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(8) Dynamic Design Factors. The material presented in NAVFAC P397
is limited to single degreeoffreedom systems only. The design or
transformation factors used to convert the actual system to the equivalent
dynamic system are contained in Table 10. These factors include the load
factor, mass factor, and the loadmass factor for the elastic,
elastoplastic, and plastic ranges of behavior. The loadmass factor is
used for the vast majority of design cases. The load and mass factors are
required to analyze complex design situations.
(9) Dynamic Analysis. When a concrete slab supported by beams is
subjected to a blast load, the slab and beams act together to resist the
load. The beamslab system is actually a twomass system and should be
treated as such. However, a reasonable design can be achieved by
considering the slab and beams separately. That is, the slab and beams are
transformed into single degreeoffreedom systems completely independent of
each other and are analyzed separately. The dynamic analysis of slabs is
treated extensively in NAVFAC P397 and beams are analyzed in much the same
way.
(a) The response of a beam subjected to a dynamic load is
defined in terms of its maximum deflection, Xm, and the time, tm, to
reach this maximum deflection. The dynamic load is defined by its peak
value, B, and duration, T, while the single degreeoffreedom system is
defined in terms of its ultimate resistance, ru, elastic deflection, XE,
and natural period of vibration, TN. For the ratios of B/ru and T/TN,
the ductility ratio, Xm/XE, and tm/T are obtained from Figure 67 of
NAVFAC P397.
(b) A beam is designed to resist the blast load acting over the
tributary area supported by the beam. Therefore, the peak value of the
blast load, B, is the product of the unit peak blast pressure and the
spacing of the beams. The peak blast load then has the unit of pounds per
inch.
(c) In addition to the short term effect of the blast load, a
beam must be able to withstand the long term effect of the slab resistance
when the response time of the slab is equal to or greater than the duration
of the blast load. To insure against premature failure, the ultimate
resistance of the beam must be greater than the reaction of the slab applied
to the beam as a static load.
(d) Since the supported slab does, in fact, act with the beam, a
portion of the mass of the slab acts with the mass of the beam to resist the
dynamic load. It is, therefore, recommended that 20 percent of the mass of
the slab on each side of the beam be added to the actual mass of the beam.
This increased mass is then used to compute the natural period of vibration,
TN, of the beam. It should be noted that in the calculation of TN the
values used for the effective mass and stiffness of the beam depends upon
the allowable maximum deflection. When designing for completely elastic
behavior, the elastic stiffness is used while, in other cases, the
equivalent elastoplastic stiffness, KE, is used. The elastic value of
the effective mass is used for the elastic range, while, in the
elastoplastic range, the effective mass is the average of the elastic and
elastoplastic values. For plastic deformations, the value of the effective
mass is equal to the average of the equivalent elastic value and the plastic
value.
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