Calculation of Stresses in Footings Subjected to Uniaxial or Biaxial Moments

AB

tCACB

Lever arm ofhorizontal force

HB

HA

MAMB

1

2

3

4 AB

tCACB

Lever arm ofhorizontal force

HB

HA

MAMB

1

2

3

4

Design calculation sheetProject no.: Ex. Date: 6/10/2005 Sheet no.: 1 of 2 Computed by: Tarek Hassan

Subject: VerificationChecked by:Approved by:

Footings Subjected to Uniaxial or Biaxial Moment

Footing ID: F1

Input Data:

0.5 m (Column's dimension parallel to A direction)

0.5 m (Column's dimension parallel to B direction)A = 3 m (Long dimension of footing or dimension resisting moment in case of uniaxial moment)B = 2 m (Short dimension of footing)t = 0.8 m (Total thickness of footing)

Foundation depth = 1.2 m (Distance measured from foundation level to finished ground level )1.8 (Specific gravity of soil)15 (Net bearing capacity)

Type of stress used : GROSS ("Net" or "Gross" )% Taken of Backfilling = 100 % (Considered in checking overturning and sliding)

-20 t (Total column service load (-ve) value for compression & (+ve) value for tension)-5 t (Total load of walls, grade beams and any additional load)2 t (Total horizontal force parallel to A direction)0 t (Total horizontal force parallel to B direction)

Arm for Horizontal Force = 1.2 m (Lever arm of horizontal force)25 mt (Total additional moment in A direction)

-15 mt (Total additional moment in B direction)

27.40 mt (Total moment in A direction)-15.00 mt (Total moment in B direction)

-7.5 t (Column service load (-ve) value for compression & (+ve) value for tension due to D.L)

-2.5 t (Column load due to walls, grade beams and any additional D.L load)1 t (Horizontal force parallel to A direction due to D.L ONLY)0 t (Horizontal force parallel to B direction due to D.L ONLY)12.5 mt (Additional moment in A direction due to D.L ONLY)0 mt (Additional moment in B direction due to D.L ONLY)

13.70 mt (Total moment in A direction due to D.L ONLY)0.00 mt (Total moment in B direction due to D.L ONLY)

Output Data:-12.00 t (Gross O.W of footing)17.16 (Gross bearing capacity)

Area = 6.00 (Spread area of footing)4.502.00-4.14 t (Load of backfilling)

CA =

CB =

Gs = t/m3

qall(net) = t/m2

Forces and Moments Due to Total Load Including D.LPC =

Pw&g.b =HA =HB =

MA(add) =

MB(add) =MA (Total ) =

MB (Total) =

Forces and Moments due to D.L ONLYPC D.L =

Pw&g.b D.L =HA D.L =HB D.L =

MA(add) D.L =MB(add) D.L =

MA (Total) D.L =MB (Total) D.L =

Po.w =qall(gross) = t/m2

m2

IA = m4 (Inertia resisting MA)IB = m4 (Inertia resisting MB)

Pb.f =

AB

tCACB

Lever arm ofhorizontal force

HB

HA

MAMB

1

2

3

4 AB

tCACB

Lever arm ofhorizontal force

HB

HA

MAMB

1

2

3

4

Design calculation sheetProject no.: Ex. Date: 6/10/2005 Sheet no.: 1 of 2 Computed by: Tarek Hassan

Subject: VerificationChecked by:Approved by:

Stresses on Soil Due to D.L ONLY (Gross stresses are always considered)

-26.14 t Total D.L0.21 (Unsafe)-8.92 (Safe)-8.92 (Safe)0.21 (Unsafe)

Unsafe … Increase Footing Dimensions

Check of Overturning Due to Total Load:-41.14 t (Total service load)0.666 m (e<L/3 Safe ) -0.365 m (e<L/3 Safe )0.083 <1/9 (Overturning is Safe)

Stresses on Soil Due to Total Load : Backfilling is taken as 0% in Net stesses and 100% in Gross stresses

-41.14 t (Total service load for gross stesses)9.78 (Redistribution is required) -23.49 (Unsafe!)-8.49 (Safe) -5.22 (Safe)

*Redistribution of Stresses Due to Total Load:0.222 0.666 m -0.365 m0.1824.26 (Fintel Coefficient For Stress Distribution)-29.20 (Unsafe!) (Redistribution of stresses took place!)

Check of sliding Due to Total Load (Passive earth pressure is neglected)-41.14 t (Total service load)0.3

F.S against sliding = 6.17 >=1.5 (Safe)

Pserv D.L =F1 D.L = t/m2

F2 D.L = t/m2

F3 D.L = t/m2

F4 D.L = t/m2

Pserv =eA = eB =

(eA/A)^2+(eB/B)^2 =

Pserv =F1 = t/m2 F3 = t/m2

F2 = t/m2 F4 = t/m2

eA1 /A = eA1= eB1=eB1 /B =

C3 =Fmax = t/m2

Pserv = coefficient of friction(m) =

MB

MA

A

BCA

CB

1

4

2

3

HA

HB

AB

tCACB

Lever arm ofhorizontal force

HB

HA

MAMB

1

2

3

4 AB

tCACB

Lever arm ofhorizontal force

HB

HA

MAMB

1

2

3

4

Design calculation sheetProject no.: Ex. Date: 6/10/2005 Sheet no.: 1 of 2 Computed by: Tarek Hassan

Subject: VerificationChecked by:Approved by:

Design calculation sheetProject no.: EX. Date: 11/10/2005 Sheet no.: 1 of 1 Computed by: Tarek Hassan

Subject: VerificationChecked by:Approved by:

Footings Subjected to Uniaxial or Biaxial MomentFooting ID: F1Input Data:

0.5 m (Column's dimension parallel to A direction)

0.5 m (Column's dimension parallel to B direction)A = 3 m (Long dimension of footing or dimension resisting moment in case of uniaxial moment)B = 2 m (Short dimension of footing)t = 0.8 m (Total thickness of footing)

Foundation depth = 1.2 m (Distance measured from foundation level to finished ground level )1.8 (Specific gravity of soil)15 (Net bearing capacity)

Type of stress used : NET ("Net" or "Gross" )% Taken of Backfilling = 0 % (Considered in checking overturning and sliding)

-20 t (Total column service load (-ve) value for compression & (+ve) value for tension)-5 t (Total load of walls, grade beams and any additional load)2 t (Total horizontal force parallel to A direction)0 t (Total horizontal force parallel to B direction)

Arm for Horizontal Force = 1.2 m (Lever arm of horizontal force)15 mt (Total additional moment in A direction)

15 mt (Total additional moment in B direction)

17.40 mt (Total moment in A direction)15.00 mt (Total moment in B direction)

Output Data:

-3.36 t (Net O.W of footing)

17.16 (Gross bearing capacity)

Area = 6.00 (Spread area of footing)

4.502.00-4.14 t (Load of backfilling)

Check of Overturning Due to Total Load:-37 t (Total service load)0.470 m (e<L/3 Safe ) 0.405 m (e<L/3 Safe )0.066 <1/9 (Overturning is Safe)

Stresses on Soil Due to Total Load : Backfilling is taken as 0% in Net stesses and 100% in Gross stresses

-28.36 t (Total service load for net stesses)-6.43 (Safe) -3.03 (Safe)-18.03 (Unsafe!) 8.57 (Redistribution is required)

*Redistribution of Stresses Due to Total Load:0.157 0.470 m 0.405 m0.2034.26 (Fintel Coefficient For Stress Distribution)-20.12 (Unsafe!) (Redistribution of stresses took place!)

Check of sliding Due to Total Load (Passive earth pressure is neglected)

CA =

CB =

Gs = t/m3

qall(net) = t/m2

PC =Pw&g.b =

HA =HB =

MA(add) =

MB(add) =MA (Total ) =

MB (Total) =

Po.w =qall(gross) = t/m2

m2

IA = m4 (Inertia resisting MA)IB = m4 (Inertia resisting MB)

Pb.f =

Pserv =eA = eB =

(eA/A)^2+(eB/B)^2 =

Pserv =F1 = t/m2 F3 = t/m2

F2 = t/m2 F4 = t/m2

eA1 /A = eA1= eB1=eB1 /B =

C3 =Fmax = t/m2

AB

tCACB

Lever arm ofhorizontal force

HB

HA

MAMB

1

2

3

4 AB

tCACB

Lever arm ofhorizontal force

HB

HA

MAMB

1

2

3

4

Design calculation sheetProject no.: EX. Date: 11/10/2005 Sheet no.: 1 of 1 Computed by: Tarek Hassan

Subject: VerificationChecked by:Approved by:

-37.00 t (Total service load)0.3 F.S against sliding = 5.55 >=1.5 (Safe)

Pserv = coefficient of friction(m) =

0.4 0.3 0.2 0.18 0.16 0.14 0.120.4 37.5 18.8 12.5 11.6 10.9 10.2 9.60.3 18.8 9.4 6.2 5.8 5.4 5.1 4.80.2 12.5 6.2 4.1 3.9 3.6 3.4 3.20.18 11.6 5.8 3.9 3.6 3.4 3.2 30.16 10.9 5.4 3.6 3.4 3.2 3 2.80.14 10.2 5.1 3.4 3.2 3 2.8 2.60.12 9.6 4.8 3.2 3 2.8 2.6 2.50.1 9 4.5 3 2.8 2.6 2.5 2.30.08 8.5 4.2 2.8 2.6 2.5 2.3 2.20.06 8 4 2.7 2.5 2.3 2.2 2.10.04 7.5 3.8 2.5 2.3 2.2 2.1 20.02 7.1 3.5 2.4 2.2 2.1 2 1.8

0 6.7 3.3 2.2 2.1 2 1.8 1.7

(eA/A) (eB/B)

0.1 0.08 0.06 0.04 0.02 09 8.5 8 7.5 7.1 6.74.5 4.2 4 3.8 3.5 3.33 2.8 2.7 2.5 2.4 2.22.8 2.6 2.5 2.3 2.2 2.12.6 2.5 2.3 2.2 2.1 22.5 2.3 2.2 2.1 2 1.82.3 2.2 2.1 2 1.8 1.72.2 2.1 2 1.8 1.7 1.62.1 2 1.8 1.7 1.6 1.52 1.8 1.7 1.6 1.5 1.41.8 1.7 1.6 1.5 1.4 1.21.7 1.6 1.5 1.4 1.2 1.11.6 1.5 1.4 1.2 1.1 1