Sizing of Frame Members

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(4) Loads in Frame Members.  Estimates of the peak axial forces in
the girders and the peak shears in the columns are obtained from Figure 45.
In applying the equations of Figure 45, the equivalent horizontal static
load shall be computed using the dynamic load factor for a panel or combined
sidesway mechanism.
Preliminary values of the peak axial loads in the columns and the peak
shears in the girders may be computed by multiplying the equivalent vertical
static load by the roof tributary area.  Since the axial loads in the
columns are due to the reaction from the roof girders, the equivalent static
vertical load should be computed using the dynamic load factor for the beam
mechanism.
(5) Sizing of Frame Members.  Each member in a frame under the
action of horizontal and vertical blast loads is subjected to combined
bending moments and axial loads.  However, the phasing between critical
values of the axial force and bending moment cannot be established from a
simplified analysis.  Therefore, it is recommended that the peak axial loads
and moments obtained from Figure 45 be assumed to act concurrently for the
purpose of beam-column design.  The resistance of the frame depends upon the
ultimate strength of the members acting as beam-columns.
(a) The columns and girders in the exterior frames are subject
to biaxial bending due to the simultaneous action of vertical pressures on
the roof and horizontal pressures on the exterior walls.  Interior girders
are subjected to bending in one direction only.  However, interior columns
may be subjected to uniaxial or biaxial bending depending upon the direction
of the applied blast load.  When the plane of the shock front is parallel to
a face of the building, frame action occurs in one direction, namely, in the
direction of shock front propagation.  The frames in the transverse
direction are subjected to equal loads at each end, hence no sidesway and
therefore no frame action.  When a blast wave impinges on the building from
a quartering direction, frame action occurs in the two directions due to the
unbalanced loads in each direction.  In such cases, the moments and forces
are calculated by analyzing the response of the frame in each direction for
the appropriate components of the load.  The results in each direction are
then superimposed in order to perform the analysis or design of the beams,
columns, and beam-columns of the structure.  This approach is generally
conservative since it assumes that the peak values of the forces in each
direction occurs simultaneously throughout the three-dimensional structure.
(b) Having estimated the maximum values of the forces and
moments throughout the frame, the preliminary sizing of the members can be
performed using the criteria previously presented for beams and columns.
(6) Stiffness and Deflection.  The stiffness factor, K, for
defined in Table 24.  Considering an equivalent single degree-of-freedom
system, the sidesway natural period of this frame is:
EQUATION:
TN = 2[pi](me/KKL)1/2
(112)
2.08-159