Box Culvert at Chainage 83.10 m.xlsx Depth 4.1 m
Transcript of Box Culvert at Chainage 83.10 m.xlsx Depth 4.1 m
Project: Verdun Trianon Link RoadElement: Box Culvert at Chainage 83.10 m- Chainage 35.46 to 49.4 mJob No.: M 133 Date: 7-Apr-23 Page No.: 1
Made by: RN Checked by: HKM Approved by: HKMCulvert Details
Road LevelVertical Stress
4.127.93
5 55
5
Soil Parameters 99.97
18
20
Unit weight of water= 9.81
Internal Friction angle,φ(°) = 30
Height of water table(m)= 5
10Coefficient of active pressure, ka= 0.33
27.9399.9725
Assuming 50 mm thick surfacing layer Depth of soil retained by Upper Slab(m)= 4.1
2374.95
Culvert width (m)= 5Culvert depth(m)= 5
Thickness of wall (mm)= 500Thickness of Upper Slab (m)= 500Thickness of base Slab(mm)= 500
BS 5400 PART 2:2006BD 37/01 Part 14 - Clause 3.2.9.3.1 -Notional lane width (m)= 2.5
Loaded length of Box Culvert, L(m)= 10.5
Note that the loaded length will be the width of the Box Culvert
(a) Calculation of HA UDLHA UDL per m of loaded length (k N/m)= 336 (1/L)^0.67 = 69.5
Knife Edge Load(KEL) per notional lane(k N)= 1200.685
(For loaded length 0<L(m)<20)For a metre width of deck, Ha (kN/m) = 19.0
For a metre width of deck , KEL (k N)= 32.88
(b) Calculation of HB Load
BD 37 Chapter 4
Class of Road carried by structure=
Number of Units for Hb load (k N)= 45Nominal Load per axle (k N)= 450
Nominal Load per wheel (k N)= 112.5
Soil ReactionLength of Culvert (m)= 16.2Width of Culvert (m)= 11.5Height of Culvert (m)= 6
186.3Culvert Load
Total Weight of Box Culvert (k N)= 7695Hb load
Hb load (k N)= 1259Soil Cover Load
Soil Cover Load (kN)= 13963.19Beam Load
Perimeter BeamBreadth (mm) = 900
Depth (mm)= 1000 (inclusive of Base 500 mm)Beam Load (k N)= 182.25
Central BeamBreadth(mm)= 1000
Depth (mm)= 1000 (inclusive of Base 500 mm)Beam Load (k N)= 202.5
Total Load in k N= 23301
Unit Weight of Soil unsaturated ,γ(k N/m3)=
Unit Weight of Soil saturated ,γsat(k N/m3)=
BS 8002 :1994 Clause 3.3.4.1
Surcharge due to vehicular Traffic (k N/m2)=
Lateral Pressure at top of wall (kN/m2)= Lateral Pressure at bottom of wall (kN/m2)=
Unit weight of concrete (k N/m3)=
Unit weight of surfacing layer (k N/m3)=Load per m2 of soil on upper slab (k N/m2)=
Clause 6.2 Type HA Loading
BD 37 Part 14 Table 14 -HA Lane Factors
First Lane load Factor, β1 = 0.274bl=
Clause 6.3 Type HB Loading
Motorways and Trunk Roads
Area of Culvert in Contact with Earth (m2) =
Soil Above
125Pressure on Base of Culvert (k N/m2)=
Project: Verdun Trianon Link RoadElement: Box Culvert at Chainage 83.10 m- Chainage 35.46 to 49.4 mJob No.: M 133 Date: 7-Apr-23 Page No.: 2
Made by: RN Checked by: HKM Approved by: HKM
Dispersal of Wheel loads
BS 5400 Part 2 2006Clause 6.26
The effect of the Vertical load is calculated using Boussineq's equatiion:
CULVERT112.5 kN
4.10
Point Load, Q (kN) = 112.5r= 2.21
Depth of Soil,z(m)= 4.10r/z 0.54
0.252
1.68885119175Assumption
For 4 wheels,σz (kN/m²) = 6.8
Volume 2 Section 2 Part 12BD 31/01 Pg
3/3
For Cover exceeding depth 0.6m, the HAUDL/KEL does not adequately model traffic loading. In these circumstances the HA UDL/KEL combination shall be replaced by 30 Units HB Loading, dispersed through the fill. However, in this case Hb Load = 45 k N, hence for analysis purposes Ha loading has been ignored.
Reynold'sReinforced concrete Designer's Manual Handbook
11th Edn. Pg 9 Section 2.4.9
Disperssal of wheel loads
For the Hb vehicle, one unit of Hb corresponds to 2.5 k N per wheel, the side of the square contact area becomes approximately 260mm for 30 units,290 mm for 37.5 Units and 320mm for 45 Units.Therefore use 320 mm as we are designing for motorways.
Volume 2 Section 2 Part 12BD 31/01 Pg
3/5
Dispersal of the single nominal wheel load at a spread to depth ratio of 1 horizontally to 2 Vertically through asphalt and similar surfacing may be assumed ,where it is considered that this may take place.
Influence factor, Ip =
Vertical Stress, σz (kN/m²) =
Joint Dispersal of wheel load on deck of Culvert, therefore multiply vertical stress by 4.
ELEMENT DESIGN to BS 8110:1997 SOLID SLABS
INPUT LocationDeck Mid SpanDesign moment, M 1350.0 kNm/m fcu 35 N/mm² 1.50
ßb 1.00 fy 460 N/mm² 1.05span 5600 mm
Height, h 800 mm Section location SIMPLY SUPPORTED SPANBar Ø 25 mmcover 100 mm to this reinforcement
OUTPUT Deck Mid Span Compression steel = Nominald = 800 - 100 - 25/2 = 687.5 mm .
(3.4.4.4) K' = 0.156 > K = 0.082 ok .(3.4.4.4) z = 687.5 [0.5 + (0.25 - 0.082 /0.9)^½ = 618.2 > 0.95d = 653.1 mm(3.4.4.1) As = 1350.00E6 /460 /618.2 x 1.05 = 4985 > min As = 1040 mm²/m
PROVIDE T25 @ 100 = 4909 mm²/.(Eqn 8) fs = 2/3 x 460 x 4985 /4909 /1.00 = 311.4 N/mm²(Eqn 7) Tens mod factor = 0.55 + (477 - 311.4) /120 /(0.9 + 2.856) = 0.9(Equation 9) Comp mod factor = 1 + 0.13/(3 + 0.13) = 1.042(3.4.6.3) Permissible L/d = 20.0 x 0.917 x 1.042 = .
Actual L/d = 5600 /687.5 = 8.145 ok .
Originated from RCC11.xls on CD © 1999 BCA for RCC
gc =gs =
ELEMENT DESIGN to BS 8110:1997 SOLID SLABS
INPUT LocationUpper Slab SupportDesign moment, M 305.0 kNm/m fcu 35 N/mm² 1.50
ßb 1.00 fy 460 N/mm² 1.05span 5500 mm
Height, h 500 mm Section location SUPPORTBar Ø 16 mmcover 50 mm to this reinforcement
OUTPUT Upper Slab Support Compression steel = Noned = 500 - 50 - 16/2 = 442.0 mm .
(3.4.4.4) K' = 0.156 > K = 0.045 ok .(3.4.4.4) z = 442.0 [0.5 + (0.25 - 0.045 /0.9)^½ = 418.9 > 0.95d = 419.9 mm(3.4.4.1) As = 305.00E6 /460 /418.9 x 1.05 = 1662 > min As = 650 mm²/m
PROVIDE T16 @ 100 = 2011 mm²/.. .. .. .. . .
. .
Originated from RCC11.xls on CD © 1999 BCA for RCC
gc =gs =
ProjectBox Culvert Verdun Trianon Link Road REINFORCED CONCRETE COUNCIL
Client BCEG Ltd Made by Date Page Location Upper Slab RN 07-Apr-2023 1
Crack Width Calculations to BS8110: 1997/ BS8007:1987 Checked Revision Job NoHKM HKM M133
CRACK WIDTH CALCULATIONS - FLEXURE -
INPUTfcu= 35
46020111000 mm500 mm442 mm50 mm100 mm16 mm
68.6 mm "acr " is distance from the point considered to the surface of the nearest longitudinal bar
131.0 KNm
CALCULATIONS13.5
200.014.810.005135 mm
3971644.88
0.000976
Usedn/a
0.0003600.000616
CALCULATED CRACK WIDTH, 'w' = 0.12 mm
Originated from RCC14.xls on CD © 1999 BCA for RCC
N/mm2
fy= N/mm2
Area of reinforcement " As " = mm2
b =h =d =
Minimum cover to tension reinforcement " CO " =Maxmum bar spacing " S " =
Bar dia " DIA " = " acr " =(((S/2)^2+(CO+DIA/2)^2)^(1/2)-DIA/2) as default or enter other value =
Applied service moment " Ms "=
moduli of elasticity of concrete " Ec" = (1/2)*(20+0.2*fcu) = KN/mm2
moduli of elasticity of steel " Es " = KN/mm2
Modular ratio " a " = (Es/Ec) = " r " = As/bd =
depth to neutral axis, "x" = (-a.r +((a.r)2 + 2.a.r)0.5.d =
" Z " = d-(x/3) =Reinforcement stress " fs " = Ms/(As*Z) = N/mm2
Concrete stress " fc " = (fs*As)/(0.5*b*x) = N/mm2
Strain at soffit of concrete beam/slab " e1 " = (fs/Es)*(h-x)/(d-x) =Strain due to stiffening effect of concrete between cracks " e2 " =
e2 = b.(h-x)2/(3.Es.As.(d-x)) for crack widths of 0.2 mme2 = 1.5.b.(h-x)2/(3.Es.As.(d-x)) for crack widths of 0.1 mm
e2 = Average strain for calculation of crack width " em "= e1-e2 =
Calculated crack width, " w " = 3.acr.em/(1+2.(acr-c)/(h-x))
ELEMENT DESIGN to BS 8110:1997 SOLID SLABS
INPUT LocationWallDesign moment, M 230.0 kNm/m fcu 35 N/mm² 1.50
ßb 1.00 fy 460 N/mm² 1.05span 5500 mm
Height, h 500 mm Section location SIMPLY SUPPORTED SPANBar Ø 16 mmcover 50 mm to this reinforcement
OUTPUT Wall Compression steel = Noned = 500 - 50 - 16/2 = 442.0 mm .
(3.4.4.4) K' = 0.156 > K = 0.034 ok .(3.4.4.4) z = 442.0 [0.5 + (0.25 - 0.034 /0.9)^½ = 424.8 > 0.95d = 419.9 mm(3.4.4.1) As = 230.00E6 /460 /419.9 x 1.05 = 1250 > min As = 650 mm²/m
PROVIDE T16 @ 150 = 1340 mm²/.(Eqn 8) fs = 2/3 x 460 x 1250 /1340 /1.00 = 286.0 N/mm²(Eqn 7) Tens mod factor = 0.55 + (477 - 286.0) /120 /(0.9 + 1.177) = 1.3(3.4.6.3) Permissible L/d = 20.0 x 1.316 = 26.320. Actual L/d = 5500 /442.0 = 12.443 ok .
. .
Originated from RCC11.xls on CD © 1999 BCA for RCC
gc =gs =
ProjectBox Culvert Verdun Trianon Link Road REINFORCED CONCRETE COUNCIL
Client BCEG Ltd Made by Date Page Location WALL CRACK WIDTH RN 07-Apr-2023 1
Crack Width Calculations to BS8110: 1997/ BS8007:1987 Checked Revision Job NoHKM HKM M 133
CRACK WIDTH CALCULATIONS - FLEXURE -
INPUTfcu= 35
46020111000 mm500 mm442 mm50 mm100 mm16 mm
68.6 mm "acr " is distance from the point considered to the surface of the nearest longitudinal bar
191.0 KNm
CALCULATIONS13.5
200.014.810.005135 mm
3972397.12
0.001423
Usedn/a
0.0003600.001063
CALCULATED CRACK WIDTH, 'w' = 0.20 mm
Originated from RCC14.xls on CD © 1999 BCA for RCC
N/mm2
fy= N/mm2
Area of reinforcement " As " = mm2
b =h =d =
Minimum cover to tension reinforcement " CO " =Maxmum bar spacing " S " =
Bar dia " DIA " = " acr " =(((S/2)^2+(CO+DIA/2)^2)^(1/2)-DIA/2) as default or enter other value =
Applied service moment " Ms "=
moduli of elasticity of concrete " Ec" = (1/2)*(20+0.2*fcu) = KN/mm2
moduli of elasticity of steel " Es " = KN/mm2
Modular ratio " a " = (Es/Ec) = " r " = As/bd =
depth to neutral axis, "x" = (-a.r +((a.r)2 + 2.a.r)0.5.d =
" Z " = d-(x/3) =Reinforcement stress " fs " = Ms/(As*Z) = N/mm2
Concrete stress " fc " = (fs*As)/(0.5*b*x) = N/mm2
Strain at soffit of concrete beam/slab " e1 " = (fs/Es)*(h-x)/(d-x) =Strain due to stiffening effect of concrete between cracks " e2 " =
e2 = b.(h-x)2/(3.Es.As.(d-x)) for crack widths of 0.2 mme2 = 1.5.b.(h-x)2/(3.Es.As.(d-x)) for crack widths of 0.1 mm
e2 = Average strain for calculation of crack width " em "= e1-e2 =
Calculated crack width, " w " = 3.acr.em/(1+2.(acr-c)/(h-x))
ELEMENT DESIGN to BS 8110:1997 SOLID SLABS
INPUT LocationBase SlabDesign moment, M 31.0 kNm/m fcu 35 N/mm² 1.50
ßb 1.00 fy 460 N/mm² 1.05span 5500 mm
Height, h 500 mm Section location SIMPLY SUPPORTED SPANBar Ø 16 mmcover 50 mm to this reinforcement
OUTPUT Base Slab Compression steel = Noned = 500 - 50 - 16/2 = 442.0 mm .
(3.4.4.4) K' = 0.156 > K = 0.005 ok .(3.4.4.4) z = 442.0 [0.5 + (0.25 - 0.005 /0.9)^½ = 439.8 > 0.95d = 419.9 mm(3.4.4.1) As = 31.00E6 /460 /419.9 x 1.05 = 169 < min As = 650 mm²/m
PROVIDE T16 @ 300 = 670 mm²/m.(Eqn 8) fs = 2/3 x 460 x 169 /670 /1.00 = 77.1 N/mm²(Eqn 7) Tens mod factor = 0.55 + (477 - 77.1) /120 /(0.9 + 0.159) = 2.00(3.4.6.3) Permissible L/d = 20.0 x 2.000 = 40.000. Actual L/d = 5500 /442.0 = 12.443 ok .
. .
Originated from RCC11.xls on CD © 1999 BCA for RCC
gc =gs =
ProjectBox Culvert Verdun Trianon Link Road REINFORCED CONCRETE COUNCIL
Client BCEG Ltd Made by Date Page Location BASE CRACK WIDTH RN 07-Apr-2023 1
Crack Width Calculations to BS8110: 1997/ BS8007:1987 Checked Revision Job NoHKM HKM M 133
CRACK WIDTH CALCULATIONS - FLEXURE -
INPUTfcu= 35
46020111000 mm500 mm452 mm40 mm100 mm16 mm
61.3 mm "acr " is distance from the point considered to the surface of the nearest longitudinal bar
28.0 KNm
CALCULATIONS13.5
200.014.810.004137 mm
40634
1.010.000197
Usedn/a
0.000347-0.000149
CALCULATED CRACK WIDTH, 'w' = -0.02 mm
Originated from RCC14.xls on CD © 1999 BCA for RCC
N/mm2
fy= N/mm2
Area of reinforcement " As " = mm2
b =h =d =
Minimum cover to tension reinforcement " CO " =Maxmum bar spacing " S " =
Bar dia " DIA " = " acr " =(((S/2)^2+(CO+DIA/2)^2)^(1/2)-DIA/2) as default or enter other value =
Applied service moment " Ms "=
moduli of elasticity of concrete " Ec" = (1/2)*(20+0.2*fcu) = KN/mm2
moduli of elasticity of steel " Es " = KN/mm2
Modular ratio " a " = (Es/Ec) = " r " = As/bd =
depth to neutral axis, "x" = (-a.r +((a.r)2 + 2.a.r)0.5.d =
" Z " = d-(x/3) =Reinforcement stress " fs " = Ms/(As*Z) = N/mm2
Concrete stress " fc " = (fs*As)/(0.5*b*x) = N/mm2
Strain at soffit of concrete beam/slab " e1 " = (fs/Es)*(h-x)/(d-x) =Strain due to stiffening effect of concrete between cracks " e2 " =
e2 = b.(h-x)2/(3.Es.As.(d-x)) for crack widths of 0.2 mme2 = 1.5.b.(h-x)2/(3.Es.As.(d-x)) for crack widths of 0.1 mm
e2 = Average strain for calculation of crack width " em "= e1-e2 =
Calculated crack width, " w " = 3.acr.em/(1+2.(acr-c)/(h-x))
9 (C)10 (C)11 (C)12 (C)13 (C)14 (C)15 (C)16 (C)
ULS Dead+ Surfacing+Ha UDL+HaKEL(midspan)+Ev+Eh 1 1.15 2 1.75ULS Dead+ Surfacing+Ha UDL+HaKEL(support)+Ev+Eh 1 1.15 2 1.75ULS Dead+ Surfacing+Hb(midspan)+Ev+Eh 1 1.15 2 1.75ULS Dead+ Surfacing+Hb(support)+Ev+Eh 1 1.15 2 1.75SLS Dead+ Surfacing+Ha UDL+HaKEL(midspan)+Ev+Eh 1 1 2 1.2SLS Dead+ Surfacing+Ha UDL+HaKEL(support)+Ev+Eh 1 1 2 1.2SLS Dead+ Surfacing+Hb(midspan)+Ev+Eh 1 1 2 1.2SLS Dead+ Surfacing+Hb(support)+Ev+Eh 1 1 2 1.2
4 1.5 5 1.54 1.5 6 1.54 1.5 7 1.34 1.5 8 1.34 1 5 1.24 1 6 1.24 1 7 1.14 1 8 1.1