Three Dimensional Formulation of Large Displacement Problems: The Zipper Frame Example

Abstract

A zipper frame is a conventional braced frame with chevron type braces at all floors, connected through a zipper column linking their midpoints. Under lateral force, a 3 stories frame is expected to behave as follows: after the 1st floor braces buckle, the zipper column transmits the unbalance vertical force to the 2nd story, forcing them to buckle. The new unbalanced vertical force is then transmitted to the third story, which is designed to remain elastic. This is known as the zipper mechanism. Three shaking table tests were performed to evaluate the seismic response of a 3 story suspended zipper frame model. In every shaking table test performed, the braces buckled out of plane but the zipper mechanism did not always develop. Following the test results, a new analytical tool was developed to capture the 3 dimensional phenomena of buckling. It is based on the well known corotational formulation. Every element is described independently. The rigid body modes are removed by using a corotated coordinate system. Within the deformed shape, the element can undergo large rotations and large strains, which are evaluated respect to the corotated origin. The structural problem is solved in the state space, where displacements as well as velocities are variables. The final set of equations is a combination of differential and algebraic equations that is solved using the IDA software. This paper presents the main results of the shaking table tests as well as some general description of the proposed formulation and its capability to verify the shaking table findings.