Review
Failure criteria and cumulative damage models for steel components under cyclic loading

https://doi.org/10.1016/j.jcsr.2008.12.007Get rights and content

Abstract

In this paper the behaviour of welded beam-to-column connections under low-cycle fatigue is investigated in terms of failure criteria. A damage index and a failure criterion for steel components under cyclic loading, based on the capacity of the structural details to dissipate energy, are presented and discussed.

After a review of some cyclic test results obtained for steel beam-to-column connections, a comparison is presented between the cumulative damage model based on the damage index and failure criterion previously introduced, and other models and failure criteria available in the literature.

Introduction

Within the design process, it is usually assumed that Moment Resisting Steel Frames (MRSF) have sufficient strength, ductility and energy dissipation capacity to resist, without severe damage, strong earthquake motion. Modern seismic codes 1., 2., 3. are based on the concept of capacity design: frames are conceived with weak beams and strong columns and with the dissipative zones concentrated at the beam ends and at the base of the columns; moreover the nodal zones must be designed so as to have sufficient strength and rotation capacity in order to avoid brittle failure. The Northridge (1994) and the Kobe (1995) earthquakes, in fact, highlighted unexpected brittle failure in the connections of MRSF systems that, until then, were considered ductile and therefore able to resist large plastic cycles. For this reason, various experimental research programs have been carried out, in the world, with the scope of studying the cyclic behaviour of welded connections.

Various damage accumulation models and failure criteria have been proposed, and are available in the literature, in order to interpret the behaviour of structural components under cyclic/seismic loading. Some of these models (and criteria) were proposed for steel structures although, most of them, were proposed for r.c. members.

The scope of this paper is a comparison of some of the damage models and failure criteria available in the literature, in order to assess their capability to correctly interpret the actual cyclic behaviour of typical steel beam-to-column connections, in terms of deterioration of their mechanical properties and energy absorption capacity.

To achieve this goal, of course, reference should be made to available experimental data. In this paper reference is made to some tests carried out at the Instituto Superior Técnico of Lisbon and at Politecnico di Milano with the aim of appraising the cyclic behaviour of welded beam-to-column connections. These tests were carried out within international research programs in the field of seismic behaviour of steel structures, with the scope of defining the seismic design criteria for steel structures with rigid and semi-rigid connections. The experimental results for some types of steel beam-to-column connections commonly employed in Europe for steel structures are analysed in terms of rotational capacity of the connections, plastic rotation of the panel zone, cyclic energy dissipation capacity and collapse mode.

The specimens were subjected to displacement controlled loading histories. Monotonic, cyclic (with constant and stepwise increasing cycle amplitudes, according to the basic loading history recommended by ECCS [4]) as well as variable amplitude cyclic loading histories were adopted. The experimental results are re-analysed on the base of some of the most common damage models available in the literature.

Section snippets

Collapse criteria

Structural collapse under seismic loading is a complex phenomenon involving different aspects: global and local buckling, cyclic hardening and softening, failure of the connections, low cycle fatigue and fracture.

The structural response to a strong earthquake is characterised by a small number of cycles with large excursions in the plastic field. Generally the structural engineer is interested in understanding the global behaviour of the whole structure and of the structural elements rather

Damage models

Structural details under cyclic loading are subjected to damage accumulation and, finally, to failure.

A number of damage accumulation models, proposed by various authors are available in the literature. Although some of these models were proposed for the case of high cycle fatigue (e.g. Miner) and other specifically for seismic loading (e.g. Krawinkler, Park & Ang), hereafter a brief review of some of these models is carried out.

The experimental results

In order to carry out a comparison among the different damage models reference should be made to experimental results, available to the authors.

In this paper, reference is made to two different sets of data, having different characteristics. The first set was obtained in Lisbon, and refers to cyclic tests carried out under constant or stepwise increasing amplitude loading [30]. The second set of data refers to cyclic tests carried out in Milano, under variable amplitude loading 31., 32., 8..

Comparison between indices of damage

In Fig. 15, Fig. 16, Fig. 17, Fig. 18, Fig. 19, Fig. 20 a comparison between the various damage models applied to single experimental test of BCC5 and BCC6 series is presented. The parameters governing the various models were calibrated against the experimental data, in such a way that the damage index attains a value of 1.0, when failure of the specimen is reached.

In Fig. 21 the cumulative energy reduction index has been calculated for the twelve specimens (BCC5 and BCC6); it is possible to

Conclusions

In this paper the behaviour of welded beam-to-column connections subject to cyclic quasi-static loading histories were investigated in terms of damage accumulation and failure modes. A failure criterion and a model of damage accumulation were introduced based on the reduction of the energy dissipation capacity of the structure. A comparison between the proposed damage model and the most common damage models available in the technical literature is presented and discussed, with reference to two

References (37)

  • G. Ballio et al.

    Seismic behaviour of steel sections

    Journal of Constructional Steel Research

    (1994)
  • G. Ballio et al.

    A unified approach for the design of steel structures under low/or high cycle fatigue

    Journal of Constructional Steel Research

    (1995)
  • Krawinkler et al.

    Cumulative damage in steel structures subjected to earthquake ground motion

    Computers & Structures.

    (1983)
  • UBC-97. Uniform building code. In: International conference of building officials;...
  • IBC-03. International building code. In: International conference of building officials;...
  • EN 1998-1:2005. Design of structures for earthquake resistance. Part 1: General rules, seismic actions and rules for...
  • ECCS. Seismic design. Recommended testing procedure for assessing the behaviour of structural steel elements under...
  • Castiglioni CA, Bernuzzi C, Agatino MR. Design and damage assessment of structural steel components under seismic...
  • Castiglioni CA, Bernuzzi C, Calado L, Agatino MR. Experimental study on steel beam-to-column joints under cyclic...
  • Bernuzzi C, Calado L, Castiglioni CA. Low cycle fatigue of structural steel components: A method for re-analysis of...
  • C.A. Castiglioni et al.

    Constant and variable amplitude cyclic behaviour of welded steel beam-to-column connections

    Journal of Earthquake Engineering

    (2007)
  • Calado L, Castiglioni CA. Steel beam-to-column connections under low-cycle fatigue: Experimental and numerical...
  • Castiglioni CA, Calado L. Low cycle fatigue behavior and damage assessment of semi-rigid beam-to-column connections in...
  • M.A. Miner

    Cumulative damage in fatigue

    Transactions on ASME Journal of Applied Mechanics

    (1945)
  • G. Ballio et al.

    Low cycle fatigue behaviour of structural steel members and connections

    Fatigue and Fracture of Engineering Materials and Structures

    (1997)
  • D. Darwin et al.

    Energy dissipation in RC. beams under cyclic load

    Journal of Structural Engineering.

    (1986)
  • H. Krawinkler

    Performance assessment of steel components

    Earthquake Spectra

    (1981)
  • N.K. Gosain et al.

    Shear requirement for load reversals on RC members

    Journal of Structural Engineering

    (1977)
  • Cited by (80)

    View all citing articles on Scopus
    View full text