. Canadian engineer. ance /> is measured to the same scaleas the load line. The value ^^ is obtained by the use of the formula =/! MydsEI ;- The y elastic curve AliC is thus seen to be the in-fluence line of the horizontal reaction and the horizontalreaction produced by a load P at any point is equal to thecorresponding y elastic curve ordinate multiplied by the P constant —~. The remarkable simplicity of this method must be ap-parent to any one who has computed reactions with a clean sheet of paper, the writer made theanalysis shown in Fig. i and determined th
. Canadian engineer. ance /> is measured to the same scaleas the load line. The value ^^ is obtained by the use of the formula =/! MydsEI ;- The y elastic curve AliC is thus seen to be the in-fluence line of the horizontal reaction and the horizontalreaction produced by a load P at any point is equal to thecorresponding y elastic curve ordinate multiplied by the P constant —~. The remarkable simplicity of this method must be ap-parent to any one who has computed reactions with a clean sheet of paper, the writer made theanalysis shown in Fig. i and determined the reactions forunit loads at each of the 19 panel points in just seventyminutes. The results tabulated below show the degree ofaccuracy which was obtained with the small scale dia-grams, the length of the arch rib being only about 13inches. The flatness of the arch rib also decreased thesize of s and increased the error. Comparison of Graphical with True Theoretical Reactions. HP Per cent. /•/•/>/>/»/»/. Load a t s Graph. True. error. I 19-3 2 37-75 0-S99 1-54 3 55-25 1-55 4 I-137 5 85-75 1-3812 6 97-75 I-55I 1-5759 7 107-5 8 II4-5 1-8457 9 10 1-913 s = Fig. 2.—Construction of Elastic Curve—Two=hinged Arch This summation is performed graphically by means ofthe funicular polygon ABC which is drawn with itssides perpendicular to the rays of the force polygon pre-viously used. It should not be necessary to go into theproperties of funicular polygons here. They are fullyexplained in Churchs Mechanics and other texts. Thesmooth curve tangent to the sides of the funicular polygonis the -v-elastic curve and from it the x or horizontal dis-placement of any point relative to any other point can beobtained by measuring the horizontal distance between thetwo corresponding points on the elastic curve. The hori-zontal displacem
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