Stiffness and Deflection

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where,
me is the equivalent lumped mass
K is the frame stiffness, k/in
The product KKL is the equivalent stiffness due to a unit load applied at
me.  The load factor, KL, is given by:
EQUATION:
KL = 0.55 (1 - 0.25[beta])
(113)
where,
[beta] = base fixity factor; 0 for pinned base; 1.0 for fixed base
(a) The equivalent mass, me, to be used in calculating the
period of a sidesway mode consists of the total roof mass plus 1/3 of the
column and wall masses.  Since all of these masses are considered to be
concentrated at the roof level, the mass factor, KM = 1.0.
The limiting resistance, Ru, is given by:
EQUATION:
Ru =[alpha]wH
(114)
where,
w = equivalent static load based on the dynamic load factor for a
panel or combined sidesway mechanism.
The equivalent elastic deflection, XE, corresponding to Ru is:
EQUATION:
XE = Ru/KE
(115)
(b) The ductility ratio for the sidesway deflection of the frame
can be computed using the dynamic response chart, Figure 6-7 of NAVFAC
P-937.  The maximum deflection, Xm, is then calculated from:
EQUATION:
Xm = [mu]XE
(116)
where,
[mu] = ductility ratio in sidesway.
2.08-162