Kansas University quarterly . rd now common among the whites inOsage Co., Kas.) work: to dupe, as We worked him for a five, He tried to workme. wrangle: to manage sheep or other stock. (Wyoming). wrangler: a herd manager. Maximum Bending Moments for MovingLoads in a Parabolic Arch-Rib Hinged at the End. BV E. C. MURPHY. As a moving load passes over a prismatic beam resting on supportsat the ends the bending moment at every point of the beam changesas the load passes from point to point over the beam. It is zero atthe supports or hinges and at no other points, and is a maximum atthe center of t
Kansas University quarterly . rd now common among the whites inOsage Co., Kas.) work: to dupe, as We worked him for a five, He tried to workme. wrangle: to manage sheep or other stock. (Wyoming). wrangler: a herd manager. Maximum Bending Moments for MovingLoads in a Parabolic Arch-Rib Hinged at the End. BV E. C. MURPHY. As a moving load passes over a prismatic beam resting on supportsat the ends the bending moment at every point of the beam changesas the load passes from point to point over the beam. It is zero atthe supports or hinges and at no other points, and is a maximum atthe center of the span when the concentrated load is at the center, orwhen the uniformly distributed load covers the whole span. Thechange 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 asimple beam: It is the object of this paper to bring out some of thesedifferences. We consider two cases: first, a concentrated load; and second, auniformly distributed FIG. 1. Let A C B, Fig. i, represent a parabolic arch-rib hinged at theabutments; 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 anypoint 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 4haxes 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. 144 KANSAS UNIVERSITY QUARTERLY. Px we find V^= . from 2 (vertical components)=o we find Vn=P ( 1 ( , These vertical reactions are independent of the shape of the rib as^they do not involve z or y and are the same as for a straight beam. Making a section at any point n to the right of the load, consider-ing the left portion of the rib as a free body and denoting the momentby Mr, we have Mr=VjZ-P(z--x)-Hy. Substituting for V, and y thei
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