Slenderness Ratio

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c.
Slenderness Effects.
(1) General.
(a) The preceding section discussed the capacity of short
compression members.  The strength of these members is based primarily on
their cross section.  The effects of buckling and lateral deflection on the
strength of these short members are small enough to be neglected.  Such
members are not in danger of buckling prior to achieving their ultimate
strength based on the properties of the cross section.  Further, the lateral
deflections of short compression members subjected to bending moments are
small, thus contributing little secondary bending moment (axial load, P,
multiplied by lateral deflection).  These buckling and deflection effects
reduce the ultimate strength of a compression member below the value given
in the preceding section for short columns.
(b) In the design of columns for blast resistant buildings, the
use of short columns is preferred.  The cross section is selected for the
given height and support conditions of the column in accordance with
criteria presented below for short columns.  If the short column cross
section results in a capacity much greater than required, the dimensions may
be reduced to achieve an economical design.  However, slenderness effects
must be evaluated to insure an adequate design.  It should be noted that for
shear wall type structures, the interior columns are not subjected to
sidesway deflections since lateral loads are resisted by the stiff shear
walls.  Consequently, slenderness effects due to buckling and secondary
bending moments (P[W-DELTA]) are the only effects that must be considered.
(2) Slenderness Ratio.
(a) The unsupported length, Lu, of a compression member is
taken as the clear distance between floor slabs, beams, or other members
capable of providing lateral support for the compression member.  Where
column capitals or haunches are present, the unsupported length is measured
to the lower extremity of capital or haunch in the plane considered.
(b) The effective length of a column, kLu, is actually the
equivalent length of a pin ended column.  For a column with pin ends, the
effective length is equal to the actual unsupported length (k = 1.0).  Where
translation of the column at both ends is adequately prevented (braced
column), the effective length of the column is the distance between points
of inflection (k less than 1.0).  It is recommended that for the design of
columns in shear wall type structures, the effective length factor, k, may
be taken as 0.9 for columns that are definitely restrained by beams and
girders at the top and bottom.  For all other cases k shall be taken as 1.0
unless analysis shows that a lower value may be used.
(c) For columns braced against sidesway, the effects of
slenderness may be neglected when:
kLu
M1
EQUATION:
< 34 - 12
(69)
r
M2
2.08-97