INTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING
Volume 3, No 3, 2013
© Copyright by the authors - Licensee IPA- Under Creative Commons license 3.0
Research article
ISSN 0976 – 4399
Design coefficients for single and two cell box culvert
Sujata Shreedhar1, R.Shreedhar2
1- Assistant Professor, Maratha Mandal’s Engineering College, Belgaum, Karnataka, India
2- Associate Professor, KLS Gogte Institute of Technology, Belgaum, Karnataka, India
[email protected]
doi:10.6088/ijcser.201203013044
ABSTRACT
Multiple cell reinforced box culverts are ideal bridge structure if the discharge in a drain
crossing the road is large and if the bearing capacity of the soil is low as the single box
culvert becomes uneconomical because of the higher thickness of the slab and walls. In such
cases, more than one box can be constructed side- by- side monolithically.
The box culvert has to be analyzed for moments, shear forces and thrusts developed due to
the various loading conditions by any classical methods such as moment distribution method,
slope deflection method etc. It becomes very tedious for the designer to arrive at design
forces for various loading conditions. Hence a study is made to arrive at the coefficients for
moments, shear forces and axial thrusts for different loading cases and for different ratios of
L/H = 1.0, L/H = 1.25, L/H = 1.5, L/H = 1.75 and L/H = 2.0 for three cell box culvert.
This enables the designer to decide the combination of various loading cases to arrive at the
maximum design forces at the critical section thus saving considerable design time and effort.
Keywords: Design coefficients, single cell, two cell, culvert, moment, axial thrust, shear.
1. General
RCC box culverts comprising of top slab, base slab and stem are cast monolithically to carry
live load, embankment load, water pressure and lateral earth pressure in a better way. They
may be either single cell or multiple cells. The top of the box may be at road level or it may at
a depth below the road level if the road is in embankment. The required height and number of
boxes depends on hydraulic and other requirements at the site such as road level, nalla bed
level, scour depth etc. The barrel of the box culvert should be of sufficient length to
accommodate the carriageway and the kerbs.
1.1 Loads
The loads considered for the analysis of box culverts are Dead load, Live load, Soil pressure
on side walls, Surcharge due to live load, and Water pressure from inside.
1.2 Uniform distributed load
The weight of embankment, deck slab and the track load are considered to be uniformly
distributed loads on the top slab with the uniform soil reaction on the bottom slab. For live
load distribution, the width of dispersion perpendicular to the span is computed first. Width
of dispersion parallel to the span is also calculated. Then the maximum magnitude of load is
Received on January 2013 Published on March 2013
475
Design coefficients for single and two cell box culvert
Sujata Shreedhar, R.Shreedhar
divided by width of dispersion parallel to span and width of dispersion perpendicular to the
span to get the load intensity on the top slab.
1.3 Weight of side walls
The self weight of two side walls acting as concentrated loads are assumed to produce
uniform soil reaction on the bottom slab.
1.4 Water pressure inside culvert
The pressure distribution on side walls is assumed to be triangular with a maximum pressure
intensity of p=wh at the base, where w is the density of water and h is the depth of flow.
1.5 Earth pressure on vertical side walls
The earth pressure on the vertical side walls of the box culvert is computed according to the
Coloumb’s theory. The earth pressure intensity on the side walls is given by p=KaγH, where
Ka is coefficient of active earth pressure, γ is the density of soil and H is he vertical height of
box.
1.6 Uniform lateral load on side walls
Uniform lateral pressure on vertical side walls is considered due to the sum of effect of
embankment loading and live load surcharge. Also the uniform lateral pressure on vertical
side walls is considered due to embankment loading alone.
2. Design moments, shears and thrusts
The box culvert is analysed for moments, shear forces and axial thrusts developed at the
critical sections due to the various loading conditions by moment distribution method. The
critical sections considered are at the centre of top slab, bottom slab and vertical slab and at
the corners of top slab, bottom slab and vertical wall. The moments, shear forces and axial
thrusts at the critical sections for different loading cases are computed for different ratios of
L/H = 1.0, L/H = 1.25, L/H = 1.5, L/H = 1.75 and L/H = 2.0 for single cell and two cell box
culverts.
2.1 Design coefficients for moments, shears and thrusts
The design coefficients for moments, shear forces and axial thrusts at the critical sections for
different loading cases are computed for different ratios of L/H = 1.0, L/H = 1.25, L/H = 1.5,
L/H = 1.75 and L/H = 2.0 for single cell and two cell box culverts.
2.2 Uniform distributed load
Design coefficient for moment = M/wL2
Design coefficient for shear
= V/ wL
Design coefficient for thrust
= N /wL
where,
w is the sum of weight of embankment, deck slab and track load.
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International Journal of Civil and Structural Engineering
Volume 3 Issue 3 2013
Design coefficients for single and two cell box culvert
Sujata Shreedhar, R.Shreedhar
2.3 Weight of side walls
Design coefficient for moment = M / WL
Design coefficient for shear
=V/W
Design coefficient for thrust
=N/W
where,
W is the weight of each vertical side wall
2.4 Water pressure inside culvert
Design coefficient for moment = M / pL2
Design coefficient for shear
= V / pL
Design coefficient for thrust
= N / pL
where,
p is the maximum pressure intensity at the base which is given by wh
w is the density of water and h is the depth of flow
2.5 Earth pressure on vertical side walls
Design coefficient for moment = M / pL2
Design coefficient for shear
= V / pL
Design coefficient for thrust
= N / pL
where,
M, N, V are the moment, axial thrust and shear at the critical section
p is the earth pressure intensity which is equal to KaγH
γ is the density of soil
H is the vertical height of the box
2.6 Sign conventions
The following sign conventions are used in the analysis for moment, shear and thrust:
1. Positive moment indicates tension on inside face.
2. Positive shear indicates that the summation of force at the left of the section acts
outwards when viewed from within.
3. Positive thrust indicates compression on the section.
3. Results and discussions
The results are presented in the form of tables and graphs for the box culvert analysed for
moments, shear forces and axial thrusts developed at the critical sections due to the various
loading conditions. The critical sections considered are at the centre of top slab, bottom slab
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International Journal of Civil and Structural Engineering
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Design coefficients for single and two cell box culvert
Sujata Shreedhar, R.Shreedhar
and vertical slab and at the corners of top slab, bottom slab and vertical wall. The design
coefficients for moments, shear forces and axial thrusts at the critical sections for different
loading cases are computed for different ratios of L/H = 1.0, L/H = 1.25, L/H = 1.5, L/H =
1.75 and L/H = 2.0 for single cell and two cell box culverts.
3.1 Single cell box culvert
The results for the box culvert analysed for moments, shears, and thrusts at the critical
sections for various loading conditions are presented in tables 1 to 5 and graphs (figure no.s 2
to 7). The variation of bending moment, shear forces and thrusts for various ratios of box
culvert can be observed from the graphs plotted for various loading cases. This enables to
arrive at the design forces resulting from the combination of the various cases yielding
maximum moments and forces at the support and midspan sections. The various loading
cases are as given below:
1. Case 1: Uniform Distributed Load due to weight of embankment, deck slab and track
load
2. Case 2 : Weight of side walls
3. Case 3 : Water pressure from inside
4. Case 4 : Earth pressure on side walls
5. Case 5a : Uniform lateral earth pressure due to superimposed dead load and live load
6. Case 5b : Uniform lateral earth pressure due to superimposed dead load only
The critical sections considered for analysis of the box culvert are as shown in figure 1.
Figure 1: Critical Sections for single cell box culvert
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Design coefficients for single and two cell box culvert
Sujata Shreedhar, R.Shreedhar
Table1: Coefficients for moment, Shear and thrust for ratio 1:1
L:H
Section
B1
A2
A3
1:1
E4
D5
D6
C7
Coefficients
for
M
N
M
N
V
M
N
V
M
N
M
N
V
M
N
V
M
N
1
+0.084
0
-0.042
0
+0.500
-0.042
+0.500
0
-0.042
+0.500
-0.042
+0.500
0
-0.042
0
-0.500
+0.084
0
2
+0.021
-0.120
+0.021
-0.120
0
+0.021
0
+0.120
-0.041
+0.500
-0.103
+1.000
+0.120
-0.103
+0.120
-1.000
+0.146
+0.120
Loading Case
3
+0.019
-0.167
+0.019
-0.167
0
+0.019
0
+0.167
-0.045
0
+0.023
0
-0.333
+0.023
-0.333
0
+0.023
-0.133
4
-0.019
+0.162
-0.019
+0.162
0
-0.019
0
-0.162
+0.047
0
-0.023
0
+0.333
-0.023
+0.338
0
-0.023
+0.338
5
-0.042
+0.500
-0.042
+0.500
0
-0.042
0
-0.500
+0.083
0
-0.042
0
+0.500
-0.042
+0.500
0
-0.042
+0.500
Table 2: Coefficients for moment, Shear and thrust for ratio 1.25:1
L:H
Section
B1
A2
A3
1.25:1
E4
D5
D6
C7
Coefficients
for
M
N
M
N
V
M
N
V
M
N
M
N
V
M
N
V
M
N
1
+0.078
0
-0.047
0
+0.500
-0.047
+0.500
0
-0.047
+0.500
-0.047
+0.500
0
-0.047
0
-0.500
+0.078
0
2
+0.019
-0.170
+0.019
-0.170
0
+0.019
0
+0.170
-0.047
+0.500
-0.113
+1.000
+0.170
-0.113
+0.170
-1.000
+0.137
+0.170
Loading Case
3
+0.011
-0.133
+0.011
-0.133
0
+0.011
0
+0.133
-0.031
0
+0.013
0
-0.266
+0.013
-0.266
0
+0.013
-0.266
4
-0.011
+0.130
-0.011
+0.130
0
-0.011
0
-0.131
+0.032
0
-0.013
0
+0.269
-0.013
+0.269
0
-0.013
+0.269
5
-0.023
+0.400
-0.023
+0.400
0
-0.023
0
-0.400
+0.057
0
-0.023
0
+0.400
-0.023
+0.400
0
-0.023
+0.400
Table 3: Coefficients for moment, Shear and thrust for ratio 1.5:1
L:H
Section
B1
A2
Coefficients
for
M
N
M
N
1
+0.075
0
-0.050
0
2
+0.018
-0.210
+0.018
-0.210
Loading Case
3
+0.007
-0.111
+0.007
-0.111
4
-0.007
+0.109
-0.007
+0.109
5
-0.015
+0.333
-0.015
+0.333
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Design coefficients for single and two cell box culvert
Sujata Shreedhar, R.Shreedhar
1.5:1
A3
E4
D5
D6
C7
V
M
N
V
M
N
M
N
V
M
N
V
M
N
+0.500
-0.050
+0.500
0
-0.050
+0.500
-0.050
+0.500
0
-0.050
0
-0.500
+0.075
0
0
+0.018
0
+0.210
-0.050
+0.500
-0.118
+1.000
+0.210
-0.118
+0.210
-1.000
+0.132
+0.210
0
+0.007
0
+0.111
-0.022
0
+0.008
0
-0.222
+0.008
-0.222
0
+0.008
-0.222
0
-0.007
0
-0.109
+0.023
0
-0.008
0
+0.224
-0.008
+0.224
0
-0.008
+0.224
0
-0.015
0
-0.333
+0.041
0
-0.015
0
+0.333
-0.015
+0.333
0
-0.015
+0.333
Table 4: Coefficients for moment, Shear and thrust for ratio 1.75:1
L:H
Section
B1
A2
A3
1.75:1
E4
D5
D6
C7
Coefficients
for
M
N
M
N
V
M
N
V
M
N
M
N
V
M
N
V
M
N
1
+0.072
0
-0.053
0
+0.500
-0.053
+0.500
0
-0.053
+0.500
-0.053
+0.500
0
-0.053
0
-0.500
+0.072
0
Loading Case
2
3
4
+0.017
+0.005
-0.005
-0.250
-0.095
+0.094
+0.017
+0.005
-0.005
-0.250
-0.095
+0.094
0
0
0
+0.017
+0.005
-0.005
0
0
0
+0.250
+0.095
-0.094
-0.053
-0.017
+0.017
+0.500
0
0
-0.123
+0.005
-0.005
+1.000
0
0
+0.250
-0.131
+0.192
-0.123
+0.005
-0.005
+0.250
-0.191
+0.192
-1.000
0
0
+0.127
+0.005
-0.005
+0.250
-0.191
+0.192
5
-0.010
+0.286
-0.010
+0.286
0
-0.010
0
-0.286
+0.031
0
-0.010
0
+0.286
-0.010
+0.286
0
-0.010
+0.286
Table 5: Coefficients for moment, Shear and thrust for ratio 2:1
L:H
Section
B1
A2
A3
Coefficients
for
M
N
M
N
V
M
N
V
1
+0.069
0
-0.056
0
+0.500
-0.056
+0.500
0
2
+0.016
-0.290
+0.016
-0.290
0
+0.016
0
+0.290
Loading Case
3
+0.0032
-0.083
+0.0032
-0.083
0
+0.0032
0
+0.083
4
-0.0031
+0.082
-0.0031
+0.082
0
-0.0031
0
-0.082
5
-0.007
+0.249
-0.007
+0.249
0
-0.007
0
-0.249
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Design coefficients for single and two cell box culvert
Sujata Shreedhar, R.Shreedhar
2:1
E4
D5
D6
C7
M
N
M
N
V
M
N
V
M
N
-0.056
+0.500
-0.056
+0.500
0
-0.056
0
-0.500
+0.069
0
-0.056
+0.500
-0.127
+1.000
+0.290
-0.127
+0.290
-1.000
+0.124
+0.290
-0.013
0
+0.004
0
-0.166
+0.004
-0.166
0
+0.004
-0.166
+0.013
0
-0.004
0
+0.167
-0.004
+0.167
0
-0.004
+0.167
+0.024
0
-0.007
0
+0.249
-0.007
+0.249
0
-0.007
+0.249
Figure 2: Coefficients for BM in single cell box culvert at section B1
Figure 3: Coefficients for BM in single cell box culvert at section A2 & A3
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Design coefficients for single and two cell box culvert
Sujata Shreedhar, R.Shreedhar
Figure 4: Coefficients for BM in single cell box culvert at section C7
Figure 5: Coefficients for BM in single cell box culvert at section D5 & D6
Figure 6: Coefficients for BM in single cell box culvert at section E4
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International Journal of Civil and Structural Engineering
Volume 3 Issue 3 2013
Design coefficients for single and two cell box culvert
Sujata Shreedhar, R.Shreedhar
Figure 7: Coefficients for SF in single cell box culvert at section A3
It is seen from figure 2 that the maximum positive moment develop at the centre of top slab
when the culvert is running full and uniform lateral pressure due to superimposed dead load
only. As the span increases, there is significant contribution to positive bending moment due
to dead load and live load only as the contribution due to earth pressure becomes less
significant. The decrease in BM is about 18% due to superimposed dead load and live load on
the top slab whereas the decrease in BM due to weight of side walls is about 24%.
It is seen from figure 3 that the maximum negative moment develop at the corner of top slab
when the culvert is empty and the top slab carries the dead load and live load. The weight of
side walls decreases the net negative moment as the moment due to side walls is positive. As
the span increases, there is significant contribution to negative bending moment due to dead
load and live load only as the contribution due to earth pressure becomes less significant. The
increase in BM is about 33% due to superimposed dead load and live load on the top slab.
It is seen from figure 4 that the maximum positive moment develop at the centre of bottom
slab when the culvert is running full and uniform lateral pressure due to superimposed dead
load only. As the span increases, there is significant contribution to positive bending moment
due to dead load and live load only as the contribution due to earth pressure becomes less
significant. The decrease in BM is about 18% due to superimposed dead load and live load on
the top slab whereas the decrease in BM due to weight of side walls is about 15%.
It is seen from figure 5 that the maximum negative moment develop at the corner of bottom
slab when the culvert is empty and the top slab carries the dead load and live load. There is
significant contribution to maximum negative moment due to weight of side walls. As the
span increases, there is contribution to negative bending moment due to dead load and live
load only as the contribution due to earth pressure becomes less significant. The increase in
BM is about 25% due to superimposed dead load and live load on the top slab and due to
weight of side walls.
It is seen from figure 6 that the maximum negative moment develop at the centre of vertical
wall when the culvert is running full and when uniform lateral pressure due to superimposed
dead load acts only. As the span increases, there is significant contribution to negative
bending moment due to dead load and live load only as the contribution due to water pressure
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International Journal of Civil and Structural Engineering
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Design coefficients for single and two cell box culvert
Sujata Shreedhar, R.Shreedhar
becomes less significant. The increase in BM is about 37% due to superimposed dead load
and live load on the top slab.
As seen in figures 7 and 8, the maximum positive shear occurs at the bottom of vertical wall
and maximum negative shear occurs at the top of vertical wall when the culvert is empty.
3.2 Two cell box culvert
The results for the box culvert analysed for moments, shears, and thrusts at the critical
sections for various loading conditions are presented in tables 6 to 10 and graphs (figure no.s
9 to 21). The variation of bending moment, shear forces and thrusts for various ratios of box
culvert can be observed from the graphs plotted for various loading cases. This enables the
designer to arrive at the design forces resulting from the combination of the various cases
yielding maximum moments and forces at the support and midspan sections.
The critical sections considered for analysis of the box culvert are as shown in figure 5.
Figure 5: Critical Sections for two celled box culvert
Table 6: Coefficients for Moment, Shear and Thrust in two celled box culvert for ratio 1:1
L:H
Section
B1
A2
A3
E4
D5
D6
C7
Coefficients
for
M
N
M
N
V
M
N
V
M
N
M
N
V
M
N
V
M
1
+0.059
0
-0.028
0
+0.417
-0.028
+0.417
0
-0.028
+0.417
-0.028
+0.417
0
-0.028
0
-0.417
+0.059
2
+0.004
-0.075
+0.017
-0.075
-0.025
+0.017
-0.352
+0.075
-0.021
+0.148
-0.058
+0.648
+0.075
-0.058
+0.075
-0.648
-0.021
Loading Case
3
+0.006
-0.160
+0.024
-0.160
-0.037
0.024
-0.037
+0.160
-0.036
-0.037
0.031
-0.047
-0.340
+0.031
-0.340
+0.047
+0.008
4
-0.006
+0.160
-0.024
+0.160
+0.037
-0.024
+0.037
-0.160
+0.036
+0.037
-0.031
+0.047
+0.340
-0.031
+0.340
-0.047
-0.008
5
-0.014
+0.500
-0.056
+0.500
+0.083
-0.056
+0.083
-0.500
+0.069
+0.083
-0.056
+0.083
+0.500
-0.056
+0.500
-0.083
-0.014
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Design coefficients for single and two cell box culvert
Sujata Shreedhar, R.Shreedhar
1:1
F8
F9
G10
H11
H12
N
M
N
V
N
N
N
M
N
V
0
-0.111
0
+0.583
+1.167
+1.167
+1.167
-0.111
0
-0.583
+0.075
-0.158
+0.075
+0.852
+1.704
+1.204
+0.704
-0.008
-0.075
-0.025
-0.340
-0.016
-0.340
+0.047
+0.093
+0.093
+0.073
-0.012
-0.160
-0.037
+0.340
+0.016
+0.340
-0.047
-0.093
-0.093
-0.073
+0.012
+0.160
+0.037
+0.500
+0.028
+0.500
-0.083
-0.167
-0.167
-0.167
+0.028
+0.500
+0.083
Table 7: Coefficients for moment, Shear and thrust in two celled box culvert for ratio 1.25:1
L:H
Section
B1
A2
A3
E4
D5
1.25:1
D6
C7
F8
F9
G10
H11
H12
Coefficients
for
M
N
M
N
V
M
N
V
M
N
M
N
V
M
N
V
M
N
M
N
V
N
N
N
M
N
V
1
+0.057
0
-0.032
0
+0.424
-0.032
+0.424
0
-0.032
+0.424
-0.032
+0.424
0
-0.032
0
-0.424
+0.057
0
-0.109
0
+0.576
+1.153
+1.153
+1.167
-0.109
0
-0.576
2
+0.006
-0.109
+0.021
-0.109
-0.029
+0.021
-0.361
+0.139
-0.023
+0.139
-0.066
+0.639
+0.109
-0.066
+0.109
-0.639
-0.023
+0.109
-0.162
+0.109
+0.861
+1.721
+0.721
+0.704
-0.009
-0.109
-0.029
Loading Case
3
+0.004
-0.129
+0.014
-0.129
-0.022
0.014
-0.022
+0.129
-0.024
-0.022
0.018
-0.027
-0.271
+0.018
-0.271
+0.027
+0.005
-0.271
-0.009
-0.271
+0.027
+0.054
+0.043
+0.073
-0.007
-0.129
-0.022
4
-0.004
+0.129
-0.014
+0.129
+0.022
-0.014
+0.022
-0.129
+0.024
+0.022
-0.018
+0.027
+0.271
-0.018
+0.271
-0.027
-0.005
+0.271
+0.009
+0.271
-0.027
-0.054
-0.054
-0.043
+0.007
+0.129
+0.022
5
-0.008
+0.400
-0.033
+0.400
+0.049
-0.033
+0.049
-0.400
+0.047
+0.049
-0.033
+0.049
+0.400
-0.033
+0.400
-0.049
-0.008
+0.400
+0.016
+0.400
-0.049
-0.098
-0.098
-0.098
+0.016
+0.400
+0.049
Table 8: Coefficients for moment, Shear and thrust in two celled box culvert for ratio 1.5:1
L:H
Section
B1
A2
Coefficients
for
M
N
M
N
V
1
+0.056
0
-0.036
0
+0.429
2
+0.007
-0.143
+0.024
-0.143
-0.033
Loading Case
3
+0.002
-0.107
+0.009
-0.107
-0.014
4
-0.002
+0.107
-0.009
+0.107
+0.014
5
-0.005
+0.333
-0.021
+0.333
+0.032
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Design coefficients for single and two cell box culvert
Sujata Shreedhar, R.Shreedhar
1.5:1
A3
E4
D5
D6
C7
F8
F9
G10
H11
H12
M
N
V
M
N
M
N
V
M
N
V
M
N
M
N
V
N
N
N
M
N
V
-0.036
+0.429
0
-0.036
+0.429
-0.036
+0.429
0
-0.036
0
-0.429
+0.056
0
-0.107
0
+0.571
+1.143
+1.143
+1.143
-0.107
0
-0.571
+0.024
-0.369
+0.143
-0.024
+0.131
-0.072
+0.631
+0.143
-0.072
+0.143
-0.631
-0.024
+0.143
-0.165
+0.143
+0.869
+1.738
+1.238
+0.738
-0.009
-0.143
-0.033
0.009
-0.014
+0.107
-0.018
-0.014
0.012
-0.018
-0.225
+0.012
-0.225
+0.018
+0.003
-0.225
-0.006
-0.225
+0.018
+0.035
+0.035
+0.028
-0.005
-0.107
-0.014
-0.009
+0.014
-0.107
+0.018
+0.014
-0.012
+0.018
+0.225
-0.012
+0.225
-0.018
-0.003
+0.225
+0.006
+0.225
-0.018
-0.035
-0.035
-0.028
+0.005
+0.107
+0.014
-0.021
+0.032
-0.333
+0.034
+0.032
-0.021
+0.032
+0.333
-0.021
+0.333
-0.032
-0.005
+0.333
+0.011
+0.333
-0.032
-0.063
-0.063
-0.063
+0.011
+0.333
+0.032
Table 9: Coefficients for Moment, Shear and thrust in two celled box culvert for ratio 1.75:1
L:H
Section
B1
A2
A3
E4
D5
1.75:1
D6
C7
F8
F9
G10
H11
H12
Coefficients
for
M
N
M
N
V
M
N
V
M
N
M
N
V
M
N
V
M
N
M
N
V
N
N
N
M
1
+0.055
0
-0.039
0
+0.434
-0.039
+0.434
0
-0.039
+0.434
-0.039
+0.434
0
-0.039
0
-0.434
+0.055
0
-0.105
0
+0.566
+1.133
+1.133
+1.133
-0.105
2
+0.008
-0.182
+0.027
-0.182
-0.037
+0.027
-0.378
+0.182
-0.025
+0.122
-0.077
+0.622
+0.182
-0.077
+0.182
-0.622
-0.025
+0.182
-0.168
+0.182
+0.878
+1.757
+1.257
+0.757
-0.010
Loading Case
3
+0.002
-0.093
+0.006
-0.093
-0.010
0.006
-0.010
+0.093
-0.014
-0.010
0.008
-0.012
-0.193
+0.008
-0.193
+0.012
+0.002
-0.193
-0.004
-0.193
+0.012
+0.024
+0.024
+0.019
-0.003
4
-0.002
+0.093
-0.006
+0.093
+0.010
-0.006
+0.010
-0.093
+0.014
+0.010
-0.008
+0.012
+0.193
-0.008
+0.193
-0.012
-0.002
+0.193
+0.004
+0.193
-0.012
-0.024
-0.024
-0.019
+0.003
5
-0.004
+0.286
-0.014
+0.286
+0.022
-0.014
+0.022
-0.286
+0.026
+0.022
-0.014
+0.022
+0.286
-0.014
+0.286
-0.022
-0.004
+0.286
+0.007
+0.286
-0.022
-0.043
-0.043
-0.043
+0.007
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Design coefficients for single and two cell box culvert
Sujata Shreedhar, R.Shreedhar
N
V
0
-0.566
-0.182
-0.037
-0.093
-0.010
+0.093
+0.010
+0.286
+0.022
Table 10: Coefficients for Moment, Shear and thrust in two celled box culvert for ratio 2:1
L:H
Section
B1
A2
A3
E4
D5
2:1
D6
C7
F8
F9
G10
H11
H12
Coefficients
for
M
N
M
N
V
M
N
V
M
N
M
N
V
M
N
V
M
N
M
N
V
N
N
N
M
N
V
1
+0.054
0
-0.042
0
+0.438
-0.042
+0.438
0
-0.042
+0.438
-0.042
+0.438
0
-0.042
0
-0.438
+0.054
0
-0.104
0
+0.562
+1.124
+1.124
+1.124
-0.104
0
-0.562
2
+0.010
-0.122
+0.029
-0.122
-0.039
+0.029
-0.383
+0.222
-0.026
+0.117
-0.081
+0.617
+0.122
-0.081
+0.222
-0.617
-0.026
+0.122
-0.170
+0.122
+0.883
+1.766
+1.266
+0.766
-0.010
-0.222
-0.039
Loading Case
3
+0.001
-0.081
+0.005
-0.081
-0.007
0.005
-0.007
+0.081
-0.012
-0.007
0.006
-0.008
-0.168
+0.006
-0.168
+0.008
+0.001
-0.168
-0.003
-0.168
+0.008
+0.017
+0.017
+0.014
-0.002
-0.081
-0.007
4
-0.001
+0.081
-0.005
+0.081
+0.007
-0.005
+0.007
-0.081
+0.012
+0.007
-0.006
+0.008
+0.168
-0.006
+0.168
-0.008
-0.001
+0.168
+0.003
+0.168
-0.008
-0.017
-0.017
-0.014
+0.002
+0.081
+0.007
5
-0.003
+0.249
-0.010
+0.249
+0.015
-0.010
+0.015
-0.249
+0.021
+0.015
-0.010
+0.015
+0.249
-0.010
+0.249
-0.015
-0.003
+0.249
+0.005
+0.249
-0.015
-0.031
-0.031
-0.031
+0.005
+0.249
+0.015
Figure 9: Coefficients for BM in two celled box culvert at section B1
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Design coefficients for single and two cell box culvert
Sujata Shreedhar, R.Shreedhar
Figure 10: Coefficients for BM in two celled box culvert at section A2 & A3
Figure 11: Coefficients for BM in two celled box culvert at section C7
Figure 12: Coefficients for BM in two celled box culvert at section D5 & D6
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Design coefficients for single and two cell box culvert
Sujata Shreedhar, R.Shreedhar
Figure 13: Coefficients for BM in two celled box culvert at section E4
Figure 14: Coefficients for BM in two celled box culvert at section H12
Figure 15: Coefficients for BM in two celled box culvert at section F8
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International Journal of Civil and Structural Engineering
Volume 3 Issue 3 2013
Design coefficients for single and two cell box culvert
Sujata Shreedhar, R.Shreedhar
Figure 16: Coefficients for SF for two cell box culvert at section A2
Figure 17: Coefficients for SF for two cell box culvert at section D6
Figure 18: Coefficients for SF for two cell box culvert at section H12
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Volume 3 Issue 3 2013
Design coefficients for single and two cell box culvert
Sujata Shreedhar, R.Shreedhar
Figure 19: Coefficients for SF for two cell box culvert at section F8
Figure 20: Coefficients for Normal Thrust for two cell box culvert at section E4
Figure 21: Coefficients for Normal Thrust for two cell box culvert at section G10
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International Journal of Civil and Structural Engineering
Volume 3 Issue 3 2013
Design coefficients for single and two cell box culvert
Sujata Shreedhar, R.Shreedhar
The maximum positive moment develop at the centre of top slab when the culvert is running
full and uniform lateral pressure due to superimposed dead load only as shown in figure 9. As
the span increases, there is significant contribution to positive bending moment due to dead
load and live load only as the contribution due to earth pressure becomes less significant. The
decrease in BM is about 30% due to superimposed dead load and live load on the top slab
only for ratio 1:1 and for ratio 2:1 the decrease in BM is observed to be 22% as compared to
single cell box culvert.
It is seen from figure 10 that the maximum negative moment develop at the corner of top slab
when the culvert is empty and the top slab carries the dead load and live load. The weight of
side walls decreases the net negative moment as the moment due to side walls is positive. As
the span increases, there is significant contribution to negative bending moment due to dead
load and live load only as the contribution due to earth pressure becomes less significant. The
decrease in BM is about 33% due to superimposed dead load and live load on the top slab
only for ratio 1:1 and for ratio 2:1 the decrease in BM is observed to be 25% as compared to
single cell box culvert.
The maximum positive moment develop at the centre of bottom slab when the culvert is
running full and uniform lateral pressure due to superimposed dead load only ( referring
fig.11). As the span increases, there is significant contribution to positive bending moment
due to dead load and live load only as the contribution due to earth pressure becomes less
significant. The decrease in BM is about 30% due to superimposed dead load and live load on
the top slab only for ratio 1:1 and for ratio 2:1 the decrease in BM is observed to be 22% as
compared to single box culvert. The weight of side walls also has the significant effect on net
positive bending moment since its effect is negative as compared to single box culvert.
The maximum negative moment develop at the corner of bottom slab when the culvert is
empty and the top slab carries the dead load and live load as shown in figure 12. There is
significant contribution to maximum negative moment due to weight of side walls. As the
span increases, there is contribution to negative bending moment due to dead load and live
load only as the contribution due to earth pressure becomes less significant. The decrease in
BM is about 33% due to superimposed dead load and live load on the top slab only for ratio
1:1 and for ratio 2:1 the decrease in BM is observed to be 36% as compared to single box
culvert. Also the decrease in BM due weight of side walls is 44% for ratio 1:1 and 36% for
ratio 2:1 as compared to single cell box culvert.
From figure 13 , it can be seen that the maximum negative moment develop at the centre of
vertical wall when the culvert is running full and when uniform lateral pressure due to
superimposed dead load acts only. As the span increases, there is significant contribution to
negative bending moment due to dead load and live load only as the contribution due to water
pressure becomes less significant. The decrease in BM is about 33% due to superimposed
dead load and live load on the top slab only for ratio 1:1 and for ratio 2:1 the decrease in BM
is observed to be 22% as compared to single box culvert. Also the decrease in BM due weight
of side walls is 49% for ratio 1:1 and 54% for ratio 2:1 as compared to single cell box culvert.
The maximum negative moment as seen from figure 14 and 15 develops at the corner of top
slab (section H12) and bottom slab (section F8) when the culvert is empty and the top slab
carries the dead load and live load. The weight of side walls has significant contribution to
negative moment for section F8. As the span increases, there is significant contribution to
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Design coefficients for single and two cell box culvert
Sujata Shreedhar, R.Shreedhar
negative bending moment due to dead load and live load only as the contribution due to earth
pressure becomes less significant.
The maximum positive shear force occurs at section A2 in the top slab and at section F8 in
the bottom slab due to the superimposed dead load and live load case only as seen from
figures 16 and 19. As seen in figures 18 and 17, the maximum negative shear occurs at
section H12 in the top slab and at section D6 in the bottom slab. There is significant
contribution to shear force values due to weight of side walls at section D6 and F8. The
maximum positive normal thrust occurs at mid height of vertical wall due to superimposed
dead and live load and due to weight of side walls as seen in figures 20 and 21.
4. Conclusions
The present study makes an effort to evaluate the design coefficients for bending moment,
shear force and normal thrust for single cell, two celled and three celled box culvert subject to
various loading cases. An attempt is made to provide the information of the effects for
different ratios of L/H = 1.0, L/H = 1.25, L/H = 1.5, L/H = 1.75 and L/H = 2.0 for single cell,
two cell and three celled box culverts. The results of the study lead to the following
conclusions:
1. The design coefficients developed for bending moment, shear and normal thrust at
critical sections for various loading cases enables the designer to arrive at design
forces thus reducing design time and effort.
2. The designer has option to select the number of cells with desired span to depth ratio
suiting to hydraulic conditions at site.
3. The critical sections considered are the centre of span of top and bottom slabs and the
support sections and at the centre of the vertical walls since the maximum design
forces develop at these sections due to various combinations of loading patterns.
4. The study shows that the maximum design forces develop for the following loading
conditions:
1. When the top slab supports the dead load and live load and the culvert is empty.
2. When the top slab supports the dead load and live loads and the culvert is
running full.
3. When the sides of the culvert do not carry the live load and the culvert is
running full.
5. The study shows that the maximum positive moment develop at the centre of top and
bottom slab for the condition that the sides of the culvert not carrying the live load
and the culvert is running full of water.
6. The maximum negative moments develop at the support sections of the bottom slab
for the condition that the culvert is empty and the top slab carries the dead load and
live load.
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Design coefficients for single and two cell box culvert
Sujata Shreedhar, R.Shreedhar
7. The maximum negative moment develop at the centre of vertical wall when the
culvert is running full and when uniform lateral pressure due to superimposed dead
load acts only.
8. The maximum shear forces develop at the corners of top and bottom slab when the
culvert is running full and the top slab carries the dead and live load,
9. The study shows that there is significant contribution to positive normal thrust at
centre of vertical wall (section E4) due to superimposed dead load & live load and
weight of side walls.
10. The study shows that the multi celled box culverts are more economical for larger
spans compared to single cell box culvert as the maximum bending moment and shear
force values decreases considerably, thus requiring thinner sections.
Acknowledgements
Authors thank the Principal and Management of Maratha Mandal’s Engineering College,
Belgaum and KLS Gogte Institute of Technology, Belgaum for the continued support and
cooperation in carrying out this research study.
5. References
1. IRC: 6-2000, Standard Specifications and Code of Practice for Road BridgesSection:II Loads and Stresses.
2. IRC:21-2000,Standard Specifications and Code of Practice for Road BridgesSection:III Cement Concrete(Plain and Reinforced)
3. Krihnaraju,N., “Design of Bridges”, Third Edition Oxford and IBH publishing
Co.Pvt.Ltd New Delhi.
4. Victor Johnson,D., “Essentials of Bridge Engineering” Oxford and IBH Publishing
Co.Pvt.Ltd New Delhi.
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