A method is given for calculating the elements of the kinetic energy matrix for rotation for any molecule. The treatment includes the effects due to any number of linked rotating groups, balanced or unbalanced. In a simple case these equations reduce to the simpler ones of the two previous papers of this series. This rotational matrix is then converted into the matrix of the internal rotations. The reduced moments of inertia that form the latter are then used with the methods of the previous papers of this series to calculate energy levels and thermodynamic functions.
Tall buildings are one of the few constructed facilities whose design relies solely upon analytical and scaled models, which, though based upon fundamental mechanics and years of research and experience, has yet to be systematically validated in full scale. In response to this need, through the combined efforts of members of academe, a design firm and a commercial wind tunnel testing laboratory, a program was initiated to monitor the full-scale response of representative tall buildings and compare this to the predicted response from wind tunnels and finite-element models used commonly in design. As part of this monitoring program, in situ periods and damping ratios over a range of response amplitudes are also being evaluated. This paper provides an overview of the monitoring program, which includes three tall buildings in the city of Chicago, details their instrumentation and modeling, and provides an example of the full-scale response data analyses being conducted.
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