. The action of materials under stress; . bent by that loading, will still be straight, as far as canbe observed from most careful examination; but they will nowconverge to a point known as the centre of curvature forthat part of the beam. An assumption, then, that any and all right sections ofthe beam, \>Qxx\g plane before flexure, are still plane after the flexitre of this beam, is reasonable. If the right sections be-came warped, that warping would apparently cause a cumula-tive endwise movement of the particles at successive sections,especially in a beam subjected to a constant maximum
. The action of materials under stress; . bent by that loading, will still be straight, as far as canbe observed from most careful examination; but they will nowconverge to a point known as the centre of curvature forthat part of the beam. An assumption, then, that any and all right sections ofthe beam, \>Qxx\g plane before flexure, are still plane after the flexitre of this beam, is reasonable. If the right sections be-came warped, that warping would apparently cause a cumula-tive endwise movement of the particles at successive sections,especially in a beam subjected to a constant maximum bend-ing moment over a considerable portion of its span; and sucha movement and resulting distortion of the trace of the sec-tional plane ought therefore to become apparent to the a warping can be perceived in shafts, other than cylin-drical, subjected to a twisting couple, but cannot be found inbeams. The lines A C and B D just referred to will be found to befarther apart at the convex side of the beam, and nearer to- BEAMS. 65. ftC gether at the concave side than they first were; hence a lineG H, lying somewhere between A B and C D, is unchanged inlength. If, in Fig. 24, a line parallel to A C is drawn throughH, the extremity of the fibreG H which has not changedin length, K L will represent ^ ]the shortening which I L hasundergone in its reductionto I K, and N O will repre-sent the lengthening whichM N has experienced, instretching to M O. The lengthening or shortening of the fibres, whose length wasoriginally G H =: ds, is directly proportional to the distanceof the fibre from G H, the place of no change of length, andhence of no longitudinal or normal stress. The diagram, Fig. i, representing the elongation orshortening of a bar under increasing stresses, shows that, forstresses within the elastic limit, equal increments of length-ening and shortening are occasioned by equal increments ofstress. If this beam has not been loaded so heavily as toproduce a unit stres
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Keywords: ., bookcentury1800, bookdecade1890, booksubjectstrengt, bookyear1897
