154 UNIVERSITY OF COLORADO STUDIES 



is very nearly: ZD, = 204,800 X ^^' ^^ = 215,000 pounds. 

 •^ ' ' 27o,130 ^ 



By laying off a new load line A,Bi = 289,700 pounds, and draw- 

 ing a perpendicular at its middle point, the pole D, can be located on 

 the perpendicular. A ray joining the pole D, with either A, or B, 

 gives in amount and direction the total maximum thrust upon the 

 abutment. The point of application of this thrust only is slightly in 

 doubt but with experience it can be located closely enough for all 

 practical purposes. 



Piers between two arched ribs should be designated for one span 

 wholly loaded and the other wholly unloaded to give the greatest 

 eccentricity of pressure on the foundation bed. 



For either an abutment or an intermediate pier the resultant 

 pressure on the foundation bed is found by graphically combining 

 the proper arch thrust or thrusts with the dead weight of the abut- 

 ment or pier, the dead weight acting at the centroid of the founda- 

 tion mass. If the foundations are in water the dead weight of the 

 pier or abutment may have to be reduced by a buoyant pressure. 



The computations in this article were made with an ordinary 

 slide rule and will not be found rigorously exact. They are, however, 

 correct far within the necessary limits of practical accuracy. 



Thermal Stresses. 



Thermal stresses in the past have been generally ignored in 

 concrete- steel arches. And yet, especially in flat arches, even for 

 small variations of temperature these stresses reach very considerable 

 amounts. They should be computed and if necessary allowed for. 

 For arches of metal, thermal stresses must always be computed. 



But since this article has already much exceeded the intended 

 limits of the writer, the discussion and computation of thermal 

 stresses will be given in a future number of this publication. 



