Graphical limit state analysis of hyperstatic structures

This paper suggests a methodology that applies Graphic Statics to the limit state analysis of bended structures within the framework of Plastic Theory. For rather simple statically indeterminate bended structures like beams or frames it shows that this approach could be an alternative method to classical algebraic methods – like applications of the Principle of Virtual Works – for evaluating the structural safety. By application of the Lower Bound Theorem of Plasticity, a ‘safe’ value for the collapse load factor can be graphically determined by means of specific constructions of the reciprocal Form and Force Diagrams that is expressed as a scale factor applicable to the latter in order to transform it into a collapse Force Diagram. The advantages of this methodology are outlined in case of analysing geometrically complex existing structures