# 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}=l_{0}/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