Journal of Constructional Steel Research 65 (2009) 1015–1028
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Journal of Constructional Steel Research
journal homepage: www.elsevier.com/locate/jcsr
Review
Plastic design of eccentrically braced frames, II: Failure mode control
Luigi Mastrandrea
*
, Vincenzo Piluso
University of Salerno, Department of Civil Engineering, Salerno, Italy
article info
Article history:
Received 1 April 2008
Accepted 7 October 2008
Keywords:
Eccentrically braced frames
Limit design
Collapse mechanism
Capacity design
Static non-linear analysis
Local ductility demands
abstract
A design methodology aiming at the development of a collapse mechanism of a global type for
eccentrically braced frames is presented in this paper. This result is of primary importance in earthquake
resistant design, because partial and local failure modes are responsible of the worsening of the energy
dissipation capacity leading to an increased risk of collapse under destructive ground motions.
The proposed method is based on the assumption that horizontal member sections are known, as
they are designed to resist internal actions due to vertical loads and design horizontal forces. Conversely,
column and diagonal sections constitute the unknowns of the design problem. In particular, the presented
approach also includes the influence of second order effects which are accounted for by means of the
concept of mechanism equilibrium curve. The design requirements are derived by means of the kinematic
theorem of plastic collapse. Column and diagonal sections are obtained by imposing that the mechanism
equilibrium curve corresponding to the global mechanism has to lie below those corresponding to
the undesired mechanisms within a displacement range compatible with the local ductility supply.
Moreover, the introduction of the equivalent moment concept presented in a companion paper provides
the proposed method with the ability to deal with short, intermediate and long links in the same manner.
Aiming at the evaluation of the accuracy of the presented procedure, the inelastic performances of
eccentrically braced frames designed by means of the proposed method are investigated, by means of
static and dynamic non-linear analyses, in terms of collapse mechanism typology, available ductility and
energy dissipation capacity.
© 2008 Elsevier Ltd. All rights reserved.
Contents
1. Introduction........................................................................................................................................................................................................................ 1016
2. Equilibrium curves of analysed mechanisms ................................................................................................................................................................... 1018
2.1. Mechanism equilibrium curve .............................................................................................................................................................................. 1018
2.2. Global mechanism ................................................................................................................................................................................................. 1019
2.3. Type-1 mechanisms............................................................................................................................................................................................... 1019
2.4. Type-2 mechanisms............................................................................................................................................................................................... 1019
2.5. Type-3 mechanisms............................................................................................................................................................................................... 1020
3. Design conditions for failure mode control ...................................................................................................................................................................... 1020
3.1. Basic requirements ................................................................................................................................................................................................ 1020
3.2. Conditions to avoid type-1 mechanisms .............................................................................................................................................................. 1021
3.3. Conditions to avoid type-2 mechanisms .............................................................................................................................................................. 1021
3.4. Conditions to avoid type-3 mechanisms .............................................................................................................................................................. 1022
3.5. Calculation of the parameters ρ
im
......................................................................................................................................................................... 1022
4. Design of link sections ....................................................................................................................................................................................................... 1023
5. Evaluation of the axial load in the columns and in the diagonals at the collapse state ................................................................................................ 1023
6. Design algorithm................................................................................................................................................................................................................ 1023
7. Worked example ................................................................................................................................................................................................................ 1024
7.1. Structural scheme and preliminary design of links ............................................................................................................................................. 1024
7.2. Selection of design ultimate displacement .......................................................................................................................................................... 1025
*
Corresponding address: University of Salerno, Department of Civil Engineering, via Ponte Don Melillo, 84084 Salerno, Italy. Tel.: +39 089 96 3411; fax: +39 089 96 4097.
E-mail addresses: lmastrandrea@unisa.it (L. Mastrandrea), v.piluso@unisa.it (V. Piluso).
0143-974X/$ – see front matter © 2008 Elsevier Ltd. All rights reserved.
doi:10.1016/j.jcsr.2008.10.001