A LIGHTENED CURVILINEAR BAR FOR LONGITUDINAL-TRANSVERSE BENDING,

An effort is made to obtain a closed form solution and to design a curvilinear bar of uniform strength for longitudinal-transverse bending with simultaneously varying cross-sectional height and width. The problem is formulated as follows for given initial conditions, the laws of variation are wanted for the sizes of cross sections taken along the bars axis such that the maximal stresses in any section along the bar axis are equal to the design stresses, and the greatest displacement does not exceed the maximum allowable displacement. Another requirement of the solution is that the difference in the curvatures of any segments of the deformed bar be constant. The author demonstrates that, subject to certain assumptions, a closed form solution can be found for several sets of design conditions. The solution method makes it possible to find the displacement and the moment of inertia of bar cross sections which meet the problem conditions.