I 24.54m Girder_Linkslab
February 2, 2017 | Author: Sumane Suma | Category: N/A
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CALCULATION SHEET OF PC-I PRE-TENSIONING 24.54M
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1. INITIAL DATA 1.1. GENERAL CONDITIONS Design standard: 22TCN - 272 - 05 Live Load: HL-93 c
Wb Weff
c
n@a
Wb Total width of cross section =12.00 m wp Walk & Bicycle Lane Width =2.00 m Carriage Way Width w =7.00 m Width of Curb c =0.50 m Number of girder n =7.00 girders Depth of Girder Section h = 1143 mm Spacing of girder S =1.75 m S Distance from CL of external girder to extreme edge of deck slab =0.75 m 1 Length of Girder L =24.54 m Ls Length Span between Bearings =24.24 m Skew angle of bridge =90 deg. α tw Thickness of wearing surface =50 mm 1.2. MATERIAL 1.2.1. Prestressing Steel Prestress classification: ASTM A416-90a ‘Uncoated Seven Wires Stress Relieved Strand for Pre-stressed Concrete” Type of presstresing steel: Low-relaxation Ep Modulus of elasticity =197000 MPa fpu Tensile strength =1860 MPa f Yield strength =1674 MPa py Stress limits for Pretensioning Tendons 0.75fpu Immediately prior transfer =1395 MPa 0.80f At Service limit state after losses =1339 MPa py Strand Properties Dp Nominal diameter =12.7 mm A Nominal Area =99 mm2 p fpj Stress in the prestressing steel at jacking =1395 MPa Pj Jacking Force =138 KN 1.2.2. Reinforcing Steel Enter "1" for ASTM A615 Enter "0" for TCVN 1651-1 Reinf . Standard: (Enter "0" for TCVN 1651-2-2008, "1" for ASTM A615) 0 Es fy fyr
Modulus of elasticity Yield strength for deform bar Yield strength for round bar Reinforcing bar Area
=200000 Mpa =400 Mpa =300 Mpa
Diameter (mm2)
10 79
14 151
16 202
18 254
20 314
22 380
25 491
28 616
32 801
1.2.3. Concrete Density of concrete Coefficient of thermal expansion for normal concrete Poisson's ratio Average ambient relative humidity PC-I Girder Specified compressive strength of concrete at 28 days Compressive strength of concrete at time of initial prestress Modulus of elasticity
γc p H f'c f'ci Ec Eci fr 0.6f'ci
Modulus of rupture for normal concrete Limits of compressive stress of concerete at time of initial prestress Limits of tensile stress of concrete at time of initial prestress 0.58√f'c Limits of compressive stress of concrete at service limit state after losses 0.6f'c Due to the sum of eff. pretress, permanent loads and transient loads 0.45f'c Due to the sum of effective prestress and permanent loads 0.4f'c Due to live load and 1/2 the sum of eff. prestress and permanent loads Limits of tensile stress of concrete at limit state after losses Moderate corrosion conditions (for stage II) 0.5√f'c Severe corrosive conditions (for stage III) 0.25√f'c Cast-in-place Slab f'cs Specified compressive strength of concrete at 28 days Ecs Modulus of elasticity Limits of compressive stress of concrete at service limit state after losses 0.45f'cs Due to the sum of effective prestress and permanent loads 0.4f'cs Due to live load and 1/2 the sum of eff. prestress and permanent loads Material Modulus Ratio npi = Ep/Eci np = Ep/Ec nsi = Ep/Eci ns = Ep/Ec ncs = Eci/Ec
=24.5 KN/m3 =1.08E-05 / 0C =0.2 =75 % =50 Mpa =42.5 Mpa =38007 Mpa =35041 Mpa =4.45 Mpa =25.50 Mpa =-3.78 Mpa =30.00 Mpa =22.50 Mpa =20.00 Mpa =-3.54 Mpa =-1.77 Mpa =30 Mpa =29440 Mpa =13.50 Mpa =12.00 Mpa =5.622 =5.183 =5.708 =5.262 =0.775
2. PARAMETERS OF GROSS SECTION Cross-section Dimensions at Middle section
Notes: - Counter-clockwise adds to section - Clockwise subtracts from section s be
g f
e
Precast Plank
d j k c m
h
b a
Dimensions (mm) a 178 b 190 c 483 d 114 e 178 f g 180 j k 410 m 178 n 558
n
Cross-section Dimensions at End section s be
g f
e
Precast Plank
d j k c h
m
b a
n
Dimensions (mm) a 178 b 74 c 891 d e f g 180 j k m 410 n 558
2.1. Properties of Section at End section Point 1 2 3 4 5 6 7 8 9 10 11 12
yi
zi
A-i
Sy-i
Sz-i
Iyi
Iz-i
Iyz-i
Pi
(mm)
(mm)
(m2)
(m3)
(m3)
(m4)
(m4)
(m4)
(mm)
0.00000 0.00157 0.00474 0.30284 1.83672 0.30284 0.00474 0.00157 0.00000 -
0.00108 0.01029 0.00599 0.02303 0.01969 0.02303 0.00599 0.01029 0.00108 -
0.00004 0.00365 0.00523 0.07835 -0.07835 -0.00523 -0.00365 -0.00004 -
0.2046
0.0084
-0.0000
0 254 279 279 205 205 -205 -205 -279 -279 -254 0
0 0 20 178 252 1143 1143 252 178 20 0 0
Total
0.0051 0.0441 0.0338 0.1827 0.4686 0.1827 0.0338 0.0441 0.0051 0.5000
0.00010 0.00873 0.01454 0.25480 1.07129 0.25480 0.01454 0.00873 0.00010 0.2713
0.00271 0.02460 0.01637 0.07489 -0.07489 -0.01637 -0.02460 -0.00271 -
1200 1000 800
z-z
600 400 200 0 -400
-200
0
y-y
200
400
A ey
=0.500 m2 =0.000 m
ez
=0.543 m
Iy
=0.057 m4
Iz
=0.008 m4
Ix
=-0.000 m4
yb
=0.543 m
yt
=0.600 m
Sb
=0.106 m3
St
=0.096 m3 =152 mm
A/P
254.0 32.0 158.0 104.7 891.0 410.0 891.0 104.7 158.0 32.0 254.0 3289.3
2.2. Properties of Section at Middle section Point 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
yi
zi
A-i
Sy-i
Sz-i
Iyi
Iz-i
Iyz-i
Pi
(mm)
(mm)
(m2)
(m3)
(m3)
(m4)
(m4)
(m4)
(mm)
0 254 279 279 89 89 205 205 -205 -205 -89 -89 -279 -279 -254 0
0 0 20 178 368 851 965 1143 1143 965 851 368 178 20 0 0
Total
0.0051 0.00010 0.00271 0.0441 0.00873 0.02460 0.0868 0.04741 0.03195 0.0430 0.05240 0.00765 -0.0886 -0.16084 -0.02604 0.0365 0.07692 0.01496 0.4686 1.07129 0.0365 0.07692 -0.01496 -0.0886 -0.16084 0.02604 0.0430 0.05240 -0.00765 0.0868 0.04741 -0.03195 0.0441 0.00873 -0.02460 0.0051 0.00010 -0.00271 0.3612
0.1868
-
0.00000 0.00157 0.02020 0.05041 -0.21936 0.12190 1.83672 0.12190 -0.21936 0.05041 0.02020 0.00157 0.00000 -
0.00108 0.01029 0.00960 0.00102 -0.00604 0.00460 0.01969 0.00460 -0.00604 0.00102 0.00960 0.01029 0.00108 -
0.00004 0.00365 0.01230 0.00700 -0.03576 0.02365 -0.02365 0.03576 -0.00700 -0.01230 -0.00365 -0.00004 -
0.1488
0.0051
-0.0000
1200
1000
800
z-z
600
400
200
0 -400
-200
0
y-y
200
400
A ey
=0.361 m2 =0.000 m
ez
=0.517 m
Iy
=0.052 m4
Iz
=0.005 m4
Ix
=-0.000 m4
yb
=0.517 m
yt
=0.626 m
Sb
=0.101 m3
St
=0.083 m3 =104 mm
A/P
254.0 32.0 158.0 268.7 483.0 162.6 178.0 410.0 178.0 162.6 483.0 268.7 158.0 32.0 254.0 3482.7
2.3. Properties of Comp.Section at End section 2.3.1. For internal girder Effective width of slab is: B1' = min (1/4 Ls, S, 12g + m) =
1.75 m Because concrete class of slab and girder is different, the width of slab should be modified: Modulus ratio n= Ecs / Ec= 0.775 Therefore, effective width of slab is: Point 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
B' =
yi
zi
A-i
(mm)
(mm)
(m )
0 254 279 279 205 205 678 678 -678 -678 -205 -205 -279 -279 -254 0
1.36 m
Sy-i
Sz-i
(m ) (m ) 0.0051 0.00010 0.00271 0.0441 0.00873 0.02460 0.0338 0.01454 0.01637 0.1827 0.25480 0.07489 -0.5404 -1.23531 -0.47703 0.1220 0.30085 0.16538 1.7934 4.74530 0.1220 0.30085 -0.16538 -0.5404 -1.23531 0.47703 0.1827 0.25480 -0.07489 0.0338 0.01454 -0.01637 0.0441 0.00873 -0.02460 0.0051 0.00010 -0.00271 2
0 0 20 178 252 1143 1143 1323 1323 1143 1143 252 178 20 0 0
Total
3
0.7439
3
0.5721
-
Iyi
Iz-i
Iyz-i
Pi
(m )
(m )
(m )
(mm)
4
4
4
0.00000 0.00157 0.00474 0.30284 -2.11793 0.55741 9.41704 0.55741 -2.11793 0.30284 0.00474 0.00157 0.00000 -
0.00108 0.01029 0.00599 0.02303 -0.34603 0.16813 0.82384 0.16813 -0.34603 0.02303 0.00599 0.01029 0.00108 -
0.00004 0.00365 0.00523 0.07835 -0.81787 0.30586 -0.30586 0.81787 -0.07835 -0.00523 -0.00365 -0.00004 -
0.5762
0.0457
0.0000
1400
1323
1323
A ey
=0.744 m2 =0.000 m
ez
=0.769 m
Iy
=0.136 m4
Iz
=0.046 m4
600
Ix
=0.000 m4
400
yb
=0.769 m
252 178
yt
=0.554 m
Sb
=0.177 m3
020
St
=0.246 m3 =134 mm
1200
1143
1143
1143
1143
1000 800
z-z
252 178
200
20 0
0 -1000 -800
-600
-400
-200
0 0
y-y
200
400
600
800
1000
A/P
254.0 32.0 158.0 104.7 891.0 472.8 180.0 1355.5 180.0 472.8 891.0 104.7 158.0 32.0 254.0 5540.4
2.3.2. For external girder Effective width of slab is: B2' = min (B1'/2+1/8 Ls, B1'/2+S1, 6g+max(m/2+k/4)) Modulus ratio
n= Ecs / Ec=
Therefore, effective width of slab is: Point 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
= 1.27 m
0.775 B' =
0.98 m
yi
zi
A-i
Sy-i
Sz-i
Iyi
Iz-i
Iyz-i
Pi
(mm)
(mm)
(m2)
(m3)
(m3)
(m4)
(m4)
(m4)
(mm)
0 254 279 279 205 205 492 492 -492 -492 -205 -205 -279 -279 -254 0
0 0 20 178 252 1143 1143 1323 1323 1143 1143 252 178 20 0 0
0.0051 0.00010 0.00271 0.0441 0.00873 0.02460 0.0338 0.01454 0.01637 0.1827 0.25480 0.07489 -0.3286 -0.75108 -0.22915 0.0886 0.21859 0.08730 1.3030 3.44780 0.0886 0.21859 -0.08730 -0.3286 -0.75108 0.22915 0.1827 0.25480 -0.07489 0.0338 0.01454 -0.01637 0.0441 0.00873 -0.02460 0.0051 0.00010 -0.00271 -
Total
0.6772
0.4899
-
0.00000 0.00157 0.00474 0.30284 -1.28772 0.40500 6.84215 0.40500 -1.28772 0.30284 0.00474 0.00157 0.00000 -
0.00108 0.01029 0.00599 0.02303 -0.12665 0.06449 0.31599 0.06449 -0.12665 0.02303 0.00599 0.01029 0.00108 -
0.00004 0.00365 0.00523 0.07835 -0.39288 0.16147 -0.16147 0.39288 -0.07835 -0.00523 -0.00365 -0.00004 -
0.4746
0.0227
-0.0000
1400
1323
1323
A ey
=0.677 m2 =0.000 m
ez
=0.723 m
Iy
=0.120 m4
Iz
=0.023 m4
600
Ix
=-0.000 m4
400
yb
=0.723 m
1200
1143
1143
1143
1143
1000 800
z-z
252 178
200
20 0
0 -1000 -800
-600
-400
-200
252 178
yt
=0.600 m
Sb
=0.166 m3
020
St
=0.201 m3 =141 mm
0 0
y-y
200
400
600
800
1000
A/P
254.0 32.0 158.0 104.7 891.0 287.4 180.0 984.9 180.0 287.4 891.0 104.7 158.0 32.0 254.0 4799.1
2.4. Properties of Comp.Section at Middle section 2.4.1. For internal girder Point 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
yi
zi
A-i
Sy-i
Sz-i
Iyi
Iz-i
Iyz-i
Pi
(mm)
(mm)
(m2)
(m3)
(m3)
(m4)
(m4)
(m4)
(mm)
0 254 279 279 89 89 205 205 678 678 -678 -678 -205 -205 -89 -89 -279 -279 -254 0
0 0 20 178 368 851 965 1143 1143 1323 1323 1143 1143 965 851 368 178 20 0 0
0.0051 0.0441 0.0868 0.0430 -0.0886 0.0365 -0.5404 0.1220 1.7934 0.1220 -0.5404 0.0365 -0.0886 0.0430 0.0868 0.0441 0.0051 -
Total
0.00010 0.00873 0.04741 0.05240 -0.16084 0.07692 -1.23531 0.30085 4.74530 0.30085 -1.23531 0.07692 -0.16084 0.05240 0.04741 0.00873 0.00010 -
0.6052
0.00271 0.02460 0.03195 0.00765 -0.02604 0.01496 -0.47703 0.16538 -0.16538 0.47703 -0.01496 0.02604 -0.00765 -0.03195 -0.02460 -0.00271 -
0.4876
-
0.00000 0.00157 0.02020 0.05041 -0.21936 0.12190 -2.11793 0.55741 9.41704 0.55741 -2.11793 0.12190 -0.21936 0.05041 0.02020 0.00157 0.00000 -
0.00108 0.01029 0.00960 0.00102 -0.00604 0.00460 -0.34603 0.16813 0.82384 0.16813 -0.34603 0.00460 -0.00604 0.00102 0.00960 0.01029 0.00108 -
0.00004 0.00365 0.01230 0.00700 -0.03576 0.02365 -0.81787 0.30586 -0.30586 0.81787 -0.02365 0.03576 -0.00700 -0.01230 -0.00365 -0.00004 -
0.5205
0.0424
-0.0000
1400
1323 1200
1323
1143
1000
1143
1143
965
965
851 851
800
z-z
1143
600 400
368 368
200
178 20 0
0 -1000 -800
178
-600
-400
-200
020
0 0
y-y
200
400
600
800
1000
A ey
=0.605 m2 =0.000 m
ez
=0.806 m
Iy
=0.128 m4
Iz
=0.042 m4
Ix
=-0.000 m4
yb
=0.806 m
yt
=0.517 m
Sb
=0.158 m3
St
=0.247 m3 =106 mm
A/P
254.0 32.0 158.0 268.7 483.0 162.6 178.0 472.8 180.0 1355.5 180.0 472.8 178.0 162.6 483.0 268.7 158.0 32.0 254.0 5733.8
2.4.2. For external girder Point 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
yi
zi
A-i
Sy-i
Sz-i
Iyi
Iz-i
Iyz-i
Pi
(mm)
(mm)
(m2)
(m3)
(m3)
(m4)
(m4)
(m4)
(mm)
0 254 279 279 89 89 205 205 492 492 -492 -492 -205 -205 -89 -89 -279 -279 -254 0
0 0 20 178 368 851 965 1143 1143 1323 1323 1143 1143 965 851 368 178 20 0 0
0.0051 0.0441 0.0868 0.0430 -0.0886 0.0365 -0.3286 0.0886 1.3030 0.0886 -0.3286 0.0365 -0.0886 0.0430 0.0868 0.0441 0.0051 -
Total
0.00010 0.00873 0.04741 0.05240 -0.16084 0.07692 -0.75108 0.21859 3.44780 0.21859 -0.75108 0.07692 -0.16084 0.05240 0.04741 0.00873 0.00010 -
0.5385
0.00271 0.02460 0.03195 0.00765 -0.02604 0.01496 -0.22915 0.08730 -0.08730 0.22915 -0.01496 0.02604 -0.00765 -0.03195 -0.02460 -0.00271 -
0.4054
-
0.00000 0.00157 0.02020 0.05041 -0.21936 0.12190 -1.28772 0.40500 6.84215 0.40500 -1.28772 0.12190 -0.21936 0.05041 0.02020 0.00157 0.00000 -
0.00108 0.01029 0.00960 0.00102 -0.00604 0.00460 -0.12665 0.06449 0.31599 0.06449 -0.12665 0.00460 -0.00604 0.00102 0.00960 0.01029 0.00108 -
0.00004 0.00365 0.01230 0.00700 -0.03576 0.02365 -0.39288 0.16147 -0.16147 0.39288 -0.02365 0.03576 -0.00700 -0.01230 -0.00365 -0.00004 -
0.4188
0.0194
0.0000
1400
1323 1200
1323
1143
1000
1143
1143
965
965
851 851
800
z-z
1143
600 400
368 368
200
178 20 0
0 -1000 -800
178
-600
-400
-200
020
0 0
y-y
200
400
600
800
1000
A ey
=0.538 m2 =0.000 m
ez
=0.753 m
Iy
=0.114 m4
Iz
=0.019 m4
Ix
=0.000 m4
yb
=0.753 m
yt
=0.570 m
Sb
=0.151 m3
St
=0.199 m3 =108 mm
A/P
254.0 32.0 158.0 268.7 483.0 162.6 178.0 287.4 180.0 984.9 180.0 287.4 178.0 162.6 483.0 268.7 158.0 32.0 254.0 4992.5
3. CABLES ARRANGEMENT Strands profile: offset from soffit (mm) (Ltt/2) Strand no. Number At bearing yps0 yps4 of strand nps
GROUP I 31 32
1…10 11…18 19…24 25,26 27,28 29,30 31,32
29 30 27 28
50 2@45 38
25 26 19 20 21
22 23 24
11 12 13 14 1
2 3
4
15 16 17 18 5 6
7 8
9 10
GROUP II
69
3@45
3@50
3@45
69
558
nstr Parameters of strands Strand no. L (mm) 1…10 24540.0 11…18 24540.0 19…24 24540.0 25,26 24586.8 27,28 24590.1 29,30 24593.4 31,32 24596.9
α
tan(α)
sin(α)
cos(α)
(deg) 0.000 0.000 0.000 4.079 4.218 4.357 4.496
0.000 0.000 0.000 0.071 0.074 0.076 0.079
0.000 0.000 0.000 0.071 0.074 0.076 0.078
1.000 1.000 1.000 0.997 0.997 0.997 0.997
Center of strands from bottom (Cps) and top (dp) of girder Center
unit
At bearing
(Ltt/2)
Cps
m
0.265
0.092
dp
m
0.878
1.051
10 8 6 2 2 2 2
mm 50 95 140 730 775 820 865 =32 Strands
mm 50 95 140 73 95 118 140
4. SECTION PROPERTIES The concrete section properties will be calculated in three main stages: Stage I : Girder Manufacture Stage II : Casting deck slab Stage III : Service. L L1
L2
L2
L3
L1
L1 L2 L3 L1 + L2
Hg
=0.150 m =0.920 m =22.400 m =1.070 m
xi Ls
xi/Ls
Section xi Row A No.=10
Row B No.=8
Row C No.=6
Row D No.=2
Profile of Strands Row E Row F No.=2 No.=2
Row G No.=2
Total
Astrands
(m) (strands) (strands) (strands) (strands) (strands) (strands) (strands) (strands) (m2) 0.000 0.000 50 95 140 730 775 820 865 32 0.003158 0.006 0.150 50 95 140 719 764 809 853 32 0.003158 0.044 1.070 50 95 140 654 696 738 781 32 0.003158 0.050 1.212 50 95 140 644 686 728 770 32 0.003158 0.100 2.424 50 95 140 557 596 635 674 32 0.003158 0.150 3.636 50 95 140 471 507 543 579 32 0.003158 0.200 4.848 50 95 140 384 417 451 484 32 0.003158 0.250 6.060 50 95 140 298 328 358 388 32 0.003158 0.300 7.272 50 95 140 211 239 266 293 32 0.003158 0.350 8.484 50 95 140 125 149 174 198 32 0.003158 0.400 9.696 50 95 140 73 95 118 140 32 0.003158 0.450 10.908 50 95 140 73 95 118 140 32 0.003158 0.500 12.120 50 95 140 73 95 118 140 32 0.003158 Notes: - Astrands: total area of all strands. - z: distance from bottom of girder to centroid of all strands.
xi/Ls 0.000 0.006 0.044 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500
Section xi (m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120
Stage I (at time of initial prestress) - Stage II Iconc. econc. eb_(I) et_(I) Asec_(I)
Hsec
Aconc.
(m) 1.143 1.143 1.143 1.143 1.143 1.143 1.143 1.143 1.143 1.143 1.143 1.143 1.143
(m ) 0.5000 0.5000 0.3612 0.3612 0.3612 0.3612 0.3612 0.3612 0.3612 0.3612 0.3612 0.3612 0.3612 2
(m ) 0.0574 0.0574 0.0523 0.0523 0.0523 0.0523 0.0523 0.0523 0.0523 0.0523 0.0523 0.0523 0.0523 4
(m) 0.5426 0.5426 0.5426 0.5171 0.5171 0.5171 0.5171 0.5171 0.5171 0.5171 0.5171 0.5171 0.5171
(m) 0.5347 0.5346 0.5310 0.5064 0.5056 0.5047 0.5038 0.5029 0.5020 0.5011 0.5006 0.5006 0.5006
(m) 0.6083 0.6084 0.6120 0.6366 0.6374 0.6383 0.6392 0.6401 0.6410 0.6419 0.6424 0.6424 0.6424
(m ) 0.5145 0.5145 0.3758 0.3758 0.3758 0.3758 0.3758 0.3758 0.3758 0.3758 0.3758 0.3758 0.3758 2
Isec_(I) (m4) 0.0585 0.0585 0.0535 0.0533 0.0535 0.0537 0.0539 0.0541 0.0544 0.0546 0.0548 0.0548 0.0548
z (m) 0.2650 0.2622 0.2449 0.2423 0.2196 0.1968 0.1741 0.1514 0.1287 0.1060 0.0923 0.0923 0.0923
xi/Ls 0.000 0.006 0.044 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500 Notes:
Section xi (m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120
Hsec (m) 1.323 1.323 1.323 1.323 1.323 1.323 1.323 1.323 1.323 1.323 1.323 1.323 1.323
Hgirder (m) 1.143 1.143 1.143 1.143 1.143 1.143 1.143 1.143 1.143 1.143 1.143 1.143 1.143
Aconc.
Stage III - For internal girder Iconc. econc. eb_(III) et_(III)
(m2) 0.7439 0.7439 0.6052 0.6052 0.6052 0.6052 0.6052 0.6052 0.6052 0.6052 0.6052 0.6052 0.6052
(m4) 0.1362 0.1362 0.1276 0.1276 0.1276 0.1276 0.1276 0.1276 0.1276 0.1276 0.1276 0.1276 0.1276
(m) 0.7690 0.7690 0.8057 0.8057 0.8057 0.8057 0.8057 0.8057 0.8057 0.8057 0.8057 0.8057 0.8057
(m) 0.7602 0.7602 0.7937 0.7937 0.7932 0.7927 0.7922 0.7917 0.7913 0.7908 0.7905 0.7905 0.7905
(m) 0.3828 0.3828 0.3493 0.3493 0.3498 0.3503 0.3508 0.3513 0.3517 0.3522 0.3525 0.3525 0.3525
et_slab_(III) (m) 0.5628 0.5628 0.5293 0.5293 0.5298 0.5303 0.5308 0.5313 0.5317 0.5322 0.5325 0.5325 0.5325
Asec_(III) (m2) 0.7572 0.7572 0.6184 0.6184 0.6184 0.6184 0.6184 0.6184 0.6184 0.6184 0.6184 0.6184 0.6184
Isec_(III) (m4) 0.1395 0.1395 0.1316 0.1317 0.1320 0.1323 0.1327 0.1331 0.1335 0.1339 0.1341 0.1341 0.1341
- eb_(I), eb_(III): distance from bottom of girder to centroid of girder and composite girder included all strands, respectively. - et_(I), et_(III): distance from top of girder to centroid of girder and composite girder included all strands, respectively. - et_slab_(III): distance from top of slab to centroid of composite girder included all strands. - Asec_(I), Asec_(III): area of girder and composite girder included all strands, respectively. - Isec_(I), Isec_(III): moment of inertia of girder and composite girder included all strands, respectively.
xi/Ls 0.000 0.006 0.044 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500
Section xi (m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120
Hsec (m) 1.323 1.323 1.323 1.323 1.323 1.323 1.323 1.323 1.323 1.323 1.323 1.323 1.323
Hgirder (m) 1.143 1.143 1.143 1.143 1.143 1.143 1.143 1.143 1.143 1.143 1.143 1.143 1.143
Aconc.
Stage III - For external girder Iconc. econc. eb_(III) et_(III)
(m2) 0.6772 0.6772 0.5385 0.5385 0.5385 0.5385 0.5385 0.5385 0.5385 0.5385 0.5385 0.5385 0.5385
(m4) 0.1203 0.1203 0.1137 0.1137 0.1137 0.1137 0.1137 0.1137 0.1137 0.1137 0.1137 0.1137 0.1137
(m) 0.7233 0.7233 0.7528 0.7528 0.7528 0.7528 0.7528 0.7528 0.7528 0.7528 0.7528 0.7528 0.7528
(m) 0.7146 0.7145 0.7406 0.7406 0.7400 0.7395 0.7389 0.7384 0.7378 0.7373 0.7370 0.7370 0.7370
(m) 0.4284 0.4285 0.4024 0.4024 0.4030 0.4035 0.4041 0.4046 0.4052 0.4057 0.4060 0.4060 0.4060
et_slab_(III) (m) 0.6084 0.6085 0.5824 0.5824 0.5830 0.5835 0.5841 0.5846 0.5852 0.5857 0.5860 0.5860 0.5860
Asec_(III) (m2) 0.6904 0.6904 0.5517 0.5517 0.5517 0.5517 0.5517 0.5517 0.5517 0.5517 0.5517 0.5517 0.5517
Isec_(III) (m4) 0.1230 0.1230 0.1170 0.1170 0.1173 0.1177 0.1180 0.1183 0.1187 0.1191 0.1193 0.1193 0.1193
III. DISTRIBUTION FACTOR OF LIVELOAD 1.Distribution factor of moment • Spacing of girders
S=
1750.00 mm
• Depth of girder
1143.00 mm
• Depth of concrete slab
d= ts =
• Effective length of span
L=
24240.00 mm
• Distance from the center of ex-girder to in-edge of curb
Sc =
250.00 mm
• Number of girders
Nb =
• The longitudinal stiffness parameter: Kg = n (I + A.eg2)
Kg =
3.E+11
n= Ec / Ecs=
1.29
180.00 mm
7 girders
I=
5.E+10 mm4
A=
361214 mm2
eg=
716 mm
1.1. Interior girder Strength limit state, service limit state 1.1.1. For one design lane loaded Gi = 0.06 + ( S / 4300 )0.4 ( S / L ) 0.3 (Kg / L . Ts3)0.1
Gi =
0.403
Gi =
0.547
Gi =
0.547
GF =
0.336
Gi =
0.457
1.1.2. Two or more design lanes loaded Gi = 0.075 + ( S / 2900 )0.6 ( S / L ) 0.2 (Kg / L . Ts3)0.1 • Conclusion : ( use larger value of 1.1.1 & 1.1.2 ) For fatigue limit state GF = Gi / 1.2 1.2. Exterior girder 1.2.1. For one design lane loaded ( lever rule ) Ge= (S + Sc -1200)/S) 1.2.2. Two or more design lanes loaded • Distance from the ex-web of ex-girder to in-edge of curb Ge = e.Gi = ( 0.77 + de/2800 ).Gi • Conclusion : ( use larger value of 1.2.1 & 1.2.2 )
de =
161.00 mm
Ge =
0.452
Gi =
0.457
Gi =
0.590
Gi =
0.458
Gi =
0.590
GF =
0.492
Ge =
0.457
Ge =
0.299
Ge =
0.457
2.Distribution factor of shear force 2.1. Interior girder Strength limit state, service limit state 2.1.1. For one design lane loaded Gi = 0.36 + ( S / 7600 ) 2.1.2. Two or more design lanes loaded Gi = 0.2 + ( S / 7600 )0.8 ( S / 10700 ) 0.1 • Conclusion : ( use larger value of 2.1.1 & 2.1.2 ) For fatigue limit state GF = Gi / 1.2 2.2. Exterior girder 2.2.1. For one design lane loaded ( lever rule ) Ge= (S + Sc -1200)/S) 2.2.2. Two or more design lanes loaded Ge = e.Gi = ( 0.6 + de/3000 ).Gi • Conclusion : ( use larger value of 2.2.1 & 2.2.2 )
14
15
5. LOAD CASES 5.1. Deadload Seftweight of Girder Seftweight of Precast Plank Seftweight of Cast-in-place Slab
DC1 DC2 DC3 DC3 DC4 DC5 DC5 DW1 DW1 DW2 DW2 DW3
: for internal girder : for external girder
Seftweight of Diaphragms Dead load of Curb
: for internal girder : for external girder : for internal girder : for external girder : for internal girder : for external girder
Dead load of Wearing Surface Dead load of Railing Dead load of Utilities 5.1.1. For internal girder
xi/Ls 0.000 0.006 0.044 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500
xi/Ls 0.000 0.006 0.044 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500
Section xi (m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120 Section xi (m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120
=9.654 KN/m =0.000 KN/m =7.718 KN/m =6.505 KN/m =0.955 KN/m =0.000 KN/m =5.292 KN/m =1.969 KN/m =1.659 KN/m =0.000 KN/m =0.200 KN/m =0.000 KN/m
MOMENT (KNm) Stage I Due to DC1
Stage II Due to DC3
Due to DC2
17.4 119.7 134.7 255.3 361.6 453.8 531.8 595.6 645.3 680.7 702.0 709.1
-
13.9 95.7 107.7 204.1 289.1 362.8 425.1 476.1 515.8 544.2 561.2 566.8
Due to DC4
Stage III Due to Due to DW1 DW2
Due to DC5
1.7 11.8 13.3 25.3 35.8 44.9 52.6 58.9 63.8 67.3 69.5 70.2
-
3.6 24.4 27.5 52.1 73.7 92.5 108.4 121.5 131.6 138.8 143.2 144.6
Due to DW3 -
-
SHEAR (KN) Stage I Due to DC1 117.0 115.6 106.7 105.3 93.6 81.9 70.2 58.5 46.8 35.1 23.4 11.7 -
Stage II Due to DC3
Due to DC2 -
93.5 92.4 85.3 84.2 74.8 65.5 56.1 46.8 37.4 28.1 18.7 9.4 -
Due to DC4 11.6 11.4 10.6 10.4 9.3 8.1 6.9 5.8 4.6 3.5 2.3 1.2 -
Stage III Due to Due to DW1 DW2
Due to DC5 -
23.9 23.6 21.8 21.5 19.1 16.7 14.3 11.9 9.5 7.2 4.8 2.4 -
Due to DW3 -
-
5.1.2. For external girder
xi/Ls 0.000 0.006 0.044 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500
xi/Ls 0.000 0.006 0.044 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500
Section xi (m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120 Section xi (m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120
MOMENT (KNm) Stage I Due to DC1
Stage II Due to DC3
Due to DC2
17.4 119.7 134.7 255.3 361.6 453.8 531.8 595.6 645.3 680.7 702.0 709.1
-
11.8 80.6 90.8 172.0 243.7 305.8 358.3 401.3 434.8 458.6 473.0 477.8
Stage II Due to DC3
Due to DC2
117.0 115.6 106.7 105.3 93.6 81.9 70.2 58.5 46.8 35.1 23.4 11.7 -
-
78.8 77.9 71.9 71.0 63.1 55.2 47.3 39.4 31.5 23.7 15.8 7.9 -
P4 P5
9.6 65.6 73.8 139.9 198.2 248.8 291.5 326.5 353.7 373.1 384.8 388.7
Due to DC5
11.6 11.4 10.6 10.4 9.3 8.1 6.9 5.8 4.6 3.5 2.3 1.2 -
64.1 63.3 58.5 57.7 51.3 44.9 38.5 32.1 25.7 19.2 12.8 6.4 -
m
Wheel Spacing
Design Truck 35 kN V1 145 kN V2 145 kN Design Tandem 110 kN V3 110 kN Design Lane Load
Due to DC4
nL
Live load
P1 P2 P3
1.7 11.8 13.3 25.3 35.8 44.9 52.6 58.9 63.8 67.3 69.5 70.2
Due to DC5
Stage III Due to Due to DW1 DW2 3.0 20.6 23.2 43.9 62.2 78.0 91.4 102.4 110.9 117.0 120.7 121.9
Due to DW3
0.4 2.5 2.8 5.3 7.5 9.4 11.0 12.3 13.4 14.1 14.5 14.7
-
SHEAR (KN) Stage I Due to DC1
5.2. Liveload Number of lanes Mutiple Presence Factors of Live Load
Forces
Due to DC4
4.3m 4.3m
1.2m
Stage III Due to Due to DW1 DW2 20.1 19.9 18.3 18.1 16.1 14.1 12.1 10.1 8.0 6.0 4.0 2.0 -
Due to DW3
2.4 2.4 2.2 2.2 1.9 1.7 1.5 1.2 1.0 0.7 0.5 0.2 -
-
=3 Lanes =0.850
Dynamic Load Allowance Component Deck Joint - All Limit States All Other Components Fatigue and Fracture Limit State All Other Limit States
IM 75% 15% 25%
WL
9.3 kN/m
Design Truck
Design Tandem 1.200m
110kN Designm Lane load V1 = 4.3m 35kN
m
110kN
m 9.3 kN/m
V2 = 4.3m - 9.0m
145kN
145kN
• Inm the below table,mcaculation for one design m lane loaded, is not composed of distribution factor • With Truck load : Vz =(145•(L-x)+ 145•(L-x-4.3) + 35•(L-x-8.6))/L • With lane load : • In fatigue No
0.000 0.006 0.044 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500
Section x(m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120
My =(145•(L-x)•x + 145•(L-x-4.3)•x + 35•(L-x-2•4.3)•x)/L Vz =9.3•(L-x)2/(2•L) My =9.3•(L-x)•x/2 My =(145•(L-x)•x + 145•(L-x-9)•x + 35•(L-x-13.3)•x)/L
M = P•x•(L - x)/L kN.m V = P•(L - x)/L kN
Truck load + IM Lane Load Fatigue Truck load Truck load + IM Truck load TL+IM Vz ( kN ) My ( kNm ) Vz ( kN ) My ( kNm ) Vz ( kN ) My( kNm ) My ( kNm ) My ( kNm ) 286.861 0.000 358.576 0.000 112.716 0.000 0.000 284.849 42.727 356.062 53.409 111.325 16.803 37.492 43.116 272.514 291.590 340.643 364.488 102.985 115.282 254.246 292.383 270.611 327.980 338.263 409.975 101.726 129.781 285.680 328.532 254.361 616.570 317.951 770.713 91.300 245.901 531.970 611.766 238.111 865.770 297.638 1082.213 81.437 348.360 738.870 849.701 221.861 1075.580 277.326 1344.475 72.138 437.158 906.380 1042.337 205.611 1246.000 257.013 1557.500 63.403 512.294 1034.500 1189.675 189.361 1377.030 236.701 1721.288 55.231 573.770 1123.230 1291.715 173.111 1468.670 216.388 1835.838 47.623 621.584 1172.570 1348.456 156.861 1520.920 196.076 1901.150 40.578 655.737 1182.520 1359.898 140.611 1533.780 175.763 1917.225 34.097 676.228 1153.080 1326.042 124.361 1507.250 155.451 1884.063 28.179 683.059 1084.250 1246.888
• With Tandem Load :Vz =(110•(L-x)+ 110•(L-x-1.2))/L • With lane load :
No
0.000 0.006 0.044 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500
Section x(m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120
No
0.000 0.006 0.044 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500
My =(110•(L-x)•x + 110•(L-x-1.2)•x)/L Vz =9.3•(L-x)2/(2•L) My =9.3•(L-x)•x/2
M = P•x•(L - x)/L kN.m V = P•(L - x)/L kN
Tandem + IM Lane Load Fatigue Tandem Tandem+IM Tandem Tandem+IM Vz ( kN ) My ( kNm ) Vz ( kN ) My ( kNm ) Vz ( kN ) My( kNm ) My ( kNm ) My ( kNm ) 214.554 0.000 268.193 0.000 112.716 0.000 0.000 0.000 213.193 31.979 266.491 39.974 111.325 16.803 31.979 36.776 204.843 219.182 256.054 273.978 102.985 115.282 219.182 252.060 203.554 246.708 254.443 308.385 101.726 129.781 246.708 283.714 192.554 466.752 240.693 583.440 91.300 245.901 466.752 536.765 181.554 660.132 226.943 825.165 81.437 348.360 660.132 759.152 170.554 826.848 213.193 1033.560 72.138 437.158 826.848 950.875 159.554 966.900 199.443 1208.625 63.403 512.294 966.900 1111.935 148.554 1080.288 185.693 1350.360 55.231 573.770 1080.288 1242.331 137.554 1167.012 171.943 1458.765 47.623 621.584 1167.012 1342.064 126.554 1227.072 158.193 1533.840 40.578 655.737 1227.072 1411.133 115.554 1260.468 144.443 1575.585 34.097 676.228 1260.468 1449.538 104.554 1267.200 130.693 1584.000 28.179 683.059 1267.200 1457.280
Section xi (m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120
LIVE LOAD (Total) LIVE LOAD (ex-beam) LIVE LOAD (in-beam) Moment Shear Moment Shear Moment Shear KNm KN KNm KN KNm KN 0.0 471.3 0.0 215.4 0.0 278.2 70.2 467.4 32.1 213.7 38.4 275.9 479.8 443.6 219.3 202.8 262.3 261.9 539.8 440.0 246.7 201.1 295.1 259.7 1016.6 409.3 464.7 187.1 555.8 241.6 1430.6 379.1 654.0 173.3 782.1 223.8 1781.6 349.5 814.5 159.8 974.1 206.3 2069.8 320.4 946.2 146.5 1131.6 189.1 2295.1 291.9 1049.2 133.5 1254.8 172.3 2457.4 264.0 1123.4 120.7 1343.5 155.8 2556.9 236.7 1168.9 108.2 1397.9 139.7 2593.5 209.9 1185.6 95.9 1417.9 123.9 2567.1 183.6 1173.5 83.9 1403.5 108.4
6. LOADS COMBINATIONS Q = Σ ηi γi Qi The total factored force effect shall be taken as: ηi Where: = Load modifier Qi = Force effects γi = Load factors Load Factors (γi) Load Combination Limit State DC DW LL Strength - I Service - I Service - III
1.25 1.00 1.00
Where: DC DW LL ηD ηR ηI ηi = ηD.ηR.ηI > 0.95 ηi = 1/(ηD.ηR.ηI) ≤ 1.0
1.50 1.00 1.00
1.75 1.00 0.80
ηD 1.00 1.00 1.00
Load Modifiers ηR ηI 1.00 1.00 1.00
1.00 1.00 1.00
: Dead load structural components : Dead load of wearing surfaces and utilities : Vehicular live load : a factor relating to ductility : a factor relating to redundancy : a factor relating to operational importance : for maximum value of γi : for minimum value of γi
6.1. For internal girder
xi/Ls 0.000 0.006 0.044 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500
xi/Ls 0.000 0.006 0.044 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450
Section xi (m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120 Section xi (m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908
MOMENT (KNm) STAGE I STAGE II STAGE III Strength-I Service-I Strength-I Service-I Strength-I Service-I Service-III 21.8 17.4 19.6 15.7 72.5 41.9 34.3 149.6 119.7 134.4 107.5 495.6 286.7 234.2 168.4 134.7 151.3 121.0 557.6 322.6 263.6 319.1 255.3 286.6 229.3 1050.7 607.9 496.7 452.0 361.6 406.1 324.9 1479.3 855.9 699.4 567.3 453.8 509.6 407.7 1843.4 1066.6 871.8 664.8 531.8 597.2 477.7 2143.0 1240.1 1013.7 744.5 595.6 668.8 535.1 2378.0 1376.2 1125.3 806.6 645.3 724.6 579.7 2548.6 1475.1 1206.4 850.9 680.7 764.4 611.5 2654.6 1536.7 1257.1 877.5 702.0 788.3 630.6 2696.1 1561.1 1277.5 886.3 709.1 796.2 637.0 2673.0 1548.1 1267.4 SHEAR (KN) STAGE I STAGE II STAGE III Strength-I Service-I Strength-I Service-I Strength-I Service-I Service-III 146.3 117.0 131.4 105.1 522.6 302.0 246.4 144.5 115.6 129.8 103.8 518.1 299.4 244.3 133.3 106.7 119.8 95.8 490.9 283.6 231.2 131.6 105.3 118.3 94.6 486.7 281.2 229.2 117.0 93.6 105.1 84.1 451.4 260.7 212.3 102.4 81.9 92.0 73.6 416.6 240.5 195.7 87.8 70.2 78.8 63.1 382.5 220.6 179.3 73.1 58.5 65.7 52.6 348.9 201.1 163.2 58.5 46.8 52.6 42.0 315.9 181.9 147.4 43.9 35.1 39.4 31.5 283.5 163.0 131.8 29.3 23.4 26.3 21.0 251.6 144.5 116.5 14.6 11.7 13.1 10.5 220.4 126.3 101.5
ηi 1.00 1.00 1.00
0.500
12.120
-
-
-
-
189.7
108.4
86.7
6.2. For external girder
xi/Ls 0.000 0.006 0.044 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500
xi/Ls 0.000 0.006 0.044 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500
Section xi (m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120 Section xi (m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120
MOMENT (KNm) STAGE I STAGE II STAGE III Strength-I Service-I Strength-I Service-I Strength-I Service-I Service-III 21.8 17.4 16.8 13.5 73.2 45.0 38.6 149.6 119.7 115.6 92.5 500.4 308.0 264.1 168.4 134.7 130.1 104.1 563.0 346.5 297.2 319.1 255.3 246.6 197.2 1061.9 653.8 560.9 452.0 361.6 349.3 279.4 1496.7 921.9 791.1 567.3 453.8 438.3 350.7 1867.4 1150.6 987.7 664.8 531.8 513.7 410.9 2173.9 1340.1 1150.9 744.5 595.6 575.3 460.2 2416.2 1490.4 1280.5 806.6 645.3 623.2 498.6 2594.5 1601.4 1376.7 850.9 680.7 657.5 526.0 2708.6 1673.1 1439.3 877.5 702.0 678.0 542.4 2758.6 1705.6 1468.5 886.3 709.1 684.9 547.9 2744.4 1698.8 1464.1 SHEAR (KN) STAGE I STAGE II STAGE III Strength-I Service-I Strength-I Service-I Strength-I Service-I Service-III 146.3 117.0 113.0 90.4 491.0 302.1 259.0 144.5 115.6 111.6 89.3 486.5 299.3 256.5 133.3 106.7 103.0 82.4 458.8 281.8 241.3 131.6 105.3 101.7 81.4 454.6 279.1 238.9 117.0 93.6 90.4 72.3 418.6 256.4 219.0 102.4 81.9 79.1 63.3 383.0 234.0 199.3 87.8 70.2 67.8 54.2 348.0 211.8 179.8 73.1 58.5 56.5 45.2 313.3 189.8 160.5 58.5 46.8 45.2 36.2 279.1 168.1 141.4 43.9 35.1 33.9 27.1 245.4 146.7 122.6 29.3 23.4 22.6 18.1 212.1 125.5 103.9 14.6 11.7 11.3 9.0 179.3 104.6 85.4 146.9 83.9 67.2
7. LOSS OF PRESTRESSING 7.1. Loss due to Elastic Shortening E Δf pES= p f cg p The loss due to elastic shortening in pre-tensioned members shall be taken as: E ci Where: fcgp : sum of concrete stresses at the center of gravity of prestresing tendons due to prestressing force at transfer and the self weight of the member at section of maximum moment
xi/Ls 0.000 0.006 0.044 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500
Section xi (m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120
fcgp1
LOSS DUE TO ELASTIC SHORTENING fcgp2 fcgp3 fcgp ∆fpES
(Mpa) 8.56 8.56 11.72 11.72 11.72 11.72 11.72 11.72 11.72 11.72 11.72 11.72 11.72
(Mpa) 5.48 5.59 6.74 5.77 6.74 7.77 8.88 10.05 11.29 12.59 13.41 13.41 13.41
(Mpa)
(Mpa) 14.04 14.07 17.82 16.82 17.09 17.43 17.83 18.33 18.93 19.65 20.06 19.90 19.85
-0.08 -0.64 -0.67 -1.36 -2.07 -2.78 -3.45 -4.09 -4.67 -5.07 -5.23 -5.28
(Mpa) 78.95 79.11 100.21 94.58 96.11 97.97 100.24 103.03 106.41 110.47 112.78 111.89 111.59
fcgp1 fcgp2 fcgp3
: due to Axial Compression of Prestressing Force : due to of Prestressing Force : due to Girder Self-weight (Stage 1) 7.2. Loss due to Shrinkage For pretensioned members, Loss of prestress due to shrinkage may be taken as: ∆fpSR = εshEp The strain due to shrinkage, esh, at time, t, mat be taken as: Where: t kh
ks
ε sh=−k s k h
t 0 . 51×10−3 35 . 0t
: Drying time (day) : Humidity Factor kh = (140-H ) / 70 for H < 80% kh = 3(100-H )/ 70 for H ≥ 80%
kh =0.929 : Size factor specified Figure 5.4.2.3.3-2 of AASHTO LRFD 2004 or taken as:
[
t 26 e 0 . 0142 A/ P t k s= t 45 t
Item Drying time, t (day) Volume to Surface ratio, A/P (mm) kh ks Strain due to shrinkage, εsh Loss due to Shrinkage, ∆fpSR (MPa)
]
[
1064 −3 . 70 A / P 923
]
Stage II Stage III 100 10950 104 106 0.929 0.501 -0.00018 34.61
0.929 0.725 -0.00034 67.42
7.3. Loss due to Creep Prestress loss due to creep may be taken as:
Δ f p C R−II = f c g pψ II E p / E c
At Casting deck slab:
Δf pC R−III = f cg pψ III−1Δcdp− M 2 ψ III−2 Δcdp−M3 ψ III−3 E p / E c At Service: Where: fcgp : Concrete stress at center of gravity of prestressing steel at tranfer ∆fcdp : Change in concrete stress at center of gravity of prestressing steel due to permanent loads, with the exception of the load acting at the time the prestressing force is applied. The creep coefficient may be estimated as: ψ t , t i =3 . 5k c k
Where: kf = 62/(42+f'c)
f
1 . 58−
[
k c=
t −t i 26 e 0 . 0142
A/P
t −t i t −t i 45 t −t i
Item
]
[
1 . 80 1 . 77 e −0 .0213 2 . 587
A/ P
Stage II
ti (day)
3 100 103.7 0.520 0.674 0.627
Maturity of concrete (day) Volume to Surface ratio, P/A (mm) kc kf Creep coefficient, ψ(t,ti) Section
0.000 0.006 0.044 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500
0 .6
i
: Factor for the effect of concrete strength : Maturity of concrete (day) : Age of concrete when load is initially applied (day) : Factor for the effect of the volume-to-surface ratio of the component specified Figure 5.4.2.3.2-1 of AASHTO LRFD 2004 or taken as:
t ti kc
xi/Ls
0 .6
t−t i H t 120 i−0 .118 10 . 0 t−t
fcgp
MDL2
30 10950 106 0.763 0.674 1.109
] Stage III 100 10950 106 0.763 0.674 0.962
LOSS DUE TO CREEP MDL3 ∆fcdp-M2 ∆fcdp-M3
xi (m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120 MDL2 MDL3
(Mpa) 14.04 14.07 17.82 16.82 17.09 17.43 17.83 18.33 18.93 19.65 20.06 19.90 19.85
(KNm) 15.67 107.51 121.03 229.31 324.86 407.67 477.74 535.06 579.65 611.50 630.61 636.98
(KNm) 12.92 88.65 99.80 189.09 267.88 336.16 393.94 441.21 477.98 504.24 520.00 525.25
: Moment due to Stage 2 Dead Load : Moment due to Stage 3 Dead Load
(Mpa) 0.14 1.06 1.14 2.15 3.03 3.79 4.41 4.91 5.28 5.55 5.73 5.78
(Mpa) 0.05 0.37 0.42 0.82 1.21 1.57 1.90 2.19 2.44 2.62 2.71 2.73
150 10950 106 0.763 0.674 0.917
Stage II ∆fpCR-II (Mpa) 45.62 45.71 57.91 54.65 55.54 56.61 57.93 59.53 61.49 63.84 65.17 64.65 64.48
Stage III ∆fpCR-III (Mpa) 80.71 81.80 109.48 104.36 112.88 121.00 128.78 136.31 143.65 150.88 155.43 155.77 155.89
7.4. Loss due to Relaxation 7.4.1. At Transfer For low-relaxation strand: Δf Where: t
pR1 =
[
]
log24t f pj 0.55 f 40. 0 f py
pj
: Time estimated in days from stressing to tranfer
t ∆fpR1
=3 days =18.35 Mpa
7.4.2. After Transfer For pretensioning with stress-relieved strands:
Δf ¿pR2=138−0. 4Δf pE S−0. 2 Δf pSRΔf pCR For low relation prestress steel, loss due to relaxation, ∆fpR2, is taken 30% of ∆f*pR2 Section xi/Ls
0.000 0.006 0.044 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500
xi (m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120
∆fpES (Mpa) 78.95 79.11 100.21 94.58 96.11 97.97 100.24 103.03 106.41 110.47 112.78 111.89 111.59
LOSS DUE TO RELAXATION AFTER TRANSFER Stage II Stage III ∆fpSR-II ∆fpCR-II ∆fpR2-II ∆fpSR-III ∆fpCR-III
∆fpR2-III
(Mpa) 34.61 34.61 34.61 34.61 34.61 34.61 34.61 34.61 34.61 34.61 34.61 34.61 34.61
(Mpa) 23.04 22.95 18.76 19.74 19.05 18.34 17.60 16.81 15.97 15.05 14.50 14.58 14.61
(Mpa) 45.62 45.71 57.91 54.65 55.54 56.61 57.93 59.53 61.49 63.84 65.17 64.65 64.48
(Mpa) 27.11 27.09 23.82 24.70 24.46 24.17 23.82 23.39 22.86 22.24 21.88 22.02 22.06
(Mpa) 67.42 67.42 67.42 67.42 67.42 67.42 67.42 67.42 67.42 67.42 67.42 67.42 67.42
(Mpa) 80.71 81.80 109.48 104.36 112.88 121.00 128.78 136.31 143.65 150.88 155.43 155.77 155.89
7.5. Total loss of Prestress ∆fpT = ∆fpES + ∆fpSR + ∆fpCR + ∆fpR2 In posstension members, total loss of prestress taken as: ∆fpT Where: : Total loss ( MPa) ∆fpES : Loss due to elastic shortening (MPa) ∆fpSR : Loss due to shrinkage (MPa) ∆fpCR : Loss due to creep of concrete (MPa) ∆fpR2 : Loss due to relaxation of steel after transfer (MPa)
xi/Ls 0.000 0.006 0.044 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500
Section xi (m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120
∆fpT-I
Loss of Prestress ∆fpT-II ∆fpT-III
(Mpa) 97.3 97.5 118.6 112.9 114.5 116.3 118.6 121.4 124.8 128.8 131.1 130.2 129.9
(Mpa) 186.3 186.5 216.5 208.5 210.7 213.4 216.6 220.6 225.4 231.2 234.4 233.2 232.7
(Mpa) 250.1 251.3 295.9 286.1 295.5 304.7 314.0 323.6 333.4 343.8 350.1 349.7 349.5
7.6. Transfer and development length 7.6.1. Transfer length lt = 60 . Dp = Formula:
762 7.6.2. Development length Formula: ld ≥ κ. (0.15fps - 0.097.fpe) . Db
mm
(5.11.4.1) (5.11.4.2)
Where: - κ = 1 for fully bonded strands - κ = 2.0 for partially debonded strands - fps: average stress in prestressing steel at the time for which the nominal resistance of the member is required (Mpa)
æ cö ÷ ç fps = fpu ç 1- k ÷ ÷ ç ÷ ç d è pø
æ f ö÷ ç k =2ç 1,04 - py ÷ ÷ ç ç fpu ø÷ è - fpu: tensile strength - fpy: yield strength - dp: distance from top of slab to centroid of strands - c: distance between the neutral axis and the compressive face, is taken by Part - 8. To simplify the calculations, c is taken by the maximum value of internal and external girder. - fpe: effective stress in the prestressing steel after looses (Mpa) fpe = fpj - ∆fpT-i - fpj: stress in the prestressing steel at jacking - fpT-i: total loss at the stage (i) - Db: nominal strand diameter (mm)
xi/Ls 0.000 0.006 0.044 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500
Section xi (m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120
dp (mm)
k
0.28 1058.00 0.28 1060.81 0.28 1078.06 0.28 1080.72 0.28 1103.43 0.28 1126.15 0.28 1148.87 0.28 1171.58 0.28 1194.30 0.28 1217.02 0.28 1230.75 0.28 1230.75 0.28 1230.75 Average
Therefore, development length is: ld = For stage I: ld = ld = For stage II: ld = ld = For stage III: ld =
c (mm)
118.91 118.92 118.98 118.99 119.06 119.13 119.20 119.27 119.34 119.40 119.43 119.43 119.43
fps (Mpa)
1801.47 1801.62 1802.52 1802.66 1803.81 1804.91 1805.96 1806.98 1807.96 1808.91 1809.46 1809.46 1809.46 1805.78
fpe-I (Mpa)
1297.69 1297.54 1276.44 1282.07 1280.54 1278.68 1276.40 1273.62 1270.24 1266.17 1263.87 1264.76 1265.06 1276.39
1868 mm : for fully bonded strands 3735 mm : for partially debonded strands 1988 mm : for fully bonded strands 3977 mm : for partially debonded strands 2105 mm : for fully bonded strands 4210 mm : for partially debonded strands
fpe-II (Mpa) fpe-III (Mpa)
1208.71 1208.48 1178.45 1186.47 1184.29 1181.65 1178.41 1174.44 1169.63 1163.85 1160.57 1161.84 1162.26 1178.39
1144.89 1143.72 1099.13 1108.91 1099.55 1090.28 1080.96 1071.43 1061.56 1051.18 1044.88 1045.34 1045.50 1083.64
lt
A
lt
ld
ld
9220 12270
No. of bonded strands = 32
24540/2=12270
Gr o up 1: 24 St r ands f ul l y bo nded Gr o up 2: 8 St r and s par t ial l y debo nded
pOINT WHERE BONDING BEGINS FOR 8 STRANDS
No. of bonded strands = 24 L=1160
A
fpe
1.16 m fpe
Bonded Strand Debonded Strand fpj
150
pOINT WHERE BONDING BEGINS FOR 24 STRANDS
c .l bear ing
fpj
Group 1: 24 strands Group 2: 8 strands Total: 32 strands Lengh of debonded strands:
1143
Section A-A
Section B-B
p.s f o r c e in g r o up 2
p.s f o r c e in g r o up 1
B
3050
B
xi/Ls
0.000 0.006 0.044 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500
xi/Ls
0.000 0.006 0.044 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500
xi/Ls
0.000 0.006 0.044 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500
Section Dis. From xi Girder End (m) (m) -0.150 0.000 0.000 0.150 0.150 0.300 1.070 1.220 1.212 1.362 2.424 2.574 3.636 3.786 4.848 4.998 6.060 6.210 7.272 7.422 8.484 8.634 9.696 9.846 10.908 11.058 12.120 12.270
For Stage I P.S Prestressing Force after losses Fully Partially Group 1 Group 2 Total (Mpa) (Mpa) KN KN KN #VALUE! #VALUE! 0 0 0 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!
Section Dis. From xi Girder End (m) (m) -0.150 0.000 0.000 0.150 0.150 0.300 1.070 1.220 1.212 1.362 2.424 2.574 3.636 3.786 4.848 4.998 6.060 6.210 7.272 7.422 8.484 8.634 9.696 9.846 10.908 11.058 12.120 12.270
For Stage II P.S Prestressing Force after losses Fully Partially Group 1 Group 2 Total (Mpa) (Mpa) KN KN KN #VALUE! #VALUE! 0 0 0 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!
Section Dis. From xi Girder End (m) (m) -0.150 0.000 0.000 0.150 0.150 0.300 1.070 1.220 1.212 1.362 2.424 2.574 3.636 3.786 4.848 4.998 6.060 6.210 7.272 7.422 8.484 8.634 9.696 9.846 10.908 11.058 12.120 12.270
For Stage III P.S Prestressing Force after losses Fully Partially Group 1 Group 2 Total (Mpa) (Mpa) KN KN KN #VALUE! #VALUE! 0 0 0 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!
KN
TOTAL PRESTRESSING FORCE-FOR STAGE I 5000 C.L bearing 4500 4000 3500 3000 2500 2000 1500 1000 500 0 Column N 0.00 Column I
2.00
4.00
Column G Column H
6.00
8.00
10.00
12.00
m
KN
TOTAL PRESTRESSING FORCE-FOR STAGE II 5000 C.L bearing 4500 4000 3500 3000 2500 2000 1500 1000 500 0 Column N 0.00 Column I
2.00
4.00
Column G Column H
6.00
8.00
10.00
12.00
m
KN
TOTAL PRESTRESSING FORCE-FOR STAGE III 5000 C.L bearing 4500 4000 3500 3000 2500 2000 1500 1000 500 0 Column N 0.00 Column I Column G Column H
2.00
4.00
6.00
m
8.00
10.00
12.00
8. SERVICE LIMIT STATE CHECK fg-top : Stress at Top Fiber of Girder (MPa) fg-bot : Stress at Bottom Fiber of Girder (MPa) fs-top : Stress at Top Fiber of Cast-in-place Slab (MPa) fgL-comp : Compresion stress Limit of Girder Concrete (MPa) fsL-comp : Compresion stress Limit of Cast-in-place Slab Concrete (MPa) fgL-tens : Tension Stress Limit of Girder Concrete (MPa) Np : Axial Force due to Prestressing Load Mp : Moment due to Prestressing Load Mi : Moment due to Loads during Stage "i" ∆Np : Axial Force due to Loss of Prestressing Load ∆Mp : Moment due to Loss of Prestressing Load 8.1. Stress check in Stage I
xi/Ls
Sec. xi
STAGE I ( At Tranfer) Np Mp M1
Asec_(I)
Isec_(I)
et_(I)
eb_(I)
0.000 0.006 0.044 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500
(m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120
(m2) 0.515 0.515 0.376 0.376 0.376 0.376 0.376 0.376 0.376 0.376 0.376 0.376 0.376
(m4) 0.058 0.059 0.054 0.053 0.054 0.054 0.054 0.054 0.054 0.055 0.055 0.055 0.055
(m) 0.608 0.608 0.612 0.637 0.637 0.638 0.639 0.640 0.641 0.642 0.642 0.642 0.642
(m) 0.535 0.535 0.531 0.506 0.506 0.505 0.504 0.503 0.502 0.501 0.501 0.501 0.501
fgL-comp
fgL-tens
(KN) (KNm) (KNm) (Mpa) (Mpa) 25.50 ### ### ### ### ### ### ### 17 ### ### ### ### ### 120 ### ### ### ### ### 135 ### ### ### ### ### 255 ### ### ### ### ### 362 ### ### ### ### ### 454 ### ### ### ### ### 532 ### ### ### ### ### 596 ### ### ### ### ### 645 ### ### ### ### ### 681 ### ### ### ### ### 702 ### ### ### ### ### 709 ### ### ###
fg-top
fg-bot
-3.78 ### ### ### ### ### ### ### ### ### ### ### ### ###
CHECK STRESS - STAGE I 30.0 25.0
Stress (MPa)
20.0 15.0 10.0 5.0 0.0 -5.0F Column Column G0.0 Column D Column E
5.0
10.0
Distance (m)
15.0
20.0
8.2. Stress check in Stage II
xi/Ls
Sec. xi
Asec_(II)
Isec_(II)
et_(II)
eb_(II)
STAGE II ∆Np ∆Mp
M2
fg-top
fg-bot
fgL-comp
fgL-tens
(m) (m2) (m4) (m) (m) (KN) (KNm) (KNm) (Mpa) (Mpa) 30.00 0.000 0.000 0.515 0.058 0.608 0.535 ### ### ### ### ### 0.006 0.150 0.515 0.059 0.608 0.535 ### ### 16 ### ### ### 0.044 1.070 0.376 0.054 0.612 0.531 ### ### 108 ### ### ### 0.050 1.212 0.376 0.053 0.637 0.506 ### ### 121 ### ### ### 0.100 2.424 0.376 0.054 0.637 0.506 ### ### 229 ### ### ### 0.150 3.636 0.376 0.054 0.638 0.505 ### ### 325 ### ### ### 0.200 4.848 0.376 0.054 0.639 0.504 ### ### 408 ### ### ### 0.250 6.060 0.376 0.054 0.640 0.503 ### ### 478 ### ### ### 0.300 7.272 0.376 0.054 0.641 0.502 ### ### 535 ### ### ### 0.350 8.484 0.376 0.055 0.642 0.501 ### ### 580 ### ### ### 0.400 9.696 0.376 0.055 0.642 0.501 ### ### 612 ### ### ### 0.450 10.908 0.376 0.055 0.642 0.501 ### ### 631 ### ### ### 0.500 12.120 0.376 0.055 0.642 0.501 ### ### 637 ### ### ### Notes: M2 is taken by maximum value of internal & external girder.
-3.78 ### ### ### ### ### ### ### ### ### ### ### ### ###
CHECK STRESS - STAGE II 35.0 30.0
Stress (MPa)
25.0 20.0 15.0 10.0 5.0 0.0 Column -5.0J Column K0.0 Column H Column I
5.0
0.000 0.006 0.044 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500
15.0
20.0
Distance (m)
8.3. Stress check in Stage III 8.3.1. For internal girder 8.3.1.1. Check girder Stresses Sec. xi/Ls xi Asec_(III) Isec_(III) (m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120
10.0
(m2) 0.757 0.757 0.618 0.618 0.618 0.618 0.618 0.618 0.618 0.618 0.618 0.618 0.618
(m4) 0.140 0.140 0.132 0.132 0.132 0.132 0.133 0.133 0.133 0.134 0.134 0.134 0.134
STAGE III ∆Mp M3-ser1 M3-ser3
et_(III)
eb_(III)
∆Np
fgL-comp
fgL-tens
(m) 0.383 0.383 0.349 0.349 0.350 0.350 0.351 0.351 0.352 0.352 0.353 0.353 0.353
(m) 0.760 0.760 0.794 0.794 0.793 0.793 0.792 0.792 0.791 0.791 0.790 0.790 0.790
(KN) (KNm) (KNm) (KNm) (Mpa) (Mpa) 30.00 ### ### 0 ### ### ### ### ### 42 34.27 ### ### ### ### ### 287 234.25 ### ### ### ### ### 323 263.55 ### ### ### ### ### 608 496.7 ### ### ### ### ### 856 699.45 ### ### ### ### ### 1067 871.79 ### ### ### ### ### 1240 ### ### ### ### ### ### 1376 ### ### ### ### ### ### 1475 ### ### ### ### ### ### 1537 ### ### ### ### ### ### 1561 ### ### ### ### ### ### 1548 1267.4 ### ### ###
-1.77 ### ### ### ### ### ### ### ### ### ### ### ### ###
fg-top
fg-bot
8.3.1.2. Check slab Stresses xi/Ls Sec. xi Asec_(III) Isec_(III) 0.000 0.006 0.044 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500
(m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120
(m2) 0.757 0.757 0.618 0.618 0.618 0.618 0.618 0.618 0.618 0.618 0.618 0.618 0.618
(m4) 0.140 0.140 0.132 0.132 0.132 0.132 0.133 0.133 0.133 0.134 0.134 0.134 0.134
et_sl_(III) (m) 0.563 0.563 0.529 0.529 0.530 0.530 0.531 0.531 0.532 0.532 0.533 0.533 0.533
eb_sl_(III) (m) 0.383 0.383 0.349 0.349 0.350 0.350 0.351 0.351 0.352 0.352 0.353 0.353 0.353
STAGE III ∆Np ∆Mp M3-ser1 M3-ser3
fs-top
CHECK GIRDER STRESS - STAGE III - SERVICE 35.0 30.0
Stress (MPa)
25.0 20.0 15.0 10.0 5.0 0.0 -5.0 Column U Column V 0.0 Column N Column O
5.0
10.0
15.0
20.0
Distance (m)
Stress (MPa)
CHECK SLAB STRESS - STAGE III - SERVICE 15.0 13.0 11.0 9.0 7.0 5.0 3.0 1.0 -1.0 -3.0 -5.0
Column T0.0 Column L Column M
5.0
fs-bot
fsL-comp
(KN) (KNm) (KNm) (KNm) (Mpa) (Mpa) 13.50 ### ### 0 ### ### ### ### ### 42 34.27 ### ### ### ### ### 287 234.25 ### ### ### ### ### 323 263.55 ### ### ### ### ### 608 496.7 ### ### ### ### ### 856 699.45 ### ### ### ### ### 1067 871.79 ### ### ### ### ### 1240 ### ### ### ### ### ### 1376 ### ### ### ### ### ### 1475 ### ### ### ### ### ### 1537 ### ### ### ### ### ### 1561 ### ### ### ### ### ### 1548 1267.4 ### ### ###
10.0 Distance (m)
15.0
20.0
8.3.2. For external girder 8.3.2.1. Check girder Stresses Sec. xi/Ls xi Asec_(III) Isec_(III) 0.000 0.006 0.044 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500
(m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120
(m2) 0.690 0.690 0.552 0.552 0.552 0.552 0.552 0.552 0.552 0.552 0.552 0.552 0.552
(m4) 0.123 0.123 0.117 0.117 0.117 0.118 0.118 0.118 0.119 0.119 0.119 0.119 0.119
8.3.2.2. Check slab Stresses xi/Ls Sec. xi Asec_(III) Isec_(III) 0.000 0.006 0.044 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500
(m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120
(m2) 0.690 0.690 0.552 0.552 0.552 0.552 0.552 0.552 0.552 0.552 0.552 0.552 0.552
(m4) 0.123 0.123 0.117 0.117 0.117 0.118 0.118 0.118 0.119 0.119 0.119 0.119 0.119
STAGE III ∆Mp M3-ser1 M3-ser3
et_(III)
eb_(III)
∆Np
fgL-comp
fgL-tens
(m) 0.428 0.428 0.402 0.402 0.403 0.404 0.404 0.405 0.405 0.406 0.406 0.406 0.406
(m) 0.715 0.715 0.741 0.741 0.740 0.739 0.739 0.738 0.738 0.737 0.737 0.737 0.737
(KN) (KNm) (KNm) (KNm) (Mpa) (Mpa) 30.00 ### ### 0 ### ### ### ### ### 45 38.6 ### ### ### ### ### 308 264.11 ### ### ### ### ### 347 297.19 ### ### ### ### ### 654 560.88 ### ### ### ### ### 922 791.06 ### ### ### ### ### 1151 987.73 ### ### ### ### ### 1340 ### ### ### ### ### ### 1490 ### ### ### ### ### ### 1601 ### ### ### ### ### ### 1673 ### ### ### ### ### ### 1706 ### ### ### ### ### ### 1699 ### ### ### ###
-1.77 ### ### ### ### ### ### ### ### ### ### ### ### ###
et_sl_(III) (m) 0.608 0.608 0.582 0.582 0.583 0.584 0.584 0.585 0.585 0.586 0.586 0.586 0.586
eb_sl_(III) (m) 0.428 0.428 0.402 0.402 0.403 0.404 0.404 0.405 0.405 0.406 0.406 0.406 0.406
fg-top
STAGE III ∆Np ∆Mp M3-ser1 M3-ser3
fs-top
CHECK GIRDER STRESS - STAGE III - SERVICE 30.0
Stress (MPa)
25.0 20.0 15.0 10.0 5.0 0.0 5.0
fs-bot
fsL-comp
(KN) (KNm) (KNm) (KNm) (Mpa) (Mpa) 13.50 ### ### 0 ### ### ### ### ### 45 38.6 ### ### ### ### ### 308 264.11 ### ### ### ### ### 347 297.19 ### ### ### ### ### 654 560.88 ### ### ### ### ### 922 791.06 ### ### ### ### ### 1151 987.73 ### ### ### ### ### 1340 ### ### ### ### ### ### 1490 ### ### ### ### ### ### 1601 ### ### ### ### ### ### 1673 ### ### ### ### ### ### 1706 ### ### ### ### ### ### 1699 ### ### ### ###
35.0
-5.0 Column U Column V 0.0 Column R Column S
fg-bot
10.0 Distance (m)
15.0
20.0
Stress (MPa)
CHECK SLAB STRESS - STAGE III - SERVICE 15.0 13.0 11.0 9.0 7.0 5.0 3.0 1.0 -1.0 -3.0 -5.0
Column T0.0 Column P Column Q
5.0
10.0 Distance (m)
15.0
20.0
8. STRENGTH LIMIT STATE CHECK 8.1. Resistance Factor ϕm Resistance factor for Flexure: ϕv Resistance factor for Shear: 8.2. Flexural 8.2.1. Flexural resistance The factored resistance, Mr, shall be taken as: Mr = ϕmMn The normal flexural resistance, Mn, shall be taken as:
When hf < a:
M n = A ps f
ps
When hf > a:
M n= A ps f
ps
where: Aps fps
d p−
a A s f 2
d p−
a As f 2
b bw hf a = β1 c β1 c
y
d s−
a −A ' s f 2
d s−
a −A ' s f 2
y
y
d ' s−
a a h 0. 85 f ' c b−b w β 1 h f − f 2 2 2
d ' s−
a 2
: Arer of prestressing steel : Average stress in prestressing steel when fpe ≥ 0.5fpu
f p s= f p u 1−k dp As ds A's d's
y
= 1.0 = 0.9
c dp
k=2 1. 04−
where:
f
py
f
pu
= 0.280
: Distance from extreme compression fiber to the centroid of prestressing tendons : Area of tension reinforcement : Distance from extreme compression fiber to the centroid of tensile reinforcement : Area of cpmpression reinforcement : Distance from extreme compression fiber to the centroid of compression reinforcement : Width of compressive face : Web width : Compresion flange depth : depth of the equivalent stress block β1 : Stress block factor = 0.693 : Distance between the neutral axis and the compressive face
c 1=
A ps f
pu A s
f y − A ' s f y −0. 85 β 1 f ' c b−b w h f
0 . 85 f ' c β 1 bkA p
s
f pu dp
c 2=
A ps f pu A s f y −A ' s f 0.85 f ' c β 1 bkA p
s
y
f pu dp
8.2.2. Limits for Reinforcement Maximum Reinforcement c ≤0. 42 The maximum amount reinforcement shall be such that: de for which: de : Effective depth from the extreme compression fiber to the centroid of the tensile for in the tensile reinforcement.
d e=
A ps f
ps d p A s
f yds
A ps f ps A s f y
Minimum Reinforcement The amount of tensile reinforcement shall be adequate to develop a factorad flexural resistance, Mr, at least equal to the lesser of: • 1.2 times the cracking moment, Mcr, determined on the basis of elastic stress distribution and the modulus of rupture, fr, of the concrete;
• 1.33 times the factored moment. Cracking moment, Mcr, may be taken as: Mcr = Sc fr where: Sc : Section modulus of gross section fr : Modulus of rupture. For normal density concrete:
f r =0 .6 3 f ' c
f r =0 .6 3 f ' c 8.3. Shear 8.3.1. Regions requiring transverse reinforcement Excep for slabs, footings, and culverts, transverse reinforcement shall be provided where:Vu > 0.5ϕv(Vc+Vp) where: Vu : Factored shear force Vc : Nominal shear resistance of concrete Vp : Component of prestressing force in direction of the shear force 8.3.2. Minimum transverse reinforcement b s The area of transverse reinforcement shall not be less than: Av min=0 . 083 f ' c v fy where: Avmin : Area of a transverse reinforcement within distance "s" s : Spacing of transverse reinforcement bv = b 8.3.3. Maximum spacing of transverse reinforcement The spacing of the transverse reinforcement shall not exceed the following: • If vu < 0.125f'c, then: s ≤ 0.8dv ≤ 600mm • If vu ≥ 0.125f'c, then: s ≤ 0.4dv ≤ 300mm where: dv = de -a/2 : Effective shear depth; it need not be taken to be less than the greater of 0.9de of 0.72h vu : Shear stress 8.3.4. Norminal shear resistance The norminal shear resistance, Vn, shall be determined as the lesser of: Vn1 = Vc + Vs + Vp Vn2 = 0.25f'cbvdv + Vp for which: where:
V c =0. 0 8 3β f ' c bv d v
and
V s=
A v f y d v cot gθcot gα sin α s
: Factor indicating ability of diagonally crackes concrete to transmit tension β : Angle of inclination of diagonal compressive stresses θ : Angle of inclination of transverse reinforcement to longitudinal axis α Determination of β and θ: V − ϕV p vu= u • The shear stress on the concrete shall be determined as: ϕb v d v
• The strain in the reinforcement on the flexural tension side of the member shall be determined as: If the section contains at least the minumum transverse reinforcement:
ε x1 =
Mu dv
0 . 5N u0 . 5 V u−V
p
cot gθ − A ps f p0
2 E s A s E p A ps
≤0 . 001
If the section contains less than the minimum transverse reinforcement:
ε x2=
Mu dv
0 . 5N u0 . 5 V u−V p cot gθ− A ps f
p0
E s A s E p A ps
≤0 . 002
If the value of εx is negative, the strain shall be taken as:
ε x3=
where: fp0 Ac
Mu dv
0 . 5N u 0 . 5 V u −V p cot gθ− A ps f
p0
2 E c A c E s A s E p A ps : Stress in prestressing steel when the surrounding concrete is 0. : Area of concrete on the flexural tension side
• The crack spacing parameter sxe shall be determined as: where:
s xe =s x
35 ≤ 2000 mm a g 16
ag : Maximum aggregate size sx = min(dv,maximum distance between layers of long. crack control Reinf.)
8.4. Checking for internal girder Section LOADS xi/Ls xi Mu Vu 0.000 0.006 0.044 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500
(m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120
Section Pre. Steel xi Aps (m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120 Section xi (m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120
mm2 3158 3158 3158 3158 3158 3158 3158 3158 3158 3158 3158 3158 3158 "1"="Include ", "2"="Exclude " Comp. Reinf.
2 2 2 2 2 2 2 2 2 2 2 2 2
KNm 114 780 877 1656 2337 2920 3405 3791 4080 4270 4362 4356
KN 800 792 744 737 673 611 549 488 427 367 307 248 190
Nu KN -
Tension Reinforcement Ds ns As mm
bars -
c1
c2
mm
mm
-90 -90 -239 -577 -579 -582 -585 -587 -589 -592 -593 -593 -593
111 111 111 111 111 111 111 111 111 111 111 111 111
b mm 1750 1750 1750 1750 1750 1750 1750 1750 1750 1750 1750 1750 1750
bw
DIMENSIONS: hf
mm 410 410 294 178 178 178 178 178 178 178 178 178 178
Compression Reinforcement D's n's A's mm
mm2 -
h mm 1323 1323 1323 1323 1323 1323 1323 1323 1323 1323 1323 1323 1323
bars
Design value
a Check
111 111 111 111 111 111 111 111 111 111 111 111 111
a< or >hf
mm 77 77 77 77 77 77 77 77 77 77 77 77 77
Exclude Exclude Exclude Exclude Exclude Exclude Exclude Exclude Exclude Exclude Exclude Exclude Exclude
< < < < < < < < < < < < <
dp
ds
mm 1058 1061 1078 1081 1103 1126 1149 1172 1194 1217 1231 1231 1231
mm 1263 1263 1263 1263 1263 1263 1263 1263 1263 1263 1263 1263 1263
d's mm 60 60 60 60 60 60 60 60 60 60 60 60 60
Transverse Reinforcement nv Av sv
mm -
c mm
Dv
mm2
-
mm 180 180 194 211 211 211 211 211 211 211 211 211 211
bars 10 10 10 10 10 10 10 10 10 10 10 10 10
8 8 6 5 5 5 5 5 5 5 5 5 5
mm2 628 628 471 393 393 393 393 393 393 393 393 393 393
fps
Mn
Mr
Mpa
KNm
KNm
1806 1806 1807 1807 1808 1809 1810 1811 1812 1812 1813 1813 1813
5815 5831 5932 5948 6081 6214 6347 6480 6613 6746 6827 6827 6827
5815 5831 5932 5948 6081 6214 6347 6480 6613 6746 6827 6827 6827
mm 100 100 150 200 200 200 200 200 200 200 200 200 200
Check OK OK OK OK OK OK OK OK OK OK OK OK OK
Section xi (m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120 Section xi (m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120 Section xi (m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120
Maximum Reinforcement: de c/de Check mm 1058 0.105 OK 1061 0.104 OK 1078 0.103 OK 1081 0.102 OK 1103 0.100 OK 1126 0.098 OK 1149 0.097 OK 1172 0.095 OK 1194 0.093 OK 1217 0.091 OK 1231 0.090 OK 1231 0.090 OK 1231 0.090 OK Regions requiring trans. Reinf.
dv mm 1020 1022 1040 1042 1065 1088 1110 1133 1156 1179 1192 1192 1192
α
fp0
deg.
Mpa 90 90 90 90 90 90 90 90 90 90 90 90 90
1395 1395 1395 1395 1395 1395 1395 1395 1395 1395 1395
bv
Check mm 410 Need 410 Need 294 Need 178 Need 178 Need 178 Need 178 Need 178 Need 178 Need 178 Need 178 Need 178 no Need 178 no Need
θ deg. 30.00 30.90 27.00 24.05 25.49 26.86 27.00 27.00 27.00 27.00 27.00 27.00 27.00
Sc mm3 1.84E+08 1.84E+08 1.66E+08 1.66E+08 1.66E+08 1.67E+08 1.68E+08 1.68E+08 1.69E+08 1.69E+08 1.70E+08 1.70E+08 1.70E+08
KNm 817 818 739 739 741 744 746 749 751 754 756 756 756
Min. Trans. Reinf. Avmin Check mm2 60 OK 60 OK 65 OK 52 OK 52 OK 52 OK 52 OK 52 OK 52 OK 52 OK 52 OK -
Suppose value of θ εx1 εx2 0.00056 0.00062 -0.00235 -0.00220 -0.00172 -0.00133 -0.00099 -0.00074 -0.00057 -0.00047 -0.00042 -0.00041 -0.00046
Mcr
0.00111 0.00124 -0.00470 -0.00440 -0.00345 -0.00266 -0.00199 -0.00148 -0.00114 -0.00094 -0.00084 -0.00081 -0.00091
εx3 0.00006 0.00007 -0.00037 -0.00054 -0.00042 -0.00032 -0.00024 -0.00018 -0.00014 -0.00011 -0.00010 -0.00010 -0.00011
Minimum Reinforcement: 1.2Mcr 1.33Mu KNm 981 981 886 887 890 892 895 899 902 905 907 907 907
KNm 151 1037 1167 2203 3109 3884 4529 5043 5426 5679 5801 5793
Min KNm 151 886 887 890 892 895 899 902 905 907 907 907
Check OK OK OK OK OK OK OK OK OK OK OK OK OK
Maximum spacing of Transverse Reinf. vu 0.125f'c smax Check Mpa Mpa mm 2.13 6.25 600 OK 2.10 6.25 600 OK 2.70 6.25 600 OK 4.41 6.25 600 OK 3.95 6.25 600 OK 3.51 6.25 600 OK 3.09 6.25 600 OK 2.69 6.25 600 OK 2.31 6.25 600 OK 1.94 6.25 600 OK 1.61 6.25 600 OK 1.30 6.25 0.99 6.25 Choice εx 0.00056 0.00062 -0.00037 -0.00054 -0.00042 -0.00032 -0.00024 -0.00018 -0.00014 -0.00011 -0.00010 -0.00081 -0.00091
Check OK OK OK OK OK OK OK OK OK OK OK OK OK
vu/f'c 0.043 0.042 0.054 0.088 0.079 0.070 0.062 0.054 0.046 0.039 0.032 0.026 0.020
1000εx 0.56 0.62 -0.37 -0.54 -0.42 -0.32 -0.24 -0.18 -0.14 -0.11 -0.10 -0.81 -0.91
Section xi (m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120 Section xi (m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120
θ deg. 29.91 30.94 27.00 25.15 26.45 27.00 27.00 27.00 27.00 27.00 27.00 27.00 27.00
Long. Crack control Reinf. DL AL sL ag mm 10 10 10 10 10 10 10 10 10 10 10 10 10
β
2.48 2.44 4.88 4.02 4.62 4.88 4.88 4.88 4.88 4.88 4.88 4.88 4.88
mm2 157 157 157 157 157 157 157 157 157 157 157 157 157
mm 160 160 160 160 160 160 160 160 160 160 160 160 160
mm -
Vc
Vs
Vp
KN 608 601 875 438 515 555 566 578 589 601 608 608 608
KN 4452 4284 2563 1743 1681 1676 1711 1746 1781 1816 1837 1837 1837
KN -
For no need Trans. Reinf. or Av < Avmin 0.003bv*sx sx sxe Check mm mm mm2 160 350 85 OK 160 350 85 OK
Vn1
Vn2
Vn
Vr
KN 5060 4885 3438 2181 2195 2230 2277 2323 2370 2417 2445 2445 2445
KN 5226 5240 3821 2319 2370 2420 2471 2521 2572 2622 2653 2653 2653
KN 5060 4885 3438 2181 2195 2230 2277 2323 2370 2417 2445 2445 2445
KN 4554 4396 3095 1963 1976 2007 2049 2091 2133 2175 2200 2200 2200
FLEXURAL RESISTANCE 8000 7000
Moment (KNm)
6000 5000 4000 3000 2000 1000 0 Column0.0 X Column W
5.0
10.0 Distance (m)
15.0
20.0
Check OK OK OK OK OK OK OK OK OK OK OK OK OK
SHEAR RESISTANCE 5000 4500 4000
Shear (KN)
3500 3000 2500 2000 1500 1000 500 0 0.0
Column Z Column Y
5.0
10.0 Distance (m)
15.0
20.0
8.5. Checking for external girder Section LOADS xi/Ls xi Mu Vu 0.000 0.006 0.044 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500
(m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120
Section Pre. Steel xi Aps (m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120 Section xi (m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120
mm2 3158 3158 3158 3158 3158 3158 3158 3158 3158 3158 3158 3158 3158 "1"="Include ", "2"="Exclude " Comp. Reinf.
2 2 2 2 2 2 2 2 2 2 2 2 2
KNm 112 766 862 1628 2298 2873 3352 3736 4024 4217 4314 4316
KN 750 743 695 688 626 565 504 443 383 323 264 205 147
Nu KN -
Tension Reinforcement Ds ns As mm
bars -
c1
c2
mm
mm
-41 -41 -173 -477 -479 -481 -483 -485 -487 -489 -490 -490 -490
119 119 119 119 119 119 119 119 119 119 119 119 119
b mm 1625 1625 1625 1625 1625 1625 1625 1625 1625 1625 1625 1625 1625
bw
DIMENSIONS: hf
mm 410 410 294 178 178 178 178 178 178 178 178 178 178
Compression Reinforcement D's n's A's mm
mm2 -
h mm 1323 1323 1323 1323 1323 1323 1323 1323 1323 1323 1323 1323 1323
bars
Design value
a Check
119 119 119 119 119 119 119 119 119 119 119 119 119
a< or >hf
mm 82 82 82 82 82 83 83 83 83 83 83 83 83
Exclude Exclude Exclude Exclude Exclude Exclude Exclude Exclude Exclude Exclude Exclude Exclude Exclude
< < < < < < < < < < < < <
dp
ds
mm 1058 1061 1078 1081 1103 1126 1149 1172 1194 1217 1231 1231 1231
mm 1263 1263 1263 1263 1263 1263 1263 1263 1263 1263 1263 1263 1263
d's mm 60 60 60 60 60 60 60 60 60 60 60 60 60
Transverse Reinforcement nv Av sv
mm -
c mm
Dv
mm2
-
mm 180 180 195 214 214 214 214 214 214 214 214 214 214
bars 10 10 10 10 10 10 10 10 10 10 10 10 10
8 8 6 5 5 5 5 5 5 5 5 5 5
mm2 628 628 471 393 393 393 393 393 393 393 393 393 393
fps
Mn
Mr
Mpa
KNm
KNm
1801 1802 1803 1803 1804 1805 1806 1807 1808 1809 1809 1809 1809
5785 5802 5903 5918 6051 6184 6318 6451 6584 6717 6797 6797 6797
5785 5802 5903 5918 6051 6184 6318 6451 6584 6717 6797 6797 6797
mm 100 100 150 200 200 200 200 200 200 200 200 200 200
Check OK OK OK OK OK OK OK OK OK OK OK OK OK
Section xi (m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120 Section xi (m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120 Section xi (m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120
Maximum Reinforcement: de c/de Check mm 1058 0.112 OK 1061 0.112 OK 1078 0.110 OK 1081 0.110 OK 1103 0.108 OK 1126 0.106 OK 1149 0.104 OK 1172 0.102 OK 1194 0.100 OK 1217 0.098 OK 1231 0.097 OK 1231 0.097 OK 1231 0.097 OK Regions requiring trans. Reinf.
dv mm 1017 1020 1037 1039 1062 1085 1108 1130 1153 1176 1189 1189 1189
α
fp0
deg.
Mpa 90 90 90 90 90 90 90 90 90 90 90 90 90
1395 1395 1395 1395 1395 1395 1395 1395 1395 1395 1395
bv
Check mm 410 Need 410 Need 294 Need 178 Need 178 Need 178 Need 178 Need 178 Need 178 Need 178 Need 178 no Need 178 no Need 178 no Need
θ deg. 29.66 30.64 27.00 24.05 25.49 26.86 27.00 27.00 27.00 27.00 27.00 27.00 27.00
Sc mm3 1.84E+08 1.84E+08 1.66E+08 1.66E+08 1.66E+08 1.67E+08 1.68E+08 1.68E+08 1.69E+08 1.69E+08 1.70E+08 1.70E+08 1.70E+08
KNm 817 818 739 739 741 744 746 749 751 754 756 756 756
Min. Trans. Reinf. Avmin Check mm2 60 OK 60 OK 65 OK 52 OK 52 OK 52 OK 52 OK 52 OK 52 OK 52 OK -
Suppose value of θ εx1 εx2 0.00053 0.00059 -0.00240 -0.00226 -0.00178 -0.00139 -0.00106 -0.00081 -0.00063 -0.00054 -0.00048 -0.00046 -0.00051
Mcr
0.00106 0.00118 -0.00480 -0.00451 -0.00356 -0.00278 -0.00212 -0.00162 -0.00127 -0.00107 -0.00097 -0.00093 -0.00102
εx3 0.00006 0.00007 -0.00037 -0.00055 -0.00043 -0.00034 -0.00026 -0.00020 -0.00015 -0.00013 -0.00012 -0.00011 -0.00012
Minimum Reinforcement: 1.2Mcr 1.33Mu KNm 981 981 886 887 890 892 895 899 902 905 907 907 907
KNm 149 1018 1146 2165 3056 3821 4459 4969 5352 5609 5738 5740
Min KNm 149 886 887 890 892 895 899 902 905 907 907 907
Check OK OK OK OK OK OK OK OK OK OK OK OK OK
Maximum spacing of Transverse Reinf. vu 0.125f'c smax Check Mpa Mpa mm 2.00 6.25 600 OK 1.97 6.25 600 OK 2.53 6.25 600 OK 4.13 6.25 600 OK 3.68 6.25 600 OK 3.25 6.25 600 OK 2.84 6.25 600 OK 2.45 6.25 600 OK 2.07 6.25 600 OK 1.72 6.25 600 OK 1.39 6.25 1.08 6.25 0.77 6.25 Choice εx 0.00053 0.00059 -0.00037 -0.00055 -0.00043 -0.00034 -0.00026 -0.00020 -0.00015 -0.00013 -0.00097 -0.00093 -0.00102
Check OK OK OK OK OK OK OK OK OK OK OK OK OK
vu/f'c 0.040 0.039 0.051 0.083 0.074 0.065 0.057 0.049 0.041 0.034 0.028 0.022 0.015
1000εx 0.53 0.59 -0.37 -0.55 -0.43 -0.34 -0.26 -0.20 -0.15 -0.13 -0.97 -0.93 -1.02
Section xi (m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120 Section xi (m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120
θ deg. 29.91 30.94 27.00 25.15 26.45 27.00 27.00 27.00 27.00 27.00 27.00 27.00 27.00
Long. Crack control Reinf. DL AL sL ag mm 10 10 10 10 10 10 10 10 10 10 10 10 10
β
2.48 2.44 4.88 4.02 4.62 4.88 4.88 4.88 4.88 4.88 4.88 4.88 4.88
mm2 157 157 157 157 157 157 157 157 157 157 157 157 157
mm 160 160 160 160 160 160 160 160 160 160 160 160 160
mm -
Vc
Vs
Vp
KN 606 599 873 437 513 553 565 576 588 599 606 606 606
KN 4440 4272 2556 1738 1676 1671 1706 1741 1776 1811 1832 1832 1832
KN -
For no need Trans. Reinf. or Av < Avmin 0.003bv*sx sx sxe Check mm mm mm2 160 350 85 OK 160 350 85 OK 160 350 85 OK
Vn1
Vn2
Vn
Vr
KN 5046 4871 3429 2175 2189 2224 2271 2318 2364 2411 2439 2439 2439
KN 5211 5226 3810 2313 2363 2414 2464 2515 2565 2616 2646 2646 2646
KN 5046 4871 3429 2175 2189 2224 2271 2318 2364 2411 2439 2439 2439
KN 4542 4384 3086 1958 1970 2002 2044 2086 2128 2170 2195 2195 2195
FLEXURAL RESISTANCE 8000 7000
Moment (KNm)
6000 5000 4000 3000 2000 1000 0 Column0.0 AB Column AA
5.0
10.0 Distance (m)
15.0
20.0
Check OK OK OK OK OK OK OK OK OK OK OK OK OK
SHEAR RESISTANCE 5000 4500 4000
Shear (KN)
3500 3000 2500 2000 1500 1000 500 0 0.0
Column AD Column AC
5.0
10.0 Distance (m)
15.0
20.0
Prepared by
CALCULATION SHEET OF LINK SLAB
1
Input Effective length of span Temperature range:
Lp =
24.24 m
Tmax =
47.00 0C
Tmin =
10.00 C 37.00 0C 180 mm 1340 mm
Concrete of girder
0
δT = h = B =
h : Depth of link slab B : Width of link slab
2 2-1
Check by
Concrete of slab Ln : Length of link slab C : Length of any gap between the two adjacent girders
fc ' =
50 Mpa
Eb =
###
fc ' = Eb = Ln = C=
30 Mpa ### 2050 mm 350 mm
Calculation internal force Internal force due to angle and vertical displacement a
Angle displacement Formula:
ϕ=
0,7 . M H Lp 3 . Es . J
In which: Left span Right span MH : Moment due to service load at stage III MH = 2956 2956 Lp : Effective length of span Lp = 24240 24240 η : The factor considered space-working η = 1 1 E : Elastic modulus of concrete E= 38007 38007 J : Moment of inertial of girder J = 1.362.E+11 1.362.E+11 ϕt = 0,7x1.0E+06 x 2955.77 Left angle x 24240 / (24x38006.99 x1.362.E+11) ϕp = 0,7x1.0E+06 x 2955.77 Right angle x 24240 / (24x38006.99 x1.362.E+11) b
c
Units KN.m mm Mpa mm4 =0.00040 Rad =0.00040 Rad
Vertical displacement Formula: Ln : Length of link slab
y =
Left displacement
yt =
( 2050 -
350)x0.5
x 0.0004
= 0.343 mm
Right displacement
yp =
( 2050 -
350)x0.5
x 0.0004
= 0.343 mm
( Ln - C ) x 0,5 x ϕ = Ln = C =
2050 mm 350 mm
Moment at the fix section of link slab Formula:
M =−
2 . E n. Jn. K 2. E n. Jn. K xϕt − xϕ p Ln Ln
In which: Left En : Elastic modulus of slab Jn : Moment of inertial of link slab h : Depth of link slab B : Width of link slab Ln : Length of link slab K : Reduce stiff factor MT : Moment due to dead load at the stage III ϕ: Rotation angle due to dead load at the stage III
En = Jn = h = B = Ln = K = MT = ϕ =
Right 29440 651240000 180 1340 2050 0.8 1491 0.00040
29440 Mpa 651240000 mm4 180 mm 1340 mm 2050 mm 0.8 1491 KN.m 0.00040 Rad
Moment at the fix section: M = -2x 29440.09 -2x 29440.09 x 651240000
x 0.8 / x 2050 + x 2050 = -12080880.7 N.mm = -12.08 KN.m Length of left and right span is the same, so shear force is zero. 2-2
### x0
Internal force due to longitudinal slope of bridge Nd =
Formula: Pf : Weight of span
n . Pf . i Pf = i = n =
i : Longitudinal slope n : Number of span 2-3
x0 x 0.8 /
= 29.52 KN 245.98 KN 0.04 3
Internal force due to locally live load Impact factor: Load factor: a
1 + m= n =
Moment at the fix section Formula:
Mn=−
1.25 1.75
p. d . ln d2 3− 2 . n. 1μ 24 ln
In which: p : Load distribution in the longitudinal of bridge p = P : Weight of one axles b1 : Width transfers force down to link slab in transverse d : Length transfer force down to link slab in longitudinal B : Width of link slab Length of link slab:
b
c
Shear at the fix section Formula:
Qn =
P /( b1 .d) P = b1 = d = B = Ln* = Mn =
p . d . (1 + m ) . n .B . 0.5
Moment at the middle span section Formula:
Mg=
=1006.94 KN.m2 145 KN 0.8 m 0.18 m 1.34 m 2.05 m -101.34 KN.m
=
266 KN.
p . d . ln d 2 2d 3 2 − . n . 1 μ = 24 ln ln
Shear force is zero. 2-4
Internal force due to sub-dead load and selfweight a
Moment at the fix section Formula: = In which: q : Uniform dead load h : Depth of link slab h* : Depth of surfacing wearing B : Width of link slab n: Load factor Ln : Length of link slab
b
−n . q . Lb 2 12
-1.25 x
7.42 x q= h = h* = B = n = Ln =
###
3.247 KN.m
7.42 KN/m 0.18 m 0.05 m 1.34 m 1.25 2.05 m
Shear at the fix section Qnt = =
c
Mgt =
n . q . Lb2 . 0.5 = 1.25 x 7.42 x
Moment at the middle span section Formula:
Mgt =
−n . q . Lb 2 24
2.05
= 9.50 KN
96 KN.m
Mgt = = Effective length of link slab 2-5
Internal force due to temperature Formula:
−n . q . Lb 2 24
1.25 x Ln* = Q = 0
7.42 x 2.05 m
2.05^2
/ 24 =
1.623 KN.m
Nt =−n . fi . Ai =
3 x 0.05 x 245.98 = In which: n : Number fixed bearing of continuous deck slab n = fi : Bearing friction factor fi = Ai : Reaction of bearing Ai = 3
3 0.05 246 KN
Combination force Components
Fix section M (KN.m) Q (KN)
Combination 1 - Angle and vertical displacement - Axial due to longitudinal slope of bridge Sum: Combination 2 - Live load at the link slab - Dead load of link slab - Axial due to longitudinal slope of bridge Combination 3 - Displacement at the service stage - Live load at the link slab - Dead load of link slab - Axial due to temperature - Axial due to longitudinal slope of bridge Conclusion:
Sum: Choose fix section to check
Checking section Slab section: Depth of slab: Effective depth: Caculate width:
H = Ho= B =
Cheking at the fix section Design shear for per unit length of slab Design moment for per unit length of slab Design axial for per unit length of slab Section:
Middle section M (KN.m) Q (KN)
-12.08
-
-
-
-12.08
0.000
0.000
0.000
-101.34 3.25
265.64 9.50
95.91 1.62
-
-98
275.147
97.536
0.000
-12.08 -101.34 3.25
265.64 9.50
95.91 1.62 0.00
0.00
-110
275
98
0
Sum:
4
37 KN.m
180 mm 132.6 mm 1340 mm
Qtt = Mtt = Ntt = B= H=
Checking limit moment Tensile reinforcement Diameter of bar Number of bar Distance from edge of tensile fiber to central of bar Area of bars Yield strength Compressive reinforcement Diameter of bar Number of bar Distance between bar-layers Distance from edge of compressive fiber to central of bar
205 KN 82 KN.m 206 KN 1000 mm 180 mm
Effective Web
Av
D = n = c = As = fy = d =
22 mm 8 47.4 mm 2914 mm2 400 Mpa 132.6 mm
D = n = s= c =
0 mm 0 0 mm 47.4 mm
Axial KN 29.52 29.518
29.52 29.518 0.00 0.00 245.98 29.52 276
Area of bars
A's = dp=
0 mm2 133
Prestress tendon Diameter of tendon Number of tendon Distance between tendon-layers
D = n = s= Distance from edge of compressive fiber to central of tendon c = Area of tendons Aps = dp= fpy = Yield strength
0 mm2 0 0 mm 65 mm 0 mm2 115
1670 Mpa Elastic modulus of tendon Esp = 197000.00 Mpa Class of concrete 30 fc = 30 Mpa Mpa Φ = Resistance factor 0.9 Distance from extreme compressive fiber to centroid of tensile reinforcement (Aps.fps+As*fy-A'sf'y) / (0,85 *f'c * b ) a = a = (0 x 1670 + 2914.35 x 400 -0 x400) / ( 0.85 x 30 x 1340 ) = Limit moment Φ Mn = Φ ( Aps * fpy * ( dp - 0.5 * a )+ ( As * fy * ( d - 0.5 * a )- ( As' * fy' * ( ds' - 0.5 * a ) Φ Mn =
0.9
x (0 + (2914.35 - (0
Mn =
x 1670 x 400 x 400
x (115 x (132.6 x (65
121 kN.m
>
- 0.5 - 0.5 - 0.5 Mmax =
34.116 mm
x 34.12 x 34.12 x 34.12 ) = 121222822.91N.mm 82 OK
Crack checking Pmin >= 0,03 f'c/fy =
Balanced bar ratio
= 0.23% =1.2% > z / (dc . A ) 1/3
ρ Stress in tensile reinforcement
fs = dc =
0.23%
OK
50 mm A = 17478 mm2 z = 30000 N/mm Fsall = 30000 / ( 50 x 17478.26 ) 1/3 = 313.78 Mpa > 0,6 fy = 240 Mpa Stress in bar follow formula as: fs = Ms / (As . j . d ) Ms = 62 kN.m ( Service load design ) As = 2914.35 mm2 As* = 0.00 Ej = 1- k/3 ; k = sqrt (2.p.n + (p.n)^2))-p.n ; p = As/(b.d) ; n= Es/b Elastic modulus of concrete Ec = 38007 Mpa Elastic modulus of steel Es = 200,000 Mpa n = 5.26 p = 1.208% k = 0.299 j = 0.900 d = 132.6 mm Check fs = 179 Mpa < Fsall = 240 Mpa OK Effect area
Checking limit shear Formula: Vn = Vc + Vs Vn = 0,25 . f'c . bv . dv
= =
313 KN 994.5 KN
Vc = 0,0083 x bv x dv x √ f'c = bv = 1000 mm dv = Vs = ( Av x fy x dv x (cotagθ + cotgα) sinα )/ s = Shear reinforcement Diameter of bar D = Spacing of bars s= Number of bar n' = Area of bars Av = α = Bar inclination β = Factor 2 Yield strength fy =
6.03 KN 133 mm
In which:
Effective Web
307 KN 12 mm 150 mm 8 867.08 mm2 90 degree θ = 400 Mpa
45 degree
Av
α
The norminal shear resistance
Vn =
=
313
KN >
205
OK
Bảng tra deta q 0 0.05 27 0.08 27 0.1 23.5 0.13 23.5 0.15 25 0.18 26.5 0.2 27.5 0.23 29 0.25 30 Bảng tra góc beta
0.13 27 27 24 26 27 28 29 30.5 31
Ex*1000 0.25 28.5 27.5 26.5 28 29 30 31 32 32
0.5 29 30 30.5 31.5 32 32.5 33 33 33
0.75 33 33.5 34 34 34 34 34 34 34
1 36 36 36 36 36 36 34.5 34.5 35.5
1.5 41 40 38 37 36.5 35.5 35 36.5 38.5
2 43 v/f'c1 42 v/f'c2 39 ex1 38 ex2 37 36 36 39 41.5
V/f'c
0.13 3.99 3.65 2.61 2.57 2.5 2.41 2.37 2.33 2.28
Ex*1000 0.25 3.49 3.01 2.54 2.5 2.45 2.39 2.33 2.27 2.01
0.5 2.51 2.47 2.41 2.37 2.28 2.2 2.1 1.92 1.64
0.75 2.37 2.33 2.28 2.18 2.06 1.95 1.82 1.67 1.52
1 2.23 2.16 2.09 2.01 1.93 1.74 1.58 1.43 1.4
1.5 1.95 1.9 1.72 1.6 1.5 1.21 1.21 1.18 130
2 1.72 1.65 v/f'c1 1.45 v/f'c2 1.35 ex1 1.24 ex2 1 1 1.14 1.25
V/f'c
0.05 0.08 0.1 0.13 0.15 0.18 0.2 0.23 0.25
DETA BETA
0 4.88 4.88 3.26 2.6 2.55 2.5 2.45 2.37 2.3
1 2 3 4 5 6 7 8 9 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!
Mặt cắt ex x 1000 v/f'c deta θ1 deta θ2 deta θ3 deta θ4 deta θ12 deta θ34 deta θ deta θ31 deta θ41 deta θ3141 deta θ
1 0.56 0.04 #N/A #N/A #N/A #N/A #N/A #N/A #N/A 29 33 29.91 29.91
2 0.62 0.04 #N/A #N/A #N/A #N/A #N/A #N/A #N/A 29 33 30.94 30.94
Giá trị thực tế θ beta β1 #N/A #N/A beta β2 #N/A #N/A beta β3 #N/A #N/A beta β4 #N/A #N/A beta β12 #N/A #N/A beta β34 #N/A #N/A beta β #N/A #N/A beta β31 2.51 2.51 beta β41 2.37 2.37 beta β3141 2.48 2.44 beta β 2.48 2.44 10 11 12 13 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!
3 -0.37 0.05 #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A
4 -0.54 0.09 #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A
5 -0.42 0.08 #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A
6 -0.32 0.07 #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A
7 -0.24 0.06 #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A
8 -0.18 0.05 #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A
#N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A
#N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A
#N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A
#N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A
#N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A
#N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A
9 -0.14 0.05 #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A
10 -0.11 0.04 #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A
11 -0.1 0.03 #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A
12 -0.81 0.03 #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A
13 -0.91 0.02 #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A
#N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A
#N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A
#N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A
#N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A 2
#N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A 3
Tra deta Mặt cắt v/f'c1 v/f'c2 ex1 ex2
4
5
6
7
8
1 #N/A #N/A 0.5 0.75
9
2 #N/A #N/A 0.5 0.75
3 0.05 0.08 #N/A #N/A
4 0.08 0.1 #N/A #N/A
5 0.08 0.1 #N/A #N/A
6 0.05 0.08 #N/A #N/A
7 0.05 0.08 #N/A #N/A
8 0.05 0.08 #N/A #N/A
9 #N/A #N/A #N/A #N/A
10 #N/A #N/A #N/A #N/A
11 #N/A #N/A #N/A #N/A
12 #N/A #N/A #N/A #N/A
13 #N/A #N/A #N/A #N/A
10. DAPPED BEAM-END DESIGN 10.1. Input data Sec. Width, b =800 mm Hg =1143 mm hh =0 mm h1 =100 mm h2 =943 mm h3 =100 mm h4 =100 mm h5 =1143 mm h6 =-200 mm dh =800 mm dD =1200 mm d1 =350 mm d2 =450 mm d3 =100 mm d4 =1000 mm d5 =100 mm d6 =1212 mm α1 -20.0 deg. α2 43.3 deg. α3 -9.4 deg. 10.2. Axial force from Strut-and-Tie model Member AB AD BC Force (KN) 2341.7 -2200.7 745.2 10.3. Ties Check The area of reinforcement required for Tie: where: Resistance Factor U bars
Check
Beam-End Design
Hg
h4
Diameter (mm) Number Spacing (mm) Area, As (mm2)
α
h6 α
1
3
A
E'
E D
Nu
Vu
C α h5
h2
F'' 450
F
2
F' h3
d1
d2 d3 dh
Comb. Strength I Service I
BD -338.0
d5
d4
Tension Comprestion
dD
Reaction (KN) Vu
Nu
800 524
0 0
BE -466.8
CD -1808.0
ϕ two-legged Closed Stirrups
two-legged Closed Stirrups
2
4
CF 1315.4
DE -1166.5
EF 800.3
=0.90
Ld
3
Choice
hh
bars
Member Mark N (N) As-required (mm2)
h1
B
As-required = N/(ϕfy)
Framing bars
1
d6
bars AD 1 -2200741 -6113 32 8 100 6408 OK
Date: 06/03/2011
U bars BC 2 745238 2070 22 10 100 7600 OK
CF 3 1315395 3654 20 14 100 4396 OK
EF 4 800269 2223 16 12 100 4848 OK
Page: 56 of 65
10.4. Truts Check Limiting compresive stress in Strut:
f cu= where: αs εs
f 'c ≤0.85 f ' c 0. 8170ε 1
for which: ε1 = εs + (εs + 0.002)cotg2αs
: The smalest angle between the compressive strut and adjoining tension ties : The tensile strain in the concrete in the direction of the tension tie Required width for strut: wstrut-required = (N/ϕ - fyAss)/(fcub) Acs : The effective cross-section area of Strut Ass : Area of reinforcement in the trut ϕ
ϕ
: Resistance factor
=0.70
B E A D C
F
Member N (N) εs (mm/mm) αs (deg.) ε1 (mm/mm) fcu (Mpa)
AB BD BE DE -2341728 338026 466753 1166458 0.0020 0.0020 0.0020 0.0020 -20.0 -9.4 90.0 46.7 0.0323 0.1489 0.0020 0.0056 8.0 1.9 42.5 28.7 Diameter (mm) Reinf. Number Area, Ass (mm2) wstrut-required (mm) -525 315 20 73 Choice wstrut (mm) 150 100 50 200 Note: Checking whether Strut width fit in the space available 10.5. Design the Nodal Zone and Check the Anchorages To satisfy the stress limit in node A and D, the tie reinforcement must engage an effective depth of concrete at least equal to: N AD for which: fcu = νf'c ϕf c u b Resistance factor For node anchorage only tie
ϕ ν fcu
NAD/(ϕfcub) Check: 10.6. Check crack control reinforcement Horizontal Reinforcement Space of Horizotal Reinforcement Diameter of Horizoltal Reinforcement Area of Horizontal Reinforcement Ratio of reinforcement area to gross concrete area
sh Dh Ah Ah/(b*sh) Check:
Vertical Reinforcement Space of Vertical Reinforcement Diameter of Vertical Reinforcement Area of Vertical Reinforcement Ratio of reinforcement area to gross concrete area
sv D Av Av/(b*sv) Check:
Beam-End Design
Date: 06/03/2011
CD 1808010 0.0020 46.7 0.0056 28.7 113 300
=0.70 =0.75 =37.50 Mpa =-105 mm OK
=150 mm =16 mm =404 mm2 =0.0034 OK =150 mm =16 mm =404 mm2 =0.0034 OK
Page: 57 of 65
CHECK STRESSES Sec. No
1 2 3 4 5 6 7 8 9 10 11 12 13 12 11 10 9 8 7 6 5 4 3 2 1
xi
0.000 0.006 0.044 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500 0.550 0.600 0.650 0.700 0.750 0.800 0.850 0.900 0.950 0.956 0.994 1.000
xi
STAGE 1 ( At Tranfer) fg-top
fg-bot
fgL-comp
STAGE 2 fgL-tens
fg-top
fg-bot
fgL-comp
fgL-tens
fs-top
For internal girder fs-bot fg-top
fg-bot
fs-top
STAGE 3 For external girder fs-bot fg-top
fg-bot
fsL-comp
fgL-comp
(m) (Mpa) (Mpa) (Mpa) (Mpa) (Mpa) (Mpa) (Mpa) (Mpa) (Mpa) (Mpa) (Mpa) (Mpa) (Mpa) (Mpa) (Mpa) (Mpa) (Mpa) (Mpa) 0.000 ### ### 25.50 -3.78 ### ### 30.00 -3.78 ### ### ### ### ### ### ### ### 13.50 30.00 0.150 ### ### 25.50 -3.78 ### ### 30.00 -3.78 ### ### ### ### ### ### ### ### 13.50 30.00 1.070 ### ### 25.50 -3.78 ### ### 30.00 -3.78 ### ### ### ### ### ### ### ### 13.50 30.00 1.212 ### ### 25.50 -3.78 ### ### 30.00 -3.78 ### ### ### ### ### ### ### ### 13.50 30.00 2.424 ### ### 25.50 -3.78 ### ### 30.00 -3.78 ### ### ### ### ### ### ### ### 13.50 30.00 3.636 ### ### 25.50 -3.78 ### ### 30.00 -3.78 ### ### ### ### ### ### ### ### 13.50 30.00 4.848 ### ### 25.50 -3.78 ### ### 30.00 -3.78 ### ### ### ### ### ### ### ### 13.50 30.00 6.060 ### ### 25.50 -3.78 ### ### 30.00 -3.78 ### ### ### ### ### ### ### ### 13.50 30.00 7.272 ### ### 25.50 -3.78 ### ### 30.00 -3.78 ### ### ### ### ### ### ### ### 13.50 30.00 8.484 ### ### 25.50 -3.78 ### ### 30.00 -3.78 ### ### ### ### ### ### ### ### 13.50 30.00 9.696 ### ### 25.50 -3.78 ### ### 30.00 -3.78 ### ### ### ### ### ### ### ### 13.50 30.00 10.908 ### ### 25.50 -3.78 ### ### 30.00 -3.78 ### ### ### ### ### ### ### ### 13.50 30.00 12.120 ### ### 25.50 -3.78 ### ### 30.00 -3.78 ### ### ### ### ### ### ### ### 13.50 30.00 13.332 ### ### 25.50 -3.78 ### ### 30.00 -3.78 ### ### ### ### ### ### ### ### 13.50 30.00 14.544 ### ### 25.50 -3.78 ### ### 30.00 -3.78 ### ### ### ### ### ### ### ### 13.50 30.00 15.756 ### ### 25.50 -3.78 ### ### 30.00 -3.78 ### ### ### ### ### ### ### ### 13.50 30.00 16.968 ### ### 25.50 -3.78 ### ### 30.00 -3.78 ### ### ### ### ### ### ### ### 13.50 30.00 18.180 ### ### 25.50 -3.78 ### ### 30.00 -3.78 ### ### ### ### ### ### ### ### 13.50 30.00 19.392 ### ### 25.50 -3.78 ### ### 30.00 -3.78 ### ### ### ### ### ### ### ### 13.50 30.00 20.604 ### ### 25.50 -3.78 ### ### 30.00 -3.78 ### ### ### ### ### ### ### ### 13.50 30.00 21.816 ### ### 25.50 -3.78 ### ### 30.00 -3.78 ### ### ### ### ### ### ### ### 13.50 30.00 23.028 ### ### 25.50 -3.78 ### ### 30.00 -3.78 ### ### ### ### ### ### ### ### 13.50 30.00 23.170 ### ### 25.50 -3.78 ### ### 30.00 -3.78 ### ### ### ### ### ### ### ### 13.50 30.00 24.090 ### ### 25.50 -3.78 ### ### 30.00 -3.78 ### ### ### ### ### ### ### ### 13.50 30.00 24.240 ### ### 25.50 -3.78 ### ### 30.00 -3.78 ### ### ### ### ### ### ### ### 13.50 30.00
fgL-tens
Mu
(Mpa) -1.77 -1.77 -1.77 -1.77 -1.77 -1.77 -1.77 -1.77 -1.77 -1.77 -1.77 -1.77 -1.77 -1.77 -1.77 -1.77 -1.77 -1.77 -1.77 -1.77 -1.77 -1.77 -1.77 -1.77 -1.77
KNm 114 780 877 1656 2337 2920 3405 3791 4080 4270 4362 4356 4362 4270 4080 3791 3405 2920 2337 1656 877 780 114 -
For internal girder Mr Qu KNm 5815 5831 5932 5948 6081 6214 6347 6480 6613 6746 6827 6827 6827 6827 6827 6746 6613 6480 6347 6214 6081 5948 5932 5831 5815
KNm 800 792 744 737 673 611 549 488 427 367 307 248 190 248 307 367 427 488 549 611 673 737 744 792 800
Qr KNm 4554 4396 3095 1963 1976 2007 2049 2091 2133 2175 2200 2200 2200 2200 2200 2175 2133 2091 2049 2007 1976 1963 3095 4396 4554
Mu KNm 112 766 862 1628 2298 2873 3352 3736 4024 4217 4314 4316 4314 4217 4024 3736 3352 2873 2298 1628 862 766 112 -
For external girder Mr Qu KNm 5785 5802 5903 5918 6051 6184 6318 6451 6584 6717 6797 6797 6797 6797 6797 6717 6584 6451 6318 6184 6051 5918 5903 5802 5785
KNm 750 743 695 688 626 565 504 443 383 323 264 205 147 205 264 323 383 443 504 565 626 688 695 743 750
Qr KNm 4542 4384 3086 1958 1970 2002 2044 2086 2128 2170 2195 2195 2195 2195 2195 2170 2128 2086 2044 2002 1970 1958 3086 4384 4542
Caculate the θ and β in table A.5.8.3.4.2.1 1000εx
vu/f'c
for Calculate Value of θ
0.5569 0.0425
7
θ
= 29.91
β
= 2.48
8
0.5
0.75
1
0.05
εx x 10000.5569 = v/f'c = 0.0425
1
29
θ
29.91
29.91
= 29.91
β
0.05
33
= 2.48 7
8
0.5
0.75
29
33
29.91 29.91
Table 5.8.3.4.2-1 Values of θ for Sections with Transverse Reinforcement εxx1000
vu/f'c -0.200
-0.100
-0.050
0.000
0.125
0.250
0.500
0.750
1.000
1
2
3
4
5
6
7
8
9
0.0750
1
22.300
20.400
21.000
21.800
24.300
26.600
30.500
33.700
36.400
0.1000
2
18.100
20.400
21.400
22.500
24.900
27.100
30.800
34.000
36.700
0.1250
3
19.900
21.900
22.800
23.700
25.900
27.900
31.400
34.400
37.000
0.1500
4
21.600
23.300
24.200
25.000
26.900
28.800
32.100
34.900
37.300
0.1750
5
23.200
24.700
25.500
26.200
28.000
29.700
32.700
35.200
36.800
0.2000
6
24.700
26.100
26.700
27.400
29.000
30.600
32.800
34.500
36.100
0.2250
7
26.100
27.300
27.900
28.500
30.000
30.800
32.300
34.000
35.700
0.2500
8
27.500
28.600
29.100
29.700
30.600
31.300
32.800
34.300
35.800
Table 5.8.3.4.2-1 Values of β for Sections with Transverse Reinforcement εxx1000
vu/f'c -0.200
-0.100
-0.050
0.000
0.125
0.250
0.500
0.750
1.000
1
2
3
4
5
6
7
8
9
7
8
0.0750
1
6.320
4.750
4.100
3.750
3.240
2.940
2.590
2.380
2.230
0.1000
2
3.790
3.380
3.240
3.140
2.910
2.750
2.500
2.320
2.180
0.1250
3
3.180
2.990
2.940
2.870
2.740
2.620
2.420
2.260
2.130
0.1500
4
2.880
2.790
2.780
2.720
2.600
2.520
2.360
2.210
2.080
0.1750
5
2.730
2.660
2.650
2.600
2.520
2.440
2.280
2.140
1.960
0.2000
6
2.630
2.590
2.520
2.510
2.430
2.370
2.140
1.940
1.790
0.2250
7
2.530
2.450
2.420
2.400
2.340
2.140
1.860
1.730
1.640
0.2500
8
2.390
2.390
2.330
2.330
2.120
1.930
1.700
1.580
1.500
Table 5.8.3.4.2-1 - Values of θ for Sections with Transverse Reinforcement εx x 1000
v/f'c -0.2
-0.15
-0.1
0
0.13
0.25
0.5
0.75
1
1.5
2
1
2
3
4
5
6
7
8
9
10
11
###
1
27.0
27.0
27.0
27.0
27.0
28.5
29.0
33.0
36.0
41.0
43.0
0.05
0.08
2
27.0
27.0
27.0
27.0
27.0
27.5
30.0
33.5
36.0
40.0
42.0
0.08
0.1
3
23.5
23.5
23.5
23.5
24.0
26.5
30.5
34.0
36.0
38.0
39.0
0.1
0.13
4
20.0
21.0
22.0
23.5
26.0
28.0
31.5
34.0
36.0
37.0
38.0
0.13
0.15
5
22.0
22.5
23.5
25.0
27.0
29.0
32.0
34.0
36.0
36.5
37.0
0.15
0.18
6
23.5
24.0
25.0
26.5
28.0
30.0
32.5
34.0
35.0
35.5
36.0
0.18
0.2
7
25.0
25.5
26.5
27.5
29.0
31.0
33.0
34.0
34.5
35.0
36.0
0.2
0.23
8
26.5
27.0
27.5
29.0
30.5
32.0
33.0
34.0
34.5
36.5
39.0
0.23
0.25
9
28.0
28.5
29.0
30.0
31.0
32.0
33.0
34.0
35.5
38.5
41.5
0.25
-0.2
-0.15
-0.1
0
0.13
0.25
0.5
0.75
1
1.5
2
x
0.5569
7
8x
0.56
y
0.0425
0.5
0.75 y
0.04
1
0.05
2.51
2.37
2.48 2.48
Table 5.8.3.4.2-1 Values of θ for Sections with Less than Minimum Transverse Reinforcement
εxx1000
sxe (mm)
-0.200
-0.100
-0.050
0.000
0.125
0.250
0.500
0.750
1.000
1.500
2.000
1
2
3
4
5
6
7
8
9
10
11
130
25.400
25.500
25.900
26.400
27.700
28.900
30.900
32.400
33.700
35.600
37.200
250
27.600
27.600
28.300
29.300
31.600
33.500
36.300
38.400
40.100
42.700
44.700
380
29.500
29.500
29.700
31.100
34.100
36.500
39.900
42.400
44.400
47.400
49.700
500
31.200
31.200
31.200
32.300
36.000
38.800
42.700
45.500
47.600
50.900
53.400
750
34.100
34.100
34.100
34.200
38.900
42.300
46.900
50.100
52.600
56.300
59.000
1000
36.600
36.600
36.600
36.600
41.200
45.000
50.200
53.700
56.300
60.200
63.000
1500
40.800
40.800
40.800
40.800
44.500
49.200
55.100
58.900
61.800
65.800
68.600
2000
44.300
44.300
44.300
44.330
47.400
52.300
58.700
62.800
65.700
69.700
72.400
Table 5.8.3.4.2-1 Values of θ and β for Sections with Less than Minimum Transverse Reinforcement εxx1000
sxe (mm)
-0.200
-0.100
-0.050
0.000
0.125
0.250
0.500
0.750
1.000
1.500
2.000
1
2
3
4
5
6
7
8
9
10
11
130
6.360
6.060
5.560
5.150
4.410
3.910
3.260
2.860
2.580
2.210
1.960
250
5.780
5.780
5.380
4.890
4.050
3.520
2.880
2.500
2.230
1.880
1.650
380
5.340
5.340
5.270
4.730
3.820
3.280
2.640
2.260
2.010
1.680
1.460
500
4.990
4.990
4.990
4.610
3.650
3.090
2.460
2.090
1.850
1.520
1.310
750
4.460
4.460
4.460
4.430
3.390
2.820
2.190
1.840
1.600
1.300
1.100
1000
4.060
4.060
4.060
4.060
3.200
2.620
2.000
1.660
1.430
1.140
0.950
1500
3.500
3.500
3.500
3.500
2.920
2.320
1.720
1.400
1.180
0.920
0.750
2000
3.100
3.100
3.100
3.100
2.710
2.110
1.520
1.210
1.010
0.760
0.620
Table 5.8.3.4.2-1 - Values of β for Sections with Transverse Reinforcement
εx x 1000
v/f'c -0.2
-0.15
-0.1
0
0.13
0.25
0.5
0.75
1
1.5
2
###
1
6.8
6.2
5.6
4.9
4.0
3.5
2.5
2.4
2.2
2.0
1.7
0.05
0.08
2
6.8
6.2
5.6
4.9
3.7
3.0
2.5
2.3
2.2
1.9
1.7
0.08
0.1
3
6.5
5.9
5.3
3.3
2.6
2.5
2.4
2.3
2.1
1.7
1.5
0.1
0.13
4
2.7
2.7
2.7
2.6
2.6
2.5
2.4
2.2
2.0
1.6
1.4
0.13
0.15
5
2.7
2.6
2.6
2.6
2.5
2.5
2.3
2.1
1.9
1.5
1.2
0.15
0.18
6
2.6
2.6
2.5
2.5
2.4
2.4
2.2
2.0
1.7
1.2
1.0
0.18
0.2
7
2.6
2.5
2.5
2.5
2.4
2.3
2.1
1.8
1.6
1.2
1.0
0.2
0.23
8
2.5
2.4
2.4
2.4
2.3
2.3
1.9
1.7
1.4
1.2
1.1
0.23
0.25
9
2.4
2.3
2.4
2.3
2.3
2.0
1.6
1.5
1.4
1.3
1.3
0.25
MINH LUONG - THU BAY PROJECT (GMS SCCP)
7. LOSS PRESTRESSING 7.1. Loss due to Elastic Shortening E The loss due to elastic shortening in pre-tensioned members shall be taken as: Δf pES= p f cgp E ci Where: fcgp : sum of concrete stresses at the center of gravity of prestresing tendons due to prestressing force at transfer and the self weight of the member at section of maximum moment
xi/Ls 0.000 0.006 0.044 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500
Section xi (m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120
LOSS DUE TO ELASTIC SHORTENING fcgp1 fcgp2 fcgp3 fcgp ∆fpES (Mpa) (Mpa) (Mpa) (Mpa) (Mpa) 8.56 5.48 14.04 78.95 8.56 5.59 -0.08 14.07 79.11 11.72 6.74 -0.64 17.82 100.21 11.72 5.77 -0.67 16.82 94.58 11.72 6.74 -1.36 17.09 96.11 11.72 7.77 -2.07 17.43 97.97 11.72 8.88 -2.78 17.83 100.24 11.72 10.05 -3.45 18.33 103.03 11.72 11.29 -4.09 18.93 106.41 11.72 12.59 -4.67 19.65 110.47 11.72 13.41 -5.07 20.06 112.78 11.72 13.41 -5.23 19.90 111.89 11.72 13.41 -5.28 19.85 111.59
fcgp1
: due to Axial Compression of Prestressing Force
fcgp2
: due to of Prestressing Force
fcgp3
: due to Girder Self-weight (Stage 1)
7.2. Loss due to Shrinkage For pretensioned members, Loss of prestress due to shrinkage may be taken as:
Δf pSR=117−1.03H
=39.750 Mpa
7.3. Loss due to Creep Δf pCR=12. 0f cgp−7. 0Δfcdp≥0 Prestress loss due to creep may be taken as: Where: fcgp : Concrete stress at center of gravity of prestressing steel at tranfer ∆fcdp
: Change in concrete stress at center of gravity of prestressing steel due to permanent loads, with the exception of the load acting at the time the prestressing force is applied.
xi/Ls 0.000 0.006 0.044 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500
Loss
Section xi (m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120
fcgp (Mpa) 14.04 14.07 17.82 16.82 17.09 17.43 17.83 18.33 18.93 19.65 20.06 19.90 19.85
LOSS DUE TO CREEP MDL2 MDL3 ∆fcdp (KNm) (KNm) (Mpa) 15.67 3.56 0.09 107.51 24.40 0.68 121.03 27.47 0.71 229.31 52.06 1.45 324.86 73.75 2.19 407.67 92.54 2.92 477.74 108.45 3.62 535.06 121.46 4.28 579.65 131.59 4.87 611.50 138.82 5.28 630.61 143.15 5.45 636.98 144.60 5.50
MDL2
: Moment due to Stage 2 Dead Load
MDL3
: Moment due to Stage 3 Dead Load Date: 06/03/2011
∆fpCR (Mpa) 168.52 168.26 209.16 196.86 194.97 193.74 193.50 194.55 197.19 201.74 203.76 200.70 199.68
Page: 64 of 65
7.1. Loss due to Elastic Shortening The loss due to elastic shortening in pre-tensioned members shall be taken as: 7.4. Loss due to Relaxation 7.4.1. At Transfer For low-relaxation strand:
Δf pR1 = Where: t
[
]
log24t f pj 0.55 f 40. 0 f py
Δf pES=
Ep E ci
f
cgp
pj
: Time estimated in days from stressing to tranfer
t ∆fpR1
=5 days =20.54 Mpa
7.4.2. After Transfer For pretensioning with stress-relieved strands:
Δf ¿pR2=138−0. 4Δ f pES−0. 2 Δf pSRΔf pC R For low relation prestress steel, loss due to relaxation, ∆fpR2, is taken 30% of ∆f*pR2
xi/Ls 0.000 0.006 0.044 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500
Section xi (m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120
LOSS DUE TO RELAXATION AFTER TRANSFER ∆fpES ∆fpSR ∆fpCR ∆f*pR2 ∆fpR2 (Mpa) (Mpa) (Mpa) (Mpa) (Mpa) 78.95 39.75 168.52 64.76 19.43 79.11 39.75 168.26 64.75 19.43 100.21 39.75 209.16 48.14 14.44 94.58 39.75 196.86 52.85 15.85 96.11 39.75 194.97 52.61 15.78 97.97 39.75 193.74 52.11 15.63 100.24 39.75 193.50 51.25 15.38 103.03 39.75 194.55 49.93 14.98 106.41 39.75 197.19 48.05 14.41 110.47 39.75 201.74 45.51 13.65 112.78 39.75 203.76 44.19 13.26 111.89 39.75 200.70 45.16 13.55 111.59 39.75 199.68 45.48 13.64
7.5. Total loss of Prestress In posstension members, total loss of prestress taken as: Where:
∆fpT
:
total loss ( MPa)
∆fpES
:
loss due to elastic shortening (MPa)
∆fpSR
:
loss due to shrinkage (MPa)
∆fpCR
:
loss due to creep of concrete (MPa)
∆fpR2
:
loss due to relaxation of steel after transfer (MPa)
xi/Ls 0.000 0.006 0.044 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500
Loss
∆fpT = ∆fpES + ∆fpSR + ∆fpCR + ∆fpR2
Section xi (m) 0.000 0.150 1.070 1.212 2.424 3.636 4.848 6.060 7.272 8.484 9.696 10.908 12.120
∆fpES (Mpa) 78.95 79.11 100.21 94.58 96.11 97.97 100.24 103.03 106.41 110.47 112.78 111.89 111.59
∆fpSR (Mpa) 39.75 39.75 39.75 39.75 39.75 39.75 39.75 39.75 39.75 39.75 39.75 39.75 39.75
LOSS OF PRESTRESS ∆fpCR ∆fpR1 ∆fpR2 (Mpa) (Mpa) (Mpa) 168.52 20.54 19.43 168.26 20.54 19.43 209.16 20.54 14.44 196.86 20.54 15.85 194.97 20.54 15.78 193.74 20.54 15.63 193.50 20.54 15.38 194.55 20.54 14.98 197.19 20.54 14.41 201.74 20.54 13.65 203.76 20.54 13.26 200.70 20.54 13.55 199.68 20.54 13.64
Date: 06/03/2011
∆fpi (Mpa) 99.50 99.66 120.75 115.12 116.65 118.51 120.79 123.57 126.96 131.02 133.32 132.43 132.13
∆fpT (Mpa) 306.65 306.55 363.55 347.04 346.61 347.10 348.87 352.30 357.77 365.62 369.54 365.88 364.66
Page: 65 of 65
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