84 Notes on Iron Arches. 



depended upon in lieu of the central hinge, and by properly- 

 proportioning the transverse dimensions of the rib it is 

 possible to ensure that within a given range of temperature 

 the metal shall not be strained to any dangerous extent. 

 An arch of this second kind will be manifestly less econo- 

 mical in material than one of the first, seeing that it is 

 rec[uired to endure considerable stresses- due to variations of 

 temperature over and above those due to the load supported. 

 Nevertheless there are certain practical considerations — such 

 as simplicity of construction, facility of erection, &c. — which 

 may be reasonably held in some cases to justify its use in 

 preference to the more theoretically perfect form previously 

 described. 



2. A second difficulty arises when in addition to the unvary- 

 ing or dead load, consisting of the weight of the structure itself, 

 we desire the a,rch to support a varying, or as it is often termed 

 a live, load, such as the weight of a crowd of people, a mob of 

 cattle, or a railway train in motion. So long as the load is 

 a perfectly unvarying one, no matter how irregularly it may 

 be distributed, it is possible to adopt a form of arch which will 

 be perfectly suited to the load to be carried, but with a varying 

 load, occuping the same position and affecting the structure 

 in the same way for no two successive instants, such adapta- 

 tion is manifestly impossible. Hence the rib will be sub- 

 jected to a cross-bending action, and be required to act 

 to a considerable extent as a beam as well as to perform its 

 proper functions as an arch ; and this cross-bending action 

 will be severe in small structures in which the live load is 

 equal to or greater than the unvarying or dead load, but will 

 become unimportant in gigantic works in which the live load 

 becomes but an insignificant fraction of the total weight 

 carried. Thus it will be seen that while in large structures 

 we may reasonably expect to realise nearly the whole of the 

 theoretical economic advantage of the arch over the girder, 

 in small ones the additional metal necessary in order to 

 provide for the extra stresses due to the varying distribution 

 of the moving or live load will greatly diminish, if not 

 altogether annul, the superior economy of the arch as com- 

 pared with its competitor. 



I may here parenthetically remark that there is one class 

 of structures in which we might at first expect to realise the 

 full theoretic gain even in the smallest examples. I refer to 

 bridges for the sole purpose of carrying water-pipes, or channels 

 for water supply or canal purposes. Further reflection will, 



