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Storey Displacements

Storey displacements are calculated from

us=1n∑iuiu_{s} = \frac{1}{n}\sum_{i}^{}u_{i}

Where ii are the nodes in the storey and nn is the number of nodes in the storey. The rotations are the calculated relative to the centre of mass, cmc_m.

The position of node i relative to the centre of mass is

c=ci−cmc = c_{i} - c_{m}

the distance from the centre of mass is

r=cx2+cy2r = \sqrt{{c_{x}}^{2} + {c_{y}}^{2}}

and the component of displacement giving rise to rotation is

u=ui−usu = u_{i} - u_{s}

The rotation of the storey is then defined as

θ=1n∑i(uycx−uxcyr2)\theta = \frac{1}{n}\sum_{i}^{}\left( \frac{u_{y}c_{x} - u_{x}c_{y}}{r^{2}} \right)