The string-net analog of flexure of prismatic beams
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Plots of the stress function (obtained graphically from enlarged photos of the string net), and of the shear-stress distribution over the normal section of beams in cantilever loading, for beams of rectangular, and of circular section, compare well with the exact mathematical solutions. Regions of increasing stress, leading to points of stress concentration are clearly shown.
String nets were built for rectangular sections of ratio of half widthb to half deptha, R=b/a=1/4, 1/2, 1, 2, 4, 8. The form of the net forR≦|1| suggested the assumption of a plane for part of φ(x, y). ForR≫|1| another simple approximation was assumed for φ(x, y). The simple approximate mathematical analyses obtained from the values of φ(x, y) helped to show where the concentrations of stress are and how they vary withR.
KeywordsMechanical Engineer Fluid Dynamics Stress Concentration Mathematical Analysis Simple Approximation
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