Propagation Buckling of Subsea Pipelines and Pipe-in-Pipe Systems

This chapter investigates buckle propagation of subsea single-walled pipeline and pipe-in-pipe (PIP) systems under hydrostatic pressure, using 2D analytical solutions, hyperbaric chamber tests and 3D FE analyses. Experimental results are presented using hyperbaric chamber tests, and are compared with a modified analytical solution and with numerical results using finite element analysis for single-walled pipelines and PIPs. The experimental investigation is conducted using commercial aluminum tubes with diameter-to-thickness (D/t) ratio in the range 20–48. The comparison indicates that the modified analytical expression presented in this work provides a more accurate lower bound estimate of the propagation buckling pressure of PIPs compared to the existing equations, especially for higher Do/to ratios. A 3D FE model is developed and is validated against the experimental results of the propagation bucking. A parametric FE study is carried out and empirical expressions are provided for buckle propagation pressures of PIPs with (Do/to) ratio in the range 15–25. Moreover, empirical expressions are proposed for the collapse pressure of the inner pipe (Pci), the proposed empirical equation for Pci, is shown to agree well with the experimental results of the tested PIPs

Buckle interaction in deep subsea pipelines

The paper investigates the interaction between propagation buckling and lateral buckling in deep subsea pipelines. Lateral buckling is a possible global buckling mode in long pipelines while the propagation buckling is a local mode that can quickly propagate and damage a long segment of a pipeline in deep water. A numerical study is conducted to simulate buckle interaction in deep subsea pipelines. The interaction produces a significant reduction in the buckle design capacity of the pipeline. This is further exasperated due to the inherent imperfection sensitivity of the problem

Transverse Shear Stiffness of Bolted Cold-Formed Steel Storage Rack Upright Frames with Channel Bracing Members

Accurately evaluating the transverse shear stiffness of cold-formed steel storage rack upright frames is crucial to calculate the frame elastic buckling load, perform earthquake design and serviceability checks. This is especially essential for high-bay racks, which are subjected to large second-order effects, and racks supporting the building enclosure, which are exposed to transverse wind loads. The shear behaviour of these frames is poorly understood and experimental testing is usually required to measure their stiffness. Previous studies have shown that Finite Element Analyses (FEA), solely using beam elements, fail to reproduce experimental test results and may overestimate the transverse shear stiffness by a factor up to 25. In this paper, a commercially used upright frame, with either bolted lip-to-lip or back-to-back channel section bracing members, has been modelled using shell elements. The model is verified against available experimental data and found to accurately predict the experimental shear stiffness with an average error of 7%. Based on the verified FE model, the factors contributing to the frame shear deformation are quantified. The different frame deformations imposed by the test set-ups in the European (EN15512) and Australian (AS4084) standards are both considered. The effects of the bracing lay-out, the bolt bending, local deformations of the uprights and bracing members at the connections on the performance of the upright frames are quantified and discussed

The impact of the frequency content of far-field earthquakes on the optimum parameters and performance of tuned mass damper inerter

Tuned mass damper inerter is a passive control device that is proven to be effective in mitigating structural responses under earthquake excitations, however, its efficiency highly depends on its design parameters. This paper aims to investigate how the optimum parameters of TMDI change with the frequency content of far-field earthquakes to minimize the need for repeatedly optimizing these parameters for varying far-field earthquakes and structural characteristics. To achieve this objective, the ratio of the earthquake's frequency to the structure's frequency is defined as an index to simultaneously represent the structure and the earthquake. Case studies of 5, 10, 15, and 20-story building structures are analyzed under twenty-three far-field earthquakes which are categorized into three main groups based on their frequency (PGA/PGV) including “Low”, “Intermediate”, and “High”. Particle Swarm Optimization (PSO) is employed to obtain the optimum parameters of TMDI including the damping and the frequency ratio to minimize two distinct objective functions: (1) the peak displacement and (2) the peak acceleration of the top story in a time domain analysis. To validate the applicability of the proposed method in determining the optimal parameters of TMDI regardless of the earthquake and structure frequency, a 10-story benchmark building is employed. Moreover, this study demonstrates the effectiveness of TMDI in minimizing the objective functions concerning the frequency content of the earthquake. It also illustrates the trend of the PSO optimization process. The results show that the index provides a discernible pattern for the variation of the optimum parameters of TMDI. Furthermore, it is demonstrated that the difference in the structural response between tuning the TMDI with the PSO algorithm and the suggested method is less than 3 % when the index is greater than 1. As the ratio of earthquake frequency to the frequency of structure increases, the objective functions will correspondingly increase. The results also indicate that, an increment in the inertance ratio leads to an increase in the value of optimum parameters of TMDI. Furthermore, among all structures analyzed, those subjected to intermediate frequency earthquakes exhibit the most significant reduction in both objective functions

Biaxial Bending of Cold-Formed Steel Storage Rack Uprights – Part II: Design Methods

This paper uses the results from the parametric studies reported in the companion paper to verify the accuracy of different forms of published direct strength method (DSM) equations. They consist of the classical DSM equations and considering the inelastic reserve capacity into these equations, with and without an extended range of the cross-sectional slenderness. The verifications are made for local and distortional buckling modes. Results show that for all investigated buckling modes, the DSM results in better predictions when the inelastic reserve capacity is considered. The appropriate form of the DSM to predict the biaxial capacity of unperforated cold-formed steel storage rack uprights is discussed

Direct Strength Method and Response of Cold-Formed Steel Storage Rack Uprights in Global Biaxial Bending

This study seeks to investigate the global (lateral-torsional) buckling capacity of cold-formed steel (CFS) storage rack uprights under biaxial bending. A previously validated biaxial bending numerical model for local and distortional buckling of CFS rack uprights is used for global buckling. Biaxial bending response of nine unperforated upright cross-sections, each with nine different biaxial bending configurations, were considered. The findings demonstrate that the biaxial bending of the investigated uprights is governed by a nonlinear interaction behavior. DSM predictions including the classical method and the use of inelastic reserve capacity are compared to numerical capacities. The use of the DSM with inelastic reserve capacity as in the AISI-S100 and AS/NZS 4600, results in an overall 3% improvement of the predictions when compared with the classical DSM. A new extended range of the inelastic reserve capacity for global buckling is proposed. When compared with the classical DSM approach, the new extended range results in 14% improvement of the DSM predictions

Biaxial Bending of Cold-Formed Steel Storage Rack Uprights – Part I: Parametric Studies and Response

This paper first introduces an advanced finite element model to determine the biaxial bending capacity of cold-formed steel storage rack upright sections. The model is found to accurately predict published experimental results with an average predicted to experimental capacity ratio of 1.02. Second, the validated model is used to run parametric studies and analyse the biaxial response of slender, semi-compact and compact unperforated storage rack upright cross-sections. Analyses are run for local and distortional buckling failure modes only. Ten and four different cross-sectional shapes are analysed for local and distortional buckling, respectively, and nine biaxial bending configurations are considered per cross-section and buckling mode. Results show that a nonlinear interactive relationship typically governs the biaxial bending of the studied uprights. This relationship is discussed in some details and analysed for the different failure modes and cross-sectional slenderness

Influence of the moisture content on the fracture energy and tensile strength of hardwood spotted gum sawn timber and adhesive bonds (gluelines)

This study aims to measure the fracture properties, including crack initiation and propagation, of Australia’s native forest grown spotted gum ([SPG], Corymbia citriodora) sawn timber and associated adhesive bonds at different moisture content levels. The collected data were used as input values to develop a numerical model to understand the delamination of SPG glulam beams when exposed to a wetting and drying process. Thus, Mode I and Mode II fracture energies for crack propagation along radial and glueline directions were experimentally investigated under various moisture content levels (8%, 12% and 16%). Single-end notched beams and compact shear specimens were used to capture the Mode I and Mode II fracture energies, respectively. For crack initiation, the tensile strength perpendicular to the grain and the shear strength (taken as the maximum stress from the Mode II fracture tests) were also measured. In total, 200 experimental tests were performed. One-way analysis of variance statistical analyses showed that the fracture energies and shear strengths were independent of the range of moisture content levels investigated. In addition, the collected data were compared with the limited published fracture properties of other hardwood species

Design of long-span lightweight timber floors subject to walking excitations: a case study

Lightweight timber construction is popular in buildings with two or more storeys in Australia. The floors are made of a floorboard supported on joists or trusses. Recently, the sector is moving towards multi-storey construction of different building classes with different floor usages and shared tenancy. Thus, a need for high performing lightweight floor systems becomes urgent. The current vibration control criteriain the Australian standard recommends limitingstatic deflection, which is a coarse method and does not necessarily guarantee satisfactory performance.In the current study, vibration performance of a 6m×6m floor system with particleboard flange and trusswebs is investigated under single walker excitations and at different walking frequencies. The vibration responses are compared to the predictions and performance criteria recommended in international standards and guidelines. The results show inconsistencies in the calculated levels of acceptance from different sourcesusing simplified expressions and more rigorous methods of analysis. This highlights the significance of the need for further research to developa harmonised method of analysis that can be used by manufacturers and engineers in Australia to confidently design floors for vibrations

8-MW wind turbine tower computational shell buckling benchmark. Part 1:an international ‘round-robin’ exercise

An assessment of the elastic-plastic buckling limit state for multi-strake wind turbine support towers poses a particular challenge for the modern finite element analyst, who must competently navigate numerous modelling choices related to the tug-of-war between meshing and computational cost, the use of solvers that are robust to highly nonlinear behaviour, the potential for multiple near-simultaneously critical failure locations, the complex issue of imperfection sensitivity and finally the interpretation of the data into a safe and economic design.This paper reports on an international ‘round-robin’ exercise conducted in 2022 aiming to take stock of the computational shell buckling expertise around the world which attracted 29 submissions. Participants were asked to perform analyses of increasing complexity on a standardised benchmark of an 8-MW multi-strake steel wind turbine support tower segment, from a linear elastic stress analysis to a linear bifurcation analysis to a geometrically and materially nonlinear buckling analysis with imperfections. The results are a showcase of the significant shell buckling expertise now available in both industry and academia.This paper is the first of a pair. The second paper presents a detailed reference solution to the benchmark, including an illustration of the Eurocode-compliant calibration of two important imperfection forms