P l a s t i c B e h a v i o r at t he C r o s s - S e c t i o n Level
W 14 X 73 0
-zo -M
2 3 H 681
F ig u r e 3 . 5 Tw o-dim ensional d is trib u tio n o f residual s tre s s e s in rolled and welded wide-flange stru ctu ra l shapes. (From L. Tall, S tru ctu ra l Steel Design, 2 n d ed., 1 9 7 4 .)
123
B u i l d i n g Co d e S e i s m i c D e s i g n P h i l o s o p h y 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 w ith an expected tensile strength, T, of RyFyA Because the expected tensile strength is generally m uch higher than the postbuckling strength of the brace, the vertical com ponent of these two forces will not balance, and will produce a net pull-down force at the m idspan of the beam . A large m om ent produced by this unbalanced form, w hich 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 Objective
In addition to the above sum m ary of the US seism ic design provisions based on ASCE 7, it is w orthw hile to briefly sum m arize the performance objectives states in various similar design requirements. The basic seism ic design philosophy that appeared in the Recommended Lateral Force Requirements and Commentary [also know n as the Blue Book and first published by the Structural Engineers Association of California (SEAOC) in 1959], stated that the intent of the recommended design provisions was to produce a structure that should be able to resist: • A minor level of earthquake ground m otion without damage • A m oderate level of ground m otion w ithout structural damage but possibly experience some nonstructural damage • A m ajor level of ground m otion having an intensity equal to the strongest, either experienced or forecast for the building site, without collapse, but possibly w ith some structural as well as nonstructural damage A lthough the SE O A C 's seism ic design philosophy intended to control bu ild ing perform ance for both structural and n onstru ctural com ponents at different levels of earthquake in tensities, both the expected bu ild ing perform ance and the ground shaking intensity w ere described in a qualitative m anner. It w asn 't until 1995 that SEA O C published Vision 2000 (SEAO C 1995) to outline a perform ance-based fram ew ork to address a broad range of bu ild ing perform ance and seism ic hazard levels. In the 1990s, efforts to develop seism ic design provisions for rehabilitating existing building structures eventually led to the first perform ance-based design code: ASCE 41—Seismic Rehabilitation of Existing Building (ASCE 2006). ASCE 41 states the rehabilitation objective in a more quantitative manner. For design of new structures,
327
D e s i g n 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
11.7
Design of Buckling-Restrained Braces The design of bu ckling-restrain ed braced fram es is in m any respects sim pler than the design of sp ecial con cen trically braced fram es (SCBF) or other braced fram es designed for ductile seism ic response. M any o f the restrictions and procedures considered necessary for SC BF due to the differing tension and com pression behavior o f bu ckling braces are u nnecessary w h en the m ore ductile buckling-restrained braces are used. The design of braces is presented in this section, follow ed by capacity design o f other elem ents in Section 11.8.
11.7.1
Brace Design
The design o f a typical bu ckling-restrained braced fram e involves sizing the brace steel cores to provide su fficient axial strength. T his is a straightforw ard design based on the m aterial strength. The brace axial design strength is determ ined b y the follow ing: * P ysc =
§ F ys c A sc
C11-6)
w here Fysc = specified m inim u m yield stress of the steel core, A gc = cross-sectional area of the yield in g segm en t o f steel core, and <]>= 0.90 for the lim it state o f yielding. This strength applies to bo th tension and com pression, as bu cklin g o f the core is com pletely restrained by the casing. T his strength is com pared w ith the required strength of the braces corresponding to the design base shear.
11.7.2
Elastic Modeling
In 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 elem ent. Brace axial stresses are largely confined to the steel core, and the axial com pression and extension of this m em ber m ust be reasonably represented in the model. The m odel m ust address the nonprismatic configuration of this core (see Figure 11.4), either directly or indirectly Som e estimate m ust be m ade of the brace area outside of the yielding zone, as w ell as the length of the yielding and nonyielding segments. For m anufactured braces the m anufacturer 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 ff ( Lysc L nysc ^conn T ^ A ysc A nysc A ^ conn j
(11.7)
669
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 B e a ms
F ig u r e 1 4 . 6
S tre ss re d istrib u tio n o f p o stb u cklin g plate. (From Bazant and Cedolin
1 9 9 1 , with perm ission.)
S: Simple support F: Free
F ig u r e 1 4 . 7
1969.)
P ostbuckling s tiffn e s s o f loaded plate. (Adapted from Bulson
O u t-o f-p lan e im p erfectio n s alw ay s ex ist in a ctu a l p la tes and assem b lies o f p lates. F ig u re 14.8 co m p ares th e a n a ly tica lly p red icted resp on se o f a p erfect p late and test resu lts, b o th for a p late w ith p la n d im en sio n s o f a and b. T h e m ain effects o f g eo m etric im p erfectio n s are the elim in a tio n o f a w ell-d efin ed b u ck lin g load
843
