. Canadian engineer. -ranted by practical considerations. The deflections are obtained by the graphical integra-tion of the familiar equations Mxds . fMds = [Myds ^ ri and ^0 = /? EI J EI the derivation of whicli may be found in Churchs Me-chanics of Engineering and other texts. It must be notedthat the integration is from the point of which the dis-placements are to be obtained to the point where the ribis considered fixed and the displacements secured arerelative to the tangent and normal at the point consideredfixed. In the case of the simple straight cantilever (Fig. i) the y displacem
. Canadian engineer. -ranted by practical considerations. The deflections are obtained by the graphical integra-tion of the familiar equations Mxds . fMds = [Myds ^ ri and ^0 = /? EI J EI the derivation of whicli may be found in Churchs Me-chanics of Engineering and other texts. It must be notedthat the integration is from the point of which the dis-placements are to be obtained to the point where the ribis considered fixed and the displacements secured arerelative to the tangent and normal at the point consideredfixed. In the case of the simple straight cantilever (Fig. i) the y displacement, Ay^ of any point O relative to the • B jvf X dstangent AB is equal to / ? or if the beam be /; EI divided into small ^ ss the value of -^ y is approximately _. B 1/f .V- A 5 As ^ ^— . If the value of ^ ^ be made a constant, EI then EIA 5 ^-B Eq. The simplicity of this equation suggests a graphicalsummation which may be accomplished by means of theforce polygon and funicular polygon, as shown in Fig. Fi^. 2.—Graphical Construction of Elastic Curve of Cantilever. he has found that it has been in use in Europe for sometime. Although .\merican engineers prefer the theory ofleast work in solving statically indeterminate structures,the theory of virtual displacements is often much simpler;and, aside from its use in determining deflections, the As an example, we will consider a cantilever beam witha wedge-shaped end. The beam is first divided into A 9small lengths so that -=- is a constant. A moment dia- tL 1 gram is then drawn for the assumed condition of loadingwhich will be taken as a concentrated load at the end. 4SS THE CANADIAN ENGINEEK Volume 30. rill ccnlros of the dilTcrint divisions ol the beam areprojected down through the moment diagram and thecorresponding moments are laid off algebraically in orderon the load line of the force poljgon. A pole is thenchosen at any convenient distance, />, from the load lineand the rays are drawn. The funicular polygon AB
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