footing design
TRANSCRIPT
PROJECT : Radha Puram Bus StandBuilding Version : 1.390 STRUDS Version : 8.9
Foundation Design Detail Report :
(Design by Limit State Method as per IS 456 : 2000)
Design of FG1
Size of col./ped, (l x b) = 0.300 x 0.460 mSBC of soil = 150.00 KN/m²fck = 20.00 Newton/mm²fy = 415.00 Newton/mm²Load combination = 1.50DL + 1.50LL
Loads On Footing
Factored axial load on column,(P) = 427.53 KN Working axial load on column,(Pw) = 285.02 KN (From analysis results)Self Weight of footing assumed = 10.00 % of Pw = 28.50 KNTotal load,(P1) = 313.52 KN BM @ x-x,(WMx) = 3.49 KN-mBM @ y-y,(WMy) = 0.16 KN-mFactored BM @ x-x,(Mx) = 5.24 KN-mFactored BM @ y-y,(My) = 0.24 KN-m
In Loadcombination with DL load case : If load factor for DL loadcase is less than 1.0,this factor will be retained while computing the working load.
Footing Area
Area for axial load,(Af) = P1/SBC = 313.52 / 150.00 = 2.090 m²Eccentricity @ x-x,(ex) = WMx/P = 0.0123 m
= 0.012 mEccentricity @ y-y,(ey) = WMy/P = 0.0006 m
= 0.001 mFooting sizeY,(B) = (0.5 x (b-l))
+ (sqrt((((0.5 x (b-l)) x (0.5 x (b-l)))+Af)))= 1.528 m
Footing sizeX,(L) = Af/B = 1.368 mModified area for Mx,(Afx) = (P/SBC) x (1 + 6.ex/B)
= (313.52/150.00) x (1 + 6 x 0.0123/1.528 )= 2.191 m²
Modified area for My,(Afy) = (P/SBC) x (1 + 6.ey/L)= (313.52/150.00) x (1 + 6 x 0.0006/1.368 ) = 2.095 m²
Size,(L x B) = 1.425 x 1.575 mArea provided ,(Ap) = 2.244 m² > Af.
SBC Check:
Upward pressure due to axial load,(Pr1w) = P / (L x B) = 126.99 KN/m²
Upward pressure due to Mx,(Pr2w) = Mx / (L x B x B/6) = 5.9281 KN/m²Upward pressure due to My,(Pr3w) = My / (B x L x L/6) = 0.3054 KN/m²Maximum upward pressure,(UpMaxw) = Pr1w + Pr2w + Pr3w = 133.23 KN/m²Minimum upward pressure,(UpMinw) = Pr1w - Pr2w - Pr3w = 120.76 KN/m²UpMaxw(133.23 KN/m²) < SBC (150.00 KN/m²),Hence ,safe.
Pressures for Different Load Combinations :
Load Combination Design Pressures(kN/m²) Working Pressures(kN/m²)
Maximum Minimum Maximum Minimum
1.50 DL + 1.50 LL 199.84 181.14 133.23 120.76
Bending Moment Calculations :  As per IS 456: 2000 /Clause 34.2.3.2,critical section for checking bending moment in the design of an isolated concrete footing which supports a column shall be a section located at the face of the column or pedestal.
Upward pressure due to axial load,(Pr1) = P / (L x B) = 190.49 KN/m²Upward pressure due to Mx,(Pr2) = Mx / (L x B x B/6) = 8.8922 KN/m²Upward pressure due to My,(Pr3) = My / (B x L x L/6) = 0.4581 KN/m²Maximum upward pressure,(UpMax) = Pr1 + Pr2 + Pr3 = 199.84 KN/m²Minimum upward pressure,(UpMin) = Pr1 - Pr2 - Pr3 = 181.14 KN/m²Projection-X,(xProj) = (L - l)/2
= (1.425 - 0.300)/2= 0.563 m
Critical upward pressure,(UpCr) = UpMin + (L - xProj) x ((UpMax - UpMin)/L)= 181.14 + (1.425 - 0.563) x ((199.84 - 181.14)/1.425)= 192.46 KN/m²
Upward pressure area,(UpPrArea) = xProj x (UpCr + UpMax)/2= 0.563 x (192.46+ 199.84)/2= 110.33 KN/m
CG distance from column face,(CGDist) = xProj x (UpCr + (2 x UpMax)) /(3 x (UpCr + UpMax))= 0.563 x (192.46 + 2 x 199.84) / (3 x (192.46 + 199.84))= 0.283 m
Design BMx,(MuX) = UpPrArea x CGDist x B= 110.33 x 0.283 x 1.575= 49.18 KN-m
Projection-Y,(yProj) = (B - b)/2= (1.575 - 0.460)/2= 0.558 m
Critical upward pressure,(UpCr) = UpMin + (L - yProj) x ((UpMax - UpMin)/L)= 181.14 + (1.575 - 0.558) x ((199.84 - 181.14)/1.575)= 193.22 KN/m²
Upward pressure area,(UpPrArea) = yProj x (UpCr + UpMax)/2= 0.558 x (193.22+ 199.84)/2= 109.57 KN/m
CG distance from column face,(CGDist) = yProj x (UpCr + (2 x UpMax)) /(3 x (UpCr + UpMax))= 0.558 x (193.22 + 2 x 199.84) / (3 x (193.22 + 199.84))= 0.280 m
Design BMy,(MuY) = UpPrArea x CGDist x L= 109.57 x 0.280 x 1.425= 43.77 KN-m
Depth Calculations :Depth required for punching shear :As per IS : 456 - 2000 - Clause 31.6.3.1,the calculated shear stress at the critical section shall not exceed ks x TauC where, ks = 0.5 + betaC, but not greater than 1,betaC being the ratio of short side to the long side of column, and TauC = 0.25 x sqrt(fck )in limit state method of design.
Depth required for punching shear is calculated by equating the actual stress to permissible stress and by solving the resulting quadratic equation.
Depth assumed,(D) = 0.700 mBottom cover = 0.050 mEffective Depth Calculation : Effective depth,(deffX) = 0.645 mEffective depth,(deffY) = 0.635 mEffective depth,(deff) = 0.645 mDepth || to X axis at critical section,(dPunchX) = 0.487 mDepth || to Y axis at critical section,(dPunchY) = 0.485 m
Resisting area || to X axis,(ArX) = dPunchX x 2 x (l + deff)= 0.487 x 2 x (0.300 + 0.645)= 0.921 m²
Resisting area || to Y axis,(ArY) = dPunchY x 2 x (b + deff)= 0.485 x 2 x (0.460 + 0.645)= 1.072 m²
Resisting area,(Ar) = ArX + ArY= 1.993 m²
Shear force,(V) = (P / Ap) x (Ap -((l + deff) x (b + deff)))= (427.53 / 2.244) x (2.244 - (0.945 x 1.105))= 228.62 KN
Actual shear stress = V / Ar= 228.62 / 1.993= 114.69 KN/m²
Permissible shear stress = 0.25 x sqrt(fck) x ksks = 0.5 + betaCbetaC = short column side/ long column side
= 0.300 / 0.460 = 0.652ks = 0.5 + 0.652 = 1.152 > 1 ,ks = 1
Permissible shear stress = 0.25 x 4.4721 x 1.000= 1.118 N/mm²= 1118.03 KN/m²
Actual shear stress < Permissible shear stress.  Hence,Safe in punching shear.
Calculation Of Moment Of Resistance :
Total depth,(D) = 0.700 mMinimum depth,(Dmin) = 0.300 mFor (Fe415),k = 0.479 R = 0.36 x fck x k x (1 - 0.42 x k)
= 0.36 x 20.000 x 0.479 x (1 - 0.42 x 0.479)= 2.756
Moment of resistanceX = R x width at NA x deffX x deffX= 2.756 x 1.354 x 0.645 x 0.645= 1173.77 KN-m > 49.18 KN-m
Moment of resistance Y = R x width at NA x deffY x deffY= 2.756 x 1.210 x 0.635 x 0.635= 946.93 KN-m > 43.77 KN-m
Steel Calculations :
For MuX :Cross sectional area,(csArea) = width at NA x deffX
= 1.354 x 0.645= 0.873 m²
val = 1 - [(4.6 x MuX)/(fck x B x deffX²)]Required steel area,(AstX) = [0.05 x (1 - sqrt(val))] x csArea/(fy/fck)
= 0.000265 m²= 265 mm²
Required steel pt. = 0.03028 % < minimum steel pt.(min-pt = 0.120 %)
Required steel area,(AstX) = min-pt x csArea/100= 0.120 x 0.873/100= 0.001048 m²= 1048 mm²
Provide 10 Tor 16 nos.(1257 mm²)
Spacing = (L - dia. - (2 x end cover))/(no - 1)
= (1.575 - 0.010 - (2 x 0.050))/(16 - 1)= 0.098 m < maximum spacing(0.200 m)
For MuY :Cross sectional area,(csArea) = width at NA x deffY
= 1.210 x 0.635= 0.768 m²
val = 1 - [(4.6 x MuY)/(fck x B x deffY²)]Required steel area,(AstY) = [0.05 x (1 - sqrt(val))] x csArea/(fy/fck)
= 0.000238 m²= 238 mm²
Required steel pt. = 0.03095 % < minimum steel pt.(min-pt = 0.120 %)
Required steel area,(AstY) = min-pt x csArea/100= 0.120 x 0.768/100= 0.000922 m²= 922 mm²
Provide 10 Tor 15 nos.(1178 mm²)
Spacing = (B - dia. - (2 x end cover))/(no - 1)= (1.425 - 0.010 - (2 x 0.050))/(15 - 1)= 0.094 m < maximum spacing(0.200 m)
Check For One Way Shear :As per IS 456: 2000 /Clause 33.2.4.1,the critical section for thiscondition shall be assumed as a vertical section located at a distance equal to the effective depth of the footing from the face of the column or pedestal.
For X-axis :Projection-X,(proj) = (L - l)/2 - deffX
= (1.425 - 0.300)/2 - 0.645= -0.083 m
As the critical section for one way shear falls outside the footing,oneway shear check is not required to be taken in this direction.
For Y-axis :Projection-Y,(proj) = (B - b)/2 - deffY
= (1.575 - 0.460)/2 - 0.635= -0.077 m
As the critical section for one way shear falls outside the footing,oneway shear check is not required to be taken in this direction.
Check For Bearing :As per IS 456: 2000 /Clause 34.4, the bearing pressure on the loaded area shall not exceedthe permissible bearing stress in direct compression multiplied by a value equal to sqrt(A1/A2), but not greater than 2.
Supporting area for bearing of footing,(A1) = (l + (4 x D))*(b + (4 x D))
= (0.300 + (4 x 0.700)) x (0.460 + (4 x 0.700))= 10.106 m² > footing area(2.244 m²)= 2.244 m²
Loaded area at the column base,(A2) = 0.138 m²sqrt(A1/A2) = sqrt(2.244/0.138) = 4.033 > 2
= 2.000Actual bearing stress = P/A2
= 427.53/0.138= 3098.07 KN/m²
Permissible bearing stress = 0.45 x fck x sqrt(A1/A2) = 0.25 x 20.00 x 2.000= 18.000 N/mm²= 18000.00 KN/m²
Actual bearing stress < Permissible bearing strees. Hence,Safe in bearing.
Check For Sliding Along X axis :
Load combination = 1.50DL + 1.50LL
Self wt. of footing = 27.42 KNStabilizing force,(W) = 454.96 KNHorizontal force,(H) = 0.34 KNSoil resistance,(S) = 174.38 KN> H
Hence,check for sliding is not required.
Check For Sliding Along Y axis :
Load combination = 1.50DL + 1.50LL
Self wt. of footing = 27.42 KNStabilizing force,(W) = 454.96 KNHorizontal force,(H) = 5.64 KNSoil resistance,(S) = 151.87 KN> H
Hence,check for sliding is not required.
Summary :Provide isolated sloped footing of size 1.425 x 1.575 x 0.700 / 0.300 mProvide 10 Tor 16 nos along the length of footing.Provide 10 Tor 15 nos along the width of footing.(Bars should be bent and carried to top.)
Design of FG2
Size of col./ped, (l x b) = 0.300 x 0.460 m
SBC of soil = 150.00 KN/m²
fck = 20.00 Newton/mm²
fy = 415.00 Newton/mm²
Load combination = 1.50DL + 1.50LL
Loads On Footing
Factored axial load on column,(P) = 278.08 KN Working axial load on column,(Pw) = 185.39 KN (From analysis results)Self Weight of footing assumed = 10.00 % of Pw = 18.54 KNTotal load,(P1) = 203.93 KN BM @ x-x,(WMx) = 0.55 KN-mBM @ y-y,(WMy) = 0.43 KN-mFactored BM @ x-x,(Mx) = 0.83 KN-mFactored BM @ y-y,(My) = 0.64 KN-m
In Loadcombination with DL load case : If load factor for DL loadcase is less than 1.0,this factor will be retained while computing the working load.
Footing Area
Area for axial load,(Af) = P1/SBC = 203.93 / 150.00 = 1.360 m²Eccentricity @ x-x,(ex) = WMx/P = 0.0030 m
= 0.003 mEccentricity @ y-y,(ey) = WMy/P = 0.0023 m
= 0.002 mFooting sizeY,(B) = (0.5 x (b-l))
+ (sqrt((((0.5 x (b-l)) x (0.5 x (b-l)))+Af)))= 1.249 m
Footing sizeX,(L) = Af/B = 1.089 mModified area for Mx,(Afx) = (P/SBC) x (1 + 6.ex/B)
= (203.93/150.00) x (1 + 6 x 0.0030/1.249 )= 1.379 m²
Modified area for My,(Afy) = (P/SBC) x (1 + 6.ey/L)= (203.93/150.00) x (1 + 6 x 0.0023/1.089 ) = 1.377 m²
Size,(L x B) = 1.100 x 1.275 mArea provided ,(Ap) = 1.403 m² > Af.
SBC Check:
Upward pressure due to axial load,(Pr1w) = P / (L x B) = 132.19 KN/m²Upward pressure due to Mx,(Pr2w) = Mx / (L x B x B/6) = 1.8523 KN/m²Upward pressure due to My,(Pr3w) = My / (B x L x L/6) = 1.6544 KN/m²Maximum upward pressure,(UpMaxw) = Pr1w + Pr2w + Pr3w = 135.69 KN/m²Minimum upward pressure,(UpMinw) = Pr1w - Pr2w - Pr3w = 128.68 KN/m²UpMaxw(135.69 KN/m²) < SBC (150.00 KN/m²),Hence ,safe.
Pressures for Different Load Combinations :
Load Combination Design Pressures(kN/m²) Working Pressures(kN/m²)
Maximum Minimum Maximum Minimum
1.50 DL + 1.50 LL 203.54 193.02 135.69 128.68
Bending Moment Calculations :  As per IS 456: 2000 /Clause 34.2.3.2,critical section for checking bending moment in the design of an isolated concrete footing which supports a column shall be a section located at the face of the column or pedestal.
Upward pressure due to axial load,(Pr1) = P / (L x B) = 198.28 KN/m²Upward pressure due to Mx,(Pr2) = Mx / (L x B x B/6) = 2.7784 KN/m²Upward pressure due to My,(Pr3) = My / (B x L x L/6) = 2.4815 KN/m²Maximum upward pressure,(UpMax) = Pr1 + Pr2 + Pr3 = 203.54 KN/m²Minimum upward pressure,(UpMin) = Pr1 - Pr2 - Pr3 = 193.02 KN/m²Projection-X,(xProj) = (L - l)/2
= (1.100 - 0.300)/2= 0.400 m
Critical upward pressure,(UpCr) = UpMin + (L - xProj) x ((UpMax - UpMin)/L)= 193.02 + (1.100 - 0.400) x ((203.54 - 193.02)/1.100)= 199.71 KN/m²
Upward pressure area,(UpPrArea) = xProj x (UpCr + UpMax)/2= 0.400 x (199.71+ 203.54)/2= 80.65 KN/m
CG distance from column face,(CGDist) = xProj x (UpCr + (2 x UpMax)) /(3 x (UpCr + UpMax))= 0.400 x (199.71 + 2 x 203.54) / (3 x (199.71 + 203.54))= 0.201 m
Design BMx,(MuX) = UpPrArea x CGDist x B= 80.65 x 0.201 x 1.275= 20.63 KN-m
Projection-Y,(yProj) = (B - b)/2= (1.275 - 0.460)/2= 0.407 m
Critical upward pressure,(UpCr) = UpMin + (L - yProj) x ((UpMax - UpMin)/L)= 193.02 + (1.275 - 0.407) x ((203.54 - 193.02)/1.275)= 200.18 KN/m²
Upward pressure area,(UpPrArea) = yProj x (UpCr + UpMax)/2= 0.407 x (200.18+ 203.54)/2= 82.26 KN/m
CG distance from column face,(CGDist) = yProj x (UpCr + (2 x UpMax)) /(3 x (UpCr + UpMax))= 0.407 x (200.18 + 2 x 203.54) / (3 x (200.18 + 203.54))
= 0.204 m
Design BMy,(MuY) = UpPrArea x CGDist x L= 82.26 x 0.204 x 1.100= 18.49 KN-m
Depth Calculations :Depth required for punching shear :As per IS : 456 - 2000 - Clause 31.6.3.1,the calculated shear stress at the critical section shall not exceed ks x TauC where, ks = 0.5 + betaC, but not greater than 1,betaC being the ratio of short side to the long side of column, and TauC = 0.25 x sqrt(fck )in limit state method of design.
Depth required for punching shear is calculated by equating the actual stress to permissible stress and by solving the resulting quadratic equation.
Depth assumed,(D) = 0.700 mBottom cover = 0.050 mEffective Depth Calculation : Effective depth,(deffX) = 0.645 mEffective depth,(deffY) = 0.635 mEffective depth,(deff) = 0.645 mDepth || to X axis at critical section,(dPunchX) = 0.389 mDepth || to Y axis at critical section,(dPunchY) = 0.395 m
Resisting area || to X axis,(ArX) = dPunchX x 2 x (l + deff)= 0.389 x 2 x (0.300 + 0.645)= 0.734 m²
Resisting area || to Y axis,(ArY) = dPunchY x 2 x (b + deff)= 0.395 x 2 x (0.460 + 0.645)= 0.873 m²
Resisting area,(Ar) = ArX + ArY= 1.608 m²
Shear force,(V) = (P / Ap) x (Ap -((l + deff) x (b + deff)))= (278.08 / 1.403) x (1.403 - (0.945 x 1.105))= 71.04 KN
Actual shear stress = V / Ar= 71.04 / 1.608= 44.19 KN/m²
Permissible shear stress = 0.25 x sqrt(fck) x ksks = 0.5 + betaCbetaC = short column side/ long column side
= 0.300 / 0.460 = 0.652ks = 0.5 + 0.652 = 1.152 > 1 ,ks = 1
Permissible shear stress = 0.25 x 4.4721 x 1.000= 1.118 N/mm²= 1118.03 KN/m²
Actual shear stress < Permissible shear stress.  Hence,Safe in punching shear.
Calculation Of Moment Of Resistance :
Total depth,(D) = 0.700 mMinimum depth,(Dmin) = 0.300 mFor (Fe415),k = 0.479 R = 0.36 x fck x k x (1 - 0.42 x k)
= 0.36 x 20.000 x 0.479 x (1 - 0.42 x 0.479)= 2.756
Moment of resistanceX = R x width at NA x deffX x deffX= 2.756 x 1.119 x 0.645 x 0.645= 1032.11 KN-m > 20.63 KN-m
Moment of resistance Y = R x width at NA x deffY x deffY= 2.756 x 0.953 x 0.635 x 0.635= 795.99 KN-m > 18.49 KN-m
Steel Calculations :
For MuX :Cross sectional area,(csArea) = width at NA x deffX
= 1.119 x 0.645= 0.722 m²
val = 1 - [(4.6 x MuX)/(fck x B x deffX²)]Required steel area,(AstX) = [0.05 x (1 - sqrt(val))] x csArea/(fy/fck)
= 0.000132 m²= 132 mm²
Required steel pt. = 0.01831 % < minimum steel pt.(min-pt = 0.120 %)
Required steel area,(AstX) = min-pt x csArea/100= 0.120 x 0.722/100= 0.000866 m²= 866 mm²
Provide 10 Tor 13 nos.(1021 mm²)
Spacing = (L - dia. - (2 x end cover))/(no - 1)= (1.275 - 0.010 - (2 x 0.050))/(13 - 1)= 0.097 m < maximum spacing(0.200 m)
For MuY :Cross sectional area,(csArea) = width at NA x deffY
= 0.953 x 0.635= 0.605 m²
val = 1 - [(4.6 x MuY)/(fck x B x deffY²)]
Required steel area,(AstY) = [0.05 x (1 - sqrt(val))] x csArea/(fy/fck)= 0.000117 m²= 117 mm²
Required steel pt. = 0.01936 % < minimum steel pt.(min-pt = 0.120 %)
Required steel area,(AstY) = min-pt x csArea/100= 0.120 x 0.605/100= 0.000726 m²= 726 mm²
Provide 10 Tor 12 nos.(942 mm²)
Spacing = (B - dia. - (2 x end cover))/(no - 1)= (1.100 - 0.010 - (2 x 0.050))/(12 - 1)= 0.090 m < maximum spacing(0.200 m)
Check For One Way Shear :As per IS 456: 2000 /Clause 33.2.4.1,the critical section for thiscondition shall be assumed as a vertical section located at a distance equal to the effective depth of the footing from the face of the column or pedestal.
For X-axis :Projection-X,(proj) = (L - l)/2 - deffX
= (1.100 - 0.300)/2 - 0.645= -0.245 m
As the critical section for one way shear falls outside the footing,oneway shear check is not required to be taken in this direction.
For Y-axis :Projection-Y,(proj) = (B - b)/2 - deffY
= (1.275 - 0.460)/2 - 0.635= -0.228 m
As the critical section for one way shear falls outside the footing,oneway shear check is not required to be taken in this direction.
Check For Bearing :As per IS 456: 2000 /Clause 34.4, the bearing pressure on the loaded area shall not exceedthe permissible bearing stress in direct compression multiplied by a value equal to sqrt(A1/A2), but not greater than 2.
Supporting area for bearing of footing,(A1) = (l + (4 x D))*(b + (4 x D))= (0.300 + (4 x 0.700)) x (0.460 + (4 x 0.700))= 10.106 m² > footing area(1.403 m²)= 1.403 m²
Loaded area at the column base,(A2) = 0.138 m²sqrt(A1/A2) = sqrt(1.403/0.138) = 3.188 > 2
= 2.000
Actual bearing stress = P/A2 = 278.08/0.138= 2015.11 KN/m²
Permissible bearing stress = 0.45 x fck x sqrt(A1/A2) = 0.25 x 20.00 x 2.000= 18.000 N/mm²= 18000.00 KN/m²
Actual bearing stress < Permissible bearing strees. Hence,Safe in bearing.
Check For Sliding Along X axis :
Load combination = 1.50DL + 1.50LL
Self wt. of footing = 17.81 KNStabilizing force,(W) = 295.89 KNHorizontal force,(H) = 0.93 KNSoil resistance,(S) = 147.07 KN> H
Hence,check for sliding is not required.
Check For Sliding Along Y axis :
Load combination = 1.50DL + 1.50LL
Self wt. of footing = 17.81 KNStabilizing force,(W) = 295.89 KNHorizontal force,(H) = 0.76 KNSoil resistance,(S) = 122.28 KN> H
Hence,check for sliding is not required.
Summary :Provide isolated sloped footing of size 1.100 x 1.275 x 0.700 / 0.300 mProvide 10 Tor 13 nos along the length of footing.Provide 10 Tor 12 nos along the width of footing.(Bars should be bent and carried to top.)
Design of FG3
Size of col./ped, (l x b) = 0.300 x 0.460 m
SBC of soil = 150.00 KN/m²
fck = 20.00 Newton/mm²
fy = 415.00 Newton/mm²
Load combination = 1.50DL + 1.50LL
Loads On Footing
Factored axial load on column,(P) = 310.49 KN Working axial load on column,(Pw) = 207.00 KN (From analysis results)Self Weight of footing assumed = 10.00 % of Pw = 20.70 KNTotal load,(P1) = 227.69 KN BM @ x-x,(WMx) = 0.41 KN-mBM @ y-y,(WMy) = 0.07 KN-mFactored BM @ x-x,(Mx) = 0.61 KN-mFactored BM @ y-y,(My) = 0.11 KN-m
In Loadcombination with DL load case : If load factor for DL loadcase is less than 1.0,this factor will be retained while computing the working load.
Footing Area
Area for axial load,(Af) = P1/SBC = 227.69 / 150.00 = 1.518 m²Eccentricity @ x-x,(ex) = WMx/P = 0.0020 m
= 0.002 mEccentricity @ y-y,(ey) = WMy/P = 0.0003 m
= 0.000 mFooting sizeY,(B) = (0.5 x (b-l))
+ (sqrt((((0.5 x (b-l)) x (0.5 x (b-l)))+Af)))= 1.315 m
Footing sizeX,(L) = Af/B = 1.155 mModified area for Mx,(Afx) = (P/SBC) x (1 + 6.ex/B)
= (227.69/150.00) x (1 + 6 x 0.0020/1.315 )= 1.532 m²
Modified area for My,(Afy) = (P/SBC) x (1 + 6.ey/L)= (227.69/150.00) x (1 + 6 x 0.0003/1.155 ) = 1.521 m²
Size,(L x B) = 1.175 x 1.325 mArea provided ,(Ap) = 1.557 m² > Af.
SBC Check:
Upward pressure due to axial load,(Pr1w) = P / (L x B) = 132.96 KN/m²Upward pressure due to Mx,(Pr2w) = Mx / (L x B x B/6) = 1.1823 KN/m²Upward pressure due to My,(Pr3w) = My / (B x L x L/6) = 0.2327 KN/m²Maximum upward pressure,(UpMaxw) = Pr1w + Pr2w + Pr3w = 134.37 KN/m²Minimum upward pressure,(UpMinw) = Pr1w - Pr2w - Pr3w = 131.54 KN/m²UpMaxw(134.37 KN/m²) < SBC (150.00 KN/m²),Hence ,safe.
Pressures for Different Load Combinations :
Load Combination Design Pressures(kN/m²) Working Pressures(kN/m²)
Maximum Minimum Maximum Minimum
1.50 DL + 1.50 LL 201.56 197.31 134.37 131.54
Bending Moment Calculations :  As per IS 456: 2000 /Clause 34.2.3.2,critical section for checking bending moment
in the design of an isolated concrete footing which supports a column shall be a section located at the face of the column or pedestal.
Upward pressure due to axial load,(Pr1) = P / (L x B) = 199.43 KN/m²Upward pressure due to Mx,(Pr2) = Mx / (L x B x B/6) = 1.7735 KN/m²Upward pressure due to My,(Pr3) = My / (B x L x L/6) = 0.3490 KN/m²Maximum upward pressure,(UpMax) = Pr1 + Pr2 + Pr3 = 201.56 KN/m²Minimum upward pressure,(UpMin) = Pr1 - Pr2 - Pr3 = 197.31 KN/m²Projection-X,(xProj) = (L - l)/2
= (1.175 - 0.300)/2= 0.437 m
Critical upward pressure,(UpCr) = UpMin + (L - xProj) x ((UpMax - UpMin)/L)= 197.31 + (1.175 - 0.437) x ((201.56 - 197.31)/1.175)= 199.98 KN/m²
Upward pressure area,(UpPrArea) = xProj x (UpCr + UpMax)/2= 0.437 x (199.98+ 201.56)/2= 87.83 KN/m
CG distance from column face,(CGDist) = xProj x (UpCr + (2 x UpMax)) /(3 x (UpCr + UpMax))= 0.437 x (199.98 + 2 x 201.56) / (3 x (199.98 + 201.56))= 0.219 m
Design BMx,(MuX) = UpPrArea x CGDist x B= 87.83 x 0.219 x 1.325= 25.49 KN-m
Projection-Y,(yProj) = (B - b)/2= (1.325 - 0.460)/2= 0.433 m
Critical upward pressure,(UpCr) = UpMin + (L - yProj) x ((UpMax - UpMin)/L)= 197.31 + (1.325 - 0.433) x ((201.56 - 197.31)/1.325)= 200.17 KN/m²
Upward pressure area,(UpPrArea) = yProj x (UpCr + UpMax)/2= 0.433 x (200.17+ 201.56)/2= 86.87 KN/m
CG distance from column face,(CGDist) = yProj x (UpCr + (2 x UpMax)) /(3 x (UpCr + UpMax))= 0.433 x (200.17 + 2 x 201.56) / (3 x (200.17 + 201.56))= 0.216 m
Design BMy,(MuY) = UpPrArea x CGDist x L= 86.87 x 0.216 x 1.175= 22.10 KN-m
Depth Calculations :Depth required for punching shear :As per IS : 456 - 2000 - Clause 31.6.3.1,the calculated shear stress at the critical section shall not exceed ks x TauC where, ks = 0.5 + betaC, but not greater than 1,betaC being the ratio of short side to the long side of column, and TauC = 0.25 x sqrt(fck )in limit state method of design.
Depth required for punching shear is calculated by equating the actual stress to permissible stress and by solving the resulting quadratic equation.
Depth assumed,(D) = 0.700 mBottom cover = 0.050 mEffective Depth Calculation : Effective depth,(deffX) = 0.645 mEffective depth,(deffY) = 0.635 mEffective depth,(deff) = 0.645 mDepth || to X axis at critical section,(dPunchX) = 0.419 mDepth || to Y axis at critical section,(dPunchY) = 0.415 m
Resisting area || to X axis,(ArX) = dPunchX x 2 x (l + deff)= 0.419 x 2 x (0.300 + 0.645)= 0.791 m²
Resisting area || to Y axis,(ArY) = dPunchY x 2 x (b + deff)= 0.415 x 2 x (0.460 + 0.645)= 0.917 m²
Resisting area,(Ar) = ArX + ArY= 1.709 m²
Shear force,(V) = (P / Ap) x (Ap -((l + deff) x (b + deff)))= (310.49 / 1.557) x (1.557 - (0.945 x 1.105))= 102.24 KN
Actual shear stress = V / Ar= 102.24 / 1.709= 59.84 KN/m²
Permissible shear stress = 0.25 x sqrt(fck) x ksks = 0.5 + betaCbetaC = short column side/ long column side
= 0.300 / 0.460 = 0.652ks = 0.5 + 0.652 = 1.152 > 1 ,ks = 1
Permissible shear stress = 0.25 x 4.4721 x 1.000= 1.118 N/mm²= 1118.03 KN/m²
Actual shear stress < Permissible shear stress.  Hence,Safe in punching shear.
Calculation Of Moment Of Resistance :
Total depth,(D) = 0.700 mMinimum depth,(Dmin) = 0.300 mFor (Fe415),k = 0.479 R = 0.36 x fck x k x (1 - 0.42 x k)
= 0.36 x 20.000 x 0.479 x (1 - 0.42 x 0.479)= 2.756
Moment of resistanceX = R x width at NA x deffX x deffX= 2.756 x 1.159 x 0.645 x 0.645= 1055.72 KN-m > 25.49 KN-m
Moment of resistance Y = R x width at NA x deffY x deffY= 2.756 x 1.012 x 0.635 x 0.635= 830.82 KN-m > 22.10 KN-m
Steel Calculations :
For MuX :Cross sectional area,(csArea) = width at NA x deffX
= 1.159 x 0.645= 0.747 m²
val = 1 - [(4.6 x MuX)/(fck x B x deffX²)]Required steel area,(AstX) = [0.05 x (1 - sqrt(val))] x csArea/(fy/fck)
= 0.000155 m²= 155 mm²
Required steel pt. = 0.02070 % < minimum steel pt.(min-pt = 0.120 %)
Required steel area,(AstX) = min-pt x csArea/100= 0.120 x 0.747/100= 0.000897 m²= 897 mm²
Provide 10 Tor 14 nos.(1100 mm²)
Spacing = (L - dia. - (2 x end cover))/(no - 1)= (1.325 - 0.010 - (2 x 0.050))/(14 - 1)= 0.093 m < maximum spacing(0.200 m)
For MuY :Cross sectional area,(csArea) = width at NA x deffY
= 1.012 x 0.635= 0.643 m²
val = 1 - [(4.6 x MuY)/(fck x B x deffY²)]Required steel area,(AstY) = [0.05 x (1 - sqrt(val))] x csArea/(fy/fck)
= 0.000135 m²= 135 mm²
Required steel pt. = 0.02104 % < minimum steel pt.(min-pt = 0.120 %)
Required steel area,(AstY) = min-pt x csArea/100
= 0.120 x 0.643/100= 0.000772 m²= 772 mm²
Provide 10 Tor 12 nos.(942 mm²)
Spacing = (B - dia. - (2 x end cover))/(no - 1)= (1.175 - 0.010 - (2 x 0.050))/(12 - 1)= 0.097 m < maximum spacing(0.200 m)
Check For One Way Shear :As per IS 456: 2000 /Clause 33.2.4.1,the critical section for thiscondition shall be assumed as a vertical section located at a distance equal to the effective depth of the footing from the face of the column or pedestal.
For X-axis :Projection-X,(proj) = (L - l)/2 - deffX
= (1.175 - 0.300)/2 - 0.645= -0.208 m
As the critical section for one way shear falls outside the footing,oneway shear check is not required to be taken in this direction.
For Y-axis :Projection-Y,(proj) = (B - b)/2 - deffY
= (1.325 - 0.460)/2 - 0.635= -0.202 m
As the critical section for one way shear falls outside the footing,oneway shear check is not required to be taken in this direction.
Check For Bearing :As per IS 456: 2000 /Clause 34.4, the bearing pressure on the loaded area shall not exceedthe permissible bearing stress in direct compression multiplied by a value equal to sqrt(A1/A2), but not greater than 2.
Supporting area for bearing of footing,(A1) = (l + (4 x D))*(b + (4 x D))= (0.300 + (4 x 0.700)) x (0.460 + (4 x 0.700))= 10.106 m² > footing area(1.557 m²)= 1.557 m²
Loaded area at the column base,(A2) = 0.138 m²sqrt(A1/A2) = sqrt(1.557/0.138) = 3.359 > 2
= 2.000Actual bearing stress = P/A2
= 310.49/0.138= 2249.95 KN/m²
Permissible bearing stress = 0.45 x fck x sqrt(A1/A2) = 0.25 x 20.00 x 2.000= 18.000 N/mm²
= 18000.00 KN/m²Actual bearing stress < Permissible bearing strees.
Hence,Safe in bearing.
Check For Sliding Along X axis :
Load combination = 1.50DL + 1.50LL
Self wt. of footing = 19.58 KNStabilizing force,(W) = 330.07 KNHorizontal force,(H) = 0.11 KNSoil resistance,(S) = 151.62 KN> H
Hence,check for sliding is not required.
Check For Sliding Along Y axis :
Load combination = 1.50DL + 1.50LL
Self wt. of footing = 19.58 KNStabilizing force,(W) = 330.07 KNHorizontal force,(H) = 0.50 KNSoil resistance,(S) = 129.11 KN> H
Hence,check for sliding is not required.
Summary :Provide isolated sloped footing of size 1.175 x 1.325 x 0.700 / 0.300 mProvide 10 Tor 14 nos along the length of footing.Provide 10 Tor 12 nos along the width of footing.(Bars should be bent and carried to top.)