Cross-sectional Stress Distribution Research Articles

On the numerical assessment of bending- and torsion-induced stresses in idealised sawn timber beams

ABSTRACT When designing timber beams for bending, shear and torsion, it is common engineering practice to use analytical formulas that neglect the cylindrical nature of the orthotropic material, the annual ring orientation, spiral grain and so on. While they result in stresses that appear reasonable, the approach is in principle theoretically flawed. In this paper a 3D finite element model is used to analyse the stress levels in sawn timber beams, taking into account the radially varying and cylindrically orthotropic material parameters, as well as a number of geometrical features. The beams are assumed to be mechanically idealised without imperfections. Parametric analyses indicate that especially the annual ring orientation has a significant impact on the maximum stresses, even though the cross-sectional stress distributions have distinct similarities with common beam theory. Furthermore, a Monte Carlo simulation is performed, randomly varying all parameters within given intervals. The simulations reveal that the maximum stresses from the finite element model, in almost all cases are noticeably larger than predicted by the analytical formulas, rendering them on the unsafe side in a theoretical sense.

Close-in blast performance of RC beams with varying cross-sectional sizes and damage assessment based on the dynamic load carrying capacity

Aiming to investigate the impact of cross-sectional size on the close-in blast performance of reinforced concrete (RC) beams, the local damage features and structural responses of RC beams with varying cross-sectional widths and depths subjected to close-in explosions were investigated experimentally and numerically. Experiments were conducted on ten RC beams with a cross-sectional size of 25 cm × 12.5 cm to study the influence of scaled distance and charge mass on the local damage size and structural responses (displacement and reaction force). The results indicate that the blasting face damage to tested beams, such as the crushing crater of concrete cover and side peeling-off damage, is more sensitive to the scaled distance (intensity of applied blast loads) compared to the rear spalling damage. And the peak reaction force exhibited a gradual increase within the range of 0.5 m/kg1/3, eventually reaching an average maximum value of 93.5 kN, and remained unchanged after the scaled distance was greater than 0.5 m/kg1/3, indicating that the dynamic load-carrying capacity of tested beams increased with the increasing scaled distance and the maximum dynamic load-carrying capacity of these beams is around 93.5 kN. Furthermore, a numerical model of RC beams subjected to close-in explosions was established based on the Fluid-Structure-Interaction (FSI) method. For validation, the local damage morphology and sizes of RC beams and their dynamic responses (displacement and reaction force) were computed and compared with the corresponding experimental results, concluding that the numerical results are in good agreement with the experimental findings. A parametric analysis was conducted to study the impact of cross-sectional size on the development process of initial local damage, stress distribution in cross sections, local damage sizes, and structural responses. Moreover, a damage index of the dynamic load-carrying capacity was derived from the relationship between the normalized maximum reaction force and the normalized maximum displacement to assess the damage degree of RC beams with varying cross-sectional sizes. This work can serve as a partial reference for relevant research.

A monitoring strategy for cross-sectional stress distribution of marine unbonded dynamic cables

Dynamic cables in offshore structures are susceptible to failure under the influence of alternating ocean environmental loads. Accurate assessment of cross-sectional stress distribution in marine unbonded dynamic cables brings a significant challenge. This study proposes a comprehensive monitoring strategy that integrates global (cable configuration) and local (cross-section) monitoring to obtain the cross-section stress distributions of unbonded cables. Our method stands out for its originality in integrating both global (cable configuration) and local (cross-section) monitoring, thereby overcoming the inherent difficulties in stress measurement in such cables. An innovative aspect of our work is the introduction of an integrated global and local algorithm. Through a meticulous analysis of the mechanical behavior of flexible cables in service, we devised a method to simplify the cable into a curved beam model subject to tension and bending loads. Simultaneously, the cable's cross-section structures were reduced to helical beam, cylindrical beam, and hollow cylinder models. The governing stress equations are utilized to establish the relationship between stress distribution in critical cable layers and the local cable configuration. Additionally, the curved beam governing equation is employed to determine the connection between the local and global cable shape, enabling a theoretical correlation between cross-sectional stress and global cable configuration. A sensor layout scheme is provided for the floating structure, along with specific locations on the cable, to obtain data on hull motions and cable inclinations. The monitoring data are then used to determine the global cable configuration, which serves as a boundary condition for the cross-sectional stress equations. This holistic approach enables real-time monitoring of the cross-sectional stress within the cable at a full scale. To validate the feasibility and accuracy of this proposed monitoring system, a model experiment and numerical simulations are meticulously executed. Comparative analysis between the numerical simulation model and monitoring results is conducted, encompassing the overall cable configuration, cross-sectional stress distribution, and the identification of maximum stress locations during cable operation. The results demonstrate that the present monitoring strategy accurately captures variations in cross-sectional stress and provides valuable technical support for the safe maintenance and operation of marine cables.

Efficient finite element modelling of helical strand cables utilising periodicity

This paper proposes a repeated unit cell (RUC) FE modelling strategy for multilayered helical strand cables subject to tensile loading and bending with an initial tensile load. The approach utilises the axial periodicity in helical structures to reduce computational domain to two cable periods. A novel mesh creation method allowing the exact geometry of helical strands to be discretised into solid elements while maintaining flat end surfaces is proposed. Periodic boundary conditions (PBC) allowing for geometric and material nonlinearity are used to implement cyclic loads to study hysteresis in single and multilayered cables. Comparisons made to existing experimental and analytical results validate the models ability to capture hysteresis due to plasticity and geometric effects such as the stick–slip transition in bending. Examination of the cross-sectional stress distribution shows plasticity initiates at contact points at loads which are 25% of the load at which the cable tensile response deviates from linearity.

Design of multi-cell T-shaped concrete-filled steel tubular columns under compression and bending

To date, a number of studies have been done on the calculation methods for predicting bearing capacities of multi-cell special-shaped concrete-filled steel tubular (MS-CFST) columns under axial, pure bending, and eccentric load. However, most of the existing methods only apply to a specific combination form of cross-section and have not been established in a unified formulation. In this study, finite element (FE) models were established to predict the performances of the four common combination forms of multi-cell T-shaped concrete-filled steel tubular (MT-CFST) sections subjected to axial, eccentric, and pure bending loads, and verified with the available test data. The parametric analyses were conducted to investigate the effects of steel thickness t, concrete strength fck, steel yield strength fy, aspect ratio of the web c/b, and slenderness ratio λ on the flexural and eccentric compressive performance based on the FE models. The study results demonstrated that the four common combination forms of MT-CFST sections showed the same changing trends of flexural capacity with different parameters, and the flexural capacity rose almost linearly with the increase of the parameters. The parameters (t, fy, fck, c/b, and λ) had a definite effect on the N/Nu-M/Mu correlation curve, especially c/b and λ. Furthermore, by analyzing the stress distribution of mid-span cross-section at ultimate state, the simplified calculation model for asymmetric flexural capacity applicable to different combination forms of MT-CFST section was put forward. The reduction factor of 0.9 for positive flexural capacity (WC) and the restricted width-to-thickness ratio 60235/fy are recommended. Based on the study of the constraint stress of steel tube to core concrete and the concrete constraint region distribution for the columns subjected to compression, the calculation method for predicting the axial bearing capacity applicable to different combination forms of MT-CFST section was proposed. According to the parametric analysis and shape of N/Nu-M/Mu correlation curve, the simplified method for N/Nu-M/Mu correlation curves applicable to different combination forms of MT-CFST sections was developed, which simultaneously took the influence of slenderness ratio into consideration. Besides, the calculation methods for MT-CFST members proposed in this paper have been verified with available test results and FE ones.

Behavior and design of circular concrete columns strengthened with textile-reinforced mortar subjected to eccentric compression

Textile-reinforced mortar (TRM) is a cheaper and eco-friendlier material for the concrete confinement than steel and fiber-reinforced polymer (FRP). The behaviors of plain concrete slender columns with circular cross-section strengthened with TRM under eccentric compression were analyzed both experimentally and analytically in this paper. The test results showed that TRM could effectively inhibit the extension of cracks in columns, and increasing the number of textile layers from one to three led to a 44% increase in ultimate load. Meanwhile, the secondary moment of columns relative to the total moment varied from 20% to 35%, which was positively related to the confinement effectiveness of TRM. Then, a comparison of the behaviors of confined concrete columns under axial load-flexural moment (P-M) loading demonstrated that the confinement provided by TRM was relatively insufficient when compared to steel and FRP, behaving a post-peak softening phase of compressive constitutive curves. However, the textile with high tensile strength improved the stress distribution of cross-section of eccentrically loaded columns, thereby observing a much slower reduction in ultimate load with the increase of the eccentric ratio. Finally, according to a cross-section bearing capacity analysis, the procedure of analytical calculations was proposed to predict the ultimate load of TRM-confined concrete columns at a given eccentric ratio. Furthermore, the proposed analytical calculations provided a parametric study to reveal the correlation between the eccentric ratio and the number of textile layers, and then a simplified regression formula for design purpose was developed. This research highlights the behavior and design of concrete strengthened with TRM under P-M loading, which would give researchers and engineers an insight.

Behavior of thread-fixed one-side bolts bolted T-stubs with arc-shaped flange to steel tube under tension

Tensile tests and Finite Element (FE) analysis were conducted on the Thread-fixed One-side Bolts (TOBs) bolted T-stub with arc-shaped flange to steel tube in this paper. Critical parameters were determined as the thickness of tube wall, the outer diameter of steel tube, the thickness of arc-shaped flange, and the center angle between bolts. Test results revealed that the connection would encounter three typical failure modes, which were: failure mode 1, thread shear failure with yielding of tube wall; failure mode 2, complete yielding failure of tube wall; failure mode 3, thread shear failure with yielding of T-stub arc-shaped flange. Developed FE models are verified and used to analyze the yield line pattern of tube wall, the hoop stress distribution of cross-section of tube wall, and the shear acting on bolt shank. Based on the experimental and numerical results, preliminary analytical models and design methods are proposed to estimate the tensile yield strength of specimens under different failure modes.

Application of Equivalent Single Layer Approach for Ultimate Strength Analyses of Ship Hull Girder

The objective of this paper is to present the application of equivalent single layer (ESL) approach for the ultimate strength assessment of ship hull girder in the context of numerical finite element (FE) simulations. In the ESL approach, the stiffened panel is replaced with a single plate, which has the equivalent stiffness of the original panel. Removal of tertiary stiffening elements from the numerical model facilitates time-savings in pre-processing and FE analysis stage. The applicability of ESL approach is demonstrated with two case studies, one compartment model and full-sized double hull tanker model in intact and damaged conditions. The damage extents are determined based on the international association of classification societies from common structural rules (IACS-CSR) for oil tanker. Ship hull girder is exposed to distributed pressure with the sinusoidal shape that bends the hull girder. This pressure load is applied separately to bottom and side structures to obtain the vertical and horizontal bending moments of the hull girder, respectively. Ultimate strength predictions obtained from ESL approach are compared to full three-dimensional finite element method (3D FEM) and IACS incremental-iterative method. The comparison between different methods is provided in terms of longitudinal bending moment and cross sectional stress distribution. Overall, ESL approach yields good agreement compared to the 3D FEM results in predicting the ultimate strength of ship hull girder while providing up to 3 times computational efficiency and ease of modeling.

Bearing Behavior of H-Shaped Honeycombed Steel Web Composite Columns with Rectangular Concrete-Filled Steel Tube Flanges under Eccentrical Compression Load

In order to investigate the bearing capacity of H-shaped honeycombed steel web composite columns with rectangular concrete-filled steel tube flanges (STHCCs) subjected to eccentrical compression load, 33 full-scale STHCCs were designed with the eccentricity(e), the slenderness ratio (λ), the cubic compressive strength of concrete(fcuk), the thickness of the steel tube flange (t1), the thickness of honeycombed steel web (t2), diameter-depth ratio (d/hw), space-depth (s/hw), and the yield strength of the steel tube (fy) as the main parameters. Considering the nonlinear constitutive model of concrete and simplified constitutive model of steel, the finite element (FE) model of STHCCs was established by ABAQUS software. By comparison with the existing test results, the rationality of the constitutive model of materials and FE modeling was verified. The numerical simulation of 33 full-scale STHCCs was conducted, and the influence of different parameters on the ultimate eccentrical compression bearing capacity was discussed. The results show that the cross-sectional stress distribution basically conforms to the plane-section assumption. With the increase in e, λ, and d/hw, the ultimate eccentrical compression bearing capacity of the full-scale STHCCs decreases, whereas it gradually increases with the increase in fcuk, t1, t2, s/hw, and fy. By introducing bias-stress stability coefficient (φ), the calculation formula of full-scale STHCCs under eccentrical compression is proposed by statistical regression, which can lay a foundation for the popularization and application of these types of composite columns in practical engineering.

A new thin beam element with cross-section distortion of the absolute nodal coordinate formulation

A novel modelling approach to beams with thin cross-sections is proposed in the absolute nodal coordinate formulation (ANCF), where the Lagrange interpolating and curve fitting techniques of numerical analysis are utilized for construction of the thin beam cross-section contour. Although the slope vector with respect to the coordinate line on cross-section contour is not considered in nodal coordinates, the cross-section distortion could be adequately captured through selecting an appropriate degree of polynomial. The main advantages of the present ANCF thin beam element are that the computational costs are more inexpensive than the ANCF shell element due to less generalized coordinates, there is very small amount of input data because slope vectors of the cross-section are eliminated, and the cross-sectional stress distribution may always be continuous on account of the fact that the cross-section is not discretized into a set of finite elements. Moreover, the formulations of elastic forces and Jacobian of thin laminated composite beam are also derived based on the continuum mechanics. Finally, several examples including both static and dynamic problems are performed to verify the new element and meanwhile demonstrate its general characteristics.

Near-perfect healing natures of silver five-fold twinned nanowire

Healing nanogap of metal nanowire is essential for the manufacturing and maintaining of nanoelectronic devices. Recent experimental study has demonstrated the feasibility of nanohealing in silver nanowire by using plasmonic heating. Here we report for the first time the effect of atomic lattice structures on the healing behavior and mechanism of silver nanowires due to plasmon, by using molecular dynamics simulation with a self-limited strategy. Three fundamental steps of the repair process are identified based on atomic behaviors, i.e. melting, recrystallizing, and healing. The five-fold twinned nanowires (FFTNW) is easier to get perfect healing than the single crystal ones. The near-perfect healing natures of FFTNW are mainly attributed to the non-linear stress distribution of cross section and the inherent five-fold twinned boundaries, which limit dislocation nucleating and provide self-healing nature. Our results provide a new microscopic perspective and understanding for the plasmonic nanohealing technology.

A new contour method for rapid evaluation of the cross-sectional residual stress distribution in complex geometries using a 3D scanner

This paper presents a new method for contour measurements using a 3D scanner to determine cross-sectional residual stresses in structural components with complex configurations. The proposed method was applied to evaluate the axial residual stress distribution in a dissimilar pipe weld and the obtained results were compared with those obtained using a benchmarked contour measurement machine (CMM) equipped with a confocal laser probe for verification. It reveals a quantitative agreement between the two methods in terms of both the measured contours and the calculated residual stresses. Most importantly, this method allows a significantly reduced measurement time by ≈99 % (≈20 min, with an effective measurement speed of ≈0.2 sec/mm2), compared to the benchmarked method (≈48 hr, with an effective measurement speed of ≈28.7 sec/mm2). Based on stress uncertainty analysis, this method guarantees a longer range of stable fits due to fewer noisy data points than the benchmarked method.

Sequential 1D/2D Finite Element analyses of tramway rails under bending and restrained torsion, based on the principle of virtual power

The increased incidence of fractures in aging tramway rails has motivated the development of a new, efficient numerical tool for studying structural mechanics problems related to such rails. We introduce virtual velocity fields reflecting axial, bending, shear, and torsional deformations, which are then translated, via the principle of virtual power, into corresponding equilibrium conditions. The resulting equations are numerically solved by means of sequential 1D and 2D Finite Element analyses, providing displacement quantities and stress resultants along the beam axis, as well as cross-sectional stress distributions. Finally, the key advantages of this modeling approach, including excellent efficiency and reliability, as well as straightforward applicability to a wide range of cross-sectional shapes and structural settings, are demonstrated via numerical examples.

Non-iterative moment capacities of complex composite beams using Fourier series

A generic procedure is formulated for the determination of the moment capacity of composite beams having a complex cross-section. The key feature is the use of Fourier series to convert the piecewise functions of the cross-sectional stress distribution into a single-rule function. This eliminates the need for several capacity expressions to cover different stress stages, since the procedure permits the use of the general moment capacity expression. It also eliminates any iteration process when determining the location of the neutral axis since equilibrium of the cross-section can be satisfied explicitly. Numerical examples are given to demonstrate the validation and the applications of the formulation.

Cross-sectional stress distribution in AlxGa1-xN heterostructure on Si(111) substrate characterized by ion beam layer removal method and precession electron diffraction

A residual stress depth gradient is characterized in a 1.8μm thick AlN/Al0.25Ga0.75N/GaN/Al0.22Ga0.78N heteroepitaxial structure grown using metallic-organic chemical vapour deposition on Si(111) substrate. The cross-sectional stress profile is evaluated with a step of 100nm using ion beam layer removal (ILR) method based (i) on a sequential focused ion beam milling of a microcantilever, (ii) on an evaluation of a cantilever bending after every milling step and (iii) on a stress profile recalculation using finite element simulation. The profile shows tensile stress of ~1.5GPa in AlN nucleation layer, stress changing from compressive to tensile in Al0.25Ga0.75N and GaN sublayers and relatively small stresses below 100MPa in the top Al0.22Ga0.72N sublayer. The stress profile is qualitatively correlated with the results from precession electron diffraction which indicates approximately the same stress behavior. The cross-sectional stress magnitude and variation are interpreted by the mismatches of lattice constants and coefficients of thermal expansion as well as by growth mode changes during Al0.25Ga0.75N and GaN sublayer formation. The approach demonstrates the possibility to resolve nanoscale variation of residual stresses in heteroepitaxial structures using ILR method.

Analysis of dynamic mechanical response in torsion

We investigate the dynamic response of industrial rubbers (styrene-butadiene random copolymers, SBR) in torsion and compare against common small amplitude oscillatory shear measurements by using a torsion rectangular fixture, a modified torsion cylindrical fixture, and a conventional parallel plate fixture, respectively, in two different rheometers (ARES 2kFRTN1 from TA Instruments, USA and MCR 702 from Anton Paar-Physica, Austria). The effects of specimen geometry (length-to-width aspect ratio) on storage modulus and level of clamping are investigated. For cylindrical specimens undergoing torsional deformation, we find that geometry and clamping barely affect the shear moduli, and the measurements essentially coincide with those using parallel plates. In contrast, a clear dependence of the storage modulus on the aspect ratio is detected for specimens having rectangular cross section. The empirical correction used routinely in this test is based on geometrical factors and can account for clamping effects, but works only for aspect ratios above a threshold value of 1.4. By employing a finite element analysis, we perform a parametric study of the effects of the aspect ratio in the cross-sectional stress distribution and the linear viscoelastic torsional response. We propose a new, improved empirical equation for obtaining accurate moduli values in torsion at different aspect ratios, whose general validity is demonstrated in both rheometers. These results should provide a guideline for measurements with different elastomers, for which comparison with dynamic oscillatory tests may not be possible due to wall slip issues.

Characterization Method of Thick Films Using the Bulge Test Technique

A new theoretical model considering the bending effect for the thick films (the ratio η of thickness to radius was larger than 1/80) using the bulge test method was established based on the energy method. The experiments of Ti films and PVDF films of different ratio η had validated the feasibility of the new theory. The universal applicability of the new theoretical model for different mechanical parameters (E and υ) was verified by FEM. The new expression of pressure-height could well predict the deformation of bulge test for the films with different thickness. As the ratio η increased, the competitive mechanism of bending energy gradually replacing stretching energy in the films was revealed. The modulus and the stress distribution of cross-section could be characterized correctly by the new theory for thick films using the bulge test technique. It will provide a powerful research tool to study the deformation mechanism of thick films in the bulge test.

Development and feasibility study of a two-dimensional ultrasonic-measurement-integrated blood flow analysis system for hemodynamics in carotid arteries.

Prevention and early detection of atherosclerosis are critical for protection against subsequent circulatory disease. In this study, an automated two-dimensional ultrasonic-measurement-integrated (2D-UMI) blood flow analysis system for clinical diagnosis was developed, and the feasibility of the system for hemodynamic analysis in a carotid artery was revealed. The system automatically generated a 2D computational domain based on ultrasound color Doppler imaging and performed a UMI simulation of blood flow field to visualize hemodynamics in the domain. In the UMI simulation, compensation of errors was applied by adding feedback signals proportional to the differences between Doppler velocities by measurement and computation while automatically estimating the cross-sectional average inflow velocity. The necessity of adjustment of the feedback gain was examined by analyzing blood flow in five carotid arteries: three healthy, one sclerosed, and one stenosed. The same feedback gain was generally applicable for the 2D-UMI simulation in all carotid arteries, depending on target variables. Thus, the present system was shown to be versatile in the sense that the parameter is patient independent. Moreover, the possibility of a new diagnostic method based on the hemodynamic information obtained by the 2D-UMI simulation, such as a waveform of the cross-sectional average inflow velocity and wall shear stress distributions, was suggested.

Estimation of Cross-Sectional Residual Stress Distributionon Hardened Layer of Carburized Chromium-Molybdenum Steel by Electron Backscattering Diffraction Method

A chromiummolybdenum steel composed of 0.20 mass% carbon was used as a starting material. Three kinds of specimens having different case depths were made by carburizing and quenching. Using the scanning electron microscope, the crystallographic information was measured on the cross-sectional hardened layer by EBSD (electron backscattering diffraction) technique. The KAM (kernel average misorientation, Θ) maps were calculated from the carburized surface to the interior below the case depth of each specimen. The area-average, Θmean, of the KAM map was compared to the case depth and the cross-sectional residual stress distribution measured by x-ray. As a result, the area-average of the hardened layer was larger than that of the interior of specimen after quenching. The estimated depth of the increment in the Θmean was found to accord to the case depth and be proportional to the depth in which large compressive residual stress was distributed on the gradually polished surface. Therefore, both the case depth and eigen strain distribution that induce the compressive residual stress are indirectly estimable by electron backscattering diffraction method.

Pass-by-pass stress evolution in multipass welds

In multipass welding, each successive thermal cycle will introduce local melting, solid state phase transformations, grain growth, grain refinement, recrystallisation and recovery, all of which lead to a complicated stress state. Most stress measurements performed on multipass welded components represent the final residual stress state. Information concerning stress evolution on a pass-by-pass basis is difficult to find. In this investigation, six pass welds were made on high strength quenched and tempered steel sections, and depth resolved strain measurements in two orthogonal directions were carried out after each weld pass using energy dispersive synchrotron X-ray diffraction. The residual stresses were calculated using biaxial Hooke’s law. A thermal–metallurgical–mechanical welding model was constructed and validated with temperature and pass-by-pass stress measurements, which improves the reliability of the model. Cross-sectional stress distributions are presented after each pass, revealing the weld stress development in multipass welds.