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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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