When rotation-invariant spectra enter structural design: interpreting RotD100 and related measures

In many design procedures, a scalar response spectrum like RotD50 or RotD100 is interpreted as a component spectrum applied independently along two orthogonal structural directions. When a maximum-direction measure such as RotD100 is used in this way, an implicit assumption is introduced: both structural axes experience the worst possible orientation of ground motion. This has contributed to the view that RotD100 is overly conservative for structural design. This paper clarifies that RotD100 is not inherently conservative, but that it represents a different type of quantity than a typical component response. Unlike RotD50, which represents a typical directional component, RotD100 represents an instantaneous peak response occurring in some direction of the horizontal plane. The properties of different rotation-invariant spectra are examined using a geometric interpretation in which the directional response field of ground motion is approximated by an ellipse. Selecting a scalar design spectrum can then be viewed as replacing this ellipse with a circle. Within this geometric framework, several common misconceptions regarding RotD100 can be clarified and avoided in seismic design. The paper concludes that the suitability of a scalar spectrum for design depends on how it is deployed in structural analysis. Ensuring consistency between the chosen intensity measure and the design-action model is therefore essential for the meaningful use of rotation-invariant spectra in structural design.