SUMMARYIn this article an analytical method is developed for identifying basic collapse mechanisms of rigidjointed two-dimensional frames. In this approach, the deformation of each member is completely deÿned by four translations and one rotation. The behaviour of such an element lies in between that of a truss element and a exural one.Once the basic collapse mechanisms are identiÿed, the genetic algorithm is used to identify the mechanism corresponding to the least possible load factor. Examples are included to illustrate the e ciency of the present method compared to the use of a simple genetic algorithm.

SUMMARYThis paper presents three new approaches for solving eigenvalue problems of non-classically damped linear dynamics systems with fewer calculations than the conventional state vector approach. In the latter, the second-order di erential equation of motion is converted into a ÿrst-order system by doubling the size of the matrices. The new approaches simplify the approach and reduce the number of calculations.The mathematical formulations for the proposed approaches are presented and the numerical results compared with the existing method by solving a sample problem with di erent damping properties. Of the three proposed approaches, the expansion approach was found to be the simplest and fastest to compute.

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The damage that can occur to structures by way of deformation in bending under the excitation of random forces (referred to hereafter as ‘bending structures') is considered a local state due to the harm caused by cracks. Its effects on the behaviour of the structure are discussed as discontinuity phenomena. For the simulation of such discontinuities, the bilinear stiffness reduction function, which results in asymmetrical behaviour of a damaged member when loaded in opposite directions, has been defined together with a corresponding crack index. For different damage scenarios, the effect of the non-linear behaviour of affected members has been investigated according to which damaged members can be identified by means of a crack index. The proposed damage identification method is not hampered by the existence of any kind of noise. The effectiveness and accuracy of the proposed method have been examined by applying a ‘closed-loop solution' to a six- and an eight-storey bending structure, using in each case an analytical model and different pre-defined damage scenarios. Taking into account these scenarios, several bilinear stiffness reduction functions were assumed not only for the column stiffness coefficient of one or more theoretically damaged storeys of the investigated structure, but also for the beam stiffness coefficient corresponding to one or more such storeys.