APPENDIX ADetailed Calculation Sheet 1 Issue: Isolated Foundation Calculation (ACI 318M-95) Project: Design Date: Revised by: Checked by: Verification example from [Nawy, P.584] Page 1 of 3 Test1 Test2 Input Data Loads (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) 1500 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 Fy Fx h Mz GWT H hw L z B x y x 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) = User Input Dimensions B (mm) = 3150 3100 L (mm) = 4410 4340 L (mm) = Approximate Footing Effective Depth d Assuming Punching Shear Governs (ACI 11.12) * Load Case 1 2 3 4 *qumax (kN/m2) 76.22 307.40 252.82 230.55 d (mm) 230.000 585.000 520.000 d (mm)= D (mm)= Fuy Muz+ Fux´ (H + h) qumax= +6 LB L2B User Input Depth 490.000 min 150mm (ACI 15.7.) min cover 70mm (ACI 7.7.) 520 590 Foundation Weight Df (kN) Concrete Slab = Pedestal = Soil above Slab = Saturated Soil = B * L * D * 25 198.447 x * y * (H+h - D) * 25 6.9375 (B*L - x*y) * (H - hw) * 20 240.313 (B*L - x*y) * (hw - D) * (20-10) 0 Total Df (kN) = 445.697 qumin d d d/2 q6 q5 q4 d/2 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 76.225 30.806 61.574 58.853 56.132 50.899 48.178 45.458 2 307.402 27.904 217.241 200.497 183.753 151.553 134.808 118.064 Isolated Foundation Calculation (ACI 318M-95) 3 252.824 -1.345 170.834 155.607 140.381 111.099 95.872 80.645 Issue: 4 230.551 20.928 162.931 150.373 137.815 113.664 101.106 88.548 Design Page APPENDIX A Detailed Calculation Sheet 2 Isolated Foundation Calculation (ACI 318M-95) Project: Date: Revised by: Checked by: Verification example from [Nawy, P.584] 0 Test1 Test2 2 of 3 CHECKING: Contact Pressure Fv (kN) = Fy + Df qmax (kN/m2) 1913.7 qGP (gross pressure) (kN/m2) = qGP = 192.077 kN/m2 ( 3qmax + qmin ) /4 > qa = q max, min= NO 190 qmin (kN/m2) 241.914 42.566 Fv Mz + Fx (H + h) ± LB BL2 Stability Against Overturning Overturning moment = Stabilizing moment = Stabilizing moment Mz + Fx * (H + h) Fv * (L/2) = Overturning moment 970 kN.m 4152.72 kN.m 4.28116 > 1.5 YES 6.96529 > 1.5 YES Stability Against Sliding Fv ´ tan q = Fh 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)* = 299.023 1138.475 Vu / 0.85Vc 0.2492 0.9489 *Vu = 0.5 * (q1+qumax) * (L/2 - x/2 - d) * B 1411.46 3 919.338 0.7663 max Vu / 0.85Vc = 0.94893 Check punching shear < 1.00 4 853.856 0.7117 YES (ACI 11.12) bo (mm) = 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 Reinforcement: Mu = 0.9 f y As ( d - < 0.59 f y As f 'c B 1.00 3715.32 5572.99 6592.88 Project: Test1 3715.32 4 1560.8806 0.4943 YES ) x - Direction Bottom Reinforcement Top Reinforcement Load Case 1 2 3 4 1 2 3 4 Mu (kN.m)* 397.273 1520.96 1230.45 1140.72 NR NR -7.6839 NR As (cm2)= 20.7397 82.1988 65.8823 60.9058 NR NR 0.39667 NR r= 0.0018 0.0051 0.00409 0.00378 NR NR 0.0018 NR max r = 0.005099184 0.0018 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) Vc (kN) = Issue: Date: Revised by: 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) Design Test1 Page 1 of 2 APPENDIX A Project: Detailed Calculation Sheet 3 Test1 Checked by: Fy = Fx = Test2 1468 kN Mz = 100 kN 800 kN.m hw = 200 GWT H= 1500 D= As (cm2) = 29.02 (in both directions) hw = 0 590 d = 520 mm L = 4340 mm As (cm2) = 40.62 (z - direction) As (cm2) = 82.2 (x - direction) z B = 3100 y= 500 x x= * Dimensions are in mm 500 Isolated Foundation Calculation (ACI) Verification example from [Nawy, P.584] Project: Issue: Date: Revised by: Design 0 Test1 Checked by: Test2 Page 1 of 2 Input Data Loads (kN) Px Dead 0 Live 0 Wind 100 E 0 Sum 100 Py 800 668 0 0 1468 Concrete Strength Foundation Properties f'c (N/mm2) = 27.6 H (mm) 1500 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 Mz (kN.m) 0 800 0 0 800 200 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 = 241.9 kN/m2 qmin = qGP (gross pressure) (kN/m2) = qGP = Stability against Overturning 4152.72 = Overturning moment Check Wide Beam Shear Check Punching Shear 970 Stabilizing moment Stabilizing moment Stability against Sliding ( 3qmax + qmin ) /4 192.1 kN/m2 > qa = 190 Overturning moment Fv ´ tan q = Fh 42.57 kN/m2 NO kN.m kN.m 4.281 > 1.5 YES 6.965 > 1.5 YES Vc (kN) max Vu (kN) 1411.459 1138.475 Load Case 2 max Vu / 0.85Vc = 0.949 < Vc (kN) 3715.325 Load Case 2 max Vu (kN) 2081.174 max Vu / 0.85Vc = 0.659 < 1.00 1.00 YES YES Results: Base Dimensions B= 3100 L= 4340 mm mm d= D= 520 590 mm mm Reinforcment As (cm2) = r= x - Direction Bottom Reinforcement 82.19884491 0.005099184 Top Reinforcement 29.016 0.0018 z - Direction Bottom Reinforcement 40.6224 0.0018 Isolated Foundation Calculation (ACI) Project: Verification example from [Nawy, P.584] Issue: Date: Revised by: Checked by: Design 0 Test1 Test2 Page 2 of 2 Fy = 1468 kN Fx = 100 kN Mz = 800 kN.m hw = 200 GWT H= 1500 As (cm2) = 29.02 (in both directions) hw = 0 D = 590 d = 520 mm L = 4340 mm As (cm2) = 40.62 (z - direction) As (cm2) = 82.2 (x - direction) z B = 3100 y = 500 x x = 500 * Dimensions are in mm Design of square footings Dead Load Live load(imposed Load) Size of column Type of column Steel bar Size Concrete Considered Steel Safe Bearing Capacity of Soil Load = ( 1.0 X DL ) + ( 1.0 X LL ) + Self weight DL LL Self weight Area of footing Calculated area of footing Round of footing Dimention 1100 KN 1000 KN 450 mm X 450 mm Square 25 mm M 20 Fe 415 200 KN/mm2 1100 KN 500 KN 100 KN 1700 8.5 M2 2.915 M 3.0 m X 3.0 m 1) Depth required for one way shear at the distane 'D" Minimum Shear Stress Tc = 0.35 N/mm2 L= length of footing a = diemention of column P = Design Load (DL+LL+Selfweight)*1.5 D= 350 3 0.45 2550 N/m2 m m KN V= V= V= V = Tc x L x d Tc x L x d = P(L-a) 2 (P + (Tc X L2)) D = 0.570394737 D=600 mm Depth required for two way shear or Punching shear Perimeter = 4 (a+d) Considering Equlibrium of forces (P/L2)*((L2 - (a+d)2)) = 4 ( a + d )*d* Tp Tp = 0.25 Square root (fck) Perimeter = 4 ( a + d ) a = Area od Column ( 570 N/M2 for Punching shear) for M 20 0.45 M d = Depth of Footing Perimeter = 4 ( a + d ) 0.57 M 4.08 M q = P /L2 P = 2550 KN (Sum of Loads )(DL+LL+Selfweight) q = P /L2 283.33333 KN /M2 Shear Force = (P/L2)*((L2 - (a+d)2)) P/L2 (L2 - (a+d)2) Shear Force = (P/L2)*((L2 - (a+d)2)) 283.33333 7.9596 2255.22 KN Permissible Shear Stress 1.118034 N/mm2 for M 20 (P/L2)*((L2 - (a+d)2)) = 4 ( a + d )*d* Tp Tp = (P/L2)*((L2 - (a+d)2)) 4 *( a + d )*d Tp = 969.7368 Tp is lesser than Allowable shear force 0.967 < 1.11803 So the effective depth is safe for Two way Shear Depth required for Bending Movement Moment at the face of the column Mu = ( P/ L2) * (L * (L-a)2 / 8 ) Moment at the face of the column 690.8906 KNm D = Sqat ( Mu / 0.138 * Fck * L ) 288.8614 m Area of Steel Dead load Weight of Slab Length Breadth Height Density KN 4 5 0.3 2400 141.12 Weight of Column 0.45 0.45 5 2400 23.814 Weight of pedastal 0.6 0.6 2 2400 16.9344 Weight of Beam 0.4 0.4 5 2400 18.816 Weight of walls 5 6 0.35 2400 246.96 Weight of floor 4 5 0.3 2400 141.12 588.7644 q = P/L2 qL ((L-a/2)-d) P/L((L-a/2)-d) P/2L ( L - a - 2d) V = Tc x L x d P/2L ( L - a - 2d) for Punching shear) for M 20 V = Shear force q = Uniform pressure for the downside L= length of footing a = diemention of column d = depth pf footing of point where the shear force acting Dead load Live Load Wind load Seismic Load Selected Concrete Concrete Strength Steel Strength Safe Soil Bearing Capacity Base Soil angle of internal Friction 1000 500 200 0 KN KN KN KN M 20 20 KN/mm2 KN/mm2 200 KN/M2 20 Density : 2240 - 2400 kg/m3 (140 - 150 lb/ft3) Compressive strength : 20 - 40 MPa (3000 - 6000 psi) Flexural strength : 3 - 5 MPa (400 - 700 psi) Tensile strength : 2 - 5 MPa (300 - 700 psi) Modulus of elasticity : 14000 - 41000 MPa (2 - 6 x 10 6 psi) Permeability : 1 x 10 -10 cm/sec Coefficient of thermal expansion : 10 -5 o C -1 (5.5 x 10 -6 o F -1 ) -4 Drying shrinkage : 4 - 8 x 10 Drying shrinkage of reinforced concrete : 2 - 3 x 10 -4 Poisson's ratio : 0.20 - 0.21 Shear stress : 6000 - 17000 MPa (1 - 3 x 106 psi) Specific heat capacity : 0.75 kJ/kg K (0.18 Btu/lbm oF (kcal/kg oC))