Section III. [ 75 ] Trans. Roy. Soc. Canada. 



IX. — An Investigation as to the Maximum Bending Moments at the Points of Sxipport 

 of Continuous Girders of n Spans. By Henry T. Bovey. 



(Communicated by Dr. Alexander Johnson, May 25, 1887.) 

 12 r — 1 r r + 1 « — 1 n 



I AAAAAAAAAAA |i 



Let the Fig. represent a continuous girder of n spans, 1, 2, 3 ... w — 1, being the n — 1 

 intermediate supports. 



Case I. — Assume all the spans to be of the same length /, and let wi, wi Wn-i, w^ be 



the intensities of loads uniformly distributed over the 1st, 2nd w — 1th and wth 



spans, respectively. 



By the Theorem of Three Moments, 



4 . m, + m, = — - . (?()j + M),) (1) 



m, + 4 . ?n, + m,, = — - • (w., + lo^ (2) 



r 



TO, 4- 4 . m^ + m, = — - • (w., + u\) (3) 



TO, 4- 4 . TO, + TO, = — |- • {u\ + W5) (4) 



p 



TO„_3 + 4 . m,._2 + »l„_i = — I (uV-2 + î"a-l) (« — 2) 



m„_2 + 4 . OT„_i = — J (w„-i + îi»,,) (n — 1) 



jMo and m„ are both zero, as the girder is supposed to be resting upon the abutments at 

 and n. 



From these {n — 1) equations, the bending-moments wii, m2 m„_i may be found in 



terms of the distributed loads. 



