대한토목학회 2001 년도 학술발표대회 풍하중을 받는 구조물의 3 차원 유한요소해석 Three-dimensional Finite Element Analyses of Structures under Wind Loads 김병완 1), 김운학 2), 이인원 3) 1) 한국과학기술원 토목공학과 박사과정 2) 국립한경대학교 토목공학과 교수 3) 한국과학기술원 토목공학과 교수

2 Contents 1. Introduction 2. Beam analyses of wind-loaded structures 3. Plate analyses of wind-loaded structures 4. Numerical example 5. Conclusions

3 1. Introduction Systematic comparison of simplified beam analyses and three- dimensional plate analyses is presented to verify disadvantages of simplified beam analyses of structures under wind loads. 2. Beam analyses of wind-loaded structures - Structural modeling with finite beam elements - Evaluation of lift, drag and moment coefficients - Calculation of lift, drag and moment per unit length - Solution of dynamic equation of motion 3. Plate analyses of wind-loaded structures - Structural modeling with triangular finite plate elements - Evaluation of pressure coefficient at each element - Calculation of wind load vector at each element - Solution of dynamic equation of motion

4 4. Numerical example Young’s modulus: 2.5  10 5 kgf/cm 2 mass density:  kgf-sec 2 /cm 4 thickness: 60 cm Poisson ratio: 0.17 damping ratio: 5 % Example structure Example wind based on the data at Skipheia(K.S. Hansen and M.S. Courtney, 1999) wind density:  kgf-sec 2 /cm 4  (angle of attack): 15, 30, 45, 60, 75 and 90 degree

5 Pressure coefficients of the example structure Lift, drag and moment coefficients of the example structure calculated from Abernathy's formula(F.H. Abernathy, 1962) Finite element model of the example structure finite beam element modelfinite plate element model

6 max. torsional moments at the edge line Member forces max. bending moments at the center line max. principal stresses at the center line

7 Member forces along the width directions bending moments along the center line (time: 154sec) torsional moments along the edge line (time: 154 sec)

8 5. Conclusions -Bending moments and principal stresses from beam analyses are similar to those from plate analyses. On the other hand, torsional moments from beam analyses are quite different from those from plate analyses. -Member forces which vary along width directions can be obtained from plate analyses, whereas those cannot be exactly calculated from beam analyses due to the limitation of the analyses that constant member forces are obtained along width directions. -Therefore, three-dimensional plate analyses are required to exactly calculate torsional moments and width-directional member forces of structures under wind loads, instead of simplified beam analyses.