- Email: [email protected]
Reply to Discussion of “Specifications of the design wind load based on wind tunnel experiments” [J. Wind Eng. Ind. Aerodyn. 91 (2003) 527–541]
ARTICLE IN PRESS
Journal of Wind Engineering and Industrial Aerodynamics 92 (2004) 781–785
Discussion
Reply to Discussion of ‘‘Specifications of the design wind load based on wind tunnel experiments’’ [J. Wind Eng. Ind. Aerodyn. 91 (2003) 527–541]$, $$ M. Kasperski* Department of Civil Engineering, Ruhr-University Bochum, D-44780 Bochum, Germany
The author appreciates the interest in his work and would like to respond to the comments as follows: In the first comment of the discussion the importance of ‘higher orders’ is pointed out. ‘Higher orders’ are required to take into account that in a single year more than one storm may occur and that a storm may last for more than 1 h. While the first point is included in the study, the second influence has been neglected in the actual study. The wind climate of Germany is governed by frontal depressions which have an average duration of 3 h and show on average a decreasing relative intensity for the second and third strongest hour with reduction factors of 0.97 and 0.93, respectively. The additional influence of the duration on the adjusting factor can be seen in Fig. 11 for the case that both variables follow a type distribution. The influence is becoming even smaller when the extreme wind speeds follow a type III distribution, as is shown in Fig. 12. On the other hand, the effect of the duration may become considerable, if the relative intensity in the second to nth storm hour is not decreasing. The second comment of the discusser refers to an almost 30-year-old paper by Peterka and Cermak [15] where it is stated that the parent distribution of pressures that have a mean value larger than 0.1 is close to a normal distribution and that $
doi of original article: 10.1016/j.jweia.2003.10.001 This Reply to the Discussion of ‘‘Specification of the design wind load based on wind tunnel experiments’’ which was published in J. Wind Eng. Ind. Aerodyn. 92 (2004) 71–76, was received and accepted immediately following the acceptance of the Discussion. It was intended for them to be published simultaneously. The Publishers regret that this Reply was delayed. *Tel.: +49-234-322-4148; fax: +49-234-321-4317. E-mail address: [email protected] (M. Kasperski).
$$
0167-6105/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jweia.2004.05.001
ARTICLE IN PRESS 782
M. Kasperski / J. Wind Eng. Ind. Aerodyn. 92 (2004) 781–785
Fig. 11. Adjusting factor for the influence of the duration (extreme value distribution v and c, type I).
τv = 0.1
τv = 0.2
Fig. 12. Adjusting factor for the influence of the duration (extreme value distribution c: type I, extreme value distribution v: type III).
pressures with a considerable negative mean value smaller than 0.25 show a skewed distribution. The respective figures in the alleged paper show a large scatter indicating that a refined analysis based on much more data (as they can be easily achieved today) may lead to different results and conclusions. Fig. 13 shows four examples of probability densities along the centre bay of the investigated low-rise building. Clearly, the positive pressures are not following a normal distribution. Furthermore, not all negative pressures show a considerably skewed probability distribution. The conclusion that the Central Limit Theorem will lead to a normal distribution for the structural responses does not hold true. Neither is the number of contributions large, nor are the single contributions independent. Fig. 14 shows the respective probability distributions for the upwind and downwind bending moment for a static system with a hinged support. Both distributions are clearly not normal. Comment three deals with the asymptotic behaviour of the hourly mean wind speeds v and the corresponding squared values q ¼ v2 : For the author, it is still difficult to understand why in Cook [16] all hourly mean wind speeds are assumed to be parent for extreme wind speeds since clearly there are more physical processes
ARTICLE IN PRESS M. Kasperski / J. Wind Eng. Ind. Aerodyn. 92 (2004) 781–785
stagnation upwind wall
reattachment downwind roof
783
separation leading edge
downwind wall
Fig. 13. Typical probability density distributions for fluctuating pressures.
upwind bending moment
downwind bending moment
Fig. 14. Typical probability density distributions for wind action effects.
contributing to the hourly mean wind speeds than are contributing to the extreme wind speeds. Furthermore, it should be noted that fitting v2 to a type I distribution leads to a trace of the non-exceedence probabilities plotted versus v that is curved in regard to the horizontal axis. Note, that fitting a type III distribution for v with a curvature parameter of t ¼ 0:082 will lead to a trace which can hardly be distinguished from the trace obtained fitting v2 to a type I distribution (see Fig. 15). The author agrees basically with comment number four, i.e. using the Poisson approach leads to better estimates for the whole range of non-exceedence probabilities of the extreme wind speeds. It is worth mentioning that in this context
ARTICLE IN PRESS M. Kasperski / J. Wind Eng. Ind. Aerodyn. 92 (2004) 781–785
784
0.999
non-exceedence probabilty
trace of v² following type I distribution trace of v following type III with τ = 0.082 0.99
0.9
0.5 0.1 0.01 0.001 0
5
10
15
20
25
30
v [m/s]
σ
σ
Fig. 15. Comparison of the trace of v2 following a type I distribution to the trace of v following a type III distribution with t ¼ 0:082:
stagnation upwind wall
separation leading edge
Fig. 16. Spectral densities of local pressures along the centre bay of low-rise building.
the definition of the epoch 1 year should not be based on a calendar year but on the wind season, e.g. from September 1 of 1 year to August 31 of the following year for frontal depressions in Western Europe. A redesign of wind tunnel tests for the analysis of extreme wind loads in thunderstorm downburst is also required due to the fact that the characteristic features of the respective wind fields may be considerably different to the usually modelled features of an idealised frontal depression. In comment five, the discusser gives possible explanations for the curvatures in some of the traces of the observed non-exceedence probabilities in the wind tunnel. The author agrees with the discusser that today’s wind tunnel techniques are still far from being perfect and that for local pressures a ‘peak-clipping effect’ might be obtained. Mismatches are usually larger in regions with separated flow and are smaller for regions in the upwind position of a model. The effect of ‘filtering’ can be evaluated with the spectral densities of the respective signals. Fig. 16 suggests that the respective influence of an erroneously filtered contribution of the variance is
ARTICLE IN PRESS M. Kasperski / J. Wind Eng. Ind. Aerodyn. 92 (2004) 781–785
785
small. For the structural responses, on the other side, the structure itself is the major filter which reduces local high-frequent components since they are correlated only over small areas. Therefore, the wind tunnel predictions for structural responses will be closer to nature than the predictions of local pressures. The description of the obtained traces in the probability paper finally is performed rather from a practical point of view, where—following Castillo [19]—the wrong rejection of a Gumbel-type distribution can be corrected in the estimation process that follows this decision. In comment six, the discusser addresses the problem of identifying erroneously a type III distribution for the extreme wind speeds. The author agrees that a certain confidence level has to be introduced to specify the design values for the windinduced actions and their respective effects in terms of structural responses. However, it has to be stated, that the proposed target confidence interval of 95% for specifying the design value of a load on the safe side is in contradiction to the recommendations used for the resistance side where a confidence level of ‘only’ 75% is introduced. The final comment of the discusser addresses a supposed logical absurdity. As can be seen in Fig. 15, from a practical point of view it is not important if v2 is fitted to a GEV (which of course leads to an identified curvature parameter t ¼ 0) or if v is fitted to a GEV which leads to an identified curvature parameter t ¼ 0:082: The design values having a non-exceedence probability of 0.999 are almost the same with vd ¼ 29:89 m/s in case of fitting v2 and vd ¼ 29:74 m/s in case of fitting v, leading to a difference in the design wind load of only 1%.
Journal of Wind Engineering and Industrial Aerodynamics 92 (2004) 781–785
Discussion
Reply to Discussion of ‘‘Specifications of the design wind load based on wind tunnel experiments’’ [J. Wind Eng. Ind. Aerodyn. 91 (2003) 527–541]$, $$ M. Kasperski* Department of Civil Engineering, Ruhr-University Bochum, D-44780 Bochum, Germany
The author appreciates the interest in his work and would like to respond to the comments as follows: In the first comment of the discussion the importance of ‘higher orders’ is pointed out. ‘Higher orders’ are required to take into account that in a single year more than one storm may occur and that a storm may last for more than 1 h. While the first point is included in the study, the second influence has been neglected in the actual study. The wind climate of Germany is governed by frontal depressions which have an average duration of 3 h and show on average a decreasing relative intensity for the second and third strongest hour with reduction factors of 0.97 and 0.93, respectively. The additional influence of the duration on the adjusting factor can be seen in Fig. 11 for the case that both variables follow a type distribution. The influence is becoming even smaller when the extreme wind speeds follow a type III distribution, as is shown in Fig. 12. On the other hand, the effect of the duration may become considerable, if the relative intensity in the second to nth storm hour is not decreasing. The second comment of the discusser refers to an almost 30-year-old paper by Peterka and Cermak [15] where it is stated that the parent distribution of pressures that have a mean value larger than 0.1 is close to a normal distribution and that $
doi of original article: 10.1016/j.jweia.2003.10.001 This Reply to the Discussion of ‘‘Specification of the design wind load based on wind tunnel experiments’’ which was published in J. Wind Eng. Ind. Aerodyn. 92 (2004) 71–76, was received and accepted immediately following the acceptance of the Discussion. It was intended for them to be published simultaneously. The Publishers regret that this Reply was delayed. *Tel.: +49-234-322-4148; fax: +49-234-321-4317. E-mail address: [email protected] (M. Kasperski).
$$
0167-6105/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jweia.2004.05.001
ARTICLE IN PRESS 782
M. Kasperski / J. Wind Eng. Ind. Aerodyn. 92 (2004) 781–785
Fig. 11. Adjusting factor for the influence of the duration (extreme value distribution v and c, type I).
τv = 0.1
τv = 0.2
Fig. 12. Adjusting factor for the influence of the duration (extreme value distribution c: type I, extreme value distribution v: type III).
pressures with a considerable negative mean value smaller than 0.25 show a skewed distribution. The respective figures in the alleged paper show a large scatter indicating that a refined analysis based on much more data (as they can be easily achieved today) may lead to different results and conclusions. Fig. 13 shows four examples of probability densities along the centre bay of the investigated low-rise building. Clearly, the positive pressures are not following a normal distribution. Furthermore, not all negative pressures show a considerably skewed probability distribution. The conclusion that the Central Limit Theorem will lead to a normal distribution for the structural responses does not hold true. Neither is the number of contributions large, nor are the single contributions independent. Fig. 14 shows the respective probability distributions for the upwind and downwind bending moment for a static system with a hinged support. Both distributions are clearly not normal. Comment three deals with the asymptotic behaviour of the hourly mean wind speeds v and the corresponding squared values q ¼ v2 : For the author, it is still difficult to understand why in Cook [16] all hourly mean wind speeds are assumed to be parent for extreme wind speeds since clearly there are more physical processes
ARTICLE IN PRESS M. Kasperski / J. Wind Eng. Ind. Aerodyn. 92 (2004) 781–785
stagnation upwind wall
reattachment downwind roof
783
separation leading edge
downwind wall
Fig. 13. Typical probability density distributions for fluctuating pressures.
upwind bending moment
downwind bending moment
Fig. 14. Typical probability density distributions for wind action effects.
contributing to the hourly mean wind speeds than are contributing to the extreme wind speeds. Furthermore, it should be noted that fitting v2 to a type I distribution leads to a trace of the non-exceedence probabilities plotted versus v that is curved in regard to the horizontal axis. Note, that fitting a type III distribution for v with a curvature parameter of t ¼ 0:082 will lead to a trace which can hardly be distinguished from the trace obtained fitting v2 to a type I distribution (see Fig. 15). The author agrees basically with comment number four, i.e. using the Poisson approach leads to better estimates for the whole range of non-exceedence probabilities of the extreme wind speeds. It is worth mentioning that in this context
ARTICLE IN PRESS M. Kasperski / J. Wind Eng. Ind. Aerodyn. 92 (2004) 781–785
784
0.999
non-exceedence probabilty
trace of v² following type I distribution trace of v following type III with τ = 0.082 0.99
0.9
0.5 0.1 0.01 0.001 0
5
10
15
20
25
30
v [m/s]
σ
σ
Fig. 15. Comparison of the trace of v2 following a type I distribution to the trace of v following a type III distribution with t ¼ 0:082:
stagnation upwind wall
separation leading edge
Fig. 16. Spectral densities of local pressures along the centre bay of low-rise building.
the definition of the epoch 1 year should not be based on a calendar year but on the wind season, e.g. from September 1 of 1 year to August 31 of the following year for frontal depressions in Western Europe. A redesign of wind tunnel tests for the analysis of extreme wind loads in thunderstorm downburst is also required due to the fact that the characteristic features of the respective wind fields may be considerably different to the usually modelled features of an idealised frontal depression. In comment five, the discusser gives possible explanations for the curvatures in some of the traces of the observed non-exceedence probabilities in the wind tunnel. The author agrees with the discusser that today’s wind tunnel techniques are still far from being perfect and that for local pressures a ‘peak-clipping effect’ might be obtained. Mismatches are usually larger in regions with separated flow and are smaller for regions in the upwind position of a model. The effect of ‘filtering’ can be evaluated with the spectral densities of the respective signals. Fig. 16 suggests that the respective influence of an erroneously filtered contribution of the variance is
ARTICLE IN PRESS M. Kasperski / J. Wind Eng. Ind. Aerodyn. 92 (2004) 781–785
785
small. For the structural responses, on the other side, the structure itself is the major filter which reduces local high-frequent components since they are correlated only over small areas. Therefore, the wind tunnel predictions for structural responses will be closer to nature than the predictions of local pressures. The description of the obtained traces in the probability paper finally is performed rather from a practical point of view, where—following Castillo [19]—the wrong rejection of a Gumbel-type distribution can be corrected in the estimation process that follows this decision. In comment six, the discusser addresses the problem of identifying erroneously a type III distribution for the extreme wind speeds. The author agrees that a certain confidence level has to be introduced to specify the design values for the windinduced actions and their respective effects in terms of structural responses. However, it has to be stated, that the proposed target confidence interval of 95% for specifying the design value of a load on the safe side is in contradiction to the recommendations used for the resistance side where a confidence level of ‘only’ 75% is introduced. The final comment of the discusser addresses a supposed logical absurdity. As can be seen in Fig. 15, from a practical point of view it is not important if v2 is fitted to a GEV (which of course leads to an identified curvature parameter t ¼ 0) or if v is fitted to a GEV which leads to an identified curvature parameter t ¼ 0:082: The design values having a non-exceedence probability of 0.999 are almost the same with vd ¼ 29:89 m/s in case of fitting v2 and vd ¼ 29:74 m/s in case of fitting v, leading to a difference in the design wind load of only 1%.