = kN mm
allow comp at
initial =
allow tension initial
0 kN-m
=
-229.24
kN-m
19.20 -1.41
MPa MPa
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 =
+
Pi/A = 9.89 MPa
=
M/Wb = 7.43 MPa
bottom
effective prestress =
71% UTS
Pi = eccentricity (ei) =
3133.66 369.32
kN mm
370.98
kN-m
Mdl = Mbeam =
-0.56 MPa
= 17.32 MPa
M = Mdl - Pi.e = allow comp at
initial =
allow tension initial =
-786.3 kN-m 19.20 -1.41
MPa MPa
control allow stress = m eet requirement
8. 3. 2. STRESS DIAGRAM AT CONST RUCTION
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 =
+
Pi/A = 9.17 MPa
=
M/Wb = 1.62 MPa
bottom
effective prestress =
66% UTS
Pi = eccentricity (ei) =
2905.42 369.32
kN mm
901.82
kN-m
Mdl = Mbeam + Madl =
6.90 MPa
= 10.79 MPa
M = Mdl - Pi.e = allow comp at initial = allow tension initial =
-171.20
kN-m
19.20 -1.41
MPa MPa
control allow stress = meet requirement
b. Stress at composite beam middle section due to asphaltic layer: slab =
P/A = 9.17 MPa
M2/Wa'= 0.15 MPa
M1/Wa = -2.28 MPa
+
P/A = 9.17 MPa
top =
+
effective prestress =
66% UTS
Pi = eccentricity (ei) =
2905.42 369.32
kN mm
Mdl = Mbe am + Ma dl =
9 01 .8 2
k N-m
7.04 MPa
=
M2/Wb'= -0.44 MPa
M1/Wb = 1.62 MPa
0.27 MPa
bottom
= 10.35 MPa
M1 = Mdl + Pi.e =
-171.20
kN-m
M2 = Masphalt =
82.45 19.20
kN-m MPa
-1.41
MPa
allow comp at
initial =
allow tension initial
=
control allow stress = meet requirement
page 9 / 15
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 =
P/A = 8.13 MPa
M2/Wa'= 2.32 MPa
M1/Wa = -0.66 MPa
+
P/A = 8.13 MPa
top =
+
58% UTS
M2/Wb'= -7.01 MPa
bottom
= 1.59 MPa
M1 = Mdl + Pi.e =
Pi =
2575.64
kN
eccentricity (ei) =
369.32
mm
Mdl = Mbe am + Ma dl =
9 01 .8 2
k N-m
9.80 MPa
=
M1/Wb = 0.47 MPa
effective prestress =
4.34 MPa
M2 = Masphalt + LL =
-49.41
kN-m
1306.87
kN-m
service =
18.00
MPa
allow tension at service =
-3.16
MPa
allow comp at
control allow stress = meet requirement
8.4 Deflection 8.4.1 Chamber due to Prestress Load Deflection on middle section : l
P
ee
pi= [ee+(5/6)(e c-ee)] x (P. l2 /8 Ec Ix) pi=
P
ec
where :
-26.52 mm
P = Prestress force Eci = Modulus Elasticity of Concrete
l/2
l/2
Ixi = Section Inertia l = length of anchor to anchor ee = Distance between c.g of strand and c.g of concrete at end ec = Distance between c.g of strand and c.g of concrete at centre
8.4.2 Deflection at initial, ere ction and service condition (based : PCI handbook 4.6.5 Long-Time Chamber Deflection) Deflection () on simple span structure : where : q = Uniform Load 4
q= (5/384)*q*L /Ec Ix)
P = Point Load
3
l = Beam Span
p= P.l /48 Ec Ix
Deflection calculation table : Estimating long-time cambers and deflections WORKING LOAD
Loading q (kN/m)
P (kN)
1. Due to Prestress force 2. Due to beam weight (DL)
Release (1)
Long time cambers and deflection (2) multipliers Erection multipliers
-26.52
1.80 x (1)
-47.74
2.20 x (1)
8.84
1.85 x (1)
16.35
2.40 x (1)
7.77
-17.68 3. Due to ADL
3.25
Service (3)
-31.39 3.31
7.86
8.00
3.00 x (2)
9.93
-27.21 2.30 x (2)
-20.08 5. Due to asphaltic (SDL)
21.21
-37.14
-28.08 4. Due to Composite Overtoping
-58.35
18.40
-8.81
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
=
2.
Deflection due to Live Load
=
3.
Total deflection with LL
=
-8.25 mm 7.48 mm < allow. deflection L/800 =
24.4375 mm OK
-0.78 mm, chamber upward
page 10 / 15
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
2. Beam Ctc 3. Span length / 4
=1600 mm …. Control =4887.5 mm
Thus, Effectif slab width is :
=1600 mm
for slab with fc' = Value =
28.00
MPa
0.85
Partial Rebar: 400 MPa 0 Dia.13 mm
fy = Use As = d=
at tension area b web =
0.00 mm2
170 mm
1190.5 mm
Partial tension rebar ratio : t = As / (bweb x d )
t =
0.00000
t =
t =
0.000
t . fy / fc
Rebar in compresion area is neglected due calculation c = c =
Low Relaxation strand : fpu =
1860
MPa
Strand stress ratio fpu / fpy = dp =
value p = 0.28
0.9 Aps =
1370.0 mm
2
2370.72 mm
Prestress ratio : p = Aps / (beff x dp ) fps = p =
beff =
1600 mm
p = 0.00108153
fpu {1 - p / (p.fpu/fc + d/dp ( t-c)))
1816.0 MPa
fps = p =
p fps/fc
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 one
Zone 3
c
i
Cc3 Cc2
Zone 3 Zone 2 a
Tps = Aps . Fps Tps = 4305180.91 N
Cc1
Zone 1
dp
d
strength reduction factor = 0.8 Tps=Aps.fps T = As.fy
COMPOSITE BEAM
Location of Depth of Concrete Compression Block (a) : hi wi Aci=hi.wi Conc. Strength fc' i Zone
Cci=0.85 fc'i.Aci
MPa
Comp (i)
4
(mm) 113.06
(mm) 1600
(mm2) 180889.95
28.00
CIP Slab
N 4305181
3
0.00
335
0
28.00
CIP Slab
0
113
2
0.00
350
0
40.00
Beam
0
113
1
0.00
170
0
40.00
Beam
0
113
Compresion
Point (mm) Point (mm) 57 56.53
Depth of Concrete Compression Block is located at zone 4 a = Tps / ( 0.85 x fc'' slab x beff )
a=
Mn = (Tps (dp - comp. point) + As.fy (d-comp. point) Mn = 4523.7873 kN.m Bridge life time design for 50 year,so Transient act factor = 1 Mn / Mult = Mult = 1x 3,489kN-m
Mn =
1.297
113.06 mm 5654.73 kN.m
>1, Moment capacity m eet with requirement
9.3 Cracking Capacity Stress at bottom girder section due to service load ( bot at service) =
1.58 MPa
Con cr ete flexur al te nsion st ren gt h fr =
4.4 MPa
Crack Moment, Mcr = (bot at service + fr ) Wb.comp + Momen Mcr = Mn / Mcr =
(DL+ADL+LL+I)
3328.03 kN.m 1.359
> 1.2 ---- Cracking Capacity requirement is achieve
page 11 / 15
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 Alternatif solution to calculated shear on prestress element is use for structure element which have effective prestress above 40% of ultimate tensile stress 40% Ultimate Tensile Strength
= 744
Effective Prestress
= 1086
Section Properties : Ix = 5.496E+10 mm4 Yb = 519.31728 mm Ag =
MPa MPa
Ixcomp =
Effective Prestress > 40% fpu
1.75E+11 mm4
Ybcomp =
938.8 mm
316750 mm2
Load : Effective prestress Pe =
2575.64 kN
Factored Load : qult DL + ADL =
26.89
kN/m
Unfactored Load : 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 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. Vn = Vc + Vs Vn = Vu /
where :
Vn = Nominal Shear force Vc = Concrete shear contribution Vs = Shear steel contribution
Vu = Ultimate Shear force = Shear reduction factor = 0.75
Zonafication for shear steel stirup calculation Zone 1
Vn < 0.5 Vc
No need to use stirup
Z on e 2
V n < V c+ [0 .3 5 or ( 75/ 12 00 ) s qr t(f c' )] bw d
R equ ir ed s ti ru p s pa ci ng wi th mi ni mu m sp ac in g :
Zone 3
Vn < Vc+0.33 sqrt(fc') bw d
S ≤ 0.75 H
S ≤ (av.fy) / (0.35 bw)
S ≤ 600mm
S ≤ (av.fy/fpu) (80/Aps) d sqrt(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
page 12 / 15
PCI Monolith H-125cm ; L-20.15m ; CTC-160cm - RSNI (Rev.04)
Shear rebar steel fy = Use Av =
400 MPa 2 leg Dia.13 mm
shear width : bw = 170
mm
650
mm
265.46 mm2
bw-e =
Shear steel requirement calculation table : ecomp dist. d=dp>0.8H Vu Mu m m m kN kN-m
dp(Vu/Mu)
Vc
Vn
Vs
Shear
kN
kN
kN
Zonasi
Use Space mm
mm
use
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
300
0.775
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
Shear Steel Requirement Position
kN 2000.0 1800.0 1600.0 1400.0 1200.0 1000.0 . 800.0 600.0 400.0 200.0 0.0
Zona1
Zona2
Zona3
Zona4
Vn =Vu/f
beam section point
Shear Rebar configuration
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
page 13 / 15
PCI Monolith H-125cm ; L-20.15m ; CTC-160cm - RSNI (Rev.04)
10.2 Horisontal Shear Width of contact surface area
bv =
200 mm
d=
1216 mm
Effective Height =
fy = Use
0.75 400 MPa 2 leg Dia.13 mm
Area horisontal Shear Steel
Avh =
Horisontal Shear steel Spacing
s= v =
Horisontal Shear steel ratio
265.46 mm2 300 mm 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 < Vnh < 350 bv.d Vult = Ultimate shear due to superimposed DL + LL Vult = Vnh =
522.00 kN
396.87 kN RESUME:
3.5 bv d =
851.20 kN
Shear horisontal : OK
Minimal Use : bys =
200 mm
Spacing =
Avh = 50 by.s / fy Avh =
Max. Spacing =
172.375 mm2/m
1540.04 mm or
4 tweb = 680 mm
300.00 mm
min no. Spacing =
66 @ 2D13 for shear horisontal / span
Resume = additional shear horizontal required
XI. END BLOCK DESIGN Block Anchor dimension type 7
a
b
dia hole
(mm)
(mm)
(mm)
165
165
51
Block Area Concrete Area A (mm ) A1 (mm ) A2 (mm ) sqrt(A2/A1) 25182.18
27225
1625000
7.73
70225
2275000
5.69
. 19
265
265
84
64683.23
.
SNI 03-2847-2002 Pasal 11.3.2 (Anchorage Zone) Maximum strand =
12
Anchor Block type =
12
Load factor = Reduction factor () =
1.2
Strand
0.85
1. End Bearing Ultimate Point Load Pu = min (1.2 x nStrand x Astrand x %JF x fpu , nstrand x Astrand x 96% x fpu) Pu =
1984.3
End Bearing stress : comp = comp =
kN Nominal concrete comp. : Pu / A 46.03
fci = MPa
32.00 Mpa
min(2, sqrt(A2/A1)) =
2.0 Nominal fci = x 0.7 x fci x min(2,sqrt (A2/A1)) > comp = Nominal fci = 38.08 46.03 MPa
ten-
Nos
Anchor
sheath
Ult. Point
Block
End Bearing
don
strand
Height
hole
Load
Area
Stress
Nominal comp. fci
(Pu) kN
(A) mm2
(EBS=Pu/A) Mpa
Mpa
( ai ) mm
Remark
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)
page 14 / 15
PCI Monolith H-125cm ; L-20.15m ; CTC-160cm - RSNI (Rev.04)
2. Stirrup and Spalling Reinforcement Load factor = Reduction factor () =
0.85
1.2
fy =
400
MPa
Bursting Steel Diameter closed stirup =
13 mm
Stirup Area =
132.7 mm2
ten-
Nos
Anchor
sheath
Jacking
Bursting
End
don
strand
Height
hole
Force
Area (Abs)
Bearing (EBS)
kN
mm2
( ai ) mm
EBS/0.7
(fcc'-fci)/4.1
fl / 0.5 fy
fcc'
fl
p
Mpa
Mpa
Mpa
sp (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 = Ult. JF =
3307.15 kN
a1 =
430.00 mm
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 = No. Leg of stirrup = Stirup Area =
13 mm 4 leg 530.9 mm2
Anchor Stirup Rebar = T bursting / 0.5 fy Anchor Stirup Rebar = use no of stirup =
3254.2 mm2 7 pcs
Spalling Rebar Spalling Force = 2% JF Spalling Force = Diameter closed stirup = Stirup Area = use no of stirup =
66.1 kN 13 mm 132.7 mm2 3 pcs
page 15 / 15
PT WIJAYA KARYA BETON
TECHNICAL CALCULATION PCI GIRDER MONOLITH FOR HIGHWAY BRIDGES Project Product Job no Rev. No.
: : : :
TOLL SURABAYA ‐ GRESIK PCI Girder Monolith H‐125cm ; L‐20.80m ; CTC ‐160cm ; fc' 50MPa 13014 B 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, 1
st
nd
& 2 floor
Jl. Jatiwaringin no. 54, Pondok Gede ‐ Bekasi Ph: +62‐21‐8497 ‐3363 fax : +62‐21‐8497 ‐3391 www.wika‐beton.co.id
PT WIJAYA KARYA BETON
TECHNICAL CALCULATION APPROVAL PCI GIRDER MONOLITH FOR HIGHWAY BRIDGES TOLL SURABAYA ‐ GRESIK PCI Girder Monolith H‐125cm ; L‐20.80m ; CTC ‐160cm ; fc' 50MPa Job no. : 13014 B Rev. : 04
Approved by :
Consultan / Owner
Approved by : 18 Juni 2013
Checked by 18 Juni 2013
Design by : 18 Juni 2013
Ir. Achmad Arifin Technical Manager
Ignatius Harry S., S.T. Chief o f Technical
Suko Technical Staff
PCI Monolith H-125cm ; L-20.80m ; CTC-160cm - RSNI (Rev.04)
RESUME OF PCI GIRDER MONOLITH TECHNICALLY CALCULATION 1. BEAM SPECIFICATION
Span Beam Height ( H )
=
20.20 m (beam length
=
1250 mm
Distance ctc of beam ( s )
=
1600 mm
Slab thickness
=
200 mm
Beam Compressive strength
=
50 MPa
Slab Compressive strength
=
28 MPa
Bridge life time
=
50 years
=
20.80 m)
Segment Arr angement
Beam Segment Length (m)
1
2
3
4
5
6
7
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
12.7
mm (PC Strand 270 grade, low relaxation)
2. STRESSING
Nos of PC Strand
=
strand
28
Strand configuration No.
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'
1
4
900
300
2
12
600
200
3
12
300
100
total
28
514.29
171.43
3. LOADING 1. Dead Load
a. Precast Beam
=
7.77
kN/m
b. Slab
=
7.86
kN/m
Slab thickness =
c. Deck Slab
=
2.31
kN/m
d. Asphalt
=
1.73
kN/m
e. Diaphragm
=
6.92
kN
4
pcs
No. Diaphragm
200
mm
Deck slab thickness =
70
mm
Asphalt thickness =
50
mm
for 1 diaphragm 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)
=
b. Knife Edge Load (KEL)
=
c. Distribution Factor (DF)
=
1.40 for span length <= 50m 49.00 kN/m 1.00
d. Distribution Load q=
9.00 kN/m2
9.00 kN/m2
For Span <= 30m
9.00 x(0,5+15/span)kN/m2
For Span > 30m
e. Live Load Distribution load : Line Load
:
q' = DF x q x s p' = DF x DLA x KEL x s
CALCULATION RESUME
= =
14.40 kN/m 109.76 kN
PCI Monolith H-125cm ; L-20.80m ; 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 support react ion :
a. Dead Load
=
78.43
kN
b. Additional Dead Load
=
129.35
kN
c. Live Load
=
255.20
kN
Ultimate support reaction =
730.57
kN
5. CONTROL OF BEAM STRESSES 1. Initial Condition
Middle span position top stress =
-0.09 MP MPa
required
>
-1.58 MP MPa
bottom stress =
19.75 MP M Pa
required
<
24.00 MP MPa
top stress =
11.16 MPa
<
22.50 MPa
bottom stress =
2.67 MP MPa
>
-3.54 MP MPa
2. Service Condition
Middle span position required required
6. CONTROL OF BEAM DEFLECTION
De f l e c t i o n a t t h e m i d d l e of of b e a m sp sp a n
1. Chamber Chamber due stressin stressing g initial
=
-17.86
mm
=
-
2. Deflection at composite DL
=
-8.12
mm
3. Deflection due live load
=
7.85
mm,required
4. Total deflection at service
=
-0.28
mm
. = 25.25 mm
7. MOMENT AND CRACKING CAPACITY OF BEAM
Moment Moment Capacit Capacit y requir ement ement :
Mult = 1,2*( ,2*(B Beam+Di m+Dia aphra hragm+D gm+Dec eck k Slab lab)+1, )+1,3 3*Sla *Slab+ b+2* 2*A Asphalt haltic ic+ +1,8 1,8*(L *(LL+I L+I) Mn
=
368 3689.3 9.39 kN.m kN.m
=
5131.84 kN kN.m
Ratio, Mn / Mu (>1)
=
Cracking Capacit Capacit y requir ement ement :
Mcrack Mn / Mcr
= =
3737.99 kN k N.m 1.37
CALCULATION RESUME
1.39
PCI Monolith H-125cm ; L-20.80m ; CTC-160cm - RSNI (Rev.04)
TECHNICAL CALCULATION OF PCI MONOLITH BEAM FOR HIGHWAY BRIDGES SPAN L = 20.20 M I. DATA
0.3
L=
20.20 M
0.3
20.80 m
Beam length
=
Beam spacing (s)
=
1600 mm
( edge anchor to to e dg dge an ch ch or or :
Concrete Slab thickness (CIP)
=
200 mm
Asphalt thickness
=
50 mm
Deck slab thickness
=
70 mm
20.50
m)
A
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
tfl-1 tfl-2 tweb
H
tfl-3 tfl-4
II. MATERIAL B
2.1 Concre Concrete te Beam
Slab
fc' =
50.0
28.0
fc'i =
40.0
[N/mm ]
0.6 * fc'i =
24.0
[N/mm ]
Tensile 0.25 * Sqrt(fc'i) = Allowable stress at service ………. ( SNI T-1 2-20 04 )
1.6
[N/m [N/mm m]
Compressive strength at service at initial
80% fc'
2
[N/mm ] 2
Allowable stress Allowable stress at initial ………… ( SNI T-1 2-20 04 ) Compressive
2
2
0.45 * fc' =
22.5
12.6
[N/mm ]
0.5 * Sqrt(fc') =
3.5
2.6
[N/mm ]
wc =
2500.0
2500.0
[kg/m ]
Ec = wc *0.043*sqrt(fc') =
38007.0
28441.8
[N/mm ]
Compressive Tensile
2
Modulus of elasticity Concrete unit weight 1.5
Eci = wc
1.5
3
2 2
*0.043*sqrt(fci') =
33994.5
[N/mm ]
f r = 0.7*sqrt(fc') =
4.9
[N/mm ]
Concrete flexural tension strength (fr) 2
2.2 Prestressing Cable [Uncoated stress relieve seven wires strand] ( ASTM A 416 Grade 270 Low Low Relaxation or JIS G 3536 ) - Diameter strand
dia
:
12.7
[mm]
- Eff. Section area
Ast
:
98.78
[mm ]
- Modulus of elasticity
Es
: 1.93E+05
[N/mm ]
- Ultimate tensile strength
fu
:
1860
[N/mm ]
- Diameter
dia
:
13
[mm]
- Eff. Section area
Ast
:
132.73
[cm ]
- Modulus of elasticity
Es
: 2.10E+05
[N/mm ]
- Yield stress
fy
:
[N/mm ]
2
2 2
2.3 Steel Reinforcement
400
2
2 2
page 1 / 15
PCI Monolith H-125cm ; L-20.80m ; CTC-160cm - RSNI (Rev.04)
III. SECTION ANALYSIS Remark : Ep 1 = Ep 2 =
2
38007
[N/mm ] [Girder]
28442
[N/mm ] [Slab]
3
2
2
5
Ya'
4 Ya
n = Ep 2 / Ep 1 n=
3
0.75
1
2
Yb
Yb'
1
Base Line
PRECAST BEAM
COMPOSITE BEAM
3.1 Precast Precast Beam Beam [in mm mm ] Zone
Section
Width
Area
Level
2
Yb
Area*Yb 3
2
Io
Ix
Area*d 4
4
4
Height
Bottom
Upper
mm
mm
mm
mm
mm
mm
mm
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
519.3
1644 93 93750
96476 98 98623
45314 85 85894 9
54 96 96255 75 7571
Level
Yb
Area*Yb
Io
Area*d
mm
mm
mm
mm
mm
mm
62 09 09265 94 9418
316750
3.2 Composite Composite Beam [in mm mm ] Zone
2 1
Height
Width
Area 2
3
2
4
Ix
4
4
Section
Bottom
Upper
mm
200.0
1197.3
1197.3
239466
1320
1420.0
3400 41 41823
79822 02 0242. 5
6 12 1294 43 43917 5
70.0
149.7
149.7
10477
1250
1285.0
13462483
4277961.612
1441454078
1445732040
1250.0
650.0
350.0
316750
0
519.3
1644 93 93750
549 62 62557 57 571
4935 96 96101 33 33
1. 04 043 22 22E +1 +1 1
.
o a
.
.
+
.
+
3.3 R e s u m e [in mm mm ] 2
Description
Area (mm )
Precast Beam Composite Beam
[composite]
Ya (mm)
Yb (mm)
4
Ix (mm )
3
Wa (mm )
3
Wb (mm )
316750
731
519.3
54962557571
75220826
105836180
566693
606
914.1
1678 60 60559 16 162
277 03 0306 29 29
1836 40 40372
[precast]
336
499692375
IV. LOADING 4.1 Dead Dead Load Load a. Precast Beam
precast girder x q1 = Ac precast q1 =
b. Slab
0.080 x
[t/m'] =
7.77
[kN/m']
0.802
[t/m'] =
7.86
[kN/m']
0.235
[t/m'] =
2.31
[kN/m']
0.176
[t/m'] =
1.73
[kN/m']
6.92
[kN']
s
2.40 =
q4 = Ac asphaltic x q4 =
e. Diaphragm
0.098 x
0.792
conc. slab
2.40 =
deck slab x q3 = Ac deck q3 =
d. Asphaltic
0.334 x
conc. Precast
2.50 =
q2 = Ac slab CIP x q2 =
c. Deck slab
0.317 x
s
2.20 =
p
= Vol diaph with 0.20m thickness x
p
=
0.294 x
2.40 =
0.706 note :
Number of diaph = Diaph. placement Location
4
diaph
[ton'] =
from kg to N, multiply by 9.8060
pcs
1
2
3
4
0.00
6.73
13.47
20.20 0.00
Support Va
6.92
4.62
2.31
Mid Moment
0.00
23.31
23.31
Total Diaphragma Flexural Moment at Middle Span eqiv eqival alen en load load q diap diaphr hrag agm m
q5= q5=
0.00 46.61
kN.m
0.91 0.91
[kN/m']
page 2 / 15
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 Item P1 kN Load 225 Impact 1.3 LL + I 292.5 kN Distance 6.100 m Va 204.17 kN Va kN M max kN-m DF = S/3.4 M x DF kN-m
P2 225 1.3 292.5 10.100 146.25
P3 50 1.3 65 15.100 16.41
M.max di x = 10.100 m DLA = 30% Impact = 1 + DLA = 1.3
366.83 2535.00 0.47 1192.94
50kN
225kN
225kN
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 :
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) DLA = 1 + 0,3
50 < Span < 90 m
=
1.30
b. Knife Edge Load (KEL)
=
49.00
c. Distribution Factor (DF)
=
1.00
Span >= 90 m
[kN/m']
d. Distribution Load q =
9.00 kN/m
q = 9 kN/m q = 9 x(0,5+15/span)kN/m
which :
for
Span <= 30 m Span > 30 m
e. Live load Distribution load, qudl = DF x q x s = 1.00 x 9.00 KEL, PKEL = DF x DLA x KEL x s =
1.00
M.max at 0.5 span = Va = M LL =
x
1.40
10.100 m
x x
1.60 49.00
x
1.60
=
14.40
[kN/m']
=
109.76
[kN']
200.32 kN 1 28 8. 76 k N. m
RESUME : Moment force cause by D Loading is bigger than Truck Loading
page 3 / 15
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
Precast beam
396.06
0.00
348.50
348.50
0.00
0.00
396.06
Subtot al
396.06
0.00
348.50
348.50
0.00
0.00
396.06
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
653.20
Type
Description
DL DL
Subtot al
LL
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
Subtot al
1288.76
0.00
1134.00
1134.00
0.00
0.00
1288.76
Total (DL + LL)
2338.02
0.00
2057.26
2057.26
0.00
0.00
2338.02
Ultimate total
3689.39
0.00
3246.35
3246.35
0.00
0.00
3689.39
Sec 4-4 20.20 -78.43 -78.43 -79.39 -17.43 -32.52 -129.35 -145.44 -109.76 -255.20
Sec 5-5 20.20 -78.43 -78.43 -79.39 -17.43 -32.52 -129.35 -145.44 -109.76 -255.20
Sec 6-6 10.10 0.00 0.00 0.00 0.00 0.00 0.00 0.00 54.88 54.88 54.88
(m)
Ultimate total = 1,2*(Beam+Diaphragm+Deck Slab)+1,3*Slab+2*Asphaltic+1,8*(LL+I) VI. SHEAR ANALYSIS [in kN] Mid
Subtot al
span 0.00 0.00 0.00 0.00 0.00 0.00 0.00 54.88 54.88
Sec 1-1 0.00 78.43 78.43 79.39 17.43 32.52 129.35 145.44 109.76 255.20
Sec 2-2 6.60 27.18 27.18 27.51 6.04 11.27 44.82 50.40 73.90 124.30
Total (DL + LL)
54.88
462.97
196.30
.
.
.
Type
Description
DL
Precast beam
DL
Slab
Subtot al
ADL
Asphaltic Layer
SDL
Diaphragm+Deck slab Subtot al
Distribution load
LL
KEL
ma e o a
Sec 3-3 13.60 -27.18 -27.18 -27.51 -6.04 -11.27 -44.82 -50.40 -73.90 -124.30 -196.30
-462.97
-462.97
-
-
-
.
.
.
(m)
.
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 ] Tension
ten-
Nos
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
4
900
300
75%
0%
75%
551
12
600
200
75%
0%
75%
1654
1
2 3
total
Profile
12
300
100
75%
0%
75%
1654
28
514.29
171.43
75%
0%
75%
3858
Pa r a b o l i c c u r v e ( Av e r a g e of St r a n d ' s p o si t i o n v e r t i c a l l y f r o m t h e b o t t o m o f b e a m ( V a l ue f o r Y a x i s ) ) 2
Y = A.x + B.x + C 2
where :
A = Constanta : ( (Ymiddle + Yedge)/(L/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 ) X + Y = 0.003263 -0.066899 X + 0.514286 Cable tendon angle : o
tg =
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)
page 4 / 15
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 ) 1.20 1.00 0.80 0.60 0.40 0.20 0.00 0
5
10
15
20
25
7.2 Losses of Prestress 1. Losses of Prestress (Short Term) a. Friction 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. The equation for calculating the loss of prestress due to friction is : - + .x Po.e Px = ( AASHTO 1992, Chapt. 9.16.1 ) Where :
80.0%
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
75.0% 70.0%
k = Wobble coefficient x = Distance from tensile point to x section
65.0% 60.0%
Friction and Wooble coeficient for grouting tendon in metal sheating = 0.20 with Seven Wire Strand :
0.00
10.00
20.00
30.00
k = 0.003
Table of calculation due to Friction Profile
% JF
a
b
ten-
Nos
don
strand
Edge
Middle
from UTS
0
0
0
0
0%
0.00000
0
0
0
0
0
0%
0.00000
Prestress force (Px) = % UTS
0.00
10.25
20.50
0.000
0.0%
0.00%
0.0%
0
0.000
0.0%
0.00%
0.0%
0.00000
0
0.000
0.0%
0.00%
0.0%
(rad)
0
0
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%
0
b. Anchor set
, . , 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 e longation is resisted by friction just as the initial elongation is resisted by friction. 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 : Cable change angle point
Cable change angle point Anchorage set area
X (effective anchorage set)
Anchorage set area
X (effective anchorage set)
page 5 / 15
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 draw in tenNos
From left side
From right side
after anchorage set = % UTS
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%
AVERAGE LOSSES OF PRESTRESS
LOSSES OF PRESTRESS DUE TO ANCHORAGE SET
75.0%
80.0% 75.0%
70.0% 70.0%
68.20%
65.0%
65.0%
60.0% 55.0%
69.85% 69.61% 69.30% 68.67%
64.02%
60.0% 0.00
10.00
20.00
30.00
0.00
5.00
Prestress tendon section
10.00
15.00
20.00
25.00
Prestress tendon section
c. Elastic Shortening ( ES ) Elastic shortening refers to the shortening of the concrete as the postensioning force is applied. As the concrete shorterns, the ten don 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 = concrete stress at the centre of gravity of prestressing tendons due to prestressing force at transfer and the self weight of the member at the section of maximum positive moment 2.39%
Assumption Losses due ES Pi = Pi =
Total prestressing force at release 68 .2% - 2. 39% = 65.82% UTS x nos x Aps =
3385.9865 kN
2
f cir = Pi / A + Pi. ec / I + Mg.ec/I f cir = so,
15.64 N/mm2 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) SH
=
(ACI 318-95, Chapt. 18.6) 1.63% percent actual SH losses = SH/fpu
30.33 N/mm2
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
"days" is the number of days between the end of moist curing and t he application of prestress.In a structures that are not moist cured, Ksh is typiclly based on when the concrete was cast Ksh =
0.64
V/S =
0.08
RH
=
Volume =
3
6.59 m
Surface =
2
81.21 m
70.00
page 6 / 15
PCI Monolith H-125cm ; L-20.80m ; CTC-160cm - RSNI (Rev.04)
e. Creep ( CR )
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 cree p. Loss of prestress due to a creep is nominally propotional to the net permanent compresive stressin the concrete. the n et permanent compressive stress is the initial compressive stress in the concrete due to the prestressing minus th e tensile stress due to self weight and superimposed deadload moments CR CR
= Kcr*(Es/Ec)*(fcir-fcds)
94.83 N/mm
=
(ACI 318-95, Chapt. 18.6)
2
percent actual CR losses = CR/fpu
5.10%
Where :
Kcr =
1.60 (for posten sion ed member)
fcir = stress at center point prestress force, initial condition fcir =
15.639 N/mm
2
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 = fcds 2 = Madl.e/Ic =
3.58 N/mm
2
0.39 N/mm
2
component of fcd due to load on the plain beam component of fcd due to load on the composite beam
3.97 N/mm
fcds = fcds 1 + fcds 2 =
2
f. Steel Relaxation ( RE ) 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 ten don at that time. Because of other prestress losses, there is a continual reduction of tendon strss; this causes a reduction in the r elaxation rate. The equation for prestress loss due to relaxation of tendons is : RE = [ Kre - J*(SH+CR+ES) ] *C
18.26 N/mm
RE =
(ACI 318-95, Chapt. 18.6)
2
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) .
=
or p
pu =
.
RESUME DUE TO SHORT & LONG TERM LOSSES Losses
I. Short Ter m Losses
Section
Elastic Total Anchor set Shortening Losses (%)
x (m)
Friction
II. Long Term Losses
Shrinkage (SH)
Creep (CR)
Steel Total Losses Relaxation (%)
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 : UTS
Friction
LOSSES OF PRESTRESS DIAGRAM
0 > x > 10.25
Anchorset ElasticShortening(ES)
80.00%
75.00% -+ 0.41% x
Shrinkage(SH)
10.3 > x > 20.50
Creep(CR) Steel Relaxation(SR)
75.00% 70.82% 68.20% 65.00%
64.02% 61.64% 60.00%
65.82% 64.19%
69.85% 69.61% 69.30% 68.67% 67.46% 67.22% 66.92% 65.83% 65.59% 65.29% 66.29% 64.66%
70.82% + 0.05% x
Long term Losses equotion : 0 > x > 10.25 53.92% + 0.41% x 10.25 > x > 14.88
59.09% 58.11%
60.73% 60.50% 60.19% 59.75% 59.51% 59.21% 59.56% 58.58%
58.11% + 0.35% x
x - 14.8798744
16.01 > x > 17.49 59.51% -+ 0.21% x
50.00% 10.25
x - 10.25
14.88 > x > 16.01 59.75% -+ 0.21% x
54.91% 53.92%
0.00
x - 10.25
14.88
16.01
Prestress tendon section
17.49
20.50
x - 16.0124668
17.49 > x > 20.50 59.21% -+ 0.21% x
x - 17.4863251
page 7 / 15
PCI Monolith H-125cm ; L-20.80m ; CTC-160cm - RSNI (Rev.04)
7.3 Effective Stress Force Resume Prestressed Force at middle % Losses of prestress
Condition
Cable
%UTS effective prestress
[N/mm ]
[mm ]
[kN]
Asp
stress 2
P
2
short term
9.2%
65.8%
1224
2765.84
3385.99
long term
16.9%
58.1%
1081
2765.84
2989.32
VIII. STRESS AND DEFFLECTION ANALYSIS Beam Segment Length (m)
1
2
3
4
5
6
6.600
7.000
6.600
0.00
0.00
0.00
Additional length at the end of the beam =
0.30
m
7
0.00 Total Length =
8
0.00 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
x - [m]
Span
0.00
6.60
13.60
20.20
20.20
10.10
[kN.m]
396.06
0.00
348.50
348.50
0.00
0.00
396.06
[kN]
3858.35
3858.35
3858.35
3858.35
3858.35
3858.35
3858.35
%
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]
-797
-776
-55
-55
-872
Moment DL Jacking Force Losses due to friction
-872
-58
2
11.51
12.18
11.74
11.53
11.58
11.58
11.51
2
-11.60
-0.77
-10.59
-10.31
-0.73
-0.73
-11.60
Allow.
Pi / A
[N/mm ]
M / Wa
[N/mm ] 2
M / Wb Initial Stresses 2
[N/mm ]
SEC 6-6
[N/mm ]
8.24
0.55
7.53
7.33
0.52
0.52
8.24
stress
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 oa o precas , s a ,
ap ragm an pres ress y
eam
=
> Live load and asphalt by composite Description Moment DL
SEC 1-1
SEC 2-2
SEC 3-3
SEC 4-4
SEC 5-5
x - [m]
Span
0.00
6.60
13.60
20.20
20.20
SEC 6-6 10.10
[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 -1038.85
P.e
[m]
-1038.85
-41.59
-896.85
-939.28
-45.23
-45.23
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
2
9.44
9.44
9.44
9.44
9.44
9.44
9.44
2
-1.03
-0.55
-0.68
-1.24
-0.60
-0.60
-1.03
2
0.73
0.39
0.48
0.88
0.43
0.43
0.73
2
2.76
0.00
2.42
2.42
0.00
0.00
2.76
Allow.
2
stress
P/A
[N/mm ]
M 1 / Wa
[N/mm ]
M 1 / Wb
[N/mm ]
M 2 / Wa'
[N/mm ]
M 2 / Wb' Stress at Service 2
[N/mm ]
Note :
( = M2 ) Middle
[N/mm ]
-7.50
0.00
-6.60
-6.60
0.00
0.00
-7.50
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
Moment DL = Moment due to dead load ( Chapter V - Moment Analysis ) Moment Bal = Moment due to uniform load in balance condition ( Chapter 7.4 - Effective Stress Force ) Moment Net = ( 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 )
page 8 / 15
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 =
+
Pi/A = 12.18 MPa
11.92 MPa
=
M/Wb = 0.18 MPa
effective prestress =
75% UTS
Pi = eccentricity (ei) =
3858.35 5.03
Mdl = Mbeam =
bottom
= 12.36 MPa
M = Mdl - Pi.e = kN mm
allow comp at
initial =
allow tension initial
0 kN-m
=
-19.41
kN-m
24.00 -1.58
MPa MPa
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 =
+
Pi/A = 11.50 MPa
=
M/Wb = 8.23 MPa
bottom
effective prestress =
71% UTS
Pi = eccentricity (ei) =
3643.15 347.89
kN mm
396.06
kN-m
Mdl = Mbeam =
-0.08 MPa
= 19.73 MPa
M = Mdl - Pi.e = allow comp at
initial =
allow tension initial =
-871.4 kN-m 24.00 -1.58
MPa MPa
control allow stress = m eet requirement
8. 3. 2. STRESS DIAGRAM AT CONST RUCTION
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 =
+
Pi/A = 10.69 MPa
=
M/Wb = 2.05 MPa
bottom
effective prestress =
66% UTS
Pi = eccentricity (ei) =
3385.99 347.89
kN mm
961.23
kN-m
Mdl = Mbeam + Madl =
7.81 MPa
= 12.74 MPa
M = Mdl - Pi.e = allow comp at initial = allow tension initial =
-216.71
kN-m
24.00 -1.58
MPa MPa
control allow stress = meet requirement
b. Stress at composite beam middle section due to asphaltic layer: slab =
P/A = 10.69 MPa
M2/Wa'= 0.18 MPa
M1/Wa = -2.88 MPa
+
P/A = 10.69 MPa
top =
+
effective prestress =
66% UTS
Pi = eccentricity (ei) =
3385.99 347.89
kN mm
Mdl = Mbe am + Ma dl =
9 61 .2 3
k N-m
7.98 MPa
=
M2/Wb'= -0.48 MPa
M1/Wb = 2.05 MPa
0.32 MPa
bottom
= 12.26 MPa
M1 = Mdl + Pi.e =
-216.71
kN-m
M2 = Masphalt =
88.03 24.00
kN-m MPa
-1.58
MPa
allow comp at
initial =
allow tension initial
=
control allow stress = meet requirement
page 9 / 15
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 =
P/A = 9.44 MPa
M2/Wa'= 2.76 MPa
M1/Wa = -1.05 MPa
+
P/A = 9.44 MPa
top =
+
58% UTS
M2/Wb'= -7.50 MPa
bottom
= 2.68 MPa
M1 = Mdl + Pi.e =
Pi =
2989.32
kN
eccentricity (ei) =
347.89
mm
Mdl = Mbe am + Ma dl =
9 61 .2 3
k N-m
11.15 MPa
=
M1/Wb = 0.74 MPa
effective prestress =
4.97 MPa
M2 = Masphalt + LL =
-78.72
kN-m
1376.79
kN-m
service =
22.50
MPa
allow tension at service =
-3.54
MPa
allow comp at
control allow stress = meet requirement
8.4 Deflection 8.4.1 Chamber due to Prestress Load Deflection on middle section : l
P
ee
pi= [ee+(5/6)(e c-ee)] x (P. l2 /8 Ec Ix) pi=
P
ec
where :
-26.87 mm
P = Prestress force Eci = Modulus Elasticity of Concrete
l/2
l/2
Ixi = Section Inertia l = length of anchor to anchor ee = Distance between c.g of strand and c.g of concrete at end ec = Distance between c.g of strand and c.g of concrete at centre
8.4.2 Deflection at initial, ere ction and service condition (based : PCI handbook 4.6.5 Long-Time Chamber Deflection) Deflection () on simple span structure : where : q = Uniform Load 4
q= (5/384)*q*L /Ec Ix)
P = Point Load
3
l = Beam Span
p= P.l /48 Ec Ix
Deflection calculation table : Estimating long-time cambers and deflections WORKING LOAD
Loading q (kN/m)
P (kN)
1. Due to Prestress force 2. Due to beam weight (DL)
Release (1)
Long time cambers and deflection (2) multipliers Erection multipliers
-26.87
1.80 x (1)
-48.37
2.20 x (1)
9.01
1.85 x (1)
16.67
2.40 x (1)
7.77
-17.86 3. Due to ADL
3.22
Service (3) -59.12 21.62
-31.71 3.34
-37.50 3.00 x (2)
10.03
-28.36 4. Due to Composite Overtoping
7.86
8.16
-27.47 2.30 x (2)
18.76
-20.21 5. due to asphaltic (SDL)
-8.71
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
=
2.
Deflection due to Live Load
=
3.
Total deflection with LL
=
-8.12 mm 7.85 mm < allow. deflection L/800 =
25.25 mm
OK
-0.28 mm, chamber upward
page 10 / 15
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
2. Beam Ctc 3. Span length / 4
=1600 mm …. Control =5050 mm
Thus, Effectif slab width is :
=1600 mm
for slab with fc' = Value =
28.00
MPa
0.85
Partial Rebar: 400 MPa 0 Dia.13 mm
fy = Use As = d=
at tension area b web =
0.00 mm2
170 mm
1190.5 mm
Partial tension rebar ratio : t = As / (bweb x d )
t =
0.00000
t =
t =
0.000
t . fy / fc
Rebar in compresion area is neglected due calculation c = c =
Low Relaxation strand : fpu =
1860
MPa
Strand stress ratio fpu / fpy = dp =
value p = 0.28
0.9 Aps =
1348.6 mm
2
2765.84 mm
Prestress ratio : p = Aps / (beff x dp ) fps = p =
beff =
1600 mm
p = 0.00128184
fpu {1 - p / (p.fpu/fc + d/dp ( t-c)))
1807.8 MPa
fps = p =
p fps/fc
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 one
Zone 3
c
i
Cc3 Cc2
Zone 3 Zone 2 a
Tps = Aps . Fps Tps = 5000162.13 N
Cc1
Zone 1
dp
d
strength reduction factor = 0.8 Tps=Aps.fps T = As.fy
COMPOSITE BEAM
Location of Depth of Concrete Compression Block (a) : hi wi Aci=hi.wi Conc. Strength fc' i Zone
Cci=0.85 fc'i.Aci
MPa
Comp (i)
4
(mm) 131.31
(mm) 1600
(mm2) 210090.85
28.00
CIP Slab
N 5000162
3
0.00
335
0
28.00
CIP Slab
0
131
2
0.00
350
0
50.00
Beam
0
131
1
0.00
170
0
50.00
Beam
0
131
Compresion
Point (mm) Point (mm) 66 65.65
Depth of Concrete Compression Block is located at zone 4 a = Tps / ( 0.85 x fc'' slab x beff )
a=
Mn = (Tps (dp - comp. point) + As.fy (d-comp. point) Mn = 5131.8386 kN.m Bridge life time design for 50 year,so Transient act factor = 1 Mn / Mult = Mult = 1x 3,689kN-m
Mn =
1.391
131.31 mm 6414.80 kN.m
>1, Moment capacity m eet with requirement
9.3 Cracking Capacity Stress at bottom girder section due to service load ( bot at service) =
2.67 MPa
Con cr ete flexur al te nsion st ren gt h fr =
4.9 MPa
Crack Moment, Mcr = (bot at service + fr ) Wb.comp + Momen Mcr = Mn / Mcr =
(DL+ADL+LL+I)
3737.99 kN.m 1.373
> 1.2 ---- Cracking Capacity requirement is achieve
page 11 / 15
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 Alternatif solution to calculated shear on prestress element is use for structure element which have effective prestress above 40% of ultimate tensile stress 40% Ultimate Tensile Strength
= 744
Effective Prestress
= 1081
Section Properties : Ix = 5.496E+10 mm4 Yb = 519.31728 mm Ag =
MPa MPa
Effective Prestress > 40% fpu
Ixcomp = 1.679E+11 mm4 Ybcomp =
914.1 mm
316750 mm2
Load : Effective prestress Pe =
2989.32 kN
Factored Load : qult DL + ADL =
26.85
kN/m
Unfactored Load : 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 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. Vn = Vc + Vs Vn = Vu /
where :
Vn = Nominal Shear force Vc = Concrete shear contribution Vs = Shear steel contribution
Vu = Ultimate Shear force = Shear reduction factor = 0.75
Zonafication for shear steel stirup calculation Zone 1
Vn < 0.5 Vc
No need to use stirup
Z on e 2
V n < V c+ [0 .3 5 or ( 75/ 12 00 ) s qr t(f c' )] bw d
R equ ir ed s ti ru p s pa ci ng wi th mi ni mu m sp ac in g :
Zone 3
Vn < Vc+0.33 sqrt(fc') bw d
S ≤ 0.75 H
S ≤ (av.fy) / (0.35 bw)
S ≤ 600mm
S ≤ (av.fy/fpu) (80/Aps) d sqrt(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
page 12 / 15
PCI Monolith H-125cm ; L-20.80m ; CTC-160cm - RSNI (Rev.04)
Shear rebar steel fy = Use Av =
400 MPa 2 leg Dia.13 mm
shear width : bw = 170
mm
650
mm
265.46 mm2
bw-e =
Shear steel requirement calculation table : ecomp dist. d=dp>0.8H Vu Mu m m m kN kN-m
dp(Vu/Mu)
Vc
Vn
Vs
Shear
kN
kN
kN
Zonasi
Use Space
use
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
300 300
0.775
0.459
1.06
682.09
544.47
1.00
969.08
909.46
-59.62
2
600
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
Shear Steel Requirement Position
kN 2000.0 1800.0 1600.0 1400.0 1200.0 1000.0 800.0 600.0 400.0 200.0 0.0
Zona1
Zona2
Zona3
Zona4
Vn= Vu/f
beam section point
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
Shear Rebar configuration
total shear rebar per half span (row) =
34
total shear rebar per span (row) =
68
page 13 / 15
PCI Monolith H-125cm ; L-20.80m ; CTC-160cm - RSNI (Rev.04)
10.2 Horisontal Shear Width of contact surface area
bv =
200 mm
d=
1216 mm
Effective Height =
fy = Use
0.75 400 MPa 2 leg Dia.13 mm
Area horisontal Shear Steel
Avh =
Horisontal Shear steel Spacing
s= v =
Horisontal Shear steel ratio
265.46 mm2 300 mm 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 < Vnh < 350 bv.d Vult = Ultimate shear due to superimposed DL + LL Vult = Vnh =
522.00 kN
406.41 kN RESUME:
3.5 bv d =
851.20 kN
Shear horisontal : OK
Minimal Use : bys =
200 mm
Spacing =
Avh = 50 by.s / fy Avh =
Max. Spacing =
172.375 mm2/m
1540.04 mm or
4 tweb = 680 mm
300.00 mm
min no. Spacing =
68 @ 2D13 for shear horisontal / span
Resume = additional shear horizontal required
XI. END BLOCK DESIGN Block Anchor dimension type 7
a
b
dia hole
(mm)
(mm)
(mm)
165
165
51
Block Area Concrete Area A (mm ) A1 (mm ) A2 (mm ) sqrt(A2/A1) 25182.18
27225
1625000
7.73
70225
2275000
5.69
. 19
265
265
84
64683.23
.
SNI 03-2847-2002 Pasal 11.3.2 (Anchorage Zone) Maximum strand =
12
Anchor Block type =
12
Load factor = Reduction factor () =
1.2
Strand
0.85
1. End Bearing Ultimate Point Load Pu = min (1.2 x nStrand x Astrand x %JF x fpu , nstrand x Astrand x 96% x fpu) Pu =
1984.3
End Bearing stress : comp = comp =
kN Nominal concrete comp. : Pu / A 46.03
fci = MPa
40.00 Mpa
min(2, sqrt(A2/A1)) =
2.0 Nominal fci = x 0.7 x fci x min(2,sqrt (A2/A1)) > comp = Nominal fci = 47.60 46.03 MPa
ten-
Nos
Anchor
sheath
Ult. Point
Block
End Bearing
don
strand
Height
hole
Load
Area
Stress
Nominal comp. fci
(Pu) kN
(A) mm2
(EBS=Pu/A) Mpa
Mpa
51
661.43
25182.18
26.27
47.60
EBS < Nominal Compresion
43107.75
46.03
47.60
EBS < Nominal Compresion
43107.75
46.03
47.60
EBS < Nominal Compresion
( ai ) mm 0
0
0
0
0
0
1
4
165
2
12
215
63
1984.29
3
12
215
63
1984.29
Remark
page 14 / 15
PCI Monolith H-125cm ; L-20.80m ; CTC-160cm - RSNI (Rev.04)
2. Stirrup and Spalling Reinforcement Load factor = Reduction factor () =
0.85
1.2
fy =
400
MPa
Bursting Steel Diameter closed stirup =
13 mm
Stirup Area =
132.7 mm2
ten-
Nos
Anchor
sheath
Jacking
Bursting
End
don
strand
Height
hole
Force
Area (Abs)
Bearing (EBS)
kN
mm2
( ai ) mm
0
0
0
0
0
0
EBS/0.7
(fcc'-fci)/4.1
fl / 0.5 fy
fcc'
fl
p
Mpa
Mpa
Mpa
sp (mm)
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
1
Anchor Zone Stirrup JF Load = Ult. JF =
3858.35 kN
a1 =
595.00 mm
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 = No. Leg of stirrup = Stirup Area =
13 mm 4 leg 530.9 mm2
Anchor Stirup Rebar = T bursting / 0.5 fy Anchor Stirup Rebar = use no of stirup =
3032.7 mm2 6 pcs
Spalling Rebar Spalling Force = 2% JF Spalling Force = Diameter closed stirup = Stirup Area = use no of stirup =
77.2 kN 13 mm 132.7 mm2 3 pcs
page 15 / 15
PT WIJAYA KARYA BETON
TECHNICAL CALCULATION PCI GIRDER MONOLITH FOR HIGHWAY BRIDGES Project Product Job no Rev. No.
: : : :
TOLL SURABAYA ‐ GRESIK PCI Girder Monolith H‐125cm ; L‐21.75m ; CTC ‐160cm ; fc' 60MPa 13014 C 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, 1
st
nd
& 2 floor
Jl. Jatiwaringin no. 54, Pondok Gede ‐ Bekasi Ph: +62‐21‐8497 ‐3363 fax : +62‐21‐8497 ‐3391 www.wika‐beton.co.id
PT WIJAYA KARYA BETON
TECHNICAL CALCULATION APPROVAL PCI GIRDER MONOLITH FOR HIGHWAY BRIDGES TOLL SURABAYA ‐ GRESIK PCI Girder Monolith H‐125cm ; L‐21.75m ; CTC ‐160cm ; fc' 60MPa Job no. : 13014 C Rev. : 04
Approved by :
Consultan / Owner
Approved by : 18 Juni 2013
Checked by 18 Juni 2013
Design by : 18 Juni 2013
Ir. Achmad Arifin Technical Manager
Ignatius Harry S., S.T. Chief o f Technical
Suko Technical Staff
PCI Monolith H-125cm ; L-21.75m ; CTC-160cm - RSNI (Rev.04)
RESUME OF PCI GIRDER MONOLITH TECHNICALLY CALCULATION 1. BEAM SPECIFICATION
Span Beam Height ( H )
=
21.15 m (beam length
=
1250 mm
Distance ctc of beam ( s )
=
1600 mm
Slab thickness
=
200 mm
Beam Compressive strength
=
60 MPa
Slab Compressive strength
=
28 MPa
Bridge life time
=
50 years
=
21.75 m)
Segment Arr angement
Beam Segment Length (m)
1
2
3
4
5
6
7
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
12.7
mm (PC Strand 270 grade, low relaxation)
2. STRESSING
Nos of PC Strand
=
strand
35
Strand configuration No.
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'
1
11
900
300
2
12
600
200
3
12
300
100
total
35
591.43
197.14
3. LOADING 1. Dead Load
a. Precast Beam
=
7.77
kN/m
b. Slab
=
7.86
kN/m
Slab thickness =
c. Deck Slab
=
2.31
kN/m
d. Asphalt
=
1.73
kN/m
e. Diaphragm
=
6.92
kN
4
pcs
No. Diaphragm
200
mm
Deck slab thickness =
70
mm
Asphalt thickness =
50
mm
for 1 diaphragm 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)
=
b. Knife Edge Load (KEL)
=
c. Distribution Factor (DF)
=
1.40 for span length <= 50m 49.00 kN/m 1.00
d. Distribution Load q=
9.00 kN/m2
9.00 kN/m2
For Span <= 30m
9.00 x(0,5+15/span)kN/m2
For Span > 30m
e. Live Load Distribution load : Line Load
:
q' = DF x q x s p' = DF x DLA x KEL x s
CALCULATION RESUME
= =
14.40 kN/m 109.76 kN
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 1. Initial Condition
Middle span position top stress =
0.66 MPa
required
>
-1.73 MPa
bottom stress =
24.05 MPa
required
<
28.80 MPa
top stress =
13.11 MPa
<
27.00 MPa
bottom stress =
4.65 MPa
>
-3.87 MPa
2. Service Condition
Middle span position required required
6. CONTROL OF BEAM DEFLECTION
De f l e c t i o n a t t h e m i d d l e of b e a m sp a n
1. Chamber due stressing initial
=
-19.65
mm
=
-
2. Deflection at composite DL
=
-9.15
mm
3. Deflection due live load
=
8.76
mm,required
4. Total deflection at service
=
-0.38
mm
. = 26.44 mm
7. MOMENT AND CRACKING CAPACITY OF BEAM
Moment Capacit y requir ement :
Mult = 1,2*(Beam+Diaphragm+Deck Slab)+1,3*Slab+2*Asphaltic+1,8*(LL+I) Mn
=
3992.69 kN.m
=
6158.26 kN.m
Ratio, Mn / Mu (>1)
=
Cracking Capacit y requir ement :
Mcrack Mn / Mcr
= =
4360.35 kN.m 1.41
CALCULATION RESUME
1.54
PCI Monolith H-125cm ; L-21.75m ; CTC-160cm - RSNI (Rev.04)
TECHNICAL CALCULATION OF PCI MONOLITH BEAM FOR HIGHWAY BRIDGES SPAN L = 21.15 M I. DATA
0.3
L=
21.15 M
0.3
21.75 m
Beam length
=
Beam spacing (s)
=
1600 mm
( edge anchor to e dge an ch or :
Concrete Slab thickness (CIP)
=
200 mm
Asphalt thickness
=
50 mm
Deck slab thickness
=
70 mm
21.45
m)
A
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
tfl-1 tfl-2 tweb
H
tfl-3 tfl-4
II. MATERIAL B
2.1 Concrete Beam
Slab
fc' =
60.0
28.0
fc'i =
48.0
[N/mm ]
0.6 * fc'i =
28.8
[N/mm ]
Tensile 0.25 * Sqrt(fc'i) = Allowable stress at service ………. ( SNI T-1 2-20 04 )
1.7
[N/mm ]
Compressive strength at service at initial
80% fc'
2
[N/mm ] 2
Allowable stress Allowable stress at initial ………… ( SNI T-1 2-20 04 ) Compressive
2
2
0.45 * fc' =
27.0
12.6
[N/mm ]
0.5 * Sqrt(fc') =
3.9
2.6
[N/mm ]
wc =
2500.0
2500.0
[kg/m ]
*0.043*sqrt(fc') =
41634.6
28441.8
[N/mm ]
*0.043*sqrt(fci') =
37239.1
[N/mm ]
f r = 0.7*sqrt(fc') =
5.4
[N/mm ]
Compressive Tensile
2
Modulus of elasticity Concrete unit weight Ec = wc Eci = wc
1.5
1.5
3
2 2
Concrete flexural tension strength (fr) 2
2.2 Prestressing Cable [Uncoated stress relieve seven wires strand] ( ASTM A 416 Grade 270 Low Relaxation or JIS G 3536 ) - Diameter strand
dia
:
12.7
[mm]
- Eff. Section area
Ast
:
98.78
[mm ]
- Modulus of elasticity
Es
: 1.93E+05
[N/mm ]
- Ultimate tensile strength
fu
:
1860
[N/mm ]
- Diameter
dia
:
13
[mm]
- Eff. Section area
Ast
:
132.73
[cm ]
- Modulus of elasticity
Es
: 2.10E+05
[N/mm ]
- Yield stress
fy
:
[N/mm ]
2
2 2
2.3 Steel Reinforcement
400
2
2 2
page 1 / 15
PCI Monolith H-125cm ; L-21.75m ; CTC-160cm - RSNI (Rev.04)
III. SECTION ANALYSIS Remark : Ep 1 = Ep 2 =
2
41635
[N/mm ] [Girder]
28442
[N/mm ] [Slab]
3
2
2
5
Ya'
4 Ya
n = Ep 2 / Ep 1 n=
3
0.68
1
2
Yb
Yb'
1
Base Line
PRECAST BEAM
COMPOSITE BEAM
3.1 Precast Beam [in mm ] Zone
Section
Width
Area
Level
2
Yb
Area*Yb 3
2
Io
Ix
Area*d 4
4
4
Height
Bottom
Upper
mm
mm
mm
mm
mm
mm
mm
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
519.3
1644 93750
96476 98623
45314 85894 9
54 96255 7571
Level
Yb
Area*Yb
Io
Area*d
mm
mm
mm
mm
mm
mm
61 19228 2045
316750
3.2 Composite Beam [in mm ] Zone
2 1
Height
Width
Area 2
3
2
4
Ix
4
4
Section
Bottom
Upper
mm
200.0
1093.0
1093.0
218602
1320
1420.0
3104 14295
72867 2054. 5
6 0463 60999 1
70.0
136.6
136.6
9564
1250
1285.0
12289510
3905226.792
1461534249
1465439476
1250.0
650.0
350.0
316750
0
519.3
1 64 49 37 50
5 49 62 55 75 71
4 44 86 42 52 57
9 94 48 98 28 28
.
o a
.
.
+
.
+
3.3 R e s u m e [in mm ] 2
Description
Area (mm )
Precast Beam Composite Beam
[composite]
Ya (mm)
Yb (mm)
4
Ix (mm )
3
Wa (mm )
3
Wb (mm )
316750
731
519.3
54962557571
75220826
105836180
544915
626
894.1
1621 06704 349
258 9891 61
1813 11348
[precast]
356
455457230
IV. LOADING 4.1 Dead Load a. Precast Beam
q1 = Ac precast girder x q1 =
b. Slab
0.080 x
[t/m'] =
7.77
[kN/m']
0.802
[t/m'] =
7.86
[kN/m']
0.235
[t/m'] =
2.31
[kN/m']
0.176
[t/m'] =
1.73
[kN/m']
6.92
[kN']
s
2.40 =
q4 = Ac asphaltic x q4 =
e. Diaphragm
0.098 x
0.792
conc. slab
2.40 =
q3 = Ac deck slab x q3 =
d. Asphaltic
0.334 x
conc. Precast
2.50 =
q2 = Ac slab CIP x q2 =
c. Deck slab
0.317 x
s
2.20 =
p
= Vol diaph with 0.20m thickness x
p
=
0.294 x
2.40 =
0.706 note :
Number of diaph = Diaph. placement Location
4
diaph
[ton'] =
from kg to N, multiply by 9.8060
pcs
1
2
3
4
0.00
7.05
14.10
21.15 0.00
Support Va
6.92
4.62
2.31
Mid Moment
0.00
24.40
24.40
Total Diaphragma Flexural Moment at Middle Span eqivalen load q diaphragm
q5=
0.00 48.80
kN.m
0.87
[kN/m']
page 2 / 15
PCI Monolith H-125cm ; L-21.75m ; 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 Item P1 kN Load 225 Impact 1.3 LL + I 292.5 kN Distance 6.575 m Va 201.57 kN Va kN M max kN-m DF = S/3.4 M x DF kN-m
P2 225 1.3 292.5 10.575 146.25
P3 50 1.3 65 15.575 17.13
M.max di x = 10.575 m DLA = 30% Impact = 1 + DLA = 1.3
364.95 2689.38 0.47 1265.59
50kN
225kN
225kN
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 :
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) DLA = 1 + 0,3
50 < Span < 90 m
=
1.30
b. Knife Edge Load (KEL)
=
49.00
c. Distribution Factor (DF)
=
1.00
Span >= 90 m
[kN/m']
d. Distribution Load q =
9.00 kN/m
q = 9 kN/m q = 9 x(0,5+15/span)kN/m
which :
for
Span <= 30 m Span > 30 m
e. Live load Distribution load, qudl = DF x q x s = 1.00 x 9.00 KEL, PKEL = DF x DLA x KEL x s =
1.00
M.max at 0.5 span = Va = M LL =
x
1.40
10.575 m
x x
1.60 49.00
x
1.60
=
14.40
[kN/m']
=
109.76
[kN']
207.16 kN 1 38 5. 54 k N. m
RESUME : Moment force cause by D Loading is bigger than Truck Loading
page 3 / 15
PCI Monolith H-125cm ; L-21.75m ; 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
7.08
14.08
21.15
21.15
10.58
Precast beam
434.19
0.00
386.63
386.63
0.00
0.00
434.19
Subtot al
434.19
0.00
386.63
386.63
0.00
0.00
434.19
Slab
439.52
0.00
391.38
391.38
0.00
0.00
439.52
ADL
Asphaltic Layer
96.50
0.00
85.93
85.93
0.00
0.00
96.50
SDL
Diaphragm+Deck Slab
177.77
0.00
158.29
158.29
0.00
0.00
177.77
713.79
0.00
635.60
635.60
0.00
0.00
713.79
Type
Description
DL DL
Subtot al
LL
Distribution load
805.18
0.00
716.98
716.98
0.00
0.00
805.18
KEL
580.36
0.00
516.78
516.78
0.00
0.00
580.36
Subtot al
1385.54
0.00
1233.76
1233.76
0.00
0.00
1385.54
Total (DL + LL)
2533.52
0.00
2255.99
2255.99
0.00
0.00
2533.52
Ultimate total
3992.69
0.00
3555.33
3555.33
0.00
0.00
3992.69
Sec 4-4 21.15 -82.12 -82.12 -83.12 -18.25 -33.62 -135.00 -152.28 -109.76 -262.04
Sec 5-5 21.15 -82.12 -82.12 -83.12 -18.25 -33.62 -135.00 -152.28 -109.76 -262.04
Sec 6-6 10.58 0.00 0.00 0.00 0.00 0.00 0.00 0.00 54.88 54.88 54.88
(m)
Ultimate total = 1,2*(Beam+Diaphragm+Deck Slab)+1,3*Slab+2*Asphaltic+1,8*(LL+I) VI. SHEAR ANALYSIS [in kN] Mid
Subtot al
span 0.00 0.00 0.00 0.00 0.00 0.00 0.00 54.88 54.88
Sec 1-1 0.00 82.12 82.12 83.12 18.25 33.62 135.00 152.28 109.76 262.04
Sec 2-2 7.08 27.18 27.18 27.51 6.04 11.13 44.68 50.40 73.04 123.44
Total (DL + LL)
54.88
479.15
195.30
.
.
.
Type
Description
DL
Precast beam
DL
Slab
Subtot al
ADL
Asphaltic Layer
SDL
Diaphragm+Deck slab Subtot al
Distribution load
LL
KEL
ma e o a
Sec 3-3 14.08 -27.18 -27.18 -27.51 -6.04 -11.13 -44.68 -50.40 -73.04 -123.44 -195.30
-479.15
-479.15
-
-
-
.
.
.
(m)
.
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 ] Tension
ten-
Nos
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
11
900
300
75%
0%
75%
1516
2
12
600
200
75%
0%
75%
1654
3
total
Profile
12
300
100
75%
0%
75%
1654
35
591.43
197.14
75%
0%
75%
4823
Pa r a b o l i c c u r v e ( Av e r a g e of St r a n d ' s p o si t i o n v e r t i c a l l y f r o m t h e b o t t o m o f b e a m ( V a l ue f o r Y a x i s ) ) 2
Y = A.x + B.x + C 2
where :
A = Constanta : ( (Ymiddle + Yedge)/(L/2) )
A=
0.003428
B = Constanta : ( L x A )
B=
-0.073526
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 ) X + Y = 0.003428 -0.0735265 X + 0.591429 Cable tendon angle : o
tg =
0.006856 X
+
-0.0735265
eccentricity of tendon at middle section Eccentricity [e]
=
Yb - Ys =
322.17
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)
page 4 / 15
PCI Monolith H-125cm ; L-21.75m ; CTC-160cm - RSNI (Rev.04)
Average of Strand's position vertically from the bottom of beam ( Value for Y axis ) 1.20 1.00 0.80 0.60 0.40 0.20 0.00 0
5
10
15
20
25
7.2 Losses of Prestress 1. Losses of Prestress (Short Term) a. Friction 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. The equation for calculating the loss of prestress due to friction is : - + .x Po.e Px = ( AASHTO 1992, Chapt. 9.16.1 ) Where :
80.0%
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
75.0% 70.0%
k = Wobble coefficient x = Distance from tensile point to x section
65.0% 60.0%
Friction and Wooble coeficient for grouting tendon in metal sheating = 0.20 with Seven Wire Strand :
0.00
10.00
20.00
30.00
k = 0.003
Table of calculation due to Friction Profile
% JF
a
b
ten-
Nos
don
strand
Edge
Middle
from UTS
0
0
0
0
0%
0.00000
0
0
0
0
0
0%
0.00000
Prestress force (Px) = % UTS
0.00
10.725
21.45
0.000
0.0%
0.00%
0.0%
0
0.000
0.0%
0.00%
0.0%
0.00000
0
0.000
0.0%
0.00%
0.0% 67.3%
(rad)
0
0
0
0
0%
1
11
900
300
75%
0.00522
-0.1118881
0.223
75.0%
69.46%
2
12
600
200
75%
0.00348
-0.0745921
0.149
75.0%
70.49%
68.3%
3
12
300
100
75%
0.00174
-0.037296
0.075
75.0%
71.55%
69.3%
total
35
591.43
197.14
75%
0.00343
-0.0735265
0.147
75.0%
70.5%
68.3%
b. Anchor set
, . , 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 e longation is resisted by friction just as the initial elongation is resisted by friction. 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 : Cable change angle point
Cable change angle point Anchorage set area
X (effective anchorage set)
Anchorage set area
X (effective anchorage set)
page 5 / 15
PCI Monolith H-125cm ; L-21.75m ; 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 draw in tenNos
From left side
From right side
after anchorage set = % UTS
don
strand
Mpa/mm
mm
X (m)
Px (% UTS)
X (m)
Px (% UTS)
0.00
10.725
21.45
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
11
0.00671
8.00
15.17
68.55%
0.00
0.00%
62.1%
67.64%
67.3%
2
12
0.00584
8.00
16.26
69.34%
0.00
0.00%
63.7%
68.19%
68.3%
3
12
0.00496
8.00
17.65
70.09%
0.00
0.00%
65.2%
68.62%
69.3%
total
35
0.00581
8.00
16.39
69.35%
0.00
0.00%
63.70%
68.17%
68.30%
AVERAGE LOSSES OF PRESTRESS
LOSSES OF PRESTRESS DUE TO ANCHORAGE SET
75.0%
80.0% 75.0%
70.0% 70.0%
68.17%
65.0%
69.61% 69.38% 69.09% 68.30%
65.0% 63.70%
60.0% 55.0%
60.0% 0.00
10.00
20.00
30.00
0.00
5.00
Prestress tendon section
10.00
15.00
20.00
25.00
Prestress tendon section
c. Elastic Shortening ( ES ) Elastic shortening refers to the shortening of the concrete as the postensioning force is applied. As the concrete shorterns, the ten don 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 = concrete stress at the centre of gravity of prestressing tendons due to prestressing force at transfer and the self weight of the member at the section of maximum positive moment 2.61%
Assumption Losses due ES Pi = Pi =
Total prestressing force at release 68 .2% - 2. 61% = 65.56% UTS x nos x Aps =
4215.7004 kN
2
f cir = Pi / A + Pi. ec / I + Mg.ec/I f cir = so,
18.73 N/mm2 ES =
48.52 N/mm2,
percent actual ES losses = Es/fpu
2.61%
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) SH
=
(ACI 318-95, Chapt. 18.6) 1.63% percent actual SH losses = SH/fpu
30.33 N/mm2
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
"days" is the number of days between the end of moist curing and t he application of prestress.In a structures that are not moist cured, Ksh is typiclly based on when the concrete was cast Ksh =
0.64
V/S =
0.08
RH
=
Volume =
3
6.89 m
Surface =
2
84.92 m
70.00
page 6 / 15
PCI Monolith H-125cm ; L-21.75m ; CTC-160cm - RSNI (Rev.04)
e. Creep ( CR )
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 cree p. Loss of prestress due to a creep is nominally propotional to the net permanent compresive stressin the concrete. the n et permanent compressive stress is the initial compressive stress in the concrete due to the prestressing minus th e tensile stress due to self weight and superimposed deadload moments CR CR
= Kcr*(Es/Ec)*(fcir-fcds) =
108.97 N/mm
(ACI 318-95, Chapt. 18.6)
2
percent actual CR losses = CR/fpu
5.86%
Where :
Kcr =
1.60 (for posten sion ed member)
fcir = stress at center point prestress force, initial condition fcir =
18.725 N/mm
2
Msd = Moment due to all superimposed permanent dead loads applied after prestressing Msd =
713.79
kN.m
fcds = Stress in a concrete at the cgs of the tendon due to all superimposed dead load fcds 1 = Msdl.e/I = fcds 2 = Madl.e/Ic =
3.62 N/mm
2
0.41 N/mm
2
component of fcd due to load on the plain beam component of fcd due to load on the composite beam
4.03 N/mm
fcds = fcds 1 + fcds 2 =
2
f. Steel Relaxation ( RE ) 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 ten don at that time. Because of other prestress losses, there is a continual reduction of tendon strss; this causes a reduction in the r elaxation rate. The equation for prestress loss due to relaxation of tendons is : RE = [ Kre - J*(SH+CR+ES) ] *C
17.77 N/mm
RE =
(ACI 318-95, Chapt. 18.6)
2
percent actual RE losses = RE/fpu
0.96%
Where :
Kre =
5000.00 (for 270 grade, low relaxation strand)
J =
0.04 (for 270 grade, low relaxation strand) .
=
or p
pu =
.
RESUME DUE TO SHORT & LONG TERM LOSSES Losses
I. Short Ter m Losses
Section
Elastic Total Anchor set Shortening Losses (%)
x (m)
Friction
II. Long Term Losses
Shrinkage (SH)
Creep (CR)
Steel Total Losses Relaxation (%)
0.00
75.00%
63.70%
61.09%
13.91%
59.46%
53.60%
52.64%
22.36%
0.00
75.00%
63.70%
61.09%
13.91%
59.46%
53.60%
52.64%
22.36%
0.00
75.00%
63.70%
61.09%
13.91%
59.46%
53.60%
52.64%
22.36%
0.00
75.00%
63.70%
61.09%
13.91%
59.46%
53.60%
52.64%
22.36%
10.73
70.53%
68.17%
65.56%
4.97%
63.93%
58.07%
57.11%
13.42%
15.17
69.61%
69.61%
67.00%
2.61%
65.37%
59.51%
58.55%
11.05%
16.26
69.38%
69.38%
66.77%
2.61%
65.14%
59.28%
58.33%
11.05%
17.65
69.09%
69.09%
66.48%
2.61%
64.85%
58.99%
58.04%
11.05%
21.45
68.30%
68.30%
65.69%
2.61%
64.06%
58.20%
57.24%
11.05%
friction Losses equotion : UTS
Friction
LOSSES OF PRESTRESS DIAGRAM
0 > x > 10.73
Anchorset Elastic Shortening (ES)
80.00%
75.00% -+ 0.42% x
Shrinkage (SH)
10.7 > x > 21.45
Creep(CR) Steel Relaxation (SR)
75.00% 70.53% 68.17% 65.00% 63.70%
69.61% 69.38% 69.09%
67.00% 66.77% 66.48% 65.37% 65.14% 64.85% 65.69% 64.06%
58.07% 57.11%
59.51% 59.28% 58.99% 58.55% 58.33% 58.04% 58.20% 57.24%
0 > x > 10.73 52.64% + 0.42% x 10.73 > x > 15.17 57.11% + 0.32% x
x - 15.1675392
16.26 > x > 17.65 58.33% -+ 0.21% x
50.00% 10.73
x - 10.725
15.17 > x > 16.26 58.55% -+ 0.21% x
53.60% 52.64%
0.00
x - 10.725
Long term Losses equotion : 68.30%
65.56% 63.93%
61.09% 59.46%
70.53% + 0.01% x
15.17
16.26
Prestress tendon section
17.65
21.45
x - 16.256324
17.65 > x > 21.45 58.04% -+ 0.21% x
x - 17.6509429
page 7 / 15
PCI Monolith H-125cm ; L-21.75m ; CTC-160cm - RSNI (Rev.04)
7.3 Effective Stress Force Resume Prestressed Force at middle % Losses of prestress
Condition
Cable
%UTS effective prestress
[N/mm ]
[mm ]
[kN]
Asp
stress 2
P
2
short term
9.4%
65.6%
1219
3457.30
4215.70
long term
17.9%
57.1%
1062
3457.30
3672.65
VIII. STRESS AND DEFFLECTION ANALYSIS Beam Segment Length (m)
1
2
3
4
5
6
7.075
7.000
7.075
0.00
0.00
0.00
Additional length at the end of the beam =
0.30
m
7
0.00 Total Length =
8
0.00 21.75
m
8.1 Stress at initial Description
Middle
SEC 1-1
SEC 2-2
SEC 3-3
SEC 4-4
SEC 5-5
x - [m]
Span
0.00
7.08
14.08
21.15
21.15
10.58
[kN.m]
434.19
0.00
386.63
386.63
0.00
0.00
434.19
[kN]
4822.93
4822.93
4822.93
4822.93
4822.93
4822.93
4822.93
%
4%
0%
3%
4%
4%
4%
4%
Pi
[kN]
4539.58
4822.93
4633.36
4538.21
4543.81
4543.81
4539.58
e (eccentricity)
[m]
0.322
-0.061
0.280
0.280
-0.061
-0.061
0.322
Pi.e
[kN.m]
-1463
295
-1298
-1272
278
278
-1463
Moment Net.
[kN.m]
-1028
295
-912
-885
278
278
-1028
2
14.33
15.23
14.63
14.33
14.35
14.35
14.33
2
-13.67
3.92
-12.12
-11.76
3.69
3.69
-13.67
Allow.
2
Moment DL Jacking Force Losses due to friction
Pi / A
[N/mm ]
M / Wa
[N/mm ]
M / Wb Initial Stresses 2
[N/mm ]
SEC 6-6
[N/mm ]
9.72
-2.79
8.61
8.36
-2.63
-2.63
9.72
stress
top ( T )
0.66
19.15
2.51
2.56
18.04
18.04
0.66
-1.7
bot ( B )
24.05
12.44
23.24
22.69
11.72
11.72
24.05
28.8
8.2 Stress at service oa o precas , s a ,
ap ragm an pres ress y
eam
=
> Live load and asphalt by composite Description Moment DL
SEC 1-1
SEC 2-2
SEC 3-3
SEC 4-4
SEC 5-5
x - [m]
Span
0.00
7.08
14.08
21.15
21.15
SEC 6-6 10.58
[kN.m]
1051.48
0.00
936.30
936.30
0.00
0.00
1051.48
Losses due to friction
%
18%
22%
19%
17%
18%
18%
18%
effective prestress P
[kN]
3668.63
3385.28
3574.85
3742.48
3685.15
3685.15
3668.63 -1181.94
P.e
[m]
-1181.94
207.04
-1001.61
-1048.58
225.38
225.38
Moment --- M1
[kN.m]
-130.46
207.04
-65.32
-112.29
225.38
225.38
-130.46
Moment --- M2
[kN.m]
1482.04
0.00
1319.69
1319.69
0.00
0.00
1482.04
2
11.59
11.59
11.59
11.59
11.59
11.59
11.59
2
-1.73
2.75
-0.87
-1.49
3.00
3.00
-1.73
2
1.23
-1.96
0.62
1.06
-2.13
-2.13
1.23
2
3.25
0.00
2.90
2.90
0.00
0.00
3.25
Allow.
2
stress
P/A
[N/mm ]
M 1 / Wa
[N/mm ]
M 1 / Wb
[N/mm ]
M 2 / Wa'
[N/mm ]
M 2 / Wb' Stress at Service 2
[N/mm ]
Note :
( = M2 ) Middle
[N/mm ]
-8.17
0.00
-7.28
-7.28
0.00
0.00
-8.17
slab ( S )
5.72
0.00
5.10
5.10
0.00
0.00
5.72
12.6
top ( T )
13.11
14.35
13.62
13.00
14.59
14.59
13.11
27.0
bot ( B )
4.65
9.64
4.93
5.38
9.47
9.47
4.65
-3.9
Moment DL = Moment due to dead load ( Chapter V - Moment Analysis ) Moment Bal = Moment due to uniform load in balance condition ( Chapter 7.4 - Effective Stress Force ) Moment Net = ( 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 )
page 8 / 15
PCI Monolith H-125cm ; L-21.75m ; 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 = 15.23 MPa
M/Wa = 4.62 MPa
top =
+
Pi/A = 15.23 MPa
19.85 MPa
=
M/Wb = -3.29 MPa
effective prestress =
75% UTS
Pi = eccentricity (ei) =
4822.93 -72.11
Mdl = Mbeam =
bottom
= 11.94 MPa
M = Mdl - Pi.e = kN mm
allow comp at
initial =
allow tension initial
0 kN-m
=
347.79
kN-m
28.80 -1.73
MPa MPa
control allow stress = meet requirement
b. Stress at beam middle section when Prestress is applied : Pi/A = 14.32 MPa
M/Wa = -13.65 MPa
top =
+
Pi/A = 14.32 MPa
=
M/Wb = 9.70 MPa
bottom
effective prestress =
71% UTS
Pi = eccentricity (ei) =
4535.56 322.17
kN mm
434.19
kN-m
Mdl = Mbeam =
0.67 MPa
= 24.02 MPa
M = Mdl - Pi.e = allow comp at
initial =
allow tension initial =
-1027.1 kN-m 28.80 -1.73
MPa MPa
control allow stress = m eet requirement
8. 3. 2. STRESS DIAGRAM AT CONST RUCTION
a. Stress at beam middle section when diaphragm, RC deck is install and finish fresh concreting composite slab Pi/A = 13.31 MPa
M/Wa = -4.08 MPa
top =
+
Pi/A = 13.31 MPa
9.23 MPa
=
M/Wb = 2.90 MPa
bottom
effective prestress =
66% UTS
Pi = eccentricity (ei) =
4215.70 322.17
kN mm
Mdl = Mbeam + Madl =
1051.48
kN-m
= 16.21 MPa
M = Mdl - Pi.e = allow comp at initial = allow tension initial =
-306.71
kN-m
28.80 -1.73
MPa MPa
control allow stress = meet requirement
b. Stress at composite beam middle section due to asphaltic layer: slab =
P/A = 13.31 MPa
M2/Wa'= 0.21 MPa
M1/Wa = -4.08 MPa
+
P/A = 13.31 MPa
top =
+
effective prestress =
66% UTS
Pi = eccentricity (ei) =
4215.70 322.17
kN mm
Mdl = Mbeam + Madl =
1051.48
kN-m
9.44 MPa
=
M2/Wb'= -0.53 MPa
M1/Wb = 2.90 MPa
0.37 MPa
bottom
= 15.67 MPa
M1 = Mdl + Pi.e =
-306.71
kN-m
M2 = Masphalt =
96.50 28.80
kN-m MPa
-1.73
MPa
allow comp at
initial =
allow tension initial
=
control allow stress = meet requirement
page 9 / 15
PCI Monolith H-125cm ; L-21.75m ; 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 =
P/A = 11.59 MPa
M2/Wa'= 3.25 MPa
M1/Wa = -1.75 MPa
+
P/A = 11.59 MPa
top =
+
57% UTS
M2/Wb'= -8.17 MPa
Pi =
3672.65
kN
eccentricity (ei) =
322.17
mm
Mdl = Mbeam + Madl =
1051.48
13.10 MPa
=
M1/Wb = 1.24 MPa
effective prestress =
5.72 MPa
bottom
M1 = Mdl + Pi.e =
-131.76
kN-m
M2 = Masphalt + LL =
1482.04
kN-m
service =
27.00
MPa
allow tension at service =
-3.87
MPa
allow comp at
kN-m
= 4.67 MPa
control allow stress = meet requirement
8.4 Deflection 8.4.1 Chamber due to Prestress Load Deflection on middle section : l
P
ee
pi= [ee+(5/6)(e c-ee)] x (P. l2 /8 Ec Ix) pi=
P
ec
where :
-29.54 mm
P = Prestress force Eci = Modulus Elasticity of Concrete
l/2
l/2
Ixi = Section Inertia l = length of anchor to anchor ee = Distance between c.g of strand and c.g of concrete at end ec = Distance between c.g of strand and c.g of concrete at centre
8.4.2 Deflection at initial, ere ction and service condition (based : PCI handbook 4.6.5 Long-Time Chamber Deflection) Deflection () on simple span structure : where : q = Uniform Load 4
q= (5/384)*q*L /Ec Ix)
P = Point Load
3
l = Beam Span
p= P.l /48 Ec Ix
Deflection calculation table : Estimating long-time cambers and deflections WORKING LOAD
Loading q (kN/m)
P (kN)
1. Due to Prestress force 2. Due to beam weight (DL)
Release (1)
Long time cambers and deflection (2) multipliers Erection multipliers
-29.54
1.80 x (1)
-53.17
2.20 x (1)
9.88
1.85 x (1)
18.29
2.40 x (1)
7.77
-19.65 3. Due to ADL
3.18
Service (3)
-34.88 3.62
7.86
8.95
3.00 x (2)
10.86
-30.40 2.30 x (2)
-22.31 5. due to asphaltic (SDL)
23.72
-41.26
-31.26 4. Due to Composite Overtoping
-64.98
20.58
-9.81
1.73
0.67
-9.15 6. due to Live Load = UDL + KEL
14.40
109.76
8.76
-0.38 Resume of deflection : 1.
Deflection at service
=
2.
Deflection due to Live Load
=
3.
Total deflection with LL
=
-9.15 mm 8.76 mm < allow. deflection L/800 =
26.4375 mm OK
-0.38 mm, chamber upward
page 10 / 15
PCI Monolith H-125cm ; L-21.75m ; 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
2. Beam Ctc 3. Span length / 4
=1600 mm …. Control =5287.5 mm
Thus, Effectif slab width is :
=1600 mm
for slab with fc' = Value =
28.00
MPa
0.85
Partial Rebar: 400 MPa 0 Dia.13 mm
fy = Use As = d=
at tension area b web =
0.00 mm2
170 mm
1190.5 mm
Partial tension rebar ratio : t = As / (bweb x d )
t =
0.00000
t =
t =
0.000
t . fy / fc
Rebar in compresion area is neglected due calculation c = c =
Low Relaxation strand : fpu =
1860
MPa
Strand stress ratio fpu / fpy = dp =
value p = 0.28
0.9
2
3457.3 mm
Aps =
1322.9 mm
Prestress ratio : p = Aps / (beff x dp ) fps = p =
beff =
1600 mm
p = 0.00163344
fpu {1 - p / (p.fpu/fc + d/dp ( t-c)))
1793.5 MPa
fps = p =
p fps/fc
0.105
Resume of Steel Index Requirement (SNI Beton 03-2847-2002 pasal 20.8) p + d/dp ( t-c) 0.36 < 0.105
0.306
<
Under Reinf, Meet With Steel Index Requirement
9.2 Momen Capacity b. eff one
Zone 3
c
i
Cc3 Cc2
Zone 3 Zone 2 a
Tps = Aps . Fps Tps = 6200726.06 N
Cc1
Zone 1
dp
d
strength reduction factor = 0.8 Tps=Aps.fps T = As.fy
COMPOSITE BEAM
Location of Depth of Concrete Compression Block (a) : hi wi Aci=hi.wi Conc. Strength fc' i Zone 4
(mm) 162.83
(mm) 1600
(mm2) 260534.71
3
0.00
335
2
0.00
350
1
0.00
170
Cci=0.85 fc'i.Aci
MPa
Comp (i)
28.00
CIP Slab
N 6200726
-3.913E-11
28.00
CIP Slab
0
163
0
60.00
Beam
0
163
0
60.00
Beam
0
163
Compresion
Point (mm) Point (mm) 81 81.42
Depth of Concrete Compression Block is located at zone 4 a = Tps / ( 0.85 x fc'' slab x beff )
a=
Mn = (Tps (dp - comp. point) + As.fy (d-comp. point) Mn = 6158.2637 kN.m Bridge life time design for 50 year,so Transient act factor = 1 Mn / Mult = Mult = 1x 3,993kN-m
Mn =
1.542
162.83 mm 7697.83 kN.m
>1, Moment capacity m eet with requirement
9.3 Cracking Capacity Stress at bottom girder section due to service load ( bot at service) =
4.65 MPa
Con cr ete flexur al te nsion st ren gt h fr =
5.4 MPa
Crack Moment, Mcr = (bot at service + fr ) Wb.comp + Momen Mcr = Mn / Mcr =
(DL+ADL+LL+I)
4360.35 kN.m 1.412
> 1.2 ---- Cracking Capacity requirement is achieve
page 11 / 15
PCI Monolith H-125cm ; L-21.75m ; CTC-160cm - RSNI (Rev.04)
X. SHEAR ANALYSIS 10.1 Shear calculation based on SNI 03-2847-2002 Alternatif solution to calculated shear on prestress element is use for structure element which have effective prestress above 40% of ultimate tensile stress 40% Ultimate Tensile Strength
= 744
Effective Prestress
= 1062
Section Properties : Ix = 5.496E+10 mm4 Yb = 519.31728 mm Ag =
MPa MPa
Effective Prestress > 40% fpu
Ixcomp = 1.621E+11 mm4 Ybcomp =
894.1 mm
316750 mm2
Load : Effective prestress Pe =
3672.65 kN
Factored Load : qult DL + ADL =
26.80
kN/m
Unfactored Load : q DL + ADL =
18.80
kN/m
qult LL =
25.92
kN/m
q sdl =
1.73
kN/m
Pult LL =
197.57
kN
q DL + ADL =
20.53
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 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. Vn = Vc + Vs Vn = Vu /
where :
Vn = Nominal Shear force Vc = Concrete shear contribution Vs = Shear steel contribution
Vu = Ultimate Shear force = Shear reduction factor = 0.75
Zonafication for shear steel stirup calculation Zone 1
Vn < 0.5 Vc
No need to use stirup
Z on e 2
V n < V c+ [0 .3 5 or ( 75/ 12 00 ) s qr t(f c' )] bw d
R equ ir ed s ti ru p s pa ci ng wi th mi ni mu m sp ac in g :
Zone 3
Vn < Vc+0.33 sqrt(fc') bw d
S ≤ 0.75 H
S ≤ (av.fy) / (0.35 bw)
S ≤ 600mm
S ≤ (av.fy/fpu) (80/Aps) d sqrt(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
page 12 / 15
PCI Monolith H-125cm ; L-21.75m ; CTC-160cm - RSNI (Rev.04)
Shear rebar steel fy = Use Av =
400 MPa 2 leg Dia.13 mm
shear width : bw = 170
mm
650
mm
265.46 mm2
bw-e =
Shear steel requirement calculation table : ecomp dist. d=dp>0.8H Vu Mu m m m kN kN-m
dp(Vu/Mu)
Vc
Vn
Vs
Shear
kN
kN
kN
Zonasi
Use Space mm
use mm
0.1
0.321
1.00
748.91
75.15
1.00
915.84
998.55
82.71
3
545
300
0.3875
0.341
1.00
731.07
287.25
1.00
915.84
974.76
58.92
2
545
300 300
0.775
0.368
1.00
707.02
563.77
1.00
915.84
942.69
26.85
2
545
1.7
0.427
1.05
649.61
1180.52
0.58
587.81
866.15
278.33
3
402
300
2
0.445
1.07
630.99
1367.43
0.49
520.24
841.32
321.08
3
354
300
3
0.500
1.13
568.92
1944.03
0.33
389.63
758.57
368.94
3
324
300
4
0.549
1.17
506.86
2449.23
0.24
320.06
675.81
355.75
3
351
300
5
0.590
1.22
444.80
2883.02
0.19
274.09
593.06
318.97
3
405
300
6
0.625
1.25
382.73
3245.41
0.15
239.28
510.31
271.03
3
490
300
7
0.653
1.28
320.67
3536.39
0.12
210.30
427.55
217.25
3
600
300
8
0.674
1.30
258.60
3755.96
0.09
184.53
344.80
160.28
3
600
300
9
0.688
1.31
196.54
3904.13
0.07
160.46
262.05
101.59
3
600
300
10
0.696
1.32
134.47
3980.89
0.04
137.18
179.30
42.11
2
600
300
10.575
0.697
1.32
98.78
3992.69
0.03
123.90
131.71
7.81
2
600
300
Shear Steel Requirement Position
kN 2000.0 1800.0 1600.0 1400.0 1200.0 1000.0 800.0 600.0 400.0 200.0 0.0
Zona1
Zona2
Zona3
Zona4
Vn= Vu/f
beam section point
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
10.575
10.575
35
Shear Rebar configuration
total shear rebar per half span (row) =
35
total shear rebar per span (row) =
70
page 13 / 15
PCI Monolith H-125cm ; L-21.75m ; CTC-160cm - RSNI (Rev.04)
10.2 Horisontal Shear Width of contact surface area
bv =
200 mm
d=
1216 mm
Effective Height =
fy = Use
0.75 400 MPa 2 leg Dia.13 mm
Area horisontal Shear Steel
Avh =
Horisontal Shear steel Spacing
s= v =
Horisontal Shear steel ratio
265.46 mm2 300 mm 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 < Vnh < 350 bv.d Vult = Ultimate shear due to superimposed DL + LL Vult = Vnh =
522.00 kN
420.37 kN RESUME:
3.5 bv d =
851.20 kN
Shear horisontal : OK
Minimal Use : bys =
200 mm
Spacing =
Avh = 50 by.s / fy Avh =
Max. Spacing =
172.375 mm2/m
1540.04 mm or
4 tweb = 680 mm
300.00 mm
min no. Spacing =
71 @ 2D13 for shear horisontal / span
Resume = additional shear horizontal required
XI. END BLOCK DESIGN Block Anchor dimension type 7
a
b
dia hole
(mm)
(mm)
(mm)
165
165
51
Block Area Concrete Area A (mm ) A1 (mm ) A2 (mm ) sqrt(A2/A1) 25182.18
27225
1625000
7.73
70225
2275000
5.69
. 19
265
265
84
64683.23
.
SNI 03-2847-2002 Pasal 11.3.2 (Anchorage Zone) Maximum strand =
12
Anchor Block type =
12
Load factor = Reduction factor () =
1.2
Strand
0.85
1. End Bearing Ultimate Point Load Pu = min (1.2 x nStrand x Astrand x %JF x fpu , nstrand x Astrand x 96% x fpu) Pu =
1984.3
End Bearing stress : comp = comp =
kN Nominal concrete comp. : Pu / A 46.03
fci = MPa
48.00 Mpa
min(2, sqrt(A2/A1)) =
2.0 Nominal fci = x 0.7 x fci x min(2,sqrt (A2/A1)) > comp = Nominal fci = 57.12 46.03 MPa
ten-
Nos
Anchor
sheath
Ult. Point
Block
End Bearing
don
strand
Height
hole
Load
Area
Stress
Nominal comp. fci
(Pu) kN
(A) mm2
(EBS=Pu/A) Mpa
Mpa
63
1818.93
43107.75
42.20
57.12
EBS < Nominal Compresion
43107.75
46.03
57.12
EBS < Nominal Compresion
43107.75
46.03
57.12
EBS < Nominal Compresion
( ai ) mm 0
0
0
0
0
0
1
11
215
2
12
215
63
1984.29
3
12
215
63
1984.29
Remark
page 14 / 15
PCI Monolith H-125cm ; L-21.75m ; CTC-160cm - RSNI (Rev.04)
2. Stirrup and Spalling Reinforcement Load factor = Reduction factor () =
0.85
1.2
fy =
400
MPa
Bursting Steel Diameter closed stirup =
13 mm
Stirup Area =
132.7 mm2
ten-
Nos
Anchor
sheath
Jacking
Bursting
End
don
strand
Height
hole
Force
Area (Abs)
Bearing (EBS)
kN
mm2
( ai ) mm
EBS/0.7
(fcc'-fci)/4.1
fl / 0.5 fy
fcc'
fl
p
Mpa
Mpa
Mpa
sp (mm)
0
0
0
0
0
0
1
11
215
63
1515.7791
43107.75
35.16
59.10
2.7
1.35%
182.5
2
12
215
63
1653.5772
43107.75
38.36
64.47
4.0
2.01%
123.0
3
12
215
63
1653.5772
43107.75
38.36
64.47
4.0
2.01%
123.0
total
35
Anchor Zone Stirrup JF Load = Ult. JF =
4822.93 kN
a1 =
645.00 mm
5787.52 kN
H=
1250 mm
T bursting = 0.25 Ult.JF (1-a1/H)
d bursting = 0.5(h-2e)
T bursting = 700.28994 kN
d bursting = 552.888713 mm
Diameter closed stirup = No. Leg of stirrup = Stirup Area =
13 mm 4 leg 530.9 mm2
Anchor Stirup Rebar = T bursting / 0.5 fy Anchor Stirup Rebar = use no of stirup =
3501.4 mm2 7 pcs
Spalling Rebar Spalling Force = 2% JF Spalling Force = Diameter closed stirup = Stirup Area = use no of stirup =
96.5 kN 13 mm 132.7 mm2 4 pcs
page 15 / 15
PT WIJAYA KARYA BETON
TECHNICAL CALCULATION PCI GIRDER MONOLITH FOR HIGHWAY BRIDGES Project Product Job no Rev. No.
: : : :
TOLL SURABAYA ‐ GRESIK PCI Girder Monolith H‐125cm ; L‐22.30m ; CTC ‐160cm ; fc' 50MPa 13014 D 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, 1
st
nd
& 2 floor
Jl. Jatiwaringin no. 54, Pondok Gede ‐ Bekasi Ph: +62‐21‐8497 ‐3363 fax : +62‐21‐8497 ‐3391 www.wika‐beton.co.id
PT WIJAYA KARYA BETON
TECHNICAL CALCULATION APPROVAL PCI GIRDER MONOLITH FOR HIGHWAY BRIDGES TOLL SURABAYA ‐ GRESIK PCI Girder Monolith H‐125cm ; L‐22.30m ; CTC ‐160cm ; fc' 50MPa Job no. : 13014 D Rev. : 04
Approved by :
Consultan / Owner
Approved by : 18 Juni 2013
Checked by 18 Juni 2013
Design by : 18 Juni 2013
Ir. Achmad Arifin Technical Manager
Ignatius Harry S., S.T. Chief o f Technical
Suko Technical Staff
PCI Monolith H-125cm ; L-22.30m ; CTC-160cm - RSNI (Rev.04)
RESUME OF PCI GIRDER MONOLITH TECHNICALLY CALCULATION 1. BEAM SPECIFICATION
Span Beam Height ( H )
=
21.70 m (beam length
=
1250 mm
Distance ctc of beam ( s )
=
1600 mm
Slab thickness
=
200 mm
Beam Compressive strength
=
50 MPa
Slab Compressive strength
=
28 MPa
Bridge life time
=
50 years
=
22.30 m)
Segment Arr angement
Beam Segment Length (m)
1
2
3
4
5
6
7
7.350
7.000
7.350
0.00
0.00
0.00
0.00
Additional length at the end of beam
=
0.30
m
Total length of the beam
=
22.30
m
Total beam weight
=
22.09
ton
12.7
mm (PC Strand 270 grade, low relaxation)
2. STRESSING
Nos of PC Strand
=
strand
30
Strand configuration No.
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
=
15.87%
at middle
0
0
0
0
fc initial
=
80.0%
fc'
0
0
0
0
1
11
600
250
2
19
300
100
total
30
410.00
155.00
3. LOADING 1. Dead Load
a. Precast Beam
=
9.30
kN/m
b. Slab
=
7.94
kN/m
Slab thickness =
c. Deck Slab
=
2.22
kN/m
d. Asphalt
=
1.73
kN/m
e. Diaphragm
=
6.68
kN
4
pcs
No. Diaphragm
200
mm
Deck slab thickness =
70
mm
Asphalt thickness =
50
mm
for 1 diaphragm equivalent load =
0.82
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)
=
b. Knife Edge Load (KEL)
=
c. Distribution Factor (DF)
=
1.40 for span length <= 50m 49.00 kN/m 1.00
d. Distribution Load q=
9.00 kN/m2
9.00 kN/m2
For Span <= 30m
9.00 x(0,5+15/span)kN/m2
For Span > 30m
e. Live Load Distribution load : Line Load
:
q' = DF x q x s p' = DF x DLA x KEL x s
CALCULATION RESUME
= =
14.40 kN/m 109.76 kN
PCI Monolith H-125cm ; L-22.30m ; 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
=
100.88
kN
b. Additional Dead Load
=
137.94
kN
c. Live Load
=
266.00
kN
Ultimate support reaction =
788.97
kN
5. CONTROL OF BEAM STRESSES 1. Initial Condition
Middle span position top stress =
-0.31 MPa
required
>
-1.58 MPa
bottom stress =
18.39 MPa
required
<
24.00 MPa
top stress =
11.14 MPa
<
22.50 MPa
bottom stress =
1.44 MPa
>
-3.54 MPa
2. Service Condition
Middle span position required required
6. CONTROL OF BEAM DEFLECTION
De f l e c t i o n a t t h e m i d d l e of b e a m sp a n
1. Chamber due stressing initial
=
-21.31
mm
=
-
2. Deflection at composite DL
=
-11.00
3. Deflection due live load
=
9.43
mm,required
4. Total deflection at service
=
-1.57
mm
. mm = 27.13 mm
7. MOMENT AND CRACKING CAPACITY OF BEAM
Moment Capacit y requir ement :
Mult = 1,2*(Beam+Diaphragm+Deck Slab)+1,3*Slab+2*Asphaltic+1,8*(LL+I) Mn
=
4280.18 kN.m
=
5539.85 kN.m
Ratio, Mn / Mu (>1)
=
Cracking Capacit y requir ement :
Mcrack Mn / Mcr
= =
4043.71 kN.m 1.37
CALCULATION RESUME
1.29
PCI Monolith H-125cm ; L-22.30m ; CTC-160cm - RSNI (Rev.04)
TECHNICAL CALCULATION OF PCI MONOLITH BEAM FOR HIGHWAY BRIDGES SPAN L = 21.70 M I. DATA
0.3
L=
21.70 M
0.3
22.30 m
Beam length
=
Beam spacing (s)
=
1600 mm
( edge anchor to e dge an ch or :
Concrete Slab thickness (CIP)
=
200 mm
Asphalt thickness
=
50 mm
Deck slab thickness
=
70 mm
22.00
m)
A
Cross Section H
=
1250
mm
tfl-1
=
75
mm
A
=
400
mm
tfl-2
=
75
mm
B
=
700
mm
tfl-3
=
100
mm
tweb =
220
mm
tfl-4
=
125
mm
tfl-1 tfl-2 tweb
H
tfl-3 tfl-4
II. MATERIAL B
2.1 Concrete Beam
Slab
fc' =
50.0
28.0
fc'i =
40.0
[N/mm ]
0.6 * fc'i =
24.0
[N/mm ]
Tensile 0.25 * Sqrt(fc'i) = Allowable stress at service ………. ( SNI T-1 2-20 04 )
1.6
[N/mm ]
Compressive strength at service at initial
80% fc'
2
[N/mm ] 2
Allowable stress Allowable stress at initial ………… ( SNI T-1 2-20 04 ) Compressive
2
2
0.45 * fc' =
22.5
12.6
[N/mm ]
0.5 * Sqrt(fc') =
3.5
2.6
[N/mm ]
wc =
2500.0
2500.0
[kg/m ]
*0.043*sqrt(fc') =
38007.0
28441.8
[N/mm ]
*0.043*sqrt(fci') =
33994.5
[N/mm ]
f r = 0.7*sqrt(fc') =
4.9
[N/mm ]
Compressive Tensile
2
Modulus of elasticity Concrete unit weight Ec = wc Eci = wc
1.5
1.5
3
2 2
Concrete flexural tension strength (fr) 2
2.2 Prestressing Cable [Uncoated stress relieve seven wires strand] ( ASTM A 416 Grade 270 Low Relaxation or JIS G 3536 ) - Diameter strand
dia
:
12.7
[mm]
- Eff. Section area
Ast
:
98.78
[mm ]
- Modulus of elasticity
Es
: 1.93E+05
[N/mm ]
- Ultimate tensile strength
fu
:
1860
[N/mm ]
- Diameter
dia
:
13
[mm]
- Eff. Section area
Ast
:
132.73
[cm ]
- Modulus of elasticity
Es
: 2.10E+05
[N/mm ]
- Yield stress
fy
:
[N/mm ]
2
2 2
2.3 Steel Reinforcement
400
2
2 2
page 1 / 15
PCI Monolith H-125cm ; L-22.30m ; CTC-160cm - RSNI (Rev.04)
III. SECTION ANALYSIS Remark : Ep 1 = Ep 2 =
2
38007
[N/mm ] [Girder]
28442
[N/mm ] [Slab]
3
2
2
5
Ya'
4 Ya
n = Ep 2 / Ep 1 n=
3
0.75
1
2
Yb
Yb'
1
Base Line
PRECAST BEAM
COMPOSITE BEAM
3.1 Precast Beam [in mm ] Zone
Section
Width
Area
Level
2
Yb
Area*Yb 3
2
Io
Ix
Area*d 4
4
4
Height
Bottom
Upper
mm
mm
mm
mm
mm
mm
mm
6
0.0
200.0
200.0
0
1250
1250.0
0
0
0
0
5
75.0
400.0
400.0
30000
1175
1212.5
36375000
14062500
13699803379
13713865879
4
75.0
220.0
400.0
23250
1100
1141.1
26531250
10592238
8493079360
8503671598
3
875.0
220.0
220.0
192500
225
662.5
1275 31250
122 81901 042
30 44804 457
15 32670 5499
2
100.0
700.0
220.0
46000
125
166.3
7650000
34855072
6312023113
6346878186
1
125.0
700.0
700.0
87500
0
62.5
5468750
113932292
19678538941
19792471233
Total
1250.0
536.7
2 03 55 62 50
1 24 55 34 31 44
5 12 28 24 92 50
6 36 83 59 23 94
Level
Yb
Area*Yb
Io
Area*d
mm
mm
mm
mm
mm
mm
68 82424 2775
379250
3.2 Composite Beam [in mm ] Zone
2 1
Height
Width
Area 2
3
2
4
Ix
4
4
Section
Bottom
Upper
mm
200.0
1197.3
1197.3
239466
1320
1420.0
3400 41823
79822 0242. 5
6 8026 02253 3
70.0
187.1
187.1
13096
1250
1285.0
16828104
5347452.015
2074277999
2079625451
1250.0
700.0
400.0
379250
0
536.7
2035 56250
636 83592 394
4653 26556 17
1. 102 16E +1 1
.
o a
.
.
+
.
+
3.3 R e s u m e [in mm ] 2
Description
Area (mm )
Precast Beam Composite Beam
[composite]
Ya (mm)
Yb (mm)
4
Ix (mm )
3
Wa (mm )
3
Wb (mm )
379250
713
536.7
63683592394
89284452
118650262
631812
633
887.0
1811 20116 238
286 1361 97
2041 90747
[precast]
363
498973168
IV. LOADING 4.1 Dead Load a. Precast Beam
q1 = Ac precast girder x q1 =
b. Slab
0.080 x
[t/m'] =
9.30
[kN/m']
0.810
[t/m'] =
7.94
[kN/m']
0.227
[t/m'] =
2.22
[kN/m']
0.176
[t/m'] =
1.73
[kN/m']
6.68
[kN']
s
2.40 =
q4 = Ac asphaltic x q4 =
e. Diaphragm
0.095 x
0.948
conc. slab
2.40 =
q3 = Ac deck slab x q3 =
d. Asphaltic
0.338 x
conc. Precast
2.50 =
q2 = Ac slab CIP x q2 =
c. Deck slab
0.379 x
s
2.20 =
p
= Vol diaph with 0.20m thickness x
p
=
0.284 x
2.40 =
0.681 note :
Number of diaph = Diaph. placement Location
4
diaph
[ton'] =
from kg to N, multiply by 9.8060
pcs
1
2
3
4
0.00
7.23
14.47
21.70 0.00
Support Va
6.68
4.45
2.23
Mid Moment
0.00
24.14
24.14
Total Diaphragma Flexural Moment at Middle Span eqivalen load q diaphragm
q5=
0.00 48.29
kN.m
0.82
[kN/m']
page 2 / 15
PCI Monolith H-125cm ; L-22.30m ; 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 Item P1 kN Load 225 Impact 1.3 LL + I 292.5 kN Distance 6.850 m Va 200.17 kN Va kN M max kN-m DF = S/3.4 M x DF kN-m
P2 225 1.3 292.5 10.850 146.25
P3 50 1.3 65 15.850 17.52
M.max di x = 10.850 m DLA = 30% Impact = 1 + DLA = 1.3
363.94 2778.75 0.47 1307.65
50kN
225kN
225kN
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 :
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) DLA = 1 + 0,3
50 < Span < 90 m
=
1.30
b. Knife Edge Load (KEL)
=
49.00
c. Distribution Factor (DF)
=
1.00
Span >= 90 m
[kN/m']
d. Distribution Load q =
9.00 kN/m
q = 9 kN/m q = 9 x(0,5+15/span)kN/m
which :
for
Span <= 30 m Span > 30 m
e. Live load Distribution load, qudl = DF x q x s = 1.00 x 9.00 KEL, PKEL = DF x DLA x KEL x s =
1.00
M.max at 0.5 span = Va = M LL =
x
1.40
10.850 m
x x
1.60 49.00
x
1.60
=
14.40
[kN/m']
=
109.76
[kN']
211.12 kN 1 44 3. 05 k N. m
RESUME : Moment force cause by D Loading is bigger than Truck Loading
page 3 / 15
PCI Monolith H-125cm ; L-22.30m ; 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
7.35
14.35
21.70
21.70
10.85
Precast beam
547.25
0.00
490.31
490.31
0.00
0.00
547.25
Subtot al
547.25
0.00
490.31
490.31
0.00
0.00
547.25
Slab
467.53
0.00
418.88
418.88
0.00
0.00
467.53
ADL
Asphaltic Layer
101.59
0.00
91.02
91.02
0.00
0.00
101.59
SDL
Diaphragm+Deck Slab
179.19
0.00
160.55
160.55
0.00
0.00
179.19
748.31
0.00
670.44
670.44
0.00
0.00
748.31
Type
Description
DL DL
Subtot al
LL
Distribution load
847.60
0.00
759.40
759.40
0.00
0.00
847.60
KEL
595.45
0.00
533.49
533.49
0.00
0.00
595.45
Subtot al
1443.05
0.00
1292.89
1292.89
0.00
0.00
1443.05
Total (DL + LL)
2738.61
0.00
2453.63
2453.63
0.00
0.00
2738.61
Ultimate total
4280.18
0.00
3834.79
3834.79
0.00
0.00
4280.18
Sec 4-4 21.70 -100.88 -100.88 -86.18 -18.73 -33.03 -137.94 -156.24 -109.76 -266.00
Sec 5-5 21.70 -100.88 -100.88 -86.18 -18.73 -33.03 -137.94 -156.24 -109.76 -266.00
Sec 6-6 10.85 0.00 0.00 0.00 0.00 0.00 0.00 0.00 54.88 54.88 54.88
(m)
Ultimate total = 1,2*(Beam+Diaphragm+Deck Slab)+1,3*Slab+2*Asphaltic+1,8*(LL+I) VI. SHEAR ANALYSIS [in kN] Mid
Subtot al
span 0.00 0.00 0.00 0.00 0.00 0.00 0.00 54.88 54.88
Sec 1-1 0.00 100.88 100.88 86.18 18.73 33.03 137.94 156.24 109.76 266.00
Sec 2-2 7.35 32.54 32.54 27.80 6.04 10.66 44.50 50.40 72.58 122.98
Total (DL + LL)
54.88
504.81
200.02
.
.
.
Type
Description
DL
Precast beam
DL
Slab
Subtot al
ADL
Asphaltic Layer
SDL
Diaphragm+Deck slab Subtot al
Distribution load
LL
KEL
ma e o a
Sec 3-3 14.35 -32.54 -32.54 -27.80 -6.04 -10.66 -44.50 -50.40 -72.58 -122.98 -200.02
-504.81
-504.81
-
-
-
.
.
.
(m)
.
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 ] Tension
ten-
Nos
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
11
600
250
75%
0%
75%
1516
2
total
Profile
19
300
100
75%
0%
75%
2618
30
410.00
155.00
75%
0%
75%
4134
Pa r a b o l i c c u r v e ( Av e r a g e of St r a n d ' s p o si t i o n v e r t i c a l l y f r o m t h e b o t t o m o f b e a m ( V a l ue f o r Y a x i s ) ) 2
Y = A.x + B.x + C 2
where :
A = Constanta : ( (Ymiddle + Yedge)/(L/2) )
A=
0.002107
B = Constanta : ( L x A )
B=
-0.046364
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 ) X + Y = 0.002107 -0.0463636 X + 0.410000 Cable tendon angle : o
tg =
0.004215 X
+
-0.0463636
eccentricity of tendon at middle section Eccentricity [e]
=
Yb - Ys =
381.73
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)
page 4 / 15
PCI Monolith H-125cm ; L-22.30m ; CTC-160cm - RSNI (Rev.04)
Average of Strand's position vertically from the bottom of beam ( Value for Y axis ) 0.80 0.60 0.40 0.20 0.00 0
5
10
15
20
25
7.2 Losses of Prestress 1. Losses of Prestress (Short Term) a. Friction 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. The equation for calculating the loss of prestress due to friction is : - + .x Po.e Px = ( AASHTO 1992, Chapt. 9.16.1 ) Where :
80.0%
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
75.0% 70.0%
k = Wobble coefficient x = Distance from tensile point to x section
65.0% 60.0%
Friction and Wooble coeficient for grouting tendon in metal sheating = 0.20 with Seven Wire Strand :
0.00
10.00
20.00
30.00
k = 0.003
Table of calculation due to Friction strand
Edge
Middle
from UTS
0
0
0
0
0%
0.00000
0
0
0
0
0
0%
0.00000
0
0%
0.00000
0
0
% JF
b
Nos
don
0
Profile
a
ten-
Prestress force (Px) = % UTS
0.00
11
22.00
0.000
0.0%
0.00%
0.0%
0
0.000
0.0%
0.00%
0.0%
0
0.000
0.0%
0.00%
0.0%
(rad)
0
0
0
0
0%
0.00000
0
0.000
0.0%
0.00%
0.0%
1
11
600
250
75%
0.00289
-0.0636364
0.127
75.0%
70.74%
68.4%
2
19
300
100
75%
0.00165
-0.0363636
0.073
75.0%
71.52%
69.2%
total
30
410.00
155.00
75%
0.00211
-0.0463636
0.093
75.0%
71.2%
68.9%
b. Anchor set
, . , 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 e longation is resisted by friction just as the initial elongation is resisted by friction. 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 : Cable change angle point
Cable change angle point Anchorage set area
X (effective anchorage set)
Anchorage set area
X (effective anchorage set)
page 5 / 15
PCI Monolith H-125cm ; L-22.30m ; 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 draw in tenNos
From left side
From right side
after anchorage set = % UTS
don
strand
Mpa/mm
mm
X (m)
Px (% UTS)
X (m)
Px (% UTS)
0.00
11
22.00
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
11
0.00554
8.00
16.69
69.56%
0.00
0.00%
64.1%
68.37%
68.4%
2
19
0.00491
8.00
17.74
70.10%
0.00
0.00%
65.2%
68.67%
69.2%
total
30
0.00514
8.00
17.36
69.90%
0.00
0.00%
64.79%
68.56%
68.92%
AVERAGE LOSSES OF PRESTRESS
LOSSES OF PRESTRESS DUE TO ANCHORAGE SET
75.0%
80.0% 75.0%
70.0%
70.04% 69.82%
70.0%
68.56%
65.0%
65.0%
68.92%
64.79%
60.0% 55.0%
60.0% 0.00
10.00
20.00
30.00
0.00
5.00
Prestress tendon section
10.00
15.00
20.00
25.00
Prestress tendon section
c. Elastic Shortening ( ES ) Elastic shortening refers to the shortening of the concrete as the postensioning force is applied. As the concrete shorterns, the ten don 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 = concrete stress at the centre of gravity of prestressing tendons due to prestressing force at transfer and the self weight of the member at the section of maximum positive moment 2.25%
Assumption Losses due ES Pi = Pi =
Total prestressing force at release 68 .6% - 2. 25% = 66.31% UTS x nos x Aps =
3655.1803 kN
2
f cir = Pi / A + Pi. ec / I + Mg.ec/I f cir = so,
14.72 N/mm2 ES =
41.79 N/mm2,
percent actual ES losses = Es/fpu
2.25%
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) SH
=
(ACI 318-95, Chapt. 18.6) 1.63% percent actual SH losses = SH/fpu
30.32 N/mm2
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
"days" is the number of days between the end of moist curing and t he application of prestress.In a structures that are not moist cured, Ksh is typiclly based on when the concrete was cast Ksh =
0.64
V/S =
0.09
RH
=
Volume =
3
8.46 m
Surface =
2
89.30 m
70.00
page 6 / 15
PCI Monolith H-125cm ; L-22.30m ; CTC-160cm - RSNI (Rev.04)
e. Creep ( CR )
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 cree p. Loss of prestress due to a creep is nominally propotional to the net permanent compresive stressin the concrete. the n et permanent compressive stress is the initial compressive stress in the concrete due to the prestressing minus th e tensile stress due to self weight and superimposed deadload moments CR CR
= Kcr*(Es/Ec)*(fcir-fcds)
84.78 N/mm
=
(ACI 318-95, Chapt. 18.6)
2
percent actual CR losses = CR/fpu
4.56%
Where :
Kcr =
1.60 (for posten sion ed member)
fcir = stress at center point prestress force, initial condition fcir =
14.721 N/mm
2
Msd = Moment due to all superimposed permanent dead loads applied after prestressing Msd =
748.31
kN.m
fcds = Stress in a concrete at the cgs of the tendon due to all superimposed dead load fcds 1 = Msdl.e/I = fcds 2 = Madl.e/Ic =
3.88 N/mm
2
0.41 N/mm
2
component of fcd due to load on the plain beam component of fcd due to load on the composite beam
4.29 N/mm
fcds = fcds 1 + fcds 2 =
2
f. Steel Relaxation ( RE ) 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 ten don at that time. Because of other prestress losses, there is a continual reduction of tendon strss; this causes a reduction in the r elaxation rate. The equation for prestress loss due to relaxation of tendons is : RE = [ Kre - J*(SH+CR+ES) ] *C
18.59 N/mm
RE =
(ACI 318-95, Chapt. 18.6)
2
percent actual RE losses = RE/fpu
1.00%
Where :
Kre =
5000.00 (for 270 grade, low relaxation strand)
J =
0.04 (for 270 grade, low relaxation strand) .
=
or p
pu =
.
RESUME DUE TO SHORT & LONG TERM LOSSES Losses
I. Short Ter m Losses
Section
Elastic Total Anchor set Shortening Losses (%)
x (m)
Friction
II. Long Term Losses
Shrinkage (SH)
Creep (CR)
Steel Total Losses Relaxation (%)
0.00
75.00%
64.79%
62.55%
12.45%
60.92%
56.36%
55.36%
19.64%
0.00
75.00%
64.79%
62.55%
12.45%
60.92%
56.36%
55.36%
19.64%
0.00
75.00%
64.79%
62.55%
12.45%
60.92%
56.36%
55.36%
19.64%
0.00
75.00%
64.79%
62.55%
12.45%
60.92%
56.36%
55.36%
19.64%
0.00
75.00%
64.79%
62.55%
12.45%
60.92%
56.36%
55.36%
19.64%
11.00
71.23%
68.56%
66.31%
4.92%
64.68%
60.13%
59.13%
12.11%
16.69
70.04%
70.04%
67.79%
2.25%
66.16%
61.60%
60.60%
9.43%
17.74
69.82%
69.82%
67.57%
2.25%
65.94%
61.38%
60.38%
9.43%
22.00
68.92%
68.92%
66.68%
2.25%
65.05%
60.49%
59.49%
9.43%
friction Losses equotion : UTS
Friction
LOSSES OF PRESTRESS DIAGRAM
0 > x > 11.00
Anchorset Elastic Shortening (ES)
80.00%
75.00% -+ 0.34% x
Shrinkage (SH)
11 > x > 22.00
Creep(CR) Steel Relaxation (SR)
75.00%
75.00% 71.23% 68.56%
65.00%
64.79%
64.79%
62.55% 60.92%
62.55% 60.92%
56.36% 55.36%
66.31% 64.68% 60.13% 59.13%
70.04% 69.82%
68.92% 67.79% 67.57% 66.16% 65.94% 66.68% 65.05% 61.60% 61.38% 60.60% 60.38% 60.49% 59.49%
71.23% + 0.03% x
x - 11
Long term Losses equotion : 0 > x > 0.00 55.36% #DIV/0! 0 > x > 11.00 55.36% + 0.34% x
x-0
11 > x > 16.69
56.36% 55.36%
59.13% + 0.26% x
x - 11
16.69 > x > 17.74 60.60% -+ 0.21% x
50.00% 0.00
0.00
11.00
16.69
Prestress tendon section
17.74
22.00
x - 16.6946322
17.74 > x > 22.00 60.38% -+ 0.21% x
x - 17.7390504
page 7 / 15
PCI Monolith H-125cm ; L-22.30m ; CTC-160cm - RSNI (Rev.04)
7.3 Effective Stress Force Resume Prestressed Force at middle % Losses of prestress
Condition
Cable
%UTS effective prestress
[N/mm ]
[mm ]
[kN]
Asp
stress 2
P
2
short term
8.7%
66.3%
1233
2963.40
3655.18
long term
15.9%
59.1%
1100
2963.40
3259.02
VIII. STRESS AND DEFFLECTION ANALYSIS Beam Segment Length (m)
1
2
3
4
5
6
7.350
7.000
7.350
0.00
0.00
0.00
Additional length at the end of the beam =
0.30
m
7
0.00 Total Length =
8
0.00 22.30
m
8.1 Stress at initial Description
Middle
SEC 1-1
SEC 2-2
SEC 3-3
SEC 4-4
SEC 5-5
x - [m]
Span
0.00
7.35
14.35
21.70
21.70
10.85
[kN.m]
547.25
0.00
490.31
490.31
0.00
0.00
547.25
[kN]
4133.94
4133.94
4133.94
4133.94
4133.94
4133.94
4133.94
%
4%
0%
3%
4%
3%
3%
4%
Pi
[kN]
3929.21
4133.94
3995.25
3932.44
3945.73
3945.73
3929.21
e (eccentricity)
[m]
0.382
0.134
0.356
0.356
0.134
0.134
0.382
Pi.e
[kN.m]
-1500
-552
-1422
-1400
-527
-527
-1500
Moment Net.
[kN.m]
-953
-552
-932
-909
-527
-527
-953
2
10.36
10.90
10.53
10.37
10.40
10.40
10.36
2
-10.67
-6.19
-10.43
-10.18
-5.91
-5.91
-10.67
Allow.
Moment DL Jacking Force Losses due to friction
Pi / A
[N/mm ]
M / Wa
[N/mm ] 2
M / Wb Initial Stresses 2
[N/mm ]
SEC 6-6
[N/mm ]
8.03
4.66
7.85
7.66
4.44
4.44
8.03
stress
top ( T )
-0.31
4.71
0.10
0.18
4.50
4.50
-0.31
-1.6
bot ( B )
18.39
15.56
18.39
18.03
14.85
14.85
18.39
24.0
8.2 Stress at service oa o precas , s a ,
ap ragm an pres ress y
eam
=
> Live load and asphalt by composite Description Moment DL
SEC 1-1
SEC 2-2
SEC 3-3
SEC 4-4
SEC 5-5
x - [m]
Span
0.00
7.35
14.35
21.70
21.70
SEC 6-6 10.85
[kN.m]
1193.97
0.00
1069.73
1069.73
0.00
0.00
1193.97
Losses due to friction
%
16%
20%
17%
15%
15%
15%
16%
effective prestress P
[kN]
3256.19
3051.45
3190.14
3306.89
3282.39
3282.39
3256.19 -1243.00
P.e
[m]
-1243.00
-407.80
-1135.43
-1176.98
-438.66
-438.66
Moment --- M1
[kN.m]
-49.02
-407.80
-65.70
-107.25
-438.66
-438.66
-49.02
Moment --- M2
[kN.m]
1544.64
0.00
1383.90
1383.90
0.00
0.00
1544.64
2
8.59
8.59
8.59
8.59
8.59
8.59
8.59
2
-0.55
-4.57
-0.74
-1.20
-4.91
-4.91
-0.55
2
0.41
3.44
0.55
0.90
3.70
3.70
0.41
2
3.10
0.00
2.77
2.77
0.00
0.00
3.10
Allow.
2
stress
P/A
[N/mm ]
M 1 / Wa
[N/mm ]
M 1 / Wb
[N/mm ]
M 2 / Wa'
[N/mm ]
M 2 / Wb' Stress at Service 2
[N/mm ]
Note :
( = M2 ) Middle
[N/mm ]
-7.56
0.00
-6.78
-6.78
0.00
0.00
-7.56
slab ( S )
5.40
0.00
4.84
4.84
0.00
0.00
5.40
12.6
top ( T )
11.14
4.03
10.63
10.17
3.68
3.68
11.14
22.5
bot ( B )
1.44
12.03
2.37
2.72
12.29
12.29
1.44
-3.5
Moment DL = Moment due to dead load ( Chapter V - Moment Analysis ) Moment Bal = Moment due to uniform load in balance condition ( Chapter 7.4 - Effective Stress Force ) Moment Net = ( 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 )
page 8 / 15
PCI Monolith H-125cm ; L-22.30m ; 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 = 10.90 MPa
M/Wa = -5.87 MPa
top =
+
Pi/A = 10.90 MPa
5.03 MPa
=
M/Wb = 4.42 MPa
effective prestress =
75% UTS
Pi = eccentricity (ei) =
4133.94 126.73
Mdl = Mbeam =
bottom
= 15.32 MPa
M = Mdl - Pi.e = kN mm
allow comp at
initial =
allow tension initial
0 kN-m
=
-523.91
kN-m
24.00 -1.58
MPa MPa
control allow stress = meet requirement
b. Stress at beam middle section when Prestress is applied : Pi/A = 10.35 MPa
M/Wa = -10.66 MPa
top =
+
Pi/A = 10.35 MPa
=
M/Wb = 8.02 MPa
bottom
effective prestress =
71% UTS
Pi = eccentricity (ei) =
3926.37 381.73
kN mm
547.25
kN-m
Mdl = Mbeam =
-0.30 MPa
= 18.37 MPa
M = Mdl - Pi.e = allow comp at
initial =
allow tension initial =
-951.6 kN-m 24.00 -1.58
MPa MPa
control allow stress = m eet requirement
8. 3. 2. STRESS DIAGRAM AT CONST RUCTION
a. Stress at beam middle section when diaphragm, RC deck is install and finish fresh concreting composite slab Pi/A = 9.64 MPa
M/Wa = -2.25 MPa
top =
+
Pi/A = 9.64 MPa
7.38 MPa
=
M/Wb = 1.70 MPa
bottom
effective prestress =
66% UTS
Pi = eccentricity (ei) =
3655.18 381.73
kN mm
Mdl = Mbeam + Madl =
1193.97
kN-m
= 11.33 MPa
M = Mdl - Pi.e = allow comp at initial = allow tension initial =
-201.33
kN-m
24.00 -1.58
MPa MPa
control allow stress = meet requirement
b. Stress at composite beam middle section due to asphaltic layer: slab =
P/A = 9.64 MPa
M2/Wa'= 0.20 MPa
M1/Wa = -2.25 MPa
+
P/A = 9.64 MPa
top =
+
effective prestress =
66% UTS
Pi = eccentricity (ei) =
3655.18 381.73
kN mm
Mdl = Mbeam + Madl =
1193.97
kN-m
7.59 MPa
=
M2/Wb'= -0.50 MPa
M1/Wb = 1.70 MPa
0.36 MPa
bottom
= 10.84 MPa
M1 = Mdl + Pi.e =
-201.33
kN-m
M2 = Masphalt =
101.59 24.00
kN-m MPa
-1.58
MPa
allow comp at
initial =
allow tension initial
=
control allow stress = meet requirement
page 9 / 15
PCI Monolith H-125cm ; L-22.30m ; 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 =
P/A = 8.59 MPa
M2/Wa'= 3.10 MPa
M1/Wa = -0.56 MPa
+
P/A = 8.59 MPa
top =
+
59% UTS
M2/Wb'= -7.56 MPa
bottom
= 1.45 MPa
M1 = Mdl + Pi.e =
Pi =
3259.02
kN
eccentricity (ei) =
381.73
mm
Mdl = Mbeam + Madl =
1193.97
11.13 MPa
=
M1/Wb = 0.42 MPa
effective prestress =
5.40 MPa
M2 = Masphalt + LL =
kN-m
1544.64
kN-m
service =
22.50
MPa
allow tension at service =
-3.54
MPa
allow comp at
kN-m
-50.10
control allow stress = meet requirement
8.4 Deflection 8.4.1 Chamber due to Prestress Load Deflection on middle section : l
P
ee
pi= [ee+(5/6)(e c-ee)] x (P. l2 /8 Ec Ix) pi=
P
ec
where :
-33.71 mm
P = Prestress force Eci = Modulus Elasticity of Concrete
l/2
l/2
Ixi = Section Inertia l = length of anchor to anchor ee = Distance between c.g of strand and c.g of concrete at end ec = Distance between c.g of strand and c.g of concrete at centre
8.4.2 Deflection at initial, ere ction and service condition (based : PCI handbook 4.6.5 Long-Time Chamber Deflection) Deflection () on simple span structure : where : q = Uniform Load 4
q= (5/384)*q*L /Ec Ix)
P = Point Load
3
l = Beam Span
p= P.l /48 Ec Ix
Deflection calculation table : Estimating long-time cambers and deflections WORKING LOAD
Loading q (kN/m)
P (kN)
1. Due to Prestress force 2. Due to beam weight (DL)
9.30
Release (1)
Long time cambers and deflection (2) multipliers Erection multipliers
-33.71
1.80 x (1)
-60.68
2.20 x (1)
12.40
1.85 x (1)
22.94
2.40 x (1)
-21.31 3. Due to ADL
3.04
Service (3) -74.17 29.76
-37.75 3.63
-44.41 3.00 x (2)
10.89
-34.11 4. Due to Composite Overtoping
7.94
9.47
-33.52 2.30 x (2)
21.79
-24.64 5. due to asphaltic (SDL)
-11.72
1.73
0.72
-11.00 6. due to Live Load = UDL + KEL
14.40
109.76
9.43
-1.57 Resume of deflection : 1.
Deflection at service
=
2.
Deflection due to Live Load
=
3.
Total deflection with LL
=
-11.00 mm 9.43 mm < allow. deflection L/800 =
27.125 mm
OK
-1.57 mm, chamber upward
page 10 / 15
PCI Monolith H-125cm ; L-22.30m ; 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
=3420 mm
2. Beam Ctc 3. Span length / 4
=1600 mm …. Control =5425 mm
Thus, Effectif slab width is :
=1600 mm
for slab with fc' = Value =
28.00
MPa
0.85
Partial Rebar: 400 MPa 0 Dia.13 mm
fy = Use As = d=
at tension area b web =
0.00 mm2
220 mm
1190.5 mm
Partial tension rebar ratio : t = As / (bweb x d )
t =
0.00000
t =
t =
0.000
t . fy / fc
Rebar in compresion area is neglected due calculation c = c =
Low Relaxation strand : fpu =
1860
MPa
Strand stress ratio fpu / fpy = dp =
value p = 0.28
0.9
2
2963.4 mm
Aps =
1365.0 mm
Prestress ratio : p = Aps / (beff x dp ) fps = p =
beff =
1600 mm
p = 0.00135687
fpu {1 - p / (p.fpu/fc + d/dp ( t-c)))
1804.8 MPa
fps = p =
p fps/fc
0.087
Resume of Steel Index Requirement (SNI Beton 03-2847-2002 pasal 20.8) p + d/dp ( t-c) 0.36 < 0.087
0.306
<
Under Reinf, Meet With Steel Index Requirement
9.2 Momen Capacity b. eff one
Zone 3
c
i
Cc3 Cc2
Zone 3 Zone 2 a
Tps = Aps . Fps Tps = 5348266.89 N
Cc1
Zone 1
dp
d
strength reduction factor = 0.8 Tps=Aps.fps T = As.fy
COMPOSITE BEAM
Location of Depth of Concrete Compression Block (a) : hi wi Aci=hi.wi Conc. Strength fc' i Zone
Cci=0.85 fc'i.Aci
MPa
Comp (i)
4
(mm) 140.45
(mm) 1600
(mm2) 224717.1
28.00
CIP Slab
N 5348267
3
0.00
385
0
28.00
CIP Slab
0
140
2
0.00
400
0
50.00
Beam
0
140
1
0.00
220
0
50.00
Beam
0
140
Compresion
Point (mm) Point (mm) 70 70.22
Depth of Concrete Compression Block is located at zone 4 a = Tps / ( 0.85 x fc'' slab x beff )
a=
Mn = (Tps (dp - comp. point) + As.fy (d-comp. point) Mn = 5539.8457 kN.m Bridge life time design for 50 year,so Transient act factor = 1 Mn / Mult = Mult = 1x 4,280kN-m
Mn =
1.294
140.45 mm 6924.81 kN.m
>1, Moment capacity m eet with requirement
9.3 Cracking Capacity Stress at bottom girder section due to service load ( bot at service) =
1.44 MPa
Con cr ete flexur al te nsion st ren gt h fr =
4.9 MPa
Crack Moment, Mcr = (bot at service + fr ) Wb.comp + Momen Mcr = Mn / Mcr =
(DL+ADL+LL+I)
4043.71 kN.m 1.370
> 1.2 ---- Cracking Capacity requirement is achieve
page 11 / 15
PCI Monolith H-125cm ; L-22.30m ; CTC-160cm - RSNI (Rev.04)
X. SHEAR ANALYSIS 10.1 Shear calculation based on SNI 03-2847-2002 Alternatif solution to calculated shear on prestress element is use for structure element which have effective prestress above 40% of ultimate tensile stress 40% Ultimate Tensile Strength
= 744
Effective Prestress
= 1100
Section Properties : Ix = 6.368E+10 mm4 Yb = 536.73368 mm Ag =
MPa MPa
Effective Prestress > 40% fpu
Ixcomp = 1.811E+11 mm4 Ybcomp =
887.0 mm
379250 mm2
Load : Effective prestress Pe =
3259.02 kN
Factored Load : qult DL + ADL =
28.59
kN/m
Unfactored Load : q DL + ADL =
20.28
kN/m
qult LL =
25.92
kN/m
q sdl =
1.73
kN/m
Pult LL =
197.57
kN
q DL + ADL =
22.01
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 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. Vn = Vc + Vs Vn = Vu /
where :
Vn = Nominal Shear force Vc = Concrete shear contribution Vs = Shear steel contribution
Vu = Ultimate Shear force = Shear reduction factor = 0.75
Zonafication for shear steel stirup calculation Zone 1
Vn < 0.5 Vc
No need to use stirup
Z on e 2
V n < V c+ [0 .3 5 or ( 75/ 12 00 ) s qr t(f c' )] bw d
R equ ir ed s ti ru p s pa ci ng wi th mi ni mu m sp ac in g :
Zone 3
Vn < Vc+0.33 sqrt(fc') bw d
S ≤ 0.75 H
S ≤ (av.fy) / (0.35 bw)
S ≤ 600mm
S ≤ (av.fy/fpu) (80/Aps) d sqrt(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
page 12 / 15
PCI Monolith H-125cm ; L-22.30m ; CTC-160cm - RSNI (Rev.04)
Shear rebar steel 400 MPa 2 leg Dia.13 mm
fy = Use Av =
shear width : bw = 220
mm
700
mm
265.46 mm2
bw-e =
Shear steel requirement calculation table : ecomp dist. d=dp>0.8H Vu Mu m m m kN kN-m
dp(Vu/Mu)
Vc
Vn
Vs
Shear
kN
kN
kN
Zonasi
Use Space mm
mm
use
0.1
0.488
1.12
782.61
78.53
1.00
1320.83
1043.48
-277.35
2
600
300
0.3875
0.501
1.13
764.32
300.27
1.00
1335.97
1019.10
-316.87
2
600
300
0.775
0.518
1.15
739.67
589.62
1.00
1355.72
986.23
-369.49
2
600
300
1.7
0.556
1.19
680.83
1236.18
0.65
948.29
907.78
-40.51
2
600
300
2
0.567
1.20
661.75
1432.51
0.55
824.99
882.33
57.34
2
600
300
3
0.602
1.24
598.14
2039.70
0.36
588.17
797.52
209.34
3
600
300
4
0.633
1.27
534.53
2574.16
0.26
464.64
712.70
248.06
3
542
300
5
0.660
1.29
470.91
3035.91
0.20
385.77
627.89
242.12
3
567
300
6
0.682
1.32
407.30
3424.94
0.16
328.67
543.07
214.40
3
600
300
7
0.701
1.33
343.69
3741.26
0.12
283.50
458.25
174.75
3
600
300
8
0.715
1.35
280.08
3984.86
0.09
245.30
373.44
128.13
3
600
300
9
0.725
1.36
216.47
4155.74
0.07
211.24
288.62
77.38
2
600
300
10
0.730
1.36
152.85
4253.91
0.05
179.54
203.81
24.27
2
600
300
10.850
0.732
1.37
98.78
4280.18
0.03
153.47
131.71
-21.76
2
600
300
Shear Steel Requirement Position
kN 3000.0 2500.0
Zona1
2000.0
Zona2
1500.0
Zona3
1000.0
Zona4
Vn= Vu/f
500.0 0.0
beam section point
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
10.85
10.85
36
Shear Rebar configuration
total shear rebar per half span (row) =
36
total shear rebar per span (row) =
72
page 13 / 15
PCI Monolith H-125cm ; L-22.30m ; CTC-160cm - RSNI (Rev.04)
10.2 Horisontal Shear Width of contact surface area
bv =
250 mm
d=
1216 mm
Effective Height =
fy = Use
0.75 400 MPa 2 leg Dia.13 mm
Area horisontal Shear Steel
Avh =
Horisontal Shear steel Spacing
s= v =
Horisontal Shear steel ratio
265.46 mm2 300 mm 0.354%
Shear horisontal Nominal Vnh = (1.8 Mpa + 0.6 v. fy) . bv .d Vnh =
805.44 KN
Requirement for shear horisontal steel : Vult < Vnh < 350 bv.d Vult = Ultimate shear due to superimposed DL + LL Vult = Vnh =
604.08 kN
428.44 kN
3.5 bv d =
1064.00 kN
RESUME: Shear horisontal : OK
Minimal Use : bys =
250 mm
Spacing =
Avh = 50 by.s / fy
Max. Spacing =
Avh = 215.46875 mm2/m
1232.03 mm or
4 tweb = 880 mm
300.00 mm
min no. Spacing =
73 @ 2D13 for shear horisontal / span
Resume = additional shear horizontal required
XI. END BLOCK DESIGN Block Anchor dimension type 7
a
b
dia hole
(mm)
(mm)
(mm)
165
165
51
Block Area Concrete Area A (mm ) A1 (mm ) A2 (mm ) sqrt(A2/A1) 25182.18
27225
1750000
8.02
70225
2450000
5.91
. 19
265
265
84
64683.23
.
SNI 03-2847-2002 Pasal 11.3.2 (Anchorage Zone) Maximum strand =
19
Anchor Block type =
19
Load factor = Reduction factor () =
1.2
Strand
0.85
1. End Bearing Ultimate Point Load Pu = min (1.2 x nStrand x Astrand x %JF x fpu , nstrand x Astrand x 96% x fpu) Pu =
3141.8
End Bearing stress : comp = comp =
kN Nominal concrete comp. : Pu / A 48.57
fci = MPa
40.00 Mpa
min(2, sqrt(A2/A1)) =
2.0 Nominal fci = x 0.7 x fci x min(2,sqrt (A2/A1)) > comp = Nominal fci = 47.60 48.57 MPa
ten-
Nos
Anchor
sheath
Ult. Point
Block
End Bearing
don
strand
Height
hole
Load
Area
Stress
Nominal comp. fci
(Pu) kN
(A) mm2
(EBS=Pu/A) Mpa
Mpa
( ai ) mm
Remark
0
0
0
0
0
0
0
0
1
11
215
63
1818.93
43107.75
42.20
47.60
EBS < Nominal Compresion
2
19
265
84
3141.80
64683.23
48.57
47.60
EBS > Nominal compresion (not good)
page 14 / 15
PCI Monolith H-125cm ; L-22.30m ; CTC-160cm - RSNI (Rev.04)
2. Stirrup and Spalling Reinforcement Load factor = Reduction factor () =
0.85
1.2
fy =
400
MPa
Bursting Steel Diameter closed stirup =
13 mm
Stirup Area =
132.7 mm2
ten-
Nos
Anchor
sheath
Jacking
Bursting
End
don
strand
Height
hole
Force
Area (Abs)
Bearing (EBS)
kN
mm2
( ai ) mm
EBS/0.7
(fcc'-fci)/4.1
fl / 0.5 fy
fcc'
fl
p
Mpa
Mpa
Mpa
sp (mm)
0
0
0
0
0
0
0
0
1
11
215
63
1515.7791
43107.75
35.16
59.10
4.7
2.33%
106.0
2
19
265
84
2618.1639
64683.23
40.48
68.03
6.8
3.42%
58.6
total
30
Anchor Zone Stirrup JF Load = Ult. JF =
4133.94 kN
a1 =
480.00 mm
4960.73 kN
H=
1250 mm
T bursting = 0.25 Ult.JF (1-a1/H)
d bursting = 0.5(h-2e)
T bursting = 763.95267 kN
d bursting = 751.733685 mm
Diameter closed stirup = No. Leg of stirrup = Stirup Area =
13 mm 4 leg 530.9 mm2
Anchor Stirup Rebar = T bursting / 0.5 fy Anchor Stirup Rebar = use no of stirup =
3819.8 mm2 8 pcs
Spalling Rebar Spalling Force = 2% JF Spalling Force = Diameter closed stirup = Stirup Area = use no of stirup =
82.7 kN 13 mm 132.7 mm2 4 pcs
page 15 / 15
PT WIJAYA KARYA BETON
TECHNICAL CALCULATION PCI GIRDER MONOLITH FOR HIGHWAY BRIDGES Project Product Job no Rev. No.
: : : :
TOLL SURABAYA ‐ GRESIK PCI Girder Monolith H‐125cm ; L‐26.10m ; CTC ‐160cm ; fc' 70MPa 13014 E 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, 1
st
nd
& 2 floor
Jl. Jatiwaringin no. 54, Pondok Gede ‐ Bekasi Ph: +62‐21‐8497 ‐3363 fax : +62‐21‐8497 ‐3391 www.wika‐beton.co.id
PT WIJAYA PT WIJAYA KARYA BETON
TECHNICAL CALCULATION APPROVAL APPROVAL PCI GIRDER PCI GIRDER MONOLITH MONOLITH FOR FOR HIGHWAY HIGHWAY BRIDGES BRIDGES TOLL SURABAYA ‐ GRESIK PCI Girder Monolith Girder Monolith H‐125cm ; 125cm ; L‐26.10m ; 26.10m ; CTC ‐160cm ; 160cm ; fc' fc' 70MPa 70MPa Job no. : 1301 3014 E Rev. : 04
Approved by Approved by ::
Consultan / Consultan / Owner Owner
Approved by Approved by :: 18 Juni 18 Juni 2 2013
Checked by 18 Juni 2013 Juni 2013
Design by : by : 18 Juni 18 Juni 2013 2013
Ir. Achmad Ir. Achmad Arifin Arifin Technical M Technical Manager
Ignatius Harry S., Harry S., S.T. Chief of Technical o f Technical
Suko Technical Staff Technical Staff
PCI Monolith H-125cm ; L-26.10m ; CTC-160cm - RSNI (Rev.04)
RESUME OF PCI GIRDER MONOLITH TECHNICALLY CALCULATION 1. BEAM SPECIFICATION
Span Beam Height ( H )
=
25.50 m (beam length
=
1250 mm
Distance ctc of beam ( s )
=
1600 mm
Slab thickness
=
200 mm
Beam Compressive strength
=
70 MPa
Slab Compressive strength
=
28 MPa
Bridge life time
=
50 years
=
26.10 m)
Segment egment Arr angement
Beam Segment Length (m)
1
2
3
4
5
6
7
5.250
5.000
5.000
5.000
5.250
0.00
0.00
Additional length at the end of beam
=
0.30
m
Total length of the beam
=
26.10
m
Total beam weight
=
25.69
ton
12.7 12.7
mm (PC (PC Str Stran and d 270 270 grad grade, e, low low rel relax axat atio ion) n)
2. STRESSING
Nos of PC Strand
=
strand
57
Strand configuration No.
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
=
19.40%
at middle
0
0
0
0
fc initial
=
80.0%
fc'
1
19
900
350
2
19
600
225
3
19
300
100
total
57
600.00
225.00
3. LOADING 1. Dead Load
a. Precast Beam
=
9.30
kN/m
b. Slab
=
7.94
kN/m
Slab thickness =
200
mm
c. Deck Slab
=
2.22
kN/m
Deck slab thickness =
70
mm
d. A Assphalt
=
1.73
kN/m
Asphalt thickness =
50
mm
e. Di D iaphragm
=
6.68
kN
5
pcs
No. Diaphragm
for 1 diaphragm equivalent load =
1.05
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)
=
b. Kn Knife Edge Load (KEL)
=
c. Di D istribution Factor (DF)
=
1.40 for span length <= 50m 49.00 kN/m 1.00
d. Distribu Distribution tion Load q=
9.00 kN/m2
9.00 kN/m2
For Span <= 30m
9.00 x(0,5+15/span)kN/m2
For Span > 30m
e. Live Live Load Load Distribution load : Line Load
:
q' = DF x q x s p' = DF x DLA x KEL x s
CALCULATION RESUME
= =
14.40 kN k N/m 109.76 kN
PCI Monolith H-125cm ; L-26.10m ; 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 support react ion :
a. Dead Load
=
118.54
kN
b. Additional Dead Load
=
164.98
kN
c. Live Load
=
293.36
kN
Ultimate support reaction =
896.01
kN
5. CONTROL OF BEAM STRESSES 1. Initial Condition
Middle span position top stress =
2.15 MP MPa
required
>
-1.87 MP MPa
bottom stress =
32.53 MP M Pa
required
<
33.60 MP MPa
top stress =
18.43 MPa
<
31.50 MPa
bottom stress =
6.47 MP MPa
>
-4.18 MP MPa
2. Service Condition
Middle span position required required
6. CONTROL OF BEAM DEFLECTION
De f l e c t i o n a t t h e m i d d l e of of b e a m sp sp a n
1. Chamber Chamber due stressin stressing g initial
=
-34.23
mm
=
-
2. Deflection at composite DL
=
-16.08
mm
3. Deflection due live load
=
15.38
mm,required
4. Total deflection at service
=
-0.70
mm
. = 31.88 mm
7. MOMENT AND CRACKING CAPACITY OF BEAM
Moment Moment Capacit Capacit y requir ement ement :
Mult = 1,2*( ,2*(B Beam+Di m+Dia aphra hragm+D gm+Dec eck k Slab lab)+1, )+1,3 3*Sla *Slab+ b+2* 2*A Asphalt haltic ic+ +1,8 1,8*(L *(LL+I L+I) Mn
=
571 5712.0 2.05 kN.m kN.m
=
9058.19 kN kN.m
Ratio, Mn / Mu (>1)
=
Cracking Capacit Capacit y requir ement ement :
Mcrack Mn / Mcr
= =
6128.23 kN k N.m 1.48
CALCULATION RESUME
1.59
PCI Monolith H-125cm ; L-26.10m ; CTC-160cm - RSNI (Rev.04)
TECHNICAL CALCULATION OF PCI MONOLITH BEAM FOR HIGHWAY BRIDGES SPAN L = 25.50 M I. DATA
0.3
L=
25.50 M
0.3
26.10 m
Beam length
=
Beam spacing (s)
=
1600 mm
( edge anchor to e dge an ch or :
Concrete Slab thickness (CIP)
=
200 mm
Asphalt thickness
=
50 mm
Deck slab thickness
=
70 mm
25.80
m)
A
Cross Section H
=
1250
mm
tfl-1
=
75
mm
A
=
400
mm
tfl-2
=
75
mm
B
=
700
mm
tfl-3
=
100
mm
tweb =
220
mm
tfl-4
=
125
mm
tfl-1 tfl-2 tweb
H
tfl-3 tfl-4
II. MATERIAL B
2.1 Concrete Beam
Slab
fc' =
70.0
28.0
fc'i =
56.0
[N/mm ]
0.6 * fc'i =
33.6
[N/mm ]
Tensile 0.25 * Sqrt(fc'i) = Allowable stress at service ………. ( SNI T-1 2-20 04 )
1.9
[N/mm ]
Compressive strength at service at initial
80% fc'
2
[N/mm ] 2
Allowable stress Allowable stress at initial ………… ( SNI T-1 2-20 04 ) Compressive
2
2
0.45 * fc' =
31.5
12.6
[N/mm ]
0.5 * Sqrt(fc') =
4.2
2.6
[N/mm ]
wc =
2500.0
2500.0
[kg/m ]
*0.043*sqrt(fc') =
44970.5
28441.8
[N/mm ]
*0.043*sqrt(fci') =
40222.8
[N/mm ]
f r = 0.7*sqrt(fc') =
5.9
[N/mm ]
Compressive Tensile
2
Modulus of elasticity Concrete unit weight Ec = wc Eci = wc
1.5
1.5
3
2 2
Concrete flexural tension strength (fr) 2
2.2 Prestressing Cable [Uncoated stress relieve seven wires strand] ( ASTM A 416 Grade 270 Low Relaxation or JIS G 3536 ) - Diameter strand
dia
:
12.7
[mm]
- Eff. Section area
Ast
:
98.78
[mm ]
- Modulus of elasticity
Es
: 1.93E+05
[N/mm ]
- Ultimate tensile strength
fu
:
1860
[N/mm ]
- Diameter
dia
:
13
[mm]
- Eff. Section area
Ast
:
132.73
[cm ]
- Modulus of elasticity
Es
: 2.10E+05
[N/mm ]
- Yield stress
fy
:
[N/mm ]
2
2 2
2.3 Steel Reinforcement
400
2
2 2
page 1 / 15
PCI Monolith H-125cm ; L-26.10m ; CTC-160cm - RSNI (Rev.04)
III. SECTION ANALYSIS Remark : Ep 1 = Ep 2 =
2
44970
[N/mm ] [Girder]
28442
[N/mm ] [Slab]
3
2
2
5
Ya'
4 Ya
n = Ep 2 / Ep 1 n=
3
0.63
1
2
Yb
Yb'
1
Base Line
PRECAST BEAM
COMPOSITE BEAM
3.1 Precast Beam [in mm ] Zone
Section
Width
Area
Level
2
Yb
Area*Yb 3
2
Io
Ix
Area*d 4
4
4
Height
Bottom
Upper
mm
mm
mm
mm
mm
mm
mm
6
0.0
200.0
200.0
0
1250
1250.0
0
0
0
0
5
75.0
400.0
400.0
30000
1175
1212.5
36375000
14062500
13699803379
13713865879
4
75.0
220.0
400.0
23250
1100
1141.1
26531250
10592238
8493079360
8503671598
3
875.0
220.0
220.0
192500
225
662.5
1275 31250
122 81901 042
30 44804 457
15 32670 5499
2
100.0
700.0
220.0
46000
125
166.3
7650000
34855072
6312023113
6346878186
1
125.0
700.0
700.0
87500
0
62.5
5468750
113932292
19678538941
19792471233
Total
1250.0
536.7
2 03 55 62 50
1 24 55 34 31 44
5 12 28 24 92 50
6 36 83 59 23 94
Level
Yb
Area*Yb
Io
Area*d
mm
mm
mm
mm
mm
mm
65 89823 7240
379250
3.2 Composite Beam [in mm ] Zone
2 1
Height
Width
Area 2
3
2
4
Ix
4
4
Section
Bottom
Upper
mm
200.0
1011.9
1011.9
202386
1320
1420.0
2873 87794
67461 9234. 2
6 5223 61800 5
70.0
158.1
158.1
11068
1250
1285.0
14222344
4519421.823
2072167895
2076687316
1250.0
700.0
400.0
379250
0
536.7
2035 56250
636 83592 394
3776 85255 78
1. 014 52E +1 1
.
o a
.
.
+
.
+
3.3 R e s u m e [in mm ] 2
Description
Area (mm )
Precast Beam Composite Beam
[composite]
Ya (mm)
Yb (mm)
4
Ix (mm )
3
Wa (mm )
3
Wb (mm )
379250
713
536.7
63683592394
89284452
118650262
592704
668
852.3
1694 27042 528
253 7504 54
1987 86072
[precast]
398
426026221
IV. LOADING 4.1 Dead Load a. Precast Beam
q1 = Ac precast girder x q1 =
b. Slab
0.080 x
[t/m'] =
9.30
[kN/m']
0.810
[t/m'] =
7.94
[kN/m']
0.227
[t/m'] =
2.22
[kN/m']
0.176
[t/m'] =
1.73
[kN/m']
6.68
[kN']
s
2.40 =
q4 = Ac asphaltic x q4 =
e. Diaphragm
0.095 x
0.948
conc. slab
2.40 =
q3 = Ac deck slab x q3 =
d. Asphaltic
0.338 x
conc. Precast
2.50 =
q2 = Ac slab CIP x q2 =
c. Deck slab
0.379 x
s
2.20 =
p
= Vol diaph with 0.20m thickness x
p
=
0.284 x
2.40 =
0.681 note :
Number of diaph = Diaph. placement Location
5
diaph
[ton'] =
from kg to N, multiply by 9.8060
pcs
1
2
3
4
5
0.00
6.38
12.75
19.13
25.50
Support Va
6.68
5.01
3.34
1.67
0.00
Mid Moment
0.00
21.28
42.56
21.28
0.00
Total Diaphragma Flexural Moment at Middle Span eqivalen load q diaphragm
q5=
85.11
kN.m
1.05
[kN/m']
page 2 / 15
PCI Monolith H-125cm ; L-26.10m ; 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 Item P1 kN Load 225 Impact 1.3 LL + I 292.5 kN Distance 8.750 m Va 192.13 kN Va kN M max kN-m DF = S/3.4 M x DF kN-m
P2 225 1.3 292.5 12.750 146.25
P3 50 1.3 65 17.750 19.75
M.max di x = 12.750 m DLA = 30% Impact = 1 + DLA = 1.3
358.14 3396.25 0.47 1598.24
50kN
225kN
225kN
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 :
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) DLA = 1 + 0,3
50 < Span < 90 m
=
1.30
b. Knife Edge Load (KEL)
=
49.00
c. Distribution Factor (DF)
=
1.00
Span >= 90 m
[kN/m']
d. Distribution Load q =
9.00 kN/m
q = 9 kN/m q = 9 x(0,5+15/span)kN/m
which :
for
Span <= 30 m Span > 30 m
e. Live load Distribution load, qudl = DF x q x s = 1.00 x 9.00 KEL, PKEL = DF x DLA x KEL x s =
1.00
M.max at 0.5 span = Va = M LL =
x
1.40
12.750 m
x x
1.60 49.00
x
1.60
=
14.40
[kN/m']
=
109.76
[kN']
238.48 kN 1 87 0. 17 k N. m
RESUME : Moment force cause by D Loading is bigger than Truck Loading
page 3 / 15
PCI Monolith H-125cm ; L-26.10m ; 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
5.25
10.25
15.25
20.25
12.75
Precast beam
755.70
0.00
494.21
726.64
726.64
494.21
755.70
Subtot al
755.70
0.00
494.21
726.64
726.64
494.21
755.70
Slab
645.61
0.00
422.21
620.78
620.78
422.21
645.61
ADL
Asphaltic Layer
140.28
0.00
91.74
134.89
134.89
91.74
140.28
SDL
Diaphragm+Deck Slab
265.88
0.00
173.88
255.66
255.66
173.88
265.88
1051.77
0.00
687.83
1011.33
1011.33
687.83
1051.77 1170.45
Type
Description
DL DL
Subtot al
LL
Distribution load
1170.45
0.00
765.45
1125.45
1125.45
765.45
KEL
699.72
0.00
457.60
672.82
672.82
457.60
699.72
Subtot al
1870.17
0.00
1223.05
1798.27
1798.27
1223.05
1870.17
Total (DL + LL)
3677.63
0.00
2405.10
3536.24
3536.24
2405.10
3677.63
Ultimate total
5712.05
0.00
3735.56
5492.44
5492.44
3735.56
5712.05
Sec 5-5 20.25 -69.73 -69.73 -59.57 -12.94 -24.53 -97.05 -108.00 -87.16 -195.16
Sec 6-6 12.75 0.00 0.00 0.00 0.00 0.00 0.00 0.00 54.88 54.88
-157.23
-361.94
54.88
-
-
(m)
Ultimate total = 1,2*(Beam+Diaphragm+Deck Slab)+1,3*Slab+2*Asphaltic+1,8*(LL+I) VI. SHEAR ANALYSIS [in kN] Mid
Subtot al
span 0.00 0.00 0.00 0.00 0.00 0.00 0.00 54.88 54.88
Sec 1-1 0.00 118.54 118.54 101.27 22.00 41.71 164.98 183.60 109.76 293.36
Sec 2-2 5.25 69.73 69.73 59.57 12.94 24.53 97.05 108.00 87.16 195.16
Sec 3-3 10.25 23.24 23.24 19.86 4.31 8.18 32.35 36.00 65.64 101.64
Total (DL + LL)
54.88
576.88
361.94
157.23
.
.
.
.
Type
Description
DL
Precast beam
DL
Slab
Subtot al
ADL
Asphaltic Layer
SDL
Diaphragm+Deck slab Subtot al
Distribution load
LL
KEL
ma e o a
Sec 4-4 15.25 -23.24 -23.24 -19.86 -4.31 -8.18 -32.35 -36.00 -65.64 -101.64 .
.
(m)
.
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 ] Tension
ten-
Nos
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
19
900
350
75%
0%
75%
2618
2
19
600
225
75%
0%
75%
2618
3
total
Profile
19
300
100
75%
0%
75%
2618
57
600.00
225.00
75%
0%
75%
7854
Pa r a b o l i c c u r v e ( Av e r a g e of St r a n d ' s p o si t i o n v e r t i c a l l y f r o m t h e b o t t o m o f b e a m ( V a l ue f o r Y a x i s ) ) 2
Y = A.x + B.x + C 2
where :
A = Constanta : ( (Ymiddle + Yedge)/(L/2) )
A=
0.002253
B = Constanta : ( L x A )
B=
-0.058140
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 ) X + Y = 0.002253 -0.0581395 X + 0.600000 Cable tendon angle : o
tg =
0.004507 X
+
-0.0581395
eccentricity of tendon at middle section Eccentricity [e]
=
Yb - Ys =
311.73
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)
page 4 / 15
PCI Monolith H-125cm ; L-26.10m ; CTC-160cm - RSNI (Rev.04)
Average of Strand's position vertically from the bottom of beam ( Value for Y axis ) 1.00 0.80 0.60 0.40 0.20 0.00 0
5
10
15
20
25
30
7.2 Losses of Prestress 1. Losses of Prestress (Short Term) a. Friction 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. The equation for calculating the loss of prestress due to friction is : - + .x Po.e Px = ( AASHTO 1992, Chapt. 9.16.1 ) Where :
80.0%
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
75.0% 70.0%
k = Wobble coefficient x = Distance from tensile point to x section
65.0% 60.0%
Friction and Wooble coeficient for grouting tendon in metal sheating = 0.20 with Seven Wire Strand :
0.00
10.00
20.00
30.00
k = 0.003
Table of calculation due to Friction Profile
% JF
a
b
ten-
Nos
don
strand
Edge
Middle
from UTS
0
0
0
0
0%
0.00000
0
0
0
0
0
0%
0.00000
Prestress force (Px) = % UTS
0.00
12.9
25.80
0.000
0.0%
0.00%
0.0%
0
0.000
0.0%
0.00%
0.0%
0.00000
0
0.000
0.0%
0.00%
0.0%
(rad)
0
0
0
0
0%
1
19
900
350
75%
0.00331
-0.0852713
0.170
75.0%
69.74%
67.1%
2
19
600
225
75%
0.00225
-0.0581395
0.116
75.0%
70.50%
67.8%
3
19
300
100
75%
0.00120
-0.0310078
0.062
75.0%
71.26%
68.6%
total
57
600.00
225.00
75%
0.00225
-0.0581395
0.116
75.0%
70.5%
67.8%
b. Anchor set
, . , 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 e longation is resisted by friction just as the initial elongation is resisted by friction. 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 : Cable change angle point
Cable change angle point Anchorage set area
X (effective anchorage set)
Anchorage set area
X (effective anchorage set)
page 5 / 15
PCI Monolith H-125cm ; L-26.10m ; 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 draw in tenNos
From left side
From right side
after anchorage set = % UTS
don
strand
Mpa/mm
mm
X (m)
Px (% UTS)
X (m)
Px (% UTS)
0.00
12.9
25.80
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
19
0.00570
8.00
16.46
69.01%
0.00
0.00%
63.0%
68.28%
67.1%
2
19
0.00518
8.00
17.27
69.59%
0.00
0.00%
64.2%
68.68%
67.8%
3
19
0.00464
8.00
18.23
70.15%
0.00
0.00%
65.3%
69.03%
68.6%
total
57
0.00517
8.00
17.32
69.58%
0.00
0.00%
64.16%
68.66%
67.82%
AVERAGE LOSSES OF PRESTRESS
LOSSES OF PRESTRESS DUE TO ANCHORAGE SET
75.0%
80.0% 75.0%
70.0%
69.76% 69.59% 69.39% 68.66%
70.0% 65.0%
65.0%
60.0% 55.0%
67.82%
64.16%
60.0% 0.00
10.00
20.00
30.00
0.00
Prestress tendon section
10.00
20.00
30.00
Prestress tendon section
c. Elastic Shortening ( ES ) Elastic shortening refers to the shortening of the concrete as the postensioning force is applied. As the concrete shorterns, the ten don 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 = concrete stress at the centre of gravity of prestressing tendons due to prestressing force at transfer and the self weight of the member at the section of maximum positive moment 3.20%
Assumption Losses due ES Pi = Pi =
Total prestressing force at release 68 .7% - 3. 20% = 65.46% UTS x nos x Aps =
6855.3141 kN
2
f cir = Pi / A + Pi. ec / I + Mg.ec/I f cir = so,
24.84 N/mm2 ES =
59.59 N/mm2,
percent actual ES losses = Es/fpu
3.20%
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) SH
=
(ACI 318-95, Chapt. 18.6) 1.63% percent actual SH losses = SH/fpu
30.32 N/mm2
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
"days" is the number of days between the end of moist curing and t he application of prestress.In a structures that are not moist cured, Ksh is typiclly based on when the concrete was cast Ksh =
0.64
V/S =
0.09
RH
=
Volume =
3
9.90 m
Surface =
2
104.51 m
70.00
page 6 / 15
PCI Monolith H-125cm ; L-26.10m ; CTC-160cm - RSNI (Rev.04)
e. Creep ( CR )
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 cree p. Loss of prestress due to a creep is nominally propotional to the net permanent compresive stressin the concrete. the n et permanent compressive stress is the initial compressive stress in the concrete due to the prestressing minus th e tensile stress due to self weight and superimposed deadload moments CR CR
= Kcr*(Es/Ec)*(fcir-fcds) =
136.35 N/mm
(ACI 318-95, Chapt. 18.6)
2
percent actual CR losses = CR/fpu
7.33%
Where :
Kcr =
1.60 (for posten sion ed member)
fcir = stress at center point prestress force, initial condition fcir =
24.838 N/mm
2
Msd = Moment due to all superimposed permanent dead loads applied after prestressing Msd =
1051.77
kN.m
fcds = Stress in a concrete at the cgs of the tendon due to all superimposed dead load fcds 1 = Msdl.e/I = fcds 2 = Madl.e/Ic =
4.46 N/mm
2
0.52 N/mm
2
component of fcd due to load on the plain beam component of fcd due to load on the composite beam
4.98 N/mm
fcds = fcds 1 + fcds 2 =
2
f. Steel Relaxation ( RE ) 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 ten don at that time. Because of other prestress losses, there is a continual reduction of tendon strss; this causes a reduction in the r elaxation rate. The equation for prestress loss due to relaxation of tendons is : RE = [ Kre - J*(SH+CR+ES) ] *C
16.76 N/mm
RE =
(ACI 318-95, Chapt. 18.6)
2
percent actual RE losses = RE/fpu
0.90%
Where :
Kre =
5000.00 (for 270 grade, low relaxation strand)
J =
0.04 (for 270 grade, low relaxation strand) .
=
or p
pu =
.
RESUME DUE TO SHORT & LONG TERM LOSSES Losses
I. Short Ter m Losses
Section
Elastic Total Anchor set Shortening Losses (%)
x (m)
Friction
II. Long Term Losses
Shrinkage (SH)
Creep (CR)
Steel Total Losses Relaxation (%)
0.00
75.00%
64.16%
60.96%
14.04%
59.33%
52.00%
51.10%
23.90%
0.00
75.00%
64.16%
60.96%
14.04%
59.33%
52.00%
51.10%
23.90%
0.00
75.00%
64.16%
60.96%
14.04%
59.33%
52.00%
51.10%
23.90%
0.00
75.00%
64.16%
60.96%
14.04%
59.33%
52.00%
51.10%
23.90%
12.90
70.50%
68.66%
65.46%
5.04%
63.83%
56.50%
55.60%
14.90%
16.46
69.76%
69.76%
66.56%
3.20%
64.93%
57.60%
56.70%
13.07%
17.27
69.59%
69.59%
66.39%
3.20%
64.76%
57.43%
56.53%
13.07%
18.23
69.39%
69.39%
66.19%
3.20%
64.56%
57.23%
56.33%
13.07%
25.80
67.82%
67.82%
64.62%
3.20%
62.99%
55.66%
54.76%
13.07%
friction Losses equotion : UTS
Friction
LOSSES OF PRESTRESS DIAGRAM
0 > x > 12.90
Anchor set ElasticShortening(ES)
80.00%
75.00% -+ 0.35% x
Shrinkage(SH)
12.9 > x > 25.80
Creep(CR) SteelRelaxation(SR)
75.00%
65.00%
64.16%
70.50% 68.66%
69.76% 69.59% 69.39%
65.46% 63.83%
66.56% 66.39% 66.19% 64.93% 64.76% 64.56% 64.62% 62.99%
56.50% 55.60%
51.10% + 0.35% x 12.9 > x > 16.46
12.90
x - 12.9
16.46 > x > 17.27 55.66% 54.76%
56.70% -+ 0.21% x
x - 16.4565324
17.27 > x > 18.23
52.00% 51.10% 0.00
0 > x > 12.90
55.60% + 0.31% x 57.60% 57.43% 57.23% 56.70% 56.53% 56.33%
x - 12.9
Long term Losses equotion : 67.82%
60.96% 59.33%
50.00%
70.50% -+ 0.07% x
56.53% -+ 0.21% x 16.46
17.27
Prestress tendon section
18.23
25.80
x - 17.2710006
18.23 > x > 25.80 56.33% -+ 0.21% x
x - 18.2342203
page 7 / 15
PCI Monolith H-125cm ; L-26.10m ; CTC-160cm - RSNI (Rev.04)
7.3 Effective Stress Force Resume Prestressed Force at middle % Losses of prestress
Condition
Cable
%UTS effective prestress
[N/mm ]
[mm ]
[kN]
Asp
stress 2
P
2
short term
9.5%
65.5%
1218
5630.46
6855.31
long term
19.4%
55.6%
1034
5630.46
5822.53
VIII. STRESS AND DEFFLECTION ANALYSIS Beam Segment Length (m)
1
2
3
4
5
6
5.250
5.000
5.000
5.000
5.250
0.00
Additional length at the end of the beam =
0.30
m
7
0.00 Total Length =
8
0.00 26.10
m
8.1 Stress at initial Description
Middle
SEC 1-1
SEC 2-2
SEC 3-3
SEC 4-4
SEC 5-5
x - [m]
Span
0.00
5.25
10.25
15.25
20.25
12.75
[kN.m]
755.70
0.00
494.21
726.64
726.64
494.21
755.70
[kN]
7854.49
7854.49
7854.49
7854.49
7854.49
7854.49
7854.49
%
4%
0%
2%
4%
5%
5%
4%
Pi
[kN]
7388.67
7854.49
7662.68
7480.01
7367.18
7333.11
7388.67
e (eccentricity)
[m]
0.312
-0.055
0.185
0.298
0.298
0.185
0.312
Pi.e
[kN.m]
-2303
429
-1417
-2226
-2193
-1356
-2303
Moment Net.
[kN.m]
-1548
429
-923
-1500
-1466
-862
-1548
2
19.48
20.71
20.20
19.72
19.43
19.34
19.48
2
-17.33
4.80
-10.34
-16.80
-16.42
-9.66
-17.33
Allow.
2
stress
Moment DL Jacking Force Losses due to friction
Pi / A
[N/mm ]
M / Wa
[N/mm ]
M / Wb Initial Stresses 2
[N/mm ]
SEC 6-6
[N/mm ]
13.04
-3.61
7.78
12.64
12.36
7.27
13.04
top ( T )
2.15
25.51
9.86
2.93
3.00
9.68
2.15
-1.9
bot ( B )
32.53
17.10
27.99
32.36
31.78
26.60
32.53
33.6
8.2 Stress at service oa o precas , s a ,
ap ragm an pres ress y
eam
=
> Live load and asphalt by composite Description Moment DL
SEC 1-1
SEC 2-2
SEC 3-3
SEC 4-4
SEC 5-5
x - [m]
Span
0.00
5.25
10.25
15.25
20.25
SEC 6-6 12.75
[kN.m]
1667.18
0.00
1090.30
1603.09
1603.09
1090.30
1667.18
Losses due to friction
%
19%
24%
22%
20%
19%
19%
19%
effective prestress P
[kN]
5817.05
5351.24
5543.04
5725.72
5898.58
5855.21
5817.05 -1813.37
P.e
[m]
-1813.37
292.16
-1025.33
-1704.26
-1755.71
-1083.07
Moment --- M1
[kN.m]
-146.19
292.16
64.97
-101.17
-152.62
7.23
-146.19
Moment --- M2
[kN.m]
2010.45
0.00
1314.79
1933.15
1933.15
1314.79
2010.45
2
15.35
15.35
15.35
15.35
15.35
15.35
15.35
2
-1.64
3.27
0.73
-1.13
-1.71
0.08
-1.64
2
1.23
-2.46
-0.55
0.85
1.29
-0.06
1.23
2
4.72
0.00
3.09
4.54
4.54
3.09
4.72
Allow.
2
stress
P/A
[N/mm ]
M 1 / Wa
[N/mm ]
M 1 / Wb
[N/mm ]
M 2 / Wa'
[N/mm ]
M 2 / Wb' Stress at Service 2
[N/mm ]
Note :
( = M2 ) Middle
[N/mm ]
-10.11
0.00
-6.61
-9.72
-9.72
-6.61
-10.11
slab ( S )
7.92
0.00
5.18
7.62
7.62
5.18
7.92
12.6
top ( T )
18.43
18.62
19.17
18.76
18.18
18.52
18.43
31.5
bot ( B )
6.47
12.89
8.19
6.48
6.91
8.68
6.47
-4.2
Moment DL = Moment due to dead load ( Chapter V - Moment Analysis ) Moment Bal = Moment due to uniform load in balance condition ( Chapter 7.4 - Effective Stress Force ) Moment Net = ( 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 )
page 8 / 15
PCI Monolith H-125cm ; L-26.10m ; 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 = 20.71 MPa
M/Wa = 5.57 MPa
top =
+
Pi/A = 20.71 MPa
26.28 MPa
=
M/Wb = -4.19 MPa
effective prestress =
75% UTS
Pi = eccentricity (ei) =
7854.49 -63.27
Mdl = Mbeam =
bottom
= 16.52 MPa
M = Mdl - Pi.e = kN mm
allow comp at
initial =
allow tension initial
0 kN-m
=
496.92
kN-m
33.60 -1.87
MPa MPa
control allow stress = meet requirement
b. Stress at beam middle section when Prestress is applied : Pi/A = 19.47 MPa
M/Wa = -17.31 MPa
top =
+
Pi/A = 19.47 MPa
=
M/Wb = 13.03 MPa
bottom
effective prestress =
70% UTS
Pi = eccentricity (ei) =
7383.19 311.73
kN mm
755.70
kN-m
Mdl = Mbeam =
2.15 MPa
= 32.50 MPa
M = Mdl - Pi.e = allow comp at
initial =
allow tension initial =
-1545.9 kN-m 33.60 -1.87
MPa MPa
control allow stress = m eet requirement
8. 3. 2. STRESS DIAGRAM AT CONST RUCTION
a. Stress at beam middle section when diaphragm, RC deck is install and finish fresh concreting composite slab Pi/A = 18.08 MPa
M/Wa = -5.26 MPa
top =
+
Pi/A = 18.08 MPa
12.81 MPa
=
M/Wb = 3.96 MPa
bottom
effective prestress =
65% UTS
Pi = eccentricity (ei) =
6855.31 311.73
kN mm
Mdl = Mbeam + Madl =
1667.18
kN-m
= 22.04 MPa
M = Mdl - Pi.e = allow comp at initial = allow tension initial =
-469.85
kN-m
33.60 -1.87
MPa MPa
control allow stress = meet requirement
b. Stress at composite beam middle section due to asphaltic layer: slab =
P/A = 18.08 MPa
M2/Wa'= 0.33 MPa
M1/Wa = -5.26 MPa
+
P/A = 18.08 MPa
top =
+
effective prestress =
65% UTS
Pi = eccentricity (ei) =
6855.31 311.73
kN mm
Mdl = Mbeam + Madl =
1667.18
kN-m
13.14 MPa
=
M2/Wb'= -0.71 MPa
M1/Wb = 3.96 MPa
0.55 MPa
bottom
= 21.33 MPa
M1 = Mdl + Pi.e =
-469.85
kN-m
M2 = Masphalt =
140.28 33.60
kN-m MPa
-1.87
MPa
allow comp at
initial =
allow tension initial
=
control allow stress = meet requirement
page 9 / 15
PCI Monolith H-125cm ; L-26.10m ; 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 =
P/A = 15.35 MPa
M2/Wa'= 4.72 MPa
M1/Wa = -1.66 MPa
+
P/A = 15.35 MPa
top =
+
56% UTS
M2/Wb'= -10.11 MPa
Pi =
5822.53
kN
eccentricity (ei) =
311.73
mm
Mdl = Mbeam + Madl =
1667.18
18.42 MPa
=
M1/Wb = 1.25 MPa
effective prestress =
7.92 MPa
bottom
M1 = Mdl + Pi.e =
-147.90
kN-m
M2 = Masphalt + LL =
2010.45
kN-m
service =
31.50
MPa
allow tension at service =
-4.18
MPa
allow comp at
kN-m
= 6.49 MPa
control allow stress = meet requirement
8.4 Deflection 8.4.1 Chamber due to Prestress Load Deflection on middle section : l
P
ee
pi= [ee+(5/6)(e c-ee)] x (P. l2 /8 Ec Ix) pi=
P
ec
where :
-54.22 mm
P = Prestress force Eci = Modulus Elasticity of Concrete
l/2
l/2
Ixi = Section Inertia l = length of anchor to anchor ee = Distance between c.g of strand and c.g of concrete at end ec = Distance between c.g of strand and c.g of concrete at centre
8.4.2 Deflection at initial, ere ction and service condition (based : PCI handbook 4.6.5 Long-Time Chamber Deflection) Deflection () on simple span structure : where : q = Uniform Load 4
q= (5/384)*q*L /Ec Ix)
P = Point Load
3
l = Beam Span
p= P.l /48 Ec Ix
Deflection calculation table : Estimating long-time cambers and deflections WORKING LOAD
Loading q (kN/m)
P (kN)
1. Due to Prestress force 2. Due to beam weight (DL)
9.30
Release (1)
Long time cambers and deflection (2) multipliers Erection multipliers
-54.22
1.80 x (1)
-97.59
2.20 x (1)
19.98
1.85 x (1)
36.97
2.40 x (1)
-34.23 3. Due to ADL
3.27
Service (3) -119.27 47.96
-60.62 6.29
-71.32 3.00 x (2)
18.87
-54.33 4. Due to Composite Overtoping
7.94
15.27
-52.45 2.30 x (2)
35.12
-39.06 5. due to asphaltic (SDL)
-17.33
1.73
1.25
-16.08 6. due to Live Load = UDL + KEL
14.40
109.76
15.38
-0.70 Resume of deflection : 1.
Deflection at service
=
-16.08 mm
2.
Deflection due to Live Load
=
15.38 mm < allow. deflection L/800 =
3.
Total deflection with LL
=
-0.70 mm, chamber upward
31.875 mm
OK
page 10 / 15
PCI Monolith H-125cm ; L-26.10m ; 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
=3420 mm
2. Beam Ctc 3. Span length / 4
=1600 mm …. Control =6375 mm
Thus, Effectif slab width is :
=1600 mm
for slab with fc' = Value =
28.00
MPa
0.85
Partial Rebar: 400 MPa 0 Dia.13 mm
fy = Use As = d=
at tension area b web =
0.00 mm2
220 mm
1190.5 mm
Partial tension rebar ratio : t = As / (bweb x d )
t =
0.00000
t =
t =
0.000
t . fy / fc
Rebar in compresion area is neglected due calculation c = c =
Low Relaxation strand : fpu =
1860
MPa
Strand stress ratio fpu / fpy = dp =
value p = 0.28
0.9 Aps =
1295.0 mm
2
5630.46 mm
Prestress ratio : p = Aps / (beff x dp ) fps = p =
beff = p =
fpu {1 - p / (p.fpu/fc + d/dp ( t-c)))
0.0027174 1749.4 MPa
fps = p =
p fps/fc
1600 mm
0.170
Resume of Steel Index Requirement (SNI Beton 03-2847-2002 pasal 20.8) p + d/dp ( t-c) 0.36 < 0.170
0.306
<
Under Reinf, Meet With Steel Index Requirement
9.2 Momen Capacity b. eff one
Zone 3
c
i
Cc3 Cc2
Zone 3 Zone 2 a
Tps = Aps . Fps Tps = 9849918.17 N
Cc1
Zone 1
dp
d
strength reduction factor = 0.8 Tps=Aps.fps T = As.fy
COMPOSITE BEAM
Location of Depth of Concrete Compression Block (a) : hi wi Aci=hi.wi Conc. Strength fc' i Zone 4
(mm) 200.00
(mm) 1600
(mm2) 320000
3 2
70.00
385
5.00
400
1
112.57
220
Cci=0.85 fc'i.Aci
MPa
Comp (i)
28.00
CIP Slab
N 7616000
26950
28.00
CIP Slab
641410
235
2000
70.00
Beam
119000
273
24764.843
70.00
Beam
1473508
331
Compresion
Point (mm) Point (mm) 100 145.47
Depth of Concrete Compression Block is located at zone 1 a = {(Tps-Cc2-Cc3-Cc4)/(twebx0.85xfc' beam)} + tslab + tflange Mn = (Tps (dp - comp. point) + As.fy (d-comp. point) Mn = 9058.1887 kN.m Bridge life time design for 50 year,so Transient act factor = 1 Mn / Mult = Mult = 1x 5,712kN-m
a= Mn =
1.586
387.57 mm 11322.74 kN.m
>1, Moment capacity m eet with requirement
9.3 Cracking Capacity Stress at bottom girder section due to service load ( bot at service) =
6.47 MPa
Con cr ete flexur al te nsion st ren gt h fr =
5.9 MPa
Crack Moment, Mcr = (bot at service + fr ) Wb.comp + Momen Mcr = Mn / Mcr =
(DL+ADL+LL+I)
6128.23 kN.m 1.478
> 1.2 ---- Cracking Capacity requirement is achieve
page 11 / 15
PCI Monolith H-125cm ; L-26.10m ; CTC-160cm - RSNI (Rev.04)
X. SHEAR ANALYSIS 10.1 Shear calculation based on SNI 03-2847-2002 Alternatif solution to calculated shear on prestress element is use for structure element which have effective prestress above 40% of ultimate tensile stress 40% Ultimate Tensile Strength
= 744
Effective Prestress
= 1034
Section Properties : Ix = 6.368E+10 mm4 Yb = 536.73368 mm Ag =
MPa MPa
Effective Prestress > 40% fpu
Ixcomp = 1.694E+11 mm4 Ybcomp =
852.3 mm
379250 mm2
Load : Effective prestress Pe =
5822.53 kN
Factored Load : qult DL + ADL =
28.86
kN/m
Unfactored Load : q DL + ADL =
20.51
kN/m
qult LL =
25.92
kN/m
q sdl =
1.73
kN/m
Pult LL =
197.57
kN
q DL + ADL =
22.24
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 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. Vn = Vc + Vs Vn = Vu /
where :
Vn = Nominal Shear force Vc = Concrete shear contribution Vs = Shear steel contribution
Vu = Ultimate Shear force = Shear reduction factor = 0.75
Zonafication for shear steel stirup calculation Zone 1
Vn < 0.5 Vc
No need to use stirup
Z on e 2
V n < V c+ [0 .3 5 or ( 75/ 12 00 ) s qr t(f c' )] bw d
R equ ir ed s ti ru p s pa ci ng wi th mi ni mu m sp ac in g :
Zone 3
Vn < Vc+0.33 sqrt(fc') bw d
S ≤ 0.75 H
S ≤ (av.fy) / (0.35 bw)
S ≤ 600mm
S ≤ (av.fy/fpu) (80/Aps) d sqrt(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
page 12 / 15
PCI Monolith H-125cm ; L-26.10m ; CTC-160cm - RSNI (Rev.04)
Shear rebar steel 400 MPa 2 leg Dia.13 mm
fy = Use Av =
shear width : bw = 220
mm
700
mm
265.46 mm2
bw-e =
Shear steel requirement calculation table : ecomp dist. d=dp>0.8H Vu Mu m m m kN kN-m
dp(Vu/Mu)
Vc
Vn
Vs
Shear
kN
kN
kN
Zonasi
Use Space mm
mm
use
0.1
0.267
1.00
889.75
89.25
1.00
1192.03
1186.34
-5.69
2
380
200
0.3875
0.283
1.00
871.78
341.93
1.00
1192.03
1162.37
-29.66
2
380
200
0.775
0.304
1.00
847.55
673.30
1.00
1192.03
1130.07
-61.97
2
380
200
1.7
0.352
1.02
789.71
1421.67
0.57
729.38
1052.95
323.56
3
335
200
2
0.367
1.03
770.95
1651.46
0.48
644.86
1027.94
383.08
3
287
200
3
0.413
1.08
708.43
2371.78
0.32
483.25
944.57
461.32
3
249
200
4
0.455
1.12
645.90
3021.83
0.24
399.54
861.20
461.66
3
258
250
5
0.492
1.16
583.37
3601.60
0.19
346.33
777.83
431.50
3
285
250
6
0.525
1.19
520.84
4111.09
0.15
307.85
694.46
386.60
3
327
300
7
0.553
1.22
458.32
4550.31
0.12
277.36
611.09
333.72
3
388
300
8
0.576
1.24
395.79
4919.26
0.10
251.50
527.72
276.22
3
424
300
9
0.596
1.26
333.26
5217.93
0.08
228.39
444.35
215.96
3
428
300
10
0.610
1.28
270.73
5446.32
0.06
206.92
360.98
154.06
3
430
300
11
0.620
1.29
208.21
5604.44
0.05
186.35
277.61
91.26
2
432
300
12
0.626
1.29
145.68
5692.28
0.03
166.18
194.24
28.06
2
433
300
12.750
0.627
1.30
98.78
5712.05
0.02
151.08
131.71
-19.37
2
433
300
Shear Steel Requirement Position
kN 3000.0 2500.0
Zona 1
2000.0
Zona 2
1500.0
Zona 3
1000.0
Zona 4
Vn =Vu/f
500.0 0.0
beam section point
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
4
4
20
Shear Rebar configuration
Shear spacing S - 250
6
2
8
Shear spacing S - 300
12.75
6.75
23
total shear rebar per half span (row) =
51
total shear rebar per span (row) =
102
page 13 / 15
PCI Monolith H-125cm ; L-26.10m ; CTC-160cm - RSNI (Rev.04)
10.2 Horisontal Shear Width of contact surface area
bv =
250 mm
d=
1216 mm
Effective Height =
fy = Use
0.75 400 MPa 2 leg Dia.13 mm
Area horisontal Shear Steel
Avh =
Horisontal Shear steel Spacing
s= v =
Horisontal Shear steel ratio
265.46 mm2 300 mm 0.354%
Shear horisontal Nominal Vnh = (1.8 Mpa + 0.6 v. fy) . bv .d Vnh =
805.44 KN
Requirement for shear horisontal steel : Vult < Vnh < 350 bv.d Vult = Ultimate shear due to superimposed DL + LL Vult = Vnh =
604.08 kN
484.25 kN
3.5 bv d =
1064.00 kN
RESUME: Shear horisontal : OK
Minimal Use : bys =
250 mm
Spacing =
Avh = 50 by.s / fy
Max. Spacing =
Avh = 215.46875 mm2/m
1232.03 mm or
4 tweb = 880 mm
300.00 mm
min no. Spacing =
85 @ 2D13 for shear horisontal / span
Resume = shear horizontal steel is provide by beam shear steel
XI. END BLOCK DESIGN Block Anchor dimension type 7
a
b
dia hole
(mm)
(mm)
(mm)
165
165
51
Block Area Concrete Area A (mm ) A1 (mm ) A2 (mm ) sqrt(A2/A1) 25182.18
27225
1750000
8.02
70225
2450000
5.91
. 19
265
265
84
64683.23
.
SNI 03-2847-2002 Pasal 11.3.2 (Anchorage Zone) Maximum strand =
19
Anchor Block type =
19
Load factor = Reduction factor () =
1.2
Strand
0.85
1. End Bearing Ultimate Point Load Pu = min (1.2 x nStrand x Astrand x %JF x fpu , nstrand x Astrand x 96% x fpu) Pu =
3141.8
End Bearing stress : comp = comp =
kN Nominal concrete comp. : Pu / A 48.57
fci = MPa
56.00 Mpa
min(2, sqrt(A2/A1)) =
2.0 Nominal fci = x 0.7 x fci x min(2,sqrt (A2/A1)) > comp = Nominal fci = 66.64 48.57 MPa
ten-
Nos
Anchor
sheath
Ult. Point
Block
End Bearing
don
strand
Height
hole
Load
Area
Stress
Nominal comp. fci
(Pu) kN
(A) mm2
(EBS=Pu/A) Mpa
Mpa
84
3141.80
64683.23
48.57
66.64
EBS < Nominal Compresion
64683.23
48.57
66.64
EBS < Nominal Compresion
64683.23
48.57
66.64
EBS < Nominal Compresion
( ai ) mm 0
0
0
0
0
0
1
19
265
2
19
265
84
3141.80
3
19
265
84
3141.80
Remark
page 14 / 15
PCI Monolith H-125cm ; L-26.10m ; CTC-160cm - RSNI (Rev.04)
2. Stirrup and Spalling Reinforcement Load factor = Reduction factor () =
0.85
1.2
fy =
400
MPa
Bursting Steel Diameter closed stirup =
13 mm
Stirup Area =
132.7 mm2
ten-
Nos
Anchor
sheath
Jacking
Bursting
End
don
strand
Height
hole
Force
Area (Abs)
Bearing (EBS)
kN
mm2
( ai ) mm
EBS/0.7
(fcc'-fci)/4.1
fl / 0.5 fy
fcc'
fl
p
Mpa
Mpa
Mpa
sp (mm)
0
0
0
0
0
0
1
19
265
84
2618.1639
64683.23
40.48
68.03
2.9
1.47%
136.6
2
19
265
84
2618.1639
64683.23
40.48
68.03
2.9
1.47%
136.6
3
19
265
84
2618.1639
64683.23
40.48
68.03
2.9
1.47%
136.6
total
57
Anchor Zone Stirrup JF Load = Ult. JF =
7854.49 kN
a1 =
795.00 mm
9425.39 kN
H=
1250 mm
T bursting = 0.25 Ult.JF (1-a1/H)
d bursting = 0.5(h-2e)
T bursting = 857.71049 kN
d bursting = 561.733685 mm
Diameter closed stirup = No. Leg of stirrup = Stirup Area =
13 mm 4 leg 530.9 mm2
Anchor Stirup Rebar = T bursting / 0.5 fy Anchor Stirup Rebar = use no of stirup =
4288.6 mm2 9 pcs
Spalling Rebar Spalling Force = 2% JF Spalling Force = Diameter closed stirup = Stirup Area = use no of stirup =
157.1 kN 13 mm 132.7 mm2 6 pcs
page 15 / 15
PT WIJAYA KARYA BETON
TECHNICAL CALCULATION PCI GIRDER MONOLITH FOR HIGHWAY BRIDGES Project Product Job no Rev. No.
: : : :
TOLL SURABAYA ‐ GRESIK PCI Girder Monolith H‐125cm ; L‐26.15m ; CTC ‐160cm ; fc' 70MPa 13014 F 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, 1
st
nd
& 2 floor
Jl. Jatiwaringin no. 54, Pondok Gede ‐ Bekasi Ph: +62‐21‐8497 ‐3363 fax : +62‐21‐8497 ‐3391 www.wika‐beton.co.id
PT WIJAYA KARYA BETON
TECHNICAL CALCULATION APPROVAL PCI GIRDER MONOLITH FOR HIGHWAY BRIDGES TOLL SURABAYA ‐ GRESIK PCI Girder Monolith H‐125cm ; L‐26.15m ; CTC ‐160cm ; fc' 70MPa Job no. : 13014 F Rev. : 04
Approved by :
Consultan / Owner
Approved by : 18 Juni 2013
Checked by 18 Juni 2013
Design by : 18 Juni 2013
Ir. Achmad Arifin Technical Manager
Ignatius Harry S., S.T. Chief o f Technical
Suko Technical Staff
PCI Monolith H-125cm ; L-26.15m ; CTC-160cm - RSNI (Rev.04)
RESUME OF PCI GIRDER MONOLITH TECHNICALLY CALCULATION 1. BEAM SPECIFICATION
Span Beam Height ( H )
=
25.55 m (beam length
=
1250 mm
Distance ctc of beam ( s )
=
1600 mm
Slab thickness
=
200 mm
Beam Compressive strength
=
70 MPa
Slab Compressive strength
=
28 MPa
Bridge life time
=
50 years
=
26.15 m)
Segment Arr angement
Beam Segment Length (m)
1
2
3
4
5
6
7
5.275
5.000
5.000
5.000
5.275
0.00
0.00
Additional length at the end of beam
=
0.30
m
Total length of the beam
=
26.15
m
Total beam weight
=
25.74
ton
12.7
mm (PC Strand 270 grade, low relaxation)
2. STRESSING
Nos of PC Strand
=
strand
57
Strand configuration No.
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
=
19.39%
at middle
0
0
0
0
fc initial
=
80.0%
fc'
1
19
900
350
2
19
600
225
3
19
300
100
total
57
600.00
225.00
3. LOADING 1. Dead Load
a. Precast Beam
=
9.30
kN/m
b. Slab
=
7.94
kN/m
Slab thickness =
c. Deck Slab
=
2.22
kN/m
d. Asphalt
=
1.73
kN/m
e. Diaphragm
=
6.68
kN
5
pcs
No. Diaphragm
200
mm
Deck slab thickness =
70
mm
Asphalt thickness =
50
mm
for 1 diaphragm equivalent load =
1.05
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)
=
b. Knife Edge Load (KEL)
=
c. Distribution Factor (DF)
=
1.40 for span length <= 50m 49.00 kN/m 1.00
d. Distribution Load q=
9.00 kN/m2
9.00 kN/m2
For Span <= 30m
9.00 x(0,5+15/span)kN/m2
For Span > 30m
e. Live Load Distribution load : Line Load
:
q' = DF x q x s p' = DF x DLA x KEL x s
CALCULATION RESUME
= =
14.40 kN/m 109.76 kN
PCI Monolith H-125cm ; L-26.15m ; 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
=
118.77
kN
b. Additional Dead Load
=
165.28
kN
c. Live Load
=
293.72
kN
Ultimate support reaction =
897.35
kN
5. CONTROL OF BEAM STRESSES 1. Initial Condition
Middle span position top stress =
2.18 MPa
required
>
-1.87 MPa
bottom stress =
32.50 MPa
required
<
33.60 MPa
top stress =
18.52 MPa
<
31.50 MPa
bottom stress =
6.39 MPa
>
-4.18 MPa
2. Service Condition
Middle span position required required
6. CONTROL OF BEAM DEFLECTION
De f l e c t i o n a t t h e m i d d l e of b e a m sp a n
1. Chamber due stressing initial
=
-34.29
mm
=
-
2. Deflection at composite DL
=
-15.76
mm
3. Deflection due live load
=
15.49
mm,required
4. Total deflection at service
=
-0.27
mm
. = 31.94 mm
7. MOMENT AND CRACKING CAPACITY OF BEAM
Moment Capacit y requir ement :
Mult = 1,2*(Beam+Diaphragm+Deck Slab)+1,3*Slab+2*Asphaltic+1,8*(LL+I) Mn
=
5731.79 kN.m
=
9058.19 kN.m
Ratio, Mn / Mu (>1)
=
Cracking Capacit y requir ement :
Mcrack Mn / Mcr
= =
6125.85 kN.m 1.48
CALCULATION RESUME
1.58
PCI Monolith H-125cm ; L-26.15m ; CTC-160cm - RSNI (Rev.04)
TECHNICAL CALCULATION OF PCI MONOLITH BEAM FOR HIGHWAY BRIDGES SPAN L = 25.55 M I. DATA
0.3
L=
25.55 M
0.3
26.15 m
Beam length
=
Beam spacing (s)
=
1600 mm
( edge anchor to e dge an ch or :
Concrete Slab thickness (CIP)
=
200 mm
Asphalt thickness
=
50 mm
Deck slab thickness
=
70 mm
25.85
m)
A
Cross Section H
=
1250
mm
tfl-1
=
75
mm
A
=
400
mm
tfl-2
=
75
mm
B
=
700
mm
tfl-3
=
100
mm
tweb =
220
mm
tfl-4
=
125
mm
tfl-1 tfl-2 tweb
H
tfl-3 tfl-4
II. MATERIAL B
2.1 Concrete Beam
Slab
fc' =
70.0
28.0
fc'i =
56.0
[N/mm ]
0.6 * fc'i =
33.6
[N/mm ]
Tensile 0.25 * Sqrt(fc'i) = Allowable stress at service ………. ( SNI T-1 2-20 04 )
1.9
[N/mm ]
Compressive strength at service at initial
80% fc'
2
[N/mm ] 2
Allowable stress Allowable stress at initial ………… ( SNI T-1 2-20 04 ) Compressive
2
2
0.45 * fc' =
31.5
12.6
[N/mm ]
0.5 * Sqrt(fc') =
4.2
2.6
[N/mm ]
wc =
2500.0
2500.0
[kg/m ]
*0.043*sqrt(fc') =
44970.5
28441.8
[N/mm ]
*0.043*sqrt(fci') =
40222.8
[N/mm ]
f r = 0.7*sqrt(fc') =
5.9
[N/mm ]
Compressive Tensile
2
Modulus of elasticity Concrete unit weight Ec = wc Eci = wc
1.5
1.5
3
2 2
Concrete flexural tension strength (fr) 2
2.2 Prestressing Cable [Uncoated stress relieve seven wires strand] ( ASTM A 416 Grade 270 Low Relaxation or JIS G 3536 ) - Diameter strand
dia
:
12.7
[mm]
- Eff. Section area
Ast
:
98.78
[mm ]
- Modulus of elasticity
Es
: 1.93E+05
[N/mm ]
- Ultimate tensile strength
fu
:
1860
[N/mm ]
- Diameter
dia
:
13
[mm]
- Eff. Section area
Ast
:
132.73
[cm ]
- Modulus of elasticity
Es
: 2.10E+05
[N/mm ]
- Yield stress
fy
:
[N/mm ]
2
2 2
2.3 Steel Reinforcement
400
2
2 2
page 1 / 15
PCI Monolith H-125cm ; L-26.15m ; CTC-160cm - RSNI (Rev.04)
III. SECTION ANALYSIS Remark : Ep 1 = Ep 2 =
2
44970
[N/mm ] [Girder]
28442
[N/mm ] [Slab]
3
2
2
5
Ya'
4 Ya
n = Ep 2 / Ep 1 n=
3
0.63
1
2
Yb
Yb'
1
Base Line
PRECAST BEAM
COMPOSITE BEAM
3.1 Precast Beam [in mm ] Zone
Section
Width
Area
Level
2
Yb
Area*Yb 3
2
Io
Ix
Area*d 4
4
4
Height
Bottom
Upper
mm
mm
mm
mm
mm
mm
mm
6
0.0
200.0
200.0
0
1250
1250.0
0
0
0
0
5
75.0
400.0
400.0
30000
1175
1212.5
36375000
14062500
13699803379
13713865879
4
75.0
220.0
400.0
23250
1100
1141.1
26531250
10592238
8493079360
8503671598
3
875.0
220.0
220.0
192500
225
662.5
1275 31250
122 81901 042
30 44804 457
15 32670 5499
2
100.0
700.0
220.0
46000
125
166.3
7650000
34855072
6312023113
6346878186
1
125.0
700.0
700.0
87500
0
62.5
5468750
113932292
19678538941
19792471233
Total
1250.0
536.7
2 03 55 62 50
1 24 55 34 31 44
5 12 28 24 92 50
6 36 83 59 23 94
Level
Yb
Area*Yb
Io
Area*d
mm
mm
mm
mm
mm
mm
65 89823 7240
379250
3.2 Composite Beam [in mm ] Zone
2 1
Height
Width
Area 2
3
2
4
Ix
4
4
Section
Bottom
Upper
mm
200.0
1011.9
1011.9
202386
1320
1420.0
2873 87794
67461 9234. 2
6 5223 61800 5
70.0
158.1
158.1
11068
1250
1285.0
14222344
4519421.823
2072167895
2076687316
1250.0
700.0
400.0
379250
0
536.7
2035 56250
636 83592 394
3776 85255 78
1. 014 52E +1 1
.
o a
.
.
+
.
+
3.3 R e s u m e [in mm ] 2
Description
Area (mm )
Precast Beam Composite Beam
[composite]
Ya (mm)
Yb (mm)
4
Ix (mm )
3
Wa (mm )
3
Wb (mm )
379250
713
536.7
63683592394
89284452
118650262
592704
668
852.3
1694 27042 528
253 7504 54
1987 86072
[precast]
398
426026221
IV. LOADING 4.1 Dead Load a. Precast Beam
q1 = Ac precast girder x q1 =
b. Slab
0.080 x
[t/m'] =
9.30
[kN/m']
0.810
[t/m'] =
7.94
[kN/m']
0.227
[t/m'] =
2.22
[kN/m']
0.176
[t/m'] =
1.73
[kN/m']
6.68
[kN']
s
2.40 =
q4 = Ac asphaltic x q4 =
e. Diaphragm
0.095 x
0.948
conc. slab
2.40 =
q3 = Ac deck slab x q3 =
d. Asphaltic
0.338 x
conc. Precast
2.50 =
q2 = Ac slab CIP x q2 =
c. Deck slab
0.379 x
s
2.20 =
p
= Vol diaph with 0.20m thickness x
p
=
0.284 x
2.40 =
0.681 note :
Number of diaph = Diaph. placement Location
5
diaph
[ton'] =
from kg to N, multiply by 9.8060
pcs
1
2
3
4
5
0.00
6.39
12.78
19.16
25.55
Support Va
6.68
5.01
3.34
1.67
0.00
Mid Moment
0.00
21.32
42.64
21.32
0.00
Total Diaphragma Flexural Moment at Middle Span eqivalen load q diaphragm
q5=
85.28
kN.m
1.05
[kN/m']
page 2 / 15
PCI Monolith H-125cm ; L-26.15m ; 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 Item P1 kN Load 225 Impact 1.3 LL + I 292.5 kN Distance 8.775 m Va 192.04 kN Va kN M max kN-m DF = S/3.4 M x DF kN-m
P2 225 1.3 292.5 12.775 146.25
P3 50 1.3 65 17.775 19.78
M.max di x = 12.775 m DLA = 30% Impact = 1 + DLA = 1.3
358.07 3404.38 0.47 1602.06
50kN
225kN
225kN
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 :
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) DLA = 1 + 0,3
50 < Span < 90 m
=
1.30
b. Knife Edge Load (KEL)
=
49.00
c. Distribution Factor (DF)
=
1.00
Span >= 90 m
[kN/m']
d. Distribution Load q =
9.00 kN/m
q = 9 kN/m q = 9 x(0,5+15/span)kN/m
which :
for
Span <= 30 m Span > 30 m
e. Live load Distribution load, qudl = DF x q x s = 1.00 x 9.00 KEL, PKEL = DF x DLA x KEL x s =
1.00
M.max at 0.5 span = Va = M LL =
x
1.40
12.775 m
x x
1.60 49.00
x
1.60
=
14.40
[kN/m']
=
109.76
[kN']
238.84 kN 1 87 6. 14 k N. m
RESUME : Moment force cause by D Loading is bigger than Truck Loading
page 3 / 15
PCI Monolith H-125cm ; L-26.15m ; 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
5.28
10.28
15.28
20.28
12.78
Precast beam
758.66
0.00
497.18
729.61
729.61
497.18
758.66
Subtot al
758.66
0.00
497.18
729.61
729.61
497.18
758.66
Slab
648.14
0.00
424.75
623.32
623.32
424.75
648.14
ADL
Asphaltic Layer
140.83
0.00
92.29
135.44
135.44
92.29
140.83
SDL
Diaphragm+Deck Slab
266.76
0.00
174.82
256.54
256.54
174.82
266.76
1055.73
0.00
691.85
1015.30
1015.30
691.85
1055.73 1175.04
Type
Description
DL DL
Subtot al
LL
Distribution load
1175.04
0.00
770.04
1130.04
1130.04
770.04
KEL
701.09
0.00
459.45
674.24
674.24
459.45
701.09
Subtot al
1876.14
0.00
1229.49
1804.29
1804.29
1229.49
1876.14
Total (DL + LL)
3690.53
0.00
2418.52
3549.19
3549.19
2418.52
3690.53
Ultimate total
5731.79
0.00
3756.23
5512.29
5512.29
3756.23
5731.79
Sec 5-5 20.28 -69.73 -69.73 -59.57 -12.94 -24.52 -97.03 -108.00 -87.10 -195.10
Sec 6-6 12.78 0.00 0.00 0.00 0.00 0.00 0.00 0.00 54.88 54.88
-157.21
-361.86
54.88
-
-
(m)
Ultimate total = 1,2*(Beam+Diaphragm+Deck Slab)+1,3*Slab+2*Asphaltic+1,8*(LL+I) VI. SHEAR ANALYSIS [in kN] Mid
Subtot al
span 0.00 0.00 0.00 0.00 0.00 0.00 0.00 54.88 54.88
Sec 1-1 0.00 118.77 118.77 101.47 22.05 41.76 165.28 183.96 109.76 293.72
Sec 2-2 5.28 69.73 69.73 59.57 12.94 24.52 97.03 108.00 87.10 195.10
Sec 3-3 10.28 23.24 23.24 19.86 4.31 8.17 32.34 36.00 65.62 101.62
Total (DL + LL)
54.88
577.77
361.86
157.21
.
.
.
.
Type
Description
DL
Precast beam
DL
Slab
Subtot al
ADL
Asphaltic Layer
SDL
Diaphragm+Deck slab Subtot al
Distribution load
LL
KEL
ma e o a
Sec 4-4 15.28 -23.24 -23.24 -19.86 -4.31 -8.17 -32.34 -36.00 -65.62 -101.62 .
.
(m)
.
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 ] Tension
ten-
Nos
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
19
900
350
75%
0%
75%
2618
2
19
600
225
75%
0%
75%
2618
3
total
Profile
19
300
100
75%
0%
75%
2618
57
600.00
225.00
75%
0%
75%
7854
Pa r a b o l i c c u r v e ( Av e r a g e of St r a n d ' s p o si t i o n v e r t i c a l l y f r o m t h e b o t t o m o f b e a m ( V a l ue f o r Y a x i s ) ) 2
Y = A.x + B.x + C 2
where :
A = Constanta : ( (Ymiddle + Yedge)/(L/2) )
A=
0.002245
B = Constanta : ( L x A )
B=
-0.058027
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 ) X + Y = 0.002245 -0.0580271 X + 0.600000 Cable tendon angle : o
tg =
0.004490 X
+
-0.0580271
eccentricity of tendon at middle section Eccentricity [e]
=
Yb - Ys =
311.73
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)
page 4 / 15
PCI Monolith H-125cm ; L-26.15m ; CTC-160cm - RSNI (Rev.04)
Average of Strand's position vertically from the bottom of beam ( Value for Y axis ) 1.00 0.80 0.60 0.40 0.20 0.00 0
5
10
15
20
25
30
7.2 Losses of Prestress 1. Losses of Prestress (Short Term) a. Friction 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. The equation for calculating the loss of prestress due to friction is : - + .x Po.e Px = ( AASHTO 1992, Chapt. 9.16.1 ) Where :
80.0%
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
75.0% 70.0%
k = Wobble coefficient x = Distance from tensile point to x section
65.0% 60.0%
Friction and Wooble coeficient for grouting tendon in metal sheating = 0.20 with Seven Wire Strand :
0.00
10.00
20.00
30.00
k = 0.003
Table of calculation due to Friction Profile
% JF
a
b
ten-
Nos
don
strand
Edge
Middle
from UTS
0
0
0
0
0%
0.00000
0
0
0
0
0
0%
0.00000
Prestress force (Px) = % UTS
0.00
12.925
25.85
0.000
0.0%
0.00%
0.0%
0
0.000
0.0%
0.00%
0.0%
0.00000
0
0.000
0.0%
0.00%
0.0%
(rad)
0
0
0
0
0%
1
19
900
350
75%
0.00329
-0.0851064
0.170
75.0%
69.74%
67.1%
2
19
600
225
75%
0.00224
-0.0580271
0.116
75.0%
70.49%
67.8%
3
19
300
100
75%
0.00120
-0.0309478
0.062
75.0%
71.26%
68.5%
total
57
600.00
225.00
75%
0.00224
-0.0580271
0.116
75.0%
70.5%
67.8%
b. Anchor set
, . , 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 e longation is resisted by friction just as the initial elongation is resisted by friction. 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 : Cable change angle point
Cable change angle point Anchorage set area
X (effective anchorage set)
Anchorage set area
X (effective anchorage set)
page 5 / 15
PCI Monolith H-125cm ; L-26.15m ; 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 draw in tenNos
From left side
From right side
after anchorage set = % UTS
don
strand
Mpa/mm
mm
X (m)
Px (% UTS)
X (m)
Px (% UTS)
0.00
12.925
25.85
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%
1
19
0.00569
8.00
16.47
69.01%
0.00
0.00%
63.0%
68.28%
67.1%
2
19
0.00517
8.00
17.28
69.59%
0.00
0.00%
64.2%
68.69%
67.8%
3
19
0.00464
8.00
18.24
70.15%
0.00
0.00%
65.3%
69.03%
68.5%
total
57
0.00517
8.00
17.33
69.58%
0.00
0.00%
64.17%
68.67%
67.82%
AVERAGE LOSSES OF PRESTRESS
LOSSES OF PRESTRESS DUE TO ANCHORAGE SET
75.0%
80.0% 75.0%
70.0%
69.76% 69.59% 69.40% 68.67%
70.0% 65.0%
65.0%
60.0% 55.0%
67.82%
64.17%
60.0% 0.00
10.00
20.00
30.00
0.00
Prestress tendon section
10.00
20.00
30.00
Prestress tendon section
c. Elastic Shortening ( ES ) Elastic shortening refers to the shortening of the concrete as the postensioning force is applied. As the concrete shorterns, the ten don 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 = concrete stress at the centre of gravity of prestressing tendons due to prestressing force at transfer and the self weight of the member at the section of maximum positive moment 3.20%
Assumption Losses due ES Pi = Pi =
Total prestressing force at release 68 .7% - 3. 20% = 65.47% UTS x nos x Aps =
6856.0055 kN
2
f cir = Pi / A + Pi. ec / I + Mg.ec/I f cir = so,
24.83 N/mm2 ES =
59.56 N/mm2,
percent actual ES losses = Es/fpu
3.20%
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) SH
=
(ACI 318-95, Chapt. 18.6) 1.63% percent actual SH losses = SH/fpu
30.32 N/mm2
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
"days" is the number of days between the end of moist curing and t he application of prestress.In a structures that are not moist cured, Ksh is typiclly based on when the concrete was cast Ksh =
0.64
V/S =
0.09
RH
=
Volume =
3
9.92 m
Surface =
2
104.71 m
70.00
page 6 / 15
PCI Monolith H-125cm ; L-26.15m ; CTC-160cm - RSNI (Rev.04)
e. Creep ( CR )
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 cree p. Loss of prestress due to a creep is nominally propotional to the net permanent compresive stressin the concrete. the n et permanent compressive stress is the initial compressive stress in the concrete due to the prestressing minus th e tensile stress due to self weight and superimposed deadload moments CR CR
= Kcr*(Es/Ec)*(fcir-fcds) =
136.14 N/mm
(ACI 318-95, Chapt. 18.6)
2
percent actual CR losses = CR/fpu
7.32%
Where :
Kcr =
1.60 (for posten sion ed member)
fcir = stress at center point prestress force, initial condition fcir =
24.826 N/mm
2
Msd = Moment due to all superimposed permanent dead loads applied after prestressing Msd =
1055.73
kN.m
fcds = Stress in a concrete at the cgs of the tendon due to all superimposed dead load fcds 1 = Msdl.e/I = fcds 2 = Madl.e/Ic =
4.48 N/mm
2
0.52 N/mm
2
component of fcd due to load on the plain beam component of fcd due to load on the composite beam
5.00 N/mm
fcds = fcds 1 + fcds 2 =
2
f. Steel Relaxation ( RE ) 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 ten don at that time. Because of other prestress losses, there is a continual reduction of tendon strss; this causes a reduction in the r elaxation rate. The equation for prestress loss due to relaxation of tendons is : RE = [ Kre - J*(SH+CR+ES) ] *C
16.77 N/mm
RE =
(ACI 318-95, Chapt. 18.6)
2
percent actual RE losses = RE/fpu
0.90%
Where :
Kre =
5000.00 (for 270 grade, low relaxation strand)
J =
0.04 (for 270 grade, low relaxation strand) .
=
or p
pu =
.
RESUME DUE TO SHORT & LONG TERM LOSSES Losses
I. Short Ter m Losses
Section
Elastic Total Anchor set Shortening Losses (%)
x (m)
Friction
II. Long Term Losses
Shrinkage (SH)
Creep (CR)
Steel Total Losses Relaxation (%)
0.00
75.00%
64.17%
60.96%
14.04%
59.33%
52.01%
51.11%
23.89%
0.00
75.00%
64.17%
60.96%
14.04%
59.33%
52.01%
51.11%
23.89%
0.00
75.00%
64.17%
60.96%
14.04%
59.33%
52.01%
51.11%
23.89%
0.00
75.00%
64.17%
60.96%
14.04%
59.33%
52.01%
51.11%
23.89%
12.93
70.50%
68.67%
65.47%
5.03%
63.84%
56.52%
55.61%
14.88%
16.47
69.76%
69.76%
66.56%
3.20%
64.93%
57.61%
56.71%
13.05%
17.28
69.59%
69.59%
66.39%
3.20%
64.76%
57.44%
56.54%
13.05%
18.24
69.40%
69.40%
66.19%
3.20%
64.56%
57.24%
56.34%
13.05%
25.85
67.82%
67.82%
64.61%
3.20%
62.98%
55.66%
54.76%
13.05%
friction Losses equotion : UTS
Friction
LOSSES OF PRESTRESS DIAGRAM
0 > x > 12.93
Anchor set ElasticShortening(ES)
80.00%
75.00% -+ 0.35% x
Shrinkage(SH)
12.9 > x > 25.85
Creep(CR) SteelRelaxation(SR)
75.00%
65.00%
64.17%
70.50% 68.67%
69.76% 69.59% 69.40%
65.47% 63.84%
66.56% 66.39% 66.19% 64.93% 64.76% 64.56% 64.61% 62.98%
56.52% 55.61%
51.11% + 0.35% x 12.93 > x > 16.47
12.93
x - 12.925
16.47 > x > 17.28 55.66% 54.76%
56.71% -+ 0.21% x
x - 16.4665699
17.28 > x > 18.24
52.01% 51.11% 0.00
0 > x > 12.93
55.61% + 0.31% x 57.61% 57.44% 57.24% 56.71% 56.54% 56.34%
x - 12.925
Long term Losses equotion : 67.82%
60.96% 59.33%
50.00%
70.50% -+ 0.07% x
56.54% -+ 0.21% x 16.47
17.28
Prestress tendon section
18.24
25.85
x - 17.279148
18.24 > x > 25.85 56.34% -+ 0.21% x
x - 18.239652
page 7 / 15
PCI Monolith H-125cm ; L-26.15m ; CTC-160cm - RSNI (Rev.04)
7.3 Effective Stress Force Resume Prestressed Force at middle % Losses of prestress
Condition
Cable
%UTS effective prestress
[N/mm ]
[mm ]
[kN]
Asp
stress 2
P
2
short term
9.5%
65.5%
1218
5630.46
6856.01
long term
19.4%
55.6%
1034
5630.46
5824.36
VIII. STRESS AND DEFFLECTION ANALYSIS Beam Segment Length (m)
1
2
3
4
5
6
5.275
5.000
5.000
5.000
5.275
0.00
Additional length at the end of the beam =
0.30
m
7
0.00 Total Length =
8
0.00 26.15
m
8.1 Stress at initial Description
Middle
SEC 1-1
SEC 2-2
SEC 3-3
SEC 4-4
SEC 5-5
x - [m]
Span
0.00
5.28
10.28
15.28
20.28
12.78
[kN.m]
758.66
0.00
497.18
729.61
729.61
497.18
758.66
[kN]
7854.49
7854.49
7854.49
7854.49
7854.49
7854.49
7854.49
%
4%
0%
2%
4%
5%
5%
4%
Pi
[kN]
7388.44
7854.49
7662.05
7479.64
7366.75
7332.25
7388.44
e (eccentricity)
[m]
0.312
-0.055
0.185
0.298
0.298
0.185
0.312
Pi.e
[kN.m]
-2303
429
-1421
-2227
-2193
-1360
-2303
Moment Net.
[kN.m]
-1545
429
-924
-1497
-1464
-863
-1545
2
19.48
20.71
20.20
19.72
19.42
19.33
19.48
2
-17.30
4.80
-10.35
-16.77
-16.39
-9.66
-17.30
Allow.
2
stress
Moment DL Jacking Force Losses due to friction
Pi / A
[N/mm ]
M / Wa
[N/mm ]
M / Wb Initial Stresses 2
[N/mm ]
SEC 6-6
[N/mm ]
13.02
-3.62
7.79
12.62
12.33
7.27
13.02
top ( T )
2.18
25.51
9.86
2.95
3.03
9.67
2.18
-1.9
bot ( B )
32.50
17.10
27.99
32.34
31.76
26.60
32.50
33.6
8.2 Stress at service oa o precas , s a ,
ap ragm an pres ress y
eam
=
> Live load and asphalt by composite Description Moment DL
SEC 1-1
SEC 2-2
SEC 3-3
SEC 4-4
SEC 5-5
x - [m]
Span
0.00
5.28
10.28
15.28
20.28
SEC 6-6 12.78
[kN.m]
1673.56
0.00
1096.74
1609.47
1609.47
1096.74
1673.56
Losses due to friction
%
19%
24%
22%
20%
19%
19%
19%
effective prestress P
[kN]
5818.89
5352.84
5545.28
5727.69
5900.45
5856.29
5818.89 -1813.94
P.e
[m]
-1813.94
292.33
-1028.46
-1705.16
-1756.59
-1086.14
Moment --- M1
[kN.m]
-140.38
292.33
68.28
-95.68
-147.12
10.60
-140.38
Moment --- M2
[kN.m]
2016.97
0.00
1321.78
1939.72
1939.72
1321.78
2016.97
2
15.36
15.36
15.36
15.36
15.36
15.36
15.36
2
-1.57
3.27
0.76
-1.07
-1.65
0.12
-1.57
2
1.18
-2.46
-0.58
0.81
1.24
-0.09
1.18
2
4.73
0.00
3.10
4.55
4.55
3.10
4.73
Allow.
2
stress
P/A
[N/mm ]
M 1 / Wa
[N/mm ]
M 1 / Wb
[N/mm ]
M 2 / Wa'
[N/mm ]
M 2 / Wb' Stress at Service 2
[N/mm ]
Note :
( = M2 ) Middle
[N/mm ]
-10.15
0.00
-6.65
-9.76
-9.76
-6.65
-10.15
slab ( S )
7.95
0.00
5.21
7.64
7.64
5.21
7.95
12.6
top ( T )
18.52
18.63
19.22
18.84
18.26
18.58
18.52
31.5
bot ( B )
6.39
12.89
8.13
6.41
6.84
8.62
6.39
-4.2
Moment DL = Moment due to dead load ( Chapter V - Moment Analysis ) Moment Bal = Moment due to uniform load in balance condition ( Chapter 7.4 - Effective Stress Force ) Moment Net = ( 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 )
page 8 / 15
PCI Monolith H-125cm ; L-26.15m ; 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 = 20.71 MPa
M/Wa = 5.57 MPa
top =
+
Pi/A = 20.71 MPa
26.28 MPa
=
M/Wb = -4.19 MPa
effective prestress =
75% UTS
Pi = eccentricity (ei) =
7854.49 -63.27
Mdl = Mbeam =
bottom
= 16.52 MPa
M = Mdl - Pi.e = kN mm
allow comp at
initial =
allow tension initial
0 kN-m
=
496.92
kN-m
33.60 -1.87
MPa MPa
control allow stress = meet requirement
b. Stress at beam middle section when Prestress is applied : Pi/A = 19.47 MPa
M/Wa = -17.28 MPa
top =
+
Pi/A = 19.47 MPa
=
M/Wb = 13.00 MPa
bottom
effective prestress =
70% UTS
Pi = eccentricity (ei) =
7382.97 311.73
kN mm
758.66
kN-m
Mdl = Mbeam =
2.19 MPa
= 32.47 MPa
M = Mdl - Pi.e = allow comp at
initial =
allow tension initial =
-1542.9 kN-m 33.60 -1.87
MPa MPa
control allow stress = m eet requirement
8. 3. 2. STRESS DIAGRAM AT CONST RUCTION
a. Stress at beam middle section when diaphragm, RC deck is install and finish fresh concreting composite slab Pi/A = 18.08 MPa
M/Wa = -5.19 MPa
top =
+
Pi/A = 18.08 MPa
12.88 MPa
=
M/Wb = 3.91 MPa
bottom
effective prestress =
65% UTS
Pi = eccentricity (ei) =
6856.01 311.73
kN mm
Mdl = Mbeam + Madl =
1673.56
kN-m
= 21.99 MPa
M = Mdl - Pi.e = allow comp at initial = allow tension initial =
-463.69
kN-m
33.60 -1.87
MPa MPa
control allow stress = meet requirement
b. Stress at composite beam middle section due to asphaltic layer: slab =
P/A = 18.08 MPa
M2/Wa'= 0.33 MPa
M1/Wa = -5.19 MPa
+
P/A = 18.08 MPa
top =
+
effective prestress =
65% UTS
Pi = eccentricity (ei) =
6856.01 311.73
kN mm
Mdl = Mbeam + Madl =
1673.56
kN-m
13.22 MPa
=
M2/Wb'= -0.71 MPa
M1/Wb = 3.91 MPa
0.55 MPa
bottom
= 21.28 MPa
M1 = Mdl + Pi.e =
-463.69
kN-m
M2 = Masphalt =
140.83 33.60
kN-m MPa
-1.87
MPa
allow comp at
initial =
allow tension initial
=
control allow stress = meet requirement
page 9 / 15
PCI Monolith H-125cm ; L-26.15m ; 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 =
P/A = 15.36 MPa
M2/Wa'= 4.73 MPa
M1/Wa = -1.59 MPa
+
P/A = 15.36 MPa
top =
+
56% UTS
M2/Wb'= -10.15 MPa
Pi =
5824.36
kN
eccentricity (ei) =
311.73
mm
Mdl = Mbeam + Madl =
1673.56
18.50 MPa
=
M1/Wb = 1.20 MPa
effective prestress =
7.95 MPa
bottom
M1 = Mdl + Pi.e =
-142.09
kN-m
M2 = Masphalt + LL =
2016.97
kN-m
service =
31.50
MPa
allow tension at service =
-4.18
MPa
allow comp at
kN-m
= 6.41 MPa
control allow stress = meet requirement
8.4 Deflection 8.4.1 Chamber due to Prestress Load Deflection on middle section : l
P
ee
pi= [ee+(5/6)(e c-ee)] x (P. l2 /8 Ec Ix) pi=
P
ec
where :
-54.43 mm
P = Prestress force Eci = Modulus Elasticity of Concrete
l/2
l/2
Ixi = Section Inertia l = length of anchor to anchor ee = Distance between c.g of strand and c.g of concrete at end ec = Distance between c.g of strand and c.g of concrete at centre
8.4.2 Deflection at initial, ere ction and service condition (based : PCI handbook 4.6.5 Long-Time Chamber Deflection) Deflection () on simple span structure : where : q = Uniform Load 4
q= (5/384)*q*L /Ec Ix)
P = Point Load
3
l = Beam Span
p= P.l /48 Ec Ix
Deflection calculation table : Estimating long-time cambers and deflections WORKING LOAD
Loading q (kN/m)
P (kN)
1. Due to Prestress force 2. Due to beam weight (DL)
9.30
Release (1)
Long time cambers and deflection (2) multipliers Erection multipliers
-54.43
1.80 x (1)
-97.98
2.20 x (1)
20.14
1.85 x (1)
37.26
2.40 x (1)
-34.29 3. Due to ADL
3.27
Service (3) -119.75 48.34
-60.72 6.33
-71.42 3.00 x (2)
19.00
-54.39 4. Due to Composite Overtoping
7.94
15.39
-52.42 2.30 x (2)
35.40
-39.00 5. due to asphaltic (SDL)
-17.02
1.73
1.26
-15.76 5. due to Live Load = UDL + KEL
14.40
109.76
15.49
-0.27 Resume of deflection : 1.
Deflection at service
=
-15.76 mm
2.
Deflection due to Live Load
=
15.49 mm < allow. deflection L/800 =
3.
Total deflection with LL
=
-0.27 mm, chamber upward
31.9375 mm OK
page 10 / 15
PCI Monolith H-125cm ; L-26.15m ; 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
=3420 mm
2. Beam Ctc 3. Span length / 4
=1600 mm …. Control =6387.5 mm
Thus, Effectif slab width is :
=1600 mm
for slab with fc' = Value =
28.00
MPa
0.85
Partial Rebar: 400 MPa 0 Dia.13 mm
fy = Use As = d=
at tension area b web =
0.00 mm2
220 mm
1190.5 mm
Partial tension rebar ratio : t = As / (bweb x d )
t =
0.00000
t =
t =
0.000
t . fy / fc
Rebar in compresion area is neglected due calculation c = c =
Low Relaxation strand : fpu =
1860
MPa
Strand stress ratio fpu / fpy = dp =
value p = 0.28
0.9 Aps =
1295.0 mm
2
5630.46 mm
Prestress ratio : p = Aps / (beff x dp ) fps = p =
beff = p =
fpu {1 - p / (p.fpu/fc + d/dp ( t-c)))
0.0027174 1749.4 MPa
fps = p =
p fps/fc
1600 mm
0.170
Resume of Steel Index Requirement (SNI Beton 03-2847-2002 pasal 20.8) p + d/dp ( t-c) 0.36 < 0.170
0.306
<
Under Reinf, Meet With Steel Index Requirement
9.2 Momen Capacity b. eff one
Zone 3
c
i
Cc3 Cc2
Zone 3 Zone 2 a
Tps = Aps . Fps Tps = 9849918.17 N
Cc1
Zone 1
dp
d
strength reduction factor = 0.8 Tps=Aps.fps T = As.fy
COMPOSITE BEAM
Location of Depth of Concrete Compression Block (a) : hi wi Aci=hi.wi Conc. Strength fc' i Zone 4
(mm) 200.00
(mm) 1600
(mm2) 320000
3 2
70.00
385
5.00
400
1
112.57
220
Cci=0.85 fc'i.Aci
MPa
Comp (i)
28.00
CIP Slab
N 7616000
26950
28.00
CIP Slab
641410
235
2000
70.00
Beam
119000
273
24764.843
70.00
Beam
1473508
331
Compresion
Point (mm) Point (mm) 100 145.47
Depth of Concrete Compression Block is located at zone 1 a = {(Tps-Cc2-Cc3-Cc4)/(twebx0.85xfc' beam)} + tslab + tflange Mn = (Tps (dp - comp. point) + As.fy (d-comp. point) Mn = 9058.1887 kN.m Bridge life time design for 50 year,so Transient act factor = 1 Mn / Mult = Mult = 1x 5,732kN-m
a= Mn =
1.580
387.57 mm 11322.74 kN.m
>1, Moment capacity m eet with requirement
9.3 Cracking Capacity Stress at bottom girder section due to service load ( bot at service) =
6.39 MPa
Con cr ete flexur al te nsion st ren gt h fr =
5.9 MPa
Crack Moment, Mcr = (bot at service + fr ) Wb.comp + Momen Mcr = Mn / Mcr =
(DL+ADL+LL+I)
6125.85 kN.m 1.479
> 1.2 ---- Cracking Capacity requirement is achieve
page 11 / 15
PCI Monolith H-125cm ; L-26.15m ; CTC-160cm - RSNI (Rev.04)
X. SHEAR ANALYSIS 10.1 Shear calculation based on SNI 03-2847-2002 Alternatif solution to calculated shear on prestress element is use for structure element which have effective prestress above 40% of ultimate tensile stress 40% Ultimate Tensile Strength
= 744
Effective Prestress
= 1034
Section Properties : Ix = 6.368E+10 mm4 Yb = 536.73368 mm Ag =
MPa MPa
Effective Prestress > 40% fpu
Ixcomp = 1.694E+11 mm4 Ybcomp =
852.3 mm
379250 mm2
Load : Effective prestress Pe =
5824.36 kN
Factored Load : qult DL + ADL =
28.86
kN/m
Unfactored Load : q DL + ADL =
20.51
kN/m
qult LL =
25.92
kN/m
q sdl =
1.73
kN/m
Pult LL =
197.57
kN
q DL + ADL =
22.24
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 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. Vn = Vc + Vs Vn = Vu /
where :
Vn = Nominal Shear force Vc = Concrete shear contribution Vs = Shear steel contribution
Vu = Ultimate Shear force = Shear reduction factor = 0.75
Zonafication for shear steel stirup calculation Zone 1
Vn < 0.5 Vc
No need to use stirup
Z on e 2
V n < V c+ [0 .3 5 or ( 75/ 12 00 ) s qr t(f c' )] bw d
R equ ir ed s ti ru p s pa ci ng wi th mi ni mu m sp ac in g :
Zone 3
Vn < Vc+0.33 sqrt(fc') bw d
S ≤ 0.75 H
S ≤ (av.fy) / (0.35 bw)
S ≤ 600mm
S ≤ (av.fy/fpu) (80/Aps) d sqrt(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
page 12 / 15
PCI Monolith H-125cm ; L-26.15m ; CTC-160cm - RSNI (Rev.04)
Shear rebar steel 400 MPa 2 leg Dia.13 mm
fy = Use Av =
shear width : bw = 220
mm
700
mm
265.46 mm2
bw-e =
Shear steel requirement calculation table : ecomp dist. d=dp>0.8H Vu Mu m m m kN kN-m
dp(Vu/Mu)
Vc
Vn
Vs
Shear
kN
kN
kN
Zonasi
Use Space mm
mm
use
0.1
0.267
1.00
891.09
89.38
1.00
1192.03
1188.13
-3.91
2
380
200
0.3875
0.283
1.00
873.12
342.45
1.00
1192.03
1164.16
-27.87
2
380
200
0.775
0.304
1.00
848.90
674.35
1.00
1192.03
1131.87
-60.17
2
380
200
1.7
0.352
1.02
791.08
1423.99
0.57
729.21
1054.77
325.56
3
333
200
2
0.367
1.03
772.33
1654.21
0.48
644.69
1029.77
385.07
3
285
200
3
0.413
1.08
709.82
2375.95
0.32
483.12
946.42
463.31
3
248
200
4
0.454
1.12
647.31
3027.44
0.24
399.44
863.08
463.64
3
257
250
5
0.492
1.16
584.80
3608.70
0.19
346.27
779.73
433.46
3
284
250
6
0.524
1.19
522.29
4119.71
0.15
307.83
696.38
388.55
3
326
300
7
0.552
1.22
459.78
4560.48
0.12
277.39
613.04
335.64
3
386
300
8
0.576
1.24
397.27
4931.01
0.10
251.58
529.69
278.11
3
424
300
9
0.595
1.26
334.76
5231.30
0.08
228.52
446.34
217.82
3
428
300
10
0.610
1.28
272.25
5461.34
0.06
207.11
363.00
155.89
3
430
300
11
0.620
1.29
209.74
5621.14
0.05
186.61
279.65
93.04
2
432
300
12
0.626
1.29
147.23
5710.70
0.03
166.52
196.31
29.79
2
433
300
12.775
0.627
1.30
98.78
5731.79
0.02
150.97
131.71
-19.26
2
433
300
Shear Steel Requirement Position
kN 3000.0 2500.0
Zona 1
2000.0
Zona 2
1500.0
Zona 3
1000.0
Zona 4
Vn =Vu/f
500.0 0.0
beam section point
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
4
4
20
Shear Rebar configuration
Shear spacing S - 250
6
2
8
Shear spacing S - 300
12.775
6.775
23
total shear rebar per half span (row) =
51
total shear rebar per span (row) =
102
page 13 / 15
PCI Monolith H-125cm ; L-26.15m ; CTC-160cm - RSNI (Rev.04)
10.2 Horisontal Shear Width of contact surface area
bv =
250 mm
d=
1216 mm
Effective Height =
fy = Use
0.75 400 MPa 2 leg Dia.13 mm
Area horisontal Shear Steel
Avh =
Horisontal Shear steel Spacing
s= v =
Horisontal Shear steel ratio
265.46 mm2 300 mm 0.354%
Shear horisontal Nominal Vnh = (1.8 Mpa + 0.6 v. fy) . bv .d Vnh =
805.44 KN
Requirement for shear horisontal steel : Vult < Vnh < 350 bv.d Vult = Ultimate shear due to superimposed DL + LL Vult = Vnh =
604.08 kN
484.98 kN
3.5 bv d =
1064.00 kN
RESUME: Shear horisontal : OK
Minimal Use : bys =
250 mm
Spacing =
Avh = 50 by.s / fy
Max. Spacing =
Avh = 215.46875 mm2/m
1232.03 mm or
4 tweb = 880 mm
300.00 mm
min no. Spacing =
86 @ 2D13 for shear horisontal / span
Resume = shear horizontal steel is provide by beam shear steel
XI. END BLOCK DESIGN Block Anchor dimension type 7
a
b
dia hole
(mm)
(mm)
(mm)
165
165
51
Block Area Concrete Area A (mm ) A1 (mm ) A2 (mm ) sqrt(A2/A1) 25182.18
27225
1750000
8.02
70225
2450000
5.91
. 19
265
265
84
64683.23
.
SNI 03-2847-2002 Pasal 11.3.2 (Anchorage Zone) Maximum strand =
19
Anchor Block type =
19
Load factor = Reduction factor () =
1.2
Strand
0.85
1. End Bearing Ultimate Point Load Pu = min (1.2 x nStrand x Astrand x %JF x fpu , nstrand x Astrand x 96% x fpu) Pu =
3141.8
End Bearing stress : comp = comp =
kN Nominal concrete comp. : Pu / A 48.57
fci = MPa
56.00 Mpa
min(2, sqrt(A2/A1)) =
2.0 Nominal fci = x 0.7 x fci x min(2,sqrt (A2/A1)) > comp = Nominal fci = 66.64 48.57 MPa
ten-
Nos
Anchor
sheath
Ult. Point
Block
End Bearing
don
strand
Height
hole
Load
Area
Stress
Nominal comp. fci
(Pu) kN
(A) mm2
(EBS=Pu/A) Mpa
Mpa
84
3141.80
64683.23
48.57
66.64
EBS < Nominal Compresion
64683.23
48.57
66.64
EBS < Nominal Compresion
64683.23
48.57
66.64
EBS < Nominal Compresion
( ai ) mm 0
0
0
0
0
0
1
19
265
2
19
265
84
3141.80
3
19
265
84
3141.80
Remark
page 14 / 15
