 # How can the centre of gravity (mass) be calculated for a structure in SCIA Engineer?

The only possibility to do so, is by means of the resultant of reactions & the position of the central point.

The resultant internal forces can be calculated back to find the centre of gravity.

Self weight +X
Self weight +Y
Self weight +Z

### 2) Equations for a 3D structure - in the centre of gravity

Mx = Rz*dY - Ry*dZ
My = Rx*dZ - Rz*dX
Mz = Ry*dX - Rx*dY

### 3) Consult the Results in the Document

You will find for each load case the resultant internal forces & the position of the central point (X, Y, Z), which is the geometrical center of the selected supports.

For the table ‘Resultant’, put ‘Selection’ to ‘All’. In that case only 3 from the 6 internal forces are different from 0 for the resultant of each load case, which simplifies the equations.

### 4) Export the Result tables to an Excel file, and calculate dX, dY, dZ

For Self weight +X :
My = Rx*dZ => dZ = My/Rx
Mz = -Rx*dY => dY = -Mz/Rx

For Self weight +Y :
Mx = -Ry*dZ => dZ = -Mx/Ry
Mz = Ry*dX => dX = Mz/Ry

For Self weight +Z :

Mx = Rz*dY => dY = Mx/Rz
My = -Rz*dX => dX = -My/Rz

### 5) Calculate now the center of gravity (Xc, Yc, Zc)

Xc = X + dX
Yc = Y + dY  Where (X, Y, Z) are the co-ordinates of the central point
Zc = Z + dZ