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A new 3 node singular finite element has been derived. This element is incompatible and has to be used in conjunction with incompatible 4 node quadrilateral elements. An extension to three dimensional problems is also presented. This element is used to compute the stress intensity factor along the crack border in a wire with a semi elliptical surface crack subject to tension and for a large variety of elliptical shapes.

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Cable-stayed bridges represent nowadays key points in transport networks and their seismic behaviour needs to be fully understood, even beyond the elastic range of materials. Both nonlinear dynamic (NL-RHA) and static (pushover) procedures are currently available to face this challenge, each with intrinsic advantages and disadvantages, and their applicability in the study of the nonlinear seismic behaviour of cable-stayed bridges is discussed here. The seismic response of a large number of finite element models with different span lengths, tower shapes and class of foundation soil is obtained with different procedures and compared. Several features of the original modal pushover analysis (MPA) are modified in light of cable-stayed bridge characteristics, furthermore, an extension of MPA and a new coupled pushover analysis (CNSP) are suggested to estimate the complex inelastic response of such outstanding structures subjected to multi-axial strong ground motions.

This is the accepted version of the paper.This version of the publication may differ from the final published version. The design of cable-stayed bridges is typically governed by the dynamic response. This work Permanent repository link