Sensitivity analysis of beam–column joint rotation angles with respect to the stiffnesses of the columns of frame structures

Damage detection of frame structures is important for guaranteeing the safety of people’s lives and property. Sensitivity analysis is an effective method for damage identification. The purpose of this paper is to conduct a sensitivity analysis of beam–column joint rotation angles for frame structures with limited flexural stiffness beams.

First, based on the D-value method and the assumption of inflection points, statically indeterminate frames were transformed to statically determinate structures, and the expressions of beam–column joint rotation angles were derived. Next, the sensitivity coefficients of beam–column joint rotation angles were obtained by taking the derivative of the expressions of beam–column joint rotation angles with respect to the linear stiffness of column. Finally, the expressions of the sensitivity coefficients were verified by a numerical example.

The analytical solutions of the sensitivity coefficients are in good agreement with finite element results. The results show that the beam–column joint rotation angles of damaged column decrease and those of intact columns within the same story increase when damage occurs.

In this study, the sensitivity coefficients of beam–column joint rotation angles with respect to the linear stiffnesses of columns were derived for frame structures. Based on the result of the sensitivity analysis, the relationship between the changes of beam–column joint rotation angles and damaged columns is revealed. The findings provide an important base to further detect damage of frame structures.