P l a s t i c B e h a v i o r a t t h e C r o s s - S e c t i o n Le ve l 123

W 14 X 730

-zo

-M

23 H 681

F ig u re 3 . 5 Two-dimensional d is tribu tion o f residual s tresses in rolled and welded wide-flange structura l shapes. (From L. Tall, S tructural Steel Design, 2nd ed., 1974 .)

B u i l d i n g Code S e i s m i c De s i g n P h i l o s o p h y 327

is a FCE, AISC 341 assumes the expected postbuckling brace strength, C, to be 30% of the expected brace compressive strength. The other brace is assumed to be yielded with an expected tensile strength, T, of RyFyA Because the expected tensile strength is generally much higher than the postbuckling strength of the brace, the vertical component of these two forces will not balance, and will produce a net pull-down force at the midspan of the beam. A large moment produced by this unbalanced form, which cannot be obtained from an elastic analysis, then needs to be considered for beam design. See Chapter 9 for a more detailed discussion.

7.8 Performance-Based Seismic Design Framework

7.8.1 Seismic Performance ObjectiveIn addition to the above summary of the US seismic design provi-sions based on ASCE 7, it is worthwhile to briefly summarize the per-formance objectives states in various similar design requirements.

The basic seismic design philosophy that appeared in the Recom-mended Lateral Force Requirements and Commentary [also known as the Blue Book and first published by the Structural Engineers Associa-tion of California (SEAOC) in 1959], stated that the intent of the rec-ommended design provisions was to produce a structure that should be able to resist:

A minor level of earthquake ground motion without damage A moderate level of ground motion without structural dam-

age but possibly experience some nonstructural damage A major level of ground motion having an intensity equal to

the strongest, either experienced or forecast for the building site, without collapse, but possibly with some structural as well as nonstructural damage

Although the SEO A C's seism ic design philosophy intended to control building perform ance for both structural and nonstruc-tural com ponents at different levels of earthquake intensities, both the expected building perform ance and the ground shaking inten-sity were described in a qualitative manner. It w asn 't until 1995 that SEAOC published Vision 2000 (SEAOC 1995) to outline a per-form ance-based fram ew ork to address a broad range of building perform ance and seism ic hazard levels.

In the 1990s, efforts to develop seismic design provisions for reha-bilitating existing building structures eventually led to the first per-formance-based design code: ASCE 41Seismic Rehabilitation of Existing Building (ASCE 2006). ASCE 41 states the rehabilitation objective in a more quantitative manner. For design of new structures,

D e s i gn of D u c t i l e B u c k l i n g - R e s t r a i n e d B r a c e d F r a m e s 669

11.7 Design of Buckling-Restrained BracesThe design of buckling-restrained braced fram es is in m any respects sim pler than the design of special concentrically braced fram es (SCBF) or other braced fram es designed for ductile seism ic response. M any of the restrictions and procedures considered necessary for SCBF due to the differing tension and com pression behavior of buck-ling braces are unnecessary w hen the m ore ductile buckling-restrained braces are used. The design of braces is presented in this section, fol-lowed by capacity design of other elem ents in Section 11.8.

11.7.1 Brace DesignThe design of a typical buckling-restrained braced fram e involves sizing the brace steel cores to provide sufficient axial strength. This is a straightforw ard design based on the m aterial strength. The brace axial design strength is determ ined by the following:

* P ysc = F yscA sc C11-6)

w here Fysc = specified m inim um yield stress of the steel core, A gc = cross-sectional area of the yielding segm ent of steel core, and = 0.90 for the lim it state of yielding. This strength applies to both tension and com pression, as buckling of the core is com pletely restrained by the casing. This strength is com pared w ith the required strength of the braces corresponding to the design base shear.

11.7.2 Elastic ModelingIn typical practice an elastic m odel is used to determ ine the brace required strengths. Elastic m odeling is used to determ ine the required brace strengths and to determ ine the elastic dynam ic characteristics of the structure. In constructing an elastic m odel w ith buckling-restrained braces, som e adjustm ents need to be m ade to properly capture the elastic stiffness of this element.

Brace axial stresses are largely confined to the steel core, and the axial compression and extension of this member must be reasonably repre-sented in the model. The model m ust address the nonprismatic configu-ration of this core (see Figure 11.4), either directly or indirectly Some estimate m ust be made of the brace area outside of the yielding zone, as well as the length of the yielding and nonyielding segments. For manu-factured braces the manufacturer can provide estimates based on the anticipated connection size, overall brace length, and other factors. For fabricated braces designed by the engineer, the following equation can be used to establish the effective axial stiffness of the brace (Tsai et al. 2002):

Kf f = y ------------- -------------- t (11.7)ff ( L L T ^ysc nysc ^conn

A A A^ ysc nysc conn j

S t a b i l i t y and R o t a t i o n C a p a c i t y of S t e e l Be a ms 8 4 3

F ig u re 1 4 . 6 Stress redistribution o f postbuckling plate. (From Bazant and Cedolin 1991, with permission.)

S: Simple support F: Free

F ig u re 1 4 . 7 Postbuckling s tiffne ss o f loaded plate. (Adapted from Bulson 1969.)

O ut-of-plane im perfections alw ays exist in actual p lates and assem blies of plates. Figure 14.8 com pares the analytically pre-dicted response of a perfect plate and test results, both for a plate w ith p lan d im ensions of a and b. The m ain effects of geom etric im perfections are the elim ination of a w ell-defined bu ckling load