The validity of the response spectrum concept for determining loads in structures excited by differential earthquake ground motion is examined. It is shown that the common definition of response spectrum for synchronous ground motion can be reconciled to remain valid in cases when the columns of extended structures experience different motions. Then, a relative displacement response spectrum for design of first-storey columns, SDC(ΒΉ, , , ), is defined. In addition to natural period, ΒΉ, and fraction of critical damping, , this spectrum depends also on the 'travel time', (of the waves in the soil over distances about one half width, or length of the structure), and on a factor, , specifying the relative displacement of the first floor. It is shown how this spectrum can be determined using existing empirical scaling equations for relative displacement spectra SD(ΒΉ, ) and for peak velocity and peak acceleration of strong ground motion. These new spectra are illustrated for a horizontal component of a record in the near field of the 1994 Northridge earthquake.
The results show that differential motions are more important for short period (stiff ) than for longer period (flexible) structures, and for structures founded on softer ground (small shear wave velocity).