Actual Bending Moment Research Articles

Bending moment characteristic analysis of utility-scale onshore wind turbine blades based on monitoring data

Bending moment is an important parameter in structural design of the wind turbine blades. The purpose of the present study is to accurately determine the actual bending moments on the blades of wind turbine in service and study the characteristics. It can be helpful to provide supports for the design load of wind turbine blades. For this purpose, a blade load monitoring system was developed and installed on a 2 MW onshore wind turbine to measure bending moments at the blade root. A simulation model which is consistent with the monitoring wind turbine was used to verify the availability of the system. Based on the monitored bending moments and operational conditions of the wind turbine, the characteristics and fatigue load of blade root bending moments were analyzed. Meanwhile, the relationship between bending moments of blade root and operational parameters was discussed. A thrust estimation method based on monitored bending moments of blade root was presented which will help to assess the loads on the tower and foundation of the wind turbine. At last, a calculation method of equivalent fatigue load based on wind speed-rotor speed joint distribution was established which will contribute to the fatigue design of blades.

Selection of optimal intensity measures for fragility assessment of circular tunnels in soft soil deposits

This study aims to identify optimal intensity measures (IMs) for use in probabilistic seismic demand models (PSDMs) for circular tunnels in soft soil deposits. To this end, we performed an extended numerical parametric study involving two-dimensional time history analyses of selected soil-tunnel configurations to evaluate the response of the selected tunnels under transverse seismic shaking. A series of 18 IMs were selected and tested, corresponding to free field conditions. The selected IMs were tested on several metrics, such as correlation, efficiency, practicality, and proficiency, based on an extended number of regression analyses between the IMs and the damage measure (DM), for the studied tunnels. DM is defined as the ratio of the actual bending moment (M) to the capacitive bending moment (MRd) of the tunnel lining. The results indicate that the peak ground acceleration (PGA) at the ground surface can be considered as the optimal IM for the shallow tunnels, whereas the peak ground velocity (PGV) can be considered as the optimal IM for both the moderately deep and deep tunnels. Finally, various fragility curves were constructed for the studied circular tunnels under the context of PSDMs. The findings of this study can serve as a reference for the seismic fragility analysis of circular tunnels in soft soil deposits, toward more reliable quantitative risk analysis (QRA), improved resilience, and adaptability of transportation networks.

Improvement of Eurocode 8 Seismic Design Envelope for Bending Moments in RC Walls of High-rise Buildings

ABSTRACT The paper focuses on the analysis of actual bending moments in RC walls of high-rise structures. A comprehensive analysis was carried out on three concrete buildings in order to evaluate the accuracy of the procedure for obtaining bending moments proposed by Eurocode 8 (EC8). The buildings are designed according to EC8 for medium ductility class (DCM) and high ductility (DCH). Nonlinear 3D models of the selected structures were subjected to 60 strong earthquake ground motions recorded on rock and stiff soil. One hundred and eighty nonlinear time-history analyses (NTHA) are carried out to compare the actual bending moments against design EC8 bending moments. Based on the findings of the conducted study, the possible improvement of EC8 bending moments design envelope for RC walls of high-rise buildings is indicated. A simple proposal for the correction of the existing EC8 bending moment envelope is introduced by its modification over the height of the wall to account bending moment increase due to the higher mode effects and by substituting EC8 design moment with wall resistance moment at the base. This improved envelope better matches the actual bending moments in RC walls of high-rise buildings. Further calibration is clearly required.

Structural Reliability Analysis of Container Ships under Combined Wave and Whipping Loads

A practical methodology for structural reliability assessment of ultra large container ships is proposed in the article. The commonly used limit state function for structural reliability analysis of oil tankers and bulk carriers was extended to take into account the whipping response due to the bow flare slamming. The ultimate vertical bending moment capacity of hull girder was considered as a fundamental safety variable in the limit state function, whereas the stochastic model of the loads consists of static still-water bending moments (SWBMs), low-frequency rigid body vertical wave bending moments and high-frequency whipping bending moments. The stochastic model of SWBM for one of the studied ships was obtained from actual bending moments recorded by the onboard loading computer in 2 years of operation. Linear vertical wave bending moment was calculated by a 3D panel seakeeping code, using International Association of Classification Societies (IACS) recommendation No. 34 for the computation of extreme global wave loads. The nonlinear correction of linear wave bending moment was obtained from the recent IACS Unified Requirement S11A for longitudinal strength of container ships. Impulsive loading was modeled by von Karman added mass variation method, whereas transient dynamic hull girder response was analyzed by Timoshenko beam finite elements. Load combinations between extreme still-water and vertical wave bending moments, and between extreme low- and high-frequency vertical wave bending moments are considered. The structural reliability analysis of two container ships of different sizes was performed using the first-order reliability method, to observe differences in safety levels due to different ship sizes. Safety indices are compared with the International Maritime Organization recommendations for double-hull oil tankers to have credible basis for assessing the obtained results. An extensive sensitivity and parametric study was performed, accounting for various operational, environmental, and modeling uncertainties, as well as for corrosion degradation. The presented study may be useful for classification societies in further development of recently introduced IACS Unified Requirements for longitudinal strength of container ships.

The Safety Assessment of Bored Pile Retaining Wall Based on Back Analysis for Bending Moment

Dynamic safety assessment of internal force of retaining wall is of great significance to ensure the safety construction of deep foundation pile, and the key is to get the actual bending moment. The curvature is acquired by curve fitting of retaining wall reformation with the least squared method, and the actual bending moment can be obtained by multiplying the curvature and retaining wall bending stiffness. This method overcomes the difficult that the actual bending moment cannot be directly measured, at the same time, the cost savings would be of great advantage. As the monitoring item of foundation pile which must be implemented, retaining wall deformation has sufficient data, which provide a solid foundation for the engineering application of back analysis of bending moment. This studied the safety assessment of bored pile retaining wall based on back analysis for bending moment and obtained some beneficial conclusions.

Fatigue resistance evaluation for couplers of existing post-tensioned, concrete bridges

The risk of a fatigue failure has to be evaluated at coupling joints of older post-tensioned, concrete bridges in Germany, because weaknesses were identified in the design of these bridges. Because of the nonlinear bearing behaviour of post-tensioned, concrete structures, the results of this analysis strongly depend on the distribution of the permanent internal forces, which are uncertain due to time-dependent losses and redistributions. In this paper, a method to determine the bearing behaviour and the actual bending moment of the examined coupling joint, which is based on non-destructive, long-term measurements under service conditions, is shown. Therefore, the crack at the coupling joint, the temperatures and the traffic loading are observed. The results are used to calibrate a finite element simulation of the cross section. With this, a more realistic fatigue evaluation could be done as of the approaches in codes for the design of new bridges are used (e.g. DIN EN 1992, 2011, Eurocode 2. Bemessung und Konstruktion von Stahlbeton- und Spannbetontragwerken, Berlin: Beuth).

Vibrations of cracked reinforced and prestressed concrete beams

The dynamic behaviour of bent reinforced concrete beams in elastic range is significantly influenced by cracks caused by former loads. Considering this fact a more accurate calculation of the eigenfrequencies of the beams is available. Experiments have shown that the features of vibration differ from the results obtained by the well-known linear model, if cracked zones exist. The cause of this phenomenon is that the bending rigidity of the cross-sections in the cracked range depends on the sign of the actual bending moment. Therefore the vibration shows non-linear characteristics in the elastic range as well. The dynamic behavior of bent prestressed concrete beams is similar. The dynamic characteristics of prestressed beams besides cracks is influenced also by the intensity and eccentricity of the axial force. For a detailed investigation of the problem, experiments and non-linear analysis were performed. On the basis of these the virtual eigenfrequencies of the non-linear vibrations were determined.

Bending Moments Distribution at the Main Structural Elements of Skew Deck-Slab and Their Implementation on Cost Effectiveness

The distribution of bending moments in T-beam deck slab varies from one T-beam to another. The design of T-beams should be based on the actual bending moments each beam is subjected to for the purpose of achieving economy especially in bridge deck slab, extended over big area. The saving in some cases is substantial due to reducing the quantities of steel and concrete.

High Strength Concrete Continuous Deep Beams — With Web Reinforcement and Shear-Span Variations

Tests under two-point loads were carried out to destruction on 12 reinforced concrete two-span continuous deep beams. The beams were tested for two shear-span/depth ratios of 0.45 and 0.24 giving clear shear-span/depth ratio of 0.21 and 0.00 respectively. Various arrangements of web reinforcement were used such as minimum and maximum vertical bars, minimum and maximum horizontal bars and minimum and maximum inclined bars. Sagging and hogging tensile steel was used in accordance with the shallow beam bending moment distribution and was kept constant for all the beams. The results of the present tests are compared with those of the moderately deep beams reported in the litterature by Rogowsky et al. and with the two-beam tests of Leonhardth and Walther. The present tests show that the current codes and design manuals covering continuous deep beams could lead to severe cracking and may be unsafe for this type of structural members. The actual bending moment distribution is completely different from that recommended by these documents, with moments at spans higher and those at internal supports lower. The tests also showed that the CIRIA guide may be too tolerant and hence unsafe towards bearing failure which, in the presence of an effective pattern of web reinforcement, is the dominant type of failure of reinforced concrete continuous deep beams.

An Integral Equation for Damage Identification of Euler-Bernoulli Beams under Static Loads

A damage identification procedure for Euler-Bernoulli beams under static loads is proposed. Use is made of an integral formulation for the static problem of damaged Euler-Bernoulli beams. This formulation originates from the observation that a variation in the bending stiffness of a linear elastic beam can be modeled as a superimposed curvature depending on damage parameters as well as on the actual bending moment distribution. Using the superposition principle, the problem is reduced to the solution of a Fredholm integral equation of the second kind characterized by a Pincherle-Goursat kernel. It is shown that the solution of this equation can always be obtained in an analytical form that may be used to set up a damage identification procedure based on the minimization of a nonlinear function of damage parameters.

A Simple Method of Estimating Wind Turbine Blade Fatigue at Potential Wind Turbine Sites

This paper presents a technique of estimating blade fatigue damage at potential wind turbine sites. The cornerstone of this technique is a simple model for the blade’s root flap bending moment. The model requires as input a simple set of wind measurements that may be obtained as part of a routine site characterization study. By using the model to simulate a time series of the root flap bending moment, fatigue damage rates may be estimated at the potential wind energy sites. The model is evaluated by comparing these estimates with damage estimates derived from actual bending moment data; the agreement between the two is good. Data from two different turbine types were used for the evaluation. For each type the model was tested at only one site because data from other sites were not available. To more firmly establish the universality of the model, further evaluation is necessary using the model applied to the same turbine located at different sites.

Retainining Wall Performance during Backfilling

Field data relating to the structural failure of a long reinforced concrete cantilever retaining wall are presented. The results of a survey of the defected form of the wall are included. Analyses of the wall are carried out using classical earth pressure theories with geotechnical data. Using the measured soil parameters, the predicted bending moment at the base of the wall stem was found to be less that 5% of the actual bending moment realized. This discrepancy is due to the effects of lateral earth pressures induced by compaction. A simple method of analysis is proposed to take into account the effects of compaction. Reanalysis of the wall using this method and the measured soil parameters gives a bending moment that is in very close agreement with actual bending moment developed.

Effective Length of Columns with Semi-Rigid Connections

The effective length of a column depends on the boundary conditions at the ends of its unbraced length. In a framed structure, the boundary conditions depend on the stiffness of the beams framed to the column. Design guides available for determining the effective length are provided for cases where beams are rigidly framed to the column and have their far ends rigidly framed to another column, fixed, or hinged. This paper will present a solution for the case where beams are framed to columns using semi-rigid connections. Frequently, in the design of frames for tall buildings, it is found that beams must be selected based on their stiffness to resist frame drift, rather than on the strength needed to resist wind forces. In this case the actual bending moments required to be resisted at the ends of beams may be substantially smaller than the moment capacity of the beams. It is economically attractive to consider the use of semi-rigid connections adequate for the actual bending moment. However, the semi-rigid connection may have a lower stiffness than an equivalent portion of the beam, since its strength is weaker than the beam. This paper will present a set-up for a general solution for the stiffness of beams with semi-rigid connections. A solution will be made for a simplified case and available information for one type of semi-rigid connection will be used to illustrate the effect on the effective length of a column.

Inelastic Analysis of Reinforced Concrete Frames

The imposed rotation method for the inelastic analysis of frames rests on the interpretation of the actual bending moment distribution as the superposition of linear elastic moment responses to loads and to unknown plastic rotations regarded as imposed strains. The method given herein is a generalized formulation, covering second-order geometric effects and moment-axial force interaction. Finite element models of frames and piecewise linear moment-rotation laws for critical sections are assumed. Recent algorithms for solving quadratic programming and linear complementarity problems are shown to be efficiently applicable to the analysis of multistory frames. The safety factor with respect to local failure because of “brittle” flexural behavior turns out to be attainable by a suitably modified linear programming procedure.

VIII.Method of analogy in the theory of structures

Short Summary It has been shown by Prof. Mohr that the deflexion curve for a bar may be regarded as the diagram for the bending moments which would be produced by imaginary forces equal in magnitude to the actual bending moments divided by the rigidity of the bar. Prof. Mohr applied this analogy to certain problems in continuous beams and plane frames. Prof. Rabinovitch used the analogy in the application of the funicular polygon to continuous beams. Prof. Gorbunoff has applied Mohr's method to a three-dimensional closed contour, consisting of rigidly jointed straight bars loaded with arbitrary forces.