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