Ultimate Strength Formulations Research Articles

Residual ultimate strength formulations of locally damaged steel stiffened cylinders under combined loads

This paper aims to derive new simple and consistently reliable residual strength equations for predicting the residual ultimate strength of steel dented stiffened cylinders under combined axial compression and radial pressure including hydrostatic pressure. For this, two types of the stiffened cylinders, namely, stringer- and/or ring-stiffened cylinders, which are generally main components of offshore marine structures used in semi-submersibles, submarines, tension legs of platforms (TLPs), and other various types of floating offshore structures, are investigated. Firstly, the various collision damage scenarios which illustrated the collision accidents of offshore stiffened cylinders with supply vessels or floating subjects, were analysed. Then, a finite element modelling of the stiffened cylinders was developed using a commercial software package ABAQUS/Explicit after being validated against available test results. Next, rigorous parametric studies on full-scaled design examples of stiffened cylinders were carried out by changing the design variables. Based on the rigorous case of the study results, new simple design equations, which are used to predict the ultimate residual strength of the damaged stiffened cylinders under combined loads are proposed through a regression study. Finally, the accuracy and reliability of the proposed equations have been compared with available test data and a nonlinear finite element analysis (NFEA). These equations can be useful for the initial design stage of stiffened cylinders under the risk conditions of offshore structures in the case of collision incidents.

Ultimate strength formulations for FPSO stiffened panels under combined compression and shear with initial imperfections and damage

Abstract Accidental collision of striking objects, such as a supply vessel, into the side panel of a FPSO highly influences its ultimate strength assessment. An empirical formula for predicting the ultimate strength of damaged stiffened panels under combined loading of shear and longitudinal compression is empirically derived in this work based on curve fitting of quasi-static nonlinear finite element (FE) analyses. Initial imperfections are introduced by scaling the first buckling mode shape and the damage is caused by residual deformation from a rigid sphere indentation. A pure shear loading is applied at several levels followed by compression loading using the modified Riks method for a number of sphere indentation damages. The suggested formula for a typical FPSO stiffened side shell panel presented an excellent correlation with the nonlinear FE results and can be particularly useful in the preliminary design phase (no damage) and for a quick estimation of the panel residual strength with indentation damage.

Ultimate strength formulation of stiffened panels under in-plane compression or tension with cracking damage

The aim of the present study is to develop closed-form formulations for predicting the ultimate compressive and tensional strength of stiffened steel panels with crack damages. First, a numerical database is generated. This database includes the ultimate strength levels of stiffened steel panels with cracks subjected to axial compressive or tensile loads. It was carried out with a series of nonlinear FEM analyses by varying the size of crack damage. In the following sections, regression analysis is used for deriving the empirical formulations. The results of the present paper can be used for the reliability and risk assessment of structures, including stiffened steel panels with cracks.

Ultimate strength formulation considering failure mode interactions of ring-stiffened cylinders subjected to hydrostatic pressure

This paper outlines empirical formulas to provide adequate predictions of the ultimate strength of ring-stiffened cylinders under hydrostatic pressure. The ultimate strength formulation was derived from published test data found in the open literature. The formulas consider the failure mode interactions, which include the parameter of shell yielding, inter-frame buckling, overall buckling, and stiffener tripping. The failure modes were inserted in the quadratic Merchant-Rankine formula. Afterward, the knockdown factors were empirically derived to best fit the actual collapse pressure. It is found that the proposed formulation can predict the ultimate strengths of ring-stiffened cylinders more accurately and consistently than other codified rules (PD5500, GL, ABS, API). The simple criterion for the assessment of failure modes was also provided. Furthermore, parametric studies were conducted to observe the effect of the design parameter on sizing the ring-stiffened cylinder when the failure modes can be predicted.

Ultimate strength of cylindrical shells with cutouts

ABSTRACTCutouts – perforations that are often made in wind turbine towers to allow access or passage – can also reduce the towers’ ultimate strength. Thus, cutouts may need to be included in the ultimate strength formulations for wind turbine towers as an influential parameter, where significant. The aims of this study are to examine the effects of cutouts on the ultimate-strength characteristics of wind turbine towers and to propose empirical formulae to predict the reduced ultimate strength under axial compression and pure bending. The structural features of cutouts and towers in real wind turbines are investigated, and the effects of different design variables – such as shape, location, aspect ratio, column slenderness ratio, and column aspect ratio – on the ultimate-strength behaviour are described. The ultimate strengths of the towers are computed using elastic–plastic large-deflection finite element analyses. Empirical formulae accommodating a whole range of actual dimensional characteristics of cutouts and towers are derived and proposed. The findings of this research and the proposed formulae have the potential to enhance the structural design and safety assessment of wind turbine towers.

Ultimate strength of box section steel bridge compression members in comparison with specifications

Initial distortion and residual stress are well known as the most important initial imperfection factors and have a significant effect in decreasing the ultimate strength of compression members. The present work focuses on predicting the ultimate strength of welded box section steel compression members regarding initial imperfection factors. Beam compared with shell type of Finite Element (FE) models varied in slenderness ratio and initial distortion are used to assess the accuracy of present numerical results. The comparison of result between FE models and design strength formulations in some specifications are used to assess the ultimate strength formulations of bridge specifications according to the behavior of current steel compression members. It can be observed from numerical results that FE models and design strength by JSHB 2012 and AISC 2005/AASHTO 2010 have good agreement each other which means that the specifications have good capability in assessing the ultimate strength of steel compression members. Parametric study of the ultimate strain varied in slenderness ratio and load versus displacement curves of compression members are also introduced in order to perform more detail steel columns displacement behaviour. Finally, present work proposed a flowchart in designing steel compression members with the expectation that it will be helpful as reference for researchers and engineers in practical fields.

Ultimate strength formulation for stiffened plates subjected to combined axial compression, transverse compression, shear force and lateral pressure loadings

A robust ultimate strength formulation is proposed for stiffened plates subjected to combined axial compression, transverse compression, shear force and lateral pressure loadings. Before deriving the formulation, a simplified numerical method was developed to trace the structural behaviour of stiffened plates under combined loadings. A rigorous parametric study was then performed using the developed numerical method to predict the ultimate strength of various stiffened plates under various combinations of loadings. The formulation was derived by a regression study using the parametric study results. The accuracy and reliability of the proposed formulation were compared with those of commercial packages, such as ABAQUS and DNV PULS, and experimental results.

Probabilistic ultimate strength analysis of submarine pressure hulls

This paper examines the application of structural reliability analysis to submarine pressure hulls to clarify the merits of probabilistic approach in respect thereof. Ultimate strength prediction methods which take the inelastic behavior of ring-stiffened cylindrical shells and hemi-spherical shells into account are reviewed. The modeling uncertainties in terms of bias and coefficient of variation for failure prediction methods in current design guidelines are defined by evaluating the compiled experimental data. A simple ultimate strength formulation for ring-stiffened cylinders taking into account the interaction between local and global failure modes and an ultimate strength formula for hemispherical shells which have better accuracy and reliability than current design codes are taken as basis for reliability analysis. The effects of randomness of geometrical and material properties on failure are assessed by a prelimnary study on reference models. By evaluation of sensitivity factors important variables are determined and comparesons are made with conclusions of previous reliability studies.

Probabilistic ultimate strength analysis of submarine pressure hulls

This paper examines the application of structural reliability analysis to submarine pressure hulls to clarify the merits of probabilistic approach in respect thereof. Ultimate strength prediction methods which take the inelastic behavior of ring-stiffened cylindrical shells and hemi-spherical shells into account are reviewed. The modeling uncertainties in terms of bias and coefficient of variation for failure prediction methods in current design guidelines are defined by evaluating the compiled experimental data. A simple ultimate strength formulation for ring-stiffened cylinders taking into account the interaction between local and global failure modes and an ultimate strength formula for hemispherical shells which have better accuracy and reliability than current design codes are taken as basis for reliability analysis. The effects of randomness of geometrical and material properties on failure are assessed by a prelimnary study on reference models. By evaluation of sensitivity factors important variables are determined and comparesons are made with conclusions of previous reliability studies.

Optimal stiffener design of moderately thick plates under uniaxial and biaxial compression

In this paper, the optimal stiffener design of moderately thick plates under uniaxial and biaxial compression is investigated on the premise that the plate thickness and the required ultimate strength are given. As the theoretical basis of stiffener design, the ultimate strength formulations of weak stiffened thick panels under in-plane biaxial compression are first developed on the basis of large deflection orthotropic plate theory, in which the post-weld initial deflection is taken into account. The von Mises yield criterion is employed to determine the limit state of the panel, and the Nelder–Mead simplex algorithm is used to obtain the efficient solution of nonlinear differential equations. The optimization method presented is based on the stiffener design principles of the overall instability stress and of the working stress. In the optimization formulation, the numbers and geometric sizes of the stiffeners are defined as design variables; the weight ratio of stiffeners to plate is taken as a single objective function; requirements against overall buckling of the panel, local buckling of the plates between the stiffeners and local buckling of the stiffeners themselves are set as constraint functions. Results of both design examples and parameter studies show that, for moderately thick plates, the stiffener weight given by the proposed optimization method is much lower than the weight determined by the current stiffener design method on the premise of the same requirement of structural safety. Using the present optimization method to obtain the lightest and the most effective stiffener layout for moderately thick plates is proposed.

Ultimate strength formulations for stiffened panels under combined axial load, in-plane bending and lateral pressure: a benchmark study

This paper develops advanced, yet design-oriented ultimate strength expressions for stiffened panels subject to combined axial load, in-plane bending and lateral pressure. The collapse patterns of a stiffened panel are classified into six groups. It is considered that the collapse of the stiffened panel occurs at the lowest value among the various ultimate loads calculated for each of the collapse patterns. The panel ultimate strengths for all potential collapse modes are calculated separately, and are then compared to find the minimum value which is then taken to correspond to the real panel ultimate strength. The post-weld initial imperfections (initial deflection and residual stress) are included in the developed panel ultimate strength formulations as parameters of influence. The validity of the developed formula is confirmed by comparing with the mechanical collapse tests and nonlinear FEA. A comparison of the present method is also made with theoretical solutions from the Det Norske Veritas classification society design guideline. Important insights developed are summarized.

Advanced Closed-Form Ultimate Strength Formulation for Ships

The aim of this paper is to develop an advanced ultimate strength formulation for ship hulls under vertical bending moment. Since the overall failure of a ship hull is normally governed by buckling and plastic collapse of the deck, bottom, and sometimes the side shell stiffened panels, it is of crucial importance to accurately calculate the ultimate strength of stiffened panels in deck, bottom and side shell for more advanced ultimate strength analyses. In this regard, the developed formulation is designed to be more sophisticated than previous simplified theoretical methods for calculating the ultimate strength of stiffened panels under combined axial load, in-plane bending and lateral pressure. Fabrication-related initial imperfections (initial deflections and residual stresses) and potential structural damage related to corrosion, collision, or grounding are included in the panel ultimate strength calculations as parameters of influence. All possible collapse modes involved in collapse of stiffened panels, including overall buckling collapse, column or beam-column type collapse (plate or stiffener induced collapse), tripping of stiffeners and local buckling of stiffener web, are considered. As illustrative examples, the paper investigates and discusses the sensitivity of parameters such as lateral pressure, fabrication-related initial imperfections, corrosion, collision and grounding damage on the ultimate strength of a typical Cape size bulk carrier hull under vertical bending.

Large deflection orthotropic plate approach to develop ultimate strength formulations for stiffened panels under combined biaxial compression/tension and lateral pressure

This paper uses the large deflection orthotropic plate approach to develop the ultimate strength formulations for steel stiffened panels under combined biaxial compression/tension and lateral pressure loads, considering the overall (grillage) buckling collapse mode. The object panel has a number of one-sided small stiffeners in either one or both orthogonal directions. The stiffened panel is then modeled as an equivalent orthotropic plate, for which the various elastic constants characterizing structural orthotropy are determined in a consistent systematic manner using classical theory of elasticity. The panel edges are considered to be simply supported. The influence of initial deflections is taken into account. The membrane stress distribution inside the panel under combined uniaxial loading (in either longitudinal or transverse direction) and lateral pressure is analyzed by solving the nonlinear governing differential equations of large deflection orthotropic plate theory. It is presumed that the panel collapses when the most highly stressed boundary location yields, resulting in closed-form expressions for the ultimate strength of the stiffened panel. Based on the insights previously developed through numerical studies, the panel ultimate strength interaction formulation between biaxial loads, with lateral pressure regarded as a secondary load component is then proposed as a relevant combination of the two sets of panel ultimate strength formulations, i.e. one for combined longitudinal axial load and lateral pressure and the other for combined transverse axial load and lateral pressure. The validity of the proposed ultimate strength formulations is verified by a comparison with nonlinear finite element and other numerical solutions.

Advanced Ultimate Strength Formulations for Ship Plating Under Combined Biaxial Compression/Tension, Edge Shear, and Lateral Pressure Loads

The aim of the present study is to develop more advanced design formulations for the ultimate strength of ship plating than available at present. Plate ultimate strength subject to any combination of the following four load components—longitudinal compression/tension, transverse compression/tension, edge shear, and lateral pressure loads—is addressed. The developed formulations are designed to be more sophisticated than existing theoretically based simplified methods. The influence of post-weld initial imperfections in the form of initial deflections and residual stresses is taken into account. It has been previously recognized that a single ultimate strength interaction equation cannot successfully represent the ultimate limit state of long and/or wide plating under all possible combinations of load components involved. This is due to the fact that the collapse behavior of the long and/or wide plating depends primarily on the predominant load components, implying that more than one strength interaction formulations may be needed to more properly predict the plate ultimate limit state. In this regard, the present study derives three sets of ultimate strength formulations for the long and/or wide plating under the corresponding primary load by treating lateral pressure as a secondary dead load. The ultimate strength interaction formula under all of the load components involved is then derived by a relevant combination of the individual strength formulas. The validity of the proposed ultimate strength equations is studied by comparison with nonlinear finite-element analyses and other numerically based solutions.

Ultimate Strength and Effective Width Formulations for Ship Plating Subject to Combined Axial Load, Edge Shear, and Lateral Pressure

The aim of the present study is to develop closed-form formulations for the ultimate strength of simply supported steel plating subject to a combination of longitudinal axial load, edge shear, and lateral pressure. The post-weld initial imperfections (initial deflections and residual stresses) are included in the strength formulations as parameters of influence. By solving the equilibrium and compatibility governing differential equations of large-deflection plate theory, the membrane stress distribution inside the plating under axial and lateral pressure loads is formulated in closed form. The ultimate strength formulation for plating under axial load and lateral pressure is then derived under the assumption that the ultimate limit state is reached if the plate edges yield. An empirical formula for the plate ultimate shear strength is suggested based on numerical FE solutions. A relevant ultimate strength relationship between axial load and edge shear is then proposed by combining the two sets of the ultimate strength formulations. As another contribution, the effective width formulation for plating under combined axial compression and edge shear which allows for the shear lag effect caused by lateral pressure as well as the influence of post-weld initial imperfections is developed. The validity of the proposed ultimate strength formulations is shown by comparing with experimental results and nonlinear finite-element analyses. Modeling uncertainty of the developed plate ultimate strength formula against the experimental and numerical results is studied in terms of bias and coefficients of variation.

Limit state formulations for TLP tendon and steel riser bodies

Existing limit state formulations for tendon and steel riser bodies used in tension leg platforms have been reviewed. These include API Bull. 5C3 (for casings), API RP 2A LRFD, BSI Sub-sea Pipeline, Danish Pipeline Code, DnV Submarine Pipeline Standard and NPD Offshore Structures Regulations, as well as formulations proposed by Johns and McConnell (Battelle), Jensen and Pedersen (Technical University of Denmark), Loh (Exxon), Murphey and Langner (Shell), Tamano et al. (Nippon Steel) and Winter et al. (TNO). Ultimate strength formulations for tension, bending and pressure acting singly or in pairs of loads are compared. There are significant differences in the strength formulae for pressure load, mainly due to the treatment of initial ovality; and for bending capacity depending upon whether plastic or first yield bending capacity is utilized. Some formulae for interaction between pressure and bending, as well as pressure and tension, imply little mode interaction, while others, specially for low diameter-to-thickness ratio, indicate strong interaction, i.e. almost a linear relationship as in all formulae for tension combined with bending.

Limit states for the ultimate strength of tubulars subjected to pressure, bending and tension loads

This paper is concerned with ultimate strength formulations for long circular tubes under combined pressure, tension and longitudinal bending. The study is motivated primarily by the design needs of tendon and riser bodies used in the offshore industry, but it also relevant for offshore pipelines. The tubulars considered have a diameter-to-thickness ratio between 15 and 40 and a yield stress primarily in the range 300–600 MPa. The stress-strain characteristics are typically like those of X-52 and X-77. The goal has been to develop a simple, explicit strength formulation that can be used in reliability analysis as well as load and resistance factor design (LRFD) checks of riser and tendon bodies. This goal is achieved by a systematic comparison of existing formulations for tubes subjected to pressure, tension and longitudinal bending, with relevant experimental data as well as numerical analyses. The study resulted in a new formulation for the interaction between the three loads.

Axial Strength of Grouted Pile‐to‐Sleeve Connections

A new equation for the calculation of axial load transfer in grouted pile‐to‐sleeve connections, either with or without shear keys, is proposed. The general form of the equation was obtained from an ultimate strength formulation for a predicted failure mode of the connection. The ultimate strength equation states that the axial strength of the connection is equal to the sum of two terms: First, the strength of the adhesion and friction between the pile and grout, and, second, the product of the confined strength of the grout and the ratio of the shear key's height to its spacing. The first term was estimated from test results. The second term was estimated from both theoretical considerations and test results, with good agreement between the two approaches. The design equation proposed was obtained by applying separate factors of safety to the two terms. Comparison of the design equation to test data gave a safety index of 3.96 for connections without shear keys, and 4.80 for connections with shear keys. ...