How to calculate resultant first order eccentricity on the compression member

A compression member is subjected by normal force and bending moments in both planes y,z. The resultant first order eccentricity is calculated as the ratio of a design normal force and bending moments plus geometrical eccentricity counted as the length of a column/ 400 for a single column.

Calculation of a first-order eccentricity and imperfections

In the navigator tree, there is the Second Order Effect tab which serves for calculation resultant first order and second-order effect on the column.

First order eccentricity :

e_0,y/z=M_0,y/z/N_ed=250/2500 = 100 mm

e_0,y/z=M_0,y/z/N_ed=150/2500 = 60 mm

Imperfections :

e_iy/z=l₀/400 = 3000/400 =7.5 mm

Calculation of a resultant first order eccentricity

The resultant eccentricity e_0ed,yz is counted as first order eccentricity e_0,y/z plus increment geometrical imperfection e_iy/z to each direction.

arctg(α) = e_0,y/e_0,z= 100/60 = 59.03 °

ei,y = sin (α) * e_i,y/z=sin (59.03)*7.5 = 6.43 mm

ei,z= cos (α) * e_i,y/z=cos (59.03)*7.5 = 3.86mm

Resultant first order eccentricity:

e_0Ed,y = e_0,y + e_i,y = 100 + 6.43 = 106.43 mm

e_0Ed,z = e_0,z + e_i,z = 60+ 3.86 = 106.43 mm