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Isolated Footing Design(ACI 318-11) - English Isolated Footing 1 · 2020. 12. 8. · Print Calculation Sheet Isolated Footing Design(ACI 318-11) - English Footing No. Group ID Foundation

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    Isolated Footing Design(ACI 318-11) - English

    Footing No. Group ID Foundation Geometry

    - - Length Width Thickness

    1 1 1.40m 1.40m 0.30m

    Footing No. Footing Reinforcement Pedestal Reinforcement

    - Bottom Reinforcement(Mz) Bottom Reinforcement(Mx) Top Reinforcement(Mz) Top Reinforcement(Mx) Main Steel Trans Steel

    1 12 - #3 12 - #3 12 - #3 12 - #3 20-#6 + 4-#5 #3 @ 9 mm

    Isolated Footing 1

    1.5 m 1.8 m

    0.3 m

    1.19 m

    Elevation

    0.7 m

    1.4 m

    0.8 m

    0.8 m

    X

    Z

    Plan

    Input Values

    Footing Geomtery

    Design Type :Calculate Dimension with user

    specified minimums as startingvalue

    Minimum Footing Length - X(Fl) : 1.40 m

    Minimum Footing Width - Z (Fw) : 1.40 m

    Footing Thickness (Ft) : 0.30 m

    Eccentricity along X (Oxd) : 0.00 in

    Eccentricity along Z (Ozd) : 0.00 in

    Column Dimensions

    Column Shape : Rectangular

    Column Length - X (Dcol) : 0.80 m

    Column Width - Z (Bcol) : 0.80 m

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  • Pedestal

    Include Pedestal : Yes

    Pedestal Shape : Rectangular

    Pedestal Height (Ph) : 1.50 m

    Pedestal Length - X (Pl) : 0.80 m

    Pedestal Width - Z (Pw) : 0.80 m

    Design Parameters

    Concrete and Rebar Properties

    Unit Weight of Concrete : 25.00 kN/m3

    Strength of Concrete : 25.00 N/mm2

    Yield Strength of Steel : 460.00 N/mm2

    Minimum Bar Size : #3

    Maximum Bar Size : #5

    Top Footing Minimum Bar Size : #3

    Top Footing Maximum Bar Size : #5

    Pedestal Minimum Bar Size : #3

    Pedestal Maximum Bar Size : #10

    Minimum Bar Spacing : 75.00 mm

    Maximum Bar Spacing : 200.00 mm

    Pedestal Clear Cover (P, CL) : 40.00 mm

    Bottom Footing Clear Cover (F, CL) : 50.00 mm

    Soil Properties

    Soil Type : Cohesive Soil

    Unit Weight : 18.04kN/m3

    Base Value of Soil Bearing Capacity : 102.00kN/m2

    Multiplying factor for soil bearing capacity for ultimateloads

    : 1.25

    Soil Bearing Capacity Type : Gross Bearing Capacity

    Soil Surcharge : 0.00kip/in2

    Height of Soil above Footing : 1.20m

    Type of Depth : Fixed Bottom

    Cohesion : 0.00kip/in2

    Bearing Capacity Input Method : Fixed Bearing Capacity

    Minimum Percentage of Slab area in Contact for ServiceLoads

    : 95.00

    Minimum Percentage of Slab area in Contact forUltimate Loads

    : 95.00

    Sliding and Overturning

    Coefficient of Friction : 0.50

    Factor of Safety Against Sliding : 2.00

    Factor of Safety Against Overturning : 2.00

    Global Settings

    Top Reinforcement Option : Always calculate based on self weight

    Concrete Design Option : Net Pressure(Gross Pressure - Self Weight Pressure)

    Top Reinforcement Factor : 1.00

    ------------------------------------------------------

    Design Calculations

    Footing Size

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  • Initial Length (Lo) = 1.40 m

    Initial Width (Wo) = 1.40 m

    Load Combinations

    Load Combination/s- Service Stress Level

    LoadCombination

    NumberLoad Combination Title

    Load CaseMultiplier

    (a)

    SoilBearing

    Factor (b)

    SelfWeight

    Factor (c)Code

    a - Value specified in the Load Multiplier tableb - Value specified in the Pile/Soil Bearing Capacity Factors tablec - Value specified in the Apply Self Weight and Dead Weight Factor table

    201 DL+LL 1.00 1.00 1.00 -

    Load Combination/s- Strength Level

    LoadCombination

    NumberLoad Combination Title

    Load CaseMultiplier

    (a)

    SoilBearing

    Factor (b)

    SelfWeight

    Factor (c)Code

    a - Value specified in the Load Multiplier tableb - Value specified in the Pile/Soil Bearing Capacity Factors tablec - Value specified in the Apply Self Weight and Dead Weight Factor table

    201 DL+LL 1.00 1.00 1.00 -

    Applied Loads on Top of Pedestal

    Before consideration of self weight and load multiplier table

    Moments are about the center of Column / Pedestal (does not include moments caused by lateral loads)For the loads shown in this table, the sign convention is the same as that for JOINT LOADS in STAAD.Pro when global Y is the vertical axis.

    Applied Loads from Column - Service Stress Level

    Load CaseFx

    (kN)

    Fy(kN)

    Downwards isnegative Upwards

    is positive

    Fz(kN)

    Mx(kNm)

    Mz(kNm)

    201 0.05 -50.70 0.12 0.00 0.00

    Applied Loads from Column - Strength Level

    Load CaseFx

    (kN)

    Fy(kN)

    Downwards isnegative Upwards

    is positive

    Fz(kN)

    Mx(kNm)

    Mz(kNm)

    201 0.05 -50.70 0.12 0.00 0.00

    Reduction of force due to buoyancy = 0.00 kN

    Effect due to adhesion = 0.00 kN

    Area from initial length and width, Ao = Lo X Wo = 1.96 m2

    Min. area required from bearing pressure, Amin = 1.17 m2

    Note: Amin is an initial estimation considering self-weight, axial load and moment against factored bearing capacity.

    Final Footing Size

    Length (L2) = 1.40 m Governing Load Case : # 201

    Width (W2) = 1.40 m Governing Load Case : # 201

    Depth (D2) = 0.30 m

    Depth is governed by Ultimate Load Case

    (Service check is performed with footing thickness requirements from concrete check)

    Area (A2) = 1.96 m2

    Final Pedestal Height = 1.50 m

    Final Soil Height = 1.20 m

    Weight of the footing + pedestal (if any) = 38.70 kN

    Soil Weight On Top Of Footing = 28.57 kN

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  • Gross Pressures at 4 Corners

    Load Case /Combination

    Pressureat top left

    corner(kN/m2)

    Pressureat topright

    corner(kN/m2)

    Pressureat bottom

    rightcorner

    (kN/m2)

    Pressureat bottomleft corner(kN/m2)

    Area offooting inuplift (Au)

    (m2)

    Gross

    Bearing

    Capacity

    (kN/m2)

    201 59.5537 59.9158 60.8289 60.4668 0.00 102.0000

    201 59.5537 59.9158 60.8289 60.4668 0.00 102.0000

    201 59.5537 59.9158 60.8289 60.4668 0.00 102.0000

    201 59.5537 59.9158 60.8289 60.4668 0.00 102.0000

    If Au is zero, there is no uplift and no pressure adjustment is necessary. Otherwise, to account for uplift, areas of negative pressure will be set to zero and the pressure

    will be redistributed to remaining corners.

    Summary of Adjusted Gross Pressures at four Corners

    Load Case /Combination

    Pressure attop leftcorner

    (kN/m2)

    Pressure attop rightcorner

    (kN/m2)

    Pressure atbottom right

    corner(kN/m2)

    Pressure atbottom left

    corner(kN/m2)

    Gross Bearing

    Capacity

    (kN/m2)

    201 59.5537 59.9158 60.8289 60.4668 102.0000

    201 59.5537 59.9158 60.8289 60.4668 102.0000

    201 59.5537 59.9158 60.8289 60.4668 102.0000

    201 59.5537 59.9158 60.8289 60.4668 102.0000

    Stability Check

    1.5 m 1.8 m

    0.3 m

    1.19 m

    .

    Frictional Force

    Sliding Force

    OTM

    Passive Earth Pressure Resistance

    Resisting Force Along X on Pedestal : 35.27 kN

    Resisting Force Along Z on Pedestal : 35.27 kN

    Resisting Force Along X on Footing : 34.71 kN

    Resisting Force Along Z on Footing : 34.71 kN

    Resisting moment about X on Pedestal : 24.54 kNm

    Resisting moment about Z on pedestal : 24.54 kNm

    Resisting moment about X on Footing : 5.01 kNm

    Resisting moment about Z on Footing : 5.01 kNm

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  • - Factor of safety against slidingFactor of safety against

    overturning

    LoadCaseNo.

    Along X-Direction

    Along Z-Direction

    ResultantRequired

    FOS

    About X-Direction

    About Z-Direction

    Required

    FOS

    201 2803.66 1111.80 1033.50 2.00 537.08 1354.37 2.00

    Critical Load Case And The Governing Factor Of Safety For Overturning And Sliding - X Direction

    Critical Load Case for Sliding along X-Direction : 201

    Governing Disturbing Force : 0.05 kN

    Governing Restoring Force : 128.97 kN

    Minimum Sliding Ratio for the Critical Load Case : 2803.66

    Critical Load Case for Overturning about X-Direction : 201

    Governing Overturning Moment : 0.21 kNm

    Governing Resisting Moment : 112.14 kNm

    Minimum Overturning Ratio for the Critical Load Case : 537.08

    Critical Load Case And The Governing Factor Of Safety For Overturning And Sliding - Z Direction

    Critical Load Case for Sliding along Z-Direction : 201

    Governing Disturbing Force : 0.12 kN

    Governing Restoring Force : 128.97 kN

    Minimum Sliding Ratio for the Critical Load Case : 1111.80

    Critical Load Case for Overturning about Z-Direction : 201

    Governing Overturning Moment : -0.08 kNm

    Governing Resisting Moment : 112.14 kNm

    Minimum Overturning Ratio for the Critical Load Case : 1354.37

    Critical Load Case And The Governing Factor Of Safety For Sliding Along Resultant Direction

    Critical Load Case for Sliding along Resultant Direction : 201

    Governing Disturbing Force : 0.12 kN

    Governing Restoring Force : 128.97 kN

    Minimum Sliding Ratio for the Critical Load Case : 1033.50

    Compression Development Length Check

    Development length calculation skipped as column reinforcement is not specified in input (Column Dimension Task Pane)

    Ultimate Gross Pressures

    The base pressures reported in this table and the area of footing in contact include the effect of buoyancy (if any).

    Load Case /

    Load

    Combination

    ID

    Pressure at

    top left

    corner

    (kN/m2)

    Pressure at

    top right

    corner

    (kN/m2)

    Pressure at

    bottom right

    corner

    (kN/m2)

    Pressure at

    bottom left

    corner

    (kN/m2)

    Area of

    footing in

    Contact with

    soil (Au)

    (m2)

    201 59.5537 59.9158 60.8289 60.4668 1.96

    Minimum Required Contact Area for Ultimate Loads : 1.86 m2

    Actual Area in Contact for all ultimate load cases exceeds the minimum required. Hence Safe

    Gross Bearing Capacity for Ultimate Loads : 127.50 kN/m2

    Maximum Corner Pressure from all ultimate load cases is less than the allowable. Hence Safe

    Shear Calculation

    Punching Shear Check

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  • 0.7 m

    0.12 m

    Plan

    X

    Z

    Total Footing Depth, D = 0.30m

    Calculated Effective Depth, d = D - Ccover - 1 * db = 0.24 m

    For rectangular column, = Bcol / Dcol = 1.00

    Effective depth, d, increased until 0.75XVc Punching Shear Force

    Punching Shear Force, Vu = 34.65kN, Load Case # 201

    From ACI Cl.11.11.2.1, bo for column= = 4.16 m

    Equation 11-31, Vc1 = = 2493.12 kN

    Equation 11-32, Vc2 = = 1791.39 kN

    Equation 11-33, Vc3 = = 1662.08 kN

    Punching shear strength, Vc = 0.75 X minimum of (Vc1, Vc2, Vc3) = 1246.56 kN

    0.75 X Vc > Vu hence, OK

    One-Way Shear in XY Plane

    (Shear Plane Parallel to Global X Axis)

    0.7 m

    0.06 m

    0.06 m

    Plan

    X

    Z

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  • From ACI Cl.11.2.1.1, Vc = = 274.01 kN

    Distance of critical section from top left corneralong Z, DZ = = 0.06 m

    Check that 0.75 X Vc > Vux where Vux is the shear force for the critical load cases at a distance d from the face of the column caused by bending about the X axis.

    From above calculations, 0.75 X Vc = 205.51 kN

    Critical load case for Vux is # 201 = 3.95 kN

    0.75 X Vc > Vux hence, OK

    One-Way Shear in YZ Plane

    (Shear Plane Parallel to Global Z Axis)

    0.7 m

    0.06 m 0.06 m

    Plan

    X

    Z

    From ACI Cl.11.2.1.1, Vc = = 274.01 kN

    Distance of critical section from top left corner alongX, DX = = 0.06 m

    Check that 0.75 X Vc > Vuz where Vuz is the shear force for the critical load cases at a distance d from the face of the column caused by bending about the Z axis.

    From above calculations, 0.75 X Vc = 205.51 kN

    Critical load case for Vuz is # 201 = 3.93 kN

    0.75 X Vc > Vuz hence, OK

    Flexure About Z-Axis

    Design For Bottom Reinforcement Parallel to X Axis

    12 - #3

    X

    Z

    Calculate the flexural reinforcement along the X direction of the footing. Find the area of steel required, A, as per Section 3.8 of Reinforced Concrete Design (5th ed.) bySalmon and Wang (Ref. 1)

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  • Critical Load Case # 201

    The strength values of steel and concrete used in the formulae are in ksi

    Bars parallel to X Direction are placed at bottom

    Effective Depth d = 0.24 m

    Factor from ACI Cl.10.2.7.3 =

    = 0.85

    From Appendix B 8.4.2, = = 0.02222

    From Appendix B 10.3.3, = = 0.01667

    From ACI Cl. 7.12.2, = = 0.00162

    From Ref.1, Eq. 3.8.4a, constant m=

    = 21.65

    Calculate reinforcement ratio for critical load case

    Design for flexure about Z axis is performed at the faceof the column at a distance, Dx =

    = 0.30 m

    Ultimate moment = = 2.41 kNm

    Nominal moment capacity required, Mn = = 2.68 kNm

    (Based on effective depth) Required = = 0.00007

    (Based on gross depth) x d / Depth = 0.00006

    Since ρ < ρmin, select ρ= ρmin ρmin Governs

    Area of Steel Required, As = = 1.05 in2

    Note - "Area of Steel required" reported here is the larger value between the calculated area of steel and minimum steel required as per code stipulations

    Selected bar Size = #3

    Minimum spacing allowed (Smin) = 75.00mm

    Selected spacing (S) = 117.32mm

    Smin

  • 12 - #3

    X

    Z

    First load case to be in pure uplift # 201

    Calculate the flexural reinforcement for Mz. Find the area of steel required

    The strength values of steel and concrete used in the formulae are in ksi

    Bars parallel to X Direction are placed at bottom

    Effective Depth d = 0.24 m

    Factor from ACI Cl.10.2.7.3 ==

    0.85

    From Appendix B 8.4.2, = = 0.02222

    From Appendix B 10.3.3, = = 0.01667

    From ACI Cl. 7.12.2, = = 0.00162

    From Ref. 1, Eq. 3.8.4a, constant m=

    = 21.65

    Calculate reinforcement ratio for critical load case

    Design for flexure about Z axis is performed at theface of the column at a distance, Dx =

    = 0.30 m

    Ultimate moment = = 1.84 kNm

    Nominal moment capacity required, Mn = = 2.04 kNm

    (Based on effective depth)Required = = 0.000057

    (Based on gross depth) x d / Depth = 0.000045

    Since ρ < ρmin, select ρ= ρmin ρmin Governs

    Area of Steel Required, As = = 1.05 in2

    Note - "Area of Steel required" reported here is thelarger value between the calculated area of steel

    and minimum steel required as per code stipulations

    Total reinforcement area, As_total = Nbar X (Area of one bar) = 1.33 in2

    Provided Steel Area / Required Steel Area = 1.26

    Selected bar Size = #3

    Minimum spacing allowed (Smin) = 75.00mm

    Selected spacing (S) = 143.39mm

    Smin

  • #3 @ 127mm o.c.

    Flexure About X-Axis

    Design For Bottom Reinforcement Parallel to Z Axis

    12 - #3

    X

    Z

    Calculate the flexural reinforcement along the Z direction of the footing. Find the area of steel required, A, as per Section 3.8 of Reinforced Concrete Design (5th ed.) bySalmon and Wang (Ref. 1)

    Critical Load Case # 201

    The strength values of steel and concrete used in the formulae are in ksi

    Bars parallel to X Direction are placed at bottom

    Effective Depth d = 0.24 m

    Factor from ACI Cl.10.2.7.3 =

    = 0.85

    From Appendix B 8.4.2, = = 0.02222

    From Appendix B 10.3.3, = = 0.01667

    From ACI Cl. 7.12.2, = = 0.00162

    From Ref.1, Eq. 3.8.4a, constant m=

    = 21.65

    Calculate reinforcement ratio for critical load case

    Design for flexure about X axis is performedat the face of the column at a distance, Dz =

    = 0.30 m

    Ultimate moment = = 2.42 kNm

    Nominal moment capacity required, Mn = = 2.69 kNm

    (Based on effective depth) Required = = 0.00008

    (Based on gross depth) x d / Depth = 0.00006

    Since ρ < ρmin, select ρ= ρmin ρmin Governs

    Area of Steel Required, As = = 1.05 in2

    Note - "Area of Steel required" reported here is the larger value between the calculated area of steel and minimum steel required as per code stipulations

    Selected Bar Size = #3

    Minimum spacing allowed (Smin) = 75.00mm

    Selected spacing (S) = 117.32mm

    Smin

  • Max spacing for Cracking Consideration = 217.64mm

    Safe for Cracking Aspect.

    Based on spacing reinforcement increment; provided reinforcement is

    #3 @ 102mm o.c.

    Required development length for bars = = 0.42 m

    Available development length for bars,DL =

    = 1.05 m

    Try bar size #3 Area of one bar = 0.11 in2

    Number of bars required, Nbar= = 12

    Because the number of bars is rounded up, make sure new reinforcement ratio < ρmax

    Total reinforcement area, As_total = Nbar X (Area of one bar) = 1.32 in2

    d = D - Ccover - 1.5 X (dia. of one

    bar)=

    0.24 m

    Reinforcement ratio, = = 0.00258

    From ACI Cl.7.6.1, minimum req'd clear distance between bars

    Cd = max (Diameter of one bar, 1.0" (25.4mm), Min. User Spacing) = 75.00mm

    Provided Steel Area / Required Steel Area = 1.25

    Bending moment for uplift cases will be calculated based solely on selfweight, soil depth and surcharge loading.

    As the footing size has already been determined based on all servicebility load cases, and design moment calculation is based on selfweight, soil depth and surchargeonly, top reinforcement value for all pure uplift load cases will be the same.

    Design For Top Reinforcement Parallel to Z Axis

    12 - #3

    X

    Z

    First load case to be in pure uplift # 201

    Calculate the flexural reinforcement for Mx. Find the area of steel required

    The strength values of steel and concrete used in the formulae are in ksi

    Bars parallel to X Direction are placed at bottom

    Effective Depth d = 0.24 m

    Factor from ACI Cl.10.2.7.3 = = 0.85

    From Appendix B 8.4.2, = = 0.02222

    From Appendix B 10.3.3, = = 0.01667

    From ACI Cl. 7.12.2, = = 0.00162

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  • From Ref. 1, Eq. 3.8.4a, constant m=

    = 21.65

    Calculate reinforcement ratio for critical load case

    Design for flexure about X axis is performed at theface of the column at a distance, Dx

    = = 0.30 m

    Ultimate moment, = = 1.84 kNm

    Nominal moment capacity required, Mn = = 2.04 kNm

    (Based on effective depth) Required = = 0.00006

    (Based on gross depth) x d / Depth = 0.00004

    Since ρ < ρmin, select ρ= ρmin ρmin Governs

    Area of Steel Required, As = = 1.05 in2

    Note - "Area of Steel required" reported here is thelarger value between the calculated area of steel and

    minimum steel required as per code stipulations

    Total reinforcement area, As_total = Nbar X (Area of one bar) = 1.33 in2

    Provided Steel Area / Required Steel Area = 1.26

    Selected bar Size = #3

    Minimum spacing allowed (Smin) = 75.00mm

    Selected spacing (S) = 143.39mm

    Smin

  • Serial No.P

    (kN)

    M

    (kNm)

    Strength Reduction Factor

    (Φ)

    14 3454.17 1348.21 0.73

    15 3713.48 1313.10 0.70

    16 3998.52 1275.73 0.68

    17 4246.92 1231.55 0.66

    18 4547.92 1202.49 0.65

    19 4901.12 1187.13 0.65

    20 5222.27 1167.88 0.65

    21 5581.42 1142.26 0.65

    22 5903.87 1113.30 0.65

    23 6238.15 1078.21 0.65

    24 6560.87 1038.46 0.65

    25 6851.92 997.31 0.65

    26 7191.47 943.69 0.65

    27 7488.26 891.05 0.65

    28 8107.03 763.61 0.65

    29 8655.52 629.83 0.65

    30 9116.93 500.30 0.65

    31 9489.42 382.47 0.65

    32 9770.95 284.62 0.65

    33 9983.22 205.49 0.65

    34 10109.43 158.62 0.65

    35 10161.25 144.03 0.65

    36 10232.98 127.81 0.65

    37 10293.18 113.65 0.65

    38 10344.81 101.27 0.65

    39 10389.98 90.45 0.65

    40 10428.86 80.76 0.65

    41 10463.05 72.12 0.65

    42 10492.54 64.29 0.65

    43 10519.09 57.25 0.65

    44 10563.26 45.04 0.65

    45 10597.57 34.89 0.65

    46 10625.38 26.40 0.65

    47 10647.44 19.31 0.65

    48 10665.69 13.30 0.65

    49 10700.75 0.00 0.65

    Moment [kNm]

    0 200 400 600 800 1000 1200 1397.099586-4000

    -2000

    0

    2000

    ϕM (68.37 deg) (kNm)

    ϕPn,max = 8560.596616

    Shear - Governing Load Case Details

    Critical Load Case for Shear Along X = 201

    Critical Load Case for Shear Along Z = 201

    Shear force along X = 0.05 kN

    Shear force along Z = 0.12 kN

    Transverse Stirrups Details

    Rebar Links = #3 @ 9.84 inches

    No. of Legs in X direction = 7

    No. of Legs in Z direction = 7

    Material Take Off

    Footing Reinforcement

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  • Direction Size Number Total Length (m) Weight (kg)

    Along Z on Bottom

    Face#3 12 15.60 8.73

    Along X on Bottom

    Face#3 12 15.60 8.73

    Along Z on Top

    Face#3 12 15.60 8.73

    Along X on Top

    Face#3 12 15.60 8.73

    Pedestal Reinforcement

    Type Size NumberTotal Bar Length

    (m)Weight (kg)

    Main Steel 1

    (Vertical)#6 20 45.24 101.12

    Main Steel 2

    (Vertical)#5 4 8.54 13.26

    Transverse Steel

    (Ties)#3 8 24.26 13.57

    Internal Steel

    (Ties)#3 80 69.79 39.05

    Total Reinforcement Weight : 201.92 kg

    Concrete

    - Length (m) Width (m) Thickness (m) Volume (m3)

    Footing 1.40 1.40 0.30 0.59

    Pedestal 0.80 0.80 1.50 0.96

    Total Concrete Volume : 1.55 m3

    Formwork

    Footing : 1.68 m2

    Pedestal : 4.80 m2

    Total : 6.48 m2

    Soil Excavation

    Pit Depth : 1.50 m

    Pit Slope (a : b) : 1 : 1 (Assumed)

    Side Distance, s : 0 (Assumed)

    Excavation Volume : 13.74 m3

    Backfill Volume : 12.38 m3

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  • 0.7 m0.7 m

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