In-plane Bending Load Research Articles

Structural fatigue investigation of transverse surface crack growth in rail steels and thermite welds subjected to in-plane and out-of-plane loading

This study investigates the structural fatigue crack growth behavior of observed transverse surface cracks in rail steel and thermite weld subjected to in-plane and out-of-plane loading. Stress Intensity Factor (SIFs) solutions were derived from finite element model analysis for transverse surface cracks located at five different crack initiation locations in the cross-section of rail steel and thermite weld. The SIFs were presented by the conventional geometry factor Y and weld magnification factor Mk solutions for rail steel and thermite weld. Fracture toughness and fatigue crack growth rate tests were conducted to determine the mechanical properties of thermite weld materials and are compared with reported data for rail steels (R260 and R350HT). Fatigue crack growth prediction algorithm was developed using the coupled root mean square integration approach and was compared with the conventional uncoupled two-degree of freedom approach for semi-elliptical surface crack growth in the depth and surface directions respectively. The fatigue crack growth algorithm and propagation life prediction provide valuable observations on the crack shape evolution. It proves that out-of-plane bending loading is a more significant failure mode as compared to in-plane bending loading for thermite weld joints at curve tracks. Fatigue crack propagation results provide fatigue stress range-life curves for weld-toe surface cracks initiated at the head-to-web region of thermite welded joint structure.

Structural behaviour and design rules of confined masonry walls: Review and proposals

Confined masonry (CM) has been adopted as a cost-effective and earthquake-resistant solution for buildings, mostly in developing countries. CM has large potential for use in Europe, but suitable rules for its application are not available in the European masonry code. This paper presents a critical review of theoretical approaches and experimental investigations on the structural behaviour of CM walls, along with the proposal of simple but suitable design rules. The behaviour to vertical compression and to in-plane shear and bending loadings are comprehensively reviewed with reference to existing studies. Concerning the vertical compressive behaviour, the contribution of each material to the vertical resistance is evaluated and a formulation is proposed. The existing theories for the shear and flexural behaviours are reviewed and the available and new proposed models are compared against experimental results. Finally, requirements for detailing of CM are reviewed from international design codes, in view to propose suitable rules for implementation in a structural code.

Size effect in the fracture properties of sandwich panels of plasterboard and core of rock wool

This paper extends the previous work of the authors and deals with the study of fracture of sandwich panels of plasterboard and rock wool under in-plane bending and tensile loading. It presents the results of the experimental campaign focused on the size effect of the tested specimens. To this end, mixed-mode (I and II) fracture tests have been carried out with specimens of three different sizes. The experimental results are compared with the values obtained from the numerical simulation of the test by using a model based on the embedded cohesive crack developed by the authors in previous published works. Comparison of the results shows how the model is able to reproduce the size effect of the specimens in this material from the parameters that characterize fracture behaviour. The aim is to use the cohesive model proposed by the authors to move from laboratory tests to a built panel.

Probabilistic analysis of the local joint flexibility in two-planar tubular DK-joints of offshore jacket structures under in-plane bending loads

Tubular DK-joints are among the most common joint types in jacket substructure of offshore wind turbines (OWTs) and oil/gas production platforms. The local joint flexibility (LJF), as an intrinsic feature of a tubular joint, is one of the factors affecting the global static and dynamic responses of an offshore structure. In the present paper, a total of 324 finite element (FE) analyses were carried out on 81 FE models of two-planar tubular DK-joints under four types of in-plane bending (IPB) moment loads. Generated FE models were validated based on the available experimental data, FE results, and parametric equations. FE analysis results were used to develop a set of probability density functions (PDFs) for the LJF factor (fLJF) in IPB-loaded DK-joints. Based on a parametric FE investigation, a sample database was prepared for the fLJF values and density histograms were generated for respective samples. Nine theoretical PDFs were fitted to the developed histograms and the maximum likelihood (ML) method was applied to evaluate the parameters of fitted PDFs. In each case, the Kolmogorov-Smirnov and chi-squared tests were used to assess the goodness of fit. Finally, the Birnbaum-Saunders model was proposed as the governing probability distribution function for the fLJF. After substituting the values of estimated parameters, four fully defined PDFs were presented for the fLJF in two-planar tubular DK-joints under four types of IPB loading.

Stress Concentration Factor of A Two-Planar Double KT Tubular Joint due to In-Plane Bending Loading in Steel Offshore Structures

The purpose of this study is to investigate the proper Stress Concentration Factor (SCF) of a 60° two-planar DKT tubular joint of a tripod wellhead offshore structure. So far, calculation of SCF for a multi-plane tubular joint was based on the formulation for the simple/uniplanar tubular joints that yield in over/under prediction of the SCF of the joint. This situation in turn decreasing the accuracy of fatigue life prediction of the structures. The SCF is one of the most important parameters in the tubular joint fatigue analysis. The tubular joint is modelled as finite element models with bending loads acting on the braces that cover a wide range of dimensionless geometrical parameters (β, τ, γ). The effect of such parameters on the SCF distribution along the weld toe of braces and chord on the joint are investigated. Validation of the finite element model has shown good agreement to the global structural analysis results. The results of parametric studies show that the peak SCF mostly occurs at around crown 2 point of the outer central brace. The increase of the β leads to decrease the SCF. While the increase of the τ and γ leads to increase the SCF. The effect of parameter β and γ on the SCF are greater than the effect of parameter τ.

Static strength of doubler plate reinforced tubular T/Y-joints under in-plane bending load

In the present paper, results of comprehensive finite element (FE) analyses performed on 210 generated models of T/Y-joints strengthened with doubler plate are presented. The results of FE models were validated against the data available from 12 experimental tests. These FE models investigate the effect of the doubler plate size and joint geometry on the static strength of doubler plate strengthened tubular T/Y subjected to in-plane bending (IPB) load. Afterwards, the ultimate capacity and deformed shapes of doubler plate and collar plate reinforced T- and Y-joints are compared. Results indicated that the doubler plate can significantly enhance the initial stiffness, ultimate capacity, and considerably improve failure patterns of T- and Y-joints under IPB load. In spite of the remarkable difference between the static capacity of un-strengthened and doubler plate strengthened T- and Y-joints subjected to IPB, the static strength of doubler plate strengthened T/Y-joints under IPB load has not been investigated so far and no design equation is available to calculate the ultimate strength of doubler plate reinforced T/Y-joints. For this reason, geometrically parametric study was followed by a set of nonlinear regression analyses to propose an ultimate capacity parametric formula for the static analyses of doubler plate strengthened tubular T/Y-joints subjected to IPB load.

A study on the Local Joint Flexibility (LJF) of two-planar tubular DK-joints in jacket structures under in-plane bending loads

In the present paper, results of a parametric study conducted on the Local Joint Flexibility (LJF) of two-planar tubular DK-joints under In-Plane Bending (IPB) loads are presented. DK-joints are among the most common joint types in jacket substructure of Offshore Wind Turbines (OWTs). A total of 324 finite element (FE) analyses were carried out on 81 FE models under four types of IPB loading in order to investigate the effect of the DK-joint’s geometrical parameters on the LJF factor (fLJF). Based on the results of parametric study, the factors leading to the LJF reduction were introduced. Generated FE models were verified using the existing experimental data, FE results, and parametric equations. The effect of the weld profile was also considered. The fLJF in two-planar DK- and uniplanar K-joints were compared. Results indicated that the effect of multi-planarity on the LJF is quite significant and consequently the use of the equations already available for uniplanar K-joints to calculate the fLJF in two-planar DK-joints may lead to highly under-/over-predicting results. To handle this issue, the FE results were used to derive a set of parametric equations for the prediction of the fLJF in IPB-loaded two-planar DK-joints. The proposed equations were checked against the acceptance criteria recommended by the UK DoE and can be reliably used for the analysis and design of tubular joints in OWTs.

Vibration analysis of FG nanoplates with nanovoids on viscoelastic substrate under hygro-thermo-mechanical loading using nonlocal strain gradient theory

According to a generalized nonlocal strain gradient theory (NSGT), dynamic modeling and free vibrational analysis of nanoporous inhomogeneous nanoplates is presented. The present model incorporates two scale coefficients to examine vibration behavior of nanoplates much accurately. Porosity-dependent material properties of the nanoplate are defined via a modified power-law function. The nanoplate is resting on a viscoelastic substrate and is subjected to hygro-thermal environment and in-plane linearly varying mechanical loads. The governing equations and related classical and non-classical boundary conditions are derived based on Hamilton\'s principle. These equations are solved for hinged nanoplates via Galerkin\'s method. Obtained results show the importance of hygro-thermal loading, viscoelastic medium, in-plane bending load, gradient index, nonlocal parameter, strain gradient parameter and porosities on vibrational characteristics of size-dependent FG nanoplates.

Asymmetric crack onset at open-holes under tensile and in-plane bending loading

Plates notched with open-holes that are subject to combined tensile and in-plane bending loading are studied in this analysis of crack onset. A finite fracture mechanics approach is employed to study the onset of asymmetric crack patterns in the notched structure. The stress field and the energy release rates required to solve the coupled stress and energy criterion are obtained from linear elastic finite element analyses. Closed-form expressions for the dependence of the solution on governing parameters as e.g. the structural size, the Young’s modulus or the ratio of bending to normal loading are given significantly reducing the computational effort required for the failure model. A comparison to experimental results and to numerical analyses using a cohesive zone model highlights the model’s ability to render brittle failure of the notched structure and to provide reliable failure load estimates. The results reveal that a certain threshold of the hole diameter exists, below which the hole does not affect the failure load. The threshold and the corresponding bearable loads are discussed using explicit solutions.

Structural behavior of tubular T/Y-joints with collar plate under static in-plane bending

This paper investigates the static strength of collar plate reinforced tubular T/Y-joints subjected to in-plane bending (IPB) load. At the first step, a finite element (FE) model was developed and validated against the data available from 12 experimental tests. Afterwards, 210 FE models were generated and analyzed to evaluate the effect of joint geometry and collar plate size on the ultimate strength and failure modes of T/Y-joints reinforced with collar plates subjected to IPB load. Results show that the collar plate reinforcement method can significantly increase the ultimate strength and improve the failure mechanisms of tubular T/Y-joints under in-IPB load. Despite the considerable effect of the collar plate on the static strength and in spite of the frequent usage of CHS T/Y joints in offshore jacket-type platform, the ultimate strength and failure modes in collar plate reinforced T/Y-joints subjected to IPB load have not been investigated so far and no design equation is available to determine the ultimate capacity of IPB-loaded joints of this type. Therefore, after the parametric investigation, a new formula is proposed, through nonlinear regression analysis, for determining the ultimate strength of T/Y-joints reinforced with collar plate subjected to IPB load.

Analysis of two box beams-joint systems under in-plane bending and axial loads by one-dimensional higher-order beam theory

• Two box beams-joint systems are analyzed by one-dimensional beam theory. • The beam systems are subjected to in-plane loads. • Higher-order deformation (bending warping and distortion) degrees are considered. • Exact matching conditions at a joint of two box beams are newly derived. • The proposed approach effectively handles arbitrarily-angled box beam systems. If two thin-walled box beams meet at a joint, significant flexibilities that cannot be dealt with by the classical Euler or Timoshenko beam theory are observed. Especially under in-plane bending and axial loads, the deformation of the two box beams-joint system near the joint region is so complicated that no theoretical one-dimensional approach that interprets its mechanical behavior correctly has yet been proposed. To establish an effective higher-order beam theory, we introduce a new additional bending distortion degree representing anticlastic curvature effects and also redefine the section-shape functions of the bending warping and bending distortion degrees. In box beams-joint systems, it is crucial to find the matching conditions among field variables at the joint, but no exact conditions applicable for the systems under in-plane bending and axial loads are available. In this paper, we newly derive the explicit form of the transformation matrix relating six field variables of two box beams at a joint–axial displacement, transverse displacement, in-plane bending/shear rotation, bending warping, and two bending distortions. The accuracy and validity of the developed higher-order beam theory and the exact matching conditions are checked by comparing the present beam based results and ABAQUS shell analysis results for various box beams with different joint angles.

A numerical finite fracture mechanics approach on asymmetric cracks in open-hole plates

Using an efficient numerical approach, a model rendering the initiation of asymmetric crack patterns in open-hole plates subject to combined tensile and in-plane bending loading is presented. In the framework of finite fracture mechanics a stress and an energy criterion are enforced simultaneously and used as a coupled condition for the formation of cracks of finite size. Using closed-form expressions for the dependence of the stress and energy quantities needed to solve the coupled criterion on the structural and material parameters, only a limited number of linear elastic finite element analyses is required for a comprehensive analysis of the notched plate. The failure load predictions of the presented model are shown to agree well with experimental results and predictions of a cohesive zone model. The finite fracture mechanics approach allows for a study of crack patterns associated to failure.

Concrete-Filled Steel and Steel Tubular T-Joints under Cyclic in-Plane Bending

A series of tests on the concrete-filled and steel tubular T-joints under in-plane bending cyclic loading are presented in this paper. Two steel tubes were welded to form T-joint specimens, and then the chord was filled with self-compact concrete. For each test specimen the chord was loaded in a constant compression while the brace was under quasi-static cyclic in-plane bending loading. In total three concrete filled steel T-joints and two pure steel T-joints were tested. The failure modes, hysteretic curves and ultimate strengths of test specimens were obtained. The failure modes of all specimens were punching shear failure of the chord. It was shown that the filled concrete greatly enhanced the stiffness, the yielding strength and the ultimate strengths of T-joints. The energy dissipation ratio of the specimens under cyclic loading was calculated. The energy dissipation ability of concrete-filled specimens was better than that of steel specimens. A method provided by ECCS was used to calculate the yield strength of the test specimens. The ultimate strengths predicted by current AISC Standard and API RP2A specifications were compared with the test results.

Probabilistic analysis of stress concentration factors in tubular KT-joints reinforced with internal ring stiffeners under in-plane bending loads

In the present research, results from the finite element (FE) stress analysis of 108 models, validated using test data obtained from the experimental investigation, was used to propose probability distribution models for stress concentration factors (SCFs) in internally ring-stiffened tubular KT-joints under four types of in-plane bending (IPB) loads. The SCF is one of the crucial parameters in the fatigue reliability analysis of tubular joints. It exhibits considerable scatter which calls for greater emphasis in accurate derivation of its governing probability function. According to the knowledge of the authors, no comprehensive research has been carried out on the probability distribution of SCFs especially in stiffened tubular joints commonly found in offshore structures. What has been used so far as the probability distribution of SCFs in the reliability analysis of this type of joints is mainly based on assumptions and limited observations, especially in terms of distribution parameters. Based on a FE parametric study, a set of sample databases was prepared for the maximum central- and outer-brace SCFs; and density histograms were generated for these samples. Nine different probability density functions (PDFs) were fitted to these histograms. The maximum likelihood method was used to compute the parameters of fitted distributions. In each case, using a developed computer code, Kolmogorov–Smirnov and chi-squared tests were applied to evaluate the goodness of fit. Finally, the best-fitted distributions were selected and after substituting the values of estimated parameters for each distribution, six fully defined PDFs were developed for the maximum weld-toe SCFs of central and outer braces in internally ring-stiffened tubular KT-joints subjected to four different types of IPB loading.

Plastic limit loads for pipe bends with circumferential through-wall crack under torsion moment

In this work, finite element (FE) method is used to determine plastic limit load solutions for pipe bends with circumferential through-wall crack under torsion moment. Both extrados and intrados crack are considered regarding of crack location. Based on FE results estimated solutions are proposed for application, and are also compared with corresponding solutions in previous literatures showing that existing solutions are unfit for prediction of torsion load. The weakening factor W decreases with crack length increasing, and the decreasing rate exhibits three typical stages which performs a similar trend to that with bending moment. Finally a detailed analysis for the mechanical behavior of pipe bends has been conducted which provides some evidence to explain the weaken effect caused by the presence of crack. In torsion mode results show that the non-uniform distributed shear stress is performing symmetric to the profile plane and may have a crucial influence on the weakening factor, while in bending mode the distribution in axial stress and circumferential stress is symmetric to the profile plane and has a decisive influence. Therefore crack is pulled open by in-plane bending load while torn open by torsion load. Some evidence also can be obtained from the Mises stress distribution, where similar variation rule will provide another argument to support such description.

Degree of bending (DoB) in tubular K-joints of offshore structures subjected to in-plane bending (IPB) loads: Study of geometrical effects and parametric formulation

The fatigue life of tubular joints in offshore structures is not only dependent on the value of hot-spot stress (HSS), but is also significantly influenced by the through-the-thickness stress distribution characterized by the degree of bending (DoB). The determination of DoB values in a tubular joint is essential for improving the accuracy of fatigue life estimation using the stress-life (S–N) method and particularly for predicting the fatigue crack growth using the fracture mechanics (FM) approach. Although the tubular K-joints are commonly found in offshore jacket structures, the DoB in K-joints subjected to in-plane bending (IPB) loads have not been investigated so far and no design equation is available to calculate the DoB for IPB-loaded joints of this type. In the present research, comprehensive finite element (FE) analyses were carried out on 81 generated models of tubular K-joints. Results of FE models were verified against experimental data and parametric equations. Data extracted from FE analyses was used to investigate the effects of geometrical parameters on the DoB values in K-joints subjected to two types of IPB loadings. Parametric study was followed by a set of nonlinear regression analyses to develop DoB parametric equations for the fatigue analysis of IPB-loaded K-joints.

Stress concentration due to in-plane bending (IPB) loads in ring-stiffened tubular KT-joints of offshore structures: Parametric study and design formulation

Although tubular KT-joints are commonly found in offshore jacket structures and despite the crucial role of stress concentration factors (SCFs) in the evaluation of the tubular joint's fatigue performance, the SCFs in internally ring-stiffened KT-joints subjected to in-plane bending (IPB) loads have not been investigated so far and no design equation is available to determine the SCFs for IPB-loaded joints of this type. In the present research, data extracted from the finite element analysis of 118 models, which were verified using test results obtained from an experimental investigation, were used to study the effect of geometrical parameters on the weld-toe SCFs of central and outer braces in internally ring-stiffened tubular KT-joints subjected to four different types of IPB loads. Parametric study was followed by a set of the nonlinear regression analyses to develop SCF parametric equations for the fatigue analysis of ring-stiffened KT-joints under IPB loadings.

Quantification of Thickness Effects for Circumferential Through-Wall Cracked Pipe Bend with Un-Uniform Thickness under In-Plane Opening Bending

An Elbow is one of the major component that make up the piping system of a nuclear power plant and chemical plant facilities. In general, the elbow is made by welding a straight pipe and bend part. So, periodic welding inspection is required due to the potential defects in weld zone. Recently, the application of induction heating pipe bend is increasing in order to reduce this problem. Pipe bend made by induction heating band is not necessary welding process because it is made by bending a straight pipe but the intrados thickness and the extrados thickness are different. On the other hand, J-integral is widely used to evaluate a structural integrity (to check crack stability) but the J estimation of pipe bend with un-uniform thickness is very difficult because of the thickness differences in each locations.This paper proposes a reference stress based J estimation scheme of circumferential through-wall cracked pipe bend with un-uniform thickness under in-plane opening bending loading condition. The pipe bend with un-uniform thickness is assumed to have different thickness between intrados and extrados and the crack to be located in the entre of the pipe bend, either at the intrados or extrados.

A simplified model of a reinforced square hollow section T-joint for stress evaluation in bus superstructures

This study aims to create a simplified model of a reinforced square hollow section SHS T-joint found in bus superstructures. The approach is to use a combination of one-and two-dimensional finite element models to represent a reference three-dimensional finite element model of the joint and determine stress correction factors as functions of the geometrical variables of the joint. This approach requires the stiffness of the simplified model to be equivalent to that of the reference model. By using a stiffness error function and a three-factor design of experiment DOE, the best of four trial models, with minimum average stiffness error, was identified. The stress correction factors were then determined under static in-plane bending loads. A polynomial regression model was used to construct the relationship between the stress correction factors and the thickness-to-width ratios of the joint. The correlation coefficient of 0.9845 indicated a strong relationship and the t score confirmed its significance.

Numerical Investigation on the Fatigue Behavior of the Multi-Planar Tubular DX-Joint under Combined Loads

The stress concentration factors (SCFs) is used in the fatigue design for calculating hot-spot stress. However a major issue can be noted that the majority of research results are focused on the SCF distribution of uni-planar tubular joints subjected to the single basic load. By aiming to find the solution of this problem, the distribution of SCFs at the weld toe of a multi-planar tubular DX-joint which is subjected to the two set of the balanced combined loading components at the end of in-plane braces is studied by the finite element method. Thus it is concluded that for the axial plus in-plane bending load case, hot-spot stress location varies between saddle and crown position; while the location is invariably at the saddle position under combined axial plus out-of-plane bending loads. At last the API RP2A equation for predicting hot-spot stress is used for comparison with the finite element analysis results. Meanwhile the distribution of SCFs is also provided, that information indicates the-hot spot location along the weld toe affects the crack initiation.