Direct analysis by an arbitrarily-located-plastic-hinge element — Part 1: Planar analysis

• A new and curved beam-column element with three plastic hinges is proposed.
• The internal plastic hinge can be arbitrarily located along the element length.
• The internal DOFs are condensed for easy programming and numerical efficiency.
• Refined plastic hinge method is adopted to simulate gradual yielding of a section.
• Verification examples show the high accuracy and good convergence.

This paper, as the first part of the two companion papers, proposes a new and curved beam-column element with arbitrarily-located plastic hinge for second-order inelastic or direct analysis of planar steel frames. Unlike the conventional plastic hinge element which requires two and more elements to capture the locations of plastic hinge along member length causing much inconvenience to model member initial imperfection, one proposed element per member is sufficient for an accurate analysis. The proposed element explicitly models the member initial imperfection allowing for member P-δ effect directly. The plastic hinge is simulated as a gradually softening spring and the corresponding formulae are presented. The additional degrees of freedom in the element are condensed so that the element can be easily incorporated into existing computer programs with dramatic improvement on numerical efficiency and accuracy. Finally, several examples are presented for verifying the accuracy and validity of the proposed element.