  The application of the TR-BDF2 method to second order problems typical of
structural mechanics and seismic engineering is discussed. A reformulation of
this method is presented, that only requires the solution of algebraic systems
of size equal to the number of displacement degrees of freedom. A linear
analysis and numerical experiments on relevant benchmarks show that the TR-BDF2
method is superior in terms of accuracy and efficiency to the classical Newmark
method and to its generalizations.
