Design moment calculations (concrete column: EC2)
Step 1  the amplifier
Calculate the "amplifier" due to buckling in each of Direction 1 and Direction 2 from Equ. 5.28 and Equ. 5.30 of EC2 as^{1},  
k_{5.28} 

1 + π^{2} /(8*(N_{B} /N_{Ed}  1)) 
k_{5.30}  =  1 + 1/(N_{B} /N_{Ed}  1) 
Where 

N_{B}  =  the (Euler) buckling load in the appropriate direction 
=  π^{2} EI/l_{o}^{2}  
l_{o}  =  the effective length in the appropriate direction which for braced columns will be ≤ 1.0L and for unbraced columns ≥ 1.0L 
N_{Ed}  =  the maximum axial compressive force in the column length under consideration (stack) 
Note:
When N_{Ed} ≤ zero i.e. tension, k_{5.28} and k_{5.30} are 1.0. 
Step 2  minimum moment
Calculate the minimum moment due to nonconcentric axial force in each of the two directions from,  
M_{min.1}  =  N_{Ed}  * MAX(h/30, 20) 
Where 

h  =  the major dimension of the column in the appropriate direction 
N_{Ed} 

the maximum axial force (compression or tension) in the column length under consideration (stack) 
Step 3  imperfection moment
Calculate the "firstorder" and "secondorder" imperfection moment in Direction 1 and Direction 2 as,  
M_{imp.1}  =  N_{Ed} * e_{i} 
M_{imp.2}  =  M_{imp.1} * k_{5.28} 
Where 

M_{imp.1}  =  the "firstorder" imperfection moment in a given direction 
M_{imp.2}  =  the "secondorder" imperfection moment in a given direction 
e_{i}  =  the effective length in the appropriate direction divided by 400 
=  l_{o} /400  
N_{Ed} 

the maximum axial compressive force in the column length under consideration (stack) 
Note:
When N_{Ed} ≤ zero i.e. tension, M_{imp.1} and M_{imp.2} are zero. 
Step 4  secondorder moment, curvature method
For rectangular and circular sections the secondorder moment, M_{2.curv}, using the Curvature Method is calculated for each direction. 

M_{2.curv}  =  N_{Ed} * e_{2} 
Where 

e_{2}  =  the deflection due to the maximum curvature achievable with the given axial force 
=  (1/r) l_{o}^{2} /c  
N_{Ed} 

the maximum axial compressive force in the column length under consideration (stack) 
Note:
When N_{Ed} ≤ zero i.e. tension, M_{2.curv} is zero. 
Step 5  secondorder moment, stiffness method
For all section shapes, the secondorder moment, M_{2.stiff}, using the Stiffness Method is calculated in each direction based on the maximum firstorder moment in the midfifth of the column, M_{e.1}, in the appropriate direction. 

M_{2.stiff} 

M_{e.1} * ( π^{2} /(8*(N_{B} /N_{Ed}  1)) 
Where 

M_{e.1}  =  the maximum absolute moment in the midfifth of the column length under consideration (stack) in the appropriate direction 
N_{Ed}  =  the maximum axial compressive force in the column length under consideration (stack) 
Note:
When N_{Ed} ≤ zero i.e. tension, M_{2.stiff} is zero. 
Step 6  lateral loading classification
For the current design combination, for each direction using the member analysis routines, check for point(s) of zero shear within the column length. If none exist or are within the midfifth of the column length then this design case is designated as having lateral loads that are "not significant". Else the lateral loads are considered as "significant".
Step 7  design moment at top
Calculate the design moment at the top of the column in each direction (for both braced and unbraced columns) taking into account if lateral loads are "significant", or "not significant".
Step 8  design moment at bottom
Calculate the design moment at the bottom of the column in each direction (for both braced and unbraced columns) taking into account if lateral loads that are "significant", or "not significant".
Step 9  design moment in midfifth
Calculate the design moment in the midfifth of the column in each direction (for both braced and unbraced columns) taking into account if lateral loads that are "significant", or "not significant".
Footnotes