APPENDIX A

Detailed Calculation Sheet 1Issue: Date: Revised by: Checked by: Design Test1 Test2 Page 1 of 3

Isolated Foundation Calculation (ACI 318M-95)Project: Verification example from [Nawy, P.584]

Input DataLoads (kN) Mz Fx Fy (kN.m) Dead 0 800 0 Live 0 668 800 Wind 100 0 0 E 0 0 0 Sum 100 1468 800 Foundation Level H (mm) 1300 h (mm) 200 hw (mm) 0 L/B 1.4 Pedestal Dimension x (mm) 500 y (mm) 500 Concrete Strength f'c (N/mm2) = 27.6 Steel Strength fy (N/mm2) = 414 Allowable Soil Pressure qa (kN/m2) = 190 Base Soil angle of internal friction

FyhGWT

Fx

Mz

H

hw L z B y xx

20

Ultimate Loads (ACI 9.2.)Load Case Factors Fux (kN) = Fuy (kN) = Muz (kN.m) = 0.9D+1.3W 0.9 1.3 130 720 0 1.4D+1.7L 1.4 1.7 0 2255.6 1360 0.75(1.4D+1.7L+1.7W) 1.05 1.275 1.275 127.5 1691.7 1020 0.75(1.4D+1.7L+1.87E) 1.05 1.275 1.4025 0 1691.7 1020

Approximate Base Dimensions B & L Based on Unfactored Loads (ACI 15.1.)Approximate Base Dimensions B (mm) = B (mm) =

User Input Dimensions

3100 3100

L (mm) = L (mm) =

4340 4340

Approximate Footing Effective Depth d Assuming Punching Shear Governs (ACI 11.12) Load Case *qumax (kN/m2) d (mm) * 1 73.55 225.000 2 307.40 585.000 3 250.20 515.000 d (mm)= D (mm)= 520 590 4 230.55 490.000 min 150mm (ACI 15.7.) min cover 70mm (ACI 7.7.)

Fuy Muz+ Fux (H + h) User Input qumax= +6 Depth 2 LB LB

Foundation Weight Df (kN)Concrete Slab = Pedestal = Soil above Slab = Saturated Soil = B * L * D * 25 198.447 x * y * (H+h - D) * 25 5.6875 (B*L - x*y) * (H - hw) * 20 187.497 (B*L - x*y) * (hw - D) * (20-10) 0 Total Df (kN) = 391.631

dd/2 d/2

d

qumin

q6

q5 q4

q3 q2

q1

qumax

Net Ultimate Stresses Profile (kN/m2)Load Case qumax (kN/m2) qumin (kN/m2) q1 (kN/m2) q2 (kN/m2) q3 (kN/m2) q4 (kN/m2) q5 (kN/m2) q6 (kN/m2) 1 73.553 33.478 60.626 58.225 55.824 51.207 48.806 46.406 2 307.402 27.904 217.241 200.497 183.753 151.553 134.808 118.064 3 250.204 1.276 169.904 154.991 140.079 111.400 96.488 81.575 4 230.551 20.928 162.931 150.373 137.815 113.664 101.106 88.548

Isolated Foundation Calculation (ACI 318M-95)

Issue:

Design

Page

Isolated Foundation Calculation (ACI 318M-95)Project: Verification example from [Nawy, P.584]

APPENDIX A

Detailed Calculation Sheet 2Date: Revised by: Checked by: 0 Test1 Test2 2 of 3

CHECKING:Contact PressureFv (kN) = Fy + Df 1859.63 qmax (kN/m2) ( 3qmax + qmin ) /4 < qa = 190 235.84 qmin (kN/m2) 40.6026 qGP (gross pressure) (kN/m2) = qGP = 187.031 kN/m2

YES950 kN.m 4035.4 kN.m

q max, min=

F M + F (H + h) v z x2 LB BL

Stability Against OverturningOverturning moment = Stabilizing moment = Mz + Fx * (H + h) Fv * (L/2) 4.24779 > 1.5

Stabilizin g moment Overturnin g moment

=

YES

Stability Against Sliding

Fv tan q = Fh

6.7685

>

1.5

YES

Check wide beam shear in the x-direction (ACI 11.3.)Vc (kN) = (1/6) * SQRT(fc) * B * d Load Case 1 2 Vu (kN)* = 291.168 1138.475 Vu / 0.85Vc 0.2427 0.9489 *Vu = 0.5 * (q1+qumax) * (L/2 - x/2 - d) * B max Vu / 0.85Vc = 0.94893 1411.46 3 911.634 0.7599 < 1.00 4 853.856 0.7117

YES

Check punching shearbo (mm) =

(ACI 11.12)3715.32 5572.99 6592.88 Vc (kN) = 3715.32

2 * [(x+d)+(y+d)] 4080 (1/3) * sqrt(f'c) * bo * d Vc (kN) = min of ( 1 + 2/(x/y) ) * (1/6) * SQRT(f'c) * bo * d ((40 * d/bo) + 2) * (1/12)* SQRT(f'c) * bo * d Load Case 1 2 3 Vu (kN)* = 664.3223 2081.1741 1560.8806 Vu / 0.85Vc 0.2104 0.6590 0.4943 *Vu (kN) = Fuy - (0.5 * (q2+q5)) * (x+d) * (y+d) max Vu / 0.85Vc = 0.65901 < 1.00

4 1560.8806 0.4943

YES

Reinforcement:

Mu = 0.9 f y As ( d -

0.59 f y As f 'c B

)z - Direction Bottom Reinforcement 1 2 3 4 196.258 614.833 461.125 461.125 10.1861 32.3042 24.1181 24.1181 0.0018 0.0018 0.0018 0.0018 0.0018 0.04247 (ACI 10.3.2)

x - Direction Bottom Reinforcement Top Reinforcement Load Case 1 2 3 4 1 2 3 4 Mu (kN.m)* 386.51 1520.96 1219.9 1140.72 NR NR NR NR As (cm2)= 20.1714 82.1988 65.2954 60.9058 NR NR NR NR r= 0.0018 0.0051 0.00405 0.00378 NR NR NR NR max r = 0.005099184 0 r min = 0.0018 (ACI 7.12.) r max = 0.75 (0.85 f'c / fy) (600 / 600+fy) = * x - direction moments: Mu (Bottom R) = q3 * B * 0.5*(L/2-x/2)^2 + 0.5*(qumax-q3) * B * (2/3)*(L/2-x/2)^2 Mu (Top R) = qumin * B * 0.5 * (L/2-x/2)^2 (approximation) * z - direction moment: Mu (Bottom R) = 0.5*(qumax+qumin) * L * 0.5*(B/2-y/2)^2

Isolated Foundation Calculation (ACI)Project: Test1

Issue: Date: Revised by:

Design Test1

Page 1 of 2

APPENDIX A

Detailed Calculation Sheet 3

Project:

Test1

Checked by:

Test2

Fy = 1468 kN

Fx = 100 kN hw = 200

Mz = 800

kN.m

GWT H= 1300As (cm2) = hw = 0

0

(in both directions)

D = 590

d = 520 mm

L = 4340 mm As (cm2) = 40.62 (z - direction) As (cm2) = 82.2 (x - direction)

z B = 3100y = 500

xx = 500

* Dimensions are in mm

Isolated Foundation Calculation (ACI)Project: Verification example from [Nawy, P.584]

Issue: Date: Revised by: Checked by:

Design 0 Test1 Test2

Page 1 of 2

Input DataLoads (kN) Px Dead 0 Live 0 Wind 100 E 0 Sum 100 Py 800 668 0 0 1468 Mz (kN.m) 0 800 0 0 800 Concrete Strength Foundation Properties f'c (N/mm2) = 27.6 H (mm) 1300 h (mm) Steel Strength hw (mm) 0 L/B fy (N/mm2) = 414 Pedestal Dimension Allowable Soil Pressure x (mm) 500 y (mm) qa (kN/m2) = 190 Base Soil angle of internal friction 20 200 1.4 500

Ultimate Loads (ACI 9.2.)Load Case Factors Pux (kN) = Puy (kN) = Muz (kN.m) = 0.9D+1.3W 0.9 1.3 130 720 0 1.4D+1.7L 1.4 1.7 0 2255.6 1360 0.75(1.4D+1.7L+1.7W) 1.05 1.275 1.275 127.5 1691.7 1020 0.75(1.4D+1.7L+1.87E) 1.05 1.275 1.4025 0 1691.7 1020

CHECKING:Contact Pressure qmax = 235.8 kN/m2 qmin = 40.6 kN/m2

qGP (gross pressure) (kN/m2) = qGP = Stability against Overturning

( 3qmax + qmin ) /4 YES

187 kN/m2 < qa = 190950 4035.4

Overturning moment Stabilizing moment

kN.m kN.m > 1.5 YES

Stabilizin g moment Overturnin g moment

=

4.248

Stability against Sliding Check Wide Beam Shear Check Punching Shear

Fv tan q = FhVc (kN) 1411.459

6.769

>

1.5

YES

max Vu (kN) 1138.475

Load Case 2

max Vu / 0.85Vc = 0.949Vc (kN) 3715.325 max Vu (kN) 2081.174