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APPENDIX C
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GENERAL
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Several general assumptions are made in the derivation of the equations of motion for
Buildings 2 and 3. It is assumed that the foundation remained stationary during the response of
the structure, Furthermore it {s assumed that all the columns of any ‘ory act ag a nit having
& stiffness k. The masses concentrated at any tioor level include the mass of the floo., girder,
and one-half the mass of the columns above and Sclow the floor in question. For the second
floor only one-third the roase of the first-story columns is included,
The syaten: used to describe th. motion of the structure has nine independent coordinates
(Fig. C. . One coordinate describes the motion of each of the (hres-flocr masses, and one
coordinate ig used for the motion of each of the six front~ and rear-wall panela between floors.
This nine-degree-of-frecdom system is used until the motion of the wall panels becomes oscilatory, A thrce-degree-nf-freedom system is then used to describes the response of the
three-floor masses for the remainder of the motion.
C.2 BUILDING 2
The V-beam sheeting of Building 2 was aasumed tc have no efiect on the loading trans
miited to the girts, Ths girts were assumed to act ag 2 unit. The mass, flexucal rigidity, anc
resistance of the girts and V-beams were disiributed uniformly over ine wialk of (ne atructure.
Since the girts were connected at the floor levels with clip angies or bolts, their ehape during
response waa taken 39 that of a pin-enced beam. The detalles derivation of ine equations of
motion lor elastic action of the froni and rear iaces 1. ,.,¢n below.
C.2.1
Deflected Shape
The following set of equations defines the deflected shapes ior the {reat and reas ‘aces,
assuming that the girts remain elastic (Fig. 1).
For the front face:
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EQUATIONS OF MOTION
136
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