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Structural Dynamics

by: Karson Dicki

Structural Dynamics CEE 511

Karson Dicki
GPA 3.76

Jerome Lynch

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Jerome Lynch
Class Notes
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This 9 page Class Notes was uploaded by Karson Dicki on Thursday October 29, 2015. The Class Notes belongs to CEE 511 at University of Michigan taught by Jerome Lynch in Fall. Since its upload, it has received 20 views. For similar materials see /class/231669/cee-511-university-of-michigan in Civil and Environmental Engineering at University of Michigan.

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Date Created: 10/29/15
E J I i ggmss 75 MODKL ramzm Awwgtg axrmquot 0N STKU Tmar Far s gtth a g m c1 m M E lirlawu m Mobxx RESPOHSEe g l vw bag AwL Maw 36PZNSEQ LanaMM E w wy M eamgk Lax E ggg s E 1ampng Q z B ZMJ 56 Comng Mama 7 Mame we me n TALGD ST 3 quotgamequot ngeaza a6 New LI Due 17 LOAD FAWN 5 o ALLJQ Is 3931201 Accepaz nm AmidJD DEAK Mom sPomga mm If A i TSKC i ZgtH7 asi am FEM K6H S PWU Response spectrum for El Centro ground motion C O 2 5 10 and 20 100 J O O U Pseudovelocity V insec 3 05 002 1 005 01 02 05 1 2 5 1O 20 50 J Natural vibration period Tn sec Figure 564 lrom Dynamics of Structures Theory andApplications to Earlhquake Engineering by Anil K Chopra PrenticeHall 2001 I I i i g M Err 07 WOULD e 5 If F wxra a2 91 AF WHEES 1 WW 1 Yang 5045196 3 MAX m alwagwaz MawVa G 2339ng Saw uff 4 Wm iquot I LJHMJKI E ak Easy an ae ga wm 3 aaam SEW1a f m w 399 me Qua Qawgmg Camsmmwg msa Smma wrwf ma Saumg g am 229 Law L24 um am Age 313134 x 2ngmgtz 2 Afmzmm warlt5 mi Wm Mawgm are wad m6 Mam eswugas am ma arra g wz C3 COMW QUA DR iav Ce x g iag CC 62 we W Amsw JUAN a Carra aifm a ipgmi befwepm 1 mm 1 i m 22141 50 SHEETS 22142 109 SHEETS 22144 200 SHEETS gimpm OH 2 3 ig 3 ifz 2 1 5 4 3353 1ng 1 U Laid4 g E fei cegf j Egygy gg SK3S I Siamg Came g 0amp0 WM Wow Mug MMM Wodle V9363 Eata Correlaticn coefficient 1 Eq 1378 Eq 13710 08 E 39 9 I 8 0 6 I 63 39 8 l39 C 020 C I quot e x J E l 39 2 04 B x O 010 I O 2 I 005 I 002 O 39 l I l l l 39 39 39 05 06 07 08 09 1 15 2 Frequency ratio 3 03 0 Figure 1371 from Dynamics of Structures Theory and Applications to Earthquake Engineering by Anil K Chopra PrenticeHall 2001 Exajnple A ve story shear building m m 100kipsg k k 3154cipsin h h 12ft FloorMas SwrySdffncss u m 4 k 143 In I n k u m 1 2 1 1 1 2 1 Mm 1 KIc 1 2 1 1 1 2 l 1 1 1 The natural frequencies modes and modal properties are computed as follows M1202851k w20831H k L 13l310 li m m m k H 114 1682 115 1919 m m T1 20SeC T2 068528ec T3 043465ec T4 03383sec T5 029663ec modal vectors I am 0395 0334 0395 Mod a m 10 P 1 1067 F2 0336 530177 F4 0099 F50045 ill3413C l scmlnvclm ily Iquot quot IquotI 139 7 l u 0 0 LA 0 o L p M Id u u o J 0 Natural vibration period Tquot sec C EX M quotS s7 39 Using the response spectrum as shown assume E 5 the oor displacements can be computed as uli WM 0 The elastic forces can be computed as i f 1 Mllill hAi M FL LHI fli f 1 l quot5diDi 0334 0641 0895 1078 1173 1067 10671009 5378 0334 0641 0895 1078 1173 1916 3677 5139 in 6188 6731 0011 l S H096 TLLSW gt a PL 4899 9401 013759 13141 kips 15817 17211 1 7 1 Mon T2 v The results of the peak displacements and static lateral forces per each mode are shown in the gure Based on the modal responses the base shear 11 base moment M1 and the displacement 05 of the top oor per each mode can be calculated as shown in the gure NOTE Alternatively one can calculate response such as the base shear and base moment using the general equation n rfiSuiT V MM 20986 kip ft MM 3718 kipf1 101Modcl 1010401122 1 mModes l i 139 114105 311111 71101251 u 110 1 j 01930 1293 0239 1 i 39 39 0290 945 0171 1 556 I 1554 39 0237 1012 i 4313 0089 i 1 I 077 10925 0313 I I 71 7772 I W I i b 60469 kins 1 24533 kjps 13 9867kips Mb 25494 kip f1 M 35433 10pr M1 90402 kipft d1 Mode 4 Mode 5 I m in 501151 us 3910 0055 0010 I 0101 0026 i 0029 0034 0077 0032 0093 0019 11 2943 Rips v s 0595 kip Modal combinations For example calculation of base shear 0 Absolute sum rule Warm lt z IVMma i1 60469 24533 9867 2943 0595 98407kips x 4 o SquareRoot SumSquare SRSS rule SQ umzc Hkv MW g I Mvi w 22 Vma 2Vln39mnz2 2 J 1 M ldc 604692 245332 98672 29432 05952 66066kips fa E 0 Complete Quadratic Combination CQC rule 7 We WMGQ Vmaa N Z Z Pij Vba mua bjmax Vch My MffI vf fm 11 3 The calculations of the natural frequency ratio 93 and the correlation coef cients pgj are shown as Natural frequency ratio g Mode ij j1 j2 j3 j4 j5 1000 0343 0217 0169 0148 2919 1000 0634 0494 0433 4602 1576 1000 0778 0683 5911 2025 1285 1000 0877 5 6742 2310 1465 1141 1000 Correlation coef cients pij Mode ij39 j1 j2 13 34 j5 0007 0003 0002 0001 0007L000 0044 0018 0012 0003 00000 0136 0062 0002 0018 0136quot 1000 0365 0001 0012 0062 0365J 000 gt5me agoatop MEEELprm M 5 KEbWVGLV EHML


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