Common Newmark analyses involve application of a recorded
horizontal ground motion parallel to an inclined plane @Fig. 5~a!#;
no motion is applied perpendicular to the plane. In this sense, the
standard analysis can be thought of as applying only a ‘‘pseudotangential’’
motion. An alternative approach would be to resolve
the recorded horizontal and vertical components in the direction
parallel to the plane, and apply the resulting ‘‘true-tangential’’
motion @Fig. 5~b!#. A third alternative would be to apply the ‘‘true
two-dimensional’’ motion @Fig. 5~c!#, in which both the horizontal
and vertical ~or, equivalently, tangential and normal! motions are
applied to the plane. Finally, the effects of three-dimensional
input motions ~two horizontal and one vertical component, or
tangential, normal, and lateral components! can be applied to
three-dimensional wedges @Fig. 5~d!#. Sequential use of each of
these alternatives, from one- to two- to three-dimensional input,
allows the effects of input motion ‘‘dimensionality’’ to be characterized.
Consider the case of a simple Newmark block resting on a
plane inclined at 20° with a static factor of safety of 1.5. Assuming
resistance on the interface is purely frictional, this combination
results in a yield acceleration of 0.171 g (u52b). A twodimensional
harmonic input motion can be defined by
u¨~t!5A sin vt (
Common Newmark analyses involve application of a recordedhorizontal ground motion parallel to an inclined plane @Fig. 5~a!#;no motion is applied perpendicular to the plane. In this sense, thestandard analysis can be thought of as applying only a ‘‘pseudotangential’’motion. An alternative approach would be to resolvethe recorded horizontal and vertical components in the directionparallel to the plane, and apply the resulting ‘‘true-tangential’’motion @Fig. 5~b!#. A third alternative would be to apply the ‘‘truetwo-dimensional’’ motion @Fig. 5~c!#, in which both the horizontaland vertical ~or, equivalently, tangential and normal! motions areapplied to the plane. Finally, the effects of three-dimensionalinput motions ~two horizontal and one vertical component, ortangential, normal, and lateral components! can be applied tothree-dimensional wedges @Fig. 5~d!#. Sequential use of each ofthese alternatives, from one- to two- to three-dimensional input,allows the effects of input motion ‘‘dimensionality’’ to be characterized.Consider the case of a simple Newmark block resting on aplane inclined at 20° with a static factor of safety of 1.5. Assumingresistance on the interface is purely frictional, this combinationresults in a yield acceleration of 0.171 g (u52b). A twodimensionalharmonic input motion can be defined byu¨~t!5A sin vt (
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