Three-dimensional Six-story Braced Frame

In this example, the Bayesian model updating method is applied to update the finite-element model of a three-dimensional six-story braced frame, which is based on a model of an actual laboratory test structure. It is square in plan with width a = 5 m. There are four columns for each floor, one at each comer. Each of them have interstory stiffnesses of 10 MN/m and 15 MN/m in the x and y directions, respectively. Furthermore, each face in each floor is stiffened by a brace and its stiffness is taken to be 20 MN/m. As a result, the interstory stiffness is 80 MN/m and 100 MN/m in the x and y directions, respectively. The floor mass is taken to be 10 metric tons for each floor. As a result, the first five modal frequencies of the stmcture are 3.432, 3.837, 6.305, 10.10 and 11.29 Hz. 

Bayesian Methods for Structural Dynamics and Civil Engineering 

The element stiffness matrix for the /th story with respect to the Oj coordinates is  

the first three DOFs and the last three DOFs correspond to the lower floor and the upper floor of the story, respectively. Each of these sets of three DOFs correspond to the x-translational, y-translational and torsional motion. 

It is assumed that only the first three x-directional and y-directional modes are measured but not any of the torsional modes. This is done deliberately to simulate a common situation where some of the modes are not excited sufficiently to be able to observe. In the identification process, it is unknown that there are some missing modes. The six measured modes correspond to the 1st (3.432 Hz), 2nd (3.837 Hz), 4th (10.10 Hz), 5th (11.29 Hz), 7th (18.08 Hz) and 9th (21.31 Hz) modes. Sensors are placed on the +y and —y faces of the 1st, 2nd, 5 th and 6th floors, and the -x face of all floors to measure the modal frequencies and mode shape components. The covariance matrix Te is diagonal with 0.5% COV for the modal data. For the simulated modal data, a sample of zero-mean Gaussian noise with covariance matrix Ze was added to the exact modal frequencies and mode shapes. Initial values for all stiffness parameters are taken to be 100 MN/m, which overestimates the values by 100% and 150% for the x and y faces, respectively. 

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