Sectional Forces Research Articles

Effect of small inclination angle on heat transfer performance of Ω-grooved bending heat pipe

Grooved bending heat pipe may operate at small inclination angle caused by practical installation errors. Previous researches mainly focused on large inclination angles of straight heat pipes, but fewer experiments were conducted at small inclination angle of bending heat pipe where liquid accumulation and gravity effect on liquid-vapor transport varies along the pipe. This paper experimentally studied the effect of small inclination angle (±3°) on heat transfer of aluminum-ammonia Ω-grooved bending heat pipe with total length of 650mm, vapor chamber diameter of 4mm and grooved wick diameter of 1.24mm. The results showed that small inclination angle significantly affect the heat transfer performance of bending heat pipe with heat transfer limit changed by 9 times form 20W to 180W and thermal resistance changed by 8 times from 0.04 K/W to 0.32 K/W. Effect of negative and positive angles in bending heat pipe is complex than that in straight heat pipe. Positive condensation end inclination enhances heat transfer due to gravity-driven liquid reflux. Negative condensation end inclination inhibits heat transfer due to anti-gravity reflux and liquid accumulation suppressing gas condensation. Positive evaporation end inclination weakens heat transfer due to anti-gravity reflux. Negative evaporation end inclination also weakens heat transfer due to thick liquid film, increasing thermal resistance and potentially blocking vapor channels. Attributed to coupling effect of liquid accumulation at bending section and capillary force dominant at tiny incline, maximum heat transfer limit of 180 W is achieved at both end inclination of -0.5°.

Shear strength of steel-concrete composite I-beams with corrugated steel webs

Corrugated steel webs have been widely applied to steel-concrete composite beams due to their excellent shear performance. However, there needs to be adequate research on the shear behavior of steel-concrete composite I-beams with corrugated steel webs, and the proportional distribution of shear forces between concrete flanges and corrugated steel webs in composite I-beams has yet to be clarified. This paper experimentally investigates steel-concrete composite I-beams with corrugated steel webs with different shear span ratios. With the increase of the shear span ratio, the shear failure mode of the beam gradually evolves from shear-dominated to flexural-dominated, the shear capacity and structural stiffness of the beam are negatively affected, and the improvement of the shear resistance of the beam after webs buckling is gradually limited. As the primary shear component, corrugated steel webs contribute about 71 % to 92 % of the total sectional shear force. Notably, accounting for 15 % to 35 % of the shear capacity of the beam, the shear contribution of the concrete flange must also be typically considered. For the generalizability of research results, parametric studies are conducted using validated numerical models to comprehensively investigate the effects of steel yield strength, concrete strength, web thickness, web height, and shear span ratio. Afterward, an efficient analytical model considering the shear capacity of the concrete flange is proposed to estimate the shear strength of composite I-beams with corrugated steel webs. The proposed analytical model agrees satisfactorily with experimental and numerical analysis results. The research results can provide valuable support for designing and optimizing steel-concrete composite I-beams with corrugated steel webs.

Numerical Simulation and On-Site Measurement of Dynamic Response of Flexible Marine Aquaculture Cages

Flexible cages are widely used in marine aquaculture, yet their mechanical features in extreme seas are still unclear. This study proposes a numerical algorithm to solve the coupled response of the multiple cage systems. The net and mooring lines are modeled using the lumped-mass model, while the flexible floating collar system is assessed with the large-deformation FEM model, and the two models are coupled through an iterative scheme. Sea trials are conducted, and the motion of the cage is obtained using an image processing technique, which validates the numerical algorithm. Using the proposed numerical algorithm, a series of simulations are performed to investigate the response of flexible cages in extreme seas. Motions, line tensions, and structural sectional forces are studied, and the effects of factors such as the wavelength of incident waves and the diameter of collar pipes are investigated.

Section force calculation in flexible substructures modelled by wind turbine design tool Bladed

Aeroelastic simulation tools are widely used to predict the coupled response for onshore, offshore and floating wind turbines. A key output of the analysis is the section forces in the flexible substructures, such as blades, towers, and floating foundations. Individual substructures are typically modelled as a single linear flexible body, which is a part of a multibody system used for modelling the complete wind turbine. However, in some floating foundation concepts, in particular those with pre-tensioned cables, geometric non-linearities in the substructure can have a significant effect. With the conventional method for calculating section forces, such non-linearities are not captured accurately. In this paper, a new equilibrium-based method for calculation of section forces is presented, as part of the wind turbine design tool Bladed. This method relies on equilibrium between the section forces and the applied loads. The section forces are determined in terms of Lagrange multipliers, which represent the internal constraint forces in the structural elements. This method is valid even when significant geometric non-linearities are present, with reduced order models, and for statically indeterminate substructures. A case study is presented demonstrating the self-consistency of the new method for the OC4 semi-submersible floating platform, modified to include pre-tensioned cables. A verification against ANSYS is also presented for some elementary cases.

Assessment of the azimuthal loads variation by a bi-rotor configuration

Multi wind turbine configurations are emerging in the offshore wind energy market. The modelling of the aerodynamics of these systems is challenging, due to the small lateral distance between rotors and the subsequent interaction between wakes. Previous analysis in the literature showed that, due to this interaction, multi wind turbine concepts present the advantage of an increment in power production, if the rotors are laterally aligned. However, the counterpart in the variation of the blade loads throughout the revolution, has yet to be analysed in depth. This study focuses on the differences observed in azimuthal cycles of blade aerodynamic loads in side-by-side bi-rotor configurations, as an initial analysis of their potential impact on fatigue loads. The analysis has been developed using two aerodynamic codes, with different levels of fidelity. These models are: a Free Vortex filament Method (FVM) combined with an unsteady Lifting Line (LL) model, and a URANS-blade resolved approach. The simulations show that the sectional blade loads are affected by the adjacent rotor, changing the shape of the aerodynamic load cycles along the azimuth. The load azimuthal distributions predicted by a FVM and a URANS models have been compared, showing agreement on the shape of the cycle with slight differences on maximum peak values, specially at the inner sections of the blade. The FVM model has predicted increments in the blade load cycles, with respect to a single rotor case, with a maximum amplitude of a 3% for out-of-plane forces, and a 8% for in-plane forces. The difference in the azimuthal position of both rotors (phase shift angle) mainly affects the azimuthal shape and not so much the characteristic amplitude of these cycles. Finally, including geometric angles as tilt or pre-cone, produces imbalances between the blade sectional forces of the different rotors.

Buffeting characteristics of cable-stayed box beam bridge based on pressure measurement test of full bridge aeroelastic model

The aim of this study is to explore the buffeting characteristics of cable-stayed box beam bridge based on pressure measurement test of full bridge aeroelastic model. The study includes the influence of turbulence integral length scale and wind yaw angle on the magnitude of buffeting force, spatial distribution of buffeting force, and buffeting displacement response. Under larger turbulence integral length scale, the buffeting force of the box beam and it’s spanwise correlation are larger, which verifies the three-dimensional effect of the buffeting force. It is worth mentioning that, unlike traditional section models, there are differences in the pressure values of the pressure strips in the aeroelastic model at the flow separation point, which may be influenced by the cables. The experimental results of different wind yaw angles show that there is little difference in the buffeting force of the box beam section under the condition of 0°∼15° wind yaw angle, indicating that the maximum buffeting response will occur in the range of 0°∼15° wind yaw angle, which is consistent with the displacement results measured by the aeroelastic model. In addition, by fixing the model with a steel wire, the static and vibration states of the model were achieved. However, due to the high stiffness of the model, it can only generate small buffeting displacement, and the self-excited force component can be almost ignored. There is no significant difference in the results between the static and vibration states.

Difference in ship response in waves between strip and 3D methods based on integrated formulation

Numerous benchmark calculations have been performed on ship motions and loads in waves. However, there are usually significant differences between codes, even for programs based on the same theory, and it is often extremely difficult to identify the factors that cause such differences. In this paper, the authors present a formulation of the strip method and 3D method in such a way that the common parts between the two are emphasized, and then develop an integrated program that can handle the two methods (STFM and zero-speed Green's function method) based on this formulation. This approach enables the extraction of the differences in the ship response between the two methods caused by the pure difference in the hydrodynamic force of them, i.e., the 3D effect. A comparison using tank tests under a wide range of conditions is performed to clarify the estimation accuracy of the two methods and the tendency of the 3D effect for ship motion, hull-girder sectional force, and hydrodynamic pressure for a container ship and a VLCC.

Effect of three-dimensional space on progressive collapse resistance of reinforced concrete frames under various column removal scenarios

In this study, high fidelity finite element (FE) model was adopted to investigate the progressive collapse resistance of reinforced concrete (RC) frame structures under various column removal scenarios. The validity of the numerical model was verified by comparing with the existing experimental results. Afterwards, to facilitate the research on possible simplified boundary conditions served for further various column removal scenarios, the effect of multi-span continuous beams was firstly evaluated and the simplified methods were compared. Then, the effect of various column removal scenarios addressing the three-dimensional effect on the progressive collapse resistance of RC frame structures with and without slab was systematically evaluated. The analysis results showed that the continuous span beams increased the internal compressive force of the beam section at compressive arch action (CAA) stage, which effectively improved the CAA strength of the substructure. For simple modeling, the use of horizontal constraints at the end of the beam could replace the continuous span beams. The presence of transverse beams and slab provided additional load transfer paths for collapse resistance. The compressive membrane action (CMA) and tensile membrane action (TMA) of the slab significantly improved the progressive collapse resistance of the substructure in the small and large deformation stages, respectively. The location of the removed column significantly affected the contribution ratio of transverse beams and slab to the progressive collapse resistance of the substructure, which was quantitatively evaluated for practical design.

Low-cost wind turbine aeroacoustic predictions using actuator lines

Aerodynamic noise is a limitation for further exploitation of wind energy resources. As this type of noise is caused by the interaction of turbulent flow with the airframe, a detailed resolution of the flow is necessary to obtain an accurate prediction of the far-field noise. Computational fluid dynamic (CFD) solvers simulate the flow field but only at a high computational cost, which is much increased when the acoustic field is resolved. Therefore, wind turbine noise predictions using numerical approaches remain a challenge. This paper presents a methodology that couples (relatively fast) wind turbine CFD simulations using actuator lines with a fast turn-around noise prediction method. The flow field is simulated using actuator lines and large eddy simulations. The noise prediction method is based on the Amiet–Schlinker’s theory for rotatory noise sources, considering leading- and trailing-edge noise as unique noise sources. A 2D panel code (XFOIL) calculates the sectional forces and boundary layer quantities. The resulting methodology for the noise prediction method is of high fidelity since the wind turbine geometry is accounted for in both flow and acoustics predictions. Results are compared with field measurements of a full-scale wind turbine for two operational conditions, validating the results of this research.

Thermo-seismic performance of the novel thermal anchor pipe frame (TAPF) structure for supporting slope in earthquake-prone permafrost regions

The thermal anchor pipe frame (TAPF) structure is a new type of permafrost slope support technology, but its thermo-seismic characteristics are still unclear. In this paper, the coupled hydro-thermal-dynamic model of the thermal anchor pipe frame permafrost slope system is established. The cooling performance of the TAPF structure is investigated and the seismic responses are comparatively analyzed for different freeze-thaw periods. Results show that the presence of “elliptical” freezing cores with lower temperatures (which ranged from −3.94 to −5.36 °C) near the active layer at the end of the thawing period, which raised the permafrost table. The strip-shaped unfrozen moisture accumulation layer appears near the upper part of the thawing front at the highest temperature in the warm season. The peak acceleration response is the largest on October 15, 52.3% greater than the peak acceleration on April 15. The peak axial force of the thermal anchor pipe during the freezing period was 119 kN, which was 32.2% greater than that during the thawing period, and the peak total axial force after the earthquake appeared at the location of the freeze-thaw interface, and the axial force of the heat-transfer free section is greater than that of the anchored section. The frame structure is sensitive to earthquakes during the freezing period, and plastic bending damage may occur, especially at connection locations with thermal anchor pipes. Seasonal effects also have a strong influence on the shape of the acceleration response spectrum. The results can provide useful references for the maintenance and safe operation of permafrost slopes along the Qinghai-Tibet Project as well as for the seismic design of the new structure.

Urban-canopy airflow dynamics: A numerical investigation of drag forces and distribution for generic neighborhoods, and their relationships with breathability

Thorough investigations of urban-canopy drag primarily stemming from pressure drag on building surfaces are necessary given the turbulent flows within complex urban areas. Moreover, a gap persists regarding the relationships between canopy drag and breathability. Therefore, this work delves into the canopy-layer airflow dynamics for generic urban neighborhoods by performing three-dimensional Reynolds-Averaged Navier-Stokes simulations. A total of 32 subcases are examined, encompassing uniform- and varying-height and diverse plan area densities (λp, categorized into groups of sparse: 0.0625/0.067, medium: 0.23/0.25, and dense: 0.53/0.56). Results for the drag distribution highlight the windward-row shelter effect for the medium and the dense, local shelter by taller buildings, and distinct shapes of sectional drag forces (F⁎Z). Local velocity and mean age of air are found strongly positively and negatively correlated to F⁎Z, respectively, with distinct slopes in relation to λp. For the uniform-height, the normalized bulk drag (F⁎bulk, referred to as drag coefficient in literature) peaks for the medium with wake-interference regime; F⁎bulk demonstrates a maximum increase of over two times with height variation; moreover, F⁎bulk for varying-height groups exhibits a marked increase from the sparse to the medium, while remaining comparable values for the dense. The frontal area averaged drag (FAf,ave) exhibits a decreasing trend against λp across all cases. Further, FAf,ave exhibits strong correlations with λp and porosity, and with bulk ventilation indices such as spatially averaged velocity, air change rate, and normalized net escape velocity. Throughout the ‘suburban-urban-suburban’ canopy, medium neighborhoods exerting larger drag cause greater streamwise outdoor pressure drops and flow reductions compared to the sparse. However, dense neighborhoods with lower drag exhibit even larger pressure losses, which should be carefully scrutinized. The findings can inform urban planners in designing more aerodynamically efficient neighborhoods and guide strategies for improving air quality within urban environments.

A GFDM based computational model for the analysis of tunnels under gravitational loadings

Based on an impedance relation, a new computational model is developed for the analysis of tunnels under gravitational loading. The shape of tunnel is arbitrary. The impedance matrix, representing the soil resistance, is evaluated through integration of the equations of elasticity by generalized finite difference method (GFDM). The rigidity matrix of tunnel ring is constructed by using two types of elements: plate and shell elements. The equations of these elements are evaluated through integration of the equations of higher order plate and shell theories again by GFDM. These element equations accommodate not only axial and bending deformations, but, also shear deformations in the ring. In the study, the rotational joint deformation is simulated through the use of rotational spring model and the slippage is considered by modifying the impedance matrix so that the tangential soil resistance force between the ring and soil medium vanishes. Some numerical results are presented, in nondimensional forms, for circular and square tunnels where the following three cases are considered for circular tunnels: a) the soil medium is infinite, the change in σv (vertical (in situ) compressional stress) in the vicinity of tunnel is disregarded b) the soil medium is infinite, the change in σv is taken into account c) the soil medium is halfspace (HS). In connection with the case of (a), a comparison is presented for the ring flexibility curves of radial displacement and section forces of circular ring with those reported in literature. In view of the interpretations of the results and comparisons, we think, the proposed model may be used reliably in the analysis of tunnels.

A multiscale modeling method with updatable ABD shells for laminated flexible solar arrays

The flexible solar array is an innovative deployable system to provide electrical power for space stations, satellites, and other spacecrafts. Due to the advantages of lightweight, large area, and high power, it has received considerable attention and applications. However, the intricate multilayer configuration, nonlinear material behavior, and low stiffness characteristic of the array have made it always challenging to accurately predict the morphology and frequencies. This paper presents a numerical nonlinear multiscale method called PWL FE2 for large-scale flexible solar arrays. The proposed method is implemented in Abaqus with Python scripts and Micromechanics plugin. Its fundamental procedure is as follows: at microscale, the nonlinear constitutive model is piecewise linearly interpolated, followed by ABD stiffness and mass homogenizations of each segment; at macroscale, material properties of general ABD shells are updated based on section forces. Benchmark tests on substrate tension show that the error between PWL FE2 and direct numerical simulation (DNS) is less than 5 %. The refined shell model with PWL FE2 algorithm proves to be computationally efficient and convergence-friendly for morphology and frequency analysis of the array. For the single array undergoing strong nonlinearity, the computational efficiency of PWL FE2 is nine times that of DNS. The out-of-plane displacement reaches up to 210 mm, and the differences in reaction forces and deformations between nonlinear and linear simulations exceed 20 %. For the global array subjected to 84 N tensile loads, the array remains planar, and the first four modes are clustered around 0.2 Hz.

Assessment of Railway Bridge Reliability Using Load Measurement Data

A methodology is introduced that allows to determine the reliability of railway bridges subject to freight trains and which comply with code based assessment according to the Swiss structural code SIA 269. The methodology uses probabilistic models for section forces from freight trains. These models are based on a large database of wheel load measurements. A case study demonstrates how the methodology is applied to determine the reliability of generic bridges and subsequently allows the assessment of the reliability for a portfolio of railway bridges. The results show that the target reliability is achieved according to SIA 269 considering the code format and current set of partial safety factors. The study identifies potential load bearing reserves for bridges with longer spans.

Dynamic centrifuge model tests on piled raft foundation and evaluation of sectional forces of piles

Dynamic centrifuge model tests on piled raft foundation and evaluation of sectional forces of piles

Sheet pile walls as a part of the substructure of bridges. Practical application in Denmark

The usage of “sheet pile wall” is very common solution in Denmark due to the geographic situation of the country – low sea level, a significant part of the state border is sea, high groundwater level, poor geotechnical conditions. The “sheet pile wall” is used for strengthening of embankments, reclaim marine territories and as a supporting walls of railway lines and roads. As a consequence of this, a very common solution is to use the sheet pile walls as a part of the substructure of bridges – overpasses of railway lines and roads when the alignment is in excavation. From one side, the “sheet pile wall” are used as wing walls of the bridge and they support the road embankment. From another side, it is used as an abutment walls of the bridge. The part of the wall acting as a bridge support is design with some concrete “hammer beam”. The “hammer” in some cases is connected to the bridge deck by means of concrete hinges. Very often, “sheet pile wall” in the zone of the wing walls is combined with anchors in order to take increased section forces. Common variants in Denmark practice for connection of the bridge superstructure and sheet pile substructure are presented and analysed in the paper.

Numerical study of flow regimes and force characteristics for cruciform cylinder in oscillatory flow

Oscillatory flow past cruciform cylinder is numerically investigated using the Large-eddy simulation (LES) technique. The flow regimes and force characteristics of the cruciform cylinder are analyzed in detail for β (frequency parameter) numbers ranging from 200 to 500 and KC (Keulegan–Carpenter) number equals 10. Three vortex shedding modes are observed at different β values, which affect the torques exerted on the cruciform cylinder. At sections far from the node, two vortices shed within each cycle. The transverse force curve exhibits a regular pattern and a significant dominant frequency is observed in the transverse force spectra. However, as the node is approached, the vortex shedding becomes increasingly complex, leading to significant changes in the amplitudes and shapes of the transverse forces. Additionally, the sectional force coefficients agree well with those on the isolated cylinder at sections far from the node, whereas they exhibit significant increases at the sections near the node. Finally, the force coefficients of the cruciform cylinder are compared with those of the isolated cylinder for 2 < KC < 30 at β = 500. The results indicate that the cruciform cylinder experiences an increase in force coefficients, attributed to the influence of the node in cruciform cylinder.

RAO-based translation process for estimating extreme value distribution of nonlinear ship response in irregular waves

The authors propose a new method named the RAO-based Translation Process (RTP) method for simply estimating the extreme value distribution of the nonlinear ship response in irregular waves based on the nonlinear response in regular waves. The proposed method combines the existing idea of the Nonlinear Correction (NLC) method, which is based on wave height-dependent RAO, with the theory of the translation process, and thus has both simplicity and a clear theoretical background. Furthermore, it is positioned as an extension of the Equivalent Design Wave (EDW) method used in conventional ship structural design. The validity of the proposed method is confirmed through a numerical study on the extreme value distribution of hull-girder sectional forces considering body nonlinear effects. The proposed method can be used for various purposes, and in particular, it can reduce the computational demand for strength evaluation by Direct Load and Structure Analysis (DLSA), which is a computationally extensive analysis method. Therefore, the proposed method is expected to make a significant contribution to structural design.

Strain based damage indicators for finite element analysis of reinforced concrete structures

Numerical analysis conducted using a finite element model provides a quantitative and detailed evaluation of damage in concrete. As a result, the performance verification based on the local damage obtained numerically is considered an effective method for achieving a rational design of RC structures. Stresses and strains computed from numerical analysis are suited to indicators for representing local damage in concrete instead of sectional forces calculated from design equations; however, the performance evaluation using stresses and strains lack versatility owing to their dependency on constitutive equations and mesh discretization in numerical models. This study presents two types of strain-based damage indicators for performance verification in the design of RC structures using nonlinear finite element analysis. The second strain invariant of the deviatoric strain tensor is used to assess tensile damage, such as the opening of flexural cracks and the development of shear cracking in concrete, whereas the normalized accumulated strain energy is used to evaluate compressive damage, i.e., concrete crushing. These scalar indicators have high general usefulness, with calculation as non-local values by a weighted average, to reduce their mesh dependency. Furthermore, numerical analyses were performed to evaluate the damage condition and failure modes of RC beams, and the proposed damage indicators helped accurately understand flexure and shear failure. Lastly, we propose threshold values of the damage indicators for the performance verification of safety, represented by the load-carrying capacity in the design of RC structures.

How vortex dynamics affects the structural load in step cylinder flow

The vortex dynamics and the structural load in a step cylinder (consisting of a small, d, and a large, D, cylinder) flow are investigated numerically at Reynolds number ( $Re_D$ ) 150 for diameter ratios $D/d=2.0, 2.4$ and 2.8. First, the formation mechanism of a non-uniform oblique vortex shedding (the vortex shedding frequency remains unchanged as the oblique shedding angle varies) behind the small cylinder is explained: an increase in the production rate of the vortex strength and a farther downstream movement of the vortex formation position occur simultaneously as the vicinity of the step is approached along the small cylinder. Second, the structural load (the drag and lift) along the step cylinder is investigated, where four local extremes (two local minima and two local maxima) are observed. An in-depth investigation of the vortex dislocation effects on the structural load is provided, showing that the decreased circulation in the near wake and the weakened staggered Kármán vortex shedding pattern cause a major reduction (90 %) of the sectional lift amplitude and a relatively modest reduction (5.7 %) of the sectional drag amplitude, compared with the corresponding sectional force when no vortex dislocation occurs. This new knowledge combined with the three-dimensional effect of the step cylinder wake (caused by the blending of the small and larger cylinder wakes around the step) explain the formation of the four local extremes and the distribution of the structural load between them. Finally, it is found that the increasing $D/d$ amplifies the structural load variation along the step cylinder.