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Dynamic Analysis.
(1) Introduction. The dynamic analysis of beams is performed in the
same manner as that given in NAVFAC P397 for slabs. The data presented for
oneway slab elements are applicable for beams. These data plus data for
additional support and loading conditions are presented for ease of
analysis. Again, it should be pointed out that slab calculations are based
on a unit area whereas beam calculations are performed for a unit length of
the beam.
(2) ResistanceDeflection Curve for Design. The maximum deflection,
Xm, of a beam is kept within the elastic, elastoplastic, and limited
plastic rages. The resistancedeflection function for design takes the form
shown in Figure 34. One and twostep systems are generally used for beams.
A threestep function is possible but only for fixed ended beams with
unequal negative moment capacities. Response charts are prepared for
onestep systems. Consequently the two and threestep functions are
replaced by an equivalent onestep function. Equations for the equivalent
functions are presented in NAVFAC P397.
(3) Ultimate Resistance. The ultimate unit resistance of beams with
various support and loading conditions is given in Table 5. For beams, the
ultimate moment, Mn and Mp, is expressed in inchpounds so that the
ultimate unit resistance, ru, is in pounds per inch and the ultimate
resistance, Ru, for concentrated loads is in pounds.
(4) Elastic and ElastoPlastic Resistances. The elastic and
elastoplastic resistances of beams with various support and loading
conditions is given in Table 6. In those cases where the elastoplastic
resistance is equal to the ultimate resistance, the value can be determined
from Table 5.
(5) ElastoPlastic Stiffness and Deflection. The elastic and
elastoplastic stiffnesses of beams with various support and loading
conditions are given in Table 7. Also the equivalent stiffness of each beam
is given. It should be noted that the moment of inertia is for the total
beam width and carries the dimension of inches to the fourth power.
Consequently, the stiffness has the units of pounds per inch per inch.
Knowing the resistances and stiffnesses, the corresponding elastic,
elastoplastic, and equivalent elastic deflections can be computed.
(6) Plastic Deflections. The maximum plastic deflection and the
ultimate plastic deflection for beams of various support and loading
conditions is given in Table 8. The deflection is given as a function of
support rotation. The ultimate support rotation of beams is limited to 2
degrees. Tests have indicated that concrete members lose their structural
integrity after support rotations in the order of 2 degrees have been
achieved.
(7) Support Shears. The support reactions for beams with various
support and loading conditions are given in Table 9.
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