Euro-SiBRAM’2002 Prague, June 24to 26, 2002, Czech Republic

Session 5

The SBRA method as the powerful technique for probabilistic design in aerodynamics and aeroelasticity of civil engineering structures

Prof. Miroš Pirner

Institute of Theoretical and Applied Mechanics

Academy of Sciences of the Czech Republic, Prosecká 76, 19000 Praha 9

pirner@itam.cas.cz

1.  Introduction

For a probabilistic reliability assessment and design of civil engineering structures it is important to have a knowledge about the variation of all relevant variables. In the area of aerodynamics and aeroelasticity the method SBRA [8] is very profitable; it fulfils all requirements of designer for determination of the response to the loadings and calculation of the probability of failure.

In [1] the static and dynamic response of TV tower shown in Fig. 1 from the view of the ability to receive the defectiveless television signal is published. The requirement of top displacement 0.91m at 99% of the operating time can be expressed as  , where  is the probability of exceeding  the 0.91 m deflection and  =0.01. The resulting amplitude of the tower top is (according to ENV [2])

                                                                (1)

Supposing that the tower deflection curve corresponds to its fundamental natural mode (with  )  we receive the safety function SF

                        .                                                                              (2)

The probability corresponding to  is calculated using the  M-Star program. The out put from the M-Star program is shown in Fig. 2. The probability of exceeding  and so the tower meets the serviceability requirement.

Fig. 1 TV tower exposed to wind load

Fig. 2 Magnitude of the resulting amplitude; output from the M-Star program

2. And now few examples in which the SBRA method is the powerful technique
The effects of the static wind action manifest themselves most intensely in the wind direction. The total along-wind force acting on a structure is usually defined by the equation

                                                                                        (3)

where  (from view of designer) are given deterministic. The wind speed  is the probabilistic value and    aerodynamic drag coefficient strong depends on the wind speed (Fig. 3a) and on turbulence intensity (Fig. 3b).

Using M-Star program; wind duration curve [8] and relations from Fig. 3 we receive the probabilistic value of  drag force  .

Vincenc Strouhal as early as 1878 [7] described the vortex trail with a frequency

                                                                                                (4)

where   is Strouhal number and  is  diameter of cylinder

Fig. 3a  Effect of   number on drag coefficient   [3]

 Fig. 3b  Effect of Renumber and turbulence intensity   on drag coefficient  [4]

Fig. 4a  Effect of Re number on Strouhal number    [5]

 Fig. 4b  Effect of Re number on Strouhal number at different turbulence intensities [6]

But   the   Strouhal   number    depends   on   wind   speed   and   the   turbulence   intensity (Fig. 4). Using  M-Star program we receive the probabilistic value of shedding frequency.

Parallel transmission line cables whose cross-section lie in the horizontal plane become unstable under certain conditions of wind and spacing. This loss of stability is caused by forces acting on a cable in the wake of another. The onset wind velocity of wake galloping is given by formula [7]

                                                                  (5)

where

                                is the mass of the unit length

                                logarithmic damping coefficient

                              first natural frequency

                                air density

                               diameter

                        aerodynamic coefficients of lift and drag

                                angle  (Fig.5)

Fig. 5 Cross-section of parallel transmission lines

From view of designer the values   are given deterministic, bat   strong depend on the wind speed    and turbulence intensity. Using M-Star program we receive the probabilistic value of onset velocity 

2.      Summary and conclusions

Aerodynamics and aeroelasticity of civil engineering structures include the wind effects as a random process and therefore the structural response enables the engineer to describe dynamic processes more accurately than by means of the deterministic methods used at present. The Simulation Based Reliability Assessment method [8] applied  in the paper can serve as a powerful tool.

Acknowledgement

This article was supported by research project GACR 103/01/0020 and 103/01/1410..

References  

[1] Marek, P., Brozetti, J., Gustar, M. (editors): Probabilistic assessment of structures, TeReCo, Prague 2001.

[2]  ENV 1991 – Zásady navrhování a zatížení konstrukcí STN P ENV 1991-2-4.

[3]  Pirner, M.: Aeroelasticity of a cylinder (in Czech), Academia, Prague, Study 15, 1990.

[4] Wooton, L.R.: The oscillations of model circular stacks due to vortex shedding at Re  numbers 10⁵÷3.10⁶, Symp. on Wind Effects on Buildings and Structures, Loughborough, University,1968.

[5]  Žuranski, J.A.: Windeinflüsse auf Baukonstruktionen, Verlag Arkady, Warszawa, 1978.

[6] Bearman, P.W.: Some effects of turbulence on the flow around bluff bodies, Symp. on Wind Effects on Buildings and Structures, Loughborough University, 1968.

[7] Koloušek, V. and al.: Wind effects on civil engineering structures, Academia, Prague 1983.

[8] Marek, P., Guštar, M., Anagnos, T.: Simulation-based reliability assessment, CRC Press, 1996.