Problem Description

This example comes from Section 5 of Scheller and Constantinou 1999 (“the SUNY Buffalo report”). It is a two-dimensional, three-story moment frame with diagonal fluid viscous dampers that have nonlinear force versus velocity behavior. The model is subjected to horizontal seismic excitation using a scaled version of the S00E component of the 1940 El Centro record (see the section titled “Earthquake Record” later in this example for more information). This model results for modal periods, interstory drift and interstory forcedeformation are compared with experimental results obtained using shake table tests. The experimental results are documented in the SUNY Buffalo report. This model is shown in the figure on the following page. Masses representing the weight at each floor level, including the tributary weight from beams and columns, are concentrated at the beam-column joints. Those masses, 2.39 N-sec2/cm at each joint, act only in the X direction. In addition, small masses, 0.002 N-sec2/cm, are assigned to the damper elements. The small masses help the nonlinear time history analyses solutions converge. Diaphragm constraints are assigned at each of the three floor levels. Beams and columns are modeled as frame elements with specified end length offsets and rigid-end factors. The rigid-end factor is typically 0.6 and the end length offsets vary as shown in the figure. The frame elements connecting the lower end of the dampers to the Level 1 and Level 2 beams are assumed to be rigid. This is achieved in this model by giving those elements section properties that are several orders of magnitude larger than other elements in the model. See the section titled “Frame Element Properties” later in this example for additional information. The dampers are modeled using two-joint, damper-type link elements. Both linear and nonlinear properties are provided for the dampers because this example uses both linear and nonlinear analyses. See the section titled “Damper Properties” and the section titled “Discussion of Nonlinear Damper Stiffness Used in SUNY Buffalo Report” later in this example for additional information. This problem is solved using a nonlinear modal time history analysis and also using a nonlinear direct integration time history analysis. See the section titled “Load Cases Used” later in this example for additional information.

Tested Features

Damper links with nonlinear velocity exponents
Frame end length offsets
Joint mass assignments
Modal analysis for ritz vectors
Nonlinear modal time history analysis
Nonlinear direct integration time history analysis
Generalized displacements

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