In rigid diaphragm structures, the rigid center is calculated by the method defined by the formulas below.

Xr= ∑ Vy(i)* X(i) ) / ∑Vy(i)

Y r = ∑ Vx (i) * Y (i) ) / ∑V x (i)

In the program, the coordinates of the rigid center are given in the Floor parameters dialog and under the Floor General Information title in the report.

Xr = The perpendicular distance of the center of rigidity of the floor to the Y axis.

Yr = The perpendicular distance of the center of rigidity of the floor to the X axis.

Vy i = Y direction i. is the shear force of the column calculated from additional non-eccentric loading.

X (i) = i. is the perpendicular distance of the center of gravity of the column to the Y axis.

Vx i = X direction i. is the shear force of the column calculated from additional non-eccentric loading.

Y (i) = i. is the perpendicular distance of the center of gravity of the column to the X axis.

The center of stiffness values ​​calculated by the program will be verified manually using the formulas given above.

Typical floor plan and dimensions:

Analysis of the structure is made by giving the ratio of the analysis settings to the eccentric as zero.

### Yr account

The shear forces calculated in the columns at Ex loading are shown below.

Y r = ∑ Vx (i) * Y (i) ) / ∑V x (i)

Yr = (0.4225 * 400 + 2.1443 * 400 + 0.6313 * 0 + 0.628 * 0) / (0.4225 + 2.1443 + 0.6313 + 0.628)

Yr = 269.03 cm

### Xr account

The shear forces calculated in columns at O ​​loading are shown below.

Xr = ∑ Vy(i)* X(i) ) / ∑Vy(i)

Xr = (0.8644*0 + 0.8787*0 + 1.1784*400 + 0.741*400) / (0.8644+0.8787+1.1784+0.741)

Xr = 209.63 cm

The values ​​that appear in the Floor Parameters in the program:

The values ​​that appear in the Floor General Information report header in the program:  Related Topics