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- ItemShallow foundation design: a comparative study of partial safety factors and full probabilistic methods(Springer Nature, 2024-06-13) Vořechovský, Miroslav; Miča, Lumír; Boštík, JiříIn the past two decades, Europe has witnessed a significant transition in the design codes used for assessing foundation structures, with the widespread adoption of the Eurocodes (EC). This shift remains a pertinent topic within the engineering community, particularly concerning the transition from traditional design methodologies to those prescribed by the Eurocodes, as well as the potential for fully probabilistic design. While the Eurocodes’ methodology is described as probabilistic, it is crucial to recognize that the achievement of the target reliability level is predominantly facilitated through a system of partial safety factors. These factors are integrated into the calculation algorithm as fixed values, rendering the process essentially deterministic. To refine these calculations for more accurate reliability estimates—expressed in terms of failure probability—a genuinely probabilistic framework is required, termed as fully probabilistic computation. This paper aims to elucidate the fully probabilistic calculation approach for the broader professional community, using the geotechnical application of shallow foundations as an illustrative example. We present a comparative analysis of this advanced approach with the standard foundation design according to EC7 and ČSN 731001, the latter being a precursor in Europe for implementing the partial safety factor method. The discussion extends to a practical demonstration of full probabilistic design juxtaposed against the conventional partial safety factor method, using a shallow foundation case study. Furthermore, the paper delves into the impact of the tail behavior of uncertain or spatially varying soil parameters on the theoretical probability of failure, underscoring its significance in foundation design.
- ItemStress projection procedure for the form-finding analysis of membrane structures(Elsevier, 2024-02-01) Lang, Rostislav; Němec, Ivan; Park, K. C.This study examines the form-finding analysis of membrane structures and presents a new general method for determining prestress called stress projection. This method addresses several deficiencies while performing the form-finding analysis, especially in the case of conical membrane structures. A key feature of the proposed stress projection procedure is the adoption of a generally oriented projection plane, where finite elements are projected onto, and the determination of their stress states, which allows for a smooth adaptation of stresses over the membrane structures. Deformation gradients are then evaluated with respect to this projection plane, as opposed to the inertial reference frame used for the computation of stress tensors in subsequent form-finding processes. The proposed stress projection procedure efficiently modifies the stresses over the structures and significantly addresses intrinsic element distortion problems within the form-finding analysis. Thus, the proposed method allows for the maintenance of regularized finite element shapes and the smooth changing of stress states throughout form-finding iteration processes, especially for conical membrane shapes. Numerical experiments demonstrate the efficiency of the implemented stress projection scheme compared with two well-known stress adaptation schemes.
- ItemTwo Stochastic Methods to Model Initial Geometrical Imperfections of Steel Frame Structures(MDPI, 2024-01-12) Jindra, Daniel; Kala, Zdeněk; Kala, JiříThe stochastic modeling of geometrically imperfect steel frame structures requires statistical inputs for imperfection parameters, often with specific mutual correlations. The stochastic input values of geometrical imperfections are derived from European Standard EN 1090-2:2018 tolerance criteria. Two advanced stochastic methods, #RSS (random storey sway) and #RSP (random storey position), are developed based on these criteria. This paper presents a verification study, using random sampling simulations, for these two stochastic methods (#RSS and #RSP) to directly model the initial global geometrical imperfections of steel frame structures. The proposed methods have been verified for structures with equidistant storey heights and for those comprising up to 24 storeys, making them applicable to a wide range standard steel frame structures. It has been found that the performance of the #RSS method is satisfactory. An advantage of #RSS is that the random parameters are statistically independent. On the other hand, the #RSP method requires the definition of these mutual correlations in order to satisfy the criterion that 95 percent of random realizations of initial imperfections fall within the tolerance limits of the corresponding European Standard. The #RSP method, however, might have certain advantages for structures with a larger number of storeys (above 24), as closely discussed in this study. Additionally, this study provides useful provisions for the advanced numerical analyses of multi-storey steel frames of various geometries.
- ItemStrain Energy and Entropy Based Scaling of Buckling Modes(MDPI, 2023-12-06) Kala, ZdeněkA new utilization of entropy in the context of buckling is presented. The novel concept of connecting the strain energy and entropy for a pin-ended strut is derived. The entropy of the buckling mode is extracted through a surrogate model by decomposing the strain energy into entropy and virtual temperature. This concept rationalizes the ranking of buckling modes based on their strain energy under the assumption of given entropy. By assigning identical entropy to all buckling modes, they can be ranked according to their deformation energy. Conversely, with identical strain energy assigned to all the modes, ranking according to entropy is possible. Decreasing entropy was found to represent the scaling factors of the buckling modes that coincide with the measurement of the initial out-of-straightness imperfections in IPE160 beams. Applied to steel plane frames, scaled buckling modes can be used to model initial imperfections. It is demonstrated that the entropy (scale factor) for a given energy roughly decreases with the inverse square of the mode index. For practical engineering, this study presents the possibility of using scaled buckling modes of steel plane frames to model initial geometric imperfections. Entropy proves to be a valuable complement to strain energy in structural mechanics.
- ItemComparison of crack growth rates of IPE beams made from stainless steel in three-point bending(Elsevier, 2023-11-24) Juhászová, Tereza; Miarka, Petr; Seitl, StanislavThe main focus of research dealing with a fatigue of steel components is mostly performed by mechanical testing with focus set on small-scale components. On the other hand, from a civil engineering viewpoint, the steel load-bearing structures or their elements have much larger dimension, when comparing them to laboratory specimens. Therefore, the fatigue testing took place on IPE 80 specimens made from two different stainless steels AISI 304 and AISI 316, loaded in three-point bending with data collection of crack mouth opening displacement placed in mid-span using clip-on extensometer. This presented study focuses on the comparison of crack propagation rate in linear region of well-known Paris’ law. For the assessment of material constants from Paris’ equation C and m, two steel grades of stainless steel, AISI 304 and AISI 316 were experimentally obtained. To evaluate the experimental data, a three-dimensional (3D) numerical model, representing IPE 80 geometry, in a finite element method (FEM) software Ansys Mechanical APDL was created. The generated numerical results were used to evaluate stress intensity factor values, which serves as a main input to crack propagation Paris’ law.