Ban tinh dam super t khue dong

Sở giao thông vận tảI tp đà nẵng
Da nang department of transport
******************************

dự án ĐầU TƯ CƠ Sở Hạ TầNG ƯU TIÊN Đà NẵNG
HợP ĐồNG: A23+A24+B37
Danang priority infrastructure investment project
Package :A23 + A24 + B27

tiểu hợp phần c12: cầu khuê đông
Subcomponent c12: khue dong bridge

Bảng tính Dầm super-T
Super-T girder calculation
(Shop drawing design stage)
(Version 1)

- Ha noi: 10 -2011 -


Sở giao thông vận tảI tp đà nẵng
Da nang department of transport
******************************

dự án ĐầU TƯ CƠ Sở Hạ TầNG ƯU TIÊN Đà NẵNG
HợP ĐồNG: A23+A24+B37
Danang priority infrastructure investment project
Package :A23 + A24 + B27

tiểu hợp phần c12: cầu khuê đông
Subcomponent c12: khue dong bridge

Bảng tính dầm super-T
Super-T girder calculation
(Shop drawing design stage)
(Version 1)

NHà thầu
Contractor

T vấn giám sát
Consultant

Chủ đầu t
Employer

- Ha noi: 10 -2011 -


SUPER-T GIRDER SPAN 37.5M


Bridge joint stock
company no.12

Project
Structure

Calculation of super-t beam

Calculate by

(Shop drawing design stage)

Bui Van Duan
Checked by
Duong Van Chien

Da Nang priority Infrastructure Investment Project
Sub_component C12 - Khue Dong bridge
Super-T beam L=37.5m

I. KÍCH THƯỚC HÌNH HỌC - STRUCTURAL PARAMETER:
Tiêu chuẩn thiết kế - Design standard:
Loại dầm - Type of beam:
Số dầm (tính cho nửa cầu) - Number of beam:
Bề rộng mặt cầu - Width of deck
Bề rộng lề bộ hành - Width of sidewalk
Bề rộng dải phân cách - Width of median
Chiều dài dầm - Length of beam
Spacing from end beam to bearing centerline:
Chiều dài nhịp tính toán - Calculation span length
Chiều cao bản mặt cầu - Height of deck slab
Chiều cao dầm - Height of beam section
Khoảng cách giữa các dầm - Spacing of beams
Lớp phủ mặt cầu - Deck overlay

22TCN272-05
Super T
5
13.15 m

2.00 m
0.65 m
37.50 m
0.35 m
36.80 m
200 mm
1,750 mm
2,440 mm
70 mm

B :
BPL :
L

:

Ls
hb
h
S

:
:
:
:
:

Date

mm

II. CƯỜNG ĐỘ VÀ ỨNG SUẤT GIỚI HẠN CỦA VẬT LIỆU - STRENGTH AND ULTIMATE STRESS OF MATERIAL
2.1. Thép - Steel:
2.1.1 Cốt thép ứng suất trước - Prestress reinforcement
Type of stress
:
Pretension stress
Modulus of elasticity
Ep
=
197,000 (MPa)
(5.4.2)
=
1,860 (MPa)
(5.4.4.1-1)
Required tensile strength of prestressing steel
fpu
Liquid limit of prestreesing steel
fpy
= 0.9 fpu
=
1,674 (MPa)
(5.4.4.1-1)
Prior to seating - short - term
fs
= 0.9 fpy
=
1,507 (MPa)
(5.9.3-1)
=

1,302 (MPa)
(5.9.3-1)
At anchorages and couplers immediately after anchor set
= 0.7 fpu
At end of seating loss zone immediately after anchor set
= 0.74 fpu
=
1,376 (MPa)
(5.9.3-1)
= 0.8 fpy
=
1,339 (MPa)
(5.9.3-1)
At service limit state after losses
fpe
(Pre-tensioning)
Before the force transferred to concrete
= 0.75 fpu
=
1,395 (MPa)
(5.9.3-1)
=
1,339 (MPa)
(5.9.3-1)
After stress loss
= 0.80 fpy
2
Area of reinforcement, class of 15.2mm
140 mm
Tension strength desinged for 1 tendon

Stress of reinforcement during kicking
2.1.2 Thanh cường độ cao - High-strength steel bar
Modulus of elasticity
Required tensile strength of steel bar
Liquid limit of steel bar
2.1.3 Cốt thép thường - Plain reiforcement
Modulus of elasticity
Liquid limit strength of reinforcement CB400-V
Tensile stress of reinforcement
Liquid limit strength of reinforcement CB300-T
Tensile stress of reinforcement
2.2. Bê tông - Concrete
Density of concrete
Thermal expansion coefficient of concrete
Hệ số tỷ lệ giữa bê tông và cốt thép
Mean humidity

Ppj
fpj
Ep
fpu
fpy

= 0.8 fpu

Es
fsy
fsa
fsyr
fsar

= 0.6 fsy

γc

#########

p
H

= 0.6 fsyr

=
195 KN
=
1395 MPa
(Standard 22TCN 272-05)
=
207,000 (MPa)
=
1,035 (MPa)
=
828 (MPa)
(Standard TCVN 1651:2008)
=
200,000 (MPa)
=
400 (Mpa)
=
240 (MPa)

=
300 (Mpa)
=
180 (MPa)
=
=
=
=

2,400 (Kg/m³)
0

10.8E-6 / C
0.2
85 %

(5.4.4)
(5.4.4.1-1)
(5.4.4.1-1)
(5.4.3.2)
(7.3.4-1)
(7.3.4-1)
(Bảng 3.5.1)
(5.4.2.2)
(5.4.2.5)

InputData-1/5


2.2.1 Dầm chủ - Main beam

Theoretical compressive strength of concrete at 28 a
Concrete compressive strength when tranfering forc
Modulus of elasticity

f'c
f'ci

= 0.85 f'c

Ec = 0.043 yc1.5 f'c0.5

=
=

50 (MPa)
42.5 (MPa)

(5.4.2.1)

=

35,750 (MPa)

(5.4.2.1)

Shear bearing capacity of plain concrete
fr
Ultimate stress of concrete
Ultimate compressive stress when force tranfer applied

=0.63f'c

=

4.45 (MPa)

(5.4.2.6)

= 0.6 f'ci

=

25.5 (MPa)

(5.9.4.1.1)

Ultimate tension stress when force tranfer applied
Ultimate compressive stress when losing stress
* Prestressing + long-term load
* Live load +1/2(prestressing+long-term load)
* Prestressing + Long-term load + Live load

=0.58f'ci0.5

=

3.78 (MPa)

(5.9.4.1.2)

= 0.45 f'c
= 0.4 f'c
= 0.6 f'c

=
=
=

22.5 (MPa)
20 (Mpa)
30 (Mpa)

(5.9.4.2.1-1)
(5.9.4.2.1-1)
(5.9.4.2.1-1)

= 0.5 f'c0.5

=

3.54 (Mpa)

(5.9.4.2.2-1)

Tension stress after losing stress
2.2.2 Mặt cầu - Bridge deck
Theoretical compressive strength of concrete at 28 a

0.5

f'cs

Modulus of elasticity
Ecs = 0.043 yc1.5 f'cs0.5
Ultimate compressive stress when losing stress
* Prestressing + long-term load
= 0.45f'cs
* Hoạt tải+1/2(Ứng suất trước+tải trọng lâu dài) = 0.4 f'cs

=

35 (MPa)

(5.4.2.1)

=

29,910 (MPa)

(5.4.2.1)

=
=

15.8 (MPa)
14 (Mpa)

(5.9.4.2.1-1)
(5.9.4.2.1-1)

2.96 (Mpa)

(5.9.4.2.2-1)

Tension stress after losing stress
= 0.5f'cs0.5
=
2.3. Material conversion factor
Prestressing reinforcement/Concrete of main beam
Rpc
= Ep / Ec
=
Reinforcement/Concrete of main beam
Rsc
= Es / Ec
=
= Ecs / Ec
=
Concrete of bridge deck/Concrete of main beam
Rdc
3. Tải trọng - Load and impact
During construction, the following loads shall be considered and calculated
- Self weight of beam.
- Tensile force of prestressing strand.
- Effect of creep shrinkage during construction
During the using, there are additional loads as follows
- Effect of creep shrinkage during the using
- Weigth of dead load , part 2 (bridge deck, hand rail, wheel guard).
- Live load of vehicle.
3.1. Design live load effects on one main beam

3.1.1. Dead load of seft beam
- Dead load of seft beam, DC1=
18.31
kN/m
- Lead load of divided wall, DC2=
0.33
kN/m
- Concrete of bridge deck, DC3=
12.38
kN/m
- Remaining formwork, DC4=
1.00
kN/m
Total:
32.02
kN/m
3.1.2. Weigth of dead load, part 2
- Hand rail, sidewalk, DC5=
2.50
kN/m
- Deck overlay, DW=
4.14
kN/m
Total:
6.64
kN/m
3.2. Live load
3.2.1. Live load of vehicle
Carriage-way width
Bx =

10.50
m
Number of lanes as designed
nx =
3
lane
Coefficient of lane
m=
0.85
Designed live load of vehicle HL-93 consists one combination of
Design truck and load of lane
or two-axled truck and load of lane

5.51
5.59
0.84

(Calculation for exteior beam)

InputData-2/5


325 kN

3.2.2. Designed truck has total of weight

4.3 m

4.3 to 9 m
P3

P2
35 kN
145 kN
145 kN
3.2.3. Designed two-axled truck
Two-axled truck consists a pair of axles 110 kN, apart 1.2m. Horizontal spacing of wheels
is 1.8m, total weigth of vehicle is :
220
KN
Impact coefficient follows to Clause 3.6.2 - Standard 22TCN272-05
1.20 m
P1

110 kN

110 kN
3.2.4. Designed load of lane

qL =

Stressing force of designed load of lane does not include impact coefficient
3.2.5. Live load of pedestrian (PL)
Width of road for pedestrian
Bpl =
Number of lanes for pedestrian
npl =
Load for pedestrian
Uniform load of pedestrian according to longitudinal of bridge

PL =

qpl =

9.3

kN/m

2.00 m
1 làn
2
3.0 kN/m
6.0 kN/m/1side

III. HỆ SỐ PHÂN BỐ - DISTRIBUTION COEFFICIENT
1. Calculate the horizontal distribution coefficient due to live load
Look up the table 4.6.2.2.1-1, we have the formula for computation of horizontal distribution coefficient as follows:
The values used for computation :
: Number of beam
= 5
beam
+ Nb
+S
: Spacing of beams
= 2440
mm
+L
: Span of beam
= 37500
mm
+ ts
: Thickness of concrete slab of bridge deck

= 200
mm
+n
: Ratio of elasticity modulus
= 0.837
+d
: Height of main beam
= 1750
mm
1.1. Distribution coefficient of moment
* Internal beam
• One design lane loaded
gM = (S/910)0,35(Sd/L2)0,25
• Two or more design lanes loaded
0,6
2 0,125
gM = (S/1900) (Sd/L )

=

0.33

=

0.56

=

0.40

=
=

0.00 mm
0.97

=

0.55

* Exterior beam
• One design lane loaded
gMSE
= 1,2gM
• Two or more design lanes loaded
de =
e = 0,97 + de/8700
gMSE

= egM

InputData-3/5


1.2. Distribution coefficient of shear force
* Internal beam
• One design lane loaded
gV = (S/3050)0.6(d/L)0.1
• Two or more design lanes loaded
0.8

0.1

gV = (S/2250) (d/L)

=

0.64

=

0.79

* Exterior beam
• One design lane loaded, lever rule
P/2

P/2

R1

R1

= P/2*1880/2440

gVSE = 1.2R11.2x0.39
=
• Two or more design lanes loaded
e = 0,8 + de/3050
gVSE

2. Effect of skewed bridge (4.6.2.2.2d)

= egV

= 0.39

P

= 0.46

P

=

0.80

=

0.63

• Skewed bridge
θ =
0o
Reduction of distribution coefficient of load for moment of longitudinal beam on skewed support
min(1.05-0.25tgθ ; 1) =
1.00
Adjustment of distribution coefficient of load for shear force of the longitudinal beam on skewed support
0.5
1 + ((Ld) /6S)tan(θ)
=

1.00
3. Computation result of distribution coefficient of load
Position of beam
Number of lane
gM
gV
Internal
1
0.33
0.64
Internal
≥2
0.56
0.79
MAX
0.56
0.79
Exterior
1
0.40
0.46
Exterior
≥2
0.55
0.63
MAX
0.55
0.63
IV. GIAI ĐOẠN TÍNH TOÁN - PERIOD OF COMPUTATION
Structure to be analysed through 2 phases as follows:

1. Giai đoạn 1 - Phase 1
- Computation with load:
+ Dead live of self section of beam (DC)
+ Dead load of divided wall (DC)
+ Acting of Prestressing (PS)
2. Giai đoạn 2 - Phase 2
- Computation with load:
+ Dead load of self beam (DC)
18.31
kN/m/1beam
+ Dead load of divided wall (DC)
0.33
kN/m/1beam
+ Dead load of self deck (DC)
12.38
kN/m/1beam
+ Dead load of remaining formwork
1.00
kN/m/1beam
+ Hand rail, sidewalk (DC)
2.50
kN/m/1beam
+ Dead load of deck overlays (DW)
4.14
kN/m/1beam
+ Wastewater treatment pipe (P)
0.00
kN/m/1beam
+ Live load of vehicle (combined compact stress) LL+ IM; human

InputData-4/5


V. TỔ HỢP TẢI TRỌNG - LOAD COMBINATION
1. Hệ số điều chỉnh tải trọng - Adjustment coefficient of load
Adjustment coefficient of load :
η= ηDηRηΙ
Relative coefficients

Flexibility
ηD

Strength limit state
Service limit state

1.00
1.00

(1.3.2)
Redundancy
ηR
1.00
1.00

Importance
ηI
1.05
1.00

2. Trạng thái giới hạn và tổ hợp tải trọng - Strength limit states and load combination coefficient:

Load combination at strength limit state I
η{1.25DC+1.5DW+1.75PL + 1.75(LL+IM)}
Load combination at service limit state
η{DC+DW+PL+(LL+IM)}

η
1.05
1.00
(3.4)

InputData-5/5


Bridge joint stock
company no.12

Calculation of super-t beam

Calculate by

(Shop drawing design stage)

Bui Van Duan
Checked by
Duong Van Chien

Da Nang priority Infrastructure Investment Project
Sub_component C12 - Khue Dong bridge
Super-T beam L=37.5m

Project
Structure

Date

ĐẶC TRƯNG MẶT CẮT - MORPHOLOGIC FEATURE OF SECTION
I.INTRODUCTION:
Character of reinforcement concrete section shall be calculated in 41 positions of length of beam (0.025Ls for 1 section)
Character of section shall be calculated with two main states :
First state
: Beam combinate strand before concreting bridge deck
Second state
: Beam combinate strand and bridge deck at the time of using
II. ĐẶC TRƯNG CÁC MẶT CẮT TÍNH TOÁN - CHARACTER OF BEAM COMPUTATION SECTION
Height of beam
1,750 (mm)
Height of beginning section of beam
0 (mm)
Height of bridge deck
0 (mm)
Width conversion of deck slab
2,041 (mm)
Length of beginning section of beam
850 (mm)
Length of plain section
1,425 (mm)
Length of hollow section
32,950 (mm)
Section
f. sup.

(mm)

0
920
1,840
2,760
3,680
4,600
5,520
6,440
7,360
8,280
9,200
10,120
11,040
11,960
12,880
13,800
14,720
15,640
16,560
17,480
18,400

Aconc
(m2)

0.943
1.671
1.671

0.692
0.692
0.692
0.692
0.692
0.692
0.692
0.692
0.692
0.692
0.692
0.692
0.692
0.692
0.692
0.692
0.692
0.692

Iconc.
(m4)

0.056
0.456
0.456
0.265
0.265
0.265
0.265
0.265

0.265
0.265
0.265
0.265
0.265
0.265
0.265
0.265
0.265
0.265
0.265
0.265
0.265

e conc.
(m)

1.399
0.993
0.993
0.888
0.888
0.888
0.888
0.888
0.888
0.888
0.888
0.888
0.888

0.888
0.888
0.888
0.888
0.888
0.888
0.888
0.888

Stage I (at the completion time of tensile)
Astrand
Istrand
estrand
A*e
(m2)
(m4)
(m3)
(m)

0.002
0.018
0.018
0.023
0.027
0.030
0.030
0.035
0.035
0.035
0.035

0.035
0.035
0.035
0.035
0.035
0.035
0.035
0.035
0.035
0.035

0.000
0.004
0.004
0.004
0.004
0.004
0.004
0.004
0.004
0.004
0.004
0.004
0.004
0.004
0.004
0.004
0.004
0.004
0.004

0.004
0.004

1.675
0.277
0.277
0.252
0.233
0.224
0.224
0.210
0.210
0.210
0.210
0.210
0.210
0.210
0.210
0.210
0.210
0.210
0.210
0.210
0.210

1.322
1.664
1.664
0.620
0.621

0.621
0.621
0.622
0.622
0.622
0.622
0.622
0.622
0.622
0.622
0.622
0.622
0.622
0.622
0.622
0.622

AcombI
(m2)

0.945
1.689
1.689
0.715
0.719
0.722
0.722
0.727
0.727
0.727

0.727
0.727
0.727
0.727
0.727
0.727
0.727
0.727
0.727
0.727
0.727

IcombI
(m4)

0.057
0.469
0.469
0.278
0.280
0.282
0.282
0.285
0.285
0.285
0.285
0.285
0.285
0.285
0.285

0.285
0.285
0.285
0.285
0.285
0.285

ecombI
(m)

1.400
0.985
0.985
0.867
0.863
0.860
0.860
0.855
0.855
0.855
0.855
0.855
0.855
0.855
0.855
0.855
0.855
0.855
0.855
0.855

0.855

Super-T 37,5m-Section-1/3


Section
f. sup.
(mm)

0
920
1,840
2,760
3,680
4,600
5,520
6,440
7,360
8,280
9,200
10,120
11,040
11,960
12,880
13,800
14,720
15,640
16,560
17,480
18,400

Section
f. sup.
(mm)

0
920
1,840
2,760
3,680
4,600
5,520
6,440
7,360
8,280
9,200
10,120
11,040
11,960
12,880
13,800
14,720
15,640
16,560
17,480
18,400

Aconc.
(m2)

0.943

1.671
1.671
0.692
0.692
0.692
0.692
0.692
0.692
0.692
0.692
0.692
0.692
0.692
0.692
0.692
0.692
0.692
0.692
0.692
0.692

AcombI
2
(m )

0.945
1.688
1.688
0.714
0.717

0.720
0.720
0.724
0.724
0.724
0.724
0.724
0.724
0.724
0.724
0.724
0.724
0.724
0.724
0.724
0.724

Iconc.
(m4)

0.056
0.456
0.456
0.265
0.265
0.265
0.265
0.265
0.265
0.265

0.265
0.265
0.265
0.265
0.265
0.265
0.265
0.265
0.265
0.265
0.265

IcombI
(m4)

0.056
0.468
0.468
0.277
0.279
0.281
0.281
0.283
0.283
0.283
0.283
0.283
0.283
0.283
0.283

0.283
0.283
0.283
0.283
0.283
0.283

econc.
(m)

Stage I (at the time of concreting the bridge deck)
Astrand
Istrand
estrand
A*e
AcombI
(m2)
(m4)
(m3)
(m2)
(m)

1.399
0.993
0.993
0.888
0.888
0.888
0.888
0.888

0.888
0.888
0.888
0.888
0.888
0.888
0.888
0.888
0.888
0.888
0.888
0.888
0.888

ecombI
(m)

1.400
0.986
0.986
0.869
0.865
0.862
0.862
0.857
0.857
0.857
0.857
0.857
0.857

0.857
0.857
0.857
0.857
0.857
0.857
0.857
0.857

0.002
0.017
0.017
0.022
0.025
0.028
0.028
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032

Aslab
(m2)

0.408
0.408
0.408
0.408
0.408
0.408
0.408
0.408
0.408
0.408
0.408
0.408
0.408
0.408
0.408
0.408
0.408
0.408
0.408
0.408
0.408

0.000
0.003
0.003
0.003

0.003
0.004
0.004
0.004
0.004
0.004
0.004
0.004
0.004
0.004
0.004
0.004
0.004
0.004
0.004
0.004
0.004

1.675
0.277
0.277
0.252
0.233
0.224
0.224
0.210
0.210
0.210
0.210
0.210

0.210
0.210
0.210
0.210
0.210
0.210
0.210
0.210
0.210

Stage II (At service)
Islab
eslab
(m4)
(m)

0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001

0.001
0.001
0.001
0.001
0.001
0.001
0.001

1.850
1.850
1.850
1.850
1.850
1.850
1.850
1.850
1.850
1.850
1.850
1.850
1.850
1.850
1.850
1.850
1.850
1.850
1.850
1.850
1.850

1.322
1.664
1.664
0.620
0.620
0.621
0.621
0.621
0.621
0.621
0.621
0.621
0.621
0.621
0.621
0.621
0.621
0.621
0.621
0.621
0.621

A*e
(m3)

2.078
2.419
2.419
1.375
1.375

1.376
1.376
1.376
1.376
1.376
1.376
1.376
1.376
1.376
1.376
1.376
1.376
1.376
1.376
1.376
1.376

0.945
1.688
1.688
0.714
0.717
0.720
0.720
0.724
0.724
0.724
0.724
0.724
0.724

0.724
0.724
0.724
0.724
0.724
0.724
0.724
0.724

AcombI
(m2)

1.353
2.096
2.096
1.122
1.125
1.128
1.128
1.133
1.133
1.133
1.133
1.133
1.133
1.133
1.133
1.133
1.133
1.133

1.133
1.133
1.133

IcombI
(m4)

0.056
0.468
0.468
0.277
0.279
0.281
0.281
0.283
0.283
0.283
0.283
0.283
0.283
0.283
0.283
0.283
0.283
0.283
0.283
0.283
0.283

IcombI

(m4)

0.116
0.715
0.715
0.529
0.533
0.536
0.536
0.542
0.542
0.542
0.542
0.542
0.542
0.542
0.542
0.542
0.542
0.542
0.542
0.542
0.542

ecombI
(m)

1.400
0.986
0.986

0.869
0.865
0.862
0.862
0.857
0.857
0.857
0.857
0.857
0.857
0.857
0.857
0.857
0.857
0.857
0.857
0.857
0.857

ecombI
(m)

1.536
1.154
1.154
1.226
1.223
1.220
1.220
1.215

1.215
1.215
1.215
1.215
1.215
1.215
1.215
1.215
1.215
1.215
1.215
1.215
1.215

Super-T 37,5m-Section-2/3


Section
f. sup.
(mm)

0
920
1,840
2,760
3,680
4,600
5,520
6,440
7,360

8,280
9,200
10,120
11,040
11,960
12,880
13,800
14,720
15,640
16,560
17,480
18,400

AcompI
(m2)

0.945
1.688
1.688
0.714
0.717
0.720
0.720
0.724
0.724
0.724
0.724
0.724
0.724
0.724

0.724
0.724
0.724
0.724
0.724
0.724
0.724

IcompI
(m4)

0.056
0.468
0.468
0.277
0.279
0.281
0.281
0.283
0.283
0.283
0.283
0.283
0.283
0.283
0.283
0.283
0.283
0.283
0.283

0.283
0.283

ecompI
(m)

Trạng thái II ( lúc khai thác) Stage II (At service)
Astrand
Istrand
estrand
A*e
AcompI
(m2)
(m4)
(m3)
(m2)
(m)

1.400
0.986
0.986
0.869
0.865
0.862
0.862
0.857
0.857
0.857
0.857
0.857

0.857
0.857
0.857
0.857
0.857
0.857
0.857
0.857
0.857

0.408
0.408
0.408
0.408
0.408
0.408
0.408
0.408
0.408
0.408
0.408
0.408
0.408
0.408
0.408
0.408
0.408
0.408
0.408
0.408

0.408

0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001

1.850
1.850
1.850
1.850
1.850
1.850

1.850
1.850
1.850
1.850
1.850
1.850
1.850
1.850
1.850
1.850
1.850
1.850
1.850
1.850
1.850

2.078
2.419
2.419
1.375
1.375
1.376
1.376
1.376
1.376
1.376
1.376
1.376
1.376
1.376

1.376
1.376
1.376
1.376
1.376
1.376
1.376

1.353
2.096
2.096
1.122
1.125
1.128
1.128
1.133
1.133
1.133
1.133
1.133
1.133
1.133
1.133
1.133
1.133
1.133
1.133
1.133
1.133

IcompI
(m4)

0.116
0.715
0.715
0.529
0.533
0.536
0.536
0.542
0.542
0.542
0.542
0.542
0.542
0.542
0.542
0.542
0.542
0.542
0.542
0.542
0.542

ecompI
(m)

1.536
1.154

1.154
1.226
1.223
1.220
1.220
1.215
1.215
1.215
1.215
1.215
1.215
1.215
1.215
1.215
1.215
1.215
1.215
1.215
1.215

Super-T 37,5m-Section-3/3


Bridge joint stock
company no.12

Calculation of super-t beam

Calculate by

(Shop drawing design stage)

Bui Van Duan
Checked by
Duong Van Chien

Da Nang priority Infrastructure Investment Project
Sub_component C12 - Khue Dong bridge
Super-T beam L=37.5m

Project
Structure

Date

CÁP DỰ ỨNG LỰC - TENDONS
I. KÍCH THƯỚC DẦM CHỦ - DIMENSION OF MAIN BEAM
Calculated length
:
36.80 mm
Height of beam
:
1750 mm
Height of section of beam edge
800 mm
Length of section at the beam edge :
mm
At the time of completion of tensile
Elasticity modulus of concrete when
32959 Mpa

Force transfer applied
Elasticity modulus of tendon
197000 Mpa
Diameter of tendon
:
15.2 mm
140
Conversion factor
:
6.0
837
At the time of concreting the bridge deck
Elasticity modulus of concrete when
35750 Mpa
concreting the bridge deck
Elasticity modulus of tendon
197000 Mpa
Diameter of tendon
:
15.2 mm
140
Conversion factor
:
5.5
771
Period of service
Elasticity modulus of concrete when
35750 Mpa
force transfer applied
Elasticity modulus of tendon

197000 Mpa
Diameter of tendon
:
15.2 mm
140
Conversion factor
:
5.5
771

mm2
mm2

1589 mm4
56757 mm4

mm2
mm2

1589 mm4
48243 mm4

mm2
mm2

1589 mm4
48243 mm4

II. VỊ TRÍ CÁP DƯL - POSITION OF STRAND

Row A
Position

From CL

1
-510
2
-300
3
-250
4
-200
5
-150
6
-100
7
-50
8
0
9
50
10
100
11
150
12
200
13

250
14
300
15
510
Total of tendons

75

Debonded length (mm)
Row B
Row C
Row D

125

175

Row E

225

1675
0

0
0
2000
3000
6000

0
6000
3000
2000
0
0

0
0
3000
4000
6000
0
0
0
6000
4000
3000
0
0

0
2000
4000
6000
0
0

0
2000

0
0
6000
4000
2000
0

2000
0

11

13

12

4

0
2

42 strands

Super-T 37,5m-Tendon-1/3


III. ĐẶC TRƯNG MẶT CẮT CÁP DƯL - CHARACTER OF TENDON SECTION:
AT THE COMPLETION TIME OF FORCE TRANFER
Section

0
0.025Ls
0.050Ls
0.075Ls
0.100Ls
0.125Ls
0.150Ls
0.175Ls
0.200Ls
0.225Ls
0.250Ls
0.275Ls
0.300Ls
0.325Ls
0.350Ls
0.375Ls
0.400Ls
0.425Ls
0.450Ls
0.475Ls
0.500Ls

Position

0
920
1,840
2,760
3,680

4,600
5,520
6,440
7,360
8,280
9,200
10,120
11,040
11,960
12,880
13,800
14,720
15,640
16,560
17,480
18,400

Row A

0
5
5
7
9
9
9
11
11
11
11

11
11
11
11
11
11
11
11
11
11

Row B

0
7
7
7
9
11
11
13
13
13
13
13
13
13
13
13
13

13
13
13
13

Row C

Row D

0
6
6
8
8
10
10
12
12
12
12
12
12
12
12
12
12
12
12
12
12

Row E

0
2
2
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4

Aconversion

Total

2

2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2

2
22
22
28
32
36
36
42
42

42
42
42
42
42
42
42
42
42
42
42
42

1,674
18,409
18,409
23,430
26,777
30,124
30,124
35,145
35,145
35,145
35,145
35,145
35,145
35,145
35,145
35,145
35,145

35,145
35,145
35,145
35,145

Distance to
bottom of
beam

1,675
277
277
252
233
224
224
210
210
210
210
210
210
210
210
210
210
210
210
210
210

Iconversion
113,514
3,634,897,381
3,634,897,381
3,710,569,052
3,780,363,267
3,803,086,186
3,803,086,186
3,853,642,198
3,853,642,198
3,853,642,198
3,853,642,198
3,853,642,198
3,853,642,198
3,853,642,198
3,853,642,198
3,853,642,198
3,853,642,198
3,853,642,198
3,853,642,198
3,853,642,198
3,853,642,198

AT THE TIME OF CONCRETING THE BRIDGE DECK
Section

0
0.025Ls
0.050Ls

0.075Ls
0.100Ls
0.125Ls
0.150Ls
0.175Ls
0.200Ls
0.225Ls
0.250Ls
0.275Ls
0.300Ls
0.325Ls
0.350Ls
0.375Ls
0.400Ls
0.425Ls
0.450Ls
0.475Ls
0.500Ls

Position

0
920
1,840
2,760
3,680
4,600
5,520
6,440
7,360

8,280
9,200
10,120
11,040
11,960
12,880
13,800
14,720
15,640
16,560
17,480
18,400

Row A

0
5
5
7
9
9
9
11
11
11
11
11
11
11
11

11
11
11
11
11
11

Row B

0
7
7
7
9
11
11
13
13
13
13
13
13
13
13
13
13
13
13
13
13

Row C

0
6
6
8
8
10
10
12
12
12
12
12
12
12
12
12
12
12
12
12
12

Row D

Row E

0

2
2
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4

Aconversion

Total

2
2
2
2
2

2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2

2
22
22
28
32
36
36
42
42
42
42
42
42

42
42
42
42
42
42
42
42

1,543
16,973
16,973
21,601
24,687
27,773
27,773
32,402
32,402
32,402
32,402
32,402
32,402
32,402
32,402
32,402
32,402
32,402
32,402
32,402
32,402

Distance to
bottom of
beam

1,675
277
277
252
233
224
224
210
210
210
210
210
210
210
210
210
210
210
210
210
210

Iconversion
96,487
3,351,119,954

3,351,119,954
3,420,861,284
3,485,192,035
3,506,125,195
3,506,125,195
3,552,711,032
3,552,711,032
3,552,711,032
3,552,711,032
3,552,711,032
3,552,711,032
3,552,711,032
3,552,711,032
3,552,711,032
3,552,711,032
3,552,711,032
3,552,711,032
3,552,711,032
3,552,711,032

Super-T 37,5m-Tendon-2/3


PERIOD OF USING
Section

0
0.025Ls
0.050Ls
0.075Ls

0.100Ls
0.125Ls
0.150Ls
0.175Ls
0.200Ls
0.225Ls
0.250Ls
0.275Ls
0.300Ls
0.325Ls
0.350Ls
0.375Ls
0.400Ls
0.425Ls
0.450Ls
0.475Ls
0.500Ls

Position

0
920
1,840
2,760
3,680
4,600
5,520
6,440
7,360
8,280

9,200
10,120
11,040
11,960
12,880
13,800
14,720
15,640
16,560
17,480
18,400

Row A

0
5
5
7
9
9
9
11
11
11
11
11
11
11
11
11

11
11
11
11
11

Row B

0
7
7
7
9
11
11
13
13
13
13
13
13
13
13
13
13
13
13
13
13

Row C

0
6
6
8
8
10
10
12
12
12
12
12
12
12
12
12
12
12
12
12
12

Row D

Row E

0
2

2
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4

Aconversion

Total

2
2
2
2
2
2

2
2
2
2
2
2
2
2
2
2
2
2
2
2
2

2
22
22
28
32
36
36
42
42
42
42
42
42
42

42
42
42
42
42
42
42

1,543
16,973
16,973
21,601
24,687
27,773
27,773
32,402
32,402
32,402
32,402
32,402
32,402
32,402
32,402
32,402
32,402
32,402
32,402
32,402
32,402

Distance to
bottom of
beam

1,675
277
277
252
233
224
224
210
210
210
210
210
210
210
210
210
210
210
210
210
210

Iconversion
96,487
3,351,119,954
3,351,119,954

3,420,861,284
3,485,192,035
3,506,125,195
3,506,125,195
3,552,711,032
3,552,711,032
3,552,711,032
3,552,711,032
3,552,711,032
3,552,711,032
3,552,711,032
3,552,711,032
3,552,711,032
3,552,711,032
3,552,711,032
3,552,711,032
3,552,711,032
3,552,711,032

Super-T 37,5m-Tendon-3/3


Bridge joint stock
company no.12

Calculation of super-t beam

Calculate by

(Shop drawing design stage)

Bui Van Duan

Da Nang priority Infrastructure Investment Project
Sub_component C12 - Khue Dong bridge
Super-T beam L=37.5m

Project
Structure

Checked by
Duong Van Chien
Date

TÍNH NỘI LỰC - COMPUTATION OF INTERNAL FORCE
I. NỘI LỰC THIẾT KẾ DO TĨNH TẢI - DESIGNED INTERNAL FORCE DUE TO DEAD LOAD

ĐAH Moment

ĐAH Shear
Table value of influence line for moment
Section
x
y
Area
(m)
(m)
(m)
(m2)
0.00

0.000
0.000
0.00
0.92
0.920
0.897
16.50
1.84
1.840
1.748
32.16
2.76
2.760
2.553
46.98
3.68
3.680
3.312
60.94
4.60
4.600
4.025
74.06
5.52
5.520
4.692
86.33
6.44
6.440
5.313

97.76
7.36
7.360
5.888
108.34
8.28
8.280
6.417
118.07
9.20
9.200
6.900
126.96
10.12
10.120
7.337
135.00
11.04
11.040
7.728
142.20
11.96
11.960
8.073
148.54
12.88
12.880
8.372
154.04
13.80

13.800
8.625
158.70
14.72
14.720
8.832
162.51
15.64
15.640
8.993
165.47
16.56
16.560
9.108
167.59
17.48
17.480
9.177
168.86
18.40
18.400
9.200
169.28

Section
(m)
0.00
0.92
1.84
2.76

3.68
4.60
5.52
6.44
7.36
8.28
9.20
10.12
11.04
11.96
12.88
13.80
14.72
15.64
16.56
17.48
18.40

Table value of influence line for shear
x
y1
y2
Area (+)
Area (+)
(m)
(m)
(m)
(m2)
(m2)
0.000

1.000
0.000
18.400
0.000
0.920
0.975
0.025
17.492
0.012
1.840
0.950
0.050
16.606
0.046
2.760
0.925
0.075
15.744
0.104
3.680
0.900
0.100
14.904
0.184
4.600
0.875
0.125
14.088
0.288
5.520

0.850
0.150
13.294
0.414
6.440
0.825
0.175
12.524
0.564
7.360
0.800
0.200
11.776
0.736
8.280
0.775
0.225
11.052
0.932
9.200
0.750
0.250
10.350
1.150
10.120
0.725
0.275
9.672
1.392
11.040

0.700
0.300
9.016
1.656
11.960
0.675
0.325
8.384
1.944
12.880
0.650
0.350
7.774
2.254
13.800
0.625
0.375
7.188
2.588
14.720
0.600
0.400
6.624
2.944
15.640
0.575
0.425
6.084
3.324
16.560

0.550
0.450
5.566
3.726
17.480
0.525
0.475
5.072
4.152
18.400
0.500
0.500
4.600
4.600

Area
(m2)
18.400
17.480
16.560
15.640
14.720
13.800
12.880
11.960
11.040
10.120
9.200
8.280
7.360

6.440
5.520
4.600
3.680
2.760
1.840
0.920
0.000

Super-T 37,5m-Loading-1/6


MÔ MEN DO TĨNH TẢI - MOMENT DUE TO DEAD LOAD
Phase I
Phase II
Section
(m)
0.00
0.92
1.84
2.76
3.68
4.60
5.52
6.44
7.36
8.28
9.20
10.12
11.04

11.96
12.88
13.80
14.72
15.64
16.56
17.48
18.40

Load of
main beam
(KNm)
0.00
302.24
588.98
860.22
1,115.95
1,356.20
1,580.94
1,790.18
1,983.92
2,162.16
2,324.91
2,472.15
2,603.89
2,720.14
2,820.89
2,906.13
2,975.88
3,030.13

3,068.88
3,092.13
3,099.87

Divided
wall
(KNm)
0.00
5.40
10.52
15.36
19.93
24.22
28.23
31.97
35.42
38.61
41.51
44.14
46.49
48.57
50.37
51.89
53.14
54.11
54.80
55.21
55.35

Remaining

forwork
(KNm)
0.00
16.52
32.18
47.00
60.98
74.11
86.39
97.82
108.41
118.15
127.04
135.08
142.28
148.64
154.14
158.80
162.61
165.57
167.69
168.96
169.38

Deck
overlay
(KNm)
0.00
68.37
133.23

194.58
252.43
306.78
357.61
404.94
448.77
489.09
525.90
559.21
589.01
615.30
638.09
657.38
673.15
685.42
694.19
699.45
701.20

Deck slab
(KNm)
0.00
204.40
398.31
581.75
754.70
917.17
1,069.16
1,210.66
1,341.69

1,462.23
1,572.29
1,671.87
1,760.97
1,839.58
1,907.71
1,965.36
2,012.53
2,049.22
2,075.42
2,091.15
2,096.39

Hand rail,
sidewalk
(KNm)
0.00
41.26
80.41
117.44
152.35
185.15
215.83
244.40
270.85
295.18
317.40
337.50
355.49
371.36

385.11
396.75
406.27
413.68
418.97
422.14
423.20

Wastewater
treatment
pipe
(KNm)
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
0.00
0.00
0.00

0.00
0.00
0.00

LỰCLCẮT DO TĨNH TẢI - SHEAR FORCE DUE TO DEAD LOAD
Phase I
Phase II
Section
(mm)
0.00
0.92
1.84
2.76
3.68
4.60
5.52
6.44
7.36
8.28
9.20
10.12
11.04
11.96
12.88
13.80
14.72
15.64
16.56
17.48
18.40

Load of
main beam
(KN)
336.94
320.10
303.25
286.40
269.55
252.71
235.86
219.01
202.17
185.32
168.47
151.62
134.78
117.93
101.08
84.24
67.39
50.54
33.69
16.85
0.00

Divided
wall
(KN)
6.02

5.72
5.41
5.11
4.81
4.51
4.21
3.91
3.61
3.31
3.01
2.71
2.41
2.11
1.80
1.50
1.20
0.90
0.60
0.30
0.00

Remaining
forwork
(KN)
18.41
17.49
16.57
15.65
14.73
13.81

12.89
11.97
11.05
10.13
9.21
8.29
7.36
6.44
5.52
4.60
3.68
2.76
1.84
0.92
0.00

Deck
overlay
(KN)
76.22
72.41
68.60
64.78
60.97
57.16
53.35
49.54
45.73
41.92
38.11

34.30
30.49
26.68
22.87
19.05
15.24
11.43
7.62
3.81
0.00

Deck slab
(KN)
227.87
216.47
205.08
193.69
182.29
170.90
159.51
148.11
136.72
125.33
113.93
102.54
91.15
79.75
68.36
56.97
45.57

34.18
22.79
11.39
0.00

Hand rail,
sidewalk
(KN)
46.00
43.70
41.40
39.10
36.80
34.50
32.20
29.90
27.60
25.30
23.00
20.70
18.40
16.10
13.80
11.50
9.20
6.90
4.60
2.30
0.00

Wastewater
treatment
pipe
(KNm)
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
0.00
0.00
0.00
0.00
0.00
0.00

Super-T 37,5m-Loading-2/6


II. NỘI LỰC THIẾT KẾ DO HOẠT TẢI - DESIGNED INTERNAL FORCE DUE TO LIVE LOAD

Section
(m)
0.00
0.92
1.84
2.76
3.68
4.60
5.52
6.44
7.36
8.28
9.20
10.12
11.04
11.96
12.88
13.80
14.72
15.64
16.56
17.48
18.40

MÔ MEN DO HOẠT TẢI - MOMENT DUE TO LIVE LOAD
Standard truck
Designed two-axle vehicle
145 KN
145 KN

35 KN
110 KN
110 KN
ΣPiyi
ΣPiyi
yi (m)
yi (m)
yi (m)
yi (m)
yi (m)
(KNm)
(KNm)
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.90
0.79
0.68
268.41
0.90
0.87
194.04
1.75
1.53
1.32
521.88

1.75
1.69
377.96
2.55
2.23
1.91
760.39
2.55
2.46
551.76
3.31
2.88
2.45
983.95
3.31
3.19
715.44
4.03
3.49
2.95
1,192.56
4.03
3.88
869.00
4.69
4.05
3.40
1,386.23
4.69
4.51

1,012.44
5.31
4.56
3.81
1,564.94
5.31
5.10
1,145.76
5.89
5.03
4.17
1,728.70
5.89
5.65
1,268.96
6.42
5.45
4.48
1,877.51
6.42
6.15
1,382.04
6.90
5.83
4.75
2,011.38
6.90
6.60
1,485.00
7.34

6.15
4.97
2,130.29
7.34
7.01
1,577.84
7.73
6.44
5.15
2,234.25
7.73
7.37
1,660.56
8.07
6.68
5.28
2,323.26
8.07
7.68
1,733.16
8.37
6.87
5.36
2,397.33
8.37
7.95
1,795.64
8.63
7.01
5.40

2,456.44
8.63
8.18
1,848.00
8.83
7.11
5.39
2,500.60
8.83
8.35
1,890.24
8.99
7.17
5.34
2,529.81
8.99
8.48
1,922.36
9.11
7.17
5.24
2,544.08
9.11
8.57
1,944.36
9.18
7.13
5.09
2,543.39
9.18

8.61
1,956.24
7.05
9.20
5.40
2,545.34
9.20
8.60
1,958.00

Load of
lane
(KNm)
0.00
153.49
299.12
436.87
566.75
688.76
802.90
909.16
1,007.55
1,098.08
1,180.73
1,255.51
1,322.42
1,381.45
1,432.62
1,475.91
1,511.33

1,538.88
1,558.56
1,570.37
1,574.30

Section
(m)
0.00
0.92
1.84
2.76
3.68
4.60
5.52
6.44
7.36
8.28
9.20
10.12
11.04
11.96
12.88
13.80
14.72
15.64
16.56
17.48
18.40

LỰC CẮT DO HOẠT TẢI - SHEAR FORCE DUE TO LIVE LOAD

Standard truck
Designed two-axle vehicle
145 KN
145 KN
35 KN
110 KN
110 KN
ΣPiyi
ΣPiyi
yi
yi
yi
yi
yi
(KN)
(KN)
1.00
0.88
0.77
299.88
1.00
0.97
216.41
0.98
0.86
0.74
291.75
0.98
0.94
210.91

0.95
0.83
0.72
283.63
0.95
0.92
205.41
0.93
0.81
0.69
275.50
0.93
0.89
199.91
0.90
0.78
0.67
267.38
0.90
0.87
194.41
0.88
0.76
0.64
259.25
0.88
0.84
188.91
0.85
0.73

0.62
251.13
0.85
0.82
183.41
0.83
0.71
0.59
243.00
0.83
0.79
177.91
0.80
0.68
0.57
234.88
0.80
0.77
172.41
0.78
0.66
0.54
226.75
0.78
0.74
166.91
0.75
0.63
0.52
218.63

0.75
0.72
161.41
0.73
0.61
0.49
210.50
0.73
0.69
155.91
0.70
0.58
0.47
202.38
0.70
0.67
150.41
0.68
0.56
0.44
194.25
0.68
0.64
144.91
0.65
0.53
0.42
186.13
0.65
0.62

139.41
0.63
0.51
0.39
178.00
0.63
0.59
133.91
0.60
0.48
0.37
169.88
0.60
0.57
128.41
0.58
0.46
0.34
161.75
0.58
0.54
122.91
0.55
0.43
0.32
153.63
0.55
0.52
117.41
0.53

0.41
0.29
145.50
0.53
0.49
111.91
0.50
0.38
0.27
137.38
0.50
0.47
106.41

Load of
lane
(KN)
171.12
162.56
154.01
145.45
136.90
128.34
119.78
111.23
102.67
94.12
85.56
77.00
68.45

59.89
51.34
42.78
34.22
25.67
17.11
8.56
0.00

Notes:

MLL+IM
(KNm)
0.00
489.01
951.46
1,387.35
1,796.69
2,179.46
2,535.68
2,865.33
3,168.43
3,444.97
3,694.95
3,918.37
4,115.23
4,285.53
4,429.27
4,546.46
4,637.08

4,701.15
4,738.65
4,749.60
4,755.97

VLL+IM
(KN)
545.97
527.25
508.54
489.83
471.12
452.41
433.69
414.98
396.27
377.56
358.84
340.13
321.42
302.71
284.00
265.28
246.57
227.86
209.15
190.43
171.72

Live load of

pedestrian
(KNm)
0.00
99.03
192.98
281.85
365.64
444.36
518.00
586.56
650.04
708.44
761.76
810.00
853.17
891.26
924.27
952.20
975.05
992.83
1,005.52
1,013.14
1,015.68

Live load of
pedestrian
(KN)
110.40
104.88
99.36

93.84
88.32
82.80
77.28
71.76
66.24
60.72
55.20
49.68
44.16
38.64
33.12
27.60
22.08
16.56
11.04
5.52
0.00

Internal force due to live load is already multiplied with impact coefficient
(impact coefficient is only applied for truck, not be applied for load of lane and pedestrian)

Super-T 37,5m-Loading-3/6


III. NỘI LỰC DẦM CHỦ - INTERNAL FORCE IN THE MAIN BEAM
Load combination at the state of strength limit I (phase I)
η{ 1.25DC}
Load combination at the state of strength limit I (phase II)
η{ 1.25DC+1.5DW+1.2P+1.75PL + 1.75(LL+IM)}

Load combination at the state of using limit
η{ DC+DW+P+PL+(LL+IM)}
Moment M(KN.m)

Section
(m)
0.00
0.92
1.84
2.76
3.68
4.60
5.52
6.44
7.36
8.28
9.20
10.12
11.04
11.96
12.88
13.80
14.72
15.64
16.56
17.48
18.40

Phase I
State of strength limit I

Exterior Intermediate
MMax
beam
beam

Phase II
State of strength limit I
State of using limit
Exterior Intermediate
Exterior Intermediate
MMax
MMax
beam
beam
beam
beam

(KNm)
0.00
403.77
786.83
1,149.19
1,490.84
1,811.79
2,112.03
2,391.56
2,650.39
2,888.51
3,105.93
3,302.63

3,478.64
3,633.93
3,768.52
3,882.41
3,975.58
4,048.06
4,099.82
4,130.88
4,141.23

(KNm)
0.00
1,528.19
2,976.53
4,345.01
5,633.64
6,842.41
7,971.33
9,020.39
9,989.60
10,878.95
11,688.44
12,418.08
13,067.86
13,637.79
14,127.86
14,538.08
14,868.44
15,118.94
15,289.59

15,380.39
15,413.38

(KNm)
0.00
403.77
786.83
1,149.19
1,490.84
1,811.79
2,112.03
2,391.56
2,650.39
2,888.51
3,105.93
3,302.63
3,478.64
3,633.93
3,768.52
3,882.41
3,975.58
4,048.06
4,099.82
4,130.88
4,141.23

(KNm)
0.00
403.77
786.83

1,149.19
1,490.84
1,811.79
2,112.03
2,391.56
2,650.39
2,888.51
3,105.93
3,302.63
3,478.64
3,633.93
3,768.52
3,882.41
3,975.58
4,048.06
4,099.82
4,130.88
4,141.23

(KNm)
0.00
1,307.25
2,545.92
3,716.03
4,817.56
5,850.53
6,814.92
7,710.74
8,537.99
9,296.67

9,986.78
10,608.32
11,161.29
11,645.69
12,061.51
12,408.77
12,687.45
12,897.56
13,039.10
13,112.07
13,139.21

(KNm)
0.00
1,528.19
2,976.53
4,345.01
5,633.64
6,842.41
7,971.33
9,020.39
9,989.60
10,878.95
11,688.44
12,418.08
13,067.86
13,637.79
14,127.86
14,538.08
14,868.44

15,118.94
15,289.59
15,380.39
15,413.38

(KNm)
0.00
1,004.24
1,956.17
2,855.79
3,703.11
4,498.11
5,240.81
5,931.20
6,569.28
7,155.05
7,688.51
8,169.67
8,598.51
8,975.05
9,299.28
9,571.20
9,790.81
9,958.12
10,073.11
10,135.80
10,158.18

(KNm)
0.00

872.21
1,698.85
2,479.93
3,215.45
3,905.41
4,549.81
5,148.64
5,701.91
6,209.61
6,671.76
7,088.34
7,459.35
7,784.81
8,064.70
8,299.03
8,487.80
8,631.01
8,728.65
8,780.73
8,799.62

(KNm)
0.00
1,004.24
1,956.17
2,855.79
3,703.11
4,498.11
5,240.81
5,931.20

6,569.28
7,155.05
7,688.51
8,169.67
8,598.51
8,975.05
9,299.28
9,571.20
9,790.81
9,958.12
10,073.11
10,135.80
10,158.18

Internal force due to live load is already multiplied with transversal distribution coefficient

Notes:

CHART BOUNDARY OF MOMENT
18,000

M(KNm)

15,000
12,000
9,000
6,000
3,000
0
0

2.5

5

7.5

10

12.5

15

17.5

20

DISTANCE FROM SUPPORT (m)
State of strength limit I(Phase 2)

State of service limit (Phase 2)

State of strength limit I(Phase 1)

Super-T 37,5m-Loading-4/6


Shearing force V(KN)

Section

(m)
0.00
0.92
1.84
2.76
3.68
4.60
5.52
6.44
7.36
8.28
9.20
10.12
11.04
11.96
12.88
13.80
14.72
15.64
16.56
17.48
18.40

Phase I
State of strength limit I
Exterior Intermediate
VMax
beam
beam
(KN)

450.13
427.63
405.12
382.61
360.11
337.60
315.09
292.59
270.08
247.57
225.07
202.56
180.05
157.55
135.04
112.53
90.03
67.52
45.01
22.51
0.00

(KN)
450.13
427.63
405.12
382.61
360.11
337.60
315.09

292.59
270.08
247.57
225.07
202.56
180.05
157.55
135.04
112.53
90.03
67.52
45.01
22.51
0.00

Phase II
State of strength limit I
State of using limit
Exterior Intermediate
Exterior Intermediate
VMax
VMax
beam
beam
beam
beam

(KN)
450.13
427.63

405.12
382.61
360.11
337.60
315.09
292.59
270.08
247.57
225.07
202.56
180.05
157.55
135.04
112.53
90.03
67.52
45.01
22.51
0.00

(KN)
1,704.48
1,627.87
1,551.26
1,474.65
1,398.05
1,321.44
1,244.83
1,168.22
1,091.61

1,015.00
938.39
861.78
785.18
708.57
631.96
555.35
478.74
402.13
325.52
248.92
172.31

(KN)
1,458.19
1,394.16
1,330.13
1,266.11
1,202.08
1,138.05
1,074.02
1,009.99
945.97
881.94
817.91
753.88
689.86
625.83
561.80
497.77

433.75
369.72
305.69
241.66
177.64

(KN)
1,704.48
1,627.87
1,551.26
1,474.65
1,398.05
1,321.44
1,244.83
1,168.22
1,091.61
1,015.00
938.39
861.78
785.18
708.57
631.96
555.35
478.74
402.13
325.52
248.92
177.64

(KN)

1,119.99
1,068.68
1,017.37
966.06
914.75
863.44
812.13
760.82
709.50
658.19
606.88
555.57
504.26
452.95
401.64
350.33
299.02
247.71
196.39
145.08
93.77

(KN)
972.81
929.01
885.20
841.39
797.59
753.78
709.97

666.16
622.36
578.55
534.74
490.94
447.13
403.32
359.52
315.71
271.90
228.09
184.29
140.48
96.67

(KN)
1,119.99
1,068.68
1,017.37
966.06
914.75
863.44
812.13
760.82
709.50
658.19
606.88
555.57
504.26
452.95

401.64
350.33
299.02
247.71
196.39
145.08
96.67

CHART BOUNDARY OF SHEAR FORCE

1,800

V(KN)

1,500
1,200
900
600
300
0
0

2.5

5

7.5

10

12.5

15

17.5

20

DISTANCE FROM SUPPORT (m)

State of strength limit I(Phase 2)

State of service limit (Phase 2)

State of strength limit I(Phase 1)

Super-T 37,5m-Loading-5/6


IV. INTERNAL FORCE IN MAIN BEAM TAKE ACCOUNT OF EFFECT OF PRESTRESSING STRAND
Load combination at the state of strength limit I (phase I)
Mgđ1= η{ 1.25DC+PS}
Load combination at the state of strength limit I (phase II)
Mgđ2= η{ 1.25DC+1.5DW+1.2P+1.75PL + 1.75(LL+IM)+PS}
Load combination at the state of using limit
Mgđ3= η{ DC+DW+P+PL+(LL+IM)+PS}
Mgđ4= η{ 0.5(DC+DW+P+PS)+PL+(LL+IM)}
Moment M(KN.m)
Phase I
State of strength limit I

Mặt cắt
(m)
0.00
0.92
1.84
2.76
3.68
4.60
5.52
6.44
7.36
8.28
9.20
10.12
11.04
11.96
12.88
13.80
14.72
15.64
16.56
17.48
18.40

MMax

Mphase1

PS

(KNm)
0.00
403.77
786.83
1,149.19
1,490.84
1,811.79
2,112.03
2,391.56
2,650.39
2,888.51
3,105.93
3,302.63
3,478.64
3,633.93
3,768.52
3,882.41
3,975.58
4,048.06
4,099.82
4,130.88
4,141.23

(KNm)
110.61
-3,056.52
-3,062.19
-3,289.35
-3,822.24
-4,307.61

-4,317.43
-5,041.94
-5,052.01
-5,061.27
-5,069.73
-5,077.37
-5,084.22
-5,090.25
-5,095.48
-5,099.91
-5,103.53
-5,106.35
-5,108.36
-5,109.56
-5,109.97

Phase II
State of using limit

State of strength limit I
MMax

(KNm)
110.61
-2,652.75
-2,275.35
-2,140.15
-2,331.39
-2,495.82
-2,205.40

-2,650.38
-2,401.62
-2,172.76
-1,963.80
-1,774.74
-1,605.58
-1,456.32
-1,326.96
-1,217.50
-1,127.94
-1,058.29
-1,008.53
-978.68
-968.73

Mphase2

PS

(KNm)
0.00
1,528.19
2,976.53
4,345.01
5,633.64
6,842.41
7,971.33
9,020.39
9,989.60
10,878.95

11,688.44
12,418.08
13,067.86
13,637.79
14,127.86
14,538.08
14,868.44
15,118.94
15,289.59
15,380.39
15,413.38

(KNm)
52.77
-3,400.94
-3,430.75
-4,432.77
-5,027.54
-5,565.42
-5,629.23
-6,353.03
-6,417.77
-6,477.33
-6,531.71
-6,580.90
-6,624.92
-6,663.76
-6,697.42
-6,725.90
-6,749.20

-6,767.32
-6,780.27
-6,788.03
-6,790.62

MMax 2

MMax 1

(KNm)
52.77
-1,872.75
-454.22
-87.75
606.10
1,277.00
2,342.10
2,667.36
3,571.83
4,401.62
5,156.73
5,837.17
6,442.94
6,974.03
7,430.44
7,812.18
8,119.24
8,351.62
8,509.33
8,592.35

8,622.76

(KNm)
0.00
1,004.24
1,956.17
2,855.79
3,703.11
4,498.11
5,240.81
5,931.20
6,569.28
7,155.05
7,688.51
8,169.67
8,598.51
8,975.05
9,299.28
9,571.20
9,790.81
9,958.12
10,073.11
10,135.80
10,158.18

PS

(KNm)
0.00
685.15

1,334.36
1,947.62
2,524.94
3,066.31
3,571.73
4,041.21
4,474.75
4,872.34
5,233.99
5,559.69
5,849.45
6,103.26
6,321.12
6,503.04
6,649.02
6,759.05
6,833.14
6,871.28
6,885.48

(KNm)
50.26
-3,238.99
-3,267.38
-4,221.68
-4,788.13
-5,300.40
-5,361.17
-6,050.50
-6,112.16

-6,168.88
-6,220.67
-6,267.53
-6,309.45
-6,346.44
-6,378.49
-6,405.62
-6,427.81
-6,445.07
-6,457.40
-6,464.80
-6,467.26

Mphase3

Mphase4

(KNm)
50.26
-2,234.75
-1,311.21
-1,365.89
-1,085.03
-802.28
-120.36
-119.30
457.12
986.17
1,467.84
1,902.14

2,289.06
2,628.61
2,920.79
3,165.58
3,363.00
3,513.05
3,615.71
3,671.00
3,690.92

(KNm)
25.13
-934.34
-299.33
-163.22
130.87
416.11
891.15
1,015.96
1,418.67
1,787.90
2,123.65
2,425.93
2,694.72
2,930.04
3,131.88
3,300.24
3,435.12
3,536.52
3,604.44

3,638.88
3,651.85

CHART BOUNDARY OF MOMENT
18,000
15,000

M(KNm)

12,000
9,000
6,000
3,000
0
-3,000

0

2.5

5

7.5

10

12.5

15

17.5

20

-6,000
DISTANCE FROM SUPPORT (m)
MPhase2 (PS)
MPhase1(PS)
State of strength limit 1(Phase1)
State of service limit (Phase2)

MPhase3 (PS)
MPhase4 (PS)
State of strength limit 1(Phase2)

Super-T 37,5m-Loading-6/6


Bridge joint stock
company no.12

Project
Structure

Calculation of super-t beam

Calculate by

(Shop drawing design stage)

Bui Van Duan
Checked by
Duong Van Chien

Da Nang priority Infrastructure Investment Project
Sub_component C12 - Khue Dong bridge
Super-T beam L=37.5m

Date

MẤT MÁT ỨNG SUẤT - LOSS STRESS
I. TỔNG MẤT MÁT ỨNG SUẤT -TOTAL OF LOSS STRESS
I.1 Total of loss stress created by:
∆fpT = ∆fpES + ∆fpSR + ∆fpCR + ∆fpR
(A.5.9.5.1-2)
Where:
∆fpT
:
Total of stress loss (Mpa)
∆fpES
:
Stress loss due to elastic shortening (Mpa)
∆fpSR
:
Stress loss due to shrinkage (Mpa)
∆fpCR
:
Stress loss due to creep (Mpa)
∆fpR
:

Stress loss due to relaxation of reinforcement (Mpa)
I.2 Stress loss due to elastic shortening
Stress loss due to elastic shortening in each tendon
∆fpES = Epfcgp/Eci
(A.5.9.5.2.3)
Where:
fcgp =
Stress in concrete at the center of tendon when force tranfer applied
and sefl load of section with maximum moment (Mpa)
fcgp =
Ep =
Eci =

(P/Ag) + (Pi*e2/Ig) - (Mg*e/Ig)
197,000 (MPa)
Elasticity modulus of tendon
32,959 (MPa)
Elasticity modulus of concrete when force transfer applied
Section
(m)
0.00
0.92
1.84
2.76
3.68
4.60
5.52
6.44
7.36
8.28

9.20
10.12
11.04
11.96
12.88
13.80
14.72
15.64
16.56
17.48
18.40

Number of
tendon
2.00
22.00
22.00
28.00
32.00
36.00
36.00
42.00
42.00
42.00
42.00
42.00
42.00
42.00
42.00
42.00

42.00
42.00
42.00
42.00
42.00

Area of
tendon
(m2)
0.00028
0.00308
0.00308
0.00392
0.00448
0.00504
0.00504
0.00588
0.00588
0.00588
0.00588
0.00588
0.00588
0.00588
0.00588
0.00588
0.00588
0.00588
0.00588
0.00588
0.00588

P
(KN)
391
4,297
4,297
5,468
6,250
7,031
7,031
8,203
8,203
8,203
8,203
8,203
8,203
8,203
8,203
8,203
8,203
8,203
8,203
8,203
8,203

fcgp
(Mpa)
0.94
6.67
6.23

13.14
15.00
16.72
16.20
19.15
18.71
18.29
17.92
17.58
17.28
17.01
16.77
16.58
16.42
16.29
16.20
16.15
16.13

∆fpES
(Mpa)
5.60
39.86
37.23
78.56
89.68
99.94
96.85
114.48
111.81

109.35
107.10
105.07
103.26
101.65
100.26
99.09
98.12
97.38
96.84
96.52
96.41

Super-T 37,5m-LossStress-1/4


I.3 Stress loss due to creep:
∆fpCR = 12*fcgp - 7*∆fcdp
(A.5.9.5.4.3)
Where:
fcgp: Stress of concrete at the center of tendon when force tranfer applied (MPa)
∆fcdp: Change of concrete stress at the center of tendon due to permanent load of each section
deduct the applied load when carrying out the prestressing
∆fcdp = - M*e/Ig
M=
(kN.m)
Moment due to formwork, bridge deck, hand rail and permanent
load at the designed sections
(m4)
Ig =

inertia moment of cross-section
e=
(m)
Distance from neutral axis to the center of tendon

Section
(m)
0.00
0.92
1.84
2.76
3.68
4.60
5.52
6.44
7.36
8.28
9.20
10.12
11.04
11.96
12.88
13.80
14.72
15.64
16.56
17.48
18.40

M

(KNm)
0.00
335.94
654.65
956.13
1,240.39
1,507.42
1,757.22
1,989.79
2,205.14
2,403.25
2,584.14
2,747.81
2,894.24
3,023.45
3,135.43
3,230.18
3,307.70
3,368.00
3,411.07
3,436.91
3,445.52

I.4 Stress loss due to shrinkage of concrete:
∆fpSR = (117-1.03*H)=
Where:
H: Surrounded relative humidity = 85 %

∆fpCR
(Mpa)

0.00
0.54
1.06
2.22
2.85
3.43
4.00
4.46
4.95
5.39
5.80
6.16
6.49
6.78
7.03
7.24
7.42
7.55
7.65
7.71
7.73

fcgp
(Mpa)
0.94
6.67
6.23
13.14
15.00
16.72

16.20
19.15
18.71
18.29
17.92
17.58
17.28
17.01
16.77
16.58
16.42
16.29
16.20
16.15
16.13

29.45 (MPa)

∆fpCR
(Mpa)
11.24
76.23
67.34
142.21
160.13
176.65
166.47
198.60
189.85
181.81

174.46
167.81
161.87
156.62
152.07
148.22
145.08
142.63
140.88
139.83
139.48

(A.5.9.5.4.2)

I.5 Stress loss due to relaxation of reinforcement:
∆fpR
= ∆fpR1 + ∆fpR2
Where:
+ ∆fpR1
: Loss due to self relaxation of reinforcement when force transfer applied (MPa)
+ ∆fpR2
: Loss due to self relaxation of reinforcement after force transfer (MPa)
I.5.1 Loss due to self relaxation of reinforcement at the time of force transfer ∆ f pR1
For the strand with low relaxation :
∆fpR1 = [log(24t)/40][f pj/fpy - 0,55]fpj
Where:
+ t : Time from apply of stress to transfer
+ fpj : Initial stress in tendon at the end of tension time
fpj = Pj/Aps - ∆fpES
+ fpy : Yield strength of tendon (MPa)

Super-T 37,5m-LossStress-2/4


Section
(m)
0.00
0.92
1.84
2.76
3.68
4.60
5.52
6.44
7.36
8.28
9.20
10.12
11.04
11.96
12.88
13.80
14.72
15.64
16.56
17.48
18.40

fpj
(Mpa)

1,389.40
1,355.14
1,357.77
1,316.44
1,305.32
1,295.06
1,298.15
1,280.52
1,283.19
1,285.65
1,287.90
1,289.93
1,291.74
1,293.35
1,294.74
1,295.91
1,296.88
1,297.62
1,298.16
1,298.48
1,298.59

fpy
(Mpa)
1,674.00
1,674.00
1,674.00
1,674.00
1,674.00
1,674.00

1,674.00
1,674.00
1,674.00
1,674.00
1,674.00
1,674.00
1,674.00
1,674.00
1,674.00
1,674.00
1,674.00
1,674.00
1,674.00
1,674.00
1,674.00

t
(date)
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00

7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00

∆fpR1
(Mpa)
21.64
19.57
19.72
17.31
16.68
16.11
16.28
15.31
15.46
15.59
15.72
15.83
15.93
16.02
16.09
16.16
16.21
16.25

16.28
16.30
16.31

I.5.2 Loss due to self relaxation of reinforcement after force transfer ∆ f pR2
∆ffpR2 = 0.3{138 - 0.4
0.4∆ffpES - 0.2(
0.2(∆ffpSR + ∆ffpCR)}
(equation 1)
∆fpES =
Loss due to elastic shortening after transfer (MPa)
∆fpSR =
Loss due to shrinkage after transfer
(MPa)
∆fpCR =
Loss due to creep after transfer
(MPa)
Section
(m)
0.00
0.92
1.84
2.76
3.68
4.60
5.52
6.44
7.36
8.28
9.20

10.12
11.04
11.96
12.88
13.80
14.72
15.64
16.56
17.48
18.40

∆fpES
(Mpa)
5.60
39.86
37.23
78.56
89.68
99.94
96.85
114.48
111.81
109.35
107.10
105.07
103.26
101.65
100.26
99.09
98.12

97.38
96.84
96.52
96.41

∆fpSR
(Mpa)
29.45
29.45
29.45
29.45
29.45
29.45
29.45
29.45
29.45
29.45
29.45
29.45
29.45
29.45
29.45
29.45
29.45
29.45
29.45
29.45
29.45

∆fpCR

(Mpa)
11.24
76.23
67.34
142.21
160.13
176.65
166.47
198.60
189.85
181.81
174.46
167.81
161.87
156.62
152.07
148.22
145.08
142.63
140.88
139.83
139.48

∆fpR2
(Mpa)
38.29
30.28
31.13
21.67
19.26

17.04
18.02
13.98
14.82
15.60
16.31
16.96
17.53
18.04
18.48
18.85
19.15
19.39
19.56
19.66
19.69

Super-T 37,5m-LossStress-3/4


I.6 Total of stress loss:
I.6.1 Total of stress loss at the time of force transfer
∆fpT1 = ∆fpES + ∆fpR1
I.6.2 Total of stress loss after force transfer
∆fpT2 = ∆fpES + ∆fpSR + ∆fpCR + ∆fpR1 + ∆fpR2
Section
(m)
0.00
0.92
1.84

2.76
3.68
4.60
5.52
6.44
7.36
8.28
9.20
10.12
11.04
11.96
12.88
13.80
14.72
15.64
16.56
17.48
18.40

Jacking
force
(KN)
391
4,297
4,297
5,468
6,250
7,031
7,031
8,203

8,203
8,203
8,203
8,203
8,203
8,203
8,203
8,203
8,203
8,203
8,203
8,203
8,203

∆fpES

∆fpCR

∆fpSR

∆fpR1

∆fpR2

∆fpT1

∆fpT2

PAll loss

(Mpa)
5.60
39.86
37.23
78.56
89.68
99.94
96.85
114.48
111.81
109.35
107.10
105.07
103.26
101.65
100.26
99.09
98.12
97.38
96.84
96.52
96.41

(Mpa)
11.24
76.23
67.34
142.21
160.13
176.65

166.47
198.60
189.85
181.81
174.46
167.81
161.87
156.62
152.07
148.22
145.08
142.63
140.88
139.83
139.48

(Mpa)
29.45
29.45
29.45
29.45
29.45
29.45
29.45
29.45
29.45
29.45
29.45
29.45
29.45

29.45
29.45
29.45
29.45
29.45
29.45
29.45
29.45

(Mpa)
21.64
19.57
19.72
17.31
16.68
16.11
16.28
15.31
15.46
15.59
15.72
15.83
15.93
16.02
16.09
16.16
16.21
16.25
16.28
16.30

16.31

(Mpa)
38.29
30.28
31.13
21.67
19.26
17.04
18.02
13.98
14.82
15.60
16.31
16.96
17.53
18.04
18.48
18.85
19.15
19.39
19.56
19.66
19.69

(Mpa)
27.24
59.42
56.95
95.87

106.37
116.05
113.14
129.79
127.27
124.94
122.82
120.90
119.18
117.67
116.36
115.25
114.34
113.63
113.13
112.82
112.72

(Mpa)
106.22
195.38
184.86
289.20
315.21
339.19
327.08
371.82
361.39
351.80
343.04

335.12
328.03
321.78
316.36
311.77
308.02
305.10
303.01
301.76
301.34

(KN)
29.74
601.76
569.38
1,133.67
1,412.15
1,709.50
1,648.49
2,186.31
2,125.00
2,068.60
2,017.10
1,970.51
1,928.82
1,892.05
1,860.17
1,833.20
1,811.13
1,793.97

1,781.71
1,774.36
1,771.91

Pafter all loss
(KN)
360.86
3,694.84
3,727.22
4,334.73
4,837.45
5,321.30
5,382.31
6,016.29
6,077.60
6,134.00
6,185.50
6,232.09
6,273.78
6,310.55
6,342.43
6,369.40
6,391.47
6,408.63
6,420.89
6,428.24
6,430.69

Prestress force before and after all losses
9,000.00

Prestress force (KN)

8,000.00
7,000.00
6,000.00
5,000.00
4,000.00
3,000.00
2,000.00
1,000.00
0.00
0.00

2.00

4.00

6.00

8.00
10.00
12.00
Distance from support (m)

P after all losses

P prestress

14.00

16.00

18.00

20.00

P all losses

Super-T 37,5m-LossStress-4/4


Bridge joint stock
company no.12

Calculation of super-t beam

Calculate by

(Shop drawing design stage)

Bui Van Duan

Da Nang priority Infrastructure Investment Project
Sub_component C12 - Khue Dong bridge
Super-T beam L=37.5m

Project
Structure

Checked by
Duong Van Chien
Date

KIỂM TRA ỨNG SUẤT DẦM CHỦ - CHECKING THE STRESS IN BEAM
I. THỜI ĐIỀM CHUYỀN LỰC SANG BÊ TÔNG - STRESS AT THE TIME OF FORCE TRANSFER
We shall check the stress of top fiber and bottom fiber of beam
Stress at top fiber of beam when force transfer applied is to be calculated as follows:
ft1 = Pworking/Agirder - Pworking*estrand1*Yt1/Igirder + Mstg1*Yt1/Igirder
Stress at bottom fiber of beam when force transfer applied is to be calculated as follows:
fb1 = Pworking/Agirder + Pworking*estrand1*Yb1/Igirder - Mstg1*Yb1/Igirder
0.5

Ultimate tensile stress when force transfer applied = - 0.58f'ci
Ultimate compressive stress when force transfer applied = 0.6f'ci
SECTION
(m)
0.00
0.92
1.84
2.76
3.68
4.60
5.52
6.44
7.36
8.28
9.20
10.12
11.04

11.96
12.88
13.80
14.72
15.64
16.56
17.48
18.40

Ptension

Pworking

Agirder

Igirder

(KN)
391
4,297
4,297
5,468
6,250
7,031
7,031
8,203
8,203
8,203
8,203
8,203

8,203
8,203
8,203
8,203
8,203
8,203
8,203
8,203
8,203

(KN)
383
4,114
4,121
5,093
5,773
6,446
6,461
7,439
7,454
7,468
7,480
7,492
7,502
7,511
7,518
7,525
7,530
7,534
7,537

7,539
7,540

(m2)

(m4)

0.945
1.689
1.689
0.715
0.719
0.722
0.722
0.727
0.727
0.727
0.727
0.727
0.727
0.727
0.727
0.727
0.727
0.727
0.727
0.727
0.727

=

=
estrand 1

0.057
0.469
0.469
0.278
0.280
0.282
0.282
0.285
0.285
0.285
0.285
0.285
0.285
0.285
0.285
0.285
0.285
0.285
0.285
0.285
0.285

(m)
-0.275
0.708
0.708
0.615

0.631
0.636
0.636
0.645
0.645
0.645
0.645
0.645
0.645
0.645
0.645
0.645
0.645
0.645
0.645
0.645
0.645

Mstg1

-3.78 (MPa)
+25.50 (MPa)

Yt1

Yb1

(KNm)
0.00
302.24

588.98
860.22
1,115.95
1,356.20
1,580.94
1,790.18
1,983.92
2,162.16
2,324.91
2,472.15
2,603.89
2,720.14
2,820.89
2,906.13
2,975.88
3,030.13
3,068.88
3,092.13
3,099.87

(m)
0.350
0.765
0.765
0.883
0.887
0.890
0.890
0.895
0.895

0.895
0.895
0.895
0.895
0.895
0.895
0.895
0.895
0.895
0.895
0.895
0.895

(m)
0.450
0.985
0.985
0.867
0.863
0.860
0.860
0.855
0.855
0.855
0.855
0.855
0.855
0.855
0.855
0.855

0.855
0.855
0.855
0.855
0.855

(Mpa)
1.06
-1.82
-1.36
-0.09
0.05
0.26
0.96
0.76
1.36
1.91
2.42
2.87
3.28
3.64
3.95
4.22
4.43
4.60
4.72
4.79
4.81

ft1

12.00

14.00

16.00

18.00

fb1
(Mpa)
-0.43
7.92
7.33
14.20
15.81
17.30
16.67
19.28
18.74
18.25
17.81
17.40
17.04
16.72
16.44
16.21
16.02
15.87
15.76

15.70
15.68

STRESS AT TRANSFER
30.00
27.00
24.00

STRESS (Mpa)

21.00
18.00
15.00
12.00
9.00
6.00
3.00
0.00
-3.00 0.00

2.00

4.00

6.00

8.00

10.00

20.00

-6.00

DISTANCE FROM SUPPORT (m)
Top fibre

Bottom fibre

Compresive stress limited

Tensile stress limited

Super-T 37,5m-StressChk-1/4