Loading to Box Culverts
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Transcript of Loading to Box Culverts
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LOADING TO BOX-CULVERTS
University of Dar es SalaamBy Dr-Ing. JK Makunza
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General AspectsBox culverts are drainage structures which
consist of two horizontal slabs and two or morevertical walls. The slabs and walls are built
monolithically, and are ideally installed for a road
or a railway bridge crossing with highembankments crossing a stream with a limited
flow. Reinforced concrete rigid frame box
culverts with square or rectangular openings areused up to spans of4.0 m. The height of the
vent (h) with respect to Figure 1, generally does
not exceed 3.0 m.
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l
L
h Ht
t s
w
f
f
standard fillet
f = 150 mm
Figure 1: Single cell box culvert.
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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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5Figure 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 dimensionalanalysis. Standard fillets which are not required formoment or shear or both shall not be considered incomputing section properties.
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Minimum Thickness
The following minimum thickness shall be used
Top slab: ts = 200 mm, but taken as 80-
100mm 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.
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Design LoadsThe 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. Concentrated Loads2. Uniform Distributed Loads
3. Weight of Side Walls
4. Water Pressure Inside Culvert
5. Earth Pressure on Vertical Side Walls6. Uniform Lateral Load on Side Walls
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1. Concentrated Loads
In cases where the top slab forms the deck of the bridge,
concentrated loads due to the wheel loads of the BS 5400HB 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 culvertslab,
W = (P/(1.75D) kN/m (1)
The soil reaction of the bottom slab is assumed to beuniform. The notations used for the box culvert and the
type of loadings to be considered are shown in Figure 4
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Concentrated Loads
Case 1(b)
P P1.80 m
Case 1(a)
P P1.80 m1.75 D
D
Figure 4: Point load due to vehicles
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2. Uniform Distributed LoadsThe 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
w/m 2
w/m 2
Case 2
s.DD
Filldepth
HA - Udl
HA - KEL
kN/m
BS 5400 HA Loading
Figure 5: Uniform distributed loads
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3. Weight of Side WallsThe self weights of two side walls
acting as concentrated loads are
assumed to produce uniform soilreaction on the bottom slab.
Ww= is the weight of one
wall, and is given by:
Ww= twHJc kN/m transversal
Where
tw= wall thickness
H= height of wall, and
Jc= density of concrete = 24kN/m3.
Case 3
Ww
Figure 6: Load from walls
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4. Water Pressure Inside Culvert
When the culvert is full
with water, the pressure
distribution on side walls is
assumed to be triangular
with a maximum pressure
intensity ofp = Jwh at thebase
where Jw= density of
water andh
is the depth offlow.
p/mp/m2 2
Case 4
h
Intensity of water pressurep = Jwh
Figure 7: Water pressure
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5. Earth Pressure on Vertical Side WallsThe earth
pressure on the
vertical side walls
of the box culvert
is computed
according to the
Coloumbs Theory.The distribution of
soil pressure on
the side wall is
shown in Figure 8. Case 5p/m2 p/m
2
D
h
I
IJ
sin1
sin1hp sSoil pressure,
Figure 8: Soil pressure
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6.Uniform Lateral Load on Side Walls
Case 6
p/m2 p/m2
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 thecases (5) and (6).
Uniform lateral pressure due to the effect of surcharge loads is obtained
from:
I
I
sin1
sin1LoadseargSurchp
Figure 9: Lateral load due to surcharge loads
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Design Moments, Shears and Thrusts
A box culvert is analyzed for moments, shear
forces and axial thrusts developed due to thevarious loading conditions by any of the classical
methods such as moment distribution, slope
deflection or column analogy procedures.
Alternatively coefficients for moments, shearsand 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
A B
Mi Mk
EI = Constant
i k
l
A B Mi Mk
q
2ql
2
ql
12ql2
12ql2
q
ql35.0 ql15.0
20ql2
30ql2
q
ql15.0 ql35.0
30
ql2 20
ql2
q qi k
lq15.0q35.0 ki lq35.0q15.0 ki 2ki l30
qq5.1 2ki l
30
q5.1q9
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Table 1b: Some standard formulae for analyzing box culverts
A B
Mk
EI = Constant
i k
l
A B Mk
q
8ql3
8
ql5
8ql2
q ql
40
11 ql
40
9 120
ql7 2
q
10
ql
5
ql2
15
ql2
q qi k
l
40
q4q11 ki
l40
q16q9 ki 2ki l120
q8q7
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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 isempty.
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 theculvert is running full.
The slab of the box culvert is reinforced on both faces with fillets
at the inside corners.