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 as1,| k5.28 | = | 1 + π2 /(8*(NB /NEd - 1)) |
| k5.30 | = | 1 + 1/(NB /NEd - 1) |
Where
| NB | = | the (Euler) buckling load in the appropriate direction |
| = | π2 EI/lo2 | |
| lo | = | the effective length in the appropriate direction which for braced columns will be ≤ 1.0L and for unbraced columns ≥ 1.0L |
| NEd | = | the maximum axial compressive force in the column length under consideration (stack) |
Note:
When NEd ≤ zero i.e. tension, k5.28 and k5.30 are 1.0.
Step 2 - minimum moment
Calculate the minimum moment due to non-concentric axial force in each of the two directions from,| Mmin.1 | = | |NEd | * MAX(h/30, 20) |
Where
| h | = | the major dimension of the column in the appropriate direction |
| NEd | = | the maximum axial force (compression or tension) in the column length under consideration (stack) |
Step 3 - imperfection moment
Calculate the "first-order" and "second-order" imperfection moment in Direction 1 and Direction 2 as,| Mimp.1 | = | NEd * ei |
| Mimp.2 | = | Mimp.1 * k5.28 |
Where
| Mimp.1 | = | the "first-order" imperfection moment in a given direction |
| Mimp.2 | = | the "second-order" imperfection moment in a given direction |
| ei | = | the effective length in the appropriate direction divided by 400 |
| = | lo /400 | |
| NEd | = | the maximum axial compressive force in the column length under consideration (stack) |
Note:
When NEd ≤ zero i.e. tension, Mimp.1 and Mimp.2 are zero.
Step 4 - second-order moment, curvature method
For rectangular and circular sections the second-order moment, M2.curv, using the Curvature Method is calculated for each direction.
| M2.curv | = | NEd * e2 |
Where
| e2 | = | the deflection due to the maximum curvature achievable with the given axial force |
| = | (1/r) lo2 /c | |
| NEd | = | the maximum axial compressive force in the column length under consideration (stack) |
Note:
When NEd ≤ zero i.e. tension, M2.curv is zero.
Step 5 - second-order moment, stiffness method
For all section shapes, the second-order moment, M2.stiff, using the Stiffness Method is calculated in each direction based on the maximum first-order moment in the mid-fifth of the column, Me.1, in the appropriate direction.
| M2.stiff | = | Me.1 * ( π2 /(8*(NB /NEd - 1)) |
Where
| Me.1 | = | the maximum absolute moment in the mid-fifth of the column length under consideration (stack) in the appropriate direction |
| NEd | = | the maximum axial compressive force in the column length under consideration (stack) |
Note:
When NEd ≤ zero i.e. tension, M2.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 mid-fifth 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 mid-fifth
Calculate the design moment in the mid-fifth of the column in each direction (for both braced and unbraced columns) taking into account if lateral loads that are "significant", or "not significant".
1 Direction 1 and Direction 2 are referring here to
the member local axes