Ha noi - Hai Phong Expressway Project

ABUTMENT CALCULATION
Package:
Bridge name:
Abutment Name:

EX-10
Lach Tray Bridge
A1, A2

1. MATERIALS
1.1. Material Unit Weights
• Unit Weight of Concrete
• Unit Weight of Soil
• Unit Weight of Saturated Soil
1.2. Concrete

=
=
=

10
71

13
129

γc
γs
γsw

→
→
→

f'c
=
35
Ec
= 31799
β1
=
0.80
fr =0.63√f'c
=
3.73
Reinf . Standart:
fy
=
420
Es
= 200000
Reinforcing bar Area
19
22
25
284
387
510


Compressive Strength of concrete at 28 days
Modulus of Elasticity
Stress Block Factor
Modulus of Rupture
1.3. Reinforcement
Yield strength
Modulus of elasticity
Diameter
(mm2)

2500 kg/m3
1800 kg/m3
1100 kg/m4

16
199

=
=
=

24.5 kN/m3
17.7 kN/m3
11.0 kN/m4

MPa
MPa
MPa
1
MPa

MPa
29
645

32
819

36
1006

2. LOADS FROM SUPERSTRUCTURE
ng
=
8 girders
Number of Girders
2.1. Dead load
=
16.50 m
Width of Bridge
W
Reaction due to dead load of super-T girder Span
Members
1 - Main Girder
2 - Deck Slab
3 - Diaphargms
4 - Precast plank
5 - Curbs
6 - Railing and other
7 - Surface wearing
DC

DW

Total
2.2. Live load
Vehicular live loading name
Number of lanes
Mutiple Presence Factors of Live Load

=
=

Volume
Gravity Reaction
(m3)
(kN/m3)
(kN)
220.00
24.5
2697.8
126.39
24.5
1549.9
15.00
24.5
183.9
11.40
24.5
139.8
28.73
24.5

352.2
10.0
48.10
22.6
542.7
4923.6
552.7

HL-93
4
0.650

Design Truck

Live load
Forces
0.004448
0.3048

V1 = 4.3m
35kN

P1
P2
P3

V2 = 4.3m - 9.0m
145kN

145kN


P4
P5
Wl

Design Truck
35 kN
V1
145 kN
V2
145 kN
Design Tandem
110 kN
V3
110 kN
Design Lane Load
9.3 kN/m

Wheel Spacing
4.3 m
4.3 m

1.2 m

Design Tandem
1.200m
Abutment-A1A2(OK).xls - SuperLoad

Date: 9/26/2011


Page: 1 of 3


Ha noi - Hai Phong Expressway Project

Design Tandem

Dynamic Load Allowance
Component
Deck Joint - All Limit States
All Other Components
Fatigue and Fracture Limit State
All Other Limit States

1.200m

110kN

110kN

Design Lane load

IM
75%
15%
25%

LIVE LOAD APPLYING ON SUPERSTRUCTURE

9.3 kN/m


Design Truck

P1

P2

P3

Ls

Total span length
Calculation span leng
Pedestrian load
Width of 1 sidewalk
Number of sidewalk
Pedestrian load

Lst
Ls

Wsw
nsw
Wp

= 38.300 m
= 37.600 m
=
=
=

=

R
P4

Design Tandem

P5

0.0 kN/m2
0.000 m
0.000
0.0 kN/m

R
Design Lane Load
WL

R

Reaction
Notes:

Design Truck
P2
P3
333.9
377.0

P1

70.2

Design Tandem
P4
P5
Total
365.0
286.0
651.0

Total
781.1

Lane
Load

Pedestrian

Load

454.6

0

Live
Load
1430.9

Reaction due to live load HL- 93 = max (Rtruck, Rtandem) + Rlane
Combine live load HL-93 and pedestrian for disadvantage


BR
=
211.3 KN
2.3. Braking force
2.4. Temprature Load
o
Uniform temperature change
+/-20.0
ΔT =
C
=
1.08E-5 /oC
Coefficient of thermal expansion
=
0.0081 m
Movement
Δu
=
1000 KPa
Shear Modulus of Elastomer
G
A
=
0.158
m2
Area of bearing
b
hrt
=

0.078 m
Height of bearing
H = G.A.Δu/hrt =
131.2 KN
Horizontal Force due to ΔT
2.5. Creep and Shrinkage Load
=20.2 oC
Convert to Uniform temperature change
ΔT =
=
0.0082 m
Movement
Δu
H = G.A.Δu/hrt =
132.6 KN
Horizontal Force due to ΔT
2.4. Wind Load
V = S.VB
The design wind velocity, V, shall be determined from:
VB:
where:
Basic 3 second gust wind velocity with 100 years return period appropriate to the Wind Zone
in which the bridge is located, as specified in table.
VB
Wind zone according to
TCVN 2737-1995
(m/s)
I
II
III

IV
S:

Abutment-A1A2(OK).xls - SuperLoad

38
Wind zone:
IV
VB
=
59.0 m/s
45
53
59
Correction factor for up wind terrain and deck height
S
=
67.3 m/s
V
Date: 9/26/2011

=

1.140

Page: 2 of 3


Ha noi - Hai Phong Expressway Project


2.5.1. Wind load on structures
Transverse wind load on structure
Overall width of the bridge between outer faces of parapets
b
Depth of superstructure, including solid parapets
d
Ratio
b/d
C
=
f(b/d)
Dag coefficient
d
At
Area of the structures for calculation of transverse wind load
Transverse wind load
PD = max(0.0006V 2.Cd.At,1.8At) =
FWSL = 0.25PD =
Longitudinal wind load
2.5.2. Wind load on vehicles (WL)
Transverse wind load on vehicle
Longitudinal wind load on vehicles
Vertical wind load
Area
Vertical wind load
2.6. Earthquke effects (EQ)
Acceleration coefficient
Seismic Performance Zones
Soil profile type
Site Coefficients

Response Modification Factor
For Stem wall
For Foundation
Elastic seismic response coefficient
Longitudinal Force due to Earthquake

Abutment-A1A2(OK).xls - SuperLoad

= 15.700 m
= 3.060 m
= 5.131
=
1.4
= 58.599 m2
= 222.7 KN
= 111.3 KN
=
=

28.7 KN
28.7 KN

Av

= 315.975 m2
Pv = 0.00045V .Av = 643.2 KN
2

A


S
R
R
Csm
EQ

Date: 9/26/2011

= 0.1168
2
IV
=
2
=
1.5
=
1.0
= 0.292
= 3198.1 KN

Page: 3 of 3


Ha noi - Hai Phong Expressway Project

3. STRUCTURE ANALYSIS
w

n
b3


t

Bearing Type:

b4
c

Move

G/L

g
j

d7

d4

m
d1

d6
0.5m

d2

h

b1


d2

a

d5

b2
d3

G/L
e
f
b

d
1
s1

2
s2

C.G.

3

s3
x1

4

s4

Pile Row

PILE DATA
si
No. of
Row
Piles
i
(m)
1
1.500
4
2
3
4
4.500
4
Total Piles - Np
8
x
x1
x2
Ip

3.750
2.250
2.250
40.50


m
m
m
m2

s1

x2

x

3.1. Other input Data
• Internal Friction Angle of Soil
• Friction Angle between Abutment and Backfill
• Friction Coefficient of Movable Bearing Shoes
• Acceleration Coefficient
=
• Skew angle (square bridge α = 90o)

Item
Stem Height
Footing Width
Stem Width
Footing Depth
Footing Slope
Bearing Seat Length
Ballast Wall Height
Ballast Wall Thickness
Wingwall Length

Soil Cover at Toe
Girder Reaction
Curb height
Bearing Seat Width
Shield Wall thickness

Abutment-A1A2(OK).xls - Analysis

φs
δ
frs
A
90.0 º

ABUTMENT DIMENSIONS (IN METRES)
Symbol
Value
Item
h
7.500 Horizontal Dimension
b
7.500 Horizontal Dimension
a
1.500 Horizontal Dimension
d
2.500 Horizontal Dimension
f
- Horizontal Dimension
n
1.000 Vertical Dimension

j
2.200 Vertical Dimension
t
0.500 Vertical Dimension
w
6.000 Vertical Dimension
e
0.500 Vertical Dimension
g
0.600 Vertical Dimension
c
1.200 Vertical Dimension
bb
0.600 Abutment Length
te
0.200 Wingwall Thickness
Footing length

Date: 9/26/2011

α

=
30.0 º
=
20.0 º
=
0.5
= 0.1168
= 1.571 rad


Symbol
b1
b2
b3
b4
m
d1
d2
d3
d4
d5
d6
d7
L
u
Lf

Value
2.500
3.500
3.500
2.000
0.400
2.950
4.550
1.500
2.000
0.100
1.500

16.500
0.800
16.500

Page: 1 of 13


Ha noi - Hai Phong Expressway Project

3.2. Internal Forces at Bottom Footing

Live Load
Surcharge

Loading Data:
Ht
=
10.000 m
KA
kh
kv
θ
δs
KAE

=
=
=
=
=

=

Vertical
Reaction

0.297
0.175
0.070
0.19 rad
0.35 rad
0.442

E

I
J
H

EQ, BR
D
G
X

PH2
Ht
B

F

K


+M

PV2
δ

P2

PH1
P1

0.5H

PV1
δ

+H

Ht/3
+V

A

A1

C

Sign Convention
(KA, KEA)γsHt


Live Load
Surcharge

ABUTMENT LOADS
Description

VERTICAL LOADS

Section A
Section A1
Section B
Section C
Section D
Section E
Section F
Section G
Section H
Section I
Section J
Bearing Seat
Concrete Block
Shield Wall
Curb
Railing
Total (DC)
Section A
Section A1
Section B
Section C
Section D

Section F
Section G
Section H
Section J
Total (WA)
Section F
Section G
Section H
Section K
Abutment-A1A2(OK).xls - Analysis

Area

Length

(m2)

(m)

Force

X1

(kN)
(m)
Selfweight
6.25
16.500
2529.1
1.250

3.75
16.500
1517.5
3.250
7.95
16.500
3217.1
3.250
8.75
16.500
3540.8
5.750
1.10
16.500
445.1
3.750
15.93
1.600
624.9
5.750
10.33
1.600
405.2
5.750
0.14
14.900
49.3
4.133
5.00
1.600

196.2
8.367
0.04
4.800
4.7
3.100
0.61
3.360
50.2
3.100
1.50
0.400
14.7
3.000
0.75
6.000
110.4
6.500
6.0
6.500
12525.2
Buoyancy effect on Abutment
Soil weight
15.93
14.900
4189.9
5.750
10.33
14.900
2716.6

5.750
1.25
16.500
364.2
1.250
Date: 9/26/2011

Arm 1

Arm 2

Moment
MLong

Moment
MTrans

(m)

(m)

(kN•m)

(kN•m)

2.500
0.500
0.500
-2.000
-2.000

-2.000
-0.383
-4.617
0.650
0.650
0.750
-2.750
-2.750

-

6322.9
758.7
1608.5
-7081.6
-1249.8
-810.3
-18.9
-905.8
3.1
32.6
11.0
-303.5
-16.5
-1649.5

-

-


-

-

-

-2.000
-2.000
2.500

-

-8379.9
-5433.1
910.5

-

Page: 2 of 13


Ha noi - Hai Phong Expressway Project

Total (EV)
Section F
Section G
Section H
Section K
Total (WA)
PV1

PV2
PV1-EQ
ESv

=
=
=
heq =

610 mm

LOADS

LONGITUDINAL

DC
DW
Live Load
WL
Earth Pressure (EH)
Horizontal pressure due to Surcharge
Braking force
Longitudinal wind load on Structure
Longitudinal wind load on Vehicle
Temprature Load
Earth Pressure due to EQ PH1-EQ
EQ from Superstructure
Section A
Section A1
Section B

Section C
Section D
Section E
Section F
Section G
Section H
Section I
Section J
Bearing Seat
Concrete Block
Shield Wall
Curb
Railing
Total

Abutment-A1A2(OK).xls - Analysis

6.25
3.75
7.95
8.75
1.10
15.93
10.33
0.14
5.00
0.04
0.61
1.50
0.75

-

7270.7
Buoyancy effect on Soil
16.500
1481.4
7.500
16.500
180.7
7.500
16.500
2204.7
7.500
14.900
561.7
5.750
Load from SuperStructure
4923.6
3.100
552.7
3.100
1430.9
3.100
643.2
3.100
16.500
4070.0
14.900
448.4
105.6

55.7
14.4
65.6
16.500
6057.4
1599.1
EQ from Abutment
16.500
738.5
16.500
443.1
16.500
939.4
16.500
1033.9
16.500
130.0
1.600
182.5
1.600
1.600
118.3
14.900
14.4
1.600
57.3
4.800
1.4
3.360
14.7

0.400
4.3
6.000
32.2
1.8
3711.7

Date: 9/26/2011

-12902.5

-

-

-

-3.750
-3.750
-3.750
-2.000

-

-5555.1
-677.7
-8267.6
-1123.5

0.650

0.650
0.650
0.650
3.333
5.000
7.850
7.850
7.850
7.850
3.333
7.850

-

3200.3
359.3
930.1
418.1
13566.7
2242.0
829.2
437.0
112.7
514.9
20191.2
12552.7

-

1.250

1.250
5.150
1.250
8.900
4.775
7.050
8.525
9.250
9.060
7.850
0.870
8.550
10.600
11.400

-

923.1
553.9
4837.8
1292.4
1156.8
871.3
1008.5
133.2
519.0
10.8
12.7
36.7
341.6

20.0
11718.0

-

Page: 3 of 13


Ha noi - Hai Phong Expressway Project

HORIZONTAL LOADS

Horizoltal Wind Load on Structure
Horizontal Wind Load on Vehicle
EQ form Superstructure

Notes:

Section A
Section A1
Section B
Section C
Section D
Section E
Section F
Section G
Section H
Section I
Section J
Bearing Seat

Concrete Block
Shield Wall
Curb
Railing
Total

6.25
3.75
7.95
8.75
1.10
15.93
10.33
0.14
5.00
0.04
0.61
1.50
0.75
-

222.7
28.7
479.7
EQ from Abutment
16.500
221.6
16.500
132.9
16.500

281.8
16.500
310.2
16.500
39.0
1.600
54.7
1.600
1.600
35.5
14.900
4.3
1.600
17.2
4.800
0.4
3.360
4.4
0.400
1.3
6.000
9.7
0.5
1113.5

-

-

7.850

7.800
7.800

-

1748.0
224.1
3741.8

-

-

1.250
1.250
5.150
1.250
8.900
4.775
7.050
8.525
9.250
9.060
7.850
0.870
8.550
10.600
11.400

-


276.9
166.2
1451.3
387.7
347.0
261.4
302.6
40.0
155.7
3.2
3.8
11.0
102.5
6.0
3515.4

1. Distance 'X' is measured horizontally from Toe of Abutment to C.G. of Section
2. Moment 'Arm' is measured from Pile C.G. Horizontally and from Underside of Footing Vertically

Description

SUMMARY LOADING AT FOOTING CENTER
Longitudinal
Vertical
Symbol
V
Hx
My


Seflweight of Abutment
DC of Superstructure
DW of Superstructure
Soil cover at toe
Earth Pressure
Vertical pressure due to LL surcharge
Horizontal pressure due to LL surcharge
Live Load from Superstructure
Braking Force
Longitudinal Wind Load on Superstructure
Longitudinal Wind Load on Vehicle
Horizontal Wind Load on Superstructure
Horizontal Wind Load on Vehicle
Vertical Wind Load
Temperature Load
Earth pressure due to EQ
EQ from Abutment
EQ from Superstructure
Buoyancy effect on Abutment
Buoyancy effect on Soil

Abutment-A1A2(OK).xls - Analysis

DC
DC
DW
EV
EH
ESV
ESL

LL
BR
WSL
WLL
WST
WLT
WSV
TU
EH-EQ
EQ
EQ
WA
WA

(kN)
12525
4924
553
7271
1481
562
181
1431
643
2205
-

Date: 9/26/2011

(kN)

4070
448
106
56
14
66
6057
3712
1599
-

(kN•m)
-1650
3200
359
-12902
8012
-1123
1564
930
829
437
113
418
515
11924
11718
12553
-


Transverce
Hy
(kN)
-

Mx
(kN•m)
-

223
29
1113
480
-

1748
224
3515
3742
-

Page: 4 of 13


Ha noi - Hai Phong Expressway Project

Description

Symbol


Seflweight of Abutment
DC of Superstructure
DW of Superstructure
Soil cover at toe
Earth Pressure
Vertical pressure due to LL surcharge
Horizontal pressure due to LL surcharge
Live Load from Superstructure
Braking Force
Longitudinal Wind Load on Superstructure
Longitudinal Wind Load on Vehicle
Horizontal Wind Load on Superstructure
Horizontal Wind Load on Vehicle
Vertical Wind Load
Temperature Load
Earth pressure due to EQ
EQ from Abutment
EQ from Superstructure
Buoyancy effect on Abutment
Buoyancy effect on Soil

STR-IA
1.25
1.25
1.50
1.35
1.50
1.75
1.50
1.75

1.75
0.50
1.00
1.00

DC
DC
DW
EV
EH
ESV
ESL
LL
BR
WSL
WLL
WST
WLT
WSV
TU
EH-EQ
EQ
EQ
WA
WA

LOAD FACTOR
Service
STR-IIIA STR-IIIB
SER-I

1.25
0.90
1.00
1.25
0.90
1.00
1.50
0.65
1.00
1.35
0.90
1.00
1.50
0.90
1.00
1.35
1.35
1.00
1.50
0.75
1.00
1.35
1.00
1.00
1.35
1.00
1.00
0.40
0.40
0.30

1.00
1.00
1.00
0.50
0.50
0.50
1.00
1.00
1.00
1.00
1.00
1.00

Strength
STR-IB
0.90
0.90
0.65
0.90
0.90
1.75
0.75
1.75
1.75
0.50
1.00
1.00

LOAD COMBINATIONS
Longitudinal

Load combinations
N
Hx
My
(kN)
(kN)
(kN.m)
Description
Symbol
Strength IA
STR-IA
38436
6995
793
Strength IB
STR-IB
27563
4217
-229
Strength IIIA
STR-IIIA
37639
6990
826
Strength IIIB
STR-IIIB
26265
4174
-812
Service I

SER-I
28927
4688
-279
Extreme IA
EXT-IA
35747
11645
22353
Extreme IB
EXT-IB
25898
11645
27311
Front side

Extreme
EXT-IA
1.25
1.25
1.50
1.35
0.50
0.50
0.50
0.50
1.00
1.00
1.00
1.00

1.00

EXT-IB
0.90
0.90
0.65
0.90
0.50
0.50
0.50
0.50
1.00
1.00
1.00
1.00
1.00

Transverce
Hy
Mx
(kN)
(kN.m)
0
0
0
0
0
1593
1593


0
0
0
0
0
7257
7257

Back fill side
ΣV

+M
+H
ΣM

ΣH

+V
P1, M1

Quy −íc

No.
1
2
3
4
5
6
7


Com.
STR-IA
STR-IB
STR-IIIA
STR-IIIB
SER-I
EXT-IA
EXT-IB

P1
(kN)
-23660
-16335
-23264
-15557
-17298
-28971
-24920

P3, M3

P2, M2

P4, M4

Internal Force at Head Pile
P2
P3
P4

M1
(kN)

(kN)
-

-

(kN)
-14775
-11228
-14375
-10708
-11629
-6775
-978

(kN.m)
-9599
-5860
-9587
-5861
-6517
-13794
-13279

M2

M3


M4

(kN.m)
-

(kN.m)
-

(kN.m)
-9599
-5860
-9587
-5861
-6517
-13794
-13279

Note: the above pile internal forces are taken from a 3D pile analysis software

Abutment-A1A2(OK).xls - Analysis

Date: 9/26/2011

Page: 5 of 13


Ha noi - Hai Phong Expressway Project

3.3. Section analysis
Live Load

surcharge
Vertical
Reaction
EQ, BR

A

PH2
Ht

X
P2

C

PV2
δ

PH1

D
B

P1

0.5H

PV1
δ
Ht/3


P1, M1

P2, M2

P3, M3

P4, M4

Live Load
surcharge

Internal Force at Section A-A
Area
Length
Force
Description
2
(m)
(kN)
(m )
Selfweight of Abutment
Section I
0.14
14.900
49.3
Section E
1.10
16.500
445.1

Curb
0.75
1.000
18.4
Total (DC)
494.5
Earth Pressure (EH)
16.500
197.0
Horizontal Pressure due to Surcharge
16.500
109.2
Earth Pressure due to EQ
16.500
293.2
EQ from Abutment
Section I
0.14
14.900
14.4
Section E
1.10
16.500
130.0
Curb
0.75
1.000
5.4
Total
144.4

Notes:

(KA, KEA)γsHt

X1
(m)

Arm
(m)

4.133
3.750
3.750

-0.383
-

-

0.880
1.100
0.880

-

0.750
1.100
2.800

Moment

(kN•m)
-18.9
-18.9
173.4
120.2
258.0
10.8
143.0
15.0
153.8

1. Distance 'X' is measured horizontally from Toe of Abutment to C.G. of Section
2. Moment 'Arm' is measured from Pile C.G. Horizontally and from Underside of Footing Vertically

Summary Load Combinatons at Section a-a
Longitudinal
Load Combinations
N
Hx
My
(kN)
(kN)
(kN)
Description
Symbol
Service
SER
494
306
275

Strength IA
STR-IA
618
487
447
Extreme IA
EXT-IA
618
492
448

Abutment-A1A2(OK).xls - Analysis

Date: 9/26/2011

Page: 6 of 13


Ha noi - Hai Phong Expressway Project

Internal Force at Section B-b
Description

Area

Length

LONGITUDINAL LOADS

VERTICAL LOADS


(m2)
Section B
Section D
Section E
Section I
Bearing Seat
Concrete Block
Shield Wall
Curb
Total (DC)
Section B
Section D
Total (WA)
DC of Superstructure
DW of Superstructure
Live Load
Reaction due to Vertical Wind Load
Earth Pressure (EH)
Horizontal pressure due to Surcharge
Braking force
Longitudinal wind load on Structure
Longitudinal wind load on Vehicle
Temprature Load
Earth Pressure due to EQ
EQ from Superstructure
Section B
Section D
Section E
Section F

Section G
Section H
Section I
Section J
Bearing Seat
Concrete Block
Shield Wall
Curb
Railing
Total

Abutment-A1A2(OK).xls - Analysis

Force

X1

(m)
(kN)
(m)
Selfweight of Abutment
7.95
16.500
3217.1
3.250
1.10
16.500
445.1
3.750
0.14

14.900
49.3
4.133
0.04
4.800
4.7
3.100
0.61
3.360
50.2
3.100
1.50
0.400
14.7
3.000
2.50
1.000
61.3
3.750
3842.4
Buoyancy effect on Abutment
4923.6
3.100
552.7
3.100
1430.9
3.100
643.2
3.100
16.500

2289.4
16.500
372.4
105.6
55.7
14.4
65.6
16.500
3407.3
1599.1
EQ from Abutment
7.95
16.500
939.4
1.10
16.500
130.0
15.93
1.600
182.5
10.33
1.600
118.3
0.14
14.900
14.4
5.00
1.600
57.3
0.04

4.800
1.4
0.61
3.360
14.7
1.50
0.400
4.3
0.75
6.000
32.2
1.8
1496.1

Date: 9/26/2011

Arm 1

Arm 2

Moment
MLong

Moment
MTrans

(m)

(m)


(kN•m)

(kN•m)

-0.500
-0.883
0.150
0.150
0.250
-

-

-222.6
-43.6
0.7
7.5
3.7
-254.2

-

-

-

0.150
0.150
0.150
0.150

3.000
3.750
5.350
5.350
5.350
5.350
3.000
5.350

-

738.5
82.9
214.6
96.5
6868.2
1396.5
565.1
297.8
76.8
350.9
10221.8
8555.0

-

2.650
6.400
2.275
6.025

6.750
6.560
5.350
-1.630
6.050
8.100
8.900

-

2489.4
831.9
415.1
712.8
97.2
375.8
7.4
-23.9
26.0
261.0
15.6
5208.2

-

Page: 7 of 13


Ha noi - Hai Phong Expressway Project


HORIZONTAL LOADS

Horizoltal Wind Load on Structure
Horizontal Wind Load on Vehicle
EQ form Superstructure

Notes:

Section B
Section D
Section E
Section F
Section G
Section H
Section I
Section J
Bearing Seat
Concrete Block
Shield Wall
Curb
Railing
Total

7.95
1.10
15.93
10.33
0.14
5.00
0.04

0.61
1.50
0.75
-

222.7
28.7
479.7
EQ from Abutment
16.500
281.8
16.500
39.0
1.600
54.7
1.600
1.600
35.5
14.900
4.3
1.600
17.2
4.800
0.4
14.900
19.5
0.400
1.3
6.000
9.7

463.4

-

-

5.350
5.350
5.350

-

1191.3
153.7
2566.5

-

-

2.650
6.400
2.275
6.025
6.750
6.560
5.350
-1.630
6.050
8.100

8.900

-

746.8
249.6
124.5
213.8
29.2
112.7
2.2
-31.8
7.8
78.3
1533.2

1. Distance 'X' is measured horizontally from Toe of Abutment to C.G. of Section
2. Moment 'Arm' is measured from Pile C.G. Horizontally and from Underside of Footing Vertically

Description

SUMMARY LOADING AT SECTION B-B
Longitudinal
Vertical
Symbol
V
Hx
My

Selfweight of Abutment

DC of Superstructure
DW of Superstructure
Earth Pressure
Horizontal pressure due to LL surcharge
Live Load from Superstructure
Braking Force
Longitudinal Wind Load on Superstructure
Longitudinal Wind Load on Vehicle
Horizontal Wind Load on Superstructure
Horizontal Wind Load on Vehicle
Vertical Wind Load
Temperature Load
Earth pressure due to EQ
EQ from Abutment
EQ from Superstructure
Buoyancy effect on Abutment

Abutment-A1A2(OK).xls - Analysis

DC
DC
DW
EH
ESH
LL
BR
WSL
WLL
WST
WLT

WSV
TU
EH-EQ
EQ
EQ
WA

(kN)
3842
4924
553
1431
643
-

Date: 9/26/2011

(kN)
2289
372
106
56
14
66
3407
1496
1599
-

(kN•m)

-254
739
83
6868
1397
215
565
298
77
96
351
10222
5208
8555
-

Transverse
Hy
(kN)
223
29
463
480
-

Mx
(kN•m)
1191
154
1533

2567
-

Page: 8 of 13


Ha noi - Hai Phong Expressway Project

Description

Symbol

Selfweight of Abutment
DC of Superstructure
DW of Superstructure
Earth Pressure
Horizontal pressure due to LL surcharge
Live Load from Superstructure
Braking Force
Longitudinal Wind Load on Superstructure
Longitudinal Wind Load on Vehicle
Horizontal Wind Load on Superstructure
Horizontal Wind Load on Vehicle
Vertical Wind Load
Temperature Load
Earth pressure due to EQ
EQ from Abutment
EQ from Superstructure
Buoyancy effect on Abutment


STR-IA
1.25
1.25
1.50
1.50
1.50
1.75
1.75
0.50
1.00

DC
DC
DW
EH
LLSl
LL
BR
WSL
WLL
WST
WLT
WSV
UT
EQW
EQL
EQ
WA

LOAD FACTOR

Service
STR-IIIA STR-IIIB
SER-I
1.25
0.90
1.00
1.25
0.90
1.00
1.50
0.65
1.00
1.50
0.90
1.00
1.50
0.75
1.00
1.35
1.35
1.00
1.35
1.35
1.00
0.40
0.40
0.30
1.00
1.00
1.00

0.50
0.50
0.50
1.00
1.00
1.00

Strength
STR-IB
0.90
0.90
0.65
0.90
0.75
1.75
1.75
0.50
1.00

Extreme
EXT-IA
1.25
1.25
1.50
0.50
0.50
0.50
0.50
1.00
1.00

1.00
1.00

EXT-IB
0.90
0.90
0.65
0.50
0.50
0.50
0.50
1.00
1.00
1.00
1.00

Summary Load Combinatons at Section B-b
Longitudinal
Transverse
Load Combinations
N
Hx
My
Hy
Mx
(kN)
(kN)
(kN)
(kN)
(kN.m)

Description
Symbol
Strength IA
STR-IA
14291
4210
14667
0
0
Strength IB
STR-IB
10753
2557
9259
0
0
Strength IIIA
STR-IIIA
13718
4205
14551
0
0
Strength IIIB
STR-IIIB
10180
2552
9143
0
0

Service I
SER-I
10750
2831
9953
0
0
Extreme IA
EXT-IA
12502
6769
25952
943
4100
Extreme IB
EXT-IB
8964
6769
25712
943
4100

Load
Comb.
STR-IA
STR-IB
STR-IIIA
STR-IIIB
SER-I
EXT-IA

EXT-IB
Note:

Internal Force at Section C-C
Internal Force at head pile
Sefl
P2
M1
M2
P1
weight
-23660
-16335
-23264
-15557
-17298
-28971
-24920

N/A
N/A
N/A
N/A
N/A
N/A
N/A

-9599
-5860
-9587

-5861
-6517
-13794
-13279

N/A
N/A
N/A
N/A
N/A
N/A
N/A

3161
2276
3161
2276
2529
3161
2276

Shear
(kN/m)
-20499
-14059
-20103
-13280
-14769
-25810
-22644


Moment
(kN•m)
-29307
-19350
-28900
-18572
-20653
-38814
-35354

• Self weight is included and
• Soil weight above pile cap is ignored

Abutment-A1A2(OK).xls - Analysis

Date: 9/26/2011

Page: 9 of 13


VERTICAL LOADS

Ha noi - Hai Phong Expressway Project

Notes:

Internal Force at Section D-D
Area
Length

Force
Description
(m)
(kN)
(m2)
Self weight
Section C
8.75
16.500
3540.8
Section F
15.93
1.600
624.9
Section G
Section H
10.33
1.600
405.2
Section I
0.14
14.900
49.3
Section J
5.00
1.600
196.2
Curb
0.75
6.000

110.4
Railing
6.0
Total
4932.7
Soil
Section F
15.93
14.900
4189.9
Section G
Section H
10.33
14.900
2716.6
Total
6906.5
heq =
610 mm
14.900
561.7
ESv

X1
(m)

Arm
(m)

Moment

(kN•m)

5.750
5.750
5.750
4.133
8.367
6.500
6.500

-1.750
-1.750
-1.750
-0.133
-4.367
-2.500
-2.500

-6196.4
-1093.6
-709.0
-6.6
-856.7
-275.9
-15.0
-9153.2

5.750
5.750


-1.750
-1.750

5.750

-1.750

-7332.4
-4754.0
-12086.3
-983.0

Shear
(kN/m)
1697
410
2098
931
1193

Moment
(kN•m)
-9526
-4240
-10316
-5281
-6219

1. Distance 'X' is measured horizontally from Toe of Abutment to C.G. of Section
2. Moment 'Arm' is measured from Pile C.G. Horizontally and from Underside of Footing Vertically

3. Buoyancy is ignored

Summary Internal Force at Section d-d
Internal Force at Head Pile
P3
P2
M4
M3
M2
N

Comb.
P4
STR-IA
STR-IB
STR-IIIA
STR-IIIB
SER-I

-14775
-11228
-14375
-10708
-11629

N/A
N/A
N/A
N/A
N/A


N/A
N/A
N/A
N/A
N/A

-9599
-5860
-9587
-5861
-6517

N/A
N/A
N/A
N/A
N/A

N/A
N/A
N/A
N/A
N/A

16473
11638
16473
11638
12822


M
-29478
-20836
-29478
-20836
-22960

Wing Wall Calculation
Wing Wall is modeled and Calculated by ACES5.5 program:
d4
=
1.5000 m
=
tgφ
h1
=
3.5000 m
Earth Pressure due to LL Surcharge =
h2
=
4.0000 m
b2
=
3.5000 m
b3
=
3.5000 m
b4
=

2.0000 m
E

b3

5.250
3.202 KN/m

LL Surcharge

b4

d4

h1

Ht
h2

0.5H

F

0.4Ht

b2

KAγsHt
LL Surcharge


Abutment-A1A2(OK).xls - Analysis

Date: 9/26/2011

Page: 10 of 13


Ha noi - Hai Phong Expressway Project

SERVICE – Element Moment X:

SERVICE – Element Moment Y:

Abutment-A1A2(OK).xls - Analysis

Date: 9/26/2011

Page: 11 of 13


Ha noi - Hai Phong Expressway Project

STRENGTH – Element Moment X:

STRENGTH – Element Moment Y:

Abutment-A1A2(OK).xls - Analysis

Date: 9/26/2011


Page: 12 of 13


Ha noi - Hai Phong Expressway Project

STRENGTH – Element Shear X:

STRENGTH – Element Shear Y:

Abutment-A1A2(OK).xls - Analysis

Date: 9/26/2011

Page: 13 of 13


Ha noi - Hai Phong Expressway Project

SECTION A-A CHECK
Vu
Mu
Nu
Ms

Factored Shear
Factored Moment
Factored Axial Force
Service Moment

=

=
=
=
=
=
=

500
16500
70
0
362
68
430

487
487
618
275

KN
KNm
KN
KNm

n's, D's

SECTION DIMENSIONS
h
b

d1
d2
d3
d's
de = ds

=
=
=
=

a

mm
mm
mm
mm
mm
mm
mm

A's•fy

d's
nv,Dv

0.85•f'c•a•b

h


ds

d3

As•fy

d2
d1
ns, Ds
b
REINFORCEMENT
Tension Reinforcement
ns
=
132
Ds
=
16
As
=
26268

Number (bars)
Diameter (mm)
Area (mm2)
Spacing (mm)

s

=


125

Compresion Reinf.
n's
=
66
D's
=
16
A's
=
13134
d
=
250

Resistance factor for Flexure:
Resistance factor for Shear:
Flexural Resistance
Distance from extreme compression fiber to the neutral axis:
Depth of the equivalent stress block:
Mr

Factored Flexural Resistance

=

c / de
Maximum Reinf.

=
1.2 times the cracking moment
1.33 times the factored moment
Min (1.2*Mcr or 1.33*Mu) =
Minimum Reinf.

ϕ
ϕv

=
=

c
a

=
=

Transverse Reinf.
nv
=
68
Dv
=
16
Av
=
13532
sv
=

500

0.90
0.90
28 mm
22 mm
>

4158 kN•m
0.065

<
1.2Mcr
1.33Mu

=
=

647 kN•m

<

2d's

487 kN•m

O.K.

0.42


O.K.

4158 kN•m

O.K.

2562 kNm
647 kNm
<

Control of cracking by distribution of reinforcement
Components shall be so proportioned that the tensile stress in the mild steel reinforcement at the service limit state
Z
does not exceed fsa, determined as: f =
≤ 0 .6 f y
sa
( d c A )1 / 3
n = Es/Ec
m=

nA s
bd s

=
=

0.023

m 2 + 2m =
j = (1-k/3) =


0.194
0.935

k = −m +

fs =

Abutment-A1A2(OK).xls - A-A

Ms
A s jd s

=

dc

6.290

26 Mpa

A
Z
fsa
0.6fy

Check:

Date: 9/26/2011


=
=
=
=
=

84
21000
30000
248
252

mm
mm
N/mm
Mpa
Mpa

OK

Page: 1 of 2


Ha noi - Hai Phong Expressway Project

SECTION A-A CHECK
Shear Resistance
dv
Effective Shear Depth
=

419 mm
bv
Effective Shear Width
=
16500 mm
Vu > 0.5 ϕVc
Regions requiring transverse reinforcement:
Vu
=
487
<
=
4937 KN
The norminal shear resistance, Vn, shall be determined as the lesser of: (Vn1 = Vc + Vs, Vn2 = 0.25f'cbvdv)
for which:
Vc = 0 .083 β f ' c b v d v
Vs =

A v f y d v (cot g θ + cot g α ) sin α

s
Determination of β and θ:
Angle of inclination of transverse Reinf. to longitudinal axis
α
Angle of inclination of diagonal compressive stresses
θ
vu = Vu/(ϕbvdv)
Shear stress on the concrete
Strain in the reinforcement on the flexural tension side of the member
Mu

+ 0 .5N u + 0 .5 Vu cot g θ
dv
εx =
2E s A s

Ratio
Factor β taken from Table 5.8.3.4.2-1 (AASHTO LRFD 2004)
Factor θ taken from Table 5.8.3.4.2-1 (AASHTO LRFD 2004)

Norminal Shear Resistance
Factored Shear Resistance

Vr

=

1000*εx
vu/f'c
β
θ
Vc
Vs
Vn1
Vn2
Vn

=
=
=


Date: 9/26/2011

90 0
24.3 0
78 KN/m2

=

0.00013

=
=
=
=
=
=
=
=
=

0.128
0.002
3.2
24.3
10972
10519
21492
60459
21492
>


19342 kN

b s
A v min = 0 .083 f ' c v
Minimum transverse reinforcement
fy
Maximum spacing of transverse reinforcement
If vu < 0.125f'c, then:
s ≤ 0.8dv ≤ 600mm
If vu ≥ 0.125f'c, then:
s ≤ 0.4dv ≤ 300mm
vu
=
0.08 Mpa
<
sv
<

Abutment-A1A2(OK).xls - A-A

No need

=

(Supposition)

≤

0.001


[ β = F(v/f'c, 1000*εx)]
0

kN
kN
kN
kN
kN
487 kN

9645 mm2

0.125f'c
smax

OK

=
=

O.K.
O.K.

4.38 Mpa
335 mm

O.K.

Page: 2 of 2



Ha noi - Hai Phong Expressway Project

SECTION B-B CHECK
Vu
Mu
Nu
Ms

Factored Shear
Factored Moment
Factored Axial Force
Service Moment

=
=
=
=
=
=
=

1500
16500
75
0
1355
70
1425


4210
14667
14291
9953

KN
KNm
KN
KNm

n's, D's

SECTION DIMENSIONS
h
b
d1
d2
d3
d's
de = ds

=
=
=
=

a

mm

mm
mm
mm
mm
mm
mm

A's•fy

d's
nv,Dv

0.85•f'c•a•b

h

ds

d3

As•fy

d2
d1
ns, Ds
b
REINFORCEMENT
Tension Reinforcement
ns
=

132
Ds
=
25
As
=
67320

Number (bars)
Diameter (mm)
Area (mm2)
Spacing (mm)

s

=

125

Compresion Reinf.
n's
=
66
D's
=
19
A's
=
18744
d

=
250

Resistance factor for Flexure:
Resistance factor for Shear:
Flexural Resistance
Distance from extreme compression fiber to the neutral axis:
Depth of the equivalent stress block:
Mr

Factored Flexural Resistance

=

c / de
Maximum Reinf.
=
1.2 times the cracking moment
1.33 times the factored moment
Min (1.2*Mcr or 1.33*Mu) =
Minimum Reinf.

ϕ
ϕv

=
=

c
a


=
=

0.051
1.2Mcr
1.33Mu

0.90
0.90
72 mm
58 mm
>

35529 kN•m

=
=

19507 kN•m

Transverse Reinf.
nv
=
68
Dv
=
16
Av
=

13532
sv
=
500

<

2d's

14667 kN•m

O.K.

<
0.42
23062 kNm
19507 kNm
<
35529 kN•m

O.K.

O.K.

Control of cracking by distribution of reinforcement
Components shall be so proportioned that the tensile stress in the mild steel reinforcement at the service limit state
Z
does not exceed fsa, determined as: f =
≤ 0 .6 f y
sa

( d c A )1 / 3
n = Es/Ec
m=

nA s
bd s

=
=

0.018

m 2 + 2m =
j = (1-k/3) =

0.173
0.942

k = −m +

fs =

Abutment-A1A2(OK).xls - B-B

Ms
A s jd s

=

dc


6.290

110 Mpa

A
Z
fsa
0.6fy

Check:

Date: 9/26/2011

=
=
=
=
=

89
22125
30000
240
252

mm
mm
N/mm
Mpa

Mpa

OK

Page: 1 of 2


Ha noi - Hai Phong Expressway Project

SECTION B-B CHECK
Shear Resistance
dv
Effective Shear Depth
=
1396 mm
bv
Effective Shear Width
=
16500 mm
Vu > 0.5 ϕVc
Regions requiring transverse reinforcement:
Vu
=
4210
<
=
12710 KN
The norminal shear resistance, Vn, shall be determined as the lesser of: (Vn1 = Vc + Vs, Vn2 = 0.25f'cbvdv)
for which:
Vc = 0 .083 β f ' c b v d v

Vs =

A v f y d v (cot g θ + cot g α ) sin α

s
Determination of β and θ:
Angle of inclination of transverse Reinf. to longitudinal axis
α
Angle of inclination of diagonal compressive stresses
θ
vu = Vu/(ϕbvdv)
Shear stress on the concrete
Strain in the reinforcement on the flexural tension side of the member
Mu
+ 0 .5N u + 0 .5 Vu cot g θ
dv
εx =
2E s A s

Ratio
Factor β taken from Table 5.8.3.4.2-1 (AASHTO LRFD 2004)
Factor θ taken from Table 5.8.3.4.2-1 (AASHTO LRFD 2004)

Norminal Shear Resistance
Factored Shear Resistance

Vr

=


1000*εx
vu/f'c
β
θ
Vc
Vs
Vn1
Vn2
Vn

=
=
=

Date: 9/26/2011

90 0
31.9 0
203 KN/m2

=

0.00061

=
=
=
=
=
=

=
=
=

0.611
0.006
2.5
31.9
28244
25477
53721
201576
53721
>

48349 kN

b s
A v min = 0 .083 f ' c v
Minimum transverse reinforcement
fy
Maximum spacing of transverse reinforcement
If vu < 0.125f'c, then:
s ≤ 0.8dv ≤ 600mm
If vu ≥ 0.125f'c, then:
s ≤ 0.4dv ≤ 300mm
vu
=
0.20 Mpa
<

sv
<

Abutment-A1A2(OK).xls - B-B

No need

=

(Supposition)

≤

0.001

[ β = F(v/f'c, 1000*εx)]
0

kN
kN
kN
kN
kN
4210 kN

9645 mm2

0.125f'c
smax


OK

=
=

O.K.
O.K.

4.38 Mpa
600 mm

O.K.

Page: 2 of 2


Ha noi - Hai Phong Expressway Project

SECTION C-C CHECK
Vu
Mu
Nu
Ms

Factored Shear
Factored Moment
Factored Axial Force
Service Moment

=

=
=
=
=
=
=

2500
16500
120
0
2260
120
2380

20499
29307
0
20653

KN
KNm
KN
KNm

n's, D's

SECTION DIMENSIONS
h
b

d1
d2
d3
d's
de = ds

=
=
=
=

a

mm
mm
mm
mm
mm
mm
mm

A's•fy

d's
nv,Dv

0.85•f'c•a•b

h


ds

d3

As•fy

d2
d1
ns, Ds
b
REINFORCEMENT
Tension Reinforcement
ns
=
132
Ds
=
25
As
=
67320

Number (bars)
Diameter (mm)
Area (mm2)
Spacing (mm)

s

=


125

Compresion Reinf.
n's
=
132
D's
=
22
A's
=
51084
d
=
125

Resistance factor for Flexure:
Resistance factor for Shear:
Flexural Resistance
Distance from extreme compression fiber to the neutral axis:
Depth of the equivalent stress block:
Mr

Factored Flexural Resistance

=

c / de
Maximum Reinf.

=
1.2 times the cracking moment
1.33 times the factored moment
Min (1.2*Mcr or 1.33*Mu) =
Minimum Reinf.

ϕ
ϕv

=
=

c
a

=
=

0.030
1.2Mcr
1.33Mu

0.90
0.90
72 mm
58 mm
>

59831 kN•m


=
=

38979 kN•m

Transverse Reinf.
nv
=
68
Dv
=
16
Av
=
13532
sv
=
500

<

2d's

29307 kN•m

O.K.

<
0.42
64060 kNm

38979 kNm
<
59831 kN•m

O.K.

O.K.

Control of cracking by distribution of reinforcement
Components shall be so proportioned that the tensile stress in the mild steel reinforcement at the service limit state
Z
does not exceed fsa, determined as: f =
≤ 0 .6 f y
sa
( d c A )1 / 3
n = Es/Ec
m=

nA s
bd s

=
=

0.011

m 2 + 2m =
j = (1-k/3) =

0.136

0.955

k = −m +

fs =

Abutment-A1A2(OK).xls - C-C

Ms
A s jd s

=

dc

6.290

135 Mpa

A
Z
fsa
0.6fy

Check:

Date: 9/26/2011

=
=

=
=
=

129
32125
30000
187
252

mm
mm
N/mm
Mpa
Mpa

OK

Page: 1 of 2


Ha noi - Hai Phong Expressway Project

SECTION C-C CHECK
Shear Resistance
dv
Effective Shear Depth
=
2351 mm
bv

Effective Shear Width
=
16500 mm
Vu > 0.5 ϕVc
Regions requiring transverse reinforcement:
Vu
=
20499
<
=
21404 KN
The norminal shear resistance, Vn, shall be determined as the lesser of: (Vn1 = Vc + Vs, Vn2 = 0.25f'cbvdv)
for which:
Vc = 0 .083 β f ' c b v d v
Vs =

A v f y d v (cot g θ + cot g α ) sin α

s
Determination of β and θ:
Angle of inclination of transverse Reinf. to longitudinal axis
α
Angle of inclination of diagonal compressive stresses
θ
vu = Vu/(ϕbvdv)
Shear stress on the concrete
Strain in the reinforcement on the flexural tension side of the member
Mu
+ 0 .5N u + 0 .5 Vu cot g θ
dv

εx =
2E s A s

Ratio
Factor β taken from Table 5.8.3.4.2-1 (AASHTO LRFD 2004)
Factor θ taken from Table 5.8.3.4.2-1 (AASHTO LRFD 2004)

Norminal Shear Resistance
Factored Shear Resistance

Vr

=

1000*εx
vu/f'c
β
θ
Vc
Vs
Vn1
Vn2
Vn

=
=
=

Date: 9/26/2011


90 0
31.9 0
587 KN/m2

=

0.00061

=
=
=
=
=
=
=
=
=

0.611
0.017
2.5
31.9
47565
42905
90470
339455
90470
>

81423 kN


b s
A v min = 0 .083 f ' c v
Minimum transverse reinforcement
fy
Maximum spacing of transverse reinforcement
If vu < 0.125f'c, then:
s ≤ 0.8dv ≤ 600mm
If vu ≥ 0.125f'c, then:
s ≤ 0.4dv ≤ 300mm
vu
=
0.59 Mpa
<
sv
<

Abutment-A1A2(OK).xls - C-C

No need

=

(Supposition)

≤

0.001

[ β = F(v/f'c, 1000*εx)]

0

kN
kN
kN
kN
kN
20499 kN

9645 mm2

0.125f'c
smax

OK

=
=

O.K.
O.K.

4.38 Mpa
600 mm

O.K.

Page: 2 of 2



Ha noi - Hai Phong Expressway Project

SECTION D-D CHECK
Vu
Mu
Nu
Ms

Factored Shear
Factored Moment
Factored Axial Force
Service Moment

=
=
=
=
=
=
=

2500
16500
166
0
2234
100
2334

1697

9526
0
6219

KN
KNm
KN
KNm

n's, D's

SECTION DIMENSIONS
h
b
d1
d2
d3
d's
de = ds

=
=
=
=

a

mm
mm
mm

mm
mm
mm
mm

A's•fy

d's
nv,Dv

0.85•f'c•a•b

h

ds

d3

As•fy

d2
d1
ns, Ds
b
REINFORCEMENT
Tension Reinforcement
ns
=
132
Ds

=
22
As
=
51084

Number (bars)
Diameter (mm)
Area (mm2)
Spacing (mm)

s

=

125

Compresion Reinf.
n's
=
132
D's
=
25
A's
=
67320
d
=
125


Resistance factor for Flexure:
Resistance factor for Shear:
Flexural Resistance
Distance from extreme compression fiber to the neutral axis:
Depth of the equivalent stress block:
Mr

Factored Flexural Resistance

=

c / de
Maximum Reinf.
=
1.2 times the cracking moment
1.33 times the factored moment
Min (1.2*Mcr or 1.33*Mu) =
Minimum Reinf.

ϕ
ϕv

=
=

c
a

=

=

0.90
0.90
55 mm
44 mm
>

44647 kN•m
0.023
1.2Mcr
1.33Mu

Transverse Reinf.
nv
=
68
Dv
=
16
Av
=
13532
sv
=
500

=
=


12670 kN•m

<

2d's

9526 kN•m

O.K.

<
0.42
64060 kNm
12670 kNm
<
44647 kN•m

O.K.

O.K.

Control of cracking by distribution of reinforcement
Components shall be so proportioned that the tensile stress in the mild steel reinforcement at the service limit state
Z
does not exceed fsa, determined as: f =
≤ 0 .6 f y
sa
( d c A )1 / 3
n = Es/Ec
m=


nA s
bd s

=
=

0.008

m 2 + 2m =
j = (1-k/3) =

0.121
0.960

k = −m +

fs =

Abutment-A1A2(OK).xls - D-D

Ms
A s jd s

=

dc

6.290


54 Mpa

A
Z
fsa
0.6fy

Check:

Date: 9/26/2011

=
=
=
=
=

77
19250
30000
263
252

mm
mm
N/mm
Mpa
Mpa

not.OK


Page: 1 of 2


Ha noi - Hai Phong Expressway Project

SECTION D-D CHECK
Shear Resistance
dv
Effective Shear Depth
=
2312 mm
bv
Effective Shear Width
=
16500 mm
Vu > 0.5 ϕVc
Regions requiring transverse reinforcement:
Vu
=
1697
<
=
27279 KN
The norminal shear resistance, Vn, shall be determined as the lesser of: (Vn1 = Vc + Vs, Vn2 = 0.25f'cbvdv)
for which:
Vc = 0 .083 β f ' c b v d v
Vs =

A v f y d v (cot g θ + cot g α ) sin α


s
Determination of β and θ:
Angle of inclination of transverse Reinf. to longitudinal axis
α
Angle of inclination of diagonal compressive stresses
θ
vu = Vu/(ϕbvdv)
Shear stress on the concrete
Strain in the reinforcement on the flexural tension side of the member
Mu
+ 0 .5N u + 0 .5 Vu cot g θ
dv
εx =
2E s A s

Ratio
Factor β taken from Table 5.8.3.4.2-1 (AASHTO LRFD 2004)
Factor θ taken from Table 5.8.3.4.2-1 (AASHTO LRFD 2004)

Norminal Shear Resistance
Factored Shear Resistance

Vr

=

1000*εx
vu/f'c
β

θ
Vc
Vs
Vn1
Vn2
Vn

=
=
=

Date: 9/26/2011

90 0
24.3 0
49 KN/m2

=

0.00013

=
=
=
=
=
=
=
=
=


0.127
0.001
3.2
24.3
60620
58124
118744
333816
118744
>

106870 kN

b s
A v min = 0 .083 f ' c v
Minimum transverse reinforcement
fy
Maximum spacing of transverse reinforcement
If vu < 0.125f'c, then:
s ≤ 0.8dv ≤ 600mm
If vu ≥ 0.125f'c, then:
s ≤ 0.4dv ≤ 300mm
vu
=
0.05 Mpa
<
sv
<


Abutment-A1A2(OK).xls - D-D

No need

=

(Supposition)

≤

0.001

[ β = F(v/f'c, 1000*εx)]
0

kN
kN
kN
kN
kN
1697 kN

9645 mm2

0.125f'c
smax

OK

=

=

O.K.
O.K.

4.38 Mpa
600 mm

O.K.

Page: 2 of 2


Ha noi - Hai Phong Expressway Project

SECTION E-E CHECK
Vu
Mu
Nu
Ms

Factored Shear
Factored Moment
Factored Axial Force
Service Moment

=
=
=
=

=
=
=

800
1000
71
0
659
70
729

120
180
0
115

KN
KNm
KN
KNm

n's, D's

SECTION DIMENSIONS
h
b
d1
d2
d3

d's
de = ds

=
=
=
=

a

mm
mm
mm
mm
mm
mm
mm

A's•fy

d's
nv,Dv

0.85•f'c•a•b

h

ds

d3


As•fy

d2
d1
ns, Ds
b
REINFORCEMENT
Tension Reinforcement
ns
=
8
Ds
=
22
As
=
3096

Number (bars)
Diameter (mm)
Area (mm2)
Spacing (mm)

s

=

125


Compresion Reinf.
n's
=
4
D's
=
19
A's
=
1136
d
=
250

Resistance factor for Flexure:
Resistance factor for Shear:
Flexural Resistance
Distance from extreme compression fiber to the neutral axis:
Depth of the equivalent stress block:
Mr

Factored Flexural Resistance

=

c / de
Maximum Reinf.
=
1.2 times the cracking moment
1.33 times the factored moment

Min (1.2*Mcr or 1.33*Mu) =
Minimum Reinf.

ϕ
ϕv

=
=

c
a

=
=

Transverse Reinf.
nv
=
4
Dv
=
16
Av
=
796
sv
=
500

0.90

0.90
55 mm
44 mm
>

828 kN•m
0.075

<
1.2Mcr
1.33Mu

=
=

239 kN•m

<

2d's

180 kN•m

O.K.

0.42

O.K.

398 kNm

239 kNm
828 kN•m

<

O.K.

Control of cracking by distribution of reinforcement
Components shall be so proportioned that the tensile stress in the mild steel reinforcement at the service limit state
Z
does not exceed fsa, determined as: f =
≤ 0 .6 f y
sa
( d c A )1 / 3
n = Es/Ec
m=

nA s
bd s

=
=

0.027

m 2 + 2m =
j = (1-k/3) =

0.206
0.931


k = −m +

fs =

Abutment-A1A2(OK).xls - E-E

Ms
A s jd s

=

dc

6.290

55 Mpa

A
Z
fsa
0.6fy

Check:

Date: 9/26/2011

=
=
=

=
=

87
21750
30000
243
252

mm
mm
N/mm
Mpa
Mpa

OK

Page: 1 of 2