University of Dar es Salaam By Dr-Ing. JK Makunza
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General Aspects Box culverts are drainage structures which consist of two horizontal slabs and two or more vertical walls. The slabs and walls are built monolithically, monolithically, and are ideally installed for a road or a railway bridge crossing with high embankments crossing a stream with a limited flow. flow. Reinforced concrete rigid frame box culverts with square or rectangular openings are used up to spans of 4.0 m. The height of the vent (h (h) with respect to Figure 1, generally does not exceed 3.0 m. m. 2
ts f f
t w
h
l
H
standard fillet f = 150 mm
L
Figure 1: Single cell box culvert. 3
Box culverts are economical due to their rigidity and monolithic action and separate foundations are not required since the bottom slab resting directly on the soil, serves as raft foundation. For small discharges, single celled box culvert is used and for large discharges, multi-celled box culverts can be employed. The barrel of the box culvert should be of sufficient length to accommodate the carriage way and the kerbs.
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Figure 2: Double cell box culvert
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Figure 3: Triple cell box culvert
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Analysis Assumptions •
Frame The box culvert shall be analyzed, as a rigid frame with all corner connections considered rigid.
•
Sidesway Sidesway is not considered in the analysis
•
Section Properties The centerlines of slab, walls and floor are used for computing section properties and for dimensional analysis. Standard fillets which are not required for moment or shear or both shall not be considered in computing section properties. 7
Minimum Thickness The following minimum thickness shall be used Top slab:
ts = 200 mm, but taken as 80100mm per 1.00m length of the span
Floor slab: tf = 250 mm Wall:
tw = 25 mm per 300 mm of wall height but not less than 230 mm. 8
Design Loads The structural design of a reinforced concrete box culvert comprises the detailed analysis of rigid frame for moments, shear forces and thrusts due to various types of loading conditions outlined below: 1. 2. 3. 4. 5. 6.
C o n c en t r at ed L o a d s U n if o r m D is t r i b u t ed L o a d s W ei g h t o f S id e W al l s W at er P r es s u r e In s i d e C u l v er t E ar t h P r es s u r e o n Ve r t i c al S i d e W al l s U n i f o r m L a ter al L o ad o n S id e W al l s
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1. C o n c en t r at ed L o ad s In cases where the top slab forms the deck of the bridge, concentrated loads due to the wheel loads of the BS 5400 HB type loading have to be considered. If P = wheel load due to HB loading which include the impact factor of.25%, the dispersal length = 1.75D, and D = depth of soil fill, then the load intensity on the culvert slab, W = (P/(1.75D) k N/m ……(1) The soil reaction of the bottom slab is assumed to be uniform. The notations used for the box culvert and the type of loadings to be considered are shown in Figure 4 10
Concentrated Loads P
P
1.80 m
Case 1(a)
P
1.80 m
1.75 D
P
D
Case 1(b)
Figure 4: Point load due to vehicles
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2. Uniform Distributed Loads The weight of embankment, wearing coat and, 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. Minimum D = 300 mm h t p e d l l i F
BS 5400 HA Loading s.D
D
HA - KEL w /m 2
w /m 2 Case 2
Figure 5: Uniform distributed loads
HA - Udl
kN/m
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3. Weight of Side Walls
Case 3
The self weights of two side walls acting as concentrated loads are assumed to produce uniform soil reaction on the bottom slab. Ww W w = is the weight of one wall, and is given by: W w = twH c kN/m transversal Where t w = wall thickness = height of wall, and H 3 c = density of concrete = 24kN/m .
Figure 6: Load from walls 13
4. Water Pressure Inside Culvert
h
p /m 2
p /m 2
where w = density of water and h is the depth of flow.
Case 4
Figure 7: Water pressure
Intensity of water pressure p =
When the culvert is full with water, the pressure distribution on side walls is assumed to be triangular with a maximum pressure intensity of p = w h at the base
w h
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5. Ea rth Press u re on Vertic al Side Walls The earth pressure on the vertical side walls of the box culvert is computed according to the Coloumb’s Theory. The distribution of soil pressure on the side wall is shown in Figure 8.
D
h
p /m 2
Soil pressure , p
Case 5
p /m 2
Figure 8: Soil pressure
s h
1 si n 1 si n
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6 .U ni fo r m L a ter al L o ad o n S id e W all s
p /m 2
p /m 2 Case 6
Uniform lateral pressure on vertical side walls has to be considered due to the effect of live load surcharge. Also trapezoidal pressure distribution on side walls due to embankment loading can be obtained by combining the cases (5) and (6).
Figure 9: Lateral load due to surcharge loads Uniform lateral pressure due to the effect of surcharge loads is obtained from:
p
Surch arg e Loads
1 si n
1 si n
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D es i g n M o m en t s , S h ear s a n d Th r u s t s A box culvert is analyzed for moments, shear forces and axial thrusts developed due to the various loading conditions by any of the classical methods such as moment distribution, slope deflection or column analogy procedures. Alternatively coefficients for moments, shears and trusts from various structural analysis books are very useful in the computation of the various force components for the different loading conditions.
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Table 1a:
Some standard formulae for analyzing box culverts
EI = Constant
i
M i
k
l
M k
B
A
q
q
A
B
ql
ql
Mi
ql
2
2
0 .35 ql
0 .15 ql
Mk 2
ql
2
12 ql
12
2
ql
2
20
0 .15 ql
q
0 .35 ql
ql
30
2
ql
2
30
q
i
q k
0 .35 q i
0 .15 q k l
0 .15 q i
0 .35 q k l
1 .5 q i 30
q k
20 l
2
9 q i
1 .5 q k 30
l
2
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Table 1b:
Some standard formulae for analyzing box culverts
EI = Constan t i k
M k
l
B
A
q
A
B
Mk
3 ql
5 ql 8
q
11 40
q
9
ql
40
ql
i
q k
8
7 ql
ql
ql 5
4 q k
40
l
9 q i
2
120
2 ql
11 q i
2
8
10
q
ql
2
15 16 q k
40
l
7 q i
8 q k
120
l
2
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Conclusion: Design Of Critical Sections The maximum design moments resulting from the combination of the various loading cases are determined. The moments at the centre of span of top and bottom slabs and the support sections and at the centre of the vertical walls are determined by suitably combining, the different loading patterns. The maximum moments generally develop for the following loading conditions: 1. When the slab supports the dead and live lads and the culvert is empty. 2. When the top slab supports the dead and live lads and the culvert is running full. 3. When the sided of the culvert do not carry the live load and the culvert is running full. The slab of the box culvert is reinforced on both faces with fillets at the inside corners. 20
