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LATERAL-FORCE DESIGN

LATERAL-FORCE DESIGN 8.15

The total seismic design force and the force distribution over the height and width of the struc-
ture for each mode can be determined by this method. The combined force distribution takes into
account the variation of mass and stiffness of the structure, unusual aspects of the structure, and the
dynamic response in the full range of modes of vibration, rather than the single mode used in the static-
force method. The combined forces are used to design the structure, and are often reduced by R in
accordance with the ductility of the structural system. In many respects, the dynamic method is much
more rational than the static-force method, which involves many more assumptions for computing
and distributing design forces. The dynamic method sometimes permits smaller seismic design
forces than the static-force method. However, while it offers many rational advantages, the dynamic
method is still a linear-elastic approximation to an inelastic-design method. As a result, it assumes
that the inelastic response is distributed throughout the structure in the same manner as predicted by
the elastic-mode shapes. This assumption may be inadequate if there is a brittle link in the system.
Other analytical methods have been used to overcome some of these latter limitations. Designers
are increasingly using inelastic-analysis methods including inelastic dynamic time–history and
inelastic pushover analysis methods. These options will be briefly discussed in Art. 8.8.2.

8.6 STRUCTURAL STEEL SYSTEMS FOR SEISMIC DESIGN

Since seismic loading is an inertial loading, the forces are dependent on the dynamic characteristics
of the acceleration record and the structure. Seismic design codes use a response spectrum as shown
in Fig. 8.4 to model these dynamic characteristics. These forces are usually reduced in accordance
with the ductility of the structure. This reduction is accomplished by the R factor in the static-force
method, and the reduction may be quite large (Art. 8.5). The designer must ensure that the structure
is capable of developing the required ductility, as it is well-known that the available ductility varies
with different structural systems. Therefore, the structural engineer must ensure that the structural
system selected for a given application is capable of achieving the ductility required for the R value
used in the design. The engineer also must complete the details of the design of members and con-
nections so that the structure lives up to these expectations.
Evaluation of Ductility. Two major factors may affect evaluation of the ductility of structural
systems. First, the ductility is often measured by the hysteretic behavior of the critical components.
The hysteretic behavior is usually examined by observing the cyclic force-deflection (or moment-
rotation) behavior as shown in Fig. 8.7. The slope of the curves represents the stiffness of the structure
or component. The enclosed areas represent the energy that is dissipated, and this can be large, because
of the repeated cycles of vibration. These enclosed areas are sometimes full and fat (Fig. 8.7a), or they
may be pinched or distorted (Fig. 8.7b). The hysteretic curves also show the inelastic deformation that
can be tolerated at various resistance levels. Structural framing with curves enclosing a large area
representing large dissipated energy, and structural framing which can tolerate large inelastic defor-
mations without excessive loss in resistance, are regarded as superior systems for resisting seismic
loading. As a result, these systems are commonly designed with larger R values and smaller seismic
loads.
Special steel moment-resisting frames and eccentric braced frames, defined in Art. 8.4, are capa-
ble of developing large plastic deformations and large hysteretic areas. As a result, they are designed
for larger values of R, thus smaller seismic forces and greater inelastic deformation. This hysteretic
behavior is important, since it dampens the inelastic response and improves the seismic performance
of the structure without requiring excessive strength or deformation in the structure. This is illus-
trated in Fig. 8.8, which shows the inelastic dynamic response of two steel moment-resisting frames,
which had identical mass, stiffness, and seismic excitation (1979, Imperial Valley College), but dif-
ferent seismic resistance. The story drift and inelastic deformation cycles are larger for the elastic
structure than for the ductile structure with lateral resistance equal to approximately 40% of that
required for elastic response. However, the structure with the smaller resistance has larger maximum
deflections and sustains permanent inelastic offset during the earthquake excitation. This shows

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