Resolução de Estruturas Hiperestáticas Método das Forças - Exercícios de Engenharia Civil

QUESTÃO 01 Considere as estruturas hiperestáticas abaixo Determine i grau de hiperestaticidade gh ii as reações de apoio e iii os diagramas de esforços internos N V e M Utilize o Método das Forças 2A 20 CASO 0 QL²8 205²8 625 kNm 20628 90 kNm 625 90 625 CASO 1 CASO 2 δ11 δ11 5 1 1 6 1 1 13 11 5 13 1 1 6 δ11 113 δ22 δ22 6 1 1 5 1 13 11 6 13 1 1 5 δ22 113 δ21 δ12 δ21 δ12 6 1 6 1 16 1 1 6 δ21 δ12 1 δ10 625 1 90 1 5 5 6 6 13 1 625 5 13 1 90 6 δ10 28416 δ20 δ20 90 1 625 1 6 6 5 5 13 90 1 6 13 625 1 5 δ20 28416 δ10 δ11 X1 δ12 X2 0 δ20 δ21 X1 δ22 X2 0 113 X1 1 X2 28416 1 X1 113 X2 28416 X1 28416 113 X2 113 28416 113 X2 X2 28416 X2 60892857 kNm X1 28416 12 60892857 3 X1 60892857 kNm ΣMB 0 X1 20 52 2 Ay 5 0 Ay 3782143 kN Xa 20 Cy ΣMC 0 DY 5 20 52 2 X2 0 DY 3782143 kN ΣMB 0 20 52 2 20 112 2 Ay 5 Cy 6 DY 11 0 CY 12217857 kN ΣFY 0 20 16 Ay Cy By DY 0 DY 12217857 kN Ay 20 5 6217857 60 CY 6217857 6217857 By 60 6217857 20 5 3782143 60 20 6 60 3782143 DY 0 CORTANTE 60 3782143 6217857 60 3782143 V kN x cm M V dx A1 37821432 2 20 3576151 A3 60 3 2 90 X0 90 2910714 MOMENTO 6089286 6089286 M kNm X cm 3576151 2910714 3576151 B 30 20 CASO 0 M1 M2 M3 M1 306²2 208 M1 700 Kwm M2 303²2 205 M2 235 Kwm M3 202 M3 40 Kwm CASO 1 M 6 M 6 Km δ11 δ11 13 6 6 6 δ11 72 δ10 δ10 16 6 700 2235 6 δ10 7020 δ10 δ11 X1 0 X1 702072 X1 975 Kw X1 BY BY 975 Kw ΣFy0 975 20 306 AY0 AY1025 Kw ΣMA0 306²2 BY6 208 MA0 MA 115 Kwm 6 AY 306 775 775 BY 20 CORTANTE 1025 775 Vkw x m A1 1025²230 17510416 MA A1 6010416 MOMENTO 115 40 6010417 x m C 30 3m 3m CASO 0 QL² 8 303²8 3375 3375 3375 CASO 1 δ11 δ11 13 1 1 3 13 1 1 3 δ11 2 δ10 δ10 13 3375 1 3 13 3375 1 3 δ10 675 δ10 δ11 X1 0 X1 6752 X1 3375 kwm MB 0 X1 30 3²2 Ay 3 0 Ay 3375 kw MB 0 Cy 3 30 3²2 BY 0 Cy 3375 kw BY 1125 kw Fy 0 30 6 Ay BY Cy 0 Ay 30 3 5625 CORTANTE 3375 5625 5625 3375 1898438 1898438 M kw x m Ay 3375² 2 30 1898438 MOMENTO 3375 1898438 1898438 M kwm x m 40 4m 3m 8m CASO 0 M1 40 7² 2 1280 kwm M2 40 7² 2 10 4 1240 kwm 1280 1280 1240 CASO 1 M1 3 7 7 KNm M2 3 3 3 KNm CASO 2 M1 18 8 KNm δ11 triangle base 7 height 7 triangle base 7 height 7 rectangle base 8 height 7 rectangle base 8 height 7 triangle base 4 height 3 triangle base 4 height 7 13 7 7 7 13 7 7 8 13 32 72 3 7 4 δ12 10513 δ22 triangle base 8 height 8 triangle base 8 height 8 rectangle base 4 height 8 rectangle base 4 height 8 13 8 8 8 8 8 4 δ22 12803 δ10 rectangle base 8 height 7 triangle base 8 height 1280 triangle base 4 height 3 triangle base 4 height 7 13 7 1280 8 16 3 2 1240 1280 4 16 7 1240 2 1280 4 δ10 1474403 δ20 triangle base 8 height 1280 triangle base 8 height 8 triangle base 4 height 1240 rectangle base 4 height 8 14 8 1280 8 12 1240 1280 8 4 δ20 60800 δ10 X1 δ11 X1 δ12 X2 0 δ20 δ21 X1 δ22 X2 0 δ12δ21 δ12δ21 8878 8434 12 8 7 8 12 8 37 4 δ12δ2164 147403 10513 x1 64 x2 0 60800 64 x1 12803 x2 0 x1999979 kN x21163643 kN Ay By 2036357 kN Bx 000023 kN Fy0 408 AY BY 0 Fx0 10 999979 BX0 MB0 MB AY 8 40822 104 AX 0 MB27908621 kNm NORMAL 1163643 1 2036357 1 CORTANTE 1163643 2036357 MOMENTO 27908704 70 70 23925668 27908704