Load Distribution Factors Research Articles

Optimal dynamic load shedding policy for generation load imbalances including characteristics of loads

Modern electrical power systems are highly interconnected and heavily loaded. An emergency may occur as a result of a sudden increase in system load or unexpected partial or total outage of a generator. This paper presents an optimal dynamic load shedding policy for generation load imbalances. The effects of voltage and frequency characteristics of system loads, transmission lines, transformers and reactive power compensator are reported. Equality and inequality system constraints are also considered in the formulation of this nonlinear programming problem. The further effects of system average time constant, speed drop factor, load reduction ratio (load frequency sensitivity factor), system inertia, load shedding and spinning reserve are included. Furthermore a simple load distribution factor is considered in this algorithm. Results of the unified power system of lower Egypt have been presented to validate the algorithm and show its effectiveness. Copyright © 1999 John Wiley & Sons, Ltd.

Effect of Continuity on Wheel Load Distribution in Steel Girder Bridges

This paper presents the finite-element results of a study of the effect of continuity on wheel load distribution factors for 78 bridges. Typical two-equal-span, two-lane, straight, composite steel girder bridges were selected for this study. Bridge parameters such as span length and girder spacing were varied within practical ranges, and their influence on the bridge continuity was investigated. The selected bridge cross sections and wheel load positions ensured that interior girders carry more live loads than the outside girders. Results of two finite-element modeling techniques were used to predict wheel load distribution factors, which were similar to the results obtained using the new formula developed as a part of NCHRP Project 12-26. They were, in general, less than the values obtained using the current AASHTO formula (S/5.5). The newly adopted AASHTO LRFD Bridge Design Specifications introduced new wheel load distribution factors based on formulas developed in NCHRP 12-26. The findings of this research encourage the use of the new wheel load distribution formula with a 5% reduction when considering multispan steel girder bridges. The new formula has been shown to be applicable to bridge decks with three girders. The engineer could also adopt an average of 15% reduction when using the AASHTO empirical distribution factor (S/5.5) when analyzing continuous bridges.

Finite-Element Analysis of Steel Girder Highway Bridges

This paper compares the performance of four finite-element modeling techniques reported in the literature used in evaluating the wheel load distribution factors of steel girder bridges. A typical one-span, simply supported, two-lane, composite bridge superstructure was selected for this study. American Association of State Highway and Transportation Officials (AASHTO) HS20-44 design truck loads were positioned to produce maximum moments in the girder. Two finite-element programs, SAP90 and ICES-STRUDL, were used to perform the analysis along with their preand postprocessing capabilities. The results of these modeling techniques were compared with AASHTO wheel load distribution factors (in 1996 and in 1994) and published experimental results. The four finite-element modeling techniques yielded similar load distribution factors. Further parametric study, varying the span length and girder spacing, was conducted and the distribution factors obtained using two of the four finite-element modeling techniques co...

Load Distribution and Impact Factors for I-Girder Bridges

This paper presents the procedure and results of field tests that were performed on two simply supported steel I-girder bridges to assess girder distribution and impact factors. The measurements were performed under normal truck traffic. Strain data were taken from bottom flanges of girders in the middle of a span. Additional strain data were obtained under passes of a control truck with known weight and configuration. A computerized data acquisition technique enabled selective recording of the significant blocks of the strain data under normal traffic. Strains were measured for two consecutive days on each bridge. Measured data consist of strain blocks from approximately 900 trucks. The strain records were filtered with a lowpass digital filter to remove the dynamic components and to obtain an equivalent static strain. The data were further processed to obtain statistical parameters (mean and standard deviation) of the girder distribution and impact factors. The results were compared with the values calculated according to American Association of State Highway and Transportation (AASHTO) methods. Measured girder distribution factors are lower than AASHTO values. Measured impact factors are well below AASHTO values.

Influence of Sidewalks and Railings on Wheel Load Distribution in Steel Girder Bridges

The conventional analysis and design of highway bridges ignore the contribution of sidewalks and/or railings in a bridge deck when calculating the flexural strength of superstructures. The presence of sidewalks and railings or parapets acting integrally with the bridge deck have the effect of stiffening the outside girders and attracting more load while reducing the load effects in the interior girders. This paper presents the results of a parametric study showing the influence of typical sidewalks and railings on wheel load distribution as well as on the load-carrying capacity of highway bridges. A typical one-span, two-lane, simply supported, composite steel girder bridge was selected in order to investigate the influence of various parameters such as: span length, girder spacing, sidewalks, and railings. A total of 120 bridges were analyzed using three-dimensional finite-element analysis. American Association of State Highway and Transportation Officials (AASHTO) HS20 design trucks were positioned in both lanes to produce the maximum moments. The finite-element analysis results were also compared with AASHTO wheel load distribution factors. The AASHTO load and resistance factor design (LRFD) wheel load distribution formula correlated conservatively with the finite-element results and all were less than the typical empirical formula (S/5.5). The presence of sidewalks and railings were shown to increase the load-carrying capacity by as much as 30% if they were included in the strength evaluation of highway bridges.

Topological generation and load distribution factors for supplement charge allocation in transmission open access

This paper introduces a simple novel method of transmission supplement charge allocation based on topological analysis of power flows in the network. The method uses the MW-MILE methodology but analyses the share, not the impact of, individual loads and generators in line flows. This results in positive contributions from all the users hence rescinding the problem of counterflows.

Lateral Distribution Factor from Bridge Field Testing

A study using field test results was conducted to determine the effect of live load for the slab-and-beam bridge structures. From the field testing of four existing bridge structures under the real truck loading, the live load distribution factors (DFs) are deducted from the measured strain gauge values and then determined by using several methods developed by the study team. The final results for each bridge are compared against some of the previously developed methods and design codes. The distribution factor concluded from testing results should be showing lower bound values. Results are given in tabulated forms and conclusions about the distribution factors for each bridge are reached from these tables.

Stretching Span Capability of Prestressed Concrete Bridges under AASHTO LRFD

A general refined analysis procedure for predicting the vehicular live load distribution on simply supported bridge girders is described. Load and Resistance Factor Design (LRFD) distribution factor formulas for flexure are carefully reviewed for modern prestressed concrete bridges made of I-girders or spread box girders with larger span-to-depth ratios. LRFD's results are compared with those obtained from the refined analysis method. Design recommendations are offered.

Shear distribution in simply supported skew composite bridges

Composite steel–concrete bridges remain one of the most common types built. Proper design of new bridges and evaluation of existing bridges requires accurate prediction of their structural response to truck loads. The American Association of State Highway and Transportation Officials has traditionally applied a load distribution factor for both moment and shear. The Ontario Highway Bridge Design Code (OHBDC) considers several parameters in establishing load distribution factors for moment. However, the method is limited to bridges with skew parameters less than a certain value specified in the code. The presence of skew reduces the longitudinal moments in the girders. However, it also causes high concentration of shear in the girder closest to the obtuse corner and reduces shear concentration in the girder closest to the acute corner as well as in the interior girders. Therefore, shear should be considered in the design of such bridges. In this paper, the influence of skew on the shear distribution factor is investigated. The influences of other factors such as girder spacing, bridge aspect ratio, number of lanes, number of girders, end diaphragms, and intermediate cross-beams are presented. An experimental program was conducted on six simply supported skew composite steel–concrete bridge models. Results from a finite element analysis showed excellent agreement with the experimental results. An extensive parametric study was conducted on prototype composite bridges subjected to OHBDC truck loading. The parametric study included more than 400 cases. The data generated were used to develop empirical formulas for shear distribution factors for OHBDC truck loading and also for dead load. An illustrative example is presented. Key words: bridges, codes of practice, composite, distribution, reaction, reinforced concrete, shear, skew, structural engineering, tests.

Marginal pricing and supplement cost allocation in transmission open access

The application of marginal costing to transmission pricing in open access schemes requires the collection of a supplement to finance the transmission systems. The paper describes the application of marginal cost based pricing in the Chilean power system and the difficulties faced in allocating the supplement among parties involved. Alternative methods for defining the allocation are formulated. Generalized generation and load distribution factors for cost allocation are formulated and implemented. The methods are applied to allocate payments for transmission services provided by the transmission network and by a distribution company.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Lateral load distribution in I-girder bridges

The results of a new lateral load distribution formula to be applied in the analysis or design of steel girders are compared with recently published field test data as well as the current AASHTO load distribution factor method. The developed formula was the result of a study of lateral load distribution in a bridge superstructure employing the finite element analysis techniques. The finite element models were developed to represent the actual geometry of the bridge deck and analyzed to obtain a better understanding of the elastic behavior of the concrete slab-on-steel girder highway bridges. The developed load distribution formula compares well with field data in predicting the behavior of bridge superstructures under highway loadings. Therefore, this paper will assist bridge engineers and researchers in predicting the actual load distribution and bending moments in I-girder highway bridges.

Load Distribution in Double Enveloping Worm Gears

A method for the determination of load sharing among the instantaneously engaged worm threads and gear teeth of double enveloping worm gears and for the calculation of load distribution along their instantaneous contact lines is presented. The bending and shearing deflection of worm thread and gear tooth, the contact deformation, the axial deformation of worm body, and the manufacturing and alignment errors of worm and gear are included. The obtained system of integral equations is solved by using approximations and an iterative technique. The corresponding computer program is developed. By using this program, the load distribution in the classical and in a new type of double enveloping worm gear drives is calculated. The influence of design parameters on load distribution factor and on maximum tooth pressure is investigated and discussed.

Analysis of slab-on-girder bridges

Grid models of three short-span steel girder bridges are developed and analyzed. The techniques used to develop grid models are discussed. Stresses and deflections from the grid analyses are compared to results of field load tests of the bridges. It is found for all three bridges that the grid analyses are able to reproduce the maximum measured stresses within 30%. The grid analysis results are also compared to results from the AASHTO wheel load distribution factor method for two of the bridges. The grid analysis results were found to match the measured results more closely in both cases.

Optimal Tooth Modifications for Spur and Helical Gears

A method for the simultaneous calculation of optimal tooth tip relief and tooth crowning for spur and helical gears is presented in this paper. The tooth profile modification is described by a linear function. Two types of crowning are introduced: linear and parabolic. The optimization of the tooth modifications is based on the following conditions: (1) The teeth are entering in mesh smoothly, without interference. (2) The load distribution factor is minimized. A computer program is developed for the calculation of the optimal tooth tip relief and crowning for spur and helical gears. By using this program the influence of type and length of optimal crowning and length of tooth tip relief on load distribution factor is investigated. Also, the influence of gear parameters on optimal tooth profile modification is discussed. On the basis of the obtained results, by regression analysis an equation is derived for the calculation of the optimal tooth tip relief.

Load and Stress Distributions in Spur and Helical Gears

A method for the determination of load and stress distributions along the contact lines of the instantaneously engaged teeth of spur and helical gears is represented in this paper. The calculation includes the tooth profile modifications and crownings, manufacturing and alignment errors of gears, tooth deflections, local contact deformations of teeth, gear body bending and torsion, and deflections of supporting shafts. The influence of gear parameters on load and stress distributions is discussed. On the basis of the obtained results, by regression analysis, equations are derived for the calculation of load and stress distribution factors.

Ultimate load distribution characteristics of a model slab-on-girder bridge

The introduction of limit states design philosophy and the ever growing demand for higher permissible loads for overload vehicles or special permit vehicles necessitates a thorough investigation of the behaviour and live load distribution characteristics of bridges beyond the working stress range. Evaluation of the live load moment capacity at ultimate utilizing elastic load distribution factors is neither realistic nor logical, as the distribution factors should reflect the ultimate structural/load responses including nonlinear behaviour, load redistribution due to yielding, etc.The purpose of this paper is to study load distribution characteristics of a slab-on-girder bridge model at ultimate loads and to develop load distribution factors for the ultimate limit state which include load redistribution, nonlinear behaviour, and other effects. Key words: load distribution factor, ultimate limit state, load redistribution, nonlinear behaviour, slab-on-girder bridge, OHBD truck.

A strength analysis of spur gears including ratio of contact. 1st Report. Mainly on the tooth deflection.

This paper presents a study of the strength analysis on the spur gears including ratio of contact. The analysis are performed based on the measurement of root stress and Finite Element Method. Spur gear used is module of 6.0, teeth number of 18, face width of 10 mm, and has a boss of total length 45 mm. FEM analysis are carried out 3 and 2 dimensions. The deflection are analyzed a single tooth and a case of ratio of contact. The main conclusions are as follows : (1) if gear has a boss, the stiffness of gear become larger but tooth deflection become smaller. (2) the top clearance is found not to have a significant effect upon the load distribution factor β. (3) if the deflection of a tooth is clearly, β could be obtained precisely.

A strength analysis of spurs gear including ratio of contact. 2nd Report. On the root stress.

The results of experiment and 3-and 2-dimensional FEM analysis to the root stress of spur gear including the ratio of contact are presented. For the experimental investigation of the root stress, the normal load are varied from 74.4-545.2 kN/m. FEM analysis is illustrate for a variety of structure model conditions and top clearances. There are appriciable differences between the root stress predicted by FEM analysis including the ratio of contact and experimental value. A set of load distribution factor β govering the FEM analysis and experimental value is a satisfactory agreement. It is found that the value of maximum root stress, occurring at the root surface, is derived from the position of strain-gage at the side of gear.

A DISCUSSION OF TENSILE RESTRAINT STRESS AND RESTRAINT COEFFICIENT OF FILLET WELDED JOINTS TACK-WELDED ON BOX GIRDER SECTIONS

The tensile restraint stress and restraint coefficient of fillet welded joints tackwelded on box girder sections are analyzed by the displacement by spontaneous expansion from weld heat input on diaphragm webs or ribs, and rigidity ratio of the diaphragm web and flange or rib and flange. The results are sumarized as follows: (1) The restraint coefficient (RF0) is directly proportional to the load distribution factor determined by the rigidity ratio of diaphragm web and flange or rib and flange. (2) The restraint coefficient (RF0) of a diaphragm web is almost constant regardress of the position, but the restraint coefficient (RF0) of a rib at the end of a welded line is about 3 times that at the center of a weld line. (3) The tensile restraint stress of a rib at the end of a weld line sometimes exceeds 70kgf/mm2.

Longitudinal Load Distribution Factor of Helical Gears

This paper deals with the longitudinal load distribution and the bending moment distribution of a pair of helical gears with a known total alignment error. The load distribution along the contact lines is calculated by the finite element method based on the plate theory including transverse shear deformation. Empirical formulas for both longitudinal load distribution factor and bending moment distribution factor are proposed for practical use. The load distribution factor in AGMA 218.01 is examined, and it is concluded that the load distribution factor is close to the calculated results if the value of unity is taken as the transverse load distribution factor.