Local Bending Moment Research Articles

On the design of fillet welds made of ultra-high-strength steel

Current static design approaches for fillet arc welds made of high- or ultra-high-strength steel (UHSS) do not differ from the design of welds made of conventional steels. However, important issues such as potential softening in heat-affected zone (HAZ), strength at fusion lines, optimal reinforcement geometry, load capacity changes due to local bending moment, and the effect of post-weld treatments on the joint strength require careful consideration in order to ensure optimum performance from these steels. This paper reprises results of previous research works and recent findings and summarizes key aspects of weld design specific to UHSS welds.

ОСОБЕННОСТИ ФОРМООБРАЗОВАНИЯ МОНОЛИТНЫХ ПАНЕЛЕЙ ПРИ ПОЛУЧЕНИИ КЕССОНА КРЫЛА БЕЗ ТЕХНОЛОГИЧЕСКИХ РАЗЪЕМОВ

The subject of the study in the article is the problem of the exact forming of individual panels in the wingbox assembling process without technological spanwise joints of the wing. The goal of the study is to create a model for an oblique curvature forming of the stiffened panels, which provides high tolerance of the panel shape and a given position of the bending axis. Objectives: a development of procedures that improve the tolerance of panel forming, reduce the amount of fitting work, reduce labor intensity, and increase productivity. The methods include: local deformation forming method by means of applying bending moments at the sweep angle and an additional correction angle, which takes into account the elastic effects of the stiffened panel; as well as numerical analysis of the forming process using ANSYS simulation. The following results are obtained. The created model of oblique curvature forming of the stiffened panels provides the capability to model the process of panel forming with the given tolerance. Using numerical approach, the magnitudes of the normal stresses and strains, deflections of the panels formed by applying local moments at the sweep angle, at the maximum load applied as well as their residual values. The results of the experiment of panel forming by unconstrained bending and local deforming on aluminum alloy samples are described. Conclusions. The scientific novelty of the research is as follows: the developed model of the stiffened panel forming process for a swept wingbox proofed the high efficiency while achieved the specified tolerance; by comparing the results, obtained by different methods, the advantages of the model applied to the local method of achieving the wing panel oblique curvature are verified. The local forming method by applying local bending moments to the ribs of the panel allows us to correct the oblique angle and achieve high tolerance due to the iterative procedure

A numerical simulation method for predicting global and local hydroelastic response of a ship based on CFD and FEA coupling

In this paper, a simulation method for predicting global and local hydroelastic response of a ship which couples CFD and FEA is developed and validated. By comparing the prediction with linear/nonlinear strip method, 3D panel method and towing tank test results under various wave conditions in terms of rigid body motions and slamming impact pressure, the effectiveness of the CFD-FEA coupling method is confirmed. The hydroelastic behavior, so-called the whipping moment, evaluated from the CFD-FEA coupling method is further validated by comparing with nonlinear strip method, 3D panel method and tank test results. Finally, the proposed method is applied to a realistic large container ship structure in severe waves. The structural response of the double bottom structure subjected to global and local bending moments is investigated.

Sensitivity analysis of structural response to position of external applied load in plate flexural condition

Procedures for discrete sensitivity analyses of the static responses of a structure, i.e., nodal displacements, mean compliance, local bending moments and stresses, are respectively developed for a plate or shell structure with regard to the position of an external load mainly because of the uncertainties related to the application point of a load in the preliminary design of an engineering structure. With the sensitivities developed herein, those responses can be estimated quickly and accurately by using the Taylor expansions after a position disturbance of the external load.Based on the classical theory of the finite element analysis, the shift influences of a point or distributed load are firstly transformed into the associated value variation of the equivalent nodal forces. As a result of this transformation, the first- and second-order derivatives of the external load to its movement are constituted readily in a regularized formulation. Subsequently, the relevant sensitivities of the structural responses aforementioned are developed upon the essential concepts of the discrete approach. Finally, two typical examples are provided to illustrate the implementation of the sensitivity analyses derived and their applications in a quick estimate of the structural response variation. The numerical results show a high accuracy of the response sensitivity calculation.

Local Limit Load Analytical Model for Thick-Walled Pipe With Axial Surface Defect

Based on the previous limit load analytical modeling for cracked thin-walled pipe (Orynyak, I. V., 2006, “Leak and Break Models of Pressurized Pipe With Axial Defects,” Proceedings of the 6th International Pipeline Conference (IPC), Calgary, Alberta, Canada, Paper No. IPC2006-10066, pp. 41–56), the limit load model for thick-walled pipe had developed. There are some additional peculiarities included in the proposed model. First, the distribution of radial stresses is taken into consideration in the limit state formulation using Tresca's criterion. Second, related to the crack location and interaction of hoop stresses (due to the inner pressure) and axial ones (caused by local bending moment) have been assessed in the limit state. Third, hoop stresses redistribution with possibility of plastic hinge formation in zone opposite to the crack is taken into account. Finally, the proposed easy to use analytical formulas have been verified by comparing with full-scale burst tests.

Simplified Analytical Method for Optimized Initial Shape Analysis of Self-Anchored Suspension Bridges and Its Verification

A simplified analytical method providing accurate unstrained lengths of all structural elements is proposed to find the optimized initial state of self-anchored suspension bridges under dead loads. For this, equilibrium equations of the main girder and the main cable system are derived and solved by evaluating the self-weights of cable members using unstrained cable lengths and iteratively updating both the horizontal tension component and the vertical profile of the main cable. Furthermore, to demonstrate the validity of the simplified analytical method, the unstrained element length method (ULM) is applied to suspension bridge models based on the unstressed lengths of both cable and frame members calculated from the analytical method. Through numerical examples, it is demonstrated that the proposed analytical method can indeed provide an optimized initial solution by showing that both the simplified method and the nonlinear FE procedure lead to practically identical initial configurations with only localized small bending moment distributions.

Elastic deformation and energy loss of flapping fly wings

During flight, the wings of many insects undergo considerable shape changes in spanwise and chordwise directions. We determined the origin of spanwise wing deformation by combining measurements on segmental wing stiffness of the blowfly Calliphora vicina in the ventral and dorsal directions with numerical modelling of instantaneous aerodynamic and inertial forces within the stroke cycle using a two-dimensional unsteady blade elementary approach. We completed this approach by an experimental study on the wing's rotational axis during stroke reversal. The wing's local flexural stiffness ranges from 30 to 40 nN m(2) near the root, whereas the distal wing parts are highly compliant (0.6 to 2.2 nN m(2)). Local bending moments during wing flapping peak near the wing root at the beginning of each half stroke due to both aerodynamic and inertial forces, producing a maximum wing tip deflection of up to 46 deg. Blowfly wings store up to 2.30 μJ elastic potential energy that converts into a mean wing deformation power of 27.3 μW. This value equates to approximately 5.9 and 2.3% of the inertial and aerodynamic power requirements for flight in this animal, respectively. Wing elasticity measurements suggest that approximately 20% or 0.46 μJ of elastic potential energy cannot be recovered within each half stroke. Local strain energy increases from tip to root, matching the distribution of the wing's elastic protein resilin, whereas local strain energy density varies little in the spanwise direction. This study demonstrates a source of mechanical energy loss in fly flight owing to spanwise wing bending at the stroke reversals, even in cases in which aerodynamic power exceeds inertial power. Despite lower stiffness estimates, our findings are widely consistent with previous stiffness measurements on insect wings but highlight the relationship between local flexural stiffness, wing deformation power and energy expenditure in flapping insect wings.

Unusual structural effects in a variable-depth box girder bridge: The Pujayo viaduct

The new Spanish highway bridge, the Pujayo Viaduct, has a single-cell box girder. Owing to the large width of 26.1 m, the box girder had to be stiffened by transverse upper and lower ribs, by haunches in the connection web-flange and by inclined webs. Together with the variable girder depth, a relatively complicated geometry was created that was analysed by means of finite-shell-element calculation. Several unusual secondary structural effects are identified and explained. The longitudinal axial force resulting from global bending causes deviation forces in the curved bottom slab, which are responsible for transverse bending in the bottom slab and axial forces in the webs. Shear lag deformation of the box section causes moderate horizontal bending of the transverse ribs. Global deflection of the bridge girder causes out-of-plane bending of inclined webs. Global bending of box girders causes local bending moment output in finite shell elements. A further conclusion is that three-dimensional finite-shell-element models are an exact and appropriate complement to the common beam-element calculation models.

A piezoelectric bone-conduction bending hearing actuator

A prototype of a novel bone-conduction hearing actuator based on a piezoelectric bending actuator is presented. The device lies flat against the skull which would allow it to form the basis of a subcutaneous bone-anchored hearing aid. The actuator excites bending in bone through a local bending moment rather than the application of a point force as with conventional bone-anchored hearing aids. Through measurements of the cochlear velocity created by the actuator in embalmed human heads, the device is shown to exhibit high efficiency, making it a possible alternative to present-day electromagnetic bone-vibration actuators.

Structural Mechanics of DNA Wrapping in the Nucleosome

Experimental X-ray crystal structures and a database of calculated structural parameters of DNA octamers were used in combination to analyse the mechanics of DNA bending in the nucleosome core complex. The 1kx5 X-ray crystal structure of the nucleosome core complex was used to determine the relationship between local structure at the base-step level and the global superhelical conformation observed for nucleosome-bound DNA. The superhelix is characterised by a large curvature (597°) in one plane and very little curvature (10°) in the orthogonal plane. Analysis of the curvature at the level of 10-step segments shows that there is a uniform curvature of 30° per helical turn throughout most of the structure but that there are two sharper kinks of 50° at ± 2 helical turns from the central dyad base pair. The curvature is due almost entirely to the base-step parameter roll. There are large periodic variations in roll, which are in phase with the helical twist and account for 500° of the total curvature. Although variations in the other base-step parameters perturb the local path of the DNA, they make minimal contributions to the total curvature. This implies that DNA bending in the nucleosome is achieved using the roll–slide–twist degree of freedom previously identified as the major degree of freedom in naked DNA oligomers. The energetics of bending into a nucleosome-bound conformation were therefore analysed using a database of structural parameters that we have previously developed for naked DNA oligomers. The minimum energy roll, the roll flexibility force constant and the maximum and minimum accessible roll values were obtained for each base step in the relevant octanucleotide context to account for the effects of conformational coupling that vary with sequence context. The distribution of base-step roll values and corresponding strain energy required to bend DNA into the nucleosome-bound conformation defined by the 1kx5 structure were obtained by applying a constant bending moment. When a single bending moment was applied to the entire sequence, the local details of the calculated structure did not match the experiment. However, when local 10-step bending moments were applied separately, the calculated structure showed excellent agreement with experiment. This implies that the protein applies variable bending forces along the DNA to maintain the superhelical path required for nucleosome wrapping. In particular, the 50° kinks are constraints imposed by the protein rather than a feature of the 1kx5 DNA sequence. The kinks coincide with a relatively flexible region of the sequence, and this is probably a prerequisite for high-affinity nucleosome binding, but the bending strain energy is significantly higher at these points than for the rest of the sequence. In the most rigid regions of the sequence, a higher strain energy is also required to achieve the standard 30° curvature per helical turn. We conclude that matching of the DNA sequence to the local roll periodicity required to achieve bending, together with the increased flexibility required at the kinks, determines the sequence selectivity of DNA wrapping in the nucleosome.

Advanced finite element modelling of perforated composite beams with flexible shear connectors

An extensive research and development programme has been undertaken by the authors to develop advanced analysis and design tools for practical design of long span composite beams in buildings. Both two- and three-dimensional finite element models employing solid and shell elements with material, geometrical and interfacial non-linearity were established to examine the full range structural behaviour of composite beams. In this paper, two-dimensional finite element models employing plane stress elements are established to examine the structural behaviour of perforated composite beams, and shear connectors with non-linear deformation characteristics are incorporated into the models through the use of both vertical and horizontal springs. It is demonstrated that after careful calibration against test data, the finite element models are able to predict the load carrying capacities of composite beams with large rectangular web openings against ‘Vierendeel’ mechanism satisfactorily. Moreover, a number of important structural quantities such as local axial and shear forces together with local bending moments acting onto the composite and the steel tee sections at failure are obtained after data analyses. Together with the load carrying capacities, these quantities compare favourably with the values obtained from a design method proposed previously by the authors, and hence, this provides quantitative justification to the proposed design method. Furthermore, the finite element models provide detailed information on the structural behaviour of shear connectors along the beam length, such as the longitudinal shear forces, the pull-out forces as well as the slippage of the shear connectors. Based on the findings of the finite element modelling, a number of recommendations on the design and construction of perforated composite beams are suggested.

Yielding in colloidal gels due to nonlinear microstructure bending mechanics

We report measurements of the nonlinear micromechanics of strongly flocculated model colloidal aggregates. Linear aggregates directly assembled using laser tweezers are subjected to bending loads until a critical bending moment is reached, which is identified by a stictionlike rearrangement of a single colloidal bond. This nanoscale phenomenon provides a quantitative basis for understanding the macroscopic shear yield stresses of strongly flocculated polystyrene latex gels, based on the maximum bending moment exceeding the critical moment of the constituent colloidal bonds of the gel microstructure. These mechanics are consistent with the local bending moment overcoming the static friction force between neighboring adhesive particles. This results in a direct relationship between the rheology of these gels and the boundary friction between Brownian particles.

횡하중을 고려한 선체보강판넬의 압축 붕괴거동에 관한 연구

선체의 갑판부와 선저부 그리고 해양구조물의 기본적인 구조는 보강판이다. 보강판넬은 한쪽방향으로 위치한 보강재 혹은 종/횡 방향으로 복잡하게 위치한 구조를 이루고 있으며, 후자의 모델을 그릴리지 구조라고 부른다 선체구조설계 단계에서 선박의 종강도 평가는 가장 중요한 항목이다. 일반적으로, 극심한 해상상태에 놓인 선박의 선저부에는 호깅조건에 의해 발생되는 횡모멘트에 기인하여 압축하중이 작용하게 되며, 이와 동시에 수압하중 작용으로 인한 국부휭모멘트가 작용된다. 본 논문에서는, 구조해석 결과의 검증을 위해서 여러 가지 해석프로그램 및 현재 사용되고 있는 선급룰과의 비교를 하여 횡하중의 영향에 따른 압축최종강도에 대해 분석하고, 여러 가지 설계변수를 변화하여, 각각의 영향을 검토하고, 최종적으로 조합하중 조건에서의 횡하중의 영향에 대해서 분석하였다. 본 연구에서 얻어진 결과들은 최종한계상태설계법에 기반을 두고, 조합하중이 작용하는 선체보강판의 구조강도 거동에 대해서 하중성분에 대한 관계를 고찰하였다. Stiffened steel plates are basic structural members on the deck and bottom structure in ship, offshore. It has a number of one sided stiffeners in either one or both directions, the latter structure was called grillage structure. At the ship structural desgn stage, one of the major consideration is evaluation for ultimate strength of the hull girder. In general, it is accepted that hull girder strength can be represented by the local strength of the longitudinal stiffened panel. In case of considering hogging condition in a stormy sea, stiffened panel was acting on the bottom structure under axial compressive load induced hull girder bending moment, also simultaneously arising local bending moment induced lateral pressure load. In this paper, results of the structural analysis have been compared with another detailed FEA program and prediction from design guideline and a series analysis was conducted consideration of changing parameters for instance, analysis range, cross-section of stiffener, web height and amplitude of lateral pressure load subjected to combined load (axial compression and lateral pressure load). It has been found that finite element modeling is capable of predicting the behaviour and ultimate load capacity of a simply supported stiffened plate subjected to combined load of axial compression and lateral pressure load It is expected that these results will be used to examine the effect of interaction between lateral pressure and axial loads for the ultimate load-carrying capacity based on the Ultimate Limit State design guideline.

On the calculation of energy release rates for cracked laminates with residual stresses

Prior methods for calculating energy release rate in cracked laminates were extended to account for heterogeneous laminates and residual stresses. The method is to partition the crack tip stresses into local bending moments and normal forces. A general equation is then given for the total energy release rate in terms of the crack-tip moments and forces and the temperature difference experienced by the laminate. The analysis method is illustrated by several example test geometries. The examples were verified by comparison to numerical calculations. The residual stress term in the total energy release rate equation was found to be essentially exact in all example calculations.

Local Bending Moment as a Measure of Adhesion: The Cantilever Beam Test

It was recently proposed (Goussev, O. A., Zeman, K. and Suter, U. W., J. Adhesion 56, 45 (1996)) to characterize the joints between materials directly by the maximum bending moment, M max, borne just prior to delamination (delamination moment). This alternative to the energy-release-rate approach was first introduced for the blister test configuration. Here we extend this idea to a cantilever beam test. We suggest, therefore, to evaluate the bending moment in the cantilever-beam experimental setup with an elastic upper plate through direct measurement of the curvature of the upper plate in the vicinity of the separation line. For the profile measurement and determination of the exact location of the delamination line, the projection-moiré technique was employed. The methodology was tested on measurement of adhesion of an epoxy adhesive to steel. It was shown that the value of the maximum bending moment remains approximately constant during the delamination, indicating that this quantity is a physical characteristic of the joints between materials.

FINITE ELEMENT FORMULATIONS FOR FRICTION PENDULUM SEISMIC ISOLATION BEARINGS

In this paper, an advanced analytical model and finite element formulations including local bending moment effects for the Friction Pendulum System (FPS) are presented. Some important findings in these investigations reveal that local bending moments which result from the movements of the isolator, should be accounted for in the engineering design. The results presented in this paper show that if the effects of local bending moments are excluded from design considerations, it may endanger structures during earthquakes. The new formulations considering local effects provide an effective tool to simulate the behaviour of FPS-isolated structures subjected to earthquake loadings. The proposed formulations can be applied directly for both two- and three-dimensional analyses without any further assumption. It is easy to implement the proposed techniques in existing finite element programs. The results obtained from the numerical analyses suggest that the local bending moment effects are of significant importance, and should be taken into account to assure the safety of isolated structures during earthquakes. © 1997 by John Wiley & Sons, Ltd.

FEM considering local bending effects for flat sliding isolators

Presented in this paper are an advanced analytical model and finite element formulations including the local bending moment effect for the flat sliding system. This study reveals that the local bending effect is a very important factor. The results presented in this paper show that the design of the isolation without considering this effect may endanger structures during earthquakes. The new formulations taking into consideration the local effect provide an effective tool for the more realistic simulation of the behavior of flat-sliding-isolated structures subjected to earthquake loadings. The proposed finite element formulations can be applied directly for both two- and three-dimensional analyses without any further assumption, and can generally be placed at any location in the structure. The implementation of the proposed techniques in existing finite element computer codes is a simple task. Examples of structures equipped with flat-sliding isolators is also given to demonstrate the paramount findings through the proposed formulations. Results obtained from the numerical analyses suggest that the local bending moment effects are extremely important, and should be taken into account to assure the safety of isolated-structures during earthquakes.

Local Bending Moment as a Measure of Adhesion: The Blister Test

Abstract We propose to characterize joints between materials by the maximum bending moment, M max, borne just prior to delamination. We suggest to evaluate M max in the blister test geometry through direct measurement of the blister curvature in the vicinity of the separation line and employ a scanning capacitance microscope for the blister profiling. The methodology and apparatus were tested on measurements of adhesion of two commercial polymer films to Plexiglas and Teflon.

Single pulse laser excitation of structural vibration using power densities below the surface ablation threshold

This paper describes sub-ablation optical excitation of flexural vibration in cantilevers and a suspended truck-wheel rim by using a single 600μs, Nd:glass laser pulse with energies between 1J and 40J. The excitation is consistent with the photothermal production of a localized thermoelastic bending moment at the site of the laser irradiation. This method of excitation has been combined with fibre optic sensing and modal analysis of the resulting vibrations to provide a practical method of remotely measuring the structural properties upon which the frequencies of vibration depend. The modal frequencies of slot-damaged cantilevers are presented to demonstrate the possible application of this non-contact measurement technique for non-destructive testing.

High-order bending of piecewise uniform sandwich beams with a tapered transition zone and a transversely flexible core

High-order bending of a piecewise uniform sandwich beam with a tapered transition zone and a transversely flexible core is presented. The behavior is described through the solutions of a uniform and a tapered sandwich beam in the various regions, interconnected while fulfilling the boundary and the continuity conditions between the regions. The longitudinal and the shear forces in the inclined skin of the tapered region yield concentrated forces at the point where the skin longitudinal layout changes, thus leading to stress concentrations in the form of high peeling and shear stresss at the interface between the skin and core, and to high local bending moment in the skin. This stress concentration emerges whether the external loads are concentrated or distributed and is an inherent part of the structure. However, the level of stresses involved can be controlled through the appropriate design of the transition zone. The characteristic behavior in the transition zone and the design parameters that affect the behavior, are studied through a parametric analysis. The fields and the governing equations of a tapered beam are presented, and the results of the parametric study in terms of shear forces and bending moments in the lower skin and shear and peeling stresses at the lower skin-core interfaces, are presented and discussed.