Project name :

ref. number : Stressing at f ci'= 80.0 % f c'

Location : 2ScSc5-19 & 1ScSc5-12 & 1ScSc5-11 (61 strands)
Beam length : 40.600 m JF = 75.8 % UTS
Date : 23-Apr-24 prepared by : TY Deflection: OK !

I. GENERAL 40.60 m

x
210.0 cm

40.00 m

Beam sectional shape : I SEGMENTAL

Composite / Non Composite Komposit Inner Diafragm,
Beam length : Lb = 40.600 m number: 5
Span length : L = 40.000 m thickness: 20.0 cm
Clear span : Ln = 39.700 m Top slab thickness: 20.0 cm
Curvature : r = 0.000 m Deck plate thickness: 7.0 cm
Girder space : s = 1.850 m
NOTE1
Segemental joint posistion, x = 17.000 m
NOTE1: ASSOCIATES VALUE NOT VALID IF MONOLITH
II. MATERIALS
2.1. Concrete
Beam Slab
2 2
* Concrete grade : cube strength, f cu : 500 [kg/cm ] 350 [kg/cm ]
2 2
cylinder strength, f c' : 432 [kg/cm ] 291 [kg/cm ]
* Modulus of elasticity Ec = 3.64E+05 [kg/cm2] 2.99E+05 [kg/cm2]
* Unit weight gc= 2500 [kg/m3] 2400 [kg/m3]
* Allowable stresses :
- At transfer condition
concrete strength at stressing : 80.00 % f c'.
2
f ci' = 345.3 [kg/cm ] 233.0 [kg/cm2]
Compressive stress : 0.55 f ci'
2 2
= 189.9 [kg/cm ] 128.2 [kg/cm ]
Tensile stress : -0.80 SQR(f ci')
2 2
= -14.9 [kg/cm ] -12.2 [kg/cm ]
- At service condition
2
f c' = 431.6 [kg/cm ] 291.3 [kg/cm2]
Compressive stress : 0.40 f c'
= 172.6 [kg/cm2] 116.5 [kg/cm2]
Tensile stress : -1.60 SQR(f c')
= -33.2 [kg/cm2] -27.3 [kg/cm2]

2.2. Steel rebar

* Diameter < 13 mm, BjTp - 24
fy = 2400 [kg/cm2]
* Diameter >= 13 mm, BjTd - 40
fy = 4000 [kg/cm2]
* Modulus of elasticity, Es = 2.1E+06 [kg/cm2]

2.3. Prestressing steel

* Uncoated stress-relieved seven wire strand.
* Grade-270 - ASTM A416.
* Nominal diameter : 12.70 mm.
* Nominal area : 98.71 mm2.
2
* Modulus of elastisity : 1.97E+06 kg/cm
* Breaking Load : 18.700 ton.
* Low-Relaxation.

III. REFERENCE and CODE

* Bridge Management System (BMS Indonesia-Australia)

IV. CROSS SECTION of GIRDER

bef = 154.8

20.0
60.0 60.0
7.0 7.0
80.0 13.0 80.0 13.0

12.0 12.0

h= 210.0 128.0 128.0

20.0 20.0

25.0 25.0

25.0 25.0
70.0 70.0

Precast Komposit
bef : 154.8 [cm]
h : 210.0 [cm] 230.0 [cm]

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COPYRIGHT PT VSL INDONESIA PAGE 1 OF 6
 Project name :
ref. number : Stressing at f ci'= 80.0 % f c'
Location : 2ScSc5-19 & 1ScSc5-12 & 1ScSc5-11 (61 strands)
Beam length : 40.600 m JF = 75.8 % UTS
Date : 23-Apr-24 prepared by : TY Deflection: OK !

2 2
Ac : 7495.0 [cm ] 10590.6 [cm ]
Ac : Y top : 109.2 [cm] 94.4 [cm]
Ya : Y bottom : 100.8 [cm] 135.6 [cm]
4 4
Yb : Ix : 41087032.6 [cm ] 72317460.3 [cm ]
3 3
W top composite : - [cm ] 766426.3 [cm ]
3
W top precast : 376260.5 [cm ] 972574.8 [cm3]
W bottom : 407602.8 [cm3] 533144.4 [cm3]

V. LOADS,and related MOMENTS at the middle of span (and at x for segemental beam)

5.1. Selfweight of beam

qsw = Ac x gc
= 1.874 ton/m.
M sw = (qbs x L^2)/8
= 374.750 ton-m. at x= 366.318 tm

5.2. Self weight of topping slab

* Thick's, t= 0.200 m.
* qts = s.t.gc
= 0.888 ton/m.
* M ts = (qts x L^2)/8
= 177.600 ton-m. at x= 173.604 tm

5.3. Superimposed dead load (SDL)

a. Deck slab
* Thick's t= 0.070 m.
* qds = s.t.gc
= 0.210 ton/m.
* M ds = (qds x L^2)/8
= 42.000 ton-m. at x= 41.055 tm
b. Diafragm
* Pd = 1.307 ton const.for formula = 0.625
* Md = 32.670 ton m at x= 31.935 tm inner diaf. = 5
c. Trotoar + Railing
* qt = [total]
= 0.000 ton/m.
* M t = (qt x L^2)/8
= 0.000 ton-m. at x= 0.000 tm
d. Trotoar Live load
* qtl = [total]
= 0.000 ton/m.
* M tl = (qtl x L^2)/8
= 0.000 ton-m. at x= 0.000 tm
e. Aspalt
* Thickness, t = 0.075 m.
* U weight, gas = 2.300 ton/m3.
qas = s x t x gas
= 0.319 ton/m.
M as = (qas x L^2)/8
= 63.825 ton-m. at x= 62.389 tm

5.4. Live load

* For calculation of strength of girders, should use "D" Load.
* Line load, P = 12.000 ton/m per way.
or Pg = P/2.75 ton.
= 8.073 ton per girder.
* Impact load: Impact need only considered for
line load "Pg".
DLA = 0.400
K= 1.400
* Uniformly distributed load:
- L < 30.0 m, pr = 2.2 ton/m/way.
- L > 30.0 m, pr = 2.2x(0.5+15/L) ton/m/way.

For L = 40.000 m
pr = 1.925 ton/m/way.
or pr = s . p/2.75 ton/m per girder.
= 1.295 ton/m per girder.
* Loading reduction factor D a= 1.000
* For moment calculation
p = a . pr
= 1.295 ton/m per balok.
P = a . K . Pg
= 11.302 ton per balok.
M LL = p.L^2/8 + P.L/4
= 372.018 ton-m. at x= 363.648 tm
* For shear calculation
p = a . pr
= 1.295 ton/m per girder.
P = a . K . Pg
= 11.302 ton per girder.

SERVICE (ton-m) ULTIMATE (ton-m)

5.5. Resume of loads and related moments at x at x
* Moment due to beam selfw't M sw = 374.75 366.32 449.70 439.58
* Moment due to slab selfw't, M ts = 177.60 173.60 213.12 208.32
* Moment due to deck plate, M ds = 42.00 41.06 84.00 82.11
* Moment due to diafragm, Md = 32.67 31.93 65.34 63.87
* Moment due to trotoal +railing, Mt = 0.00 0.00 0.00 0.00
* Moment due to trotoar live load, M tl = 0.00 0.00 0.00 0.00
* Momen beban asphalt, M as = 63.83 62.39 127.65 124.78

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COPYRIGHT PT VSL INDONESIA PAGE 2 OF 6
 Project name :
ref. number : Stressing at f ci'= 80.0 % f c'
Location : 2ScSc5-19 & 1ScSc5-12 & 1ScSc5-11 (61 strands)
Beam length : 40.600 m JF = 75.8 % UTS
Date : 23-Apr-24 prepared by : TY Deflection: OK !

* Moment due to live load, M LL = 372.02 363.65 744.04 727.30

-------------------- ------------------ ----------------- ---------------
Moment total, M and M ult, respectively = 1062.86 1038.95 1683.85 1645.96

VI. ANALYSIS
6.1. Prestressing force

2ScSc5-19 & 1ScSc5-12 & 1ScSc5-11

cgc Y1 [cm] : 100.802 11.803 100.802

cgs Yp [cm] : 100.802 100.802
Concrete cover, = 11.803 cm.
Eccentricity, e= 88.998 cm. ep = 0.000

Check at two conditions:

6.1.1. Initial condition at the middle of span

Top fiber :
s t = Pi/Ac - Pi.e/Wt + M sw/Wt => -14.9
Pi <= 1110.098 ton. ..... (1)
Bottom fiber:
s b = Pi/Ac + Pi.e/Wb - M sw/Wb <= 189.9
Pi <= 801.226 ton. ..... (2)

From (1) dan (2) obtained Pi <= 801.226 ton. ..... (3)

6.1.2. Final condition at the middle of span

Top fiber :
s t = Pe/Ac - (Pe.e-M sw)/Wtp + (M LL+M SDL)/Wtc => 172.6
Pe => 376.456 ton. ..... (4)
Bottom fiber:
s b = Pe/Acp + (Pe.e-M sw)/Wbp - (M LL+M SDL)/Wbc => -33.2
Pe => 575.210 ton. ..... (5)

From (4) and (5) obtained Pe => 575.210 ton. ..... (6)

Long term losses are assumed = 15 %.

From (3) and (6) shown that stressing shall be single stage.

Number of required strands approximatly = 51 strands

Number of provided strands = 61 strands
Type of tendons choosed 2ScSc5-19 & 1ScSc5-12 & 1ScSc5-11
( SINGLE -LIVE END)
6.2. Prestress losses
JACKING FORCE = 75.8 % UTS.
then, PJF = 864.080 ton.

6.2.1. Short term losses

6.2.1.1. Friction at anchor and jack
Loss for VSL system, dfa = 3 %.
Force at anchor, Pa = (1-dfa) . PJF
= 838.158 ton.
6.2.1.2. Firction due to curvature and wooble effect
Px = Pa.e^(-mu(alpha+beta.lx))
where
Px : prestress force at x from anchor.
mu : Coefficient for friction between duct and strand,
used mu = 0.200
alpha : number of curvature angle until x.
beta : coefficient for wobble effect,
used beta = 0.0114
Point- 2 (middle of span)
L2 = 20.300 m.
alpha = 0.087 rad.
P2 = 786.388 ton.
Titik-
3 (beam end)
L3 = 40.600 m.
alpha = 0.175 rad.
P3 = 737.816 ton.

6.2.1.3. Draw-in
draw-in influence distance at cable,
xd = SQR(dr . Ep . Ap / m)
where :
dr = draw-in occurred of used system,
at VSL system, draw-in is = 0.006 m.
Ep = Elasticity of prestressing steel
2
For used strand, Ep = 1.95E+06 kg/cm .
Ap = total area of used strands,
namely = 60.213 cm2.
m = inclination of force from diagram,
= 2(Pa - P2)/Lb = 2550.2 kg/m.
Then, obtained
xd = 16.621 m.
Hence,
P1 = 753.385 ton.
P2 = 786.388 ton.
P3 = 737.816 ton.

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COPYRIGHT PT VSL INDONESIA PAGE 3 OF 6
 Project name :
ref. number : Stressing at f ci'= 80.0 % f c'
Location : 2ScSc5-19 & 1ScSc5-12 & 1ScSc5-11 (61 strands)
Beam length : 40.600 m JF = 75.8 % UTS
Date : 23-Apr-24 prepared by : TY Deflection: OK !

Pave = 765.289 ton.

2
T2pi = 12709.7 kg/cm .
6.2.1.4. Elastic shortening of concrete
dTpe = n.Tst/2
i = (I/Ac)^0.5
= 74.040 cm.
Ke = (Ap/Ac) (1+e^2/i^2)
= 0.020
n= Ep/Ec
= 5.419
dTpe' = n.Ke.Tpi/(1+n.Ke)
= 1222.6 kg/cm2.
Due to selfweight of beam;
M= 374.750 ton-m.
dTpe = ((dTpe')-(n.M.y/I))/2
= 391.4 kg/cm2.
P2i = P2 - Ap.(dTpe)
= 762.823 ton.
6.2.2. Long term losses
6.2.2.1. Shrinkage

dTsh = Ep.Eb.ke.kh.kp
Theoritical thickness of beam = 306 mm.
From Australian Standard 1481-1978 determined;
2
Ep = 1.97E+06 kg/cm .
Eb = 4.00E-04 for humidity = 70.0 %.
ke = 0.649
kh = 0.910 for stressing after = 14.0 days
kp = 100/(100+20.r) where r = percentage of rebar.
rebar chosen, diameter
D = 13 mm.
number = 22 nos
hence, r = 0.39 %.
= 0.928

2
dTsh = 431.7 kg/cm .

6.2.2.2. Creep

dTc = kc.kd.ke.kh.Ep.Tci/Ec
where;
kc = 1.10 for humidity = 70.0 %.
kd = 1.200 for stressing after = 14.0 days
ke = 0.649
kh = 0.910
2
Ep = 1.97E+06 kg/cm .
2
Ec = 3.64E+05 kg/cm .
2
Tci = 147.1 kg/cm .

2
dTc = 621.1 kg/cm .

6.2.2.3. Relaxation of strand

dTr = Fr.R.Tpi.[1-2.(dTsh+dTc)/Tpi]
Pi = 762.823 ton.
66.9 % UTS --> Fr = 1.844
For low-relaxation strand, pure relaxation
R= 2.5 %.
2
Tpi = 12668.7 kg/cm .
2
dTsh+dTc = 1052.8 kg/cm .

2
dTr = 486.9 kg/cm .

6.2.3. Resume of prestress force in beam

* After short term losses;

P1 = 729.820 ton.
P2 = 762.823 ton. Pi max. = 801.226 ton.
P3 = 714.251 ton.

* After long term, losses;

Total long term losses;
dTt = dTsh + dTc + dTr
= 1539.6 kg/cm2.
P1 = 637.114 ton.
P2 = 670.118 ton. Pe required = 575.210 ton.
P3 = 621.545 ton.
6.2.4. Stresses at critical section
1. AT THE MIDDLE OF SPAN
* Immediately after transfer;
Stresses CHECK Allowable
Top fiber : 20.9 kg/cm2. OK ! -14.865
Bottom fiber : 176.4 kg/cm2. OK ! 189.906

* At service condition;

Slab top fiber : 56.9 kg/cm2. OK ! 116.510

Beam top fiber : 142.4 kg/cm2. OK ! 172.642
Bottom fiber : 0.1 kg/cm2. OK ! -33.240

2. AT SUPPORT

_________________________________ __________________________
COPYRIGHT PT VSL INDONESIA PAGE 4 OF 6
 Project name :
ref. number : Stressing at f ci'= 80.0 % f c'
Location : 2ScSc5-19 & 1ScSc5-12 & 1ScSc5-11 (61 strands)
Beam length : 40.600 m JF = 75.8 % UTS
Date : 23-Apr-24 prepared by : TY Deflection: OK !

* Immediately after transfer;

Top fiber : 111.8 kg/cm2. OK ! -14.865

Bottom fiber : 111.8 kg/cm2. OK ! 189.906

* At service condition;

2
Top fiber : 79.1 kg/cm . OK ! 172.642
Bottom fiber : 79.1 kg/cm2. OK ! -33.240

6.2.5. Elongation of cables due to stressing

* Force diagram at stressing;

PJF = 864.080 ton. Ljack = 0.750 m.
P1 = 838.158 ton.
P2 = 786.388 ton. L2 = 20.300 m.
P3 = 737.816 ton. L3 = 20.300 m.

* Elongation of cable is obtained by formula:

dLi = (Pi x Li) / (Ep x Ap)

Hence, dL1 = 5.5 mm.

dL2 = 139.0 mm.
dL3 = 130.4 mm.

Total elonagtion of cable is = 274.9 mm.

6.3.Ulimate capacity calculation

Ultimate moment = 1683.85 ton-m.

2
Apt = 60.21 cm .
2
fp = 19000.00 kg/cm .
2
f e min = 10580.99 kg/cm .
2
0.5*f p = 9500.00 kg/cm .
fe min > 0.5*fp OK!

s pu = f p*(1-k1*k2/j)
k1 = 0.400
k2 = 1/(bef*dp*f c')*{Apt*fp + (Ast - Asc)/f sy}
= 0.114
0.85 - 0.007*(f c'-28) = 0.843
j = 0.843
s = 17968.273 kg/cm2.
T = 1081.925 ton.

C = T ====> T = j * kud * bef * f c'

a = j * kud = 24.06 cm.

a,max = 20.00 cm.

M n = T * (dp - a/2) = 2230.560 ton-m. Strength reduction factor, f = 0.900

M cr = Zb*(f cf' + P/Ag) +P*e = 1110.956 ton-m.
M uk = fM n = 2007.504 ton-m.
Muk > Mu and Muk > 1.2*Mcr ===> OK !!! (Rebar not considered yet)

6.4. Shear Calculation

* At section with distance d from support, d = 2.18 m.

bv = 11.10 cm.
0.8h = 168.00 cm.
bw = 20.00 cm

Shear Moment
[ton] [ton-m]

- Due to selfweight of beam : 33.949 78.535

- Due to selfweight of slab : 16.089 37.219
- Due to SDL : 10.240 25.742
- Due to live load :
- Load P : 5.651 12.330
- Load p : 23.463 54.278

- Factor for dead load = 1.200

- Factor for SDL = 2.000
- Factor for live load = 2.000

- ULTIMATE LOAD : 138.753 323.605

2
vu = Vu/(bv*d ) = 57.29 kg/cm .

* Maximum concrete shear strength

Vc = 0.2 * f c' * bv * d + Pv
Pv = dy/dx * Pe = 50516.01 kg.
Vc = 251540.65 kg.

* Flexural shear cracking strength

Vc = b1 * b2 * b3* bv * d * {(Ast+Apt)*f c'/(bv*d)}^(1/3) + V0 +Pv

b1 = 1.10
b2 = 1.00
b3 = 1.00

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COPYRIGHT PT VSL INDONESIA PAGE 5 OF 6
 Project name :
ref. number : Stressing at f ci'= 80.0 % f c'
Location : 2ScSc5-19 & 1ScSc5-12 & 1ScSc5-11 (61 strands)
Beam length : 40.600 m JF = 75.8 % UTS
Date : 23-Apr-24 prepared by : TY Deflection: OK !

Ast = 0.00
2
s cp,f = Pe*ex/Wb + Pe/Ac = 82.10 kg/cm .
M 0 = Z * T cp,f = 437703.35 kg-m.
V0 = M 0/(M'/V') = 187675.00 kg.
Vc = 296189.92 kg.

* Cracking shear strength at web

Vc = Vt + Pv
Vt = 0.3*((f c')^0.5 + f pc)*bv*d = 92782.55 kg.
Vc = 143298.56 kg.

Vc, min = 143298.56 kg..

2
vs = vu/0.7 - vc = 22.68 kg/cm .

provided stirrups diameter = 10 12 13 16 mm.

2
Av = 1.57 2.26 2.65 4.02 cm .
stirrups space, s = Av*f y/(vs*bv)
s max = 14.97 21.56 42.17 63.87 cm.
VII. Control to point load T

DLA=0.3
4.7 19.0 19.0 (ton).

40.0 m.
16.0 4.0 5.0 15.0 (m).

19.447 23.242 (ton).

M mid = 370 ton-m.

* Stresses due to point load;

Slab top fiber : 56.6 kg/cm2. Ok!

Beam top fiber : 142.2 kg/cm2. Ok!
Bottom fiber : 0.5 kg/cm2. Ok!

VIII. Deflection control at the middle of span (" -"=downward, "+"=upward )

8.1. Deflection due to selfweight

Y = - 5/384 x q x L^4 / EI = -4.2 cm.
8.2. Deflection due to SDL
Y = - 5/384 x qDL x L^4 / EI - 1/48 x Pd x L^3 / EI = -0.8 cm.
8.3. Deflection due to T
Y = [appropriated formula] -2.1 cm.
8.4. Deflection due to live load
Y = - 5/384 x p x L^4 / EI - 1/48 x P x L^3 / EI = -2.2 cm.
8.5. Deflection due to effective prestress force
Y = 5/384 x (8xPxe/L^2) x L^4 / EI = +6.7 cm.

IX. Resume
Prestress force:
Pi = 762.823 ton, or 66.87 % UTS.
Pe = 670.118 ton, or 58.75 % UTS.
PJF = 864.080 ton, or 75.75 % UTS.
Elongation of strand due to stressing = 275 mm.

Deflection ; Short term Long term

Due to SW+SDL+T) = -7.1 -12.1 cm.
Due to SW+SDL+LL = -7.2 -12.2 cm.
Due to SW+SDL+T+PT = -0.4 -5.4 cm.
Due to SW+SDL+LL+PT = -0.6 -5.6 cm.
Due to live load only -2.2 OK ! cm.
Allowable defl.=L/ 800 = -5.0 CHECKED cm.

X. Rotation at support
At service condition: 1DL+1LL+1PT
R= 0.005776 rad

XI. Longitudinal displacement at beam end

due to elastic shortening DLe = 9 mm After erection of beam:
due to shrinkage DLs = 9 mm DLs+DLc+DLT = 30 mm
due to creep DLc = 14 mm
due to temperature DLT = 7 mm

XII. Vertical reaction at support

DL = 70.072 t SW = 38.037 t
LL = 31.939 t
1DL+1.5LL, Vu = 117.981 t  Bearing: [appropriated bearing]

XIII. Quantity
Weight of beam = 76.07 t
Weight of strand = 2.01 t
Concrete volume= 30.43 m3
Strand content= 66.18 kg/m3

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COPYRIGHT PT VSL INDONESIA PAGE 6 OF 6