BANG TINH DAM T CẦU ĐƯỜNG TIẾNG ANH

05. Calculation Super T Girder L=38.2m_Skew 20.xls【I.General】
SHEET NO. : 1 / 1

1. GENERAL
1.1. Design standard
Specification for Bridge Design: 22TCN-272-05
1.2. Material strength and stress limits
1.2.1 Prestressing Steel:
Type of low relaxation strand complies with : ASTM A416, Grade 270
Diameter of tendon

=

15.2 mm

Area of tendon

=

140 mm2

Tensile Strength fpu

=

1860 MPa

Yield Strength fpy

=

1674 MPa

Modulus of elasticity of strand Ep

=

197000 Modulus Ratio np = Ep/Ec

=

6.00

1395 MPa <=> Jacking Force

=

195.30 kN

Stress in the prestressing steel at jacking =
1.2.2 Reinforcing Steel:
Reinf . Standart ASTM or TCVN 1651-2008
Yield strength fs

=

400 MPa

Modulus of elasticity Es

=

200000 MPa

1.2.3 Concrete:
1.2.3.1 Main Girder:
Specified compressive strength at 28 days f'c

=

50 MPa

Compressive strength at time of initial prestress f'ci

=

42.50 MPa

Modulus of elasticity Ec

=

38007 MPa

(5.4.2.4-1)

Modulus of elastic of concrete at release time Eci

=

35041 MPa

(5.4.2.4-1)

Tensile strength of concrete at 28 days fr

=

4.45 MPa

Specified compressive strength at 28 days f'c

=

35 MPa

Modulus of elasticity Ed

=

1.2.3.2 Deck Slab:

1.3. Design loads and load combination
1.3.1 Dead Loads:
+ Unit weight of Concrete

= 2500 Kg/m3

+ Unit weight of reinforcement Concrete

= 7850 Kg/m3

+ Unit weight of asphant concrete

= 2300 Kg/m3

1.3.2 Live Loads:
+ Live Loads HL93

Checked by LEE, Jong Dae
Approved by CHO, Wan Hyoung

31799 Mpa => nd = Ed/Ec

= 0.84


05. Calculation Super T Girder L=38.2m_Skew 20.xls【II.Section】
SHEET NO. : 1 / 4
2. GEOMETRIC PROPERTIES

ELEVATION
A

B

SECTION A-A
C

B
b1

b2

h8

CL OF BEARING

h2

h5

9

3

1

h1

hd

hd

b3

10

11

b9

b9
7

5

h1-hd

5

b1
L2

bd

L3

A

B

b4

C

SECTION B-B

SECTION C-C

B

B
b3

1
3

h9

9

11

10

b9

b11

5
4

h3

h1

H

5

b3

b12

h5

10

b9

h1

3

11

b9

b2
2

h2

h5

h2

9

1

H

b1
h8

b2

h8

b1

b3

b4

b7

7

b7
b8 b8

5

h6

L1

h4

h7

6

b1

bd
b4

b3

b1

b4

b10
8

b4

7

b6
b5

b4

b3

b5

2.1. Dimension profiles
Distance from bearing to end of girder
Distance from bearing to girder notch
Length of full section (not inlcude notch)
Items
Distance to bearing
Section in/out of length of link slab
Height of girder
Height of composite section
Height of other components

Slab thickness
Thickness of precast concrete plate
Effective width of concrete slab
Width of other components

Checked by LEE, Jong Dae
Approved by CHO, Wan Hyoung

Notation

h1; hd
H
h2
h3
h4
h5
h6

h7
h8
h9
B
b1
b2
b3
b4
b5
b6
b7

L1
L2
L3

= 550 mm
= 450 mm
= 1200 mm

Sec. 1
Sec. 2 Sec. 3 Sec. 4 Sec. 5 Sec. 6
18550
14750
10950
6450
3850
1650
no
no

no
no
no
yes
1750.0
1750
1750
1750
1750
1750
1945.0
1945
1945
1945
1945
1750
75.0
75
75
75
75
75
1425.0
1425
1425
1425
1425
250.0
250
250

250
250
75.0
75
75
75
75
75
350.0
350
350
350
350
50.0
50
50
50
50
195.0
195
195
195
195
195
35.0
35
35
35
35
2350.0

2350
2350
2350
2350
2350
650.0
650
650
650
650
650
1050.0
1050
1050
1050
1050
1050
650.0
650
650
650
650
650
175.0
175
175
175
175
175.0
135.0

135
135
135
135
430.0
430
430
430
430
82.5
82.5
82.5
82.5
82.5

Sec. 7
450
yes
800
800
75

75

195
2350
650
1050
650
65

05. Calculation Super T Girder L=38.2m_Skew 20.xls【II.Section】
SHEET NO. : 2 / 4
b8
b9
b10
b11
b12
bd

Width of girder bottom

215.0
100.0
25.7
7.5
810.0
700.0

215
100
25.7
7.5
810
700

215
100
25.7

7.5
810
700

215
100
25.7
7.5
810
700

215
100
25.7
7.5
810
700

100

100

700

920

Sec. 1
Sec. 2
Sec. 3
Sec. 4

Sec. 5
Sec. 6
650
650
650
650
650
650
75
75
75
75
75
75
48750
48750
48750
48750
48750
48750
7.5
7.5
7.5
7.5
7.5
75
75
75
75
75

562.5
562.5
562.5
562.5
562.5
100
100
100
100
100
100
75.0
75
75
75
75
75
7500
7500
7500
7500
7500
7500
135
135
135
135
135
1750
1750

1750
1750
1750
472500 472500 472500 472500 472500
82.5
82.5
82.5
82.5
82.5
175.0
350
350
350
350
350
1675
28875
28875
28875
28875
28875 293125
215
215
215
215
215
50
50
50
50

50
10750
10750
10750
10750
10750
430
430
430
430
430
700
250
250
250
250
250
1675
107500 107500 107500 107500 107500 1172500
25.7
25.7
25.7
25.7
25.7
250
250
250
250
250
6425

6425
6425
6425
6425
650
650
650
650
650
650
75
75
75
75
75
75
48750
48750
48750
48750
48750
48750
1050
75
78750

Sec. 7
650
75
48750

2.2. Section properties in each stage
2.2.1 Stage I&II: Non-composite section
2.2.1.1 Section area:
Element Shape QuantityNotation
K1
chữ nhật
1
b
rectangle
h
A1
K2
tam giác
2
b
triangle
h
A2
K3
tam giác
2
b
triangle
h
A3
K4
chữ nhật
2
b

rectangle
h
A4
K5
tam giác
2
b
triangle
h
A5
K6
tam giác
2
b
triangle
h
A6
K7
chữ nhật
1
b
rectangle
h
A7
K8
tam giác
2
b
triangle
h

A8
K10
chữ nhật
1
b
rectangle
h
A10
K11
chữ nhật
1
b
rectangle
h
A11
K12

A12

Tendon

Unit
(mm)
(mm)
(mm2)
(mm)
(mm)
(mm2)
(mm)
(mm)

(mm2)
(mm)
(mm)
(mm2)
(mm)
(mm)
(mm2)
(mm)
(mm)
(mm2)
(mm)
(mm)
(mm2)
(mm)
(mm)
(mm2)
(mm)
(mm)
(mm2)
(mm)
(mm)
(mm2)
(mm2)

A I&II

Total section area

30800

30800

30800

28000

762413

762413

762413

759613

23100

18900

100
75
7500

65
725
47125

920
725
667000

650
75
48750
1050
75
78750
-

754713 1668275

897875

Sec. 1
Sec. 2
Sec. 3
Sec. 4
Sec. 5
Sec. 6
1713
1713
1713
1713
1713
1713

Sec. 7
763

2.2.1.2 Static moment of area
Items

Distance from centroid of

Notation
z1

Unit
(mm)

component to bottom fiber

z2

(mm)

1700

1700

1700

1700

1700

of girder

z3

(mm)

1650

1650

1650

1650

1650

z4

(mm)

875

875

875

875

875

z5

(mm)

367

367

367

367

367

z6

(mm)

267

267

267

267

267

Checked by LEE, Jong Dae
Approved by CHO, Wan Hyoung

1650

700

1117

483


05. Calculation Super T Girder L=38.2m_Skew 20.xls【II.Section】
SHEET NO. : 3 / 4
z7

(mm)

z8

(mm)

z10

(mm)

z11

(mm)

Tendon
Static moment of inertia of
component about bottom

z12

(mm)

s1

(mm3)

fiber of girder

s2
s3
s4
s5
s6

125

125

838

363

1713

763

1713

763

166.6667 166.667 166.667 166.667 166.667
1713

191

1713
191

1713
191

1713
195

1713
236

236

-

83484375 8.3E+07 8.3E+07 8.3E+07 8.3E+07 8.3E+07 3.7E+07
956250

956250

956250

956250

956250

-

-

12375000 1.2E+07 1.2E+07 1.2E+07 1.2E+07 1.2E+07 5250000
4.13E+08 4.1E+08 4.1E+08 4.1E+08 4.1E+08

3

10587500 1.1E+07 1.1E+07 1.1E+07 1.1E+07 3.3E+08 2.3E+07

(mm )
(mm )
3

(mm )
3

(mm3)

SI&II

125

3

(mm )

(mm )

s12

125

3

s8
s11
Tendon

(mm )

s7
s10

Total for stage I&II

3

125

3

(mm )

2866667 2866667 2866667 2866667 2866667
1070833 1070833 1070833 1070833 1070833

3

(mm )

-

-

-

83484375 8.3E+07 8.3E+07 8.3E+07 8.3E+07 8.3E+07 3.7E+07
1798125

(mm )
(mm )

-

-

13437500 1.3E+07 1.3E+07 1.3E+07 1.3E+07 9.8E+08 2.4E+08

3

3

-

5897500 5897500 5897500 5456500 5456500 4464409

800625
-

6.28E+08 6.3E+08 6.3E+08 6.3E+08 6.3E+08 1.5E+09 3.4E+08

2.2.1.3. Centroid
Distance from neutral axis
to top fiber of girder
Distance from neutral axis
to bottom fiber of girder

yt1 (mm)

-927

-927

-927

-924

-919

-854

-416

yd1 (mm)

823

823

823

826

831

896

384

Distance from center

e1

(mm)

-889

-889

-889

-887

-882

-816

-378

of component to neutral axis

e2

(mm)

-877

-877

-877

-874

-869

896

384

e3

(mm)

-827

-827

-827

-824

-819

-754

-316

e4

(mm)

-52

-52

-52

-49

-44

896

384

e5

(mm)

457

457

457

459

464

-221

-99

e6

(mm)

557

557

557

559

564

896

384

e7

(mm)

698

698

698

701

706

59

22

e8

(mm)

657

657

657

659

664

896

384

e10

(mm)

-889

-889

-889

-887

-882

-816

-378

e11

(mm)

-816

-378

e12

(mm)

660

384

22851563 2.3E+07 2.3E+07 2.3E+07 2.3E+07 2.3E+07

2E+07

Tendon

2.2.1.4. Moment of inertia
a. About centroid of components
I1
(mm4)
I2
I3
I4
I5
I6

4

(mm )

175781

631

175781

595

175781

1.97E+08

(mm )

-

2E+08

2E+08

2E+08

-

2E+08 4.6E+10

4

1493056 1493056 1493056 1493056 1493056

4

5.6E+08 5.6E+08 5.6E+08 5.6E+08 5.6E+08 2.7E+11

(mm )

-

2343750 2343750 2343750 2343750 2343750 2343750 2343750
1.21E+11 1.2E+11 1.2E+11 1.2E+11 1.2E+11

(mm4)

Checked by LEE, Jong Dae
Approved by CHO, Wan Hyoung

175781

632

4

(mm )

(mm )

I12

175781.3

632

4

I8
I11
15.2 mm
Sum (a)

(mm )

I7
I10
D=

4

632

22309028 2.2E+07 2.2E+07 2.2E+07 2.2E+07

-

1E+09
3E+10
-

4

22851563 2.3E+07 2.3E+07 2.3E+07 2.3E+07 2.3E+07

2E+07

4

4E+07

4E+07

(mm )
(mm )
4

(mm )

691748.4 691748 691748 628862 518811 518811
0E+00
1.21E+11 1.2E+11 1.2E+11 1.2E+11 1.2E+11 3.2E+11 3.1E+10


05. Calculation Super T Girder L=38.2m_Skew 20.xls【II.Section】
SHEET NO. : 4 / 4
b. Moment of inertia of components about centroid of section
I1
(mm4) 3.86E+10 3.9E+10 3.9E+10 3.8E+10 3.8E+10 3.2E+10 7E+09
I2
(mm4) 4.32E+08 4.3E+08 4.3E+08 4.3E+08 4.2E+08
4

I3
(mm ) 5.13E+09 5.1E+09 5.1E+09 5.1E+09 5E+09 4.3E+09 7.5E+08
I4
(mm4) 1.27E+09 1.3E+09 1.3E+09 1.2E+09 9.2E+08
I5
I6

6.02E+09

6E+09

6E+09 6.1E+09 6.2E+09 1.4E+10 4.6E+08

4

3.33E+09 3.3E+09 3.3E+09 3.4E+09 3.4E+09

4

(mm )

I7

(mm )

5.24E+10 5.2E+10 5.2E+10 5.3E+10 5.4E+10

I8

(mm4)

2.77E+09 2.8E+09 2.8E+09 2.8E+09 2.8E+09

I10
I11
Sum (b)
Moment of inertia stage I&II

(mm4)

4

(mm )

-

-

4E+09 3.1E+08
-

3.86E+10 3.9E+10 3.9E+10 3.8E+10 3.8E+10 3.2E+10

7E+09

4

5.2E+10 1.1E+10

4

1.23E+10 1.2E+10 1.2E+10 1.1E+10 8.2E+09 8.2E+09
1.61E+11 1.6E+11 1.6E+11 1.6E+11 1.6E+11 1.5E+11 2.7E+10
2.82E+11 2.8E+11 2.8E+11 2.8E+11 2.8E+11 4.7E+11 5.7E+10

(mm )

I12

(mm )

II&II

(mm4)

2.2.2. Stage III: Composite section
K9

chữ nhật
rectangle

1

b
h
A9

(mm2)

ΣA III

(mm2)

Distance from K9 to bottom
fiber of girder

z9

(mm)

Static moment of K9 about
bottom fiber of girder

s9

Total static moment of area

SIII

Total section area

(mm)
(mm)

2350
195
458250

2350
195

458250

2350
195
458250

2350
195
458250

2350
195
458250

-

1220663 1220663 1220663 1217863 1212963 1668275
1847.5

1847.5

1847.5

1847.5

897875

1847.5

1750

800

(mm3)

8.47E+08 8.5E+08 8.5E+08 8.5E+08 8.5E+08

-

-

(mm3)

1.47E+09 1.5E+09 1.5E+09 1.5E+09 1.5E+09 1.5E+09 3.4E+08

Distance from neutral axis
to top fiber of girder

yt2 (mm)

-542

-542

-542

-540

-535

-854

-416

Distance from neutral axis
to bottom fiber of girder

yd2 (mm)

1208

1208

1208

1210

1215

896

384

Distance from neutral axis
to top fiber of slab

yb2 (mm)

-737

-737

-737

-735

-730

-854

-416

Distance from neutral axis
to center of tendons

ec2 (mm)

1016

1016

1016

1015

979

660

384

Moment of inertia stage I&II
Distance from neutral axis
of stage I to stage II
Moment of inertia about
centroid of section at stage
II
Moment of inertia of K9
Distance from center of K9
to neutral axis of composite
section
Moment of inertia about
centroid of composite
section
Moment of inertia of
composite section

II&II

(mm4)
e (mm)
(mm4)

I9

4

(mm )
(mm)

IIII

Checked by LEE, Jong Dae
Approved by CHO, Wan Hyoung

2.82E+11 2.8E+11 2.8E+11 2.8E+11 2.8E+11 4.7E+11 5.7E+10
-385

-385

-385

-385

-384

-

-

-

-

1.13E+11 1.1E+11 1.1E+11 1.1E+11 1.1E+11
1.45E+09 1.5E+09 1.5E+09 1.5E+09 1.5E+09
-640

-640

-640

-637

-632

-756

-318

(mm4)

1.88E+11 1.9E+11 1.9E+11 1.9E+11 1.8E+11

-

-

(mm4)

5.84E+11 5.8E+11 5.8E+11 5.8E+11 5.7E+11 4.7E+11 5.7E+10


05. Calculation Super T Girder L=38.2m_Skew 20.xls【III.Tendon】
SHEET NO. : 1 / 4
3. TENDON ARRANGEMENT
3.1. Input date
Using straight tendons with diameter

2

140.0 mm

15.2 mm <=> A_ten

To reduce tensile stress at bearing locations, unbonded tendons are created by using PE tube
Effective length of tendons
Type of tendons

Effective length (m)

Remark

1

36.20

Full length tendons

2

34.20

Tendons with 1.0m unbonded

3

30.20

Tendons with 3.0m unbonded

4

26.20

Tendons with 5.0m unbonded

5

22.20

Tendons with 7.0m unbonded

Tendon

h(mm)

Number of strands

bottom

1

2

3

4

Tendon

h(mm) Number of strands

5

top

1

Row E

Row A

75

7

2

2

Row B

130

8

2

1

2

Row C

185

6

2

2

2

Row D

240

4

1690

2

2

2

h(mm): distance from center of tendons to bottom fiber of girder

510
60

ROW E
HÀNG E

ROW D - HÀNG D
ROW C - HÀNG C
ROW B - HÀNG B
ROW A - HÀNG A

55 55

75 55

250

1750

510
60

SECTION

1

3
2

50

5
4

7
6

9 11 13
8 10 12

12x50=600
700

50

TABLE OF NUMBER, LOCATION AND DEBONDING LENGTHS OF STRANDS
STRAND (Ndeg)

1

ROW E

1000
+
+
+

ROW D
ROW C
ROW B

ROW A

2

3

+
3000
+
+

5000
+
3000
+

4

5000
+
3000

5

+
7000
+

6

7000
+
5000

7

5000
+

8

7000
+
5000

TOTAL NUMBER OF STRANDS : 44 (A - E)

Checked by LEE, Jong Dae
Approved by CHO, Wan Hyoung

9

+
7000
+

10

11

12

5000
+
3000

5000
+
3000
+

+
3000
+
+

13
1000
+
+
+


05. Calculation Super T Girder L=38.2m_Skew 20.xls【III.Tendon】
SHEET NO. : 2 / 4
3.2. Sum of tendons at sections
Section

Type of tendons

Aps (mm2)

Area of tendons

1

2

3

4

5

1

2

3

4

5

1

√

√

√

√

√

3500

280

840

980

560

2

√

√

√

√

√

3500

280

840

980

560

3

√

√

√

√

√

3500

280

840

980

560

4

√

√

√

√

X

3500

280

840

980

0

5

√

√

√

X

X

3500

280

840

0

0

6

√

√

X

X

X

3500

280

0

0

0

7

X

X

X

X

X

0

0

0

0

0

Section

Distance from center of tendons to bottom fiber of girder

Distance from center of ΣA
all tendons
ps(mm

2

)

1

2

3

4

5

to bottom fiber of girder

n

1

145

1690

130

161

158

191 mm

6160

44

2

145

1690

130

161

158

191 mm

6160

44

3

145

1690

130

161

158

191 mm

6160

44

4

145

1690

130

161

0

195 mm

5600

40

5

145

1690

130

0

0

236 mm

4620

33

6

145

1690

0

0

0

260 mm

3780

27

7

0

0

0

0

0

0 mm

0

0

3.3. Force transfering length & developing length of tendons
= 60dp =

Force transfering length (mm)

912 (5.11.4.1-272-05)

Developing length of normal tendon (mm)

ld = [0.15fps-0.097fpe]dp =

2535 (5.11.4.2-272-05)

Developing length of covered tendon (mm)

ld = 2[0.15fps-0.097fpe]dp =

5071 (5.11.4.3-272-05)

Group 1:

25 tendons with bond length taken from girder edge

0 mm

Group 2:

2 tendons with bond length taken from girder edge

1000 mm

Group 3:

6 tendons with bond length taken from girder edge

3000 mm

Group 4:

7 tendons with bond length taken from girder edge

5000 mm

Group 5:

4 tendons with bond length taken from girder edge

7000 mm

Prestress of tendons at tension stage - prestress loss due to shrinkage =

1304 MPa

Prestress in tendons after all loss =

1104 MPa

Prestress of tendons for bending resistant =

1826 MPa

Checked by LEE, Jong Dae
Approved by CHO, Wan Hyoung


05. Calculation Super T Girder L=38.2m_Skew 20.xls【III.Tendon】
SHEET NO. : 3 / 4
3.4. Internal forces due to prestressed tendons at sections
PRESTRESSING FORCE FOR TENDONS
Group number

Distance from section to girder notch (mm)
14300

10500

Compression forces at tension stage
Group 1:
4563.31
Group 2:
365.06
Group 3:
1095.19
Group 4:
1277.73
Group 5:
730.13

18100

4563.31
365.06
1095.19
1277.73
730.13

4563.31 4563.31 4563.31 4563.31
365.06
365.06
365.06
80.06
1095.19 1095.19
480.35
0.00
1277.73 1277.73
0.00
0.00
730.13
0.00
0.00
0.00

0.00
0.00
0.00
0.00
0.00

Summary (kN)

8031.42

8031.42 7301.29 5408.72 4643.37

0.00

3865.63 3865.63 3865.63 3865.63

0.00

8031.42

6000

3400

1200

0

Compression forces after all prestress loss
Group 1:

3865.63

3865.63

Group 2:

309.25

309.25

309.25

309.25

309.25

67.82

0.00

Group 3:

927.75

927.75

927.75

927.75

406.91

0.00

0.00

Group 4:

1082.38

1082.38

1082.38 1082.38

0.00

0.00

0.00

Group 5:

618.50

618.50

0.00

0.00

0.00

6803.51

6803.51

6803.51 6185.01 4581.79 3933.45

0.00

6391.66 6391.66 6344.55 4152.58

0.00

Summary (kN)

618.50

0.00

Compression forces to determine resistant
Group 1:

6391.66

6391.66

Group 2:

511.33

511.33

472.17

368.55

67.82

0.00

Group 3:

1534.00

1534.00

1534.00 1177.40

406.91

0.00

0.00

Group 4:

1789.66

1789.66

1722.35 1094.65

0.00

0.00

0.00

Group 5:

1022.67

1022.67

0.00

0.00

0.00

11249.32 11249.32 10984.12 9135.88 7120.01 4220.40

0.00

Summary (kN)

511.33

824.78

0.00

Tendon Group 1 to bottom
fiber of girder (mm)

145.40

145.40

Tendon Group 2 to bottom
fiber of girder (mm)

1690.00

1690.00

Tendon Group 3 to bottom
fiber of girder (mm)

130.00

130.00

130.00

130.00

130.00

0.00

0.00

Tendon Group 4 to bottom
fiber of girder (mm)

161.43

161.43

161.43

161.43

0.00

0.00

0.00

Tendon Group 5 to bottom
fiber of girder (mm)

157.50

157.50

157.50

0.00

0.00

0.00

0.00

677.77

680.23

685.59

750.67

0.00

-866.83

-864.37

-859.01

-793.93

0.00

693.17

695.63

700.99

896.07

0.00

661.74

664.20

830.99

896.07

0.00

665.67

825.63

830.99

896.07

0.00

-4867.15 -4399.04 -3151.67 -3362.00

0.00

-4123.02 -3726.48 -2669.82 -2847.99

0.00

Prestressing moment at tension stage (kN-m)

Tendon Group 1 to neutral
axis (mm)
677.77
677.77
Tendon Group 2 to neutral
axis (mm)
-866.83
-866.83
Tendon Group 3 to neutral
axis (mm)
693.17
693.17
Tendon Group 4 to neutral
axis (mm)
661.74
661.74
Tendon Group 5 to neutral
axis(mm)
665.67
665.67
Sum of moment (kN-m)

-4867.15 -4867.15

145.40

145.40

145.40

145.40

0.00

1690.00 1690.00 1690.00 1690.00

0.00

Prestressing moment after all stress losses (kN-m)
Sum of moment (kN-m)

-4123.02 -4123.02

Checked by LEE, Jong Dae
Approved by CHO, Wan Hyoung


Lực nén - Compression force (kN)

05. Calculation Super T Girder L=38.2m_Skew 20.xls【III.Tendon】
SHEET NO. : 4 / 4
Lực nén trước và sau các mất mát ứng suất
Compression forces before and after all prestress loss
9000.00
8000.00
7000.00
6000.00
5000.00
4000.00
3000.00

2000.00
1000.00
0.00
0

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000 13000 14000 15000 16000 17000 18000 19000

Khoảng cách đến đầu dầm (mm)
Distance from girder edge (mm)
P cang cap - P at tension stage
P sau mat mat us - P after all prestress loss

Checked by LEE, Jong Dae
Approved by CHO, Wan Hyoung


05. Calculation Super T Girder L=38.2m_Skew 20.xls【IV.Distribution】
SHEET NO. : 1 / 2
4. LIVE LOAD DISTRIBUTION FACTOR
4.1. Superstructure profiles
Span length

L=

38200 mm

Distance from bearing to girder edge

550 mm
Le =

Effective span length

37100 mm

Width of all lanes

11000 mm

Width of pedestrian path (1 side)

0 mm

Width of parapet (1 side)

500 mm

Total width of deck

W=
ts =

Concrete slab thickness

11700 mm
195 mm

Number of loaded lanes

3 lanes (Section 3.6.1.1.1 - 22TCN-272-05)

Multiple presence factor (lane factor)

m=

0.85 Section 3.6.1.1.2 - 22TCN-272-05)

Width of 1 lane

3500 mm

Number of girders

Nb =

Distance between girders

2350 mm

Width of cantilever slab

S=
wo =

Width of loaded lane within cantilever slab

de =

800 mm

Depth of girder

d=

1750 mm

Width between top flanges of girder

b=

1050 mm

5 girders
1150 mm

Design for exterior/interior girder ( E/I )
4.2. Effective width of girder flange
Interior girder
1/4 Le
=
12ts + b/2
S
=> bei

E
According to Section 4.6.2.6 in 22TCN-272-05)

9275 mm

Exterior girder

bei/2 + 1/8 Le =

=

2865 mm

bei/2 + 6ts + b/4 =

=
=

2350 mm

bei/2 + wo

=

2325 mm

2350 mm

=> bee

=

2325 mm

5813 mm
2607.5 mm

According to Section 4.6.2.2.2 - 22TCN-272-05)

4.3. Live load distribution factor

Applied section according to Table 4.6.2.2.1.1 is typical section c
Moment distribution for interior girders
Scope of application
1800< S <3500=>
OK

6000
Nb> 3=> OK

For >2 loaded lanes:
gm,I = (S/1900)0.6 (Sd/L2)0.125

=

0.545

gm,I =

=

0.545

For >2 loaded lanes
gm,E = (0.97 + de/8700)gm,I

=

0.579 Table 4.6.2.2.2c-1-22TCN-272-05)

gm,E =

=

0.579

For >2 loaded lanes:
gs,I = (S/2250)0.8(d/L)0.1

=

0.761

gs,I =

=

0.761

For >2 loaded lanes:
gs,E = (0.8 + de/3050)gs,I

=

0.808 Table 4.6.2.2.3b-1-22TCN-272-05)

gs,E =

=

0.808

Moment distribution for exterior girders
0 < de < 910 =>
Scope of application

OK

Shear distribution for interior girder

Shear distribution for exterior girder

Checked by LEE, Jong Dae
Approved by CHO, Wan Hyoung


05. Calculation Super T Girder L=38.2m_Skew 20.xls【IV.Distribution】
SHEET NO. : 2 / 2
Skew angle of bridge

=

20 Degree

Reduction of load distribution factor for moment in longitudinal beams
0 < θ < 60o =>

Scope of application
OK
1.05-0.25tgθ ≤ 1
=
0.959
Correction factor for load distribution factors for support shear of the obtuse corner
Scope of application
1800< S <3500=>
OK
1+(Ld)0.5/6S tanθ

6000
Nb> 3=> OK
=

1.211

Moment distribution for exterior girder

=

0.555

Shear distribution for exterior girder

=

0.979

Checked by LEE, Jong Dae
Approved by CHO, Wan Hyoung

0 < θ < 60o =>

OK


05. Calculation Super T Girder L=38.2m_Skew 20.xls【V.Loads】
SHEET NO. : 1 / 2
5. LOADS AND LOAD COMBINATIONS
5.1. Superstructure profiles
Span length
Effective span length

L=
Le =

38.200 m
37.100 m

Width of all lanes

Wl =

11.000 m

Width of pedestrian path (1 side)

0.000 m

Width of parapet (1 side)

0.500 m

Total width of deck

11.700 m

Concrete slab thickness

W=
ts =

Wearing surface thickness

tw =

0.050 m

0.195 m

Number of loaded lanes

3.000 lanes

Multiple presence factor (lane factor)

m=

0.850

Width of 1 lane

3.500 m

Number of girders

Nb =

5.000 girders

Distance between girders

S=
wo =

2.350 m

Width of cantilever slab
Weight of 1 girder

G=

1.150 mm
714.270 kN

Weight of precast concrete plate

0.635 kN/m

Dead load of parapet (1 side)

3.850 kN/m

Dead load of Technical Box
Concrete density

γc =

0.000 kN/m
3
24.5 kN/m

Asphalt concrete density

γw =

3
22.563 kN/m

5.2. Dead load on each girder
Loads

Value

Unit

Remarks and formulas

Stage 1
Dead load of girder

18.698 kN/m

= Cross section area

Dead load of concrete slab

11.191 kN/m

= W * ts * γc / Nb

Dead load of precast plate

0.635 kN/m

x γc

Stage 2

Stage 3
Dead load of parapet

3.850 kN/m

DL of Technical Box
DL of wearing surface

0.000 kN/m

2.143 kN/m

= Wl * tw * γw / Nb

LOADS APPLIED ON GIRDERS
Design truck

Design tandem
4.3m

P1

4.3m

P2

Checked by LEE, Jong Dae
Approved by CHO, Wan Hyoung

1.2m

P3

P4

P5


05. Calculation Super T Girder L=38.2m_Skew 20.xls【V.Loads】
SHEET NO. : 2 / 2

Self weight, lane load,
dead load of concrete slab, wearing surface, parapet
Load distribution

Le

5.3. Live loads
Loads induce bending moment

P1

(truck)

kN

35

1.25

0.555

(Load x factor)
(P x DF x IM)
24.296

P2

(truck)

kN

145

1.25

0.555

100.656

P3

(truck)

kN

145

1.25

0.555

100.656

P4

(tandem)

kN

110

1.25

0.555

76.360

P5

(tandem)

kN

110

1.25

0.555

76.360

kN/m
kN/m

0.0
9.3

1.00
1.00

0.555
0.555

0.000
5.165

Loads

Unit

Pedestrian
Lane load

Value

IF = 1+ IM Dist. factor

Loads induce shear

P1

(truck)

kN

35

1.25

0.979

(Load x factor)
(P x DF x IM)
42.815

P2

(truck)

kN

145

1.25

0.979

177.375

P3

(truck)

kN

145

1.25

0.979

177.375

P4

(tandem)

kN

110

1.25

0.979

134.561

P5

(tandem)

kN

110

1.25

0.979

134.561

0.000
9.3

1.00
1.00

0.979
0.979

0.000
9.101

Loads

Unit

Value
IF = 1+ IM Dist. factor

Pedestrian
Lane load

kN/m
kN/m

5.4. Load combinations
Maximum load factor
LC
Limit state

Dead load
Stage 1

Stage 2

Live load

Lane load Shrink.

Stage 3

Creep

STRENGTH-1

1.25

1.25

1.25&1.50

1.75

1.75

0.5

SERVICE
FATIGUE

1.00
1.00

1.00
1.00

1.00
1.00

1.00
0.80

1.00
0.75

1.00
0.00

Checked by LEE, Jong Dae
Approved by CHO, Wan Hyoung


05. Calculation Super T Girder L=38.2m_Skew 20.xls【VI.Stress Losses】
SHEET NO. : 1 / 2
6. STRESS LOSSES
(-)
tensile stress
(+)
compressive stress

Section 5.9.5.1-1 - 22TCN-272-05)

6.1 Total prestress loss at Service State:
∆fpT = ∆fpES + ∆fpSR + ∆fpCR + ∆fpR2
Where:
∆fpT
:
Total stress losses (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)
6.1. Loss due to elastic shortening
Loss due to elastic shortening of each prestressing tendons
∆fpES
= = EpE

fcgp/Eci
Section 5.9.5.2.3a-1 - 22TCN-272-05)
Where:
= Sum of concrete stresses at the center of prestressing tendons due to prestressing
fcgp
force at transfer
and the selfweight of the member at the sections of maximum moment (Mpa)
Ep
= 197000 (MPa)
Elastic modulus of prestressing tendon
Eci
= 35041 (MPa)
Elastic modulus of concrete at transfer
Section

Length

Sec. 1
Sec. 2
Sec. 3
Sec. 4
Sec. 5
Sec. 6
Sec. 7

18.55
14.75
10.95
6.45
3.85

1.65
0.45

fcgp
P
Mg

Sec. 1
Sec. 2
Sec. 3
Sec. 4
Sec. 5
Sec. 6
Sec. 7

44
44
44
40
33
27
0

Area of
tendon

(m2)
0.006160
0.006160
0.006160

0.005600
0.004620
0.003780
0.000000

Tensile strength Prestress
of tendon
at transfer

(MPa)
1860
1860
1860
1860
1860
1860
1860

Note: Prestress in tendon is taken as:
fcgp:

Determine

Section

No. strands

(MPa)
1395
1395

1395
1395
1395
1395
0
75%

Total
Prestress

(kN)
8593
8593
8593
7812
6445
5273
0
of tensile strength

Ag

=( P / Ag)+(Pi*e*e/ Ig) - (Mg*e/ Ig)
=
(kN)
Axial force in tendon at midspan
=
(kN.m)
Bending moment due to selfweight at midspan
2

(m
)
=
Cross section area of girder at midspan

Ig
y
e
fcgp

=
=
=
=
y

(m)
0.823
0.823
0.823
0.826
0.831
0.896
0.384

(m4)
(m)
(m)
(MPa)
e

(m)
0.632
0.632
0.632
0.631
0.595
0.660
0.384

Checked by LEE, Jong Dae
Approved by CHO, Wan Hyoung

Mg
(kN.m)
3217
3082
2677
1848
1197
547
154

Moment of inertia of girder at midspan
Distance from neutral axis to bottom fiber of girder
Distance from center of tendon to neutral axis

Ag

Ig

2

4

(m )
0.7624
0.7624
0.7624
0.7596
0.7547
1.6683
0.8979

(m )
0.2822
0.2822
0.2822
0.2809
0.2778
0.4682
0.0574

fcgp

∆fpES

(MPa)
16.222
16.524
17.430

17.198
14.185
7.294
-1.032

(MPa)
91.20
92.90
97.99
96.69
79.75
41.01
0.00


05. Calculation Super T Girder L=38.2m_Skew 20.xls【VI.Stress Losses】
SHEET NO. : 2 / 2
6.2. Loss due to creep of concrete
∆fpCR=12*fcgp-7*∆fcdp > 0
Section 5.9.5.4.3-1 - 22TCN-272-05)
Where:
fcgp:
Stress in concrete at center of tendon at transfer (Mpa)
∆fcdp:
Change of stress in concrete at center of tendon due to permanent loads at each section
taken as ∆fcdp.
∆fcdp = Mp-Iie-II/Ig-II+Mp-IIIe-III/Ig-III
Where:
Mp:

Section
Sec. 1
Sec. 2
Sec. 3
Sec. 4
Sec. 5
Sec. 6
Sec. 7

bending moment which changes prestressing stress at center of tendon
due to permanent loads
e-II
(m)
0.632
0.632
0.632
0.631
0.595
0.660
0.384

e-III
(m)
1.016
1.016
1.016
1.015
0.979
0.660
0.384

Mp-II
(kN.m)
2034.69
1949.31
1693.15
1168.96
756.94
345.87
97.52

Mp-III
(kN.m)
1031.19
987.91
858.09
592.43
383.62
175.29
49.42

Ig-II

Ig-III

4

4

(m )

0.2822
0.2822
0.2822
0.2809
0.2778
0.4682
0.0574

(m )
0.5839
0.5839
0.5839
0.5808
0.5739
0.4682
0.0574

∆fcdp

∆fpCR

(MPa)
6.350
6.083
5.284
3.660
2.275
0.735
0.983

(MPa)
150.21
155.70
172.18
180.75
154.29
82.39
0.00

6.3. Loss due to shrinkage
∆fpSR= (117-1.03*H)
= 29.45 (MPa)
Section 5.9.5.4.2-1 - 22TCN-272-05)
Where:
H=
85% Everage annual ambient relative humidity
6.4. Loss due to relaxation and total prestress loss
∆fpR2 = 30%[138-0.4∆fpES-0.2(∆fpSR+∆fpCR)]
(MPa)
Section 5.9.5.4.4c-1-22TCN-272-05)
30% is reduction factor for relaxation rate (According to ASTM A 416M)
∆fpT = ∆fpES + ∆fpES + ∆fpCR + ∆fpCR2
Section
Sec. 1
Sec. 2
Sec. 3
Sec. 4
Sec. 5
Sec. 6
Sec. 7

∆fpES
(MPa)
91.20
92.90
97.99
96.69
79.75
41.01
0.00

∆fpSR
(MPa)
29.45
29.45
29.45
29.45
29.45
29.45
0.00

Checked by LEE, Jong Dae
Approved by CHO, Wan Hyoung

∆fpCR
(MPa)
150.21
155.70
172.18
180.75

154.29
82.39
0.00

∆fpR2
(MPa)
19.68
19.14
17.54
17.19
20.81
29.77
0.00

∆fpT
(MPa)
290.53
297.19
317.17
324.08
284.29
182.62
0.00

fpe
(MPa)
1104.47
1097.81
1077.83
1070.92

1110.71
1212.38
0.00

check fpe
OK
OK
OK
OK
OK
OK
OK


05. Calculation Super T Girder L=38.2m_Skew 20.xls【VII.Foerces】
SHEET NO. : 1 / 8
7. INTERNAL FORCES AT SECTIONS
x
x2
x3
x4
x5
x6

Center

x7

S.7

S.5

S.6

S.4

S.3

S.2

x1 =

18.550 m

x2 =

14.750 m

x3 =

10.950 m

x4 =

6.450 m

x5 =

3.850 m

x6 =

1.650 m

x7 =

0.450 m (section at notch)

Le =

37.10 m

S.1

7.1. Influence lines for bending moments
7.375

0.000

3.225

0.825

0.225
0.000

1.925

5.475

9.275

SECTION I

Ω1 =

Area of influence line (+)

172.051
7.375

8.886

0.000

2.319

0.271
0.000

0.994

3.886

6.597

SECTION II

Ω2 =

Area of influence line (+)

164.831
5.475

6.597

7.718

0.000

1.163

0.317
0.000

2.714

4.546

SECTION III

Ω3 =

Area of influence line (+)

3.225

SECTION IV

0.000

Checked by LEE, Jong Dae
Approved by CHO, Wan Hyoung

3.886

4.546

5.329

3.181

1.363

0.372
0.000

Area of influence line (+)

143.171

Ω4 =

98.846


05. Calculation Super T Girder L=38.2m_Skew 20.xls【VII.Foerces】
SHEET NO. : 2 / 8

1.925

2.319

2.714

3.181

0.000

0.403
0.000

1.479

3.450

SECTION V

Ω5 =

Area of influence line (+)

64.006

0.825
0.000

0.430
0.000

0.994

1.163

1.363

1.479

1.577

SECTION VI

Ω6 =

Area of influence line (+)

29.246
SECTION VII

0.000

0.225

0.271

0.317

0.372

0.403

0.430

0.445 0.000

Ω7 =

Area of influence line (+)

8.246

7.2. Influence lines for shear force
0.500

0.000

0.500

SECTION II

0.398-

(+) Ω2 = 6.732

(-) Ω2 = -2.932
SECTION III

0.295-

(+) Ω3 = 9.216

Checked by LEE, Jong Dae
Approved by CHO, Wan Hyoung

(-) Ω3 = -1.616

0.000

0.500

0.602

0.705

0.174-

0.104-

0.044-

0.012
0.000-

Area of influence line

(-) Ω1 = -4.638

4.638
0.602

0.295-

0.174-

0.104-

0.044-

0.012
0.000-

Area of influence line

0.000

(+) Ω1 =

0.500-

0.398-

0.295-

0.174-

0.104-

0.044-

0.012
0.000-

Area of influence line

SECTION I


05. Calculation Super T Girder L=38.2m_Skew 20.xls【VII.Foerces】
SHEET NO. : 3 / 8

(+) Ω4 = 12.661

0.000

0.500

0.602

0.705

0.826 0.174-

0.104-

0.044-

0.012
0.000-

Area of influence line

SECTION IV

(-) Ω4 = -0.561
0.500

0.602

0.705

0.826

0.896

SECTION V
0.000

0.104-

0.044-

0.012
0.000-

Area of influence line

(+) Ω5 = 14.900

(-) Ω5 = -0.200

0.500

0.602

0.705

0.826

0.896

0.000

0.012
0.000-

0.9560.044-

SECTION VI

Area of influence line

(+) Ω6 = 16.937

(-) Ω6 = -0.037
0.500

0.602

0.705

0.826

0.896

0.956

0.000

0.988 0.012
0.000-

SECTION VII

Area of influence line

(+) Ω7 = 18.103

(-) Ω7 = -0.003

7.3. Internal forces due to dead loads
Summary table of influence areas
Span length
Order
Section
L
x
(m)
(m)

WM

( m2 )

Area of influence line
W Q+
W QSW Q
( m2 )
( m2 )
( m2 )

1

Sec. 1

37.1

18.55

172.05

4.64

-4.64

0.00

2

Sec. 2

37.1

14.75

164.83

6.73

-2.93

3.80

3

Sec. 3

37.1

10.95

143.17

9.22

-1.62

7.60

4

Sec. 4

37.1

6.45

98.85

12.66

-0.56

12.10

5

Sec. 5

37.1

3.85

64.01

14.90

-0.20

14.70

6

Sec. 6

37.1

1.65

29.25

16.94

-0.04

16.90

7

Sec. 7

37.1

0.45

8.25

18.10

0.00

18.10

Value

M1

M2

M3

M4

M5

M6

MA-A

kN/m

kNm

kNm

kNm

kNm

kNm

kNm

kNm

Selfweight of girder

18.70

3217.04

3082.04

2677.04

1848.24

1196.80

546.85

154.19

Concrete slab

11.19

1925.38

1844.59

1602.19

1106.16

716.28

327.29

92.28

Precast concrete plate

0.64

109.31

104.72

90.96

62.80

40.66

18.58

5.24

Parapet

3.85

662.40

634.60

551.21

380.56

246.42

112.60

31.75

Technical Box

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

Wearing surface

2.14

368.79

353.31

306.89

211.88

137.20

62.69

17.68

Summary

36.52

6282.92

6019.26

5228.29

3609.64

2337.36

1068.01

0.00

Loads

Checked by LEE, Jong Dae
Approved by CHO, Wan Hyoung


05. Calculation Super T Girder L=38.2m_Skew 20.xls【VII.Foerces】
SHEET NO. : 4 / 8
Q1

Q2

Q3

Q4

Q5

Q6

QA-A

Loads

Value
kN/m

kN

kN

kN

kN

kN

kN

kN

Selfweight of girder

18.70

0.00

71.05

142.11

226.25

274.86

316.00

338.44

Concrete slab

11.19

0.00

42.52

85.05

135.41

164.50

189.12

202.55

Precast concrete plate

0.64

0.00

2.41

4.83

7.69

9.34

10.74

11.50

Parapet

3.85

0.00

14.63

29.26

46.59

56.60

65.07

69.69

Technical Box

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

Wearing surface

2.14

0.00

8.15

16.29

25.94

31.51

36.22

38.80

Summary

36.52

0.00

138.77

277.53

441.86

536.81

617.15

660.97

Total

7.4. Internal forces due to live loads
Applied live loads on girders

Truck

Tandem
A1=4.3

P

A2=4.3

P

1.2m

P

P

P5

4
1

2

3

7.4.1. Internal forces due to truck+lane load:
A1=
Ltt=
37.1 m

A2=

4.3 m

Influence value at
corresponding wheel axles

4.3 m

Internal forces due to wheel
axles x DF x IM

Total

Load

Y1

Y2

Y3

24.30

100.66

100.66

truck

Lane

M1

18.55

7.125

9.275

7.125

173.11

933.59

717.18

1823.88

888.60

2712.47

M2

14.75

6.295

8.886

7.176

152.95

894.41

722.33

1769.70

851.31

2621.00

M3

10.95

5.180

7.718

6.449

125.85

776.88

649.13

1551.86

739.44

2291.30

M4

6.45

3.833

5.329

4.581

93.14

536.36

461.11

1090.62

510.51

1601.13

M5

3.85

2.558

3.450

3.004

62.15

347.31

302.40

711.86

330.57

1042.43

M6

1.65

1.194

1.577

1.385

29.01

158.70

139.45

327.16

151.05

478.21

42.81

177.38

177.38

Q1

18.55

0.268

0.384

0.500

16.45

47.57

88.69

152.70

42.21

194.91

Q2

14.75

0.371

0.487

0.602

20.83

65.74

106.86

193.42

61.27

254.69

Q3

10.95

0.473

0.589

0.705

25.22

83.91

125.02

234.15

83.88

318.02

Q4

6.45

0.594

0.710

0.826

30.41

105.42

146.54

282.37

115.23

397.60

Q5

3.85

0.664

0.780

0.896

33.41

117.85

158.97

310.23

135.61

445.84

Q6

1.65

0.724

0.840

0.956

35.95

128.37

169.49

333.80

154.14

487.95

QA-A

0.45

0.756

0.872

0.988

37.33

134.11

175.22

346.66

164.76

511.42

Checked by LEE, Jong Dae
Approved by CHO, Wan Hyoung


05. Calculation Super T Girder L=38.2m_Skew 20.xls【VII.Foerces】

SHEET NO. : 5 / 8
7.4.2. Internal forces due to tandem+lane load:
A1=
Ltt=
37.1 m
1.2 m
Influence value at
corresponding wheel axles

Internal forces due to wheel
axles x DF x IM

Total

Load

Y4

Y5

76.36

76.36

truck

lane

Total

M1

18.55

8.675

9.275

210.77

933.59

1144.36

888.60

2032.96

M2

14.75

8.409

8.886

204.30

894.41

1098.71

851.31

1950.02

M3

10.95

7.364

7.718

178.92

776.88

955.80

739.44

1695.24

M4

6.45

5.120

5.329

124.40

536.36

660.76

510.51

1171.27

M5

3.85

3.326

3.450

80.81

347.31

428.12

330.57

758.69

M6

1.65

1.523

1.577

37.01

158.70

195.71

151.05

346.75

134.56

134.56

Q1

18.55

0.468

0.500

62.93

67.28

130.21

42.21

172.41

Q2

14.75

0.570

0.602

76.71

81.06

157.77

61.27

219.04

Q3

10.95

0.673

0.705

90.49

94.85

185.34

83.88

269.21

Q4

6.45

0.794

0.826

106.81

111.17

217.98

115.23

333.21

Q5

3.85

0.864

0.896

116.24

120.60

236.84

135.61

372.45

Q6

1.65

0.923

0.956

124.22

128.58

252.80

154.14

406.94

QA-A

0.45

0.956

0.988

128.58

132.93

261.50

164.76

426.26

7.4.3. Internal forces due to prestressing forces:

Pre.
Suddent Total pre.
Total area
force at prestres force at
of tendons
transfer
s loss
transfer

Total
prestress
loss

Bending
Bending
moment
Total pre. moment
due to
force after
due to
prestress
all loss
prestress
after all
at transfer
loss

(m2)

(MPa)

(MPa)

(kN)

(MPa)

(kN)

(kN.m)

(kN.m)

M1

0.0062

1395

91.20

8031

291

6804

-4867

-4123

M2

0.0062

1395

92.90

8031

297

6804

-4867

-4123

M3

0.0062

1395

97.99

8031

317

6804

-4867

-4123

M4

0.0056

1395

96.69

7301

324

6185

-4399

-3726

M5

0.0046

1395

79.75

5409

284

4582

-3152

-2670

M6

0.0038

1395

41.01

4643

183

3933

-3362

-2848

MA-A

0.0000

0

0.00

0

0

0

0

0

Checked by LEE, Jong Dae
Approved by CHO, Wan Hyoung


05. Calculation Super T Girder L=38.2m_Skew 20.xls【VII.Foerces】
SHEET NO. : 6 / 8
7.4.4. Load Combinations:
Load combination for Service State
No. Loads
Stage 1: Girder fabrication
1 Girder selfweight

Bending moment (kN-m)
M1

M2

M3

M4

M5

M6

MA-A

3217.04

3082.04

2677.04 1848.24

1196.80

546.85

154.19

3217.04

3082.04

2677.04 1848.24

1196.80

546.85

154.19

1925.38

1844.59

1602.19 1106.16

716.28

327.29

92.28

2
Total
Stage 2
3 Selfweight of concrete slab
4 Selfweight of precast concrete plate

109.31

104.72

2034.69

1949.31

5 Wearing surface dead load

368.79

353.31

306.89

6 D.L of parapet & Technical Box

662.40

634.60

551.21

2712.47

Total
Sum of all stages 1+2+3

Total

62.80

40.66

18.58

5.24

1693.15 1168.96

90.96

756.94

345.87

97.52

211.88

137.20

62.69

17.68

380.56

246.42

112.60

31.75

2621.00

2291.30 1601.13

1042.43

478.21

0.00

3743.66

3608.92

3149.40 2193.56

1426.05

653.49

49.42

8995.39

8640.27

7519.59 5210.77

3379.80

1546.21

301.13

Stage 3

7 Live load HL93
8 Pedestrian

No. Loads
Stage 1: Girder fabrication

Shear forces (kN)
Q5

Q6

0.00

71.05

142.11

226.25

274.86

316.00

338.44

0.00

71.05

142.11

226.25

274.86

316.00

338.44

3 Selfweight of concrete slab

0.00

42.52

85.05

135.41

164.50

189.12

202.55

4 Selfweight of precast concrete plate

0.00

2.41

4.83

7.69

9.34

10.74

11.50

0.00

44.94

89.88

143.10

173.84

199.86

214.05

0.00

8.15

16.29

25.94

31.51

36.22

38.80

1 Girder selfweight

Q1

Q2

Q3

Q4

QA-A

2
Total
Stage 2

Total
Stage 3
5 Wearing surface dead load
6 D.L of parapet & Technical Box

0.00

14.63

29.26

46.59

56.60

65.07

69.69

194.91

254.69

318.02

397.60

445.84

487.95

511.42

Total

194.91

277.47

363.57

470.12

533.94

589.24

619.90

Sum of all stages 1+2+3

194.91

393.46

595.56

839.46

982.65

1105.10

1172.39

7 Live load HL93
8 Pedestrian

Checked by LEE, Jong Dae
Approved by CHO, Wan Hyoung


05. Calculation Super T Girder L=38.2m_Skew 20.xls【VII.Foerces】
SHEET NO. : 7 / 8
Load combination for Strength-I Limit State
No. Loads
Coeff.
Stage 1
1 Girder selfweight

Max bending moment (kN-m)

M1
1.25

M2

M3

M4

M5

M6

MA-A

4021.30

3852.55

3346.30 2310.30

1496.00

683.56

192.74

4021.30

3852.55

3346.30 2310.30

1496.00

683.56

192.74

2002.74 1382.71

895.35

409.11

115.35

78.50

50.83

23.23

6.55

2116.44 1461.20

946.18

432.34

121.90

2

Total
Stage 2
3 Concrete slab

1.25

2406.73

2305.73

4 Precast concrete plate

1.25

136.63

130.90

2543.36

2436.63

Total

113.70

Stage 3
5 Wearing surface

1.50

553.18

529.97

460.33

317.81

205.79

94.03

26.51

6 D.L of parapet & Technical Box

1.25

828.00

793.25

689.01

475.70

308.03

140.75

39.69

7 Live load HL93

1.75

4746.83

4586.76

4009.78 2801.98

1824.26

836.86

0.00

8 Pedestrian

1.75

0.00

0.00

0.00

0.00

0.00

0.00

0.00

9 Shrinkage of concrete

0.5

24.88

24.88

24.88

24.87

24.83

37.69

21.54

10 Creep of concrete

0.5

-18.15

-15.57

-7.85

3.87

5.96

11.48

-6.88

6134.74

5919.29

5176.15 3624.22

2368.87

1120.81

80.86

12699.41 12208.47 10638.89 7395.73

4811.05

2236.71

395.50

Total
Sum of all stages 1+2+3
No. Loads

Coeff.

Stage 1
1 Girder selfweight

Max shear forces (kN)
Q1

1.25

Q2

Q3

Q4

Q5

Q6

QA-A

0.00

88.82

177.63

282.81

343.58

395.00

423.05

0.00

88.82

177.63

282.81

343.58

395.00

423.05

2
Total
Stage 2

3 Concrete slab

1.25

0.00

53.16

106.31

169.26

205.63

236.40

253.19

4 Precast concrete plate

1.25

0.00

3.02

6.04

9.61

11.67

13.42

14.37

0.00

56.17

112.35

178.87

217.30

249.83

267.56

Total
Stage 3
5 Wearing surface

1.50

0.00

12.22

24.44

38.90

47.26

54.34

58.20

6 D.L of parapet & Technical Box

1.25

0.00

18.29

36.58

58.23

70.74

81.33

87.11

7 Live load HL93

1.75

341.09

445.72

556.54

695.79

780.21

853.91

894.99

8 Pedestrian

1.75

0.00

0.00

0.00

0.00

0.00

0.00

0.00

Total

341.09

476.22

617.55

792.93

898.22

989.58

1040.29

Sum of all stages 1+2+3

341.09

621.21

907.53 1254.61

1459.10

1634.40

1730.90

Checked by LEE, Jong Dae
Approved by CHO, Wan Hyoung


05. Calculation Super T Girder L=38.2m_Skew 20.xls【VII.Foerces】
SHEET NO. : 8 / 8
Load combination for Fatigue Limit State
No. Loads
Coeff.
Stage 1
1 Girder selfweight

Max bending moment (kN-m)
M1

0.00

M2

M3

M4

M5

M6

MA-A

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

2
Total
Stage 2
3 Concrete slab

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

4 Precast concrete plate

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

Total
Stage 3
5 Wearing surface

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

6 D.L of parapet & Technical Box

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

7 Live load HL93

0.75

2034.36

1965.75

1718.48 1200.85

781.83

358.65

0.00

8 Pedestrian

0.75

0.00

0.00

0.00

0.00

0.00

0.00

Total

2034.36

1965.75

1718.48 1200.85

781.83

358.65

0.00

Sum of all stages 1+2+3

2034.36

1965.75

1718.48 1200.85

781.83

358.65

0.00

No. Loads

Coeff.

Stage 1
1 Girder selfweight

0.00

Max shear forces (kN)
Q1

0.00

Q2

Q3

Q4

Q5

Q6

QA-A

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

2
Total
Stage 2
3 Concrete slab

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

4 Precast concrete plate

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

Total
Stage 3
5 Wearing surface

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

6 D.L of parapet & Technical Box

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

7 Live load HL93

0.75

146.18

191.02

238.52

298.20

334.38

365.96

383.57

8 Pedestrian

0.75

0.00

0.00

0.00

0.00

0.00

0.00

0.00

Total

146.18

191.02

238.52

298.20

334.38

365.96

383.57

Sum of all stages 1+2+3

146.18

191.02

238.52

298.20

334.38

365.96

383.57

Checked by LEE, Jong Dae
Approved by CHO, Wan Hyoung


05. Calculation Super T Girder L=38.2m_Skew 20.xls【VIII.Resistance】
SHEET NO. : 1 / 5
8. RESISTANCE CHECK

0

8.1 Bending moment resistance
fps = fpu*(1 - k*c/dp)

Average stress in prestressing tendons
k = 2*(1.04 - fpy/fpu)
Where:

(Section 5.7.3.1.1-1-22TCN-272-05)

= 0.28
(Section 5.7.3.1.1-2-22TCN-272-05)
Aps*fpu + As*fy - A's*f'y - 0.85*β1*f'c*(b-bw)*hf

Distance from C.L to compression part c =

0.85*b1*f'c*bw + k*Aps*fpu/dp
(Section 5.7.3.1.1-3 - 22TCN-272-05 - Assume equivalent section as T-section)
Aps
=
Area of prestressing tendons
fpu
=
Ultimate tensile strength of prestressing tendon

mm2
1860 MPa

Yield strength of prestressing tendon

fpy

=

Area of tensile reinforcing bar

As

=

1674 MPa
mm2

Area of compressive reinforcing bar

A's

=

mm2

Yield strength of tensile reinforcing bar

fy

=

400 MPa

Yield strength of compressive reinforcing bar

f'y

=

400 MPa

Strength of 28-day concrete
Width of compresion flange
Thickness of compression flange

f'c
b
hf

=

=
=

50 MPa
2325 mm
195 mm

Width of girder web

bw

=

mm

Distance from extreme compression fiber to center of all tendons dp
β1
Coeff. of reduction of stress block

=

mm

=
0.69
Mr = ϕ*Mn
Bending moment resistance
(Section 5.7.3.2.1-1 - 22TCN-272-05)
Where:
ϕ=

1
Resistant factor for bending and tension of prestressed concrete
Mn = Aps*fps*(dp - a/2) + As*fî*(ds - a/2) - A's*f'y*(d's - a/2)
(Section 5.7.3.2.2-1 - 22TCN-272-05)
a = c*β1
=
mm
Depth of equivalent stress block

Distance from extreme compression fiber to center of compressiond'reinforcing
=
bars
s
ds bars
Distance from extreme compression fiber to center of tensile reinforcing
=
Items

Unit

Aps

=

mm2

dp

=

mm

b'w

=
bw
=
Equivalent section type (rectangle or T)
c
=
fps
=
a
=
As
=
ds
=
d's

=

Mn

=

Bending resitance
Bending moment at Strength-I
Bending resistance check

Checked by LEE, Jong Dae
Approved by CHO, Wan Hyoung

Mr

mm
mm

Section
Sec. 1

Sec. 2

Sec. 3

Sec. 4

Sec. 5

Sec. 6

Sec. 7

6160

6160

6160

5600

4620

3780

0

1754

1754

1754

1750

1709

1514

800

mm

270

270

270

270

270

700

920

mm
mm
Mpa
mm
mm2

2325
Rec
114
1826
79
0

2325
Rec
114
1826
79
0

2325
Rec
114

1826
79
0

2325
Rec
104
1829
72
0

2325
Rec
86
1834
59
0

2325
Rec
70
1836
49
0

2325
Rec
26
1843
18

6434

mm

0

0

0

0

0

0

750

mm

0

0

0

0

0

0

0

kNm

19282

19282

19282

17559

14226

10336

1907

kNm

19282

19282

19282

17559

14226

10336

1907

kNm

12699

12208

10639

7396

4811

2237

395

OK

OK

OK

OK

OK

OK

OK


05. Calculation Super T Girder L=38.2m_Skew 20.xls【VIII.Resistance】
SHEET NO. : 2 / 5
8.2. Shear resistance check
Vr = ϕ*Vn

Shear resistance

(Section 5.8.2.1-2 - 22TCN-272-05)

Where:
ϕ=

Resistance factor for shear and torsion of normal concrete

0.9

Vn = min(Vn1 = Vc + Vs + Vp ; Vn2 = 0.25*f'c*bv*dv + Vp)

Nominal shear resistance

(Section 5.8.3.3-2 - 22TCN-272-05)
0.5

Vc = 0.083*β*(f'c) *bv*dv

(Section 5.8.3.3-3 - 22TCN-272-05)

Vs = [ Av*fy*dv*(cotgθ + cotga)*sinα ]/s

(Section 5.8.3.3-4 - 22TCN-272-05)

Effective girder web thickness

bv =

mm

Effective shear depth

dv =

mm

Stirrup spacing

s=

100 mm

Angle between transverse reinforcement and longitudinal axis

α=

90

o

Area of transverse reinforcement within distance s

Av =

2
402 mm

Area of transverse reinforcement near bearing within distance s

Av =

2
1257 mm

Area of incline reinforcement near bearing

Ax =

2
4580 mm

Vp =
Component of effective prestressing force on direction of applied shear force
Diagonally cracked ability factor

β=

Angle of inclination of diagonal compressive stresses

θ=

Shear stresses in concrete for

(β & θ)

kN
o

Table 5.8.3.4.2-1

v = (Vu - ϕ*Vp)/(ϕ*bv*dv)
(Section 5.8.3.4.2-1 - 22TCN-272-05)
Vu =

Factored shear resistance
Strain in rebars in tensile fiber due to bending

kN

εx = (Mu/dv + 0.5*Nu + 0.5*Vu*Cotgθ - Aps*fpo) < 0.002
Es*As + Ep*Aps
(Section 5.8.3.4.2-2 - 22TCN-272-05)

If value of
Then

εx <0
|εx|

(Section 5.8.3.4.2-3 - 22TCN-272-05)
is reduced by multipling with

Area of concrete in tensile fiber
Area of prestressing tendons in tensile fiber

Fε =

Es*As + Ep*Aps
Ec*Ac + Es*As + Ep*Aps

Ac =

mm2

Aps =

mm2

Elastic modulus of prestressing tendon

Ep = 197000 MPa

Elastic modulus of rebar

Es = 200000 MPa

Elastic modulus of concrete of girder

Ec =

Factored axial force in longitudinal direction

Nu =

kN

Factored shear force

Vu =

kN

Factored bending moment

Mu =

kN.m

Stress in concrete at center of prestressing tendons

fco =

MPa

e=

mm

fpo =

MPa

Eccentricity of tendons to neutral axis
Stress in tendons while stress in surround concrete is 0

Checked by LEE, Jong Dae
Approved by CHO, Wan Hyoung

38007 MPa