Foundation Bearing Capacity (pad and strip base:EC2)
Annex A of EC7 allows bearing capacity to be checked using two sets of partial factors: A1 and A2.
In Tekla Structural Designer the bearing capacity check is performed on STR load combinations using set A1 and on GEO load combinations using set A2.
Alternatively, an option is also provided to check a Presumed Bearing Resistance in accordance with EN19971cl.6.5.2.4).
Check for Pad Base Bearing Capacity
Total vertical force: 

F _{dz}  =  γ _{G} *(F _{swt} + F _{soil} + F _{sur,G} ) + γ _{Q} * F _{sur,Q}  F _{z,sup}  


Moment about X axis: 

M _{x,c}  =  M _{x,sup} +F _{z,sup} * y _{1} + h*F _{y,sup}  


Moment about Y axis: 

M _{y,c}  =  M _{y,sup} +F _{z,sup} * x _{1} + h*F _{x,sup}  
Where: 

L _{x}  =  Length of foundation in Xdirection  
L _{y}  =  Length of foundation in Ydirection  
A  =  L _{x} * L _{y} = Foundation area  
h  =  Depth of foundation  
h _{soil}  =  Depth of soil above the foundation  
l _{x}  =  Length of column/wall in Xdirection  
l _{y}  =  Length of column/wall in Ydirection  
x _{1}  =  Offset in Xaxis. (Distance between centre of the pad to the centre of the support in Xdirection)  
y _{1}  =  Offset in Yaxis. (Distance between centre of the pad to the centre of the support in Ydirection)  
γ _{G}  =  1.35 = Permanent partial factor  unfavourable action  when Set A1 used 
=  1.0 = Permanent partial factor  unfavourable action  when Set A2 used  
γ _{Q}  =  1.5 = Variable partial factor  unfavourable action  when Set A1 used 
=  1.3 = Variable partial factor  unfavourable action  when Set A2 used  
F_{swt}  =  A * h * γ _{conc} = foundation selfweight  
F_{soil}  =  (A  A _{c} )*h _{soil} *γ _{soil} = Unfactored load from soil  
γ_{soil}  =  Density of soil  user input  
F_{sur,G}  =  (A  A _{c} )*sc _{G} = Unfactored load from surcharge for permanent loadcase  
F_{sur,Q}  =  (A  A _{c} )*sc _{Q} = Unfactored load from surcharge for variable loadcase  
sc_{G}  =  Surcharge in permanent loadcase  user input  
sc_{Q}  =  Surcharge in variable loadcase  user input  
A_{c}  =  cross section of the column/wall  
F_{z,sup}  =  Vertical load acting on support in STR/GEO limit states (from analysis)  
M_{x,sup}  =  Moment acting on support around Xaxis in STR/GEO limit states from analysis  
M_{y,sup}  =  Moment acting on support around Yaxis in STR/GEO limit states  from analysis  
F_{x,sup}  =  Horizontal force acting on support Xdirection in STR/GEO limit states  from analysis  
F_{y,sup}  =  Horizontal force acting on support Ydirection in STR/GEO limit states  from analysis  



Eccentricity in Xdirection: 

e_{x}  =  M_{y,c} / F _{dz}  


Eccentricity in Ydirection: 

e_{y}  =  M_{x,c} / F _{dz}  
Uniform rectangular stress distribution method
Effective length in Xdirection: 

L'_{x}  =  L_{x}  2e_{x}  when e_{x} > 0 
L'_{x}  =  L_{x} + 2e_{x}  when e_{x} < 0 


Effective length in Ydirection: 

L'_{y}  =  L_{y}  2e_{y}  when e_{y} > 0 
L'_{y}  =  L_{y} + 2e_{y}  when e_{y} < 0 



Design bearing pressure: 

f_{dz}  =  F_{dz} / (L'_{x} * L'_{y} ) 
Presumed bearing capacity method
If 


abs(ex) / Lx + abs(ey) / Ly  ≤  0.167 



Then Base reaction acts within middle third  no loss of contact and: 

Pad base pressures: 

q _{1}  =  F _{dz} /A  6* M _{y,c} / (L _{x} *A) + 6* M _{x,c} / (L _{y} *A) 
q _{2}  =  F _{dz} /A  6* M _{y,c} / (L _{x} *A)  6* M _{x,c} / (L _{y} *A) 
q _{3}  =  F _{dz} /A + 6* M _{y,c} / (L _{x} *A) + 6* M _{x,c} / (L _{y} *A) 
q _{4}  =  F _{dz} /A + 6* M _{y,c} / (L _{x} *A)  6* M _{x,c} / (L _{y} *A) 



Max base pressure: 

q _{max}  =  max (q _{1} , q _{2} , q _{3} , q _{4} ) 


Else base reaction acts outside middle third  loss of contact. In this case the pressure calculations are more complex  in Tekla Structural Designer these are done using sets of equations presented in an article by Kenneth E. Wilson published in the Journal of Bridge Engineering in 1997. 

Note:
Seismic combinations: The presumed bearing capacity method uses SLS combinations in the bearing checks  however as there is no clear Eurocode guidance on service factors for seismic combinations, in Tekla Structural Designer they are not currently assigned. If using the presumed bearing capacity method, to avoid the check being performed for zero loading you are advised to consider which service factors might be appropriate and update the seismic combinations manually. 
Check for Strip Base Bearing Capacity
The principles used in the strip base bearing capacity calculations are similar to those for pad foundations. Only the direction X is checked (around Yaxis) using segment widths. Design bearing pressure: 

f _{dz}  =  F _{dz} / (L' _{x} * L _{y} ) 
