Author(s): Waubke Holger, Kasess Christian
In a recent publication the stationary response of multi storey frames with hysteretic springs representing the massless columns and rigid masses for the floors is presented. As an extension the transient behaviour without an elastic restoring force shall be investigated. For the one degree of freedom case the results using the Gaussian closure technique are equivalent to the results of the statistical linearization. But this is not the case for a multi degree of freedom case. Additionally, the Gaussian closure technique allows for a system without a linear restoring force. In this case no stationarity will be reached and therefore only a transient analysis of the displacements of the floors is possible. The hysteresis is simulated using Bouc’s original model. The response is calculated with an explicit first order time step procedure for the moments derived from Gaussian closure technique. The derivation of the solution is done analytically using a recursion algorithm. This solution is based on relative displacements that can be derived in a simple manner for chain like structures like multi-storey frames in 2D. Therefore, the results produced are the relative displacements that can be transformed to absolute displacement, because the Gaussian closure will calculate all variances and co-variances of the system. The major disadvantage of the Gaussian closure method is that all co-variances and mean values have to be determined, because the number of equations that have to be solved increases almost quadratically with the number of mechanical degrees of freedom. The results of the Gaussian closure technique are compared to the results from the Monte-Carlo method.
Name: Prof Holger Waubke