Dynamic Analysis of Suspended-Floor Highrise Building Using Super-Elements
- Goodno, BJ (Author)
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This series includes technical reports prepared by faculty, students and staff who are associated with the John A. Blume Earthquake Engineering Center at Stanford University. While the primary focus of Blume Center is earthquake engineering, many of the reports in this series encompass broader topics in structural engineering and materials, computational mechanics, geomechanics, structural health monitoring, and engineering life-cycle risk assessment. Each report includes acknowledgments of the specific sponsors for the report and underlying research. In addition to providing research support, the Blume Center provides administrative support for maintaining and disseminating the technical reports. For more information about the Blume Center and its activities, see https://blume.stanford.edu.
The earthquake integrity of a new concept in multistory building construction utilizing an unconventional structural system is investigated. The primary structural elements of this system are two reinforced concrete core towers from which are suspended steel frame floors with concrete floor slabs. Steel hanger straps draped over the cores constitute the floor suspension system and allow the floors to hang down about the cores. A gap of about three inches is left between floor and core and one-inch-square steel "bumper bars" welded to the floor girders at core corners bridge this gap to provide for transmission of lateral forces due to wind and moderate earthquakes. However, these small replaceable bars are intended to fracture in a strong earthquake thereby permitting the floors to sway freely and dissipate energy. (Future modifications of this system specify that shock absorbers be used in place of the bumper bars but satisfactory devices have not yet been developed.) Finite elements are used to model the supporting core structures and the concept of a "super-element", analogous to the notion of a substructure in framed structure analysis, is developed and discussed. Unlike the substructure however, the super-element, once it is formed, is intended to be used repeatedly in modeling the structure. Hence large shear wall structures can be modeled in a refined manner with these super-element building blocks. The basic component of the super-element is a combination of two finite elements: the conforming plate bending element of Bogner, Fox, and Schmit, and the refined plane stress element of Barber, Oakberg, and Weaver. The resulting thirty-two degree of freedom basic element is itself specialized to eight different element types which may be combined to form wall elements. Wall elements in turn form the superelement which is used repeatedly in series elimination fashion in constructing the core structure stiffness and mass matrices. Nodal displacements due to applied loads and vibration frequencies and mode shapes are obtained for isolated shear cores of various shapes. Any number of different super-elements with arbitrarily located wall openings may be used in modeling the structure. Either consistent mass or assembled lumped mass formulations may be employed in the formation of the super-element mass matrix. Selected nodal degrees of freedom are eliminated through matrix condensation of stiffness and mass matrices to control problem size. However, a detailed back-substitution procedure is presented for calculation of all nodal displacements and element stresses. The question of inter-element compatibility at super-element corners is discussed. Application of the super-element concept to plane, angle, channel, and box section shear wall configurations within the tier building model is also included. A three dimensional analytical model is presented for the linear dynamic analysis of the suspended-floor highrise building. All basic components of the building are featured: core towers modeled by superelements, suspended floors idealized as laminae having infinite rigidities in their own planes, bumper bars treated as axial springs at core corners, and hanger straps considered to be axial members with very large initial tensile forces. The equations of motion for displacements of the suspended floors, with respect to any reference point in the plane of the floor, are formulated using the stiffness method in matrix form. These equations are solved by normal mode techniques to obtain the dynamic response of the structure for free vibrations, impulsive lateral loads, and horizontal ground motion. Computer programs written for this study are described in detail and several sample runs are presented to demonstrate the validity of the analytical model for the suspended-floor highrise building. The computer- generated response of the system to wind gust and earthquake loading conditions is also presented. A Hewlett-Packard 5450A Fourier Analyzer, a Kistler Servo Accelerometer, and a Ling Electromagnetic Shaker System were used to determine some of the dynamic properties (natural frequencies and damping) and response of two existing suspended-floor highrise structures under ambient and forced vibration conditions. The lED Building in Mountain View, California, and the Sherman Building in San Jose, California, were the structures tested. A comparison of measured and calculated natural frequencies for each of these structures demonstrates the validity of core tower and building analytical models presented in this dissertation.
- Preferred Citation
- Goodno, BJ. (1975). Dynamic Analysis of Suspended-Floor Highrise Building Using Super-Elements. John A. Blume Earthquake Engineering Center Technical Report 13. Stanford Digital Repository. Available at: http://purl.stanford.edu/zj133jj4675
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