BOX CULVERT SIZE 3000 X 1500
E. Live Load
Using a 2D frame model there is an opposite upward reaction from the soil caused by the water inside the culvert:
Wabottom reaction = WA bottom * Span = 13.30 kN/m
(Span + Ts)
The design live loads include the HL-93 truck and tandem loads. Since the span of the box culvert is less than 15 ft, no lane load is applied.
Dynamic Load Allowance
-27.885 = 0
The dynamic load allowance may not be taken less than zero.
The dynamic load allowance (IM) for culverts and other buried structures is reduced based on the depth of fill over the culvert. For strength and service limit states:
Live Load Distribution
Live loads are assumed to distribute laterally with depth. The specifications permit designers to increase the footprint of the load with increasing depth of fill. The load is assumed to spread laterally 1.15 times H horizontally in each direction for every foot of fill above the culvert. The intensity of live loads at any depth is assumed to be uniform over the entire footprint.
The assumed tire contact area for each wheel has a width of 20 inches and a length of 10 inches.
Using the distances between wheel lines and axles, the live load intensities at the top of the box culvert can be found. For truck and tandem loadings, the influence area or footprint of the live load is found first. Then the sum of the weights of the wheels is used to determine the intensity of the live load.
To determine the live load, use multiple presence factors (MPF). A single loaded lane with a MPF of 1.20 is used for strength and service limit states.
where Pw = 130kN
Axlespacing = 1.8m
Wtire = 0.51m g
A single 3 Axle with 600 kN Truck configuration produces a live load intensity of:
tire
W = 7.49 m
Ltire = 0.25m L= 7.23 m Therefore
WLL+IM = 5.77 kN/m
A tandem truck axle configuration produces a live load intensity of:
The live load intensities of the single and tandem axle configurations are compared. Since the tandem axle configuration produces a live load intensity slightly larger than that of the single axle
configuration, the tandem axle configuration is used for design in both the strength and service limit states.
1 Maximum Vertical Load and Maximum Horizontal Load
1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+ (1.35)(1.05)EHmax + 1.75LS 2 Maximum Vertical Lod and Minimum Horizontal Load
1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+1.00WA+(0.9/1.05)EHmin 3 Minimum Vertical load and Maximum Horizontal Load
0.90 DC + (0.9/1.05)EV + (1.35)(1.05) EHmax +1.75LS
Service Limit State
1 Maximum Vertical Load and Maximum Horizontal Load 1.00 DC + 1.00 EV + 1.00 (LL+IM)+1.00EHmax + 1.00LS 2 Maximum Vertical Lod and Minimum Horizontal Load
1.00 DC + 1.00 EV + 1.00 (LL+IM)+1.00WA+1.00EHmin
3 Minimum Vertical load and Maximum Horizontal Load 1.00 DC + 1.00EV + 1.00EHmax +1.00LS
A structural analysis is performed using a standard commercial matrix-analysis program. The bottom slab of the box culvert is assumed rigid compared to the subgrade. Reactions to vertical loads applied to the culvert (earth, water, live load) are assumed to be carried by uniform, triangular or trapezoidal distributed reactions applied to the bottom slab. Box culverts supported on stiff or rigid subgrades (rock) would require further investigation. The haunches are included in the analysis by increasing the thickness of members near each corner
Reinforcement Design
where,
F = 1
fy = 420 Mpa
fc' = 35 MPa
thickness of members near each corner.
fc' = 35 MPa
420∗ √ 176400 ^2 11.844 /5.922
Side Wall
Max @ Slab End@OS Max @ Mid Slab@IS
From staad Model
Outside Mu = 118.29 kNm Main bar dia = 16 mm
d = thickness - Cover - dm/2
d= 272 mm
As = 1,064.84 mm2 Minimum sidewall flexural reinforcement
Asmin = 0.002 x b x Ts = 640.00 mm2 therefore As = 1 064 84 mm2
therefore As 1,064.84 mm2
As Provided = 16 mm dia X 150 c/c
for 1 m length 16 mm dia X 6.67 Pcs 1,340.41 mm2
Inside Mu = 64.1 kNm Main bar dia = 16 mm
d = thickness - Cover - dm/2
d= 272 mm
As = 569.51 mm2 Minimum sidewall flexural reinforcement
Asmin = 0 002 x b x Ts = 640 00 mm2 Asmin = 0.002 x b x Ts = 640.00 mm2 therefore As = 640.00 mm2
As Provided = 16 mm dia X 150 c/c
for 1 m length 16 mm dia X 6.67 Pcs 1,340.41 mm2
Top Slab
Max @ Slab End @OS
Max @ Mid Slab @IS
From staad Model
Inside Mu = 139.01 kNm Main bar dia = 16 mm
d = thickness - Cover - dm/2
d= 272 mm
As = 1,257.83 mm2 Minimum sidewall flexural reinforcement
Asmin = 0.002 x b x Tt = 640.00 mm2 therefore As = 1,257.83 mm2
As Provided = 16 mm dia X 150 c/c
for 1 m length 16 mm dia X 6.67 Pcs 1,340.41 mm2
Outside Mu = 68.21 kNm Main bar dia = 14 mm
d = thickness - Cover - dm/2
d= 273 mm
As = 604 32 mm2
As = 604.32 mm2 Minimum sidewall flexural reinforcement
Asmin = 0.002 x b x Tt = 640.00 mm2 therefore As = 640.00 mm2
As Provided = 14 mm dia X 150 c/c
for 1 m length 14 mm dia X 6.67 Pcs 1,026.25 mm2
Bottom Slab
Max @ Slab End@OS Max @ Mid Slab @IS
From staad Model
Inside Mu = 95.74 kNm Main bar dia = 16 mm
d = thickness - Cover - dm/2
d= 312 mm
As = 743.09 mm2 Minimum sidewall flexural reinforcement
Asmin = 0.002 x b x Tb = 720.00 mm2 therefore As = 743.09 mm2
As Provided = 16 mm dia X 150 c/c
for 1 m length 16 mm dia X 6.67 Pcs 1,340.41 mm2
Outside Mu = 110.02 kNm Main bar dia = 14 mm
d = thickness - Cover - dm/2
d= 313 mm
As = 853 31 mm2
As = 853.31 mm2 Minimum sidewall flexural reinforcement
Asmin = 0.002 x b x Tb = 720.00 mm2 therefore As = 853.31 mm2
As Provided = 14 mm dia X 150 c/c
for 1 m length 14 mm dia X 6.67 Pcs 1,026.25 mm2
Checking of Shear
Top Slab
Maximum Shear (Vu) = 262.78 kN Shear Capacity (Vc) =
281.61
kN > Vu
Bottom Slab
0.17∗√ ^′
Bottom Slab
Maximum Shear (Vu) = 228.11 kN Shear Capacity (Vc) =
0.17∗√ ^′
321.83
kN > Vu
Side Wall
Maximum Shear (Vu) = 155.38 kN Shear Capacity (Vc) =
281.61
kN > Vu Final Size and Reinforcement
Box culvert Inside Dimensions = 3000 x 1500 mm Top Slab Thickness = 320 mm Bottom Slab Thickness = 360 mm
id ll hi k 320
0.17∗√ ^′
Side Wall Thickness = 320 mm Reinforcement
Dia (mm) C/C Dia (mm) C/C
16 150 14 150
16 150 14 150
16 150 16 150
Top Slab Bottom Slab
Side Wall
Location Inside Outside