Moment Magnification

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where,
k = effective length factor
Lu = unsupported length of column, in
r = radius of gyration of cross section of column, in
(r = 0.3h for tied columns and 0.25D for
circular columns)
M1 = value of small end moment on column, positive if
member is bent in single curvature and negative
if bent in double curvature, in-lb
M2 = value of larger end moment on column, in-lb
In lieu of a more accurate analysis, the value of M1/M2 may
conservatively be taken equal to 1.0.  Therefore, in the design of columns
the effect of slenderness may be neglected when:
kLu
EQUATION:
< /= 22
(70)
r
(d) The use of slender columns is not permitted in order to
avoid stability problems.  Consequently, the slenderness ratio must be
limited to a maximum value of 50.
(3) Moment Magnification.
(a) Slenderness effects due to buckling and secondary bending
moments must be considered in the design of columns whose slenderness ratio
is greater than that given by Equation (69).  The reduction in the ultimate
strength of a slender column is accounted for in the design procedure by
increasing the design moment.  The cross section and reinforcement is
thereby increased above that required for a short column.
(b) A column braced against sidesway is designed for the applied
axial load P and a magnified moment M defined by:
EQUATION:
M = [delta] M2
(71)
in which
EQUATION:
[delta] = Cm
(72)
1 - P/Pc
where
M
=
design moment, in-lb
[delta]
=
moment magnifier (greater than 1.0)
M2
=
value of larger end moment on column, in-lb
Cm
=
equivalent moment factor given by Equation (73)
P
=
design axial load, lb
Pc
=
critical axial load causing buckling defined
by Equation (74), lb
2.08-98