Box Culvert at Chainage 83.10 m.xlsx Depth 4.1 m

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Project: Verdun Trianon Link Road Element: Box Culvert at Chainage 83.10 m- Chainage 35.46 to 49.4 m Job No.: M 133 Date: 6-Jun-22 Page No.: 1 Made by: RN Checked by: HKM Approved by: HKM Culvert Details Road Level Vertical Stress 4.1 27.93 5 5 5 5 Soil Parameters 99.97 18 20 Unit weight of water= 9.81 Internal Friction angle,φ(°) = 30 Height of water table(m)= 5 10 Coefficient of active pressure, ka= 0.33 27.93 99.97 25 Assuming 50 mm thick surfacing layer Depth of soil retained by Upper Slab(m)= 4.1 23 74.95 Culvert width (m)= 5 Culvert depth(m)= 5 Thickness of wall (mm)= 500 Thickness of Upper Slab (m)= 500 Thickness of base Slab(mm)= 500 BS 5400 PART 2:2006 /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 UDL HA 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)= 120 0.685 (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)= 45 Nominal Load per axle (k N)= 450 Nominal Load per wheel (k N)= 112.5 Soil Reaction Length of Culvert (m)= 16.2 Width of Culvert (m)= 11.5 Height of Culvert (m)= 6 186.3 Culvert Load Total Weight of Box Culvert (k N)= 7695 Hb load Hb load (k N)= 1259 Soil Cover Load Soil Cover Load (kN)= 13963.19 Beam Load Perimeter Beam Breadth (mm) = 900 Depth (mm)= 1000 (inclusive of Base 500 mm) Beam Load (k N)= 182.25 Central Beam Breadth(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/m 3 )= Unit Weight of Soil saturated ,γsat(k N/m 3 )= BS 8002 :1994 Clause 3.3.4.1 Surcharge due to vehicular Traffic (k N/m 2 )= Lateral Pressure at top of wall (kN/m 2 )= Lateral Pressure at bottom of wall (kN/m 2 )= Unit weight of concrete (k N/m 3 )= Unit weight of surfacing layer (k N/m 3 )= Load per m 2 of soil on upper slab (k N/m 2 )= 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 (m 2 ) = Soil Above

Transcript of Box Culvert at Chainage 83.10 m.xlsx Depth 4.1 m

Page 1: 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

Page 2: Box Culvert at Chainage 83.10 m.xlsx Depth 4.1 m

125Pressure on Base of Culvert (k N/m2)=

Page 3: 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.: 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.

E156
Rubiraj: 4 Wheels
Page 4: Box Culvert at Chainage 83.10 m.xlsx Depth 4.1 m

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

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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

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Page 6: Box Culvert at Chainage 83.10 m.xlsx Depth 4.1 m

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))

Page 7: Box Culvert at Chainage 83.10 m.xlsx Depth 4.1 m

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 =

Page 8: Box Culvert at Chainage 83.10 m.xlsx Depth 4.1 m

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))

Page 9: Box Culvert at Chainage 83.10 m.xlsx Depth 4.1 m

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 =

Page 10: Box Culvert at Chainage 83.10 m.xlsx Depth 4.1 m

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))

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9 (C)10 (C)11 (C)12 (C)13 (C)14 (C)15 (C)16 (C)

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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

Page 13: Box Culvert at Chainage 83.10 m.xlsx Depth 4.1 m

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