Quantcast Dynamic Design for Interior Columns

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(10) Design for Rebound.  The beam must be designed to resist the
negative deflection or rebound which occurs after the maximum positive
deflection has been reached.  The negative resistance, r -, attained by
the beam when subjected to a triangular pressure-time load, is taken from
Figure 6-8 of NAVFAC P-397.  Entering the figure with the ratios of
Xm/XE and T/TN, previously determined for the positive phase of the
design, the ratio of the required rebound resistance to the ultimate
resistance, r -/ru, is obtained.  The beam must be reinforced to
withstand this rebound resistance, r -, to insure that the beam will
remain elastic during rebound.
The tension reinforcement provided to withstand rebound forces is added
to what is the compression zone during the initial loading phase.  To
determine this reinforcement, the required rebound moments are obtained from
Table 5 for the appropriate edge and loading conditions.  The beam is
designed to attain its ultimate resistance in the negative direction, that
is, r - is equal to ru.  The required amount of reinforcement is
calculated from Equation (34).
a.  General.  In a shear wall type structure, the lateral loads are
transmitted through the floor and roof slabs to the exterior (and interior,
if required) shear walls.  Due to the extreme stiffness of the shear walls,
there is negligible sidesway in the interior columns and, hence, no induced
moments due to lateral loads.  Therefore, interior columns are axially
loaded members not subjected to the effects of lateral load.  However,
significant moments can result from unsymmetrical loading conditions.
Strength of Compression Members (P-M Curve).
(1) Introduction.
(a) The capacity of a short compression member is based
primarily on the strength of its cross section.  The behavior of the member
encompasses that of both a beam and a column.  The degree to which either
behavior predominates depends upon the relative magnitudes of the axial load
and moment.  The capacity of the column can be determined by constructing an
interaction diagram as shown in Figure 35.  This curve is a plot of the
column axial load capacity versus the moment it can simultaneously
withstand.  Points on this diagram are calculated to satisfy both stress and
strain compatibility.  A single curve would be constructed for a given cross
section with a specified quantity of reinforcement.  The plot of a given
loading condition that falls within this area represents a loading
combination that the column can support, whereas a plot that falls outside
the interaction curve represents a failure combination.
(b) Three points of the interaction diagram are used to define
the behavior of compression members under combined axial and flexural loads.
These points are:  (1) pure compression (Po, M = 0), (2) pure flexure (P =
0, Mo), and (3) balanced conditions (Pb, Mb).  The eccentricity of the
design axial load for the condition of pure compression is zero.  However,
under actual conditions, pure axial load will rarely, if ever, exist.
Therefore, the maximum axial load is limited by a minimum eccentricity,
emin.  At balanced conditions, the eccentricity is defined as eb while
the eccentricity at pure flexure is infinity.  The strength of a section is
controlled by compression when the design eccentricity, e = Mu/Pu, is
smaller than the eccentricity under balanced conditions.  The strength of
the section is controlled by tension when the design eccentricity is greater
than that for balanced conditions.


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