상시미동에 의한 에펠탑의 동적거동측정과 해석 요약

2016/10영신컨설턴트

 

Dynamic characterization of the Eiffel tower

상시미동에 의한 에펠탑의 동적거동 측정과 해석

 

Silvia Castellaro Dipartimento di Fisica e Astronomia, Università di Bologna, Italy

 

에펠탑 1889년 완공 높이 324m 16 기초 separate foundations. depth of 7 m

 

구조물의 주파수는 강성(k)과 질량(m)에 비례

지반과 상시미동 측정위치

 

지반의 주파수는 전단파속도(Vs)와 밀도(ρ) 암반깊이(H)와 관계된다.

Main facts and features of the Eiffel tower.

에펠탑 제원

  

상시미동 측정기

3-component tromometer Tromino (MoHo s.r.l.)

지반의 상시미동 측정 10분 측정 분당 512, 3 장소, 3축 측정, 30초 간격 공진 주파수 2Hz

주변지반 공진주파수 2Hz 측정

 

H/V와 분산곡선에 의한 암반심도 해석 50m

Joint fit of the H/V (panel A) and MASW (panel B) recordings to get a Vs profile of the subsoil (panel C). 지반의 H/V와 MASW 결합분석에 의한 심도별 지반 전단파속도

구조물 측정 사진

구조물 측정 위치 P stands for parallel (to the tower rim), D stands for diagonal, C for central.

구조물 측정 높이 55 116 270m에서 10분 분당1024개 측정

구조물 주파수 0.32Hz flexion / rocking ASD stands for Amplitude Spectral Density.

구조물 위치2에서 중심(1.3Hz) 중간(1.7Hz) 외부(2.1Hz) 비틁림 측정

Horizontal spectra recorded at the 3 levels in the two horizontal directions parallel to the tower rim in the frequency interval [0.8, 3]Hz.

Modules of the maximum horizontal displacement recorded at the different levels of the tower at the first 5 modal frequencies. The amplitude of the first flexion mode is much larger at the top level than the others (0.56 mm), so that it goes out of the image.   측정 mode mode 1 (0.3Hz)  맞지 않음    mode 2 (1Hz) mode 3 (1.2Hz) mode 4 (1.4Hz) mode 5 (1.7Hz)

유한요소해석 FEM

Summary of the main modal frequencies of the Eiffel tower.

No	Frequency [Hz]	Period [s]	Mode name/ mechanism	% of mass (horizontal only)	Justification
1	0.32	3.1	Horizontal flexion (I)	40	At this frequency the motion involves mostly the upper-thin part of the tower. A vertical motion (rocking) is observed at all levels and this implies a deformation of the ground and the fact that the soil-structure interaction cannot be neglected
2	1	1	Horizontal flexion (II)	7	Same linear velocity in the central and peripheral location. It is invisible at level 2
3	1.2	0.7	Torsion (I)	7	Lower linear velocity in the centre compared to the periphery, which is clearly visible at level 2
4	1.4	0.8	Horizontal flexion (III)	5	Same linear velocity in the central and peripheral location. It is invisible at level 2
5	1.7	0.59	Horizontal flexion (IV)	6	Same linear velocity in the central and peripheral location
6	2.1	0.48	Torsion (II)		Lower linear velocity in the centre compared to the periphery

유한요소해석과 측정값 비교

Comparison of the experimental and the modelled modal frequencies and mechanisms of the Eiffel tower.

Mode shapes of the first 5 modes of the Eiffel tower from the FEM. Torsion modes (3 and 5) are shown in the horizontal plane. Flexion modes (1, 2, 4) are shown in the vertical plane.

real ground motions (accelerations) with PGA0 = [0.05, 0.1]g

Response spectra computed for each input ground motion

(A) Values (in MPa) of the dead stress on the main beams; (B) of the stresses induced on the beams from the average + 1 standard deviation earthquake expected at the site with a 2% probability of being exceeded in 50 years (centre); and (C) sum of the stresses in (A) and (B).

평상시와 지진시 응력

해석응력 Forces in the beams (for each leg) as computed by Eiffel

Displacement (in cm) of the tower (A) for a uniform wind load of 3 kN/m2 and (B) for a linearly increasing wind load from 2 to 4 kN/m2. 바람에 의한 변위