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<p>PÓRTICOS PLANOS COM BARRAS EXTENSÍVEIS</p><p>to (13) (13) 1 sp sw = = (13) 3 3 3 (I) IS (h'x) (v SVN 3 (T was</p><p>+ + + so 7/v3 27/339 + o SIH o (2</p><p>BARRA (AB) SISTEMAS DE EXEMPLO H=H' K=4EI (A) LOCAL GLOBAL E,I,A B 1.5m E,I,A = X 1,5m - (c) = 4m * BARRA (AC) u=v' LOCAL GLOBAL us OF MAC =9A = 32 M'CA 32</p><p>DE SISTEMA No (A) 7/3 2/3 MAB y HAB EI 2/3 53/16 -5/2 IB 11 = 12,24 HAC VAC 160/46 VA 48 12,63 EI 13/2 0 MB 4,71 HAC VAC EI + & (A) 1263 EI (B) 1224 VAB t VAC EI = - 48 (c) (B) NODAIS MBA DEFORMADA VB EI =0</p><p>ESFORCOS BARRA (AB) 18,63KN (A) 53,69KM (B) LOCAL MAB = = 17,89 KN N CKN] = -41,43 = 18,63 = -18,63 53,69 [KN] 1,75m = = + KN</p><p>BARRA (AC) 42111 16,63 LOCAL (A) = (40%) - = -17,69 Mc's = - 15,39 36KM = - (c) = 15,39 42,11 17,17 15,39 42,11 VAC = 6EF 32 KM KM V 32 + [KM] [KN]</p><p>3) TRANS FORMAÇÃO DE COORDENADAS = + send y' send + y' y DA BARRA NA INDEFORMADA X = I I [T]= u I v [t] CT] T = [t]: MATR17 DE ORTOGONAL =</p><p>4) to DE UMA BARRA GLOBAIS (IJ) (IT) (LOCAL) [K] LIJ) = (GLOBAL) (IS) =</p><p>4) DE EQUILIBRIO PARA CADA DEVE-SE TER: SISTEMA DE EM =0 MIS+ MIR + MI & HIS t HIK = HI 0 + VIL = VI : 104 E = HAS BARRAS VI (IS) (D) (IJ) MI 104 = [T] HD VIS HI (c) HIK HIL MIL V's MIK VIL VIK MI, VI : CARGAS ou NO NO (I) = (IJ) +</p><p>EXEMPLO 10KM 0,3m BKM (A) E, AT K (B) 10KN 0,2m 0,2 = 1/2 ( 40EI ) = 50 AT = 40 I A = 400I</p><p>COORDENADAS LOCAIS (4) 0,52 -0,5 (A) + (-6) -3,0 t (A) 0,3m 50 EI 0 800 0 0 + (-6) -3,0 -24 96 (-B) + (B) 0,2m 0,2 LOORDENADAS GLOBAIS 6 14,4 -1912 -14,4 19,2 BARRA (AB) (2 = (AB) t (AB) (AB) 546 -338 = - 0,6 ; [K] = [T] = EI 349 8 1 546 338 B -0,5 349 (AB) (AB) T (AB) [T] = 000100 = [T] 5,0 0,5 (13) 5,0</p><p>MATRIZ DE RIGIDEZ NO DAIS (A) (B) B -19,2 4 19,2 -0,5 (A) 546 33B -546 -338 HA HA [K]= -19,2 33B 349 -349 -15 5.0 -20 4 14.4 6 -14,4 MB 0/5 -14,4 -546 -338 19,2-336 -349 349 VB V13-5,0 x x x SISTEMA y (A) 349 -338 = EI = -338 596 0 = - 0,0717/EE DEFORMADA</p><p>(4) (AB) (AB) (AB) (AB) 0,0760 (A) (AB) (AB) (AB) (A) - 01127 = [T] } = 11,9 = 0,101 = = EI 3,96 -0,0717 (B) (B) -17,9 B) 0 -0,0430 17,6 11,9 9,85 2,96 (4) V H M 1719 3,96 (B) DLT TIRAMTE MT = EATDL = = LT LT</p><p>EXEMPLO 30KM K E,I,A 0,6m abm K SIMETRIA (B) E,C, A (c) Abm (A) A= 0,6m *</p><p>EXEMPLO 2 9 (48) =EC 12 20640-6 -2 (B) E,C,A (c) 9 12 (A) (A) 4 -3,6 3.6 -4,B 0,6m T 15 * 4 -2 (3) (3) BARRA (AB) L= 1m = 11,28 15 send=0,6 BARRA (BC) Has 1001000 00 (B) (3) (AB) 2 [T] [K] (BC) ; 20640-6 (c) (c) 0</p><p>DE no (A) (B) 4 (AB) [K]=EI -11,26 j (A) (c) 4 3,6 -4,8 -3.6 4,B 2 4 11,28 -0,96 -3,6 0,96 CA) 4,B (B) (c) 4+4 + 3,6+0 -6 [K] EI + 096+0 o o (B) 6 10 + 6 4 10 ; 10 (c) (c) 12 12</p><p>VETOR DE DO PORTICO - 10 -12 HA HA (A) VA 15 VA-15 + 2 = = - -30 15 t - 45 Mc Hc (c) Vc 0 SISTEMA OA 4 2 -4,B OA 12 OB = 3,03/EI B 316 1,2 EI 3.6 20172 -0,96 UB MB = 1,12/EI -0196 23,28 V3 -45 -</p><p>BARRA (AB) OA -10 UA joiss 25,41 (A) (AB) Vs 0 (AB) (AB) (AB) (AB) (AB) (AB) 15,25 = = [T] 1D4 = OB 3.03 EI [K'] t = 13,24 EI -7142 VB -1,64 6,7512N 13,221 14,65 V 15,25 25,41 KM 25,41 * 10 M V [KM] M</p><p>BARRA (BC) 13,25 OB 3,03 32,55 KN 11,19KM 1,12 (BC) (BC) = = Oc EI 11,19 H 13,25 (B) 32,55 32,55 V (BC) (BC) (BC) -19.31 19,31 -11,19 (c) 32,55 13,25 M</p><p>EXEMPLO: (A) (c) 2,11 0,0 1.67 -1,67 (B) (c) (x) 5,27 -5,27 (A) 1,67 E,I,A ; -1,67 (A) 5,27 0,0 (c) A=10I 1,76 * BARRA (AC) 1,90m / d = -0,527 1,05 (AC) (AC) 4,92 -0,527 -4,92 05 (A) [K] = [T] 2,11 1,58 -1,05 -2,11 1 2,11 0,527 -1,58 (AC) 0,949 10 (c) [T] = -0,316 0,949 10 2,11 0,949 01316 01949</p><p>(A) (c) -12 4+2,111 2 0.527 1-1,58 - -3,6 +10,72 0,527 -4,92 (A) (A) 4+4 10 -6 + EI + o 0 10 (B) -45 6 1-12 4+2,11 MA x HA (c) x VA x SISTEMA 6,11 OA OA = 15,64 0 UA = -2,64/EI EI 3,6 OB 2 3,6 -10,72 3,6 20,72 -0196 MB 0196 23,28 -45 VB= -3,24/ET</p><p>-6,38 2,05 MA -2,11 (AB) (AB) 12,6 (A) (AB) (AB) [T] 1,58 1 = (AB) = 104 t of = 27/7 - OB 1,44 EI 13,7 -2,47 5,41 (B) - 2,20 -3,74 OB 1,44 (BC) -6,57 (B) (BC) (B) (BC) (BC) = [T] 1 = 104 t of = = EI (c) 30,2 OA UA (AC) 3.69 (A) (AC) (AC) (AC) (AC) (AC) (AC) = [T] -9,16 = t of = - 11 D EI - 5,33 (c) 9,16</p><p>12,6 (A) (AB) = 27/7 - 16,6 13,7 5,41 (B) (B) -3,74 5,33 3 (c) -13,7 -6,57 (B) = 6,58 (c) (A) 30,2 M (A) (AC) = -5,33 (c) 9,16</p><p>12,6 (A) (AB) = - 13,7 5,41 (B) (B) 5,41 -3,74 -13,7 -6,57 (B) = 3,69 6,58 (c) 30,2 (A) M [KM] (A) (AC) = -5,33 3027 (c) 9,16</p><p>12,6 (A) (AB) = - 13,7 5,41 (B) 3,74 3012 30,2 9,16 -6,57 (B) (c) = (A) (c) 30,2 9,16 V [KN] (A) (AC) = 5,33 3027 (c)</p><p>EXEMPLO: SIMETRIA EI,A EI,A EI, (B) (A) 0,6m E,A = A= 40I (c) 0.6m 1.0m 0,6m</p><p>BARRA (A) (B) EI, (A) (B) (A) 25EI (AB) (BC) (BC) EC = III A=40I (c) (B) 12 -6 12 BARRA (BC) = 0,6 : (B) (c) 4/B -4/B (BC) (BC) -13,44 -22,1 13,44 [k'] = EC [K] = [T] = EI 29,9 -29,9 (a) (BC) T 4,0 -3,6 22,1 -13,4 -6 (c) 29,9</p><p>BARRA - L= EI, A (A) (B) = 0,694 = - 0,447 25EI 2,24 1,86 1,12 (c) 22,36 90 -22,36 (AC) (AC) = EI 2,1 libb 0/0 -2,1 2,24 -1,BB 22,36 2,1 (c) 2,24 0/64 1,12 984 -1,68 (AC) (AC) T (AC) 16,31 964 -16,31 Bill [K] = [T] [K'] [T] = EI 6,15 - 6,15 = 104 2,24 - 16,31 (c) 6,15</p><p>DE RIGIDEZ (A) (c) 10+963 X 1,12 40 0-8,11 -40 18,3 (A) 12+6,15 6 1-6,15 4+4 6+3,6 1-3,6 40+22,1 0-13,44 -22 (B) [ 3.6 13,44 1-299 X 22,1+1631 (c) X</p><p>SISTEMA 43,15 6,0 90 -12 -30 -2,4 OB => = EI = 4,B 62,1 0 UB = -12 -2,4 -13,44 41,9 VB - -20 = - 980/EI EI, (B) 101 (A) EC 25EI A= 40I (c) DEFORMADA</p><p>0,05 1,35 -1,69 (A) 20,24 (B) LAB (BC) (AL) = 1,40 = -4,0 = 1,35 -2,65 - -6,94 (B) -20,2 (c) (c) COLUHA (B) (A) (B) DL = - 1,01 EI = EA e col (c) 2,65 = - 2012 M [KN]</p>