Slenderness Requirements for Diagonal Braces

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(5) Stiffness and Deflection.  The provisions for rigid frames may
be used for braced frames with the following modifications:
(a) The sidesway natural period of a frame with supplementary
diagonal bracing is given by:
EQUATION:
TN = 2[pi][me/(KKL + Kb)]1/2
(120)
in which Kb is the horizontal stiffness of the tension bracing given by:
EQUATION:
Kb = (nAbE cos3[gamma])/L
(121)
where K, KL, and me are the equivalent frame stiffness, frame load
factor, and effective mass, respectively, as defined for rigid frames.
(b) The elastic deflection of a braced frame is given by:
EQUATION:
XE = Ru(KKL + Kb)
(122)
It should be noted that the frame stiffness, K, is equal to zero for braced
frames with non-rigid girder to column connections.
(6) Slenderness Requirements for Diagonal Braces.  The slenderness
ratio of the bracing should be less than 300 to prevent vibration and
"slapping".  This design condition can be expressed as:
EQUATION:
rb >/= lb/300
(123)
where,
rb = minimum radius of gyration of the bracing member
lb = length between points of support
The X-bracing should be connected together where they cross even though a
compression brace is not considered effective in providing resistance.  In
this manner, Lb for each brace may be taken equal to half of its total
length.
(7) Sizing of Frame Members.  Estimating the maximum forces and
moments in frames with supplementary bracing is similar to the procedures
described for rigid frames.  However, the procedure is slightly more
involved since it is necessary to assume a value for the brace area in
addition to the assumptions for the coefficients C and C1.  For frames
with non-rigid connections, C and C1 do not appear in the resistance
formula for a sidesway mechanism and Ab can be determined directly.
2.08-168

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