Vechular Crossing U-Dicth Design: 1. Dimensions

VECHULAR CROSSING U-Dicth DESIGN
* U-dicth is design as Box culverts and shall be analyzed and designed as rigid frames
1. Dimensions
Fig 1 Dimensions of U -DICTH

Clear Span, S= 0.50 m
Height of opening, H= 0.50 m
Top slab thickness, T1 = 0.15 m
Bottom slab thickness, T2 = 0.15 m
Wall thickness, T3 = 0.15 m
Tapering of Bottom slab, T4 = 0.00 m each
Wearing surface thickness, W1 = 0.00 m
Pavement layer below w1, P1 = 0.00 m
Design Fill DF = 0.00 m
2. Material Properties
Loading used : AASHTO " Design vehicular live load ", HL-93 275Mpa ( G40 )
Yield strength of reinforcement steel ,(fyk) fy = 420Mpa ( G60 )
Cylinderical compressive Concrete Strength (fck) fc ' = 20MPa ( C25 )
Concrete modulus of elasticity,
Ec = 25494 Mpa
Modulus of elasticity of steel reinforcement ES = 200000Mpa
Modulus of rupture for minimum reinforcement
fr = 0.63√fc = fr = 2.817445652
Unit weight of concrete γc = 26 KN/m3 2600
Unit weight of compacted Soil (Earth fill) γs= 20 KN/m3 1925
Unit weight of Wearing surface γs= 23 KN/m 3
Active earth pressure coefficient (Selected material ) Ka = 0.33

Internal friction angle of fill δ= 30°
3. Limit States & Load Factors
3.1 Load Combination

The total factored force effect shall be taken as:
Q = Σηiγi Qi ≤ ø Rn = Rr
where:
ηi= load modifier
Qi = force effects from loads specified herein
γi = load factors specified in Tables 3-1 and 3-2 below
ø = Resistance factor
Rn = Nominal resistance
Rr = Factored resistance
The following limit states shall be considered for box culvert design:
= STRENGTH I
= SERVICE I ( for crack width control)
3.2 Load Factors

Table 3.1 Load Factors ϒ P
Strength I
Load description Designation Service I
Minimum Maximum
Dead load of componenets DC 0.90 1.25 1.00
Active horizontal earth pressure EH 0.90 1.50 1.00
Vertical earth pressure EV 0.90 1.30 1.00
Live Load LL 0.00 1.75 1.00
Dynamic load allowance IM 0.00 1.75 1.00
Live Load surcharge LS 0.00 1.75 1.00
Table 3.2 Resistance Factors Φ

Strength I Service I
Flexure 0.90 1.00
Shear 0.85 1.00
Table 3.3 Load modifiersΦ

All limit states
Ductility, ȠD 1.00
Redundancy, ȠR 1.00
Operational import.,ȠI 1.00
Ƞ = ȠD*ȠR*ȠI 1.00
4. Loads
4.1 Dead Loads

Top slab
Self-weight of the top slab, roadway pavement layers and Earth fill weight shall be applied on top slab.
* self-weight DC1= 3.90(KN/m) per meter length ( longitudinal ) of Box culvert
* Earth fill EV1= 0.00 KN/m2
* Pavement layers DC2= 0.00 KN/m2
The weight of earth fill shall be increased for soil-structure intraction, Fe
Fe = 1 +0.20 * ( H / B ) ≤ 1.15
where H = Design fill depth and B = width of culvert normal to its longitudinal centerline.
Fe = 1.00
Hence, the factored fill materials ( EV1 + DC2 ) = 0.00 KN/m2
Bottom slab
Self-weight of shall be applied on bottom slab.
* self-weight DC3= 3.90 KN/m2
Wall
Self weight of the wall shall be neglected for wall design.but used for bottom slab design.
* self-weight DC4= 3.90 KN/m2
4.2 Live Loads
Top slab
The AASHTO " design vehicular live load," HL 93, is a combination of a " design truck" or "design tandem"
and a " design lane".
Fig 3 AASHTO-LRFD design truck : HL 93

For earth fill > 0.6m, a uniform path load, representing the tire contact area, is uniformly distributed over
a rectangular area with sides, E1 and E2, where these sides are parallel and perpendicular, respectively, to
the longitudinal side of the box culvert. The equivalent uniform live load, LL1, is equal to wheel load (P)
divided by the product of E1 & E2.
LL1 = P / (E1 * E2)
where E1 = 0.45 + 1.0 H H = Design fill depth
E2 = 0.71 + 1.0 H
Culverts shall be analysed for single loaded lane with the single lane multiple presensce factor. The uniform live load
shall be multiplied by dynamic load allowance factor.
E1 = 0.45 m E2 = 0.71 m P= 145.00KN

The equivalent uniform live load, LL1
LL1 = 226.92KN/m distributed over E2 =0.71m
Bottom slab
Live load shall be neglected for bottom slab design.
Wall
Live load shall be neglected for wall design.
4.3 Dynamic load allowance

The dynamic load allowance for buried structures c, in percent, shall be taken as:
where: DE = the minimum depth of earth cover above the structure (mm)
IM = 33.00%
4.4 Live - Load surcharge

The increase in horizontal pressure due to live load surcharge shall be estimated as :
where: Δp = constant horizontal earth pressure due to uniform surcharge (KPa)

γs = density of soil (kg /m3)
k = coefficient of earth pressure
heq = equivalent height of soil for the design truck (mm)
The live-load surchrge shall be applied uniformly at the fill faces of exterior walls.
heq = 1150mm
Δp = 21.72Kpa
LS1= 21.72 KN/m2
4.5 Lateral Pressures
Values of Lateral pressures on the walls are:
Pressure at top
EH1 = KaγsH = 0.00Kpa , for H = fill depth
Pressure at bottom
EH2 = KaγsH = 5.28Kpa ,for H = fill depth plus height of Box culvert
4.6 Bearing Pressure

The footing bearing pressure is calculated by applying the necessary load factors quoted above. Dead load of
the wall and surcharge loads are factored by the minimum and maximum values, whereas the lateral loads are
factored by the maximum values only to give the worst case load combinations.
4.6.1 Minimum dead and surcharge loads with maximum lateral pressure
The summation of moment about the edge:
M = (DL*ls2/2 *0.9 + EV *ls2* 0.9 +(SL *0 + LL * 0)) - (EH1 * lh2/2*0.9 + (EH2-EH1) * lh2/6*0.9) =
= 0.62KNm
The total vertical reaction V is:
V = DL * ls * 0.9 + EV * ls* 0.9 = 2.81KN
From statical equilibrum, the eccentricity e from the edge of the box culvert to V, is therefore:
e  L 2  M toe V  0.28m
Since the foundation material is SOIL,
q max  V L  2 e  2.25Kpa
Le = V / qmax = 1.25m
4.6.2 Maximum dead and surcharge loads with maximum lateral pressure
The summation of moment about the edge:

M = ((DL*1.25 + EV *1.3)*ls2/2+(LS + LL)* ls2*1.75/2 ) - (EH1 * lh2/2*1.5 + (EH2-EH1) * lh2/6*1.5) =
= 139.95KNm
The total vertical reaction V is:
V = DL * ls * 1.25 + EV * ls* 1.3 + LS * ls +LL*ls =
= 351.99KN
From statical equilibrum, the eccentricity e from the edge of the box culvert to V, is therefore:
e  L 2  M toe V  0.10m
Since the foundation material is SOIL,
q max  V L  2 e  351.78Kpa
Le = V / qmax = 1.00m
4.6 Remark
The the water pressure on the walls may be neglected for conservative design.
4.7 Final loads
The boxculvert is analysed as and designed as rigid frame.
4.7.1 Top slab :
Dead Load :
DC1 = 3.90 KN/m2
DC2 = 0.00 KN/m2
EV1 = 0.00 KN/m2
Max. factored DLTS = 4.88 KN/m2
Live load :
LL1 = 226.92 KN/m2
LL + IM = 301.80 KN/m2
Total live load LLTS = 301.80 KN/m2
Max factored LLTS = 528.15 KN/m2
4.7.2 Bottom slab :

Dead Load :
DC4 = 1.61 KN/m2

factored DLTS + LLTS = 224.94 KN/m2
Max. factored DLTS = 209.07 KN/m2
4.7.3 Side walls :

Lateral Loads :
EH1 = 0.00 KN/m2
EH2 = 7.92 KN/m2
LS1 = 21.72 KN/m2
Max. factored LLSS = 45.92 KN/m2
5. Internal Force Calculation
Ration of member rigidity
ls = 0.80 lh = 0.80
ts = 0.15 th = 0.15
K = (th/ts)*(lh/ls) = 1.00
5.1 Node bending moment and axial force

a - load
MaA = MaD = -(1/(K+1))Pls2/12
MaB = MaC = -(1/(K+1))Pls2/12
Node bending moment :

Top slab
P (DL for MaB & MaC ) 4.88 KN/m2
MaB = MaC = -1/(K+1)Pls2/12 = -0.13KNm
P (LL for MaB & MaC ) = 528.15 KN/m2

MaB = MaC = -1/(K+1)Pls /12 =
2
-14.08KNm
Bottom slab
P (DL for MaA & MaD ) = 209.07 KN/m2
MaA = MaD = -1/(K+1)Pls2/12 = -5.58KNm
P (EV for MaA & MaD ) = 351.78 KN/m2

MaA = MaD = -1/(K+1)Pls /12 =
2
-9.38KNm
Beam internal axial force :

Na1 = Na2 = 0
Wall internal axial force :
Na3 = Na4 = Pls /2 = 213.21KN
b - load

Side wall
P (EH1 for MbA,MbB, MbC & MbD ) = 0.00 KN/m2
Mba = MbB =MbC = MbD= -1/(K+1)Plh2/12 = 0.00KNm
P (LS1 for MbA,MbB, MbC & MbD ) = 38.00 KN/m2

Mba = MbB =MbC = MbD= -1/(K+1)Plh2/12 = -1.01KNm

Nb1 = Nb2 = Plh /2 = 15.20KN
Nb3 = Nb4 = 0
c - load
McA = McD = -(k*(3k+8)/(k+1)*(k+3))Plh2/60

McB = McC = -(k*(2k+7)/(k+1)*(k+3))Plh2/60
Side wall
P (EH2 for McA,McB, McC & McD ) = 7.92 KN/m2
Mca = McD= -0.12KNm
Mcb = McC= -0.10KNm
Nc1 =Plh /6 +(McA - McB)/lh = 1.03KN
Nc2 =Plh /3 +(McA - McB)/lh = 2.09KN
Nb3 = Nb4 = 0
Bending moment (KNm) Axial force (KN)

MA MB MC MD N1 N2 N3 N4
-16.09 -15.32 -15.32 -16.09 16.23 17.29 213.21 213.21
5.2 Member bending moment and axial force

1) Top slab
x = ls / 2 = 0.40
P= 533.02
Nx =N1 = 16.23
Mx = MB +xN3-Px2/2 = 27.32KNm
2) Bottom slab
x = ls / 2 = 0.40
w1 = 209.07
w2 = 209.07
Nx = N2 = 17.29
Mx = MA +xN3-Px2/2 = 52.47KNm
3.) Wall
x = lh / 2 = 0.40
EH1 = 0.00
EH2 = 7.92
Mx = MB +xN1-EH1*x2/2 - X3*lh*(EH2 - EH1)/6 = 8.90KNm
7. Structural Design
7.1 Design of Top slab

7.1.1 Tension at the bottom
(a) Design for flexure
The moment at the base of the stem is calculated as:

Mn = 27.32KNm/m
The cracking moment is given by Mcr = frIg / yt yt = 75mm

Where Ig = bd3/12 = 281250000mm4 fr = 0.63√fc = 2.82Mpa
Mcr = frIg / yt = 10.57KNm/m D= 150mm
b= 1000mm
fc' = 20Mpa
Dim.bar = 16mm
Cover = 60.00mm
dprov= 82.00mm
b1 = 0.85
At any section of a flectural componenet the amount of reinforcement shall be adequate to develop a factored
flectural resistance at least equal to 1.2 times the cracking moment:
1.2Mcr = 12.68 < Mn
Besides the area of reinforcement shall not be less than the minimum shrinkage and temprature reinforcement.
Therefore the nominal resistance Mn = 27.32KNm/m
The amount of steel reinforcement required is:
Mn = ΦAsfy(ds-a/2)
Where a = Asfy/0.85fc'b =
This requires a quadratic solution for As of form
As = -b ± √b2 - 4ac /2a where : a =Φfy2/2 * 0.85fc'b = 1.34946
As = 918.0831175 b =- Φfyds = -30996
c = Mn = 27319476
Area of one reinforcement = 200.96
No of bars required = 4.56848685 3bars
As,prov = 602.88mm2 384.65
Spacing = 150.00mm
So provide Φ16@150
Check maximum steel is not exceeded
c = Asfy/0.85fcβb = 17.5231557
c/ds = 0.21< 0.42
This section is therefore under-reinforced
7.1.2 Tension at the top


Mn = 15.32KNm/m

b= 1000mm
fc' = 20Mpa
Dim.bar = 10mm
Cover = 60.00mm
dprov= 85.00mm
b1 = 0.85
1.2Mcr = 12.68 < Mn
Mn = ΦAsfy(ds-a/2)
As = 486.8448922 b =- Φfyds = -32130
c = Mn = 15322480
As,prov = 314mm2 384.65
Spacing = 150.00mm
So provide Φ10@150
c = Asfy/0.85fcβb = 9.1266436
c/ds = 0.11< 0.42
Development length
The basic anchorage length is the embedemnet reqired to develop the full strength of a stright bar.
lb = (ø/4) * ( fyd / fbd)
The required anchorage length, lb,net, can be found
lb,net = a*lb* (As,cal/ As,prov)
fyd = fyk /1.15 = 365.22Mpa
fbd = 2*fctd = 2* (0.21fck2/3)/1.5 2.06Mpa
lb = 708.108943mm
lb,net = 1097.89561mm
7.1 Design of bottom slab
7.1.1 Tension at the bottom

Mn = 52.47KNm/m

b= 500mm
fc' = 20Mpa
Dim.bar = 10mm
Cover = 60.00mm
dprov= 85.00mm
b1 = 0.85
1.2Mcr = 6.34 < Mn
Mn = ΦAsfy(ds-a/2)
As = 2693.782032 b =- Φfyds = -21037.5
c = Mn = 52472350
As,prov = 471mm2 384.65
Spacing = 150.00mm
So provide Φ20@150
c = Asfy/0.85fcβb = 8.96366782
c/ds = 0.11< 0.42
7.1 Design of Wall
7.1.1 Tension at the waterside

Mn = 8.90KNm/m

b= 1000mm
fc' = 20Mpa
Dim.bar = 16mm
Cover = 60.00mm
dprov= 82.00mm
b1 = 0.85
1.2Mcr = 12.68 < Mn
Mn = ΦAsfy(ds-a/2)
As = 290.7329866 b =- Φfyds = -30996
c = Mn = 8897495.6
As,prov = 401.92mm2 384.65
Spacing = 150.00mm
So provide Φ16@150
c = Asfy/0.85fcβb = 7.64899654
c/ds = 0.09< 0.42 This section is therefore under-reinforced

Vechular Crossing U-Dicth Design: 1. Dimensions

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VECHULAR CROSSING U-Dicth DESIGN

Fig 1 Dimensions of U -DICTH

Active earth pressure coefficient (Selected material ) Ka = 0.33

3. Limit States & Load Factors

3.1 Load Combination

3.2 Load Factors

Table 3.2 Resistance Factors Φ

Table 3.3 Load modifiersΦ

4.1 Dead Loads

Fig 3 AASHTO-LRFD design truck : HL 93

E1 = 0.45 m E2 = 0.71 m P= 145.00KN

4.3 Dynamic load allowance

4.4 Live - Load surcharge

where: Δp = constant horizontal earth pressure due to uniform surcharge (KPa)

4.6 Bearing Pressure

The summation of moment about the edge:

4.7.2 Bottom slab :

DC4 = 1.61 KN/m2

4.7.3 Side walls :

5.1 Node bending moment and axial force

Node bending moment :

P (LL for MaB & MaC ) = 528.15 KN/m2

P (EV for MaA & MaD ) = 351.78 KN/m2

Beam internal axial force :

Node bending moment :

P (LS1 for MbA,MbB, MbC & MbD ) = 38.00 KN/m2

Beam internal axial force :

McA = McD = -(k*(3k+8)/(k+1)*(k+3))Plh2/60

Bending moment (KNm) Axial force (KN)

5.2 Member bending moment and axial force

Mx = MB +xN1-EH1*x2/2 - X3*lh*(EH2 - EH1)/6 = 8.90KNm

7.1 Design of Top slab

The moment at the base of the stem is calculated as:

The cracking moment is given by Mcr = frIg / yt yt = 75mm

7.1.2 Tension at the top

The moment at the base of the stem is calculated as:

The cracking moment is given by Mcr = frIg / yt yt = 75mm

The moment at the base of the stem is calculated as:

The cracking moment is given by Mcr = frIg / yt yt = 75mm

The moment at the base of the stem is calculated as:

The cracking moment is given by Mcr = frIg / yt yt = 75mm

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McA = McD = -(k(3k+8)/(k+1)(k+3))Plh2/60

Mx = MB +xN1-EH1x2/2 - X3lh*(EH2 - EH1)/6 = 8.90KNm