RC Column Design (EN1992): Calculation of first order moments for pin ends

In EC2 the first order moments (for stocky columns) are calculated as the initial moments due to design ultimate loads (M) plus the moment from eccentricity due to imperfections

M_01 = M + e_i x N_ed

The Tedds calculation includes the moment from eccentricity due to imperfections even if the moment from design ultimate loads is 0kNm.  This may appear over-conservative and has a significant knock on effect if the column is slender.

The moment due to imperfections (N_Ed*e_i) and the minimum moment (N_Ed*max(b/30,20mm)) are both moments due to eccentricity applied to the end of the column and so will be present even if the end of the column is deemed to be pinned - refer to EC2 Fig 5.1a2) (top of left hand sketch). For a simply supported beam with an equal moment M applied at both ends there is a uniform moment M along the length of the beam - this is essentially what we would have for a column pinned at both ends.