Moment and Shear Equations for Bar Vibration Analysis

Mr. E.N. Underwood (Past President), invited by the Chairman to open the discussion, said he had thoroughly enjoyed the authors’ clear description of what was a masterpiece of bridge engineering. He agreed with the Chairman that lessons learned from Brunel and Robert Stephenson could only emphasize what brilliant engineers they had been. Modern experience had proved that their systems could be applied economically today in spite of all the other modern developments.

The critical stress for a lipped plate of given geometry is normally found by solving a transcendental equation by numerical methods. By assuming that the minimum value of the buckling coefficient occurs when there is no transmission of shear loading from the lip to the flange, a solution can be obtained by a considerably simplified analysis. This is shown to give close agreement to the exact solution for a particular case. The simplified analysis allows the torsional stiffness of the lip to be taken into account; it can be applied to all lip shapes, and to many forms of constraint on the other longitudinal edge of the plate. P.S. Bulson

Professor A. C. Scordelis writes: ‘I have read with interest the paper by J. E. Gibson and was pleased to note that his computer solution checks the results obtained in an earlier study of mine. Dr. Gibson’s early pioneering work in the development of computer programmes for cylindrical shells and the publication of his books and papers have been a stimulus for similar work being carried out in the United States.'