![]() ![]() Once all differential elements have been defined using the hatch command, the CAD program sums them as follows: By making the height of the differential element small enough, numerical integration meets accuracy requirements. The approach uses rectangular differential elements, a shape of known sectional properties, where height is the spacing between hatch lines and width is the length of the hatch line. This minimizes the number of hatch lines and reduces the number of program accesses to the drawing database during calculation. To quicken the execution, hatching is done in one direction only. Instead, the approach makes use of each hatch line as a completely independent entity. Therefore, the approach does not use conventional square differential elements. This is because the differential areas are essentially impossible to identify from the hatch pattern and are not always square. An initial step is to let the CAD program crosshatch the area and then extract the hatch information in a form that’s useful for additional calculations.Īfter examining the random methods that AutoCAD uses to hatch areas, it becomes apparent that the classical method of summing square differential areas in an X and Y direction is impractical. The challenge is writing a program to calculate sectional properties using standard AutoCAD hatching commands.īecause all other sectional properties can be determined once you find the area, centroid, and first and second moments of area, the task is to calculate these values first. One way to write such a program is with AutoCAD’s AutoLisp language, which directly accesses a drawing’s database. Programs can be written within CAD packages to find sectional properties for any cross section. But when shapes are complex, more advanced methods are required to determine the necessary values. In fact, formulas for common cross sections like I-beams and other shapes are found in most mechanical design reference books. ![]() In the mechanical design of equipment and systems, sectional properties, such as centroid and moment of inertia, are necessary for calculating stresses, deflections, and buckling. ![]()
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