DESIGN OF nXED ENDED ARCHES BY THE 

 ELASTIC THEORY* 



Ghas. Derleth, Jr. 



In the following pages the writer intends to explain the methods 

 for the designing of fixed ended masonry, steel and concrete-steel 

 arches by the elastic theory. The essential parts of the theory 

 involved will be developed and the latest graphical applications 

 given. Designs showing the actual methods used in advanced 

 engineering offices will complete the article. 



Theory.^ 



The ends of an arched rib or girder are considered fixed when 

 the angles formed by their center lines with any fixed line remain 

 unchanged without loading and during the application of varying 

 loads. The piers or abutments are assumed to be immovable under 

 all changes of loading; therefore the total summation of strains at 

 any given distance from the neutral surface of the rib taken through- 

 out the entire length of a fibre must be equal to zero. 



Hence:— 2y,7iP's=0. (1) 



Here, P' is the strain of extension or compression per unit 

 length of fibre parallel to the neutral surface when that fibre is dis- 

 tant unity from the surface; z is the distance of any fibre from the 



neutral surface; and n represents the lengths of parts into which 



Y 

 that fibre has been divided. The summation sign 2-r^, indicates that 



the sum of all the products like 71^' z are to be taken and its limits 

 V and Y ' that the sum is to be taken for the entire lencfth of fibre. 



(1 ) See the treatise by Prof. W. H. Burr, "Stresses in Brida>es and Roof Trusses," published 

 by John Wiley & Sons. 



