Analytical modeling of zipper frames subjected to shaking table testing

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. It was also found that the 1st floor brace to beam gusset plate was a very important detail that affects the development of the zipper behavior. If the gusset is too stiff, the out of plane moment is transmitted to the beam, twisting it, yielding in torsion and interrupting the zipper mechanism. On the other hand, if it is flexible, the gussets bends and the beam remains straight while the zipper mechanism develops. A new analytical model was developed to capture the three-dimensional phenomena of buckling observed in the testing, while also capturing the local behavior of connections. The model is based on the well known corotational formulation of frames. Every element is described independently. Rigid body modes are removed from the analysis by using a corotated coordinate system. Within the deformed shape, the element can undergo large rotations and large strains, which are evaluated in 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 observations from the shaking table tests as well as the general description of the proposed analytical formulation and examples.