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XXIX. Note on Continuous Beams. By H. J. Tomlinson 

 and Karl Pearson, University College, London*. 



[Plate VI.] 



(1) TN a paper communicated by Professor Osborne Reynolds 

 JL to the Royal Society, and published in the R. S. Proc. 

 vol. Ixii. p. 268, 1898, Mr. George Wilson develops a novel 

 method of finding the reactions at the points of support of 

 continuous beams. The author claims that the method 

 given " affords an easy and accurate solution for continuous 

 beam problems, and especially those in which the moment of 

 inertia is variable. It also permits of the variations in the 

 stresses due to alterations in the levels of the supports being 

 investigated/" 



Mr. Wilson applies his method to a particular example in 

 which he proceeds so far as the calculation of the reactions. 

 The numerical work appears to us somewhat laborious, and 

 the support-bending moments and the deflexions of the 

 girder are not investigated. The publication of Mr. Wilson's 

 paper seems to indicate that graphical methods of solving the 

 problem of the continuous beam are not so well known in this 

 country as they should be. They appear to us to contain all 

 the requisites for the practical solution of the problem ; they 

 give a great variety of tests for the accuracy of the work at 

 each stage, and for rapidity and ease of working they excel in 

 our experience all other methods. It is well to add that they 

 allow of full consideration of slight changes of level in the 

 points of support and of slight continuous changes in the 

 flexural rigidity of the girder. 



We have accordingly thought it worth while to illustrate 

 the graphical treatment by a reduced drawing of the work 

 needed to solve Mr. Wilson's example fully, including the 

 form of the elastic line of the deflected girder. The method 

 adopted is one which has been in use in the Drawing Office of 

 University College for the last twelve years, and is familiar to 

 all senior students, the full treatment of such a beam falling into 

 the second year's course. A good draughtsman will complete 

 the work indicated in the very much reduced diagram which 

 accompanies this paper in 6 to 8 hours. 



In one point only was it needful to diverge from Mr. Wilson's 

 data. The moment of inertia of the beam, as given by 

 Mr. Wilson, was such that the beam could not have carried 

 its own weight, and as we were desirous of exhibiting the 

 deflexions, it became necessary to select a different flexural 

 rigidity. The maximum flexural rigidity was accordingly 

 * Communicated bv the Authors. 



