Dowden, Purba, and Bruneau 2012
This paper presents insights on the combined contribution of posttensioning and beam-to-column joint rocking connection in SC-SPSWs. Moment, shear, and axial force diagrams along the boundary beam are compared with nonlinear cyclic push-over analysis results, with the goal of creating a design procedure to aid in the selection of post-tension reinforcement area and HBE beam sizes.
System Concept
SPSW systems are frames having steel plates (also known as webs) connected between their beams and columns. During severe earthquakes, the unstiffened plates of SPSWs buckle in shear and yield by developing a diagonal tension field, together with plastic hinging of the beams at their ends. Whereas SPSW systems are desirable for their significant stiffness, strength, and energy dissipation, the hysteretic energy dissipation of this system, like other traditional LFRSs that inherently rely on yielding of steel, results in some level of structural damage and the likelihood of significant residual drifts of the structure after severe earthquakes.
This paper investigates the potential of achieving self-centering steel plate shear walls (SC-SPSWs) by using post-tensioned rocking beam connections between the HBEs and VBEs. This allows a joint gap opening to form between the VBE and HBE interface about a rocking point, leading to a PT elongation, which is the self-centering mechanism. In this proposed system, the SC-SPSW web plate is the replaceable energy dissipation element, and beam-plastic hinging is eliminated. The system combines the advantages of high lateral stiffness, a substantial energy dissipation capacity, and self-centering capability, at the expense of additional challenges to understanding the flow of forces within the structure compared to conventional SPSWs.
Analytical Study, Results and Discussion
Free-body-force diagrams and associated equations were constructed for the system elements, including the HBE, VBE, and web plate. After defining three zones along the HBE (Zones 1 and 2 at the ends where the web plate corners are cut out and Zone 2 where the HBE and web plate are in contact), moment, shear, and axial distributions were determined using the free-body diagrams. The presented formulations are based on a capacity design approach where the web plates have fully yielded.
To verify the formulations describing the distribution of moment, shear, and axial forces developed, comparisons were made to cyclic nonlinear push-over analysis using the computer program SAP2000. For the rigid HBE, all the tension strips yield simultaneously leading to bilinear-shape hysteretic curves, whereas for the flexible HBE, progression in yielding of the tension strips leads to stepwise-shape hysteretic curves. Re-centering is achieved in both cases and all results are in good agreement.
The authors arrived at the following design procedure for the HBE-to-VBE connection:
(1) Select initial boundary element sizes and web plate thickness (of many possible approaches, this could be done by designing a conventional SPSW, although other approaches are acceptable too).
(2) Design the self-centering connection with the least PT forces that would result in the maximum moment occurring at the HBE ends at the target drift.
(3) Select post-tension to ensure that the PT rods remain elastic at least up to 4% drift.
(4) Select the initial PT force applied to the self-centering connection to be also large enough to provide an adequate decompression moment to overcome gravity loads and possible wind loads.
(5) Select the least cross-section areas of PT rods that satisfy the previous conditions.
(6) Consider the effect of PT on reducing the HBE plastic moment as well as the effect of PT losses due to axial shortening to assess the adequacy of the HBE.
(7) Iterate as needed to reduce the HBE size, ensuring that the HBE moment capacity reduced due to axial and shear forces remains adequate.
Reference
Dowden, D., Purba, R., and Bruneau, M. (2012). ”Behavior of Self-Centering Steel Plate Shear Walls and Design Considerations.” Journal of Structural Engineering, 138(1), 11–21.