![]() ![]() I like matplotlib for plotting it is slower but produces report level graphics - making effective use of the sub plotting can give you nice results, the fill feature is nice but can take awhile to process if you have a complicated plot, if you make a gui and embed a graph start out with dummy x and y data and simply update it (can do this if you don't have a gui as well if you want to change data on the fly and speed up the plotting).Ĭode for the plot starts on line 48 of this file RE: Programming Shear and Moment Diagrams Celt83 (Structural) 2 Apr 18 15:26 If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it. I like to debate structural engineering theory - a lot. I'm happy to share any or all of this with you if you're interested. ![]() It would apply the functions at sampling intervals to generate graphical shear, moment, and deflection diagrams. I rolled the same equations into a MathCAD sheet that I used a lot in my designer days. I tested them thoroughly and actually found an error in S-Frame as a result. I did it using virtual work and the resulting equations are enormous. Deflections for the partial span trapezoidal loads, in particular, were a lot of work. I'm pretty sure that's how SAP & ETABS work actually.Īs part of a programming endeavor from my academic days, I developed closed form solutions to solve your exact problem. Theory of elasticity solutions to beam behavior are found to pretty much confirm these descriptions, and, based on this simple model, beams have been designed and validated for hundreds of years.If maximally leveraging your stiffness matrix algorithm is a high priority, Celt's idea of introducing a bunch of dummy reporting nodes is probably the way to go. This is pretty much the simple stress and strain distribution assumed to exist at each cross section. Yes you simply superpose the normal stress resulting from the bending moment with the shear stress. Is there a standard way of relating the shear and bending moment diagram to the tensor field describing the state of stress at points in a material? In addition, the assumption of a point load actually provides a factor of safety because certain measures-such as the bending moment-peak at a point rather than a slightly less impactful curve. Put another way, far from a load (say, three times the beam thickness), it doesn't matter whether the load is applied at a point or over a finite region. ![]() At the differential level, the stress tensor field of a homogeneous continuous elastic material will vary continuously from point to point.Īn important principle is Saint-Venant's principle which says that the distribution of a particular load becomes less important with increasing distance from the load. The abrupt transitions in the graphs are not typical of actual physical systems. Since you're well accustomed to self-education, I'll just provide some pointers to where to look for more information. The framework is covered in Beer & Johnston's Mechanics of Materials, for one, among several other standard textbooks on the so-called mechanics of deformable materials. You've intersected with the standard approach with which engineering students learn about stress and strain in college. Of particular interest would be the orientations of the principal axes at different points in the stressed member. Is there a standard way of relating the shear and bending moment diagram to the tensor field describing the state of stress at points in a material? I'm interested in a simple plane deformation case of the kind shown in the first diagram of the Wikipedia article. At the differential level, the stress tensor field of a homogeneous continuous elastic material will vary continuously from point to point. Since there have been a few stable structures produced by engineers over the past century or so, I will assume the method gives meaningful results. ![]() I don't recall ever encountering the so-called shear and bending momentum diagram used in engineering. That mostly covers the states of stress and strain and their relationship at a point. I've read a fair amount of material on the physics of elasticity. ![]()
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