Bending Moment Coefficient Research Articles

What are the appropriate target safety level and corresponding partial load safety factor for bolted joints on wind turbine tower frame?

During preassembly on the quayside, towers are temporarily erected on the tower frame through the supporting structures. The bottom of these structures is bolted on top of the tower frame. The degree of conservatism of applying the generic load safety factor (1.5) for the bolted joints on the tower frame has never been investigated. The objective of this study is to determine the cost-optimal target safety level and calibrate the partial load safety factor for these bolted joints. The target annual reliability index is obtained based upon a simplified cost model. The overturning bending moment is explicitly introduced to the limit state functions through the bending moment coefficient obtained in the wind tunnel tests. The load model uncertainty is quantified by a Bayesian analysis, based upon a full-scale single tower test data. The case study will justify the applicability of the approach and the possibility of decreasing the environmental partial load safety factor for bolted joints. The cost-optimal target safety level and the corresponding load safety factor can significantly help to avoid the unnecessary conservatism in designing the bolted joints on tower frame, which helps the management make decision on economic development strategy of tower frames in the future.

Experimental Study on Wind Load and Wind-Induced Interference Effect of Three High-Rise Buildings

Wind loads of high-rise buildings are a key parameter in architectural design. The magnitude and distribution characteristics of wind loads are of great importance for the safety and economy of structural design. The wind loads of high-rise buildings are quite different from those of monomer buildings. The wind-induced interference effect could significantly increase the local wind pressure of buildings, causing potential safety hazards for the main structure and enclosure structure. For the three common high-rise buildings, we adopted the wind tunnel test method to measure the surface pressure of each building. The corresponding Re number was 8.2×106. This paper studied the shape coefficients, fluctuating wind pressure coefficients and base bending moment coefficient of each building with different wind direction angles and different spacing ratios, and the maximum value of each parameter and the corresponding working condition were statistically analyzed. The results showed that, under any wind direction angle, the fluctuating wind pressure coefficients on all sides of the building were affected by the spacing ratio, and the fluctuation range was large. When the wind angle was 180º, the fluctuating wind pressure coefficients on the sides of Building 1 were most affected by the slope ratio. At this wind angle, the maximum value was 0.43 at a slope ratio of 5.0, which was 65% different from the minimum. Partition shape coefficients of some sides and top surfaces changed significantly with the spacing ratio. When the spacing ratio was 5.0, the base bending moment coefficients in the downwind and crosswind directions reached their maximum values, and the wind direction angles where the maximum values of the base bending moment coefficients in the downwind direction were 40º and 50º, respectively, and the wind direction angle where the maximum value of the base bending moment coefficients in the crosswind direction was 10º. Due to the influence of the wind angle and the building spacing ratio, the wind loads on the facades of the pyramidal group of buildings varied greatly, and the wind-induced interference effect was evident. The wind load between the building facades in the three buildings was different, and the wind disturbance effect was evident. Therefore, the most unfavorable stress state and interference state of the structure should be comprehensively considered in the wind resistance design of the three buildings. The building spacing ratio should preferably be set to 3.0, and wind angles of 10º, 40º, and 50º should be avoided whenever possible.

Effects of Vertical Rib Arrangements on the Wind Pressure and Aerodynamic Force of a High-Rise Building

Façade appurtenances such as vertical ribs are increasingly used on high-rise buildings to enhance the architectural appearance. These attached ribs may modify the wind pressure acting on a building by changing the local flow pattern around the building. This study investigated the effect of the extensional depth of the vertical rib on the wind pressures of a high-rise building with a square cross-section. The wind pressure distribution on different surfaces, layer force coefficient, base shear coefficient, and base bending moment coefficient were analyzed under various rib extensional depths. Moreover, the measured layer force coefficients along the heights were compared with those provided by the current codes. This study’s results show that when the building is under normal approaching flow, the negative pressure area on the front surface increases with the rib extensional depth (b). This may be induced by the local recirculation at the outermost vertical ribs, which enhances the flow separation around the building. The negative wind pressures on the leeward surface show a slight increase with the increase in the rib extensional depth. Compared to the test results, the resultant layer force coefficients provided by EN 1991-1-4:2015 and GB 50009-2012 are conservative while those from the wind effect code of Hong Kong 2019 result in an underestimated evaluation. Increasing the extensional depth of the attached vertical rib may significantly reduce the positive layer wind pressure on the windward surface by 28% but increase the negative layer wind pressure on the leeward surface by 17%. The installation of vertical ribs with a small external depth (e.g., b is less than 2% of the building width) may exert limited effects on the overall base shear and bending moment, but the maximum base shear and bending moment will be reduced by 8.8% and 7.4%, respectively, when b increases to 4% of the building width.

A multiobjective surrogate-assisted optimisation and exploration of low-boom supersonic transport planforms

Optimal non-planar wing planform geometries for a Mach 2.2 45-seat supersonic transport are generated using Kriging-based Bayesian optimisation techniques on a 22-variable, 3-objective problem for two wing-loading conditions. Sonic boom loudness, drag, and root bending moment are simultaneously minimised at a fixed lift. A Python-based framework is developed for rapid evaluation of designs in a parallel computation environment, automating conceptual geometry generation, optimised mesh griding, Euler CFD evaluation, and thermoviscous atmospheric boom propagation. An empirical turbulent skin friction coefficient is used to correct the Euler drag and an estimate of wave drag is performed. Self-organising maps and polynomial chaos expansion Shapley effects are used to explore the design variables and their associated sensitivities with respect to the design objectives. A geometric centroid-based proxy for trim is used to filter the results; feasible extreme designs and a compromise design are compared and discussed. The results indicate a trade-off between each of the three objectives due to competing design requirements, however an improvement in two of the objective functions is possible by sacrificing the remaining objective. One possible compromise solution reduces the root bending moment coefficient by 25% and the sonic boom loudness by 24% at the cost of a 5% increase in drag.

Experimental and numerical study on the screw connection strength of bamboo-oriented strand board compared with wood-oriented strand board

The utilization of resourceful bamboo can alleviate the wood shortage problem. Bamboo-oriented strand board (BOSB) with the highest utilization of bamboo ratio and excellent mechanical properties was considered as a good engineering and furniture material. The strength of joints affects the safety of BOSB structure. This study aims to investigate the effect of screw spacing on the tensile and compressive stiffness and strength of corner joints from BOSB by experimental method combined with finite element method (FEM) compared with wood-oriented strand board (WOSB). The results showed that (1) the strength and stiffness of the corner joint was significantly affected by the screw spacing, and it affected the compressive strength and stiffness of WOSB more significantly; (2) the bending moment and stiffness coefficient of BOSB compressed joint decreased with the increase of spacing, while that of tensile joint increased first and then decreased, and it reached the maximum value, when the spacing was 48 mm; (3) compared with WOSB joint, BOSB joint had higher strength and stiffness, and the failure of the joint was due to the yielding of self-drilling screws. This was also verified by numerical analysis results; (4) the bending moment of BOSB joints was about 2.5 times that of WOSB joints, while the difference between stiffness coefficient was small; (5) the elastic deformations resulted from experimental tests and FEM are similar. It was shown that when the screw spacing is 48 mm, the Von Mises stresses on the BOSB joint were smaller, and the bending strength and stiffness were larger, which was the most suitable screw spacing.

Parametric sensitivity research of interference-fit bolted single-lap laminates joint based on an improved analytical stiffness model

Because of the excellent static and fatigue performance, the interference-fit bolted structure has a wide application prospect in the joint field. In this paper, an improved spring-mass stiffness analytical prediction model is established for the interference-fit bolted single-lap laminated composite structure. The influences of interference-fit percentage, bolt preload, secondary bending and interface frictions are considered in the model. Combined with experimental research, the value of secondary bending moment coefficient ε is studied, and the correctness of the analytical model is verified. Based on the improved stiffness model, parametric research and regression analysis on the interference-fit percentage, preload, friction, laminate width and material properties are carried out and show that the overall structure stiffness is obviously affected by ε value, laminate width and laminates properties. The stiffness decreases with the increase of ε and increases with the increase of laminate width. And as the key factors, the interference-fit percentage mainly affects the joint local friction and bolt shear stiffness, the preload and friction coefficient mainly affect the local friction, and the laminates sizes and properties directly affect the overall structural stiffness.

Experimental investigation of wind loads on wind turbine blade under various turbulent flows

For investigation of the effects of turbulence intensity (TI) on the wind loads on wind turbine blade, a 1:20 scaled model of a typical 3D wind turbine blade is designed and used for the pressure measurement test in a wind tunnel. Five uniform flows with different turbulence intensities are simulated in the wind tunnel test. The mean and root-mean-square (RMS) wind pressure coefficients, base moment coefficients, and their power spectral densities are presented and discussed in detail. Combined with the dynamic properties of the blade structure, wind-induced displacements at the tip of the blade are calculated by the random vibration theory. The results show that the increasing of TI amplifies the aerodynamic loads on the blade in terms of RMS wind pressure coefficients and RMS bending moment coefficients. Large wind-induced displacement of the wind turbine blade may be stimulated by high TI even under the feathering condition. This article aims to further the understanding of wind loads on wind turbine blades and provide useful information for the wind-resistant design of wind farms established in regions with high turbulence levels.

Experimental investigation of wind pressure characteristics and aerodynamic optimization of a large-span cantilevered roof

Cantilevered roof is particularly vulnerable to wind because high suction loads often occur on the rooftop due to flow separation. However, wind load characteristics associated with cantilevered roof have not been fully understood. In this paper, a 1/100 scale model of a cantilevered roof, over a grandstand, has been tested in a turbulent boundary layer flow, with particular emphasis on characterizing the wind pressure distribution on the cantilevered roof, and assessing the performance of several aerodynamic optimization devices. The results indicate that large wind suction generally occurs near the windward edge on rooftop surface. The effect of approaching wind direction is evident, which can influence the distribution pattern and value of wind pressure. For the effect of roof inclination, the down-sloping roof is found to be more appropriate since it results in most significant reduction in mean wind pressure, as well as the net lifting and bending moment coefficients. Furthermore, it is shown that adding a vented leading edge slot can effectively reduce the rooftop wind suctions. The maximum reduction in mean and peak suction loads is respectively 30% and 45%.

Quantifying Trailing Edge Flap Control Capability on Wind Turbines in a Controlled Environment

As wind turbine diameters continue to increase, the cyclic loading experienced by the turbine blade due to wind shear and yaw misalignment increases dramatically hindering the development of larger more efficient turbines. Based on current literature, controlling a section of the trailing edge of the turbine blade was found to reduce cyclic loading. To quantify the load control capability of a trailing edge flap (TEF), an experimental rig was designed to evaluate a TEF on a 3.5-m-diam wind turbine operating under different tip speed ratios, yaw angles, and blade pitch angles inside a large wind generation facility. The TEF was tested at two different spanwise locations and 0.82. The instrumented blade was capable of measuring rotor torque, flapwise/edgewise blade root bending moment, and normal force coefficient at two different spanwise locations and 0.82. The experimental results show that the use of a TEF was capable of manipulating the normal force coefficient by 40% and the flapwise bending moment by 20%. The relationship between the TEF angle and both blade bending moment and normal force coefficient was linear for all the cases tested. The results also show that when the TEF was centered at it could control the turbine loading more effectively. The results presented here prove that the TEF is capable of reducing cyclic loading on wind turbine blades.

In-Blade Measurements of Cyclic Loading on Yawed Turbines with Trailing Edge Flap

Wind turbines operate predominantly in relatively unsteady flow conditions and are typically misaligned with the incoming wind. Based on the literature review, controlling a section of the trailing edge of the turbine blade is found to reduce load fluctuations on wind turbine blades. Here, a detailed experimental setup describes a 3.5 m diameter wind turbine equipped with a trailing edge flap (TEF). The instrumentation of the compact blade was capable of measuring surface pressure and root bending moment, as well as controlling a TEF simultaneously and in time-resolved fashion. The blade is of constant pitch and chord of 178 mm while the TEF covers 20% of the chord and 22% of the 1.47 m aerodynamic blade span. The turbine was tested in a controlled wind generation facility large enough to house the turbine with less than 7% blockage. The wind turbine was tested for a range of tip speed ratios, blade pitch angles, flap angles and yaw cases. Although the turbine blade is capable of cyclically and dynamically change the blade pitch and flap angle, this paper only investigates constant pitch and flap angles. The results show that changes to the flap or pitch angle are capable of manipulating the coefficient of power, root bending moment and normal force coefficient. The results also show that the flap demonstrates similar control authority to that of the pitch system with the flap occupying just 4% of the blade surface area without reducing the power output of the turbine.

Field monitoring and wind tunnel study of wind effects on roof overhang of a low‐rise building

Roof overhang is one of the most easily damaged parts of low-rise buildings during windstorms. To investigate the wind-induced pressure distributions and forces on the roof overhang of a typical low-rise building, field monitoring during two typhoons and detailed wind tunnel test are conducted in this paper. Correlation analysis is performed to analyze the wind pressures on the upper and lower surfaces of the roof overhang. Moreover, cross-comparisons among the wind tunnel testing results, full-scale measurements, and design provisions are made for validation purposes. The comparative study illustrates that the model-scale experimental results of wind pressure coefficients, lift, and bending moment coefficients on the roof overhang are generally in reasonable agreement with the full-scale measurements, except for the peak negative pressure coefficients and lift coefficients for several wind directions. In addition, it is observed that the suctions on the roof overhang determined from the wind tunnel test and the full-scale measurements are lower than those stipulated in ASCE 7-16. The combined field measurement and model testing study aims to further understand the wind effects on roof overhang during windstorms and improve the wind-resistant design of low-rise buildings in tropic cyclone-prone regions.

A Prediction Method for TBM Cutterhead Dynamic Tunneling Performance under Typical Composite Geological Conditions

The cutterhead system is a core component of TBM equipment, which works in the extremely severe environment, and the strong impact loads result in severe vibration, crack, damage failure and other engineering failures. Accordingly, the key for cutterhead system structure design and parameter matching is to evaluate and predict cutterhead tunneling performance reasonably. In this paper, a prediction method for TBM cutterhead dynamic tunneling performance is proposed under the typical composite geological conditions, based on the CSM model of multi-cutters and cutter loads field test data. Then an actual TBM cutterhead of a water conservancy project is taken as an example, a spatial three-dimensional separation zone model for cutterhead tunneling is established under the typical geological condition, and the parameters influence rules of cutterhead tunneling performance are analyzed. The results show that, the cutterhead loads and specific energy change rules with different parameters are basically similar. Moreover, under the condition of penetration p=10mm, the cutterhead bending moment coefficient of variation magnitude exceeds 20%, which is the maximum, and the normal cutter spacing optimal value is 95mm. Also, when the normal cutter spacing is kept constant in 85mm, the penetration has a greater influence on the torque and specific energy coefficient of variations, which is increased from 2mm to 10mm, and the two indexes decrease by about 73%. It is indicated that proper increase of penetration is beneficial to reduce the vibration fluctuation degree of torque and specific energy. The proposed method of TBM cutterhead dynamic tunneling performance and the analysis results can provide theoretical basis and design reference for TBM cutterhead layout and tunneling parameters matching.

Coupled Fluid-Structure Interaction Modelling of Loads Variation and Fatigue Life of a Full-Scale Tidal Turbine under the Effect of Velocity Profile

Velocity profiles in tidal channels cause cyclic oscillations in hydrodynamic loads due to the dependence of relative velocity on angular position, which can lead to fatigue damage. Therefore, the effect of velocity profile on the load variation and fatigue life of large-scale tidal turbines is quantified here. This is accomplished using Fluid Structure Interaction (FSI) simulations created using the ANSYS Workbench software, which couples the fluid solver ANSYS CFX to the structural solver ANSYS transient structural. While these load oscillations only minimally impact power and thrust fluctuation for rotors, they can significantly impact the load variations on individual rotor blades. To evaluate these loadings, a tidal turbine within a channel with a representative flow that follows a 1/7th power velocity profile and an onset turbulence intensity of 5% is simulated. This velocity profile increases the thrust coefficient variation from mean cycle value of an individual blade from 2.8% to 9% and the variation in flap wise bending moment coefficient is increased from 4.9% to 19%. Similarly, the variation from the mean cycle value for blade deformation and stress of 2.5% and 2.8% increased to 9.8% and 10.3%, respectively. Due to the effect of velocity profile, the mean stress is decreased, whereas, the range and variation of stress are considerably increased.

Performance Analysis of a Piled Raft Foundation System of Varying Pile Lengths in Controlling Angular Distortion

The performance of a vertically-loaded floating piled raft foundation in very soft and deep layers of compressible subsoil, in terms of its ability to control key factors such as bending moment and pile-raft coefficient, was presented and discussed in previous research. The other critical factor that needs to be evaluated is the angular distortion of the foundation. This paper presents the effectiveness of the piled raft foundation system in controlling the angular distortion of the foundation. A comprehensive analysis of this proposed foundation system for various pile lengths in soft compressible subsoil was carried out. Different pile groups with 9 × 9 arrangement of piles were loaded vertically. A total combination of 45 pile group cases with different pile lengths, pile spacing, and raft thicknesses was analyzed. Results showed lower angular distortion for the proposed foundation system, which indicated that a piled raft with varying pile lengths is most efficient in controlling angular distortion as compared to piled rafts with equal pile lengths.

Research on Optimization Design of High Strength Prestressed Grooved Sheet Piles

Through theoretical calculations, the cracking moment, bending moment and section bending coefficient of high-strength prestressed grooved sheet piles and high-strength prestressed corrugated sheet piles were compared and analyzed; theoretically, the optimized high-strength prestressed grooved plates were obtained. And through this method we optimize the grooved sheet pile section. The optimized mechanical properties of the section have been greatly improved, making the mechanical properties of the grooved sheet piles approach or better than that of the corrugated sheet piles of the corresponding model. Combined with production experience, a series of optimization measures have been proposed for the section of the grooved sheet piles.

Hydrodynamic loadings on a horizontal axis tidal turbine prototype

Until recently tidal stream turbine design has been carried out mainly by experimental prototype testing aiming at maximum turbine efficiency. The harsh and highly turbulent environments in which tidal stream turbines operate in poses a design challenge mainly with regards to survivability of the turbine owing to the fact that tidal turbines are exposed to significant intermittent hydrodynamic loads. Credible numerical models can be used as a complement to experiments during the design process of tidal stream turbines. They can provide insights into the hydrodynamics, predict tidal turbine performance and clarify their fluid–structure interaction as well as quantify the hydrodynamic loadings on the rotor. The latter can lead to design enhancements aiming at increased robustness and survivability of the turbine. Physical experiments and complementary large-eddy simulations of flow around a horizontal axis tidal turbine rotor are presented. The goal is to provide details of the hydrodynamics around the rotor, the performance of the turbine and acting hydrodynamic forces on the rotor blades. The simulation results are first compared with the experimental and good agreement between measured and simulated coefficients of power are obtained. Acting bending and torsional moment coefficients on the blade-hub junction are computed for idealised flow conditions. Finally, realistic environmental turbulence is added to the inflow and its impact on the turbine’s performance, hydrodynamics and rotor loadings is quantified.

Estimation of Bending Moment Coefficients of Two Way Rc Slabs: Finite Element Approach

Objective: The main objective of this study is to find out the bending moment co-efficient of two way reinforced concrete (RC) slabs. Methods/Analysis: Linear and nonlinear static analysis of single panel two way RC slabs have been performed in finite element program ANSYS 12.0. The yielding behavior of slabs for various edge restrained conditions in both linear and non-linear analysis was studied. Findings: The yield line patterns of slabs with all boundary conditions were observed. From the yielding pattern, it was studied that the longer edges yielding first followed by the shorter edges and mid-span of slab. Based on the observation of yield line pattern, the bending moment coefficients were found. The obtained values were compared with IS: 456 recommendations. The comparison of analytical results show that the method adopted to obtain the moment coefficients of two way slabs is satisfactory. Applications: Using detailed observation of yielding of slabs, the bending moment coefficients shall be arrived for the use of design of slabs of any irregular shapes.

Numerical prediction analysis of propeller bearing force for full-scale hull–propeller–rudder system

The hybrid grid was adopted and numerical prediction analysis of propeller unsteady bearing force considering free surface was performed for mode and full-scale KCS hull–propeller–rudder system by employing RANS method and VOF model. In order to obtain the propeller velocity under self-propulsion point, firstly, the numerical simulation for self-propulsion test of full-scale ship is carried out. The results show that the scale effect of velocity at self-propulsion point and wake fraction is obvious. Then, the transient two-phase flow calculations are performed for model and full-scale KCS hull–propeller–rudder systems. According to the monitoring data, it is found that the propeller unsteady bearing force is fluctuating periodically over time and full-scale propeller's time-average value is smaller than model-scale's. The frequency spectrum curves are also provided after fast Fourier transform. By analyzing the frequency spectrum data, it is easy to summarize that each component of the propeller bearing force have the same fluctuation frequency and the peak in BFP is maximum. What's more, each component of full-scale bearing force's fluctuation value is bigger than model-scale's except the bending moment coefficient about the Y-axis.

Analytical and numerical investigation of bending moment coefficient in unbalanced single lap joints

A study was conducted to investigate the bending moment coefficient in unbalanced boron/epoxy–aluminium single lap joints subjected to tensile loading. It is well known that the main feature of the single lap joint is the eccentric loading path, which results in large deflections of the outer adherend and the overlap. In addition, the joint edge moment or bending moment coefficient at the end of the overlap is a significant feature. Four different overlap lengths (13, 20, 30 and 40 mm) have been analysed. A geometrically non-linear, two-dimensional finite element analysis was also performed to provide useful comparisons with the theoretical analysis. The analytical results mainly proved that, as the overlap length increases, the bending moment coefficient mainly decreased at the stiffer adherend, while the maximum l/c ratio is also decreased. The latter conclusions show that unbalanced (asymmetrical) single lap joints should be designed and manufactured with extreme care.

Analytical and numerical investigation of bending moment coefficient in balanced single lap joints

The present study concerns with the effect of bending moment coefficient in the stress distribution in a balanced boron/epoxy single lap joints subjected to tensile loading. The main feature of the single lap joint is the eccentric loading path, which results in large deflections of the outer adherend and the overlap, and the joint edge moment or bending moment coefficient at the end of the overlap. Theoretical models such as Goland–Reissner, Oplinger and Hart-Smith are examined in detail for different l/c and η/t ratios. Four different overlap lengths have been analysed. A geometrically non-linear, two-dimensional finite element analysis is also performed to provide useful comparisons with the theoretical analysis. The analytical results mainly prove that the Oplinger's model is the most appropriate for the specific geometry and materials, and the values of the bending moment coefficient are compared with the additional model of Zhao for four different l/c ratios.