Design of Tied Columns

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where
Pu = ultimate load
for biaxial bending with eccentricities
ex and ey
Px = ultimate load
when eccentricity ex is present (ey = 0)
Py = ultimate load
when eccentricity ey is present (ex = 0)
Po = ultimate load
for concentrically loaded column (ex =
ey = 0)
Equation (78) is valid provided Pu is equal to or greater than
0.10Po.  The usual design cases for interior columns satisfy this
limitation.  The equation is not reliable where biaxial bending is prevalent
and is accompanied by an axial force smaller than 0.10Po.  In the case of
strongly prevalent bending, failure is initiated by yielding of the steel
(tension controls region of P-M curve).  In this range it is safe and
satisfactorily accurate to neglect the axial force entirely and to calculate
the section for biaxial bending only.  This procedure is conservative since
the addition of axial load in the tension controls region increases the
moment capacity.  It should be mentioned that the tension controls case
would be unusual and, if possible, should be avoided in the design.
(4) Reinforcement must be provided on all four faces of a tied
column with the reinforcement on opposite faces of the column equal.  In
applying Equation (78) to the design of tied columns, the values of Px and
Py are obtained from Equation (62) and (64) for the regions where
compression and tension control the design, respectively.  The equations are
for rectangular columns with equal reinforcement on the faces of the column
parallel to the axis of bending.  Consequently, in the calculation of Px
and Py, the reinforcement perpendicular to the axis of bending is
neglected.  Conversely, the total quantity of reinforcement provided on all
four faces of the column is used to calculate Po from Equation (56).
Calculation of Px, Py, and Po in the manner described will yield a
conservative value of Pu from Equation (78).
(5) Due to the possible complex load conditions that can result in
blast design, all tied columns shall be designed for biaxial bending.  If
computations show that there are no moments at the ends of the column or
that the computed eccentricity of the axial load is less than 0.1h, the
column must be designed for a minimum eccentricity equal to 0.1h.  The value
of h is the depth of the column in the bending direction considered.  The
minimum eccentricity shall apply to bending in both the x and y directions,
simultaneously.
(6) To insure proper behavior of a tied column, the longitudinal
reinforcement must meet certain restrictions.  The area of longitudinal
reinforcement shall not be less than 0.01 nor more than 0.04 times the gross
area of the section.  A minimum of 4 reinforcing bars shall be provided.
The size of the longitudinal reinforcing bars shall not be less than No. 6
nor larger than No. 11.  The use of No. 14 and No. 18 bars as well as the
use of bundled bars are not recommended due to problem associated with the
development and anchorage of such bars.  To permit proper placement of the
concrete, the minimum clear distance between longitudinal bars shall not be
less than 1.5 times the nominal diameter of the longitudinal bars or less
than 1.5 inches.
2.08-102