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elastic curve[i′las·tik ′kərv]
in strength of materials, the curve along which the axis of a beam is bent under the action of a load (the axis of a beam is understood as the line connecting the centers of gravity of the beam’s cross sections). If the equation for the elastic curve is known, the differential equations of the theory of bending can be used to determine the amount of deflection for any section of a beam, as well as the angle of rotation, the bending moment, and the transverse force. The equation of the elastic curve is derived from the approximate differential equation for the axis of a bent beam, which may be solved by either the analytic or the graphic-analytic method. The latter is particularly convenient when it is sufficient to find the deflection or angle of rotation at isolated points of the beam, in which case there is no need to derive analytic expressions for the elastic curve.