PROCEEDINGS 



OF 



THE ROYAL IRISH ACADEMY 



PAPERS READ BEFORE THE ACADEMY 



1. 



ON POLYGONS TO GENEEATE DIAGEAMS OF MAX. STEESS 

 ON GIRDEES DUE TO LOCOMOTIVES AND DEAD LOADS, 



TOGETHER WITH 



AN EXTENSION OF EANKINE'S^ CONJUGATE LOAD AEEAS TO 

 THE DESIGN OE MASONEY AECHES. 



By T. ALEXANDEE, M.A.L, 



AND 



J. T. JACKSON, M.A.L, 

 Assistant to the Professor of Civil Engineering, Trinity College, Dublin. 



Eead Novemher 14. Published December 21, 1921. 



In a paper read to the Eoyal Irish Academy in June, 1912, and published on 

 August 31st,* we described our new and exact treatment of the stresses on 

 girder bridges of short span due to the transit of a locomotive. This paper 

 is an extension in more general terms of the same subject, and explains a 

 method of drawing the diagrams of the square roots of maximum bending 

 moments with a template of celluloid or cardboard, which indicates on its face 

 all the maxima of maxima and their positions on the girder. The card will 

 correspond to one locomotive, and for spans increasing from the smallest 

 which can accommodate the locomotive. It can also be made to include the 

 dead load on the girder by changing the position of ' he tracing point. 



We will begin with the following regular polygons, fig. 1. The equilateral 

 triangle standing on its left side turns clock-wise over on to its base, and 

 again over on to its right side ; the vertex describes two circular arcs. The 

 square turns over three times, the tracing point describing three quadrants, 



* Proc. R.I. A., vol. XXX, sec. A, No. 2. 



p.. I. A. PROC, VOL, XXXVI, SECT. A. [Ij 



