Strands of stay cable bridges on saddles with small radii - stresses, contact pressure and wire tip forces
Final Report Abstract
Throughout this project different disciplines were engaged to get further insight into the fretting fatigue failure of strands bent over saddles: the mechanical engineering discipline to study the mechanics of wire ropes bent over saddles, the tribology and metal engineering discipline to cover the failure mechanism of fretting fatigue and the structural engineering discipline to analyse the loading and stress distribution. All three aspects were brought together to spot and to analyse the important fretting fatigue parameters to be deeply studied through the project. Many new phenomena have been discovered and analytical solutions have been provided to calculate the main fatigue parameters. Furthermore, analytical solutions have been proposed for the calculation of fatigue parameters where no solutions have been found in literature, such as the relative displacement of strands subjected to variable axial force due to the frictional losses, and the contact stress between bands and circular elements. 2D time-efficient FEM models have been proposed to simulate the discrete contact force resulting from the spiral geometry of the wires. The model gave a good estimation to the contact forces expected in strands. Being a time-efficient model made it possible to run a parametric study to investigate the effect of many variables on the contact force distribution of strands bent over saddle. The parametric study played an important role in understanding the behaviour of the strands bent over saddles and helped to optimise the experimental work carried out later. 3D models have been built using Abaqus to verify the internal stresses and the contact pressure found in the literature of wire ropes theory and the Hertz theory of contact pressure. Finally, experimental verifications have been carried out addressing each fatigue parameter which gives a high confidence in the results obtained both analytically and numerically. The results of the fatigue parameters estimation has been extended through a joint research with Prof. Scott Walbridge of the Waterloo University in Canada initiated during his Alexander von Humboldt Sabbatical at the chair of conceptual and structural design, TU Berlin. Numerical fatigue models have been employed to estimate the lifetime of strands bent over circular saddles and subjected to the loading conditions of fatigue experiments that has been carried out in the past by the former colleague Ayham Abdelsamad. Two fatigue models have been used for that purpose, the Smith Watson Topper (SWT) method and the Ding et al. (2011) method which is a modified method of the SWT method. The fatigue models have proven to be effective in estimating strands lifetime close to the ones obtained by the experiments especially the Ding et al. (2011) method. Extra to the DFG project program, preliminary dynamic experiments have been carried out to measure the fatigue parameters during the application of cyclic loadings. It was found that the coefficient of friction increases gradually with the increase of loading cycles. Therefore, it is recommended to extend the research to measure the fatigue parameters dynamically. The research project has only examined on the problem of fretting fatigue affecting steel strands bent over circular saddles. It shall be extended in this direction to use the estimated values in calculating the strands lifetime. More detailed models should be developed to enable such a task and to provide a handy tool for the engineers to design reliable saddles. Further experimental fatigue tests are of vital importance to calibrate these models.
Publications
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(2016) ‘Simple model for contact stress of strands bent over circular saddles’, Proceedings of the 19th Congress of IABSE, Stockholm
Mohareb, S., Goldack, A. and Schlaich, M.
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(2016) ‘Stress ribbon bridges - the mechanics of the stress ribbon on the saddle’, J. Bridge Eng.
Goldack, A., Schlaich, M. and Meiselbach, M.
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(2017) ‘Effect of relative displacement of strands bent over circular saddles on fatigue life under fretting conditions’, Proceedings of the 2017 fib Symposium, Maastricht
Mohareb, S., Goldack, A., Schlaich, M. and Walbridge, S.
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(2017) ‘Fretting fatigue analysis of bridge stay cables at saddle supports using multiaxial stress-based approaches’, Proceedings of the 39th IABSE Symposium, Vancouver
Mohareb, S., Goldack, A., Schlaich, M. and Walbridge, S.
