Euro-SiBRAM’2002 Prague, June 24 to 26, 2002, Czech Republic
Session 3
Snow and Wind Load
Snow and Wind Load in the framework of SBRA reliability assessment method
This paper turns attention to the representation of the snow and wind loads in the framework of the Simulation-Based Reliability Assessment method, SBRA, developed in the Czech Republic by Marek and Guštar, as documented in [1], [2], [3] and [4]. The probabilistic SBRA method is based on the application of fully probabilistic interpretation of Limit States philosophy, on expressing the input variables (including loading) by parametric as well as non-parametric distributions (such as “bounded histograms”), by analyzing the interaction of variables and the reliability function using Monte Carlo simulation, and by expressing the reliability by comparing the calculated probability of failure Pf and the target probability Pd contained in the codes (see, e.g. the Czech Code CSN 73 1401-1998 Design of steel structures, published in Prague 1998).
Considering the Arbitrary Point-in-Time Approach, APT, (see [5] and [1]). the load effects are expressed by “Load Effects Duration Curves, LEDC”. Combination of load effects is evaluated using direct Monte Carlo simulation. Note: In case of exceptional loads of very short duration, such as hurricanes, earthquake and explosions a special approach is proposed [5] and [6]. The exceptional loads (expressed by extreme values histogram) are evaluated in the instant of occurrence, while the “common” loads are expressed by LEDC, the probability of failure is calculated using simulation, and corresponding higher target probability must be applied, see [6]. For numerous solved and discussed examples of SBRA applications see books [2], [3] and [3], and more than about hundred published papers and reports listed on the website www.itam.cas.cz/SBRA.
Following paragraphs are focused on the determination of the snow load duration curves and wind load duration curves. These curves (also called as curves of the probability of non-exceedance) obtained from the evaluated long-term records in the Czech Republic, are used in the SBRA analysis.
Snow load is estimated from the water equivalent of snow cover. In the Czech Republic it is measured once a week (see [7], [8], [9] and [10]) at approximately 200 climatologic stations of the Czech Hydro-Meteorological Institute and at the majority of rain-gauge stations (there are about 700 of them in the country). Because of difficulty of the measurements and relatively high fluctuation of reading at individual stations, it is possible to use only less than half of the total number of stations for data processing for the period since the year 1961.
In
mountain regions snow cover is especially very variable however
relatively little dependent on time. Values measured once a week can
be considered as values well characterizing the state for the whole
period among individual samplings. It is practically sure that in
mountain regions the difference between the actual maximum and the
highest measured value is relatively little, whereas in lower
locations, where snow cover is very variable in time it is not
possible to guarantee that measured values can characterize the real
state. For that reason an algorithm for completing water equivalent
in days, when the measurement is not taken, was worked out and
tested. For the computation were used meteorological elements
measured at stations every day (daily precipitation total,
height of new snow cover at 7 a.m.,
total height of snow cover at
7 a.m. and mean relative air
humidity). Mean relative air humidity has to be taken over from the
nearest climatologic station.
This method enables to find possible errors in measurements and take only results of reliable stations for further processing. After this completing, which at lower attitude locations is necessary and at higher locations desirable, the data are ready for statistic processing. Data from 12 stations for the period 1975-1993 have been preliminary processed up to the present. Curves of probability of non-exceedance of the water equivalent of snow cover (that is curves of snow load duration) both for absolute values and relative ones given in per cents of the absolute maximum which occurred in the given period were obtained.
Figure 1. Snow Load Duration Curves
Considering the shape of the curve, stations were divided into “lowland”, “middle locations” and “mountain” locations. In all three groups mean relative water equivalent was determined for individual probabilities of non-exceedance. The different shape of the curve can be seen in Figure 1 (see [11] and [12]). A theoretical curve of the dependence of relative water equivalent on the probability of non-exccedance was designed. Relatively good accordance with empirical values is represented by the dependence in the form Y = a*Xc +b*Xd. In the above-mentioned equation X quantity expresses the probability of non-exceedance (0,0-1,0). The computed relative value Y = S maxS (0,0-1,0) multiplied by the value of extreme load maxS gives the absolute load value which will not be exceeded with corresponding probability X. Theoretical curves can serve as a basis for estimating snow load duration curves (and corresponding histograms) for any locality in the Czech Republic.
It can be emphasized that the existing normative (codified) regulations don’t take into consideration so far the influence of the difference between snow load duration in the mountains and in the lowlands (see, e.g., [13]).
Wind speed and direction measurements
According to the CHMI`s regulations wind speed and direction is measured at a height of 10 m above the terrain. Measurement is taken differently according to the type of station (see [7], [8], [9] and [10]):
a) At principal climatological stations with voluntary observers the wind speed is recorded using Metra anemoindicators (using Robinson cup cross as a sensor). Wind speed is taken three times a day and is given as a 10-minute average. These data have been stored in computers as part of climatological data since the year 1961.
b) Meteorological stations (there are almost 30 in the Czech Republic) were equipped with universe anemometers (their sensor consists of Robinson cross and sampling tubes for air pressure measurements). The following quantities have been registered: wind direction, average wind speed and momentary wind speed. Anemograms were formerly interpreted “handmade” and from the results monthly evaluation containing average hourly wind directions and speeds and also the highest daily momentary speeds at gusts used to be processed. The record from an anemograph also is used for determination of 10-minute speeds, eventually the highest gusts for the past period which then were part of some regular station reports (METAR, SYNOP, SYRED).
c) At the present time there are applied automatic measuring stations at meteorological stations. Wind speed and direction are continuously digitally recorded and it is therefore possible directly by means of computers to process frequencies of values for practically any sampling intervals. In view of the fact that only Robinson cross is used as a sensor, registered speeds are rather different from the values measured by the above-mentioned methods, see (a) and (b). At selected stations concurrent measurements are taken and the relationship between wind characteristics obtained from original and newly introduced measurements is considred and evaluated.
The One-Hour reports SYNOP and SYRED containing average 10-minute wind speed and direction, eventually the highest speed corresponding to the wind gust, were used for obtaining probability of non-exceedance of the given wind speed. From these data 3- and 10- second wind speeds for the whole processed period were computed. Altogether results of measurements of seven stations (Brno, Cheb, Kocelovice, Liberec, Lysá Hora, Mošnov (251 m a.s.l.) and Pøibyslav (530 m a.s.l.) were processed for the period 1982-1993.
For all seven stations tables of absolute and relative frequencies (including cumulative ones) of individual wind directions and speeds (3- and 10-second ones) and tables of wind speeds projected into single wind directions are at disposal.
A theoretical curve of distribution MAX1 (see [6]) was tested for frequencies without direction differentiation: V = Vo – (ln(-ln(P)) + 0,577) x 0,78 x S where V is wind speed in m/s, Vo represents average wind speed in m/s, P is probability of non-exceedance (0,0 to 1,0) and S is standard deviation in m/s.
Examples of the measurement results obtained from the station Praha- Ruzyne are in the following figures. Total relative cumulative frequencies of wind speed (its mean curves of the probability of non-exccedance, respectively curves of wind load duration) regardless of wind direction for the locality Praha-Ruzyne are shown in Figure 2. In Figure 3 is indicated the corresponding curve of the probability of non-exccedance for wind pressure. For the wind pressure calculation the formula w = V2/1,6 [11] was used.
Figures 2, 3, 4
In Figure 4 are frequencies of wind speeds projected into the direction 250° (it means into the direction for which the highest wind speeds was measured). In Figure 5 the two-component wind rosette indicates the wind velocity duration curves in twelve wind directions and corresponding histogram indicating the duration for these directions. For application of such rosette see examples discussed in [4] and computer programs [14].
Figure 5. Wind rosette applicable in probabilistic SBRA reliability assessment method
The given graphs is possible to process for different directions and create a new type of wind rosette for the given locality corresponding this two-component curve of load duration, eventually is possible to project curves of load duration into any direction.
Acknowledgements
The support of the Grant Agency of the Czech Republic (Projects No.103/94/0562, 103/96/K034, 103/01/1410 and 105/01/0783 is acknowledged.
References
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