Slenderness ratio | EPFL Graph Search

In architecture, the slenderness ratio, or simply slenderness, is an aspect ratio, the quotient between the height and the width of a building. In structural engineering, slenderness is used to calculate the propensity of a column to buckle. It is defined as l/k where l is the effective length of the column and k is the least radius of gyration, the latter defined by k^2=I/A where A is the area of the cross-section of the column and I is the second moment of area of the cross-section. The effective length is calculated from the actual length of the member considering the rotational and relative translational boundary conditions at the ends. Slenderness captures the influence on buckling of all the geometric aspects of the column, namely its length, area, and second moment of area. The influence of the material is represented separately by the material's modulus of elasticity E. Structural

Stabilität von Tragelementen aus Glas

Andreas Luible

Stability of load carrying elements in glass The increasing demand in modern architecture for more slender and lighter structures requires the use of new construction materials. Glass, a material that has been used for a long time in windows as a filling material, has much to offer in this regard due to its very high compressive strength and transparency. For this reason, there is a growing trend to extend the use of glass sheets to load carrying elements such as columns, beams and panels. Due to their high slenderness and high compressive strength, such elements tend to fail because of instability (i.e. column buckling, lateral torsional buckling or plate buckling). At the moment little knowledge exists about the load carrying behaviour of glass structural elements, and existing design methods for other materials (i.e. steel) have been found to be unsuitable for direct transfer to the design of glass panels. With this in mind, the main objectives of the current thesis are: The study of the load carrying behaviour of glass elements which may fail due to lack of stability by means of laboratory tests and analytical and numerical models, as well as the study of the main influencing parameters. Discussion of possible design methods for glass elements which may fail due to lack of stability for the three main stability problems (column buckling, lateral torsional buckling and plate buckling) and proposition of possible aids for design such as buckling curves. The main influencing parameters (dispersion of the glass thickness, initial deformation) on the load carrying behaviour of glass elements which may fail due to lack of stability have been measured and are evaluated herein using statistical methods. The breakage stress, the thermal prestress and the effective tensile strength are defined and explained. Existing models to determine the tensile strength of glass are discussed. The column buckling behaviour of single layer and laminated safety glass is studied by means of column buckling tests, which are compared to analytical and numerical models. The models are used to study the influence of the main parameters, particularly the shear connection due to the interlayer (PVB) in laminated safety glass, on the load carrying behaviour and buckling strength of glass elements. On the basis of this study different possible design methods for column buckling of glass elements in compression are proposed and discussed. It is shown that a second order stress analysis is the most appropriate method for glass. As a further simplification, the cross section of a laminated safety glass structural element can be modelled as a monolithic cross section with an effective thickness. Analytical and numerical models for the lateral torsional buckling of glass beams are also verified by a comparison to test results. Along with a study of the main parameters, different methods to determine the lateral torsional buckling strength are discussed, and it is shown that buckling curves for lateral torsional buckling should be developed for glass beams using a slenderness ratio based on effective tensile strength. As a result of numerical simulations, recommendations for the future development of lateral torsional buckling curves of glass beams are given. The column buckling behaviour of single layer and laminated safety glass is also studied by means of column buckling tests, analytical and numerical models. It is shown that glass panels have a large post critical load carrying capacity but the way the loads are introduced into the panels, as well as the buckling shape, have an important influence on the plate buckling capacity. A design method with buckling curves using a slenderness ratio based on effective tensile strength seems applicable for the design of glass panels. As a result of numerical simulations, recommendations for the future development of plate buckling curves for plate glass elements under compression are given.

EPFL2004

Effective Stiffness and drift capacity of modern unreinforced masonry walls

Katrin Beyer, Bastian Valentin Wilding

Code design of unreinforced masonry (URM) buildings is based on elastic analysis, which requires as input parameter the effective stiffness and the ultimate drift capacity of the in-plane force-displacement response of URM walls. Eurocode 8, for example, estimates the effective stiffness as 50% of the gross sectional elastic stiffness. Code provisions for the drift capacities are usually empirical equations relating a base drift value to the failure mode and a slenderness ratio. However, comparisons with experimental results have shown that neither approach yields accurate predictions. In this paper, 61 full-scale shear-compression tests of modern URM walls of different masonry typologies from the literature are investigated. It shows that both the initial and the effective stiffness increase with increasing axial load ratio and that the effective-to-initial stiffness ratios are approximately 75% rather than the used 50%. An empirical model for the computation of the effective-to-initial stiffness ratio is suggested based on a recently developed analytical approach, which attributes the loss in stiffness to diagonal cracking and brick crushing. As for the drift capacity, the experimental evidence supports the fact that it reduces with increasing axial load and increases with increasing shear span ratio. A recently developed analytical model for the prediction of the ultimate drift capacity for both shear and flexure controlled URM walls is presented. It considers the effect of kinematic and static boundary conditions on the drift capacity. A comparison to test results shows that the proposed models yield better estimates than current code provisions.

2018

Force-based higher-order beam element with flexural-shear-torsional interaction in 3D frames. Part II: Applications

João Saraiva Esteves Pacheco de Almeida

The specific features of the proposed force-based formulation derived in the companion paper, which is applied for the first time to higher-order beam theories, are herein thoroughly validated. Introductory numerical examples illustrate the influence of mesh refinement, boundary conditions, and slenderness ratios for isotropic linear elastic response. Specific higher-order effects—unique to the developed element—are then suitably interpreted, as well as the formulation appropriateness to consider distributed loads and to model three-dimensional behaviour, which is verified with solid finite element analyses. Extensive comparisons against existing proposals, namely other refined higher-order beam theories, emphasize the performance of the proposed approach. Finally, the nonlinear response of the element with a multiaxial J2 linear plasticity material model is analysed, highlighting its advantages in relation to a classical force-based Euler–Bernoulli beam using a one-dimensional plastic material model with kinematic hardening.

Elsevier2015

Stabilität von Tragelementen aus Glas

Andreas Luible

EPFL2004