82 Notes on Iron Arches. 



results in sites where, from lack of headway, defective 

 foundation, or other local peculiarity, a stone or brick 

 structure would be quite out of the question; and the 

 selection of lines of communication is thus greatly facilitated, 

 and their length and cost consequently diminished. 



The most tisual form in which iron is employed for bridge 

 purposes is the beam or girder, consisting of two parallel 

 llanges united by a vertical web, consisting either of a contin- 

 uous plate or of a series of diagonal bars. The average cross- 

 section of such a girder is shown in Fig. 1. In a girder 

 supported at each end the upper flange is in compression, 

 like a pillar ; the lower flange is in tension, like a chain — 

 indeed, in some girders the lower flange actually consists of 

 a chain ; while the web is in a somewhat complex state of 

 stress, being compressed in an oblique direction, and extended 

 in another oblique direction at right-angles to the first. In 

 girders with parallel flanges, subject to distributed loads of 

 the usual kind, the compression and tension of the flanges 

 attain maximum values at the centre of the span, and 

 diminish toward the ends, while the web stresses are but 

 small at mid-span, and increase towards the supports. Hence 

 the cross-sections of a theoretically perfect girder, at the 

 centre and the end, would be of the forms represented by 

 Figs. 2 and 3 respectively. 



Occasionally girders are made of varying depth, as shown 

 in Fig. 4, the bottom flange being retained straight, while 

 the top one is curved ; and if this curve be properly designed 

 in view of the special distribution of load anticipated, the 

 following results will be secured : — 



1. The tension on the lower flange will be uniform 

 throughout. 



2. The compression on the upper flange will be nearly 

 uniform throughout, increasing slightly towards the ends. 



3. The stresses on the web will vanish, and the web may 

 consequently be dispensed with. 



We have now left but two flanges, one curved and the 

 other straight, like a bow and its string, and these two 

 flanges will together contain rather less metal than an 

 ordinary parallel girder of equal depth and strength. 



In the girder as thus modified, the compression of the 

 upper or curved flange at the end of the girder may be 

 resolved into two forces — one vertical, which is balanced by 

 the upward reaction of the support, and one horizontal^., 

 which is antagonised by the tension of the lower flange. 



