Imperfect Members Research Articles

The effects of mechanical imperfections on the stability behavior of double-layer Scallop domes

Mechanical imperfections are almost inevitable in large-span spatial domes with hundreds of members and joints. The lack of fit in members is the most common form of imperfections in double-layer domes which influences the behavior of these structures under gravitational or seismic loads. In this study, the probabilistic effect of mechanical imperfections (lack of fit) on the stability behavior of double-layer Scallop domes with sinusoidal arching style under symmetric and asymmetric snow-loading is investigated. On some double-layer scallop domes, nonlinear static and dynamic analyses are carried out using Abaqus/CAE and MATLAB. The behavior of the structures with randomly distributed imperfect members is compared with those of the ideally perfect structures. A Monte Carlo simulation approach is used to statistically assess the effects of uncertainties on the response parameters and the ultimate capacity of the structures. In the first approach, named here as the “rigorous probabilistic approach”, the amount and the distribution of imperfect members are all treated as random variables, and in the second approach, named as “concise approach”, a fixed amount of imperfections are applied to a number of randomly selected critical members. No simplification method is used in the rigorous probabilistic approach to achieve a reliable assessment of the effect of uncertain parameters. Results show that the collapse behavior of double-layer Scallop domes is sensitive to random imperfections and a considerable decrease is seen in their load-bearing capacity.

Stochastic Approach on Safe Designing of Double Layer Grid Space Structure against Member Length Imperfections

The imperfections in Double Layer Grid Space Structure (DLGSS) threaten the safety of designs. The imperfections in the member length of DLGSS may result from human-based causes such as manual cuts, tolerance sensitivity in CNC cuttings and variation in temperature. Therefore, analyzing the impacts of imperfections is vital to ensure the safety of DLGSS systems. Thus, a safe design of DLGSS against member length imperfections is the main focus of this paper. A novel and practical safe design approach, which considers member length imperfections, has been proposed based on linear elastic and probabilistic analyses methods. The impacts of member length imperfections on the DLGSS behavior were also evaluated in detail. Variation in positions of imperfect members, initial size of length imperfections (longer or shorter than the ideal size) and number of imperfect members were selected as the parameters to be analyzed. A 3D computer program, which considers the initial length imperfections of members, has been codded to analyze the space trusses. The impact of imperfection on a space structure was investigated by repeating the simulations for stochastic dispersion of imperfect member position and initial member length imperfection. The results revealed that initial length imperfection might have a considerable impact on the DLGSS behavior. The DLGSS systems can safely be designed by employing the proposed design approach to overcome the defined imperfections.

Influence of Member Length Imperfection on the Capacity of Spatial Structures

Introduction:Load bearing capacity of Double Layer Grid Spatial Trusses (DLGST) majorly depend on the structures' imperfections. It is important to analyze the systems with consideration of the influences of uncertainties to ensure the safety of DLGST.Methods:The variation of imperfect members’ positions and initial size of length imperfections (being longer or shorter than the ideal size) were selected as the parameters of the current research. Member length imperfections for both long and short members were randomly taken into account according to the randomly generated numbers. These random numbers were generated using a normal distribution.Results and Conclusion:The effect of imperfection is investigated by repeating the analyses simulations on structures with a stochastic dispersion of the imperfect member position and initial length imperfection. It has been demonstrated that the length imperfections might significantly decrease safety of the structure and also shown that the position of imperfect members has effect on the structural performance.

Probabilistic estimation of the buckling strength of a CFS lipped-channel section with Type 1 imperfection

Local geometric imperfections in a cold-formed steel (CFS) member can significantly alter the force-carrying capacity of the member. These are the dents and undulations which occur during cold-rolling, handling, transportation and erection of CFS members. The buckling strength of a lipped channel section with Type 1 local imperfection is obtained and characterised statistically using finite element analyses and Monte Carlo simulations. The reduction in strength due to these imperfections are found to be significant. The quantification of reduction in strength due to these imperfections is found for different values of non-dimensional slenderness ratio. Based on the statistical analysis, design equations and strength curves are recommended for the buckling strength of geometrically imperfect members. Legitimacy of using a generalised statistics of imperfection, in the case of unavailability of specific data for a particular section, is also verified.

Simplified numerical method for latticed shells that considers member geometric imperfection and semi-rigid joints

Most finite element models of actual projects established in general finite element software are rigidly connected or connected by hinge joints. Member imperfection cannot be considered in such models, which is inconsistent with the actual situation in most projects. To estimate the influences of joint stiffness and member imperfection on the mechanical behavior of latticed shell structures, double elements and imperfect members were combined in this study. First, the accuracies of double elements and imperfect members were validated. Then, they were combined to establish imperfect elements with semi-rigid joints. The accuracy of imperfect elements with semi-rigid joints was also validated, and the relationship between joint stiffness and that of double elements was deduced. The findings validated that imperfect elements with semi-rigid joints could consider semi-rigid joints and imperfect members simultaneously and with high accuracy. In addition, imperfect elements with semi-rigid joints could be constructed conveniently in general finite element software.

How Sexist Is Aristotle's Developmental Biology?

AbstractThe aim of this paper is to evaluate the level of gender bias in Aristotle's Generation of Animals while exercising due care in the analysis of its arguments. I argue that while the GA theory is clearly sexist, the traditional interpretation fails to diagnose the problem correctly. The traditional interpretation focuses on three main sources of evidence: (1) Aristotle's claim that the female is, as it were, a "disabled" (πεπηρωμɛνo;ν) male; (2) the claim at GA IV.3, 767b6-8 that females are a departure from the kind; and (3) Aristotle's supposed claim at GA IV.3, 768a21-8 that the most ideal outcome of reproduction is a male offspring that perfectly resembles its father. I argue that each of these passages has either been misunderstood or misrepresented by commentators. In none of these places is Aristotle suggesting that females are imperfect members of the species or that they result from the failure to achieve some teleological goal. I defend the view that the GA does not see reproduction as occurring for the sake of producing males; rather, what sex an embryo happens to become is determined entirely by non-teleological forces operating through material necessity. This interpretation is consistent with Aristotle's view in GA II.5 that females have the same soul as the male (741a7) as well as the argument in Metaphysics X.9 that sexual difference is not part of the species form but is an affection (παoç) arising from the matter (1058b21-4). While the traditional interpretation has tended to exaggerate the level of sexism in Aristotle's developmental biology, the GA is by no means free of gender bias as some recent scholarship has claimed. In the final section of the paper I point to one passage where Aristotle clearly falls back on sexist assumptions in order to answer the difficult question, "Why are animals divided into sexes?". I argue that this passage in particular poses a serious challenge to anyone attempting to absolve Aristotle's developmental biology of the charge of sexism.

Advances in the Stability of Frame Structures

As far as structural engineering is concerned, scientific and technological advances are often fostered by the occurrence of collapses involving a more or less relevant amount of damage and, in the most unfortunate cases, also the loss of human lives. Indeed, it seems fair to say that every time a structural collapse takes place, designers and researchers will immediately start searching for a rational explanation; this boost of attention and interest invariably leads to the unveiling and investigation of new phenomena and also paves the way to the development of design tools intended to anticipate and prevent the detrimental effects of such phenomena. The above statements are especially true in the case of structural stability, as attested by the following illustrative examples: ~1! The progress in the theory of laced column buckling due to the collapse of the Quebec Bridge in 1907; ~2! the crucial role played by the Tacoma Narrows Bridge failure, in 1940, concerning the awareness and understanding of the aerodynamic torsional instability phenomenon; and ~3! the development of Koiter’s general elastic postbuckling theory, essentially inspired by the sudden collapse of several thin-shell structures at surprisingly low applied load levels. The very recent and unbearably tragic collapse of the World Trade Center twin towers, on September 11, 2001, highlighted the importance of devoting new attention and resources to a better understanding of behavioral, design, and safety issues related to the overall and member stability of framed structures— particularly when these structures are subjected to extreme loading conditions, such as the ones caused by impact, explosion, or fire. By publishing this Special Issue of the Journal of Engineering Mechanics, ASCE aims at making the above problems more visible, thus drawing the attention of the structural stability scientific and technological communities and encouraging them to devote new research to developing and disseminating more advanced methods for the efficient solution of these problems. At the same time, one has the opportunity of showing a representative sample of the activity currently under way in this field. The recent exponential growth in computer capabilities, affordability, compatibility, and interconnectivity is responsible for a virtual “computational revolution” in many areas related to structural analysis and design. In particular, this situation will certainly lead, in the near future, to the routine incorporation of geometrically and materially nonlinear concepts and methodologies into the daily design practice. It will also enable designers to feel more comfortable and secure when faced with the everexpanding tasks of coping with increasingly slender structures and more complex loading combinations, as they will have easy access to user-friendly tools that are able to handle advanced structural behaviors like the inelastic geometrically nonlinear behavior of initially imperfect members and framed structures, the global and local stability of nonprismatic thin-walled members,

Effect of member length imperfections on triple-layer space trusses

It is almost impossible to produce a space truss assembly with complete precision. With the hundreds of members and joints these structures typically contain, it is inevitable that some of these members will have some imperfections, primarily in the form of lack of fit. This paper presents a study on the effects of member imperfections on triple-layer space trusses. Imperfections are considered in different top, middle, bottom and diagonal members in an attempt to identify the most critical areas in which no imperfect members should be used. The use of composite action between the space truss and a top concrete slab in enhancing truss tolerance to member imperfections is also investigated. The conclusions of this study could be beneficial to triple-layer truss design and construction.

Sensitivity of Space Trusses to Member Geometric Imperfections

The existence of some geometrically imperfect members in a space truss is almost inevitable, and the fact that they produce initial internal member forces is undeniable. This paper is not about how to avoid member imperfections, but rather is a step forward towards better understanding of the implications of having imperfect members. The paper attempts to answer two main questions; how damaging are member imperfections to truss strength and behaviour; and where are the critical areas of a truss at which no imperfect member should be used? Additionally, the effect of composite action between a top concrete slab and a steel truss in suppressing truss sensitivity is assessed. The work is carried out on a non-composite and a composite square-on-square space truss.

The collapse load of pin-jointed networks of randomly imperfect rods

Twoand three-dimensional trusses are among the most frequently used structures in building practice. One has only to consider the incidence of braced structures in residential and industrial buildings, of pylons for transmission lines and cableways, and also, of structures such as single or multilayered grids and vaults with single or double curvature, that are used to cover large areas. One of the advantages of these structures is that they readily lend themselves to modular construction. The large number of possible different structures, and the repetition of elements within a particular structure, a number of which may be built, require the production of many such modules. This allows the consideration of the mass-production of modules with the associated advantages of improved quality control and economy of materials and labour. Thus, with a sufficiently high number of samples, the geometrical and mechanical characteristics of the units may be statistically determined. In particular, the statistical distribution of geometrical imperfections such as the departure from straightness of individual members, may be determined. Such imperfections can produce a dramatic reduction in the strength of the structure. Previously, the influence on the load capacity of trusses of geometrical imperfections in members has been investi. gated by attributing deterministic values of imperfection to each member. However, although maintaining constant the mean value and the standard deviation of member imperfections over the whole structure, a range of collapse loads is obtained, z's This demonstrates that a deterministic treatment of the problem of member imperfections is unrealistic. As geometrical imperfection is a typical random variable, it only seems natural to suggest a probabilistic formulation to evaluate its effect. The problem may be stated thus: given the statistical parameters of the imperfections in the members of a structure: (i), evaluate the probability of collapse under a particular load system; (ii), evaluate the expected value and the standard deviation of the collapse load of the structure. With the word 'buckling' in place of 'collapse' this becomes the central problem of the theory of elastic stability of imperfections-sensitive structures. This problem has been investigated by many authors and a comprehensive treatment together with a list of references is given elsewhere. More recently it has also been studied by Hansen and Roorda a and Roorda. 6 In this paper truss structures of elastic-perfectly plastic material will be considered. The deterministic treatment of the problem of finding the collapse load for perfect structures also allowing for member's post-buckling behaviour is given in (4) while in (5) the same treatment is extended to structures with geometrically imperfect members and in (1) some numerical results are presented. The problem stated above for the most general truss structures proves to be particularly complex. This paper, which is a first approach to the problem, provides a solution for the class of statically determinate structures.