  We present the results of a LIGO search for short-duration gravitational
waves (GWs) associated with the 2006 March 29 SGR 1900+14 storm. A new search
method is used, "stacking'' the GW data around the times of individual
soft-gamma bursts in the storm to enhance sensitivity for models in which
multiple bursts are accompanied by GW emission. We assume that variation in the
time difference between burst electromagnetic emission and potential burst GW
emission is small relative to the GW signal duration, and we time-align GW
excess power time-frequency tilings containing individual burst triggers to
their corresponding electromagnetic emissions. We use two GW emission models in
our search: a fluence-weighted model and a flat (unweighted) model for the most
electromagnetically energetic bursts. We find no evidence of GWs associated
with either model. Model-dependent GW strain, isotropic GW emission energy
E_GW, and \gamma = E_GW / E_EM upper limits are estimated using a variety of
assumed waveforms. The stacking method allows us to set the most stringent
model-dependent limits on transient GW strain published to date. We find E_GW
upper limit estimates (at a nominal distance of 10 kpc) of between 2x10^45 erg
and 6x10^50 erg depending on waveform type. These limits are an order of
magnitude lower than upper limits published previously for this storm and
overlap with the range of electromagnetic energies emitted in SGR giant flares.
