Seismic Design of Slender Structures Including Rotational Components of the Ground Acceleration Eurocode 8 Approach

Transcription

1 Seismic Design of Slender Structures Including Rotational Components of the Ground Acceleration Eurocode 8 Approach Z. Bonev E. Vaseva D. Blagov K. Mladenov 1 Chimneys Masts Towers

2 2 EN : 2005 TOWERS, CHIMNEYS and MASTS NUMERICAL MODEL of the STRUCTURE Prepared on the basis of finite elements 3D FRAME ELEMENTS SHELL ELEMENTS allowing for typical spatial deformation

3 3 SEISMIC ACTION MODEL TAKING INTO ACCOUNT SPATIAL VARIABILIRY IN-PLANE MOTION TRANSLATIONAL COMPONENT of GROUND ACCELERATION ANALYSIS APPROACH: RESPONSE SPECTRUM METHOD Elastic spectrum, type 1 Elastic spectrum, type 2 Shape of design spectra, ground type C

4 4 TRANSLATIONAL COMPONENT of GROUND ACCELERATION m 20 { } T ν = { } VECTOR OF TRANSFERRED MOTION m k ( ) E = m Φ Γ S T ik k ik i e i DESIGN SEISMIC LOAD, MODE i Tot { } [ ]{ ν ν } T m 1 { } [ ]{ Φ } i m ν Γ = i T M m m = = M i k k TOTAL MASS PARTICIPATION FACTOR, MODE i

5 5 TRANSLATIONAL COMPONENTS of GROUND ACCELERATION PEAK MODAL RESPONSES FOR SHEAR AND BENDING MOMENT AT THE E BASE 2 m BASE SHEAR, MODE i 20 Vi = Γi Mi Se Ti ( ) ( ) K. A. GUPTA m k m 1 M =Γ Γ MhS T V ρ nm = ( ) θ i i i i e i = ρ V V ij i j i j ( ) E = m Φ Γ S T ik k ik i e i M 8ξ 1 BASE MOMENT, MODE i K. A. GUPTA NEED FOR MODAL COMBINATION - CQC RULE = ρ M M ij i j i j ( + r ) 2 3/ 2 nm nm 2 2 ( 2 ) 2 1 rnm + 4ξ rnm ( 1+ rnm ) r

6 6 SEISMIC ACTION MODEL TAKING INTO ACCOUNT SPATIAL VARIABILITY ROTATIONAL COMPONENTS of GROUND ACCELERATION Rayleigh waves Love waves

7 7 ROTATIONAL COMPONENTS of GROUND ACCELERATION w&& g θ&& z,g v&& g θ&& y,g ϕ&& u&& g θ&&,g k θ θ&& g c θ Translational and rotational ground accelerations of the ground surface Rotational SDOF for rotational spectrum definition

8 8 S θ ( T) ROTATIONAL COMPONENTS of GROUND ACCELERATION Se ( T) θ = 1.7π S ( T) VT. s y ( T) Se 1.7π VT. θ = S ( T) s z ( T) Se = 2.0π VT. s Response spectra S θ and scaled to DGA = 0.27g S θ y Response spectrum scaled to DGA = 0.27g z S θ

9 9 ROTATIONAL COMPONENTS of GROUND ACCELERATION m 20 T { θ ν } = { } VECTOR OF TRANSFERRED MOTION m k ( ) E = m Φ Γ hs T θ θ θ ik k ik i i DESIGN SEISMIC LOAD, MODE i { θ} T [ ]{ θ} ( θ ν ν ν ) 2 M m m = = Tot k k k TOTAL MASS m 1 Γ = θ i T { } [ ]{ θ Φ } i m ν M i PARTICIPATION FACTOR, MODE i

10 10 ROTATIONAL COMPONENTS of GROUND ACCELERATION PEAK MODAL RESPONSES FOR SHEAR AND BENDING MOMENT AT THE E BASE m 20 m k V =Γ Γ M hs T ( ) E = m Φ Γ hs T θ θ θ ik k ik i i ( ) θ θ θ i i i i i ( ) 2 2 ( ) M = Γ MhS T θ θ θ i i i i BASE SHEAR, MODE i BASE MOMENT, MODE i V NEED FOR MODAL COMBINATION - CQC RULE = ρ V V M ijmi M j = ρ θ θ θ θ θ θ ij i j i j i j NEED FOR COMPONENT COMBINATION OF ACTION EFFECTS - SRSS m ( = ) + ( ) ( ma M = M ) + ( M θ ) mav V V θ 2 2

11 11 h = 60 m ( < 80 m nationally determined parameter, National Anne) a g S = 0.27g > 0.25g Elastic design spectrum Type 1 ANALYSIS DATA Elastic design response spectrum for horizontal accelerations, ground type C, a g = 0.27g, ξ = 5% Elastic design response spectrum for rotational accelerations around horizontal ais, ground type C, a g = 0.27g, ξ = 5%

12 12 i M i M ( Γ ) 2 i 1 Tot NUMERICAL EXAMPLE CRITERION FOR EVALUATION THE SUFFICIENCY OF THE MODES INCLUDED

13 13 BASE MOMENT: MODAL CONTRIBUTION assuming only translational component (solid line) and assuming only rotational component (dashed line)

14 BASE MOMENT: assuming both translational and rotational components (solid line) and assuming only translational component (dashed line) 14 INCLUSION of ROTATIONAL COMPONENT OVERESTIMATES 11% the RESULTS for BASE MOMENT and BASE SHEAR 11%

15 15 CONCLUSIONS: 1. Implementation of rotational ground acceleration components is an efficient method to account for the special variability of seismic ic action. 2. For tall and slender structures the influence of the rotational component is essential and cannot be neglected otherwise the design action effects will be underestimated. The influence of rotational component is larger when the height of the structure is greater. 3. The contribution of higher mode response considering rotational type of the motion should be studied carefully in each case. 4. Response spectrum method can be etended and upgraded by making use of rotational response spectra.

16 ACKNOWLEDGEMENTS: 16 The support and help of the following institutions are greatly acknowledged by the authors: Macedonian Association of Earthquake Engineering (MAEE), Personally to Prof. M. Garevski,, the President; Organizing Committee of the 14-th ECEE, Personally to Prof. M. Garevski, the Chairmen; IZIIS Skopje, Republic of Macedonia, Personally to Prof. M. Garevski,, the Director and Prof. Golubka Necevska-Cvetanovska Cvetanovska,, the Deputy Director; Chamber of Engineers in the Investment Design City of Sofia, Personally to Eng. D. Nachev the President; Ministry of Regional Development and Public Works Sofia, Personally to Eng. V. Angelieva,, Eng. S. Georgieva; Central Laboratory for Seismic Mechanics and Seismic Engineering, g, Bulgarian Academy of Sciences, Personally to Prof. Sv. Simeonov,, the Director.

17 17 THANK YOU for YOUR KIND ATTENTION!