Critical Load Estimates Research Articles

Evaluation of estimation methods and base data uncertainties for critical loads of acid deposition in Japan

Simplified steady state mass balance model for critical load (CL) estimation was applied to a test area in Japan to evaluate applicability of the model. Three different criteria for acidification limits (1: [Al3+]<0.2 eq. m−3, 2: Al/BC<1.0 mol mol−1, 3:Al depletion criterion) were used. Mean values and spatial distribution patterns of CL values calculated by these criteria were extremely different from each other. The first criterion produced much higher CL than the second criterion in the Japanese condition with high annual precipitation. Improvements including definition of the criterion were considered necessary. As quantitative data of the base cation weathering rate (BCw) was lacking, the rate was specified based on surface geology and the soil type of each site. To evaluate uncertainty of BCw used for CL calculation, ion content and particle-size distribution were measured for the soils collected from the test area, and BCw was estimated with PROFILE model based on these measurements. It appeared that BCw estimates by surface geology were adequate as a mean value, but they had uncertainty of about 50% of the average values due to variability of ion contents within the same surface geology group.

Buckling Solutions of Rectangular Mindlin Plates under Uniform Shear

This study is concerned with the elastic buckling of rectangular Mindlin plates under uniformly distributed shear loads along the edges. Based on the Rayleigh-Ritz energy approach, critical shear loads for plates with various combinations of simply supported and clamped edges are computed. The buckling solutions are presented in the form of generic design charts. Based on these charts, characteristics of buckling behavior are observed and discussed. Moreover, approximate buckling formulas are proposed to facilitate a quick estimation of critical shear loads for rectangular Mindlin plates.

Sensitivity of Critical Load Estimates for Surface Waters to Model Selection and Regionalization Schemes

AbstractA critical load is the amount of atmospheric pollutant that can be deposited on a sensitive ecosystem without causing measurable, longterm degradation in ecosystem form or function. We compare several methods for making critical load estimates of SO4 deposition to lakes; these methods are among those identified by participants in the United Nations‐Economic Commission for Europe (UNECE) Convention on Long‐Range Transboundary Air Pollution. The models were originally developed to address surface water acidification issues. Critical loads are computed here as the levels of deposition required to reduce surface water acid neutralizing capacities (ANC) from present values to either 25 µeq L−1 or 0 µeq L−1. These end points were selected to provide a common basis for comparing critical load values obtained from the various models, and are not intended to provide definitive critical load estimates. Using the amount of deposition required to decrease steady‐state surface water ANC values from 25 to 0 µeq L−1, about 9 ± 2 kgSO4 ha−1 yr−1 in the northeastern USA as a basis for comparison, we find that models make significantly different projections regarding ecosystem sensitivites to deposition. For lakes with critical load values in the range of current deposition in the Northeast (i.e., 18–56 kg SO4 ha−1 yr−1), model results differ by as much as 82 kg SO4 ha−1 yr−1. Differences in results are observed not only between models, but within models when slightly different approaches are used for estimating certain parameters. The interpretation of model results depends strongly on how systems are grouped regionally. While the results suggest that reductions in deposition from current levels would reduce adverse effects in sensitive lakes, the magnitude and timing of the reductions necessary and the determination of appropriate population end points are decisions that will ultimately be made by risk managers rather than risk assessors.

Estimation of critical convergence and rock load in coal mine roadways ? an approach based on rock mass rating

Based on field instrumentation in eight different coal mines representing varying depths and strata conditions, a relation for obtaining the critical convergence value has been established. In development heading for bord and pillar workings this relation can be used successfully to control the premature collapse of the roof. An empirical relation for rock load has been established. This can be utilized for optimum design of support system. The roofs have been categorized as stable, short-term stable and unstable. Proper attention should be provided for an unstable roof and the support design is to be changed before the convergence reaches the critical value.

The critical loads/levels approach to gaseous pollutant emission control

There is increasing pressure to control gaseous acidifying emissions to prevent harmful environmental effects; many governments are looking for a more effective and scientific means of assessing effects and planning emission controls compared with arbritrarily uniform percentage reductions. The critical loads/levels concept may offer the basis for a solution which is acceptable internationally. There is already agreement to map the critical loads and levels for countries in Europe and North America as a first step towards assessment. Recent developments in defining and quantifying critical loads and levels show the approach could be sufficiently adaptable to apply to the effects of different pollutants on a range of environmental receptors. Whilst it is difficult to arrive at an agreed single definition, various international groups have arrived at definitions which suit their own particular purposes. Despite a variety of different approaches to arriving at estimates of critical loads, there is broad agreement at the figures calculated by the different methods. An extension of the concept, the target load/level, provides a practical solution for implementing control strategies to prevent or minimize environmental effects.

Oxides of nitrogen in the greater Manchester conurbation, UK

This paper reviews the emission sources of oxides of nitrogen and provides an estimate of the contribution from the Greater Manchester conurbation. The uncertainty attached to the estimate is large. Atmospheric and rainwater concentrations of oxides of nitrogen are reported from the Greater Manchester Acid Deposition Survey network. The health and ecological implications of these concentrations are commented upon and the measured values compared to a number of environmental guidelines, including recently formulated critical load and critical level estimates. Control technologies applicable to both mobile and large combustion sources are briefly reviewed.

Buckling of Cable-Stayed Girder Bridges

A procedure for estimation of the critical load of cable- stayed girder bridges is derived using energy method. A computer program was developed and used to calculate the buckling load of four bridges with different types of cable configurations. An approximate method is suggested for the preliminary estimation of the lowest critical load. This approximate method yields very good results when it is applied to the examples in this paper. /ASCE/

Stability of tapered cantilever columns subjected to follower forces

Accurate estimates of critical loads of tapered cantilever columns with fixed or spring hinged ends subjected to follower forces are obtained in this paper. A Galerkin finite element method is used to solve the governing differential equation with variable coefficients. The effect of the stiffness of the spring hinge on the critical load is also studied.

Deformations of Geometrically Imperfect Beams

The effects of a number of representative types of imperfection on the elastic deformations of simply supported I-beams with either equal end moments or central concentrated load are investigated, and it is shown that each of these imperfections can be approximated by an equivalent sinusoidal initial crookedness or twist. The results of this investigation are then used in an examination of a linear plot method of extrapolating for the elastic critical load devised by Massey, and it is concluded that the plots obtained by this method may be nonlinear. An improved method of extrapolation is suggested and the critical load estimates made by this method from a number of experimental measurements are compared with the Massey plot estimates and the theoretical predictions.

Estimation of critical loads in elastic stability theory

Estimation of critical loads in elastic stability theory

The estimation of the critical load of a braced framework

With present methods of estimating the critical loads of triangulated frameworks by relaxation methods it is difficult to decide near the critical load whether the process is converging and the structure is stable, or whether the process is diverging and the structure unstable. This difficulty does not arise in the method presented here. Each triangle of the framework in turn is replaced by a hypothetical member until finally only one member of the truss remains, and this member has been modified in such a way as to take into account the stiffnesses of all the other members of the truss. A simple criterion for the stability of this final equivalent member is established and an example of the application of the method given.