Load Combination Method Research Articles

Study of Periodical Temperature Change Induced Deformation of an Inclined Steel Arch Bridge Exposed to Actual Environment Based on Synchronous Multi-Member Thermal Simulation

Structures exposed to the environment are affected by periodically changing temperature, and will undergo reciprocating deformation under the action of actual temperature. Steel structures are sensitive to temperature, and the effects on structure induced by changing temperatures are even more significant. The accurate calculation of temperature effects is very important to enable engineers to understand the state of a structure. However, the value of the temperature load in the current specification is set as constant, which can neither reflect the real state of the temperature field, nor its time-dependence in the actual environment. In this paper, an inclined steel arch bridge is chosen as an engineering example in order to analyze the actual temperature field of the structure in different seasons, and its deformation under the action of temperature, and the effects are compared with results based on other specifications. The comparison results show the synchronization of thermal deformation among different components and indicate the conservation of the specification. In order to further determine the most unfavorable situation under the effect of temperature changes, the deformation of multiple examples are compared, according to a standard load combination method, which verifies the feasibility of the load combination method in the calculation of temperature effects. It is found that the result can reflect, to a certain extent, the combined effect of the temperature changes of different components.

Seismic performance assessment of concrete bridges with traffic-induced fatigue damage

This paper proposes a universal analytical method for the seismic performance assessment of concrete bridges with initial fatigue damage caused by traffic loads. Load modeling is firstly performed, and random models of traffic load and seismic loads are established using stochastic processes. Subsequently, the theoretical approach for deterministic seismic response analysis of concrete bridges with initial traffic-induced fatigue damage is established by a combination of the micro-meso stochastic damage constitutive models and the finite element numerical method. In this manner, the seismic damage and failure mechanism of concrete bridges with initial fatigue damage can be elucidated. Further, considering the randomness of loads, the stochastic seismic analytical framework of concrete bridges damaged by traffic loads is put forward, in accordance with the probability space partition-based random load combination method and the probability density evolution theory. In such a way, the seismic reliability and safety of existing damaged concrete bridges can be well evaluated. Finally, a railway concrete bridge, as a practical engineering application, is investigated to validate the applicability of the proposed method.

On the combination of nonlinear load effects of structures

A new method for combination of nonlinear load effects of structures is suggested in the paper. At first, the concepts of load combination and load effect combination are discussed, respectively. A load combination method based on probability space partition is introduced, through which the load effects of structures could be accurately estimated. Afterwards, the principle of nonlinear load effect combination of structures under multiple loads is presented. In order to reflect the nonlinear performances of structures, the physical equations of solid mechanics with a reasonable elastoplastic damage constitutive model are applied to derive structural deterministic nonlinear responses. The probability density evolution equation (PDEE) is used to acquire the stochastic response characteristics of structures under multiple random loads. Hence, the combination of nonlinear load effects of structures is well realized. Furthermore, the reliability of structures under multiple loads is evaluated by using the physical synthesis method. Finally, in order to illustrate the proposed method, the nonlinear load effect combination analyses for a reinforced concrete (RC) plane frame under gravity load and earthquake and a concrete bridge under long-term vehicular loads and earthquakes are carried out. The analysis results demonstrate the applicability and superiority of the proposed method.

Joint Distribution of Wind Speed, Wind Direction, and Air Temperature Actions on Long-Span Bridges Derived via Trivariate Metaelliptical and Plackett Copulas

Abstract Comprehensive bridge design should consider simultaneous actions of wind and temperature. The current load combination method of directly superposing extreme wind and temperature actions i...

Study on the aerodynamic damping for the seismic analysis of wind turbines in operation

Abstract The continuous cost reduction of wind turbines has consolidated the competitiveness of wind energy. With the increasing installation of wind turbines in seismic-prone regions, it is likely that earthquakes will strike farms in operation. A practical approach to predict the dynamic behavior of a wind turbine under simultaneous seismic and operational wind loads is investigated in this work. The combined action can be determined by analyzing the wind and the seismic-induced responses separately. However, an accurate definition of the aerodynamic damping is required for this purpose and there are few experimental studies on the additional damping source. A 1/100-scaled wind turbine model was designed and the aerodynamic damping of the model was identified. Subsequently, the ground motion was applied in the model by means of a shake table and the combined wind/earthquake response that was measured experimentally was compared with the response predicted by several combination rules. A numerical study using the FAST analysis package for wind turbines was also conducted to complement the experiments with fully-coupled simulations that include aeroelastic effects. This work provides a necessary experimental reference for structural engineers to use adequate aerodynamic damping and load combination methods for the seismic analysis of wind turbines in operation.

Sensitivity analysis of hull girder reliability in intact condition based on different load combination methods

The paper focuses on hull girder reliability and sensitivity analysis of an oil tanker and a bulk carrier in intact condition. After a brief review of the theoretical background concerning the reliability analysis, Turkstra rule, Ferry-Borges and Castanheta, Moan and Jiao load models are applied and compared to investigate the incidence on hull girder reliability of different load combination methods for ships in full load (sagging) and ballast load (hogging) conditions. Subsequently, sensitivity analysis is carried out to investigate the incidence on the hull girder failure probability of the main parameters affecting the still-water and vertical wave bending moment stochastic processes, namely the maximum still-water bending moment reported in the loading manual, the ship voyage duration, the shape parameter of the long-term Weibull distribution of vertical wave bending moment and the mean wave period. Two reference ships, namely the ISSC oil tanker and bulk carrier, are assumed as test case for reliability and sensitivity analysis, that are performed by Monte Carlo simulation based on a dedicated programme developed in Matlab MathWorks. Obtained results are discussed and some suggestions are provided to improve the effectiveness of reliability analysis.

The Evaluation of Axial Stress in Continuous Welded Rails via Three-Dimensional Bridge–Track Interaction

The crucial differences between conventional rail with split-type connectors and continuous welded rails are axial stress in the longitudinal direction and stability, as well as other issues generated under the influence of loading effects. Longitudinal stresses generated in continuously welded rails on railway bridges are strongly influenced by the nonlinear behavior of the supporting system comprising sleepers and ballasts. Thus, the track structure interaction cannot be neglected. The rail-support system mentioned above has properties of non-uniform material distribution and uncertainty of construction quality. The linear elastic hypothesis therefore cannot correctly evaluate the stress distribution within the rails. The aim of this study is to apply the nonlinear finite element method using the nonlinear coupling interface between the track and structural model and to illustrate the welded rail behavior under the loading effect and uncertain factors of the ballast. Numerical results of nonlinear finite analysis with a three-dimensional solid and frame element model are presented for a typical track–bridge system. A composite plate girder, modeled by solid and shell elements, is also analyzed to consider the behavior of the welded rail. The analysis result showed buckling under the independent calculations of load cases, including ‘temperature change’, ‘bending of the supporting structure’, and ‘braking’ of the railway vehicle. A parametric study of the load combination method and the loading sequence is also included in this analysis.

Fracture mechanics analysis for a mooring system subjected to Gaussian load processes

An investigation on the fracture mechanics (FM) analysis using various load combination methods for a mooring system subjected to Gaussian load processes is conducted in this paper. Low frequency (LF) and wave frequency (WF) tensions of mooring lines are predicted by a frequency-domain analysis taking into account environmental effects including wind, wave and current. The LF and WF load processes are regarded as two random processes. The narrow-band method, general wide-band methods (Dirlik method and Tovo and Benasciutti method), and dual narrow-band methods (Jiao and Moan method, Fu and Cebon method and modified Fu and Cebon method) are used for predicting the combined load induced by LF and WF motions in the FM analysis. A comparison between mooring fatigue lives predicted by the FM analysis using these load combination methods is performed and the results show that the FM analysis based on the narrow-band method generally offers the most conservative fatigue life prediction and the difference of fatigue lives of mooring chains estimated based on general wide-band methods and dual narrow-band methods is not significant. However, in some cases, the FM analysis based on Dirlik method, Jiao and Moan method, Fu and Cebon method or modified Fu and Cebon method even provides more conservative results compared with the narrow-band method.

Incidence of load combination methods on time-variant oil tanker reliability in intact conditions

Reliability analysis of an oil tanker in intact conditions is performed to investigate the incidence of load combination methods on hull girder sagging/hogging time-variant failure probability. Particularly, Turkstra rule, Ferry Borges and Castanheta method and Poisson square wave model are applied to evaluate the statistical distribution of bending moment, with reference to both one voyage and 1-year period. Statistical properties of time-variant ultimate strength are determined by Monte Carlo simulation, up to 25-year ship lifetime; bending capacity is determined by means of a modified incremental-iterative method, to account for corrosion wastage of structural members contributing to hull girder strength, welding residual stresses and material properties randomness. After determining the still water load combination factors, based on statistical properties of still water, wave and total vertical bending moments, with reference to 1-year time interval, reliability analysis is performed by Monte Carlo simulation, based on limit state formulations relative to different load combination methods. Finally, the VLCC double hull oil tanker, benchmarked in the 2012 ISSC report, is assumed as a reference ship and obtained results are fully discussed.

Probabilistic Load Combination Factors of Wave and Whipping Bending Moments

Extreme values of wave and whipping bending moments are important in structural design of large containerships. Since the extreme values of these two, partially correlated processes do not occur at the same time instant and even at the same environmental conditions, it is necessary to combine them by using probabilistic load combination methods. The correlation analysis between wave and whipping bending moments is performed and a practical method for calculation of the most probable load combination factor between considered bending moments is presented. Short-term load combination factors are calculated by reconstruction of the signal from the frequency domain solution. Results are validated by comparison with model test data of the 9400-TEU containership for various sea states and speeds and heading angles. Practical regression equations for estimation of the most probable short-term load combination factor are formulated. Regression equations are then used in the computation of the long-term distribution of combined bending moment. The procedure is demonstrated on the example of the two large containerships.

Probabilistic Load Combination Factors of Wave and Whipping Bending Moments

Extreme values of wave and whipping bending moments are important in structural design of large containerships. Since the extreme values of these two, partially correlated processes do not occur at the same time instant and even at the same environmental conditions, it is necessary to combine them by using probabilistic load combination methods. The correlation analysis between wave and whipping bending moments is performed and a practical method for calculation of the most probable load combination factor between considered bending moments is presented. Short-term load combination factors are calculated by reconstruction of the signal from the frequency domain solution. Results are validated by comparison with model test data of the 9400-TEU containership for various sea states and speeds and heading angles. Practical regression equations for estimation of the most probable short-term load combination factor are formulated. Regression equations are then used in the computation of the long-term distribution of combined bending moment. The procedure is demonstrated on the example of the two large containerships.

Thermal–structural analysis of ITER triangular support for dominant load verification

The triangular support is located on the lower inner shell of vacuum vessel of ITER, which should be designed to withstand various loads such as nuclear heat, coolant pressure and so on. The appropriateness of its design is evaluated under the dominant load that could represent the most conservative condition among the design loads. In order to decide the dominant load, a valid method for thermal–structural analysis is firstly verified considering contradictory behaviors between heat and structural loads.In this paper, two approaches; one-way coupling and load combination, are introduced for thermal–structural analysis. The one-way coupling is a method generally used but has a limit to apply on contradictory conditions. The load combination could give a proper solution since it evaluates each load independently and then adds up each result linearly. Based on the results of each case, structural analysis for another load case, baking condition with incident, is conducted to find out which load is dominant for triangular support.Consequently, it is found that the baking condition is the dominant load for triangular support bracket. The proposed load combination method gives a physically reasonable solution which can be used as a reference for checking the validity of other thermal–structural analysis. It is expected that these results could be applied for manufacturing design of the triangular support under various load conditions.

Comparison of Load Combination Methods for Determining Maximum Ship’s Hull Girder Bending Moment

Several load combination methods have been developed for predicting the maximum loads acting on a ship’s hull girder within a specified time period. However, these methods have not been verified by a comparison with measurements. This paper compares predicted and measured maximum hull girder bending moment of a container ship. Point-crossing method, load coincidence method, Ferry Borges-Castanheta model, Moan and Jiao’s method, peak coincidence method, Turkstra’s rule, method of square root of the sum of squares (SRSS) and Söding formula are used for the comparison. The results show that (1) Ferry Borges-Castanheta model and Söding formula provide best estimates, (2) point-crossing method, load coincidence method and Moan and Jiao method provide sufficiently accurate estimates, (3) Turkstra’s rule provide reasonable estimates, (4) method of SRSS provides fairly low estimates and (5) peak coincidence method provides very conservative estimates.

Uncertainty Analysis of Load Combination Factors for Global Longitudinal Bending Moments of Double-hull Tankers

The present article aims at assessing the probabilistic characteristics of the load combination factors for global longitudinal bending moments of double-hull tankers. The calculations are performed based on a sample of oil tankers representative of the range of application of the Association of Classification Societies' (IACS)–Common Structural Rules (CSR) design rules. The article starts by reviewing the probabilistic models that have been proposed to model stillwater and wave-induced loads and their characteristic extreme values. Different load combination methods are also reviewed including an analytical method that provides the combined characteristic value of stillwater and wave-induced bending moments based on the Poisson assumption for upcrossing events and using the first-order reliability method in combination with the point-crossing method. The predictions of the different load combination methods are assessed on the basis of a sample of five oil tankers adopted during the IACS-CSR design rules development process. A parametric and an uncertainty propagation study are then performed to identify the range of variation and the probabilistic models of the load combination factors that are applicable to double-hull tankers.

Uncertainty Analysis of Load Combination Factors for Global Longitudinal Bending Moments of Double-hull Tankers

The present article aims to assess the probabilistic characteristics of the load combination factors for global longitudinal bending moments of double-hull tankers. The calculations are performed based on a sample of oil tankers representative of the range of application of the Association of Classification Societies' (IACS)-Common Structural Rules (CSR) design rules. The article starts by reviewing the probabilistic models that have been proposed to model stillwater and wave-induced loads and their characteristic extreme values. Different load combination methods are also reviewed including an analytical method that provides the combined characteristic value of stillwater and wave-induced bending moments based on the Poisson assumption for upcrossing events and using the first-order reliability method in combination with the point-crossing method. The predictions of the different load combination methods are assessed on the basis of a sample of five oil tankers adopted during the IACS-CSR design rules development process. A parametric and an uncertainty propagation study are then performed to identify the range of variation and the probabilistic models of the load combination factors that are applicable to double-hull tankers.

The Experimental Study on College Psychical Education Professional Men Load Combination Methods of Fast Strength

Through training for six months to the three no different groups using the load combination method of fast strength, then horizontally,vertically compare and analyze the fast strength indicators statistic results of three groups,The aim is to find out the best load combina- tion methods of fast strength. It is an indisputable fact that fast strength has played a decisive role in most sports. However, fast strength has a wide variety of training methods and means, and different situations may use different training methods and tools; then no matter what kind of training methods and means, must add a certain load. And according to training requirements, changes in training load should also continue to impose different load combinations. Then how the load can be combined to improve the fast strength more effectively and economically? In this regard, in order to provide a quick reference for the efficient improvement of strength training, having adopted dovuments, interviews with experts and other methods, based on the results of previous studies, we have selected three combiniations of loads to find the best combination of training load method by six-month experimental study on three no different groups using three different load combination methods.

515 摩擦を考慮した多入力配管系の地震応答解析における最大応答量推定法

A load combination method for seismic response calculation of piping systems with friction characteristics to multiple support excitations is presented. This method has an advantage, such that the cross-correlation among support excitations and "response reduction factor" due to friction are taken into account by use of a stationary random vibration theory approach. This method is supplied to various correlation cases of two support excitations and friction characteristics and the maximum responses of piping is calculated. From these calculation results, it is clear that the maximum acceleration responses of nonlinear piping systems can also depend on the cross-correlation among support excitations and can be reduced due to the friction effect. Finally, the conventional equation of the response reduction factor and the maximum response calculated by the proposed method are presented for practical use.

C07 多入力を受ける配管系の地震応答解析(OS7 機械・機械構造物の耐震・免震・振動制御(1))

This study proposes a load combination method considering the correlation coefficient among support excitations for response analysis of multi-supported piping system. The traditional combination methods can lead to large errors depending on the combination of inputs because of neglecting the correlation among inputs. However, because this proposed method should lead to small errors regardless the combination of inputs, it is expected that designing comes more rational. In the simulation of single- degree-of-freedom system, the comparison of results of this method and traditional methods showed us the availability of this method. And, the simulation of two-degree-of-freedom system showed us the availability of using the combination method considering the correlation among modes in addition to this method.

Resistance factors and companion-action load factors for reinforced concrete building design in Canada

The currently used safety factors for concrete buildings do not reflect current levels of quality control, refined knowledge of variabilities as established by recent studies, load-resistance correlation in the tension failure of columns, and so on. Revision of load combination methods can also achieve more consistent reliability. The primary objective of this investigation is to develop an optimum set of load and resistance factors for the design of reinforced concrete buildings in Canada. The companion-action load factor format is selected because it models real load combinations more accurately than the probability factor format that is used in the National Building Code of Canada and CSA Standard A23.3-94. The reliability analysis is based on a variable limit state equation developed by combining the true limit state, where the structure is about to fail, and the design limit state that is used in the design office. Present levels of quality control and present specifications are reflected in the variables used. Resistance factors for concrete and non-prestressed reinforcement are calibrated for use with the companion-action load factors developed in this study. The resistance factor for concrete is increased, leading to a general improvement in economy. Adequate and more uniform safety is achieved through revised load combinations and factors.

Stochastic and deterministic combinations of still water and wave bending moments in ships

Probabilistic models are presented for the still water bending moment (SWBM) and vertical wave bending moment (VWBM). Different stochastic and deterministic methods are applied for the combination of the long-term SWBM and VWBM. It is found that commonly applicable deterministic load combination methods, namely, the peak coincidence method, the Turkstra's rule and the SRSS rule, are either very conservative or nonconservative. Using stochastic methods, including the exact point-crossing method, approximate load coincidence method and Ferry Borges method, leads to identical predictions for the current load combination problem. For code application, load combination factors are introduced for both sagging and hogging conditions to reduce the conservatism inherent in the existing ship rules. Case studies are performed for an offshore production ship. A considerable reduction of the total design bending moment is found when the load coincidence is properly considered instead of combining the maximum of each load.