Resultant Bending Moment Research Articles

On the Influence of Wave-Shaped Tool Path Strategies on Geometric Accuracy in Incremental Sheet Forming

In incremental sheet forming (ISF), the geometrical accuracy is still a challenge that is only solved for specific applications. The underlying mechanisms of geometrical defects in ISF are very complex and still not fully understood. Nevertheless, the process understanding is constantly evolving. Recent work has shown, for example, how bending moments resulting from residual stresses affect geometric accuracy. It has become clear that resulting bending moments with an axis parallel to the main tool path direction are dominant. Based on that, the current paper investigates the hypothesis that linear and parallel tool paths lead to an unfavourable accumulation of residual bending moments along a common axis, and whether this accumulation effect can be reduced by wave-shaped tool paths. Thus, the described research investigates the influence of novel path strategies on the residual bending moments and the resulting geometrical deviations. The path strategies are based on wave-shaped path lines, whereas the curvature is within the sheet plane. The investigations focussed on a rectangular sheet that is clamped at its shortest edges and a part geometry-sensitive to springback. Experimental and numerical investigations show a significantly positive influence of some investigated path strategies on the geometric deviation, compared to a conventional path strategy.

An Attempt to Design of High-Rise Structures Using ETABS

Abstract: This paper aims to discuss about ETABS (i.e., Extended Three Dimensional Analysis of Building Systems) and its various stages of Design civil engineering structures. Designer will be able to specify the loads and perform the analysis all conveniently and quickly. It helps in understanding the overall behavior of the structure in terms of resulting bending moment, shear forces and deformations which can be viewed or plotted. Define the boundary conditions, assign material properties. Designer will be able to generate the geometry

Structural performance of perforated arched self-compacted reinforced concrete beams under concentrated static loading

Arched reinforced concrete (RC) beams are a viable solution for use as the main supporting system for large-span halls. This is because of the developed normal force owing to the curvature, which approaches the line of pressure under loading, leading to a balance of the resulting bending moment. Therefore, the curved beam can sustain more applied loads than the ordinary straight beam for the same span. However, providing web openings along the entire span of the arched beam can compromise the ultimate capacity. Thus, the behavior of two-hinged perforated arched RC beams made of self-compacting concrete was investigated experimentally and numerically. The experimental program consisted of 11 RC beams, one straight and 10 arched beams, divided into five groups to study the effects of arching, perforation shape and size, and reinforcement configuration around the perforations. In addition, a parametric numerical study using the ABAQUS program was conducted to investigate the relevant parameters in detail. It was found that the arched beam exhibited remarkable ultimate capacity compared to that of the straight beam; however, the strength gains due to the arching effect reduced significantly due to providing web openings. In addition, it was found that providing additional web reinforcement in both the circular and cross-bar configurations around the perforations significantly enhanced the overall behavior. Furthermore, it was found that the best rise-to-span ratio of arched beams was 0.18 for both solid and perforated ones.

Seismic Behaviour of Multistorey Steel Framed Tall Buildings Using Intentionally Eccentric Braces

Braces with intentional eccentricity (BIE) are recently proposed to improve the seismic behaviour of conventional buckling braces (CBBs) by inserting intentional eccentricity along the brace length. Due to this eccentricity and the resultant bending moment, the BIE bends uniformly from small storey drifts and moves smoothly into the postbuckling behaviour under compression and sustains trilinear behaviour under tension. This behaviour delays the appearance of midlength local buckling which causes unstable energy dissipation. BIEs have a desirable postyielding stiffness which results in stable energy dissipation during cyclic loading and are capable of dissipating energy during low-intensity earthquakes. The seismic behaviour of structures with BIEs for use in buildings has not yet been investigated, specifically in tall buildings. Therefore, this study concentrates on investigating the seismic behaviour of tall buildings equipped with BIEs that uses a 3-dimensional (3D) finite element model in ETABS. In the first step, a 20-storey structure is designed using both eccentric brace frame (EBF) and BIE system and their seismic performance under the TABAS earthquake record is compared. In the second step, the seismic performance of a 25-storey irregular structure is assessed to evaluate the efficiency of the BIE system in irregular structures. Results show the desirable performance and energy dissipation capacity of the BIE system but it also shows large out-of-plane deformation in some cases.

Optimal yaw strategy and fatigue analysis of wind turbines under the combined effects of wake and yaw control

Yaw control is one of the most important farm-level active control strategies with the aim of power maximization and load mitigation. However, improper yaw strategies may induce a significant load increase on wind turbines (WTs) although a power enhancement can be achieved. Therefore, it is essential to conduct a comprehensive fatigue analysis of wind turbines under yaw control before proposing an optimal yaw control strategy. In this study, fatigue analysis of WTs under shear flow is conducted first under various environmental and yaw conditions. Bending moments at not only blade root and yaw bearing, but also non-rotating component like tower base are investigated. Furthermore, various wake conditions including both full wake and partial wake are generated to explore the combined effects of wake flow and yaw control. Different load trends and variation rates are obtained in the analysis. To determine the optimal yaw angle at different practical inflow and yaw conditions, a cost function is proposed by using resultant bending moments and further integrating loads at different components together. The results show that efficient yaw ranges all appear in the positive yaw direction and optimal yaw angle increases with the increase of inflow speeds. The comprehensive fatigue analysis and the proposed cost function for optimal yaw control in this work are expected to contribute to the research and applications of multi-objective active yaw control strategies and therefore to increase total power output while extending operation lifetime of wind turbines.

Classical and homogenized expressions for the bending solutions of FGM plates based on the four variable plate theories

Exact correspondence relations between the bending solutions of a simply supported rectangular functionally graded material plate based on the four variable refined higher-order shear deformation theory and those of the corresponding reference homogenous Kirchhoff plate based on the classical plate theory are derived analytically for the material properties varying continuously in the thickness direction. The deflection, stress components, the resultant forces and bending moments of a thick functionally graded material plate are expressed analytically in terms of the deflection of the reference homogenous Kirchhoff plate with the same geometry, loadings and boundary constraints. Consequently, the bending solution of a functionally graded material plate based on the higher-order shear deformation theory is simplified as calculations of three scaling factors which can be easily determined analytically for the specified material gradient profile, the shear stress shape function and the aspect ratio of the functionally graded material plate, because the solution of the reference homogenous Kirchhoff plate can be easily found even in the text book. As examples, particular solutions for a functionally graded material plate subjected to both uniformly and sinusoidally distributed loads are presented, which illustrate the validity of this new approach. Accuracy of the present solutions are demonstrated by comparing them with those obtained by different palate theories with different shear stress shape functions available in the literature. The analytical solutions can be used as benchmarks to check numerical solutions of static bending of functionally graded material plates based on different higher-order shear deformation theories.

Research on Wind Load Characteristics on the Surface of a Towering Precast Television Tower with a Grid Structure Based on Large Eddy Simulation

Local wind pressures on tiny rods of complex grid structures are difficult to obtain through wind tunnel tests due to their small sizes after scaling down, resulting in a lack of data support in wind load calculations for similar structures. However, local wind pressures on tiny rods can be obtained through numerical wind tunnel simulation using full-sized models. In order to investigate the wind pressure distribution of a grid structure and the influence of grid structures on the wind load of core tubes, three different television tower models are established based on an engineering example for large eddy simulations. A turbulence inlet generator (NSRFG) is adopted in the simulations while reproducing a portion of the wind tunnel test section including the mean and fluctuating pressures for validation. The results indicate that the mean wind pressures on the intersection of rods in the windward zone of the grid structure are higher than those on adjacent rods. Distinct reductions in the mean and fluctuating wind pressure of the grid structure are found in different zones. Moreover, resultant wind load forces and bending moments in the X and Y direction of the grid structure generally exceed 70% of the total wind loads. Based on simulation results, extreme net wind pressures of the grid structure and shape coefficients of enclosed regular octagonal cross-section buildings with the grid structure are provided for reference.

Failure analysis of a parabolic spring belonging to a railway wagon

This paper describes the study of three fractured parabolic springs belonging to a two-axle wagon suspension system. In order to determine the causes of the failures, a material analysis was performed, followed by a detailed study of the fracture’s surface both visually and using optical and scanning electron microscopy. The observations of fracture surfaces of the three springs revealed that the fractures began in the contact zones between the leaf springs, suggesting a fretting fatigue mechanism. The mechanism of failure of the springs fracture was a fatigue process. The propagation of fatigue cracks is more pronounced and extensive in one of the leaf springs. Finite element analyses were also performed taking into account the service conditions in order to determine the stress and strain distribution along the leaf springs. From the numerical simulations it can be concluded that the maximum stresses occur in two different zones: in the central section of the leaf spring and along the distance to the central section, in the sections where the relationship between the thickness reduction of the leaf spring and the resulting bending moment is most unfavourable. The Goodman's criterion shows a safety factor of approximately 1 and it can be concluded that this value is not enough to prevent the fatigue failure.

A Straightforward Approach to Site-Wide Assessment of Wind Turbine Tower Lifetime Extension Potential

This contribution presents a novel methodology to evaluate the lifetime extension potential of wind turbines—taking towers as the key component that preserves onshore turbines’ structural integrity—as a consequence of the difference between design and site-specific loads. Specifically, attention is drawn to the site-specific wind direction distribution, which provides an additional source of lifetime extension potential. For this purpose, variants of closed-form solutions (based on the tower section’s normal stress) are developed to enable fatigue damage accumulation due to fore-aft and side-to-side bending moments at any point on the tower circumference without the need for further information on tower section geometry or material properties. Based on the degree of data availability, different scenarios are defined to estimate lifetime extension potential from the accurate tower’s normal stress and approximations using resultant bending moment, fore-aft bending moment, and finally, wind rose data only. The methodology is applied to a wind farm case study using the actual SCADA data with a partially validated turbine’s aeroelastic model to obtain operational loads. The results indicate that this quick and fairly accurate approach can be used as an initial stage in identifying wind turbines across large farms, which have the largest lifetime extension potential.

In vivo analysis of hip joint loading on Nordic walking novices

ObjectiveTo evaluate the influence of Nordic walking (NW) on hip joint loads in order to determine whether it can be safely performed during postoperative physiotherapy in patients after orthopeadic surgery of the hip.MethodsInternal hip joint loads were directly measured in vivo in 6 patients using instrumented hip prostheses during NW and ordinary walking (OW). All patients received training in two different NW techniques (double-poling and the diagonal technique) by a certified NW instructor. Measurements were conducted on a treadmill at a speed of 4 km/h on level ground, at 10% inclination and at 10% slope as well as on a level lawn at a self chosen comfortable speed. Resultant contact force (Fres), bending moment (Mbend) and torsional torque (Mtors) were compared between NW and OW as well as between both NW techniques.ResultsJoint loads showed a double peak pattern during all setups. Neither NW technique significantly influenced hip joint loads at the time of the first load peak during contralateral toe-off (CTO), which was also the absolute load peak, in comparison to OW. Compared to OW, double-poling significantly reduced Fres and Mbend at the time of the second load peak during the contralateral heel strike (CHS) on level ground both on the treadmill (− 6% and − 7%, respectively) and on the lawn (− 7% and − 9%). At 10% inclination, the diagonal technique increased Fres and Mbend at CHS (by + 6% and + 7%), but did not increase the absolute load peak at CTO.ConclusionJoint loads during NW are comparable to those of OW. Therefore, NW can be considered a low-impact activity and seems to be safe for patients that are allowed full weight bearing, e.g. during postoperative rehabilitation after THA.

Simplified Mechanical Tests Can Simulate Physiological Mechanics of a Fixation Construct for Periprosthetic Femoral Fractures.

Plate fractures after fixation of a Vancouver Type B1 periprosthetic femoral fracture (PFF) are difficult to treat and could lead to severe disability. However, due to the lack of direct measurement of in vivo performance of the PFF fixation construct, it is unknown whether current standard mechanical tests or previous experimental and computational studies have appropriately reproduced the in vivo mechanics of the plate. To provide a basis for the evaluation and development of appropriate mechanical tests for assessment of plate fracture risk, this study applied loads of common activities of daily living (ADLs) to implanted femur finite element (FE) models with PFF fixation constructs with an existing or a healed PFF. Based on FE simulated plate mechanics, the standard four-point-bend test adequately matched the stress state and the resultant bending moment in the plate as compared with femur models with an existing PFF. In addition, the newly developed constrained three-point-bend tests were able to reproduce plate stresses in models with a healed PFF. Furthermore, a combined bending and compression cadaveric test was appropriate for risk assessment including both plate fracture and screw loosening after the complete healing of PFF. The result of this study provides the means for combined experimental and computational preclinical evaluation of PFF fixation constructs.

Stress resultant plasticity for plate bending in the context of roll forming of sheet metal

AbstractModeling of roll forming process of sheet metal requires efficient treatment of plastic deformations of thin shells and plates. We suggest a new general approach toward constructing the governing equations of bending of an elastic‐plastic Kirchhoff plate on the structural mechanics level. The generic function of the isotropic hardening law is formulated in terms of variables, which are meaningful for a material surface, namely resultant bending moments and dissipative work. This function is then identified by comparison of the exact solutions for a uni‐axial or isotropic bending experiment within the structural model and with the continuum model of a through‐the‐thickness element. We validate the approach against both the fully three‐dimensional simulations as well as the results of the traditional elastic‐plastic plate analysis, the latter one featuring the continuum laws of plasticity treated in the integration points along the thickness direction. We considered benchmark problems from the literature as well as a prototype for the roll forming problem. Besides good agreement regarding the shape of plastic zones and force‐deflection characteristics, experiments also demonstrate higher computational efficiency of the new stress resultant model.

Active flap control with the trailing edge flap hinge moment as a sensor: using it to estimate local blade inflow conditions and to reduce extreme blade loads and deflections

Abstract. Active trailing edge flaps are a promising technology that can potentially enable further increases in wind turbine sizes without the disproportionate increase in loads, thus reducing the cost of wind energy even further. Extreme loads and critical deflections of the blade are design-driving issues that can effectively be reduced by flaps. In this paper, we consider the flap hinge moment as a local input sensor for a simple flap controller that reduces extreme loads and critical deflections of the DTU 10 MW Reference Wind Turbine blade. We present a model to calculate the unsteady flap hinge moment that can be used in aeroelastic simulations in the time domain. This model is used to develop an observer that estimates the local angle of attack and relative wind velocity of a blade section based on local sensor information including the flap hinge moment of the blade section. For steady wind conditions that include yawed inflow and wind shear, the observer is able to estimate the local inflow conditions with errors in the mean angle of attack below 0.2∘ and mean relative wind speed errors below 0.4 %. For fully turbulent wind conditions, the observer is able to estimate the low-frequency content of the local angle of attack and relative velocity even when it is lacking information on the incoming turbulent wind. We include this observer as part of a simple flap controller to reduce extreme loads and critical deflections of the blade. The flap controller's performance is tested in load simulations of the reference turbine with active flaps according to the IEC 61400-1 power production with extreme turbulence group. We used the lifting line free vortex wake method to calculate the aerodynamic loads. Results show a reduction of the maximum out-of-plane and resulting blade root bending moments of 8 % and 7.6 %, respectively, when compared to a baseline case without flaps. The critical blade tip deflection is reduced by 7.1 %. Furthermore, a sector load analysis considering extreme loading in all load directions shows a reduction of the extreme resulting bending moment in an angular region covering 30∘ around the positive out-of-plane blade root bending moment. Further analysis reveals that a fast reaction time of the flap system proves to be critical for its performance. This is achieved with the use of local sensors as input for the flap controller. A larger reduction potential of the system is identified but not reached mainly because of a combination of challenging controller objectives and the simple controller architecture.

Analysis of hip joint loading during walking with different shoe types using instrumented total hip prostheses

Hip joint loads need careful consideration during postoperative physiotherapy after joint replacement. One factor influencing joint loads is the choice of footwear, but it remains unclear which footwear is favorable. The objective of the present study was to investigate the influence of footwear on hip joint loads in vivo. Instrumented hip endoprostheses were used for in vivo load measurements. The parameters resultant contact force (Fres), bending moment (Mbend) and torsional moment (Mtors) were evaluated during treadmill walking at 4 km/h with different shoe types. In general, footwear tended to increase hip joint loading, with the barefoot shoe having the least influence. Fres and Mbend were significantly increased during heel strike for all shoe types in comparison to barefoot walking, with everyday shoe (34.6%; p = 0.028 and 47%; p = 0.028, respectively) and men’s shoe (33.2%; p = 0.043 and 41.1%; p = 0.043, respectively) resulting in the highest changes. Mtors at AbsMax was increased by all shoes except for the barefoot shoe, with the highest changes for men’s shoe (+ 17.6%, p = 0.043) and the shoe with stiffened sole (+ 17.5%, p = 0.08). Shoes, especially those with stiff soles or elaborate cuishing and guiding elements, increase hip joint loads during walking. The influence on peak loads is higher for Mtors than for Fres and Mbend. For patients in which a reduction of hip joints loads is desired, e.g. during physiotherapy after recent surgery or to alleviate symptoms of osteoarthritis, low profile shoes with a flexible sole may be preferred over shoes with a stiff sole or elaborate cushioning elements.

Effects of Monopile Installation on Subsequent Lateral Response in Sand. II: Lateral Loading

AbstractMonopiles under in-service conditions are subjected to lateral forces and resultant bending moments from the offshore environment. The subsequent lateral response following installation is ...

Design and Analysis of Ribbed Raft Foundation Resting on Swell-Shrink Soils

Expansive soils shrink and swell with drying and wetting cycles. The shrink-swell capacity of expansive soils can result in differential movement beneath foundations which is a very common cause of foundation problems. Ribbed slab, often called waffle slab, is one of the efficient and inexpensive foundation solutions for use under light structures resting on shrink-swell soils. This paper presents a numerical analysis that is used to calculate displacement and internal forces in ribbed slab foundations resting on swell/shrink soil. The stiffness of the ribbed slab is modelled as an equivalent flat slab of constant thickness and the straining actions are calculated for the case of central heave. A parametric study of the effect of beam dimensions and rib spacing is performed to assess the optimum configuration. Dimensioning of the waffle slab system; slab thickness, depth and width of beams and spacing, is performed according to the Egyptian Code of Practice for the design of concrete structures. The results show that beam depths of 0.4 m and 0.45 m were safe and recommended under this condition of heave scenario. All beams with depths of 0.3 m cannot resist the resulting bending moments, While beams with 0.35 m depth are only safe when the beam width is not less than 0.2 m.

Characterizing flexural behaviour of panel-to-panel connections in cross-laminated timber floor systems

Cross-laminated timber floor systems are currently designed by treating them as one-way systems. The one-way assumption is conservative but two-way model would overestimate the system stiffness if the presence of semi-rigid panel-to-panel connections is not properly considered in the analysis. These connections allow for partial transfer of bending moment from one panel to the adjacent panel. The primary objective of this research was to characterize the flexural behaviour of typical panel-to-panel connections used in cross-laminated timber floors. Two types of connections employing self-tapping screws and surface splines were examined through testing. The resulting bending moment versus rotation curves were used to determine the rotational stiffness and moment capacity of connection assemblies. The influences of screw quantity, screw diameter and length, and spline thickness on connection stiffness and capacity were studied. Test results indicated that the flexural properties were significantly dependent on the number of screws used in the connection. Screw diameter and spline thickness also influenced flexural performance but to a less extent. However, the longer screws resulted in smaller stiffness and capacity with high variability for butt joints. It was found that the capability of moment transfer is very limited for these tested connections and less than 6% rotational stiffness was achieved by comparing with those of intact beams. A secondary objective of the research was to evaluate the experimental procedure developed for this research to measure flexural properties of panel-to-panel connection. Overall, the experience and results indicate that the experimental procedure used was practical.

Microstructure effects on the material behaviour of magnesium sheet in bending dominated forming

Abstract Predicting springback in the bending of magnesium sheet is difficult because it has high mechanical anisotropy leading to significant differences in the material behaviour in tension and compression. The tension/compression yield mismatch in magnesium is affected by the twinning behaviour which depends on the grain size and the direction of loading in regard to the crystal (C-axis) orientation. In this study the C-axis orientation of magnesium sheet was controlled by cutting sheets from a hot rolled block. Combined with heat treatment to produce different conditions for grain size and material strength this enabled for the first time to separately analyse the effect of material strength, grain size and C-axis orientation on the springback of AZ31 sheet metal. Pure and V-bending tests were performed and combined with advanced Digital Image Correlation (DIC) to experimentally determine the neutral layer shift for different levels of outer fibre bending strain before and after springback. Our study shows that springback in AZ31 reduces with increasing grain size but that it does not change with the C-axis orientation despite a reversal in the neutral layer position. The variation of springback shows more correlation with the bending yield strength measured directly from the pure bend test rather than the tensile yield strength and strongly correlates with the change in neutral layer shift in relation to grain size. Based on the experimental results analytical equations were developed to account for the effect of grain size on springback in magnesium. The model assumes the fully plastic, plane strain bending of strip and takes into account the effect of the tension/compression yield mismatch on the neutral layer position to determine the resulting bending moment. The developed equations provide, for the first time, a simple and clear mathematical explanation for the effect of material anisotropy (Yield strength mismatch) on the bending behaviour and springback of magnesium. If tuned with experiments, the model enables the estimation of springback as a function of the microstructure (grain size) in industrial practice.

Significance of wave data source selection for vessel response prediction and fatigue damage estimation

The availability of detailed environmental hindcast data opens the door for virtual structural health monitoring; however, the impact of hindcast wave data selection on the results of such an approach have not been explored. While studies on the differences between wave models have been conducted in the past, extensions of these comparisons to resultant vessel response predictions and fatigue damage estimates are limited. At three separate geographical locations, this work compared hindcast wave data from NOAA's WAVEWATCH III (NWW3) Multigrid Production Hindcast, the EU's CMEMS Global Ocean Waves Analysis and Forecasting Product, and National Data Buoy Center buoys. In addition to comparisons of wave parameters at each location, the resultant heave, pitch, and vertical bending moment responses and fatigue damage of a destroyer-sized naval combatant, the DTMB 5415, were compared. The novelty of this work lies in its large scope, which calculated responses every 3 h for all of 2017 in 32 speed and heading combinations for each location and wave data source. The results show that differences between wave data sources propagated to the vessel response predictions. These differences were then amplified in the calculation of fatigue damage causing significant discrepancies between data sources after just one year.

On finite bending of visco-hyperelastic materials: a novel analytical solution and FEM

In this paper, an analytical approach is proposed to examine the finite strain time-dependent behavior of incompressible, isotropic visco-hyperelastic elastomeric material under bending. Phenomenological hyperelastic invariant-based strain energy density function, Yeoh model, and N-termed Prony series are utilized to define the strain-dependent and time-dependent parts of the visco-hyperelastic constitutive model, respectively. 3D finite element analysis of the problem is carried out using ABAQUS/Visco to verify the analytical solution results. Material parameters of polyurea are calibrated using an optimization framework for experimental results under five different strain rates, simultaneously. Two well-known tests of viscoelastic materials, stress relaxation and creep tests, are investigated both analytically and numerically. Distribution of the Cauchy stress components and the resultant bending moment versus time, and the variation of the mentioned results with different rise times and ultimate bent angles are provided for the stress relaxation test. Moreover, the strain and bending angle results are plotted in a creep test for different rise times and applied moments. Besides, a multi-step relaxation test and creep recovery test are performed for different loading conditions. Finite element method results confirm the analytical approach with great compatibility.