# Center of Rigidity

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

**X _{r}= ∑ Vy_{(i)}* X_{(i)} ) / ∑V_{y(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.

X_{r }= ∑ Vy_{(i)}* X_{(i)} ) / ∑V_{y(i)}

X_{r} = (0.8644*0 + 0.8787*0 + 1.1784*400 + 0.741*400) / (0.8644+0.8787+1.1784+0.741)

**X _{r} = 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: