. The Encyclopaedia Britannica; ... A dictionary of arts, sciences and general literature. estone will slip on the other. The abutment producing by its reac-tion the force <, must not yield with a less force than (3, and mustnot be pushed forward so as to produce a greater foice than t^. The*line NABCQ, if inverted, is in form identical with that which acord would assume, loaded at the pointy A, B, and C, with the loads1, 2, and 3, and having the direction of N A determined. This lineWill, in the rest of this article, be called an equilibrated polygon. When the joints are supposedindefinite
. The Encyclopaedia Britannica; ... A dictionary of arts, sciences and general literature. estone will slip on the other. The abutment producing by its reac-tion the force <, must not yield with a less force than (3, and mustnot be pushed forward so as to produce a greater foice than t^. The*line NABCQ, if inverted, is in form identical with that which acord would assume, loaded at the pointy A, B, and C, with the loads1, 2, and 3, and having the direction of N A determined. This lineWill, in the rest of this article, be called an equilibrated polygon. When the joints are supposedindefinitely near, or the voussoirsthin sheets, the equilibrated polygon becomes a curve called a lineararclu The reasoning applied to three blocks is clearly applicableto any number, and we may therefore say that any seriesof loaded voussoirs will be in equilibrium when a reactionof known magnitude and direction is applied at oneabutment, provided the equilibrated polygon required bythis reaction and the given loads can be drawn so that itssides cut all the joints within the ring (or within the. Fig. 45a. middle third, where strength is an element of the question;at an angle greater than the complement of the angle ofrepose for the material used. An equilibrated polygon, ABC Q, for a complete arch is shown in fig. 45 Fig. 45a is the diagram giving the slopes KJ, JI, &c., as for theloaded chain fig. 30 and 31- § 39. It will bo shown in next paragraph that the arcbwill be in equilibrium if with any value of the horizontalthnist h an equilibrated polygon can be drawn fulfillingthe conditions required. In most arches equilibratedpolygons fulfilling these conditions can be drawn withvalues of h varying between two limits differing by aconsiderable amount. In that case the smallest value ofh will be the true value, and give the true stresses ; for theabutments being inert will not give back a greater thrustthan is just required to balance This wouldrender the thrust h determin
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