1. 한국강구조학회 2001 년도 학술발표대회 Three Dimensional Finite Element Analysis of Structures under Wind Loads *Byoung-Wan Kim 1), Woon-Hak Kim 2) and In-Won Lee 3) 1) Ph.D. Candidate, Department of Civil Engineering, KAIST 2) Professor, Department of Civil Engineering, Hankyong Univ. 3) Professor, Department of Civil Engineering, KAIST

2. 2 1. introduction 2. analysis procedures of wind-loaded structures - beam analysis procedure - plate analysis procedure 3. numerical examples 4. analysis results 5. conclusions Contents

3. 3 1. introduction 1)Compare conventional simplified beam analyses with exact three dimensional plate analyses through numerical examples with plates under wind loads 2)Show the disadvantages of conventional beam analyses of wind-loaded structures

4. 4 2. beam analysis procedure 1) finite element modeling with beam elements 2) evaluate lift coeff., drag coeff. and moment coeff. 3) calculate distributed lift forces, drag forces and moments 4) solve equation of motion Ref.) Simiu, Emil and Scanlan, Robert H., Wind Effects on Structures, John Wiley & Sons, Inc., 1996.

5. 5 3. plate analysis procedure 1) finite element modeling with triangular plate elements 2) evaluate pressure coeff. 3) calculate wind load vectors 4) solve equation of motion

6. 6 4. numerical examples Young’s modulus: 2.5  10 5 kgf/cm 2 Poisson ratio: 0.17 thickness: 60 cm density: 2.446  10 -6 kgf-sec 2 /cm 4 damping ratio: 5 % 6 m 30 m center lineedge line example structures

7. 7 Skipheia, Norway, 1993 density: 1.250  10 -9 kgf-sec 2 /cm 4 - time history of wind velocity example winds Ref.) Hansen, Kurt S. and Courtney, Michael S., “http://www.winddata.com,” 1999 European Wind Energy Conference, March 1-5, 1999 in Nice, France.

8. 8 15º 45º - wind direction (angle of attack) x yz 60º 90º z yx 30º 75º

9. 9 evaluation of pressure coeff. C pb C pl z y Ref.) Abernathy, F. H., “Flow over an Inclined Plate,” Journal of Basic Engineering -Transactions of the ASME, vol. 84, 1962, pp. 380-388.

10. 10 - transformed coordinates along plate width direction - real coordinates along plate width direction

11. 11 - parameters

12. 12 evaluation of lift coeff. and moment coeff.

13. 13 pressure coeff. distriutions lift coeff. and moment coeff.

14. 14 modeling with beam elements modeling with plate elements - number of nodes: 31 - number of beam elements: 30 - number of nodes: 217 - number of plate elements: 360

15. 15 5. analysis results bending moments at center line

16. 16 torsional moments at edge line

17. 17 principal stresses at center line

18. 18 distributed bending moments along center line time = 154 sec

19. 19 distributed torsional moments along edge line time = 154 sec

20. 20 6. conclusions 1)Bending moments and principal stresses from beam analyses are similar to those from plate analyses but torsional moments are not. 2)It is possible to get member forces which are variant along width directions from plate analyses but not from beam analyses due to constant distributions of member forces along width directions. 3)Instead of conventional simplified beam analyses, exact three dimensional plate analyses are required in the analyses of wind-loaded structures.