Structures designed in accordance with even the most modern buildings codes are expected to sustain damage during a severe earthquake; however; these structures are expected to protect the lives of the occupants. Damage to the structure can require expensive repairs; significant business downtime; and in some cases building demolition. If damage occurs to many structures within a city or region; the regional and national economy may be severely disrupted. To address these shortcomings with current seismic lateral force resisting systems and to work towards more resilient; sustainable cities; a new class of seismic lateral force resisting systems that sustains little or no damage under severe earthquakes has been developed. These new seismic lateral force resisting systems reduce or prevent structural damage to nonreplaceable structural elements by softening the structural response elastically through gap opening mechanisms. To dissipate seismic energy; friction elements or replaceable yielding energy dissipation elements are also included. Post-tensioning is often used as a part of these systems to return the structure to a plumb; upright position (self-center) after the earthquake has passed. This paper summarizes the state-of-the art for self-centering seismic lateral force resisting systems and outlines current research challenges for these systems.

https://www.mdpi.com/2075-5309/4/3/520/pdf

Self-Centering Seismic Lateral Force Resisting Systems: High Performance Structures for the City of Tomorrow

The objective of this paper is to provide a brief review of recent (over approximately the last five years) advances in the application, analysis and design of cold-formed steel structures. Attention here is focused on load-bearing cold-formed steel structures; as opposed to secondary systems, curtain walls, etc. Cold-formed steel applications continue to advance in three primary categories: framing, metal buildings, and racks. Examples largely derived from the author’s experiences in North America are used to illustrate the applications. The behaviour of cold-formed steel structures can be complicated due to the thin-walled nature of the sections; thus, analysis advances are required. Recent work in Generalized Beam Theory and the constrained Finite Strip Method demonstrate that, at least when it comes to thin-walled members, significant advances in structural analysis are still possible and desirable. Design of cold-formed steel structures continues to see significant improvements and refinements. Recent efforts related to the Direct Strength Method of design are highlighted, including novel extensions from the member to the system level. Finally, similar to many other areas of structural engineering, seismic engineering has motivated notable advances in applications, analysis, and design. For cold-formed steel structures these advances are reviewed to demonstrate current progress and future directions in this important area.

Cold‐formed steel structures around the world

In this paper the generalization of the constrained finite strip method (cFSM) is discussed. cFSM is a special version of the semi-analytical finite strip method (FSM), where carefully defined constraints are applied which enforce the thin-walled member to deform in accordance with specific mechanics, e.g., to allow buckling only in flexural, lateral–torsional, or a distortional mode. In the original cFSM only open cross-section members are handled, here the method is extended to cover any flat-walled member, including those with closed cross-sections or cross-sections with open and closed parts. Moreover, in the original cFSM only 4 deformation classes are defined, here the deformation field is decomposed into additional, mechanically meaningful, sub-fields. Formal mechanical criteria are given for the deformation classes, and implementation of the criteria regardless of cross-section topology is illustrated. In this paper, the primary deformation classes are presented in detail. Primary deformations are associated with minimal cross-section discretization, i.e. nodal lines located at folds and ends only. This paper is accompanied by a companion, where secondary modes and additional practical aspects in the selection of base vectors for the deformation classes are discussed. With the proposed modifications the powerful cFSM capabilities of buckling mode decomposition and identification are extended to essentially arbitrary thin-walled cross-sections.

Generalized constrained finite strip method for thin-walled members with arbitrary cross-section: Primary modes

The stability of thin-walled members is decidedly complex. The recently developed constrained Finite Strip Method (cFSM) provides a means to simplify thin-walled member stability solutions through its ability to identify and decompose mechanically meaningful stability behavior, notably the formal separation of local, distortional, and global deformation modes. The objective of this paper is to provide a review of the most recent developments in cFSM. This review includes: fundamental advances in the development of cFSM; applications of cFSM in design and optimization; identifying buckling modes and collapse mechanisms in shell finite element models; and, additional stability research initiated by the cFSM methodology. A brief summary of the cFSM method, in its entirety, is provided to explain the method and highlight areas where research remains active in the fundamental development. The application of cFSM to cold-formed steel member design and optimization is highlighted as the method has the potential to automate generalized strength prediction of thin-walled cold-formed steel members. Extensions of cFSM to shell finite element models is also highlighted, as this provides one path to bring the useful identification features of cFSM to general purpose finite element models. A number of alternative methods, including initial works on a constrained finite element method, initiated by cFSM methods, are also detailed as they provide insights on potential future work in this area. Research continues on fundamentals such as methods for generalizing cFSM to arbitrary cross-sections, improved design and optimization methods, and new ideas in the context of shell finite element method applications.

Review: Constrained finite strip method developments and applications in cold-formed steel design

Controlled rocking steel braced frames (CRSBFs) are being developed as a seismic force resisting system that can be constructed economically to avoid structural damage and residual deformations following an earthquake. In a CRSBF, selected columns are permitted to uplift from the foundation in response to severe seismic loading, and posttensioning and energy dissipation are selected to control the magnitude of the rocking response. Despite extensive experimental testing to demonstrate that this behavior is stable and repeatable, there has been a lack of comprehensive guidance for potential designers of CRSBFs. This paper proposes a performance-based design methodology for CRSBFs, which consists of defining the performance objectives, designing the base rocking joint based on a single-degree-of-freedom (SDOF) model, and capacity protecting the rest of the structure for the maximum forces expected during the rocking response. This paper focuses on the design of the base rocking joint, while Part II ...

Performance-Based Seismic Design of Controlled Rocking Steel Braced Frames. I: Methodological Framework and Design of Base Rocking Joint

The objective of this paper is to demonstrate an approximate method whereby eigen buckling modes from a shell finite element method (FEM) analysis of a thin-walled member can be quantified in terms of the fundamental buckling classes, namely, global, distortional, local, or other. The buckling classes are defined using the mechanical definitions employed in the constrained finite strip method (cFSM). The cFSM base vectors are used to approximate an arbitrary FEM buckling mode. The resulting identification and its associated error is investigated, including dependency on FEM discretization, the number of cFSM functions considered, boundary conditions, and loading. The long-term goal of the work is to provide a generalized method for identification of local, distortional, and global buckling modes for arbitrary thin-walled members modeled in general purpose finite element codes.

Buckling mode identification of thin-walled members by using cFSM base functions

This paper presents a new design approach for the stability design of thin-walled members. The proposed approach is based on the buckling modes and critical forces/moments determined by a linear buckling analysis performed on a regular shell finite element model. A fully automatic buckling mode identification technique is applied, by using the modal base functions of the newly proposed constrained finite strip method, where the various buckling types are separated by clearly defined mechanical
criteria. The paper briefly summarizes the determination of modal base functions which then are used to approximate finite element displacement functions (i.e., buckling modes). The mode identification method provides the lowest critical values (forces or moments) to all the three characteristic buckling types: global, distortional and local, on the basis of which the buckling resistance can be calculated by using the design formulae of the direct strength method. The proposed new approach, which is potentially more general than any of the existing design approaches, is demonstrated on Z columns and beams with simple loading and boundary conditions. Critical values as well as resistances are calculated for some selected cases, the results are compared to those of another design method. The comparisons prove the applicability of the proposed procedure. Further research is necessary to extend the proposal for more general and more complex practical cases.

/pdf/fem-based-approach-for-the-stability-design-of-thin-walled-2rmzok1bi8.pdf

FEM-based approach for the stability design of thin-walled members by using cFSM base functions

Previous studies on stressed skin effect of industrial steel buildings showed discrepancies between the ECCS formulae and experimental results. To clarify the discrepancies full-scale experimental test program was planned and executed by the Budapest University of Technology and Economics, Department of Structural Engineering. The aims of the full-scale tests were to refine the stressed skin design method and to adjust it to the nonstandard cladding structural system applied by an industrial partner. During execution of the full-scale experiments the shear flexibility of those industrially applied nonstandard diaphragms were examined, where the application of seam fasteners were rejected. Next to the building section a loading frame was built, so that tension and compression force could be applied to each frame, in order to examine the in-plane shear flexibility of the whole nonstandard diaphragm assembly, including the shear flexibility of the portal frame. In the test series four purlin and two trapezoidal sheeting height configurations were combined in more than 100 tests. This paper, denoted as Part I shows the test setup and introduces the results derived from the ECCS formulae, underlining the importance of extending the applicability of the current design formulae to nonstandard cases, which are often applied in industrial practice all over Europe. A companion paper (Part II) presents the comparative results between the various cladding configurations, also the main conclusions regarding the stiffening effect of the applied diaphragm configurations, and reports the effect of change in section size to shear flexibility. Besides this in Part II the effect of different structural components in regards to shear flexibility is underlined.

Attila László Joó

Papers

Buckling mode identification of thin-walled members by using cFSM base functions

FEM-based approach for the stability design of thin-walled members by using cFSM base functions

Experimental full-scale tests on steel portal frames for development of diaphragm action – Part I experimental results

Improvement of stressed skin design procedure based on experimental and numerical simulations

Evaluation of performance-based design methodology for steel self-centering braced frame