(1) Introduction. The dynamic analysis of beams is performed in the
same manner as that given in NAVFAC P-397 for slabs. The data presented for
one-way 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
(2) Resistance-Deflection Curve for Design. The maximum deflection,
Xm, of a beam is kept within the elastic, elasto-plastic, and limited
plastic rages. The resistance-deflection function for design takes the form
shown in Figure 34. One- and two-step systems are generally used for beams.
A three-step function is possible but only for fixed ended beams with
unequal negative moment capacities. Response charts are prepared for
one-step systems. Consequently the two- and three-step functions are
replaced by an equivalent one-step function. Equations for the equivalent
functions are presented in NAVFAC P-397.
(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 inch-pounds 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 Elasto-Plastic Resistances. The elastic and
elasto-plastic resistances of beams with various support and loading
conditions is given in Table 6. In those cases where the elasto-plastic
resistance is equal to the ultimate resistance, the value can be determined
from Table 5.
(5) Elasto-Plastic Stiffness and Deflection. The elastic and
elasto-plastic 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,
elasto-plastic, 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
(7) Support Shears. The support reactions for beams with various
support and loading conditions are given in Table 9.