Maximum Bending Moments for Moving 

 Loads in a Parabolic Arch-Rib 



Hinged at the End.' 



BV E. C. MURPHY. 



As a moving load passes over a prismatic beam resting on supports 

 at the ends the bending moment at every point of the beam changes 

 as the load passes from point to point over the beam. It is zero at 

 the supports or hinges and at no other points, and is a maximum at 

 the center of the span when the concentrated load is at the center, or 

 when the uniformly distributed load covers the whole span. The 

 change in the bending moment at any point of the arch-rib we are 

 •considering as the load passes over it is very different from that of a 

 simple beam: It is the object of this paper to bring out some of these 

 differences. 



We consider two cases: first, a concentrated load; and second, a 

 uniformly distributed load. 



FIG. 1. 



Let A C B, Fig. i, represent a parabolic arch-rib hinged at the 

 abutments; Vj and V^ the vertical reactions and H the horizontal re- 

 action at the ends; h the rise, 1 the span, z, y the coordinates of any 

 point on the curve and x the distance of P, the concentrated load, 

 from A. 



The equation of this parabola referred to the point A as origin and 



4h 

 axes X and y, as shown in tig. r, is y=-— (zl — z~). 



Taking moments about A, considering the whole rib as a free body, 



rl43) KAN. UNIV. QIIAR., vol,. T., NO. I!, -JAN., 1893. 



