7/25/2021
DESIGN OF SHORT SPAN BRIDGE STRUCTURE
Bridge Abutment - Analysis
The Institution of Engineers, Malaysia (Kelantan Branch)
29 July 2021
By,
Muhd Salmizi Jaafar
Pengajian Kejuruteraan Awam, UiTM
1
Example
HORIZONTAL FORCES
for
Single Span Bridge - 40.0 m
1
7/25/2021
Horizontal Forces
HORIZONTAL FORCES
CREEP, SHRINKAGE & TEMPERATURE
A1
A2
L=
39.2
M
BEARING SIZE (for stiffness calculation purposes)
Shear Modulus, G =
Area of Elastomeric Bearing, A =
Thickness of elastomer;
tq fr ;
tq fx ;
900
350
7
kN/m2
x
(IRHD 60)
400
Beam Length =
CL of bearing to Beam End =
Expansion Gap =
140000 mm2
=
Thickness of Bearing =
Steel Plate Thickness =
Nos. of Steel Plate =
51 mm
3 mm
4 mm
Thickness of Bearing =
Steel Plate Thickness =
Nos. of Steel Plate =
27 mm
3 mm
2 mm
tq fr =
39
mm
tq fx =
21
mm
40
0.4
50
m
m
mm
Shear stiffness of elastomeric bearing, kb
kb = nAG/t
Kb fr = 9.00E+02
x
A = plan area of the bearing
G = Shear modulus of the elastomer
t = total thickness of the elastomer
n = number of bearing on top of the pier under consideration.
140000
1.00E-06
=
3.23
140000
1.00E-06
=
6.00
39
Kb fx = 9.00E+02
x
21
Horizontal Forces
kp is the force at the top of the pier/abutment causing translatory movement
3
a) For cantilever column,
kp = 3nEI/h
b) For built-in columns where n is the number of column in the pier;
34
E OF CONCRETE (E)
I, Moment of Inertia (mm4)
h, height of column (mm)
LOCATION
k PILE
k PIER
k BEARINGS
ko
3
kp = 12nEI/h
kN/mm2
LENGTH
=1 / S (1/k i)
A1
100
inf.
42.000
A2
100
inf.
22.615
CST
CST
TRACTION
TRACTION
MOVEMENT
FORCE
FORCE
MOVEMENT
29.577
15.056
6.745
199.502
351.074
11.870
18.444
24.144
10.817
199.502
218.926
11.870
48.02163
Expansion Length =
29.577
CST =
4.48E-04
Traction Force =
8x
FA1 =
351.074 kN
FA2 =
218.926 kN
0
+
48.0216
Temp
CS
40
+ 250
18.444
39.2
=
15.055951
1.44E-04
3.04E-04
=
570
kN
2
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Horizontal Forces
Max. Movement
Hence, Thorma Joint of
Movement
A1
=
18.615 mm
TRUE
Movement
A2
=
22.686 mm
TRUE
50
mm
movement is enough
Horizontal Forces
A1
135.376
64.126
351.074
550.576
CS
Temp
Traction
TOTAL
A2
135.376
64.126
218.926
418.428
Horizontal Forces
HORIZONTAL FORCES DUE TO CREEP, SHRINKAGE, TEMP. & TRACTION AT ABUTMENT, A1
(i) one span loaded
Description
Total
Force
(kN)
Skew angle, q =
0
Lever arm, z =
3.3
m
Longitudinal Dir.
Force (kN)
Transverse Dir.
Moment (kN.m)
Force (kN)
Moment (kN.m)
Unfactored
ULS
Unfactored
ULS
Unfactored
ULS
Unfactored
ULS
Creep &
Shrinkage
163.445
163.445
215.747
539.369
711.966
0.000
0.000
0.000
0.000
Temp.
77.421
77.421
110.712
255.489
365.350
0.000
0.000
0.000
0.000
Traction
347.046
347.046
477.188
1145.252 1574.721
0.000
0.000
0.000
0.000
587.912
803.648
1940.110 2652.037
0.000
0.000
0.000
0.000
3
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Example
CALCULATION of LOADS
for
Single Span Bridge - 40.0 m
CALCULATION OF LOADS
SINGLE SPAN BRIDGE - 40.0 M
Loads Calculation - Bottom of Pile Cap at Abutment , A1
o
Skew angle, q =
=
1) Self weight of Pile Cap and Soil
Description
Length (m)
0 0' 0''
0
Width (m) /
Depth (m)
Dia. (m)
Loads
Unfactored
(KN)
ULS
(KN)
Ecct. with respect
to the c.g. of pile
cap (m)
Moment in longitudinal
direction
Unfactored
(KN.m)
ULS
(KN.m)
Pile Cap (1)
13.480
4.800
1.500
2426.400
3069.396
0
0.000
0.000
Pile Cap (2)
13.480
0.000
0.000
0.000
0.000
0
0.000
0.000
Pile Cap (3)
13.480
0.000
0.000
0.000
0.000
0
0.000
0.000
Abutment Wall
13.480
1.500
1.800
909.900
1151.024
-0.1
-90.990
-115.102
Ballast Wall
13.480
0.400
2.325
313.410
396.464
-0.65
-203.717
-257.701
Soil (behind)
13.480
1.550
4.125
1637.567
2161.589
-1.625
-2661.047
-3512.582
Soil (front)
0.000
0.000
0.000
0.000
0.000
0
0.000
0.000
Wingwall (1)(2 nos.)
7.000
0.350
0.600
73.500
92.978
-4.35
-319.725
-404.452
Wingwall (2)(2 nos.)
7.000
3.2
0.350
1.600
196.000
247.940
-3.183
-623.868
-789.193
5556.777
7119.389
-3899.346
-5079.031
TOTAL
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CALCULATION OF LOADS
2) Loads from Superstructure
Length of Beam, L
40
m
Loads
Unit Weight
Unfactored
ULS
(KN/m3)
(KN)
(KN)
Length (m)
Area
(m2)
Beam
20
0.6811
25
3064.950
3877.162
Nos. of beam
Deck Slab
20
2.174
25
1087.200
1375.308
Slab Thickness
20
18.804
0
0.604
23
277.840
534.842
Soil on Median
0
19
0.000
0.000
Diaphragm
20.22
0.792
25
400.356
40
0.3
25
20
TOTAL
0.4645
22
Description
Wearing Course
Parapet (b/sides)
P/formwork
Deck width
9
(T10 Beam)
180
mm
12080
mm
Wearing course
50
mm
506.450
Diaphragm
400
mm
300.000
379.500
Beam depth
1980
mm
204.380
5334.726
258.541
6931.803
CALCULATION OF LOADS
3) Vertical Load due to Live Load Surcharge
For HB30 :V=
13.480
x
=
1.550
250.728
330.961
x
KN
KN
12
(unfactored)
(ULS)
Total Vertical Loads from Substructure and Superstructure (except Live Load),
S V =
=
5556.78
+
11142.23 KN
5334.726
(unfactored)
+
250.728
S V =
=
7119.39
+
14382.15 KN
6931.803
(ULS)
+
330.961
For HB45 :V=
13.480
x
=
1.550
417.880 KN
551.6016 KN
x
20
(unfactored)
(ULS)
Total Vertical Loads from Substructure and Superstructure (except Live Load),
S V =
=
5556.78
+
11309.38 KN
5334.726
(unfactored)
+
417.880
S V =
=
7119.39
+
14602.79 KN
6931.803
(ULS)
+
551.602
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CALCULATION OF LOADS
4) Live Loads - HB30
(I) Live Load Case 1 : All HA UDL and KEL
BD37/88 : Clause 3.2.9.3.1 - Carriageway Width =
13
m
Above 10.95 up to and including 14.6, number of notional lanes =
Width of notional lane =
3.250
4
m
P1
A1
3.250
b4 HA
b3 HA
3.250
KEL
b2 HA
3.250
b1 HA
Loaded span length, L =
=
39.2
40
3.250
0.4
m
CALCULATION OF LOADS
Clause 6.2.1 :Nominal uniformly distributed load (UDL), W =
336 (1/L)
0.67
=
28.377
KN/m
=
8.731
KN/m on each notional lane
2
Clause 6.4.1.1 & Table 14 : HA Lane Factors
20 < L = or < 40
HA-UDL :
==>
First lane factors, b1 =
a2 =
0.0137 [ bL (40-L) +3.65 (L-20)]
=
0.0137
=
1.0001
2nd. lane factors, b2 =
a2 =
3rd. lane factors, b3 =
0.6
4th. lane factors, b4 =
0.6a2 =
1st notional lane =
567.587
KN
2nd notional lane =
567.587
KN
3rd notional lane =
340.518
KN
4th notional lane =
340.552
KN
S HA UDL =
73.000
1.0001
0.6001
1816.245 KN
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CALCULATION OF LOADS
Clause 6.2.2 : Nominal Knife Edge Load
HA-KEL :
1st notional lane =
120.012
KN
2nd notional lane =
120.012
KN
3rd notional lane =
72.000
KN
4th notional lane =
72.0072 KN
S HA KEL =
312.024
KN
Total Vertical Live Loads =
2128.269 KN
(unfactored)
=
3511.643 KN
(ULS)
Moment due to transverse eccentrity of live load,
=
687.599
x
4.875
+
-
412.518
x
1.625
-
412.559
x
4.875
= 1787.8247 KN.m
(unfactored)
= 2949.911 KN.m
(ULS)
687.599
x
1.625
CALCULATION OF LOADS
(II) Live Load Case 2 : HB30 on 1st lane + HA UDL + KEL on others lane
Loaded Span Length, L
P1
A1
3.250
b3 HA
KEL
b2 HA
3.250
b1HA
+
+
+
+
(i)
75
1.8
75
+
+
+
+
75
6.0
HB30
+
+
+
+
3.250
+
+
+
+
3.250
75
1.8
30
RA1 =
266.327 kN
RA1
A
0.4
39.2
Total Vertical Load =
0.4
1065.306 kN (Unfactored)
1523.388 kN (ULS)
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CALCULATION OF LOADS
Clause 6.4.1.1 & Table 14 : HA Lane Factors
20 < L = or < 40 ==>First lane factors, b1 =
HA-UDL :
a2 =
0.0137 [ bL (40-L) +3.65 (L-20)]
=
0.0137
=
1.0001
2nd. lane factors, b2 =
a2 =
1.0001
3rd. lane factors, b3 =
0.6
1st notional lane =
HB30
2nd notional lane =
567.587
KN
3rd notional lane =
567.587
KN
4th notional lane =
340.518
KN
S HA UDL =
73.000
1475.692 KN
CALCULATION OF LOADS
Clause 6.2.2 : Nominal Knife Edge Load
HA-KEL :
1st notional lane =
HB30
2nd notional lane =
0.000
KN
3rd notional lane =
120.012
KN
4th notional lane =
S HA KEL =
72 KN
192.012
KN
Total Vertical Live Loads =
2733.010 KN
(unfactored)
=
4509.467 KN
(ULS)
Moment due to transverse eccentrity of live load,
= 1065.306
x
4.875
+
-
687.599
x
1.625
-
412.518
x
4.875
= 2987.3216 KN.m
(unfactored)
= 4929.081 KN.m
(ULS)
567.587
x
1.625
8
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CALCULATION OF LOADS
(III) Live Load Case 3 : HB45 on centre line of carriageway + HA UDL & KEL (one span loaded)
Loaded Span Length, L
P1
A1
3.250
b3 HA
KEL
b2 HA
+
+
+
+
+
+
HB45
+
+
+
+
+
+
3.250
+
+
+
+
3.250
b1HA
(i)
112.5
1.8
112.5
112.5
6.0
1.8
3.250
112.5
30
RA1 =
399.49 kN
RA1
A
0.4
39.2
0.4
Total Vertical Load =
1597.959 kN (Unfactored)
2285.082 kN (ULS)
CALCULATION OF LOADS
Clause 6.4.1.1 & Table 14 : HA Lane Factors
20 < L = or < 40 ==>First lane factors, b1 =
HA-UDL :
a2 =
0.0137 [ bL (40-L) +3.65 (L-20)]
=
0.0137
=
1.0001
2nd. lane factors, b2 =
a2 =
1.0001
3rd. lane factors, b3 =
0.6
1st notional lane =
567.587
2nd notional lane =
HB45
3rd notional lane =
567.587
KN
4th notional lane =
340.518
KN
S HA UDL =
73.000
KN
1475.692 KN
9
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CALCULATION OF LOADS
Clause 6.2.2 : Nominal Knife Edge Load
HA-KEL :
1st notional lane =
0.000
KN
2nd notional lane =
0.000
KN
3rd notional lane =
0.000
KN
4th notional lane =
72 KN
S HA KEL =
72.000
KN
Total Vertical Live Loads =
3145.652 KN
(unfactored)
=
5190.325 KN
(ULS)
Moment due to transverse eccentrity of live load,
=
567.587
x
4.875
+
-
567.587
x
1.625
-
412.518
x
4.875
= 2430.315 KN.m
(unfactored)
= 4010.021 KN.m
(ULS)
1597.959
x
1.625
Example
CALCULATION
of
EARTH PRESSURE
10
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EARTH PRESSURE
EARTH PRESSURE AND LIVE LOAD SURCHARGE
Pa2
H=
5.625
Pa1
L=
13.48
m
Ka = 0.333
19
g=
Live load Surcharge =
12
3
kN/m
3
kN/m
EARTH PRESSURE
Earth Pressure
Horizontal Earth Pressure (for 1m length);
= 0.5 x Ka x g x h2
=
100.095
kN/m
Horizontal Earth Pressure (for total length);
= 1349.282 kN (Unfactored)
= 2226.316 kN (ULS)
Moment at bottom of PileCap;
= Pa1 x H/3
= 2529.904 kNm (Unfactored)
= 4174.342 kNm (ULS)
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EARTH PRESSURE
Surcharge Presure
Horizontal Surcharge Pressure (for 1m length);
= Ka x q x h
= 22.478
Horizontal Surcharge Pressure (for total length);
= 302.997
kN/m
kN (Unfactored)
=
499.945
kN (ULS)
=
852.178
kNm (Unfactored)
Moment at bottom of PileCap;
= Pa1 x H/3
= 1406.094 kNm (ULS)
Total Horizontal Force
= 1652.279 kN (Unfactored)
= 2726.260 kN (ULS)
Total Bending Moment
= 3382.082 kNm (Unfactored)
= 5580.436 kNm (ULS)
EARTH PRESSURE
EARTH PRESSURE AND LIVE LOAD SURCHARGE
Pa2
H = 5.625
Pa1
L=
13.48
m
Ka = 0.333
19
g=
Live load Surcharge =
20
3
kN/m
3
kN/m
12
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EARTH PRESSURE
Earth Pressure
Horizontal Earth Pressure (for 1m length);
2
= 0.5 x Ka x g x h
=
100.095
kN/m
Horizontal Earth Pressure (for total length);
= 1349.282 kN (Unfactored)
= 2226.316 kN (ULS)
Moment at bottom of PileCap;
= Pa1 x H/3
= 2529.904 kNm (Unfactored)
= 4174.342 kNm (ULS)
EARTH PRESSURE
Surcharge Presure
Horizontal Surcharge Pressure (for 1m length);
= Ka x q x h
= 37.463
Horizontal Surcharge Pressure (for total length);
= 504.995
=
833.241
kN/m
kN (Unfactored)
kN (ULS)
Moment at bottom of PileCap;
= Pa1 x H/3
= 1420.297 kNm (Unfactored)
= 2343.490 kNm (ULS)
Total Horizontal Force
= 1854.277 kN (Unfactored)
= 3059.557 kN (ULS)
Total Bending Moment
= 3950.201 kNm (Unfactored)
= 6517.832 kNm (ULS)
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SUMMARY OF LOADS
Designed By : mizi
SUMMARY OF LOADS AND MOMENTS AT BOTTOM OF PILECAP
Description Load Cases
Case 1 : Live Load Case 1
Selfweight
Vertical, V
11142.23
Live Load
Mom. CST
Mom. Soil
Mom. SW
Mom. LL
Hor. Soil
Hor. CST
V
1940.1096
Moment, MT
0
3382.08231 -3899.34628
1652.27888
1422.846 kNm
MT
1787.825 kNm
587.912
HL
2240.191 kN
0
HT
Hor, HT
Vertical, V
14382.15
Live Load
Mom. CST
Mom. Soil
Mom. SW
Mom. LL
Hor. Soil
Hor. CST
V
2652.03734
Moment, MT
0
5580.4358 -5079.03062
2949.91069
Hor, HL
2726.26015
Selfweight
Vertical, V
11142.23
Live Load
Mom. CST
Mom. Soil
Mom. SW
Mom. LL
Hor. Soil
2949.911 kNm
HL
3529.908 kN
0
HT
Hor. CST
Moment, MT
0
3382.08231 -3899.34628
2987.32162
Hor, HL
1652.27888
Vertical, V
14382.15
Mom. CST
Mom. Soil
Mom. SW
Mom. LL
Hor. Soil
1422.846 kNm
MT
2987.322 kNm
HL
2240.191 kN
0
HT
Hor. CST
V
2652.03734
Moment, MT
0
5580.4358 -5079.03062
2726.26015
18891.620 kN
ML
3153.443 kNm
MT
4929.081 kNm
803.64768
HL
3529.908 kN
0
HT
0.000 kN
4929.08067
Hor, HL
0.000 kN
Total (ULS)
4509.46732
Moment, ML
13875.242 kN
ML
587.912
Hor, HT
Live Load
0.000 kN
Total (UNFACTORED)
V
1940.1096
Selfweight
3153.443 kNm
MT
2733.0105
Moment, ML
17893.796 kN
ML
803.64768
Hor, HT
Case 2 : Live Load Case 2
0.000 kN
Total (ULS)
3511.64323
Moment, ML
13270.500 kN
ML
1787.82466
Hor, HL
Selfweight
Total (UNFACTORED)
2128.26863
Moment, ML
Hor, HT
SUMMARY OF LOADS
Case 3 : Live Load Case 3
Selfweight
Vertical, V
11309.38
Live Load
Mom. CST
Mom. Soil
Mom. SW
Mom. LL
Hor. Soil
Hor. CST
V
1940.1096
Moment, MT
0
3950.20112 -3899.34628
1854.27668
1990.964 kNm
MT
2430.315 kNm
587.912
HL
2442.189 kN
0
HT
Hor, HT
Mom. CST
Mom. Soil
Moment, ML
2652.03734
6517.83184 -5079.03062
Moment, MT
0
Vertical, V
Hor, HL
Hor, HT
14602.79
Live Load
Mom. SW
Mom. LL
Hor. Soil
Hor. CST
0.000 kN
Total (ULS)
5190.32507
V
19793.119 kN
ML
4090.839 kNm
MT
4010.021 kNm
803.64768
HL
3863.204 kN
0
HT
0.000 kN
4010.02054
3059.55652
14455.035 kN
ML
2430.31548
Hor, HL
Selfweight
Total (UNFACTORED)
3145.65156
Moment, ML
14
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Thank You
15