On the dynamics of steel structures with X-type bracing

In steel construction X-type bracings are very often designed under the assumption that the compression diagonal will go slack and only the tension diagonal is accounted for in the structural analysis. With higher horizontal loads, when heavier diagonal sections are required, this assumption does not hold because the compression diagonal develops a considerable buckling load and thus will contribute to the horizontal stiffness of the bracing.
If we look at the dynamic behaviour of such a bracing we will find, that we cannot define a natural frequency in the classical sense, since the stiffness of the system is switching during its cyclic motion. This has also implications on the maximum amplitude which will develop under harmonic excitation. These effects are investigated with realistic cross section of a steel structure; conclusions for practical design are given.