Page 384 - Structural Steel Designers Handbook AISC, AASHTO, AISI, ASTM, and ASCE-07 Design Standards

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LATERAL-FORCE DESIGN

8.38 CHAPTER EIGHT

Setting the sum of the moments equal to zero gives

3lA + lA = 25 h and A = . h (8.40)
125
5
4
2 5 l
Axial forces in the columns can be determined at other levels by the same procedure. Other shear
forces and bending moments can be determined by application of the equations of equilibrium for
individual subassemblages, as for the portal method.
Analysis of Dual Systems. Approximate analysis of braced frames can be performed as if the
bracing were a truss. However, many braced structures are dual systems that combine moment-
resisting-frame behavior with braced-frame behavior. Under these conditions, an approximate analysis
can be performed by first distributing the lateral forces between the braced-frame and moment-
resisting-frame portions of the structure in proportion to the relative stiffness of the components.
Braced frames are commonly very stiff and normally would carry the largest portion of the lateral
loads. Once this distribution is completed, the moment-resisting frame can be approximately analyzed
by the portal or cantilever method and the braced frame can be analyzed as a truss.

8.8.1 Linear Elastic Computer Analysis
Initial estimates of member and connection forces can be used to complete a preliminary design. At
this time, it is possible to reanalyze the structure by any of a number of linear-elastic, finite-element
computer programs. While many major, existing structures were designed without benefit of com-
puter analysis techniques, it is not advantageous to design modern buildings for wind and earthquake
loading without this capability. It is needed to predict realistic structural response to wind loading
and to evaluate occupant comfort, as well as for dynamic design for seismic loading, especially for
buildings of unusual geometry. Both the seismic and wind-load provisions in ASCE 7 standards
result in local anomalies in the distribution of design forces due to the distribution of mass, stiffness,
or local wind pressure, and many elements such as slabs and diaphragms may distribute large forces
from one load element to another. Connections in braced frames are not true pins, and many
moment-resisting frame connections are not truly rigid, fully restrained, connections. The conse-
quences of these variations may have a significant impact on structure performance, and finite-
element analysis provides a much more realistic indication of system performance. The combination
of these factors results in the need for finite-element analysis.

8.8.2 Nonlinear Analysis of Structural Frames
Although nonlinear analysis is not commonly used for structural design, it is important for seismic
design for several reasons. First, while the seismic-design provisions of various building codes rely
on linear-elastic concepts, they are based on inelastic response. Seismic behavior of structures dur-
ing major earthquakes depends on nonlinear material behavior caused by yielding of steel and crack-
ing of concrete. The reduced stiffness due to yielding makes the stability of structures of great
concern, and ensuring stability requires consideration of geometric nonlinearities. Nonlinear analy-
sis permits treatment of these stability effects with P−∆ moments (Fig. 8.20).
Second, design methods such as load-and-resistance-factor design encourage use of flexible, partially
restrained (PR) connections. Such connections are inherently nonlinear in their response. Hence, it is
necessary to analyze structures with attention to the contribution of connection flexibility. Further
nonlinearity may occur due to the effects of connection flexibility on frame stability and P–∆
moments. These nonlinear effects are not commonly considered in design at present. However, com-
puter programs are available to model nonlinear frame behavior and their use is growing.
Third, current seismic-design criteria are based on life safety and collapse prevention, but struc-
tural engineers are increasingly concerned with performance-based design and the evaluation of eco-
nomic damage at various earthquake excitation levels. FEMA 356 (“NEHRP Guidelines for Seismic

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