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Diagrammatic Reasoning by Propagating Constraints Through Geometric Objects : An Application to Truss Analysis

A diagrammatic reasoning for structural analysis on trusses is proposed and demonstrated on many examples . In the reasoning, deflected shape of a substructure is drawn at first then it is reasoned how the remaining substructure is affected by the deflection . By identifying the elongated parts are in tension and shortened parts are in compression, a qualitative stress analysis can be done diagrammatically . The method is implemented on a graphical tool that allows direct operation on geometrical objects constraining with each other by geometric constraints. Some theoretical correspondence between drawing diagram and qualitative determinacy of a stress is also addressed.