Uwe Starossek

Progressive Collapse of Structures: Nomenclature and Procedures

Definitions for the terms collapse resistance and robustness are proposed. Based on an analysis of the shortcomings of current design methods, a pragmatic approach for designing against progressive collapse is suggested and a set of design criteria is presented. Design strategies based on preventing or presuming local failure are compared. Furthermore, the alternate-load-paths approach is compared with the compartmentalization approach concerning their applicability to different types of structures and design objectives.

Approaches to measures of structural robustness

Robustness is a desirable property of structural systems which mitigates their susceptibility to progressive collapse. It is defined as the insensitivity of a structure to local failure. To examine a structure in terms of its robustness, a quantitative description by means of a measure would be useful. The measure could be used for evaluation, optimisation and regulation of robustness. To achieve these tasks, the measure must be expressive, objective, simple, calculable, and generally applicable. Some simple formulations of stiffness, damage, or energy-based measures of robustness developed by the authors are presented and discussed regarding the suggested requirements and possible applications. It is shown that the requirements cannot all be satisfied to the same level at the same time. Structures which tend towards different types of collapse may be favourably described by different measures of robustness.

Disproportionate Collapse: Terminology and Procedures

A variety of terms are used to describe structural characteristics and concepts in the context of disproportionate collapse of structures. Some of these terms, namely collapse resistance, robustness, and vulnerability as well as redundancy, continuity, ductility, and integrity are discussed in this paper. It is shown that they are often used differently by different writers and that there is not always a general agreement today as to their precise meaning. This paper distinguishes these terms and the associated structural characteristics and suggests working definitions. Based thereupon, a general performance-based framework for preventing disproportionate collapse is presented and the methods available for enhancing the collapse resistance of a structure are discussed.

PROGRESSIVE COLLAPSE STUDY OF A MULTI-SPAN BRIDGE

The overall structural response to local failure has become an issue of attention for certain types of large-scale structures. The significance of such considerations is discussed here. A progressive collapse study of a multi-span prestressed concrete bridge is presented. The analysis strategy, the results obtained, and the ensuing impact on the design of this bridge are discussed.

Cable loss and progressive collapse in cable-stayed bridges

The failure of one structural element can lead to the failure of other structural elements and thus to collapse of large sections or the entire structure. Such disproportionate collapses have been discussed and investigated for some years, but mainly for buildings. In the field of bridge engineering, this phenomenon attracts only sporadic attention. Although international guidelines for cable-stayed bridges require that the loss of one cable must not lead to the collapse of the entire structure, comprehensive analyses that include non-linear dynamic effects are rare. To simply account for dynamic effects, a quasi-static analysis with a dynamic amplification factor of 2.0 is recommended. This value is possibly too large, leading to uneconomic solutions. Therefore, this work examines the structural response of a cable-stayed bridge to the loss of one cable by means of dynamic analyses including large displacements. The effects of cable sag, transverse cable vibrations, and structural damping are determined and dynamic amplification factors are computed.

Progressive Collapse: Design Strategies

Local failure of one structural element may result in the failure of another element of the same structure. Failure might thus progress throughout a major part or all of the structure. Design criteria for preventing such a progression of collapse are discussed. Investigative methods and design strategies for creating collapse-resistant structures are presented and compared. In addition to the better-known approaches providing specific local resistance or alternate load paths, an approach based on isolation of collapsing sections is described and discussed.

Optimized topology extraction of steel-framed DiaGrid structure for tall buildings

This study presents an optimal angle and a topology extraction of diagonal members in a DiaGrid structural system for tall buildings. The angle and topology of diagonal members are achieved by using a computer-oriented SIMP topology optimization. The objective function for the design optimization is to both maximize Eigenfrequency for resisting dynamic responses and minimize mean compliance for static responses. Relative densities subjected to SIMP penalty law are used for both optimization design variables and material properties, and then finite element analysis is carried out by using the relative element density. Frequency and mean compliance sensitivities with respect to relative density are straightforwardly derived by discrete sensitivity formulations. Based on the design sensitivity analysis, an initial topology with a given fixed support is shifted toward a final topology charged by almost voids (0) and solids (1) during every optimization procedure. An optimal DiaGrid topology with the highest stiffness is finally determined to resist both static and dynamic behaviors. Numerical examples with varied fixed support models are studied to find out optimal angles and topologies of diagonal members for a DiaGrid system design.

Progressive Collapse Nomenclature

Structural robustness is recognised as a desirable property of structural systems which mitigates their susceptibility to progressive collapse. However, there is some confusion in the literature regarding the usage of the terms structural robustness and collapse resistance as well as competing expressions such as prescriptive vs. performance-based, threat-specific vs. threatindependent or indirect vs. direct design. This article tries to distinguish between the different meanings of these four pairs of terms, which are important concepts in the field of progressive collapse. In this context, design strategies and associated methods to prevent progressive collapse are briefly explained.

Robustness of structures

Disproportionate collapse is prevented by ensuring collapse resistance, a property defined as the insensitivity of a structure to abnormal events. Enhancing robustness and reducing vulnerability are two different structural measures for achieving collapse resistance. The vulnerability of a structure is its susceptibility to become initially damaged by abnormal events; robustness is its insensitivity to such initial damage. Another option for preventing disproportionate collapse is the reduction of the exposure of the structure to abnormal events. The design strategy reducing vulnerability aims at preventing failure initiation whereas the strategy enhancing robustness aims at preventing disproportionate failure spreading. These two approaches are compared. Robustness can be achieved by the design methods alternative load paths and segmentation, which are also discussed. Furthermore, measures for the quantification of robustness are discussed.

Avoiding Disproportionate Collapse of Major Bridges

Avoiding disproportionate collapse following some small triggering event is an important aspect in the design of major bridges. A general approach for designing structures against disproportionate collapse is outlined and applied to bridges. Compared with buildings, bridges are primarily horizontally aligned structures with one main axis of extension. The provision of alternative load paths, therefore, is often not only more difficult but also less important. It is found that continuous girder bridges are preferably made collapse resistant by segmentation—which can require the insertion of joints or hinges—or by reducing the probability of key element failure. In cable-stayed or suspension bridges, the stay cables or hangers are the key elements that are particularly vulnerable. A collapse triggered by the loss of a cable is prevented by designing the bridge for loss-of-cable load cases; corresponding nonlinear dynamic analyses are presented. This measure should be complemented by protecting the cables against vehicle impact and malicious action. The robustness of suspension bridges can be raised by the methods of segmentation and alternative paths. The protection of the components of the suspension cables against malicious action deserves particular attention. Arch bridges have similarities with suspension bridges and much of the respective statements apply.