Modal Interaction in Design of Improved Stiffened Trapezoidal Profiled Sheeting: Shape Grammar, Elastic Stability and Strength Analysis

The main goal of the present research is to investigate a procedure to design of improved stiffened trapezoidal profiled sheeting. In recent work, the authors have combined shape grammar and linear elastic analysis in a semi-automatic procedure to achieve improved solutions with a fitness function based on flexural bending moment critical values (top compression and bottom compression). The profile's signature curves presented the interesting characteristic of three minimum with equivalent critical values, which suggests the possibility of strength erosion by modal interaction. Two questions have been proposed: (i) what the amount of strength erosion is induced by modal interaction in "best shapes" from elastic stability criteria, (ii) how to find solutions where this interaction has less pronounced effects in the neighborhood of the best shapes. Two procedures were performed to answer these questions: (a) the semi-automatic shape grammar procedure keeps the records from the start point to best solution, which leads to identify how geometric parameters induces buckling modes with a certain difference of critical values. Many solutions were tested and compared with results from closed formulae of Direct Strength Method to measure strength erosion and (b) Direct Strength Method has been implemented in the semi-automatic procedure Shape Grammar / Linear Elastic Stability Analysis where Local and Distortional buckling modes are identified by half-wave length criteria, according to experience in similar problems; after this, best solutions were investigated in detail by non-linear elasto-plastic analysis in Finite Element Method. There are some possible conclusions from comparisons: if procedures (a) and (b) achieves the same result ("best" shape), so Direct Strength Method is properly calibrated for these cold-formed sections and the procedure (b) is most appropriate because requires less computational effort; else, it may be necessary to choose between computational or manufacturing costs. Finally, if results from Finite Element Analysis and Direct Strength Method diverge, more research will be necessary.

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