  Fragility curves are commonly used in civil engineering to assess the
vulnerability of structures to earthquakes. The probability of failure
associated with a prescribed criterion (e.g. the maximal inter-storey drift of
a building exceeding a certain threshold) is represented as a function of the
intensity of the earthquake ground motion (e.g. peak ground acceleration or
spectral acceleration). The classical approach relies on assuming a lognormal
shape of the fragility curves; it is thus parametric. In this paper, we
introduce two non-parametric approaches to establish the fragility curves
without employing the above assumption, namely binned Monte Carlo simulation
and kernel density estimation. As an illustration, we compute the fragility
curves for a three-storey steel frame using a large number of synthetic ground
motions. The curves obtained with the non-parametric approaches are compared
with respective curves based on the lognormal assumption. A similar comparison
is presented for a case when a limited number of recorded ground motions is
available. It is found that the accuracy of the lognormal curves depends on the
ground motion intensity measure, the failure criterion and most importantly, on
the employed method for estimating the parameters of the lognormal shape.
