39 6 2011 12 Journal of Fuzhou University Natural Science Edition Vol 39 No 6 Dec 2011 DOI CNKI 35-1117 /N 20111220 0901 002 1000-2243 2011 06-0923 - 07 350108 105 m 14 69% TU311 3 A Seismic analysis of long - span connected structures under multi - support and multi - dimensional earthquake excitations LIN Wei CHEN Shang - hong QI Ai HUANG Li - zhi College of Civil Engineering Fuzhou University Fuzhou Fujian 350108 China Abstract Seismic response of long - span connected structure under multi - dimensional and multi - support excitation is investigated Algorithms for seismic analysis under multi - dimensional and multi - support excitations are first established and the effect of different earthquake components and wave passage effect are analyzed And then numerical simulation is carried out on a long - span connected structure under one - dimensional and three - dimensional uniform and travelling wave excitations The results show that seismic response will be increased if multi - dimensional earthquake excitation was considered wave - passage effect will greatly amplify the seismic responses of vertical earthquake components the seismic responses of different elements can either be increased or decreased if wave passage effect was considered and great influence of wave passage effect was noticed for braces near connections between the main tower and corridor furthermore dominant internal force of the corridor structure may be increased by 14 69% under travelling wave excitation Therefore it is necessary for aseismic design of long - span connected structure to take into account of multi - dimensional and multi - support excitation Keywords long - span connected structure seismic analysis multi - dimensional excitation multi - support excitation 0 2011-05 - 06 1980 - E - mail cewlin@ fzu edu cn 51108089 2011J05128
924 39 1 LaDefense Arch Petronas Towers 2009 CCTV MOMA 2 3-4 5-6 Newmark 7 1969 Hahn Liu 8 Heredia - Zavoni Barranco 9 Heredia - Zavoni Leyva 10 1 11 M ss M sb M bs M bb Ẍ s Ẍb + C ss C sb C C bs bb s + K ss K sb K bs Kbb b M C K Ẍ b s F b 1 s b = 0 F b 1 M ss Ẍ s + M sb Ẍ b + C ss s + C sb b + K ss s + K sb b = 0 2 s Y s Y d 0 s b = Y s b + Y d 0 α = - K -1 ss K sb 3 Y s = - K -1 ss K sb b = α b 4
6 925 Y s 2 M ss Ÿ d + C ss Y d + K ss Y d = - M ss Ÿ s - C ss Y s - M sb Ẍ b - C sb b 5 Y 12 s 1 d 0 b 4 6 M ss Ÿ d + C ss Y d + K ss Y d = - M ss Ÿ s - M sb Ẍ b 6 M ss Ÿ d + C ss Y d + K ss Y d = - M ss α + M sb Ẍ b 7 K sb M sb M ss Ÿ d + C ss Y d + K ss Y d = - M ss αẍ b 8 8 2 2 1 60 50 m 105 00 m 39 85 m 55 85 m ANSYS ANSYS 1 ANSYS Matlab 1 x 1 Fig 1 Finite element model 2 2 ANSYS 10 1 2 6 1 2
926 39 Tab 1 1 10 First ten natural frequencies of the structure 1 2 3 4 5 6 7 8 9 10 f /Hz 0 790 0 831 1 015 1 158 1 306 1 631 1 668 2 135 2 236 2 756 Fig 2 2 6 First six mode shapes of the structure 2 3 1976 NS 0 15g x y z x y z 1 0 85 0 65 3 Fig 3 3 Time - history stress response under single - and multi - dimensional excitations
6 927 50001 50004 60048 3 50001 60048 43 7% 69 5% 50004 129 4% 3 c 8 s 4 100 m s - 1 50001 x 19 5% 50004 x 18 4% 22 1% 60048 24 3% 166 9% Fig 4 4 100 m s - 1 5 Time - history of stress responses under single - and Fig 5 Time - history stress responses under travelling wave multi - dimensional travelling wave excitations excitation with different apparent velocities
928 39 2 4 100 500 800 m s - 1 5 2 3 2 3 5 50001 100 m s - 1 31 3% 60048 100 m s - 1 37 4% Tab 2 2 Comparison of peak stress responses under multi - dimensional and multi - point excitations with different apparent velocities MPa 800 m s - 1 500 m s - 1 100 m s - 1 x 12 128 3 11 556 9 9 923 2 10 142 1 50001 17 651 4 13 265 1 14 678 1 10 217 8 17 661 8 16 539 4 15 037 0 12 120 4 x 9 459 4 10 358 9 8 707 6 8 927 3 50004 21 693 7 18 273 0 16 917 3 10 574 1 21 700 8 20 201 4 16 891 8 10 897 5 x 3 064 3 2 476 1 2 075 7 3 164 0 60048 5 193 1 4 893 0 4 990 8 3 935 9 6 146 4 5 671 4 4 408 0 8 445 9 Tab 3 3 Comparison of RMS stress responses under multi - dimensional and multi - point excitations with different apparent velocities MPa 800 m s - 1 500 m s - 1 100 m s - 1 x 4 880 7 4 687 1 4 103 5 4 543 0 50001 5 797 5 4 730 1 4 919 0 3 007 1 5 791 5 5 308 3 4 663 5 3 750 0 x 3 988 3 4 000 3 3 509 1 3 910 1 50004 7 370 2 5 132 1 6 137 8 3 318 4 7 359 5 6 628 3 5 764 8 3 246 1 x 1 260 4 1 151 4 0 983 3 1 421 8 60048 1 936 1 1 742 0 1 767 4 1 164 7 2 055 4 1 939 9 1 587 9 3 235 8 2 5 4 4
6 929 14 69% Tab 4 4 Locations and control forces of control bars under Tianjin earthquake excitations with different apparent velocities l /m p /MPa 12 30 28 931 5-800 m s - 1 12 30 29 462 0 1 83% 500 m s - 1 5 40 26 251 0-9 26% 100 m s - 1 2 70 33 182 8 14 69% 3 1 2 3 4 14 69% 1 J 2009 39 S2 7-10 2 J 2010 31 1 101-109 3 J 2009 29 1 50-57 4 Wang J Cooke N Moss P J The response of a 344 m long bridge to non - uniform earthquake ground motions J Engineering Structures 2009 31 11 2 554-2 567 5 J 2001 18 3 359-364 6 J 2010 26 1 1-6 7 Newmark N M Torsion in symmetrical buildings C / /Proceedings 4th World Conference Earthquake Engineering Santiago s n 1969 19-32 8 Hahn G D Liu Torsional response of unsymmetrical buildings to incoherent ground motions J Journal of Structural Engineering 1994 120 4 1 158-1 181 9 Heredia - Zavoni E Barranco F Torsion in symmetric structures due to ground motion spatial vibration J Journal of Engineering Mechanics 1997 122 9 834-843 10 Heredia - Zavoni E Leyva A Torsional response of symmetric buildings to incoherent and phase delayed earthquake ground motion J Earthquake Engineering and Structural Dynamics 2003 32 1 021-1 038 11 J 2007 24 3 97-103 12 J 2002 19 3 25-30