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DISCIPLINA Estruturas Isostáticas e Hiperestáticas Nome LISTA DE EXERCÍCIOS 1 Determinar as reações de apoio e os diagramas de Momento Fletor M Força Cortante V e Força Normal N das estruturas a seguir C B A C B A b a F E D C B A C B A d c e f g i j h C B A D C B A L F E D C k D C B A m n C B A F E D C B A Diagram of beam with 5 ft load forces BX AY BY ΣFx0 BX0 tf ΣMA0 515BY40 BY1875 tf ΣFy0 5BYAY0 AY3125 tf NORMAL Ntf xcm CORTANTE 3125 1875 Vtf xcm A1A2312515 A1A246875 MOMENTO Mtfm xcm 46875 Diagram of beam with load forces BX AY BY ΣFx0 BX0 tf ΣMA0 BY 65 2 6522 3 50 BY880769 tf ΣFy0 2 65 3 BY AY0 AY71923 tf NORMAL Ntf xcm CORTANTE AY 252180769 Vtf xcm 71923 2180769 580769 880769 A171923222129323 A22180769222197078 A31096153 MOMENTO Mtfm xcm diagram with 129323 and 1096153 X719232 X35961 m Diagram of beam with forces AX AY MA ΣFx0 AX0 tf ΣFy0 152 3 AY0 AY6 tf ΣMA0 MA 15 222 3 30 MA12 tfm NORMAL Ntf xcm CORTANTE 6 3 3 V tf X m A1 6 3 2 2 A1 9 A2 3 1 A2 3 MOMENTO 12 3 M tfm x m ΣFx 0 Bx 0 tf BY ΣMA 0 2 1 3 1 3 3 7 BY 5 5 0 ΣFY 0 AY BY 1 3 3 2 0 BY 5091 tf AY 2909 tf 2 AY 0909 0909 3 1 2091 CORTANTE 0909 3 V tf X m 2 2091 NORMAL N tf X m MOMENTO A1 2 1 2 A4 2091 2 2 1 21861 A6 3 15 A2 0909 15 13635 A6 45 A3 0909² 2 1 04134 A5 2091 1 2091 M tfm x m 2 06364 02231 24081 45 ΣFx0 Ax0 tf ΣFY0 AY 25 1 1 1 2 1 0 AY 65 tf MA MA 25 1² 2 2 15 1 2 1 1 15 0 MA 65 tfm 6 NORMAL N tf X m CORTANTE 65 4 35 V tf X m 15 1 A1 65 4 1 2 52 A3 15 05 2 05 1 A2 4 35 05 2 1875 MOMENTO 775 25 0625 M tfm x m Fx0 BX0 tf BY AY BY MA0 23²2 245 315 BY30 BY6 tf Fy0 3 23 2 AY BY0 AY8 tf NORMAL N tf x m CORTANTE 5 2 V tf x m 3 4 A131545 A3422326 A25²2341603 A42153 MOMENTO 45 033 3 M tfm x m Fx0 BX0 tf MA0 315²2 221 465 BY50 BY9075 tf Fy0 315 22 4 AY BY0 AY3425 tf NORMAL N tf x m AY 315 1075 1075 22 5075 CORTANTE 3425 V tf x m 1 1075 5075 A1 3425²23 19551 A2 1075²23 01926 17625 A4 1075 5075 2 2 6125 MOMENTO 6 M tfm x m 19551 17625 015 ΣFX0 BX0 ΣMA0 3122535BY7235535050 BY17357 AY6643 ΣFY0 325435AYBY0 NORMAL Pn tf x m CORTANTE 6 1V tf x m 3 3643 1643 3357 11357 AY33643 364321643 A1313 A2364327286 61071 102543 45 A3164323286 A4335711357 2 214714 MOMENTO 45 1M tfm x m 3 6073 10243 ΣFX0 Ax0 ΣFY0 2154211Ay0 Ay10 tf MOMENTO ΣMA0 2215415225112MA0 MA1725 tfm NORMAL 9N tf x m CORTANTE 10 7 3 2 1V tf x m 102157 743 A1107 2 151275 A23212 25 MOMENTO 1725 45 25 M tfm X m ΣFX0 Dx0 DY2tf Ay0 tf ΣMA0 223DY40 ΣFY0 2AYDY0 NORMAL 1Ntf xm CORTANTE 1Vtf xm 2 MOMENTO 1Mtfm xm 2 2 K ΣFx0 BX0 ΣMA0 4 1 3 2 3 6 3 3 5 BY 6 0 ΣFY0 4 3 6 3 AY BY 0 BY 10 tf AY 6 tf AY 4 2 2 3 1 1 6 7 CORTANTE 6 2 3 1 7 Vtf x m NORMAL 1Ntf xm A1 6 1 6 A2 2 1 2 8 A3 1 1 1 A4 7 1 7 A5 3 1 3 MOMENTO 3 1Mt1m xm 6 8 5 4 ΣFx0 BX0 ΣMB0 3 2 322 2 45 CY 30 ΣFy0 2 3 2 CY BY0 CY 7 tf BY 1 tf NORMAL 1Ntf xm CORTANTE 1 2 4 Vtf xm 5 A1 12 2 2 025 A2 52 2 2 625 MOMENTO tM tfm x m Σ FX0 AX0 tf AY7 tf Σ FY0 21522 AY0 ΣMA0 21522 215 22 MA0 MA925 tfm CORTANTE fV tf x m MOMENTO tM tfm x m A1 742 15 825 A2 205 1 Σ FX0 BX0 tf Σ MB0 222 2 42 323 64 BY 6 380 EY116 tf TF Σ FY0 BY EY 4 6 3 22 320 BY113 tf tf NORMAL tN tf x m CORTANTE 22 AY 73 73 4 33 33 32 26 26 6 86 A1 42 8 A2 73 2 146 MOMENTO tM tfm x m 4 6 106 325185 113
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DISCIPLINA Estruturas Isostáticas e Hiperestáticas Nome LISTA DE EXERCÍCIOS 1 Determinar as reações de apoio e os diagramas de Momento Fletor M Força Cortante V e Força Normal N das estruturas a seguir C B A C B A b a F E D C B A C B A d c e f g i j h C B A D C B A L F E D C k D C B A m n C B A F E D C B A Diagram of beam with 5 ft load forces BX AY BY ΣFx0 BX0 tf ΣMA0 515BY40 BY1875 tf ΣFy0 5BYAY0 AY3125 tf NORMAL Ntf xcm CORTANTE 3125 1875 Vtf xcm A1A2312515 A1A246875 MOMENTO Mtfm xcm 46875 Diagram of beam with load forces BX AY BY ΣFx0 BX0 tf ΣMA0 BY 65 2 6522 3 50 BY880769 tf ΣFy0 2 65 3 BY AY0 AY71923 tf NORMAL Ntf xcm CORTANTE AY 252180769 Vtf xcm 71923 2180769 580769 880769 A171923222129323 A22180769222197078 A31096153 MOMENTO Mtfm xcm diagram with 129323 and 1096153 X719232 X35961 m Diagram of beam with forces AX AY MA ΣFx0 AX0 tf ΣFy0 152 3 AY0 AY6 tf ΣMA0 MA 15 222 3 30 MA12 tfm NORMAL Ntf xcm CORTANTE 6 3 3 V tf X m A1 6 3 2 2 A1 9 A2 3 1 A2 3 MOMENTO 12 3 M tfm x m ΣFx 0 Bx 0 tf BY ΣMA 0 2 1 3 1 3 3 7 BY 5 5 0 ΣFY 0 AY BY 1 3 3 2 0 BY 5091 tf AY 2909 tf 2 AY 0909 0909 3 1 2091 CORTANTE 0909 3 V tf X m 2 2091 NORMAL N tf X m MOMENTO A1 2 1 2 A4 2091 2 2 1 21861 A6 3 15 A2 0909 15 13635 A6 45 A3 0909² 2 1 04134 A5 2091 1 2091 M tfm x m 2 06364 02231 24081 45 ΣFx0 Ax0 tf ΣFY0 AY 25 1 1 1 2 1 0 AY 65 tf MA MA 25 1² 2 2 15 1 2 1 1 15 0 MA 65 tfm 6 NORMAL N tf X m CORTANTE 65 4 35 V tf X m 15 1 A1 65 4 1 2 52 A3 15 05 2 05 1 A2 4 35 05 2 1875 MOMENTO 775 25 0625 M tfm x m Fx0 BX0 tf BY AY BY MA0 23²2 245 315 BY30 BY6 tf Fy0 3 23 2 AY BY0 AY8 tf NORMAL N tf x m CORTANTE 5 2 V tf x m 3 4 A131545 A3422326 A25²2341603 A42153 MOMENTO 45 033 3 M tfm x m Fx0 BX0 tf MA0 315²2 221 465 BY50 BY9075 tf Fy0 315 22 4 AY BY0 AY3425 tf NORMAL N tf x m AY 315 1075 1075 22 5075 CORTANTE 3425 V tf x m 1 1075 5075 A1 3425²23 19551 A2 1075²23 01926 17625 A4 1075 5075 2 2 6125 MOMENTO 6 M tfm x m 19551 17625 015 ΣFX0 BX0 ΣMA0 3122535BY7235535050 BY17357 AY6643 ΣFY0 325435AYBY0 NORMAL Pn tf x m CORTANTE 6 1V tf x m 3 3643 1643 3357 11357 AY33643 364321643 A1313 A2364327286 61071 102543 45 A3164323286 A4335711357 2 214714 MOMENTO 45 1M tfm x m 3 6073 10243 ΣFX0 Ax0 ΣFY0 2154211Ay0 Ay10 tf MOMENTO ΣMA0 2215415225112MA0 MA1725 tfm NORMAL 9N tf x m CORTANTE 10 7 3 2 1V tf x m 102157 743 A1107 2 151275 A23212 25 MOMENTO 1725 45 25 M tfm X m ΣFX0 Dx0 DY2tf Ay0 tf ΣMA0 223DY40 ΣFY0 2AYDY0 NORMAL 1Ntf xm CORTANTE 1Vtf xm 2 MOMENTO 1Mtfm xm 2 2 K ΣFx0 BX0 ΣMA0 4 1 3 2 3 6 3 3 5 BY 6 0 ΣFY0 4 3 6 3 AY BY 0 BY 10 tf AY 6 tf AY 4 2 2 3 1 1 6 7 CORTANTE 6 2 3 1 7 Vtf x m NORMAL 1Ntf xm A1 6 1 6 A2 2 1 2 8 A3 1 1 1 A4 7 1 7 A5 3 1 3 MOMENTO 3 1Mt1m xm 6 8 5 4 ΣFx0 BX0 ΣMB0 3 2 322 2 45 CY 30 ΣFy0 2 3 2 CY BY0 CY 7 tf BY 1 tf NORMAL 1Ntf xm CORTANTE 1 2 4 Vtf xm 5 A1 12 2 2 025 A2 52 2 2 625 MOMENTO tM tfm x m Σ FX0 AX0 tf AY7 tf Σ FY0 21522 AY0 ΣMA0 21522 215 22 MA0 MA925 tfm CORTANTE fV tf x m MOMENTO tM tfm x m A1 742 15 825 A2 205 1 Σ FX0 BX0 tf Σ MB0 222 2 42 323 64 BY 6 380 EY116 tf TF Σ FY0 BY EY 4 6 3 22 320 BY113 tf tf NORMAL tN tf x m CORTANTE 22 AY 73 73 4 33 33 32 26 26 6 86 A1 42 8 A2 73 2 146 MOMENTO tM tfm x m 4 6 106 325185 113