170 



STRENGTH OF MATERIALS 



for a roadway three feet above the crown of the arch, with a spandrel filling of 



earth weighing 100 lb./ft. 3 . 



Solution. In this case the weight of a cubic foot of 1 



weight of a cubic foot of the arch ring as 100 : 140. Therefore the load line is 



obtained by redwing the 

 intercept, on eai-h ordinal*- 

 between the roadway and 

 the extrados in the ratio 

 110:100. Thus, in Fig. 1 1'' 1 ., 

 reducing any ordinatu AB 

 in this ratio \\v obtain the 

 ordinate BC, etc. By car- 

 ry ing out this reduction 

 on a MiHieient nuin: 

 ordinates, and joining the 

 points C so found, the load 

 line DECFG is obtained. 



139. Linear arch. Suppose that the voussoirs of an arch have 

 slightly curved surfaces so that they can rock on cue am it lu- 

 sh own in Fig. 127. The points of contact of successive voussoirs are 

 then called centers of pressure, and the line joining them the li: 

 pressure, or linear arch. It is evident, from the figure, or from a model 

 constructed as above, that with every change of loading the voussoirs 

 change their position more or less, thus altering the f>nn .it tin- 

 linear arch. In a model constructed as above, the linear arch can 

 alter its shape consider- 

 ably without overthrow- 

 ing the structure, the only 

 condition necessary to 

 assure stability being that 

 the linear arch shall lie 

 between the intrados and 

 the extrados.* 



In a masonry arch the 

 pressure on any joint 

 is ordinarily distributed 

 over the entire surfaces in contact. In this case the center of pres- 

 sure is the point of application of the resultant joint pressure, and 



* See discussion of arches in article by Fleeminp Jenkin, cntitlr.l " 

 dopssdia Britannica, 9th ed., Vol. IV. pp. _:.-. 



" ; 



