<div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/0866faf6-6ca2-4fe6-bc14-45a600308a4f/bg1.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls0 ws0">1 </div><div class="c x1 y3 w2 h3"><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls0 ws0"> </div></div><div class="t m0 x1 h4 y5 ff2 fs1 fc1 sc0 ls0 ws0">Análise de Estruturas I - Resumo </div><div class="t m0 x1 h4 y6 ff2 fs1 fc1 sc0 ls0 ws0"> </div><div class="t m0 x1 h5 y7 ff3 fs2 fc0 sc0 ls0 ws0">VIGAS III </div><div class="t m0 x1 h6 y8 ff3 fs3 fc1 sc0 ls0 ws0"> </div><div class="t m0 x1 h6 y9 ff3 fs3 fc1 sc0 ls0 ws0">Introdução </div><div class="t m0 x1 h7 ya ff2 fs4 fc0 sc0 ls0 ws0"> <span class="_0 blank"> </span>Nesta aula vamos avançar mais um pouco<span class="_1 blank"> </span> sobre os tipos de vigas que podemos </div><div class="t m0 x1 h7 yb ff2 fs4 fc0 sc0 ls0 ws0">encontrar <span class="_2 blank"> </span>nos <span class="_2 blank"> </span>nossos <span class="_2 blank"> </span>projetos. <span class="_2 blank"> </span>Em <span class="_2 blank"> </span>aulas <span class="_2 blank"> </span>passadas <span class="_2 blank"> </span>já <span class="_2 blank"> </span>vimos vi<span class="_3 blank"></span>gas <span class="_2 blank"> </span>biapoiadas, <span class="_2 blank"> </span>vigas </div><div class="t m0 x1 h7 yc ff2 fs4 fc0 sc0 ls0 ws0">engastadas <span class="_4 blank"> </span>e <span class="_4 blank"> </span>livres <span class="_4 blank"> </span>e <span class="_4 blank"> </span>vigas <span class="_4 blank"> </span>com <span class="_4 blank"> </span>balanços, <span class="_4 blank"> </span>todas <span class="_4 blank"> </span>elas <span class="_4 blank"> </span>retas. <span class="_4 blank"> </span>Hoje <span class="_4 blank"> </span>veremos <span class="_4 blank"> </span>um <span class="_4 blank"> </span>po<span class="_3 blank"></span>uco </div><div class="t m0 x1 h7 yd ff2 fs4 fc0 sc0 ls0 ws0">sobre vigas do tipo Gerber e vigas inclinadas. </div><div class="t m0 x1 h7 ye ff2 fs4 fc0 sc0 ls0 ws0"> <span class="_0 blank"> </span>Avançaremos <span class="_5 blank"></span>nosso <span class="_5 blank"></span>conhecimento <span class="_5 blank"></span>sobre <span class="_5 blank"></span>decomposição <span class="_5 blank"></span>d<span class="_3 blank"></span>e <span class="_5 blank"></span>vigas, <span class="_5 blank"></span>e <span class="_5 blank"></span>veremos <span class="_5 blank"></span>um </div><div class="t m0 x1 h7 yf ff2 fs4 fc0 sc0 ls0 ws0">novo esforço que deve ser analisado quando trabalh<span class="_3 blank"></span>amos com vigas inclinadas.<span class="_1 blank"> </span> </div><div class="t m0 x1 h7 y10 ff2 fs4 fc0 sc0 ls0 ws0"> </div><div class="t m0 x1 h6 y11 ff3 fs3 fc1 sc0 ls0 ws0">Vigas Gerber </div><div class="t m0 x1 h7 y12 ff2 fs4 fc1 sc0 ls0 ws0">Introdução </div><div class="t m0 x1 h7 y13 ff2 fs4 fc0 sc0 ls0 ws0"> <span class="_0 blank"> </span>Precisamos <span class="_1 blank"> </span>construir <span class="_1 blank"> </span>uma <span class="_1 blank"> </span>ponte <span class="_1 blank"> </span>para <span class="_1 blank"> </span>vencer <span class="_1 blank"> </span>um <span class="_1 blank"> </span>rio<span class="_6 blank"> </span>. <span class="_1 blank"> </span>No <span class="_1 blank"> </span>entanto, <span class="_1 blank"> </span>sabemos <span class="_1 blank"> </span>que </div><div class="t m0 x1 h7 y14 ff2 fs4 fc0 sc0 ls0 ws0">construir a ponte \u201cde uma vez\u201d não é um processo simples. </div><div class="t m0 x3 h7 y15 ff2 fs4 fc0 sc0 ls0 ws0"> </div><div class="t m0 x1 h7 y16 ff2 fs4 fc0 sc0 ls0 ws0">Dessa <span class="_1 blank"> </span>forma, <span class="_6 blank"> </span>a <span class="_1 blank"> </span>solução<span class="_1 blank"> </span> <span class="_1 blank"> </span>que <span class="_6 blank"> </span>o <span class="_1 blank"> </span>engenheiro <span class="_6 blank"> </span>Gerber <span class="_1 blank"> </span>trouxe <span class="_6 blank"> </span>foi <span class="_1 blank"> </span>de <span class="_6 blank"> </span>separar <span class="_6 blank"> </span>o <span class="_1 blank"> </span>trecho <span class="_6 blank"> </span>AB <span class="_1 blank"> </span>da<span class="_1 blank"> </span> </div><div class="t m0 x1 h7 y17 ff2 fs4 fc0 sc0 ls0 ws0">estrutura <span class="_7 blank"> </span>restante. <span class="_7 blank"> </span>A <span class="_7 blank"> </span>viga <span class="_7 blank"> </span>AB <span class="_7 blank"> </span>será <span class="_7 blank"> </span>apoiad<span class="_3 blank"></span>a <span class="_7 blank"> </span>nos <span class="_7 blank"> </span>trechos <span class="_7 blank"> </span>fixos <span class="_7 blank"> </span>através <span class="_7 blank"> </span>de <span class="_7 blank"> </span>rót<span class="_3 blank"></span>ulas </div><div class="t m0 x1 h7 y18 ff2 fs4 fc0 sc0 ls0 ws0">(chamadas dentes Gerber). A figura acima ilustra este detalhe do dent<span class="_3 blank"></span>e. </div><div class="t m0 x1 h7 y19 ff2 fs4 fc1 sc0 ls0 ws0">Propriedades do dente Gerber </div><div class="t m0 x1 h7 y1a ff2 fs4 fc0 sc0 ls0 ws0"> <span class="_0 blank"> </span>A representação de um dente Gerber é feita através do uso de rótulas, como na </div><div class="t m0 x1 h7 y1b ff2 fs4 fc0 sc0 ls0 ws0">viga <span class="_8 blank"> </span>abaixo. <span class="_8 blank"> </span>Nestes <span class="_8 blank"> </span>pontos <span class="_8 blank"> </span>haverá <span class="_4 blank"> </span>uma <span class="_8 blank"> </span>transmissão <span class="_8 blank"> </span>de <span class="_8 blank"> </span>esforços <span class="_8 blank"> </span>cortantes <span class="_8 blank"> </span>e <span class="_8 blank"> </span>normais<span class="_6 blank"> </span> </div><div class="t m0 x1 h7 y1c ff2 fs4 fc0 sc0 ls0 ws0">(se houver), mas não haverá transmissão de momento. </div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/0866faf6-6ca2-4fe6-bc14-45a600308a4f/bg2.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls0 ws0">2 </div><div class="c x1 y3 w2 h3"><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls0 ws0"> </div></div><div class="t m0 x4 h7 y1d ff2 fs4 fc0 sc0 ls0 ws0"> </div><div class="t m0 x1 h7 y1e ff2 fs4 fc0 sc0 ls0 ws0"> <span class="_0 blank"> </span>O <span class="_1 blank"> </span>momento <span class="_1 blank"> </span>na <span class="_1 blank"> </span>rótula <span class="_6 blank"> </span>será <span class="_1 blank"> </span>igual <span class="_1 blank"> </span>a <span class="_6 blank"> </span>zero, <span class="_1 blank"> </span>tanto <span class="_1 blank"> </span>se<span class="_1 blank"> </span> <span class="_1 blank"> </span>calcularmos <span class="_1 blank"> </span>à <span class="_6 blank"> </span>direita <span class="_1 blank"> </span>quanto <span class="_1 blank"> </span>à </div><div class="t m0 x1 h7 y1f ff2 fs4 fc0 sc0 ls0 ws0">esquerda. </div><div class="t m0 x5 h8 y20 ff4 fs4 fc0 sc0 ls0">\ue72f</div><div class="t m0 x6 h9 y21 ff4 fs5 fc0 sc0 ls0 ws1">\uebe5ó\uebe7,\uebd8\uebe6\uebe4<span class="_9 blank"> </span><span class="fs4 ws2 v1">= \ue72f</span></div><div class="t m0 x7 ha y21 ff4 fs5 fc0 sc0 ls0 ws1">\uebe5ó\uebe7,\uebd7\uebdc\uebe5<span class="_9 blank"> </span><span class="fs4 ws2 v1">= 0<span class="ff2 ws0"> </span></span></div><div class="t m0 x1 h7 y22 ff2 fs4 fc0 sc0 ls0 ws0"> <span class="_0 blank"> </span>A <span class="_2 blank"> </span>expressão <span class="_2 blank"> </span>acima <span class="_a blank"> </span>inclui <span class="_a blank"> </span>mais <span class="_2 blank"> </span>uma <span class="_2 blank"> </span>equação <span class="_a blank"> </span>de <span class="_2 blank"> </span>equilíbrio <span class="_2 blank"> </span>no <span class="_a blank"> </span>nosso <span class="_2 blank"> </span>sistema. </div><div class="t m0 x1 h7 y23 ff2 fs4 fc0 sc0 ls0 ws0">Portanto, <span class="_5 blank"></span>agora podem<span class="_3 blank"></span>os <span class="_5 blank"></span>ter casos <span class="_5 blank"></span>com <span class="_5 blank"></span>4 <span class="_3 blank"></span>(ou <span class="_5 blank"></span>mais, <span class="_5 blank"></span>dependendo <span class="_3 blank"></span>do <span class="_5 blank"></span>número d<span class="_5 blank"></span>e<span class="_1 blank"> </span> <span class="_5 blank"></span>rótulas) </div><div class="t m0 x1 h7 y24 ff2 fs4 fc0 sc0 ls0 ws0">equações de equilíbrio. </div><div class="t m0 x1 h7 y25 ff2 fs4 fc0 sc0 ls0 ws0"> <span class="_0 blank"> </span>Os esforços são transmitidos normalmente. </div><div class="t m0 x1 h7 y26 ff2 fs4 fc1 sc0 ls0 ws0">Análise de uma viga Gerber </div><div class="t m0 x1 h7 y27 ff2 fs4 fc0 sc0 ls0 ws0"> <span class="_0 blank"> </span>Podemos <span class="_4 blank"> </span>analisar <span class="_4 blank"> </span>uma <span class="_4 blank"> </span>estrutura <span class="_8 blank"> </span>longa <span class="_4 blank"> </span>como <span class="_4 blank"> </span>várias <span class="_4 blank"> </span>estruturas <span class="_4 blank"> </span>menores, <span class="_4 blank"> </span>e <span class="_8 blank"> </span>de </div><div class="t m0 x1 h7 y28 ff2 fs4 fc0 sc0 ls0 ws0">cálculo <span class="_5 blank"></span>mais <span class="_5 blank"></span>simples. <span class="_b blank"></span>Essas <span class="_b blank"></span>vigas <span class="_5 blank"></span>menores <span class="_5 blank"></span>serão <span class="_b blank"></span>selecionadas <span class="_5 blank"></span>de <span class="_5 blank"></span>forma <span class="_b blank"></span>que <span class="_5 blank"></span>todas <span class="_5 blank"></span>sejam </div><div class="t m0 x1 h7 y29 ff2 fs4 fc0 sc0 ls0 ws0">estáveis e <span class="_1 blank"> </span>isostáticas. <span class="_1 blank"> </span>Representamos <span class="_1 blank"> </span>os <span class="_1 blank"> </span>apoios <span class="_1 blank"> </span>que <span class="_1 blank"> </span>substituem as <span class="_1 blank"> </span>rótulas <span class="_1 blank"> </span>como <span class="_1 blank"> </span>de <span class="_1 blank"> </span>2º </div><div class="t m0 x1 h7 y2a ff2 fs4 fc0 sc0 ls0 ws0">gênero. Vamos ver como exemplo a viga abaixo. </div><div class="t m0 x8 h7 y2b ff2 fs4 fc0 sc0 ls0 ws0"> </div><div class="t m0 x1 h7 y2c ff2 fs4 fc0 sc0 ls0 ws0"> <span class="_0 blank"> </span>Podemos <span class="_1 blank"> </span>calcular <span class="_1 blank"> </span>essa <span class="_1 blank"> </span>estrutura <span class="_6 blank"> </span>de <span class="_1 blank"> </span>forma<span class="_1 blank"> </span> <span class="_1 blank"> </span>completa, <span class="_1 blank"> </span>ou <span class="_6 blank"> </span>decompondo <span class="_1 blank"> </span>em <span class="_1 blank"> </span>duas </div><div class="t m0 x1 h7 y2d ff2 fs4 fc0 sc0 ls0 ws0">estruturas independentes, viga AB e viga BC. </div><div class="t m0 x1 hb y2e ff5 fs4 fc1 sc1 ls0 ws0">Aná<span class="_5 blank"></span>lise d<span class="_5 blank"></span>a estru<span class="_5 blank"></span>tura c<span class="_5 blank"></span>omp<span class="_3 blank"></span>leta<span class="_5 blank"></span> </div><div class="t m0 x1 h7 y2f ff2 fs4 fc0 sc0 ls0 ws0"> <span class="_0 blank"> </span>Neste caso, <span class="_1 blank"> </span>devemos <span class="_1 blank"> </span>aplicar <span class="_1 blank"> </span>as três <span class="_1 blank"> </span>equações <span class="_1 blank"> </span>de <span class="_1 blank"> </span>equilíbrio fundamentais, <span class="_1 blank"> </span>mais </div><div class="t m0 x1 h7 y30 ff2 fs4 fc0 sc0 ls0 ws0">a equação de momento igual a zero na rótula B. </div><div class="t m0 x9 h8 y31 ff4 fs4 fc0 sc0 ls0">\ue72f</div><div class="t m0 xa h9 y32 ff4 fs5 fc0 sc0 ls0 ws3">\uebbb,\uebd8\uebe6\uebe4<span class="_9 blank"> </span><span class="fs4 ws0 v1">=<span class="_7 blank"> </span>0<span class="_c blank"> </span>\u2192<span class="_c blank"> </span>2\ue747\ue730<span class="_1 blank"> </span>/\ue749<span class="_1 blank"> </span> .<span class="_2 blank"> </span>3\ue749<span class="_1 blank"> </span> .<span class="_2 blank"> </span>1<span class="_1 blank"> </span>,5\ue749 \u2212<span class="_d blank"> </span>\ue738</span></div><div class="t m0 x7 h9 y32 ff4 fs5 fc0 sc0 ls1">\uebba<span class="fs4 ls0 ws0 v1"> .<span class="_2 blank"> </span>3\ue749<span class="_7 blank"> </span>=<span class="_c blank"> </span>0<span class="_7 blank"> </span>\u2192<span class="_c blank"> </span>\ue738</span></div><div class="t m0 xb hc y32 ff4 fs5 fc0 sc0 ls2">\uebba<span class="fs4 ls3 v1">=<span class="ls0 ws4 v2">9\ue747\ue730 .<span class="_2 blank"> </span>\ue749</span></span></div><div class="t m0 xc hd y33 ff4 fs4 fc0 sc0 ls0 ws5">3\ue749 <span class="ws6 v3">=<span class="_c blank"> </span>3\ue747\ue730 <span class="ff2 ws0"> </span></span></div><div class="t m0 xd h8 y34 ff4 fs4 fc0 sc0 ls0 ws7">\u2211\ue728</div><div class="t m0 xe h9 y35 ff4 fs5 fc0 sc0 ls4">\uebec<span class="fs4 ls0 ws8 v1">= 0 \u2192 \ue738</span></div><div class="t m0 xf h9 y35 ff4 fs5 fc0 sc0 ls5">\uebba<span class="fs4 ls0 ws9 v1">+ \ue738</span></div><div class="t m0 x10 he y35 ff4 fs5 fc0 sc0 ls6">\uebbc<span class="fs4 ls0 wsa v1">\u2212<span class="_d blank"> </span>2\ue747\ue730/\ue749 .<span class="_2 blank"> </span><span class="ws7 v4">(</span>3\ue749<span class="_d blank"> </span>+<span class="_d blank"> </span>2\ue749<span class="ls7 v4">)</span><span class="ws8">= 0 \u2192 \ue738</span></span></div><div class="t m0 x11 ha y35 ff4 fs5 fc0 sc0 ls8">\uebbc<span class="fs4 ls0 ws2 v1">= 10\ue747\ue730<span class="_d blank"> </span>\u2212<span class="_d blank"> </span>3\ue747\ue730 = 7\ue747\ue730<span class="_1 blank"> </span><span class="ff2 ws0"> </span></span></div><div class="t m0 x12 h8 y36 ff4 fs4 fc0 sc0 ls0 ws7">\u2211\ue72f</div><div class="t m0 xd h9 y37 ff4 fs5 fc0 sc0 ls9">\uebbc<span class="fs4 ls0 ws8 v1">= 0 \u2192 \u2212\ue738</span></div><div class="t m0 x13 h9 y37 ff4 fs5 fc0 sc0 lsa">\uebba<span class="fs4 ls0 ws0 v1"> .<span class="_2 blank"> </span>5\ue749<span class="_d blank"> </span>+ 2\ue747\ue730<span class="_1 blank"> </span>/\ue749<span class="_1 blank"> </span> .<span class="_2 blank"> </span>5\ue749<span class="_1 blank"> </span> .<span class="_2 blank"> </span>2,5\ue749<span class="_d blank"> </span>+ \ue72f</span></div><div class="t m0 x14 h9 y37 ff4 fs5 fc0 sc0 ls9">\uebbc<span class="fs4 ls0 wsb v1">= 0 \u2192 \ue72f</span></div><div class="t m0 x15 h9 y37 ff4 fs5 fc0 sc0 ls9">\uebbc<span class="fs4 ls0 ws4 v1">=<span class="_c blank"> </span>15\ue747\ue730 .<span class="_e blank"> </span>\ue749<span class="_d blank"> </span>\u2212<span class="_f blank"> </span>25\ue747\ue730 .<span class="_2 blank"> </span>\ue749</span></div><div class="t m0 x16 h7 y38 ff4 fs4 fc0 sc0 ls0 wsa">=<span class="_c blank"> </span>\u221210\ue747\ue730 .<span class="_e blank"> </span>\ue749 <span class="ff2 ws0"> </span></div><div class="t m0 x1 hb y39 ff5 fs4 fc1 sc1 ls0 ws0">Aná<span class="_5 blank"></span>lise d<span class="_5 blank"></span>a estru<span class="_5 blank"></span>tura d<span class="_5 blank"></span>ecom<span class="_5 blank"></span>posta<span class="_5 blank"></span> </div><div class="t m0 x1 h7 y3a ff2 fs4 fc0 sc0 ls0 ws0"> <span class="_0 blank"> </span>A <span class="_a blank"> </span>viga <span class="_a blank"> </span>AB <span class="_a blank"> </span>deve <span class="_2 blank"> </span>se <span class="_a blank"> </span>apoiar <span class="_a blank"> </span>na <span class="_2 blank"> </span>viga <span class="_a blank"> </span>BC. <span class="_a blank"> </span>Veremos <span class="_2 blank"> </span>primeiramente <span class="_a blank"> </span>o <span class="_a blank"> </span>cálculo <span class="_a blank"> </span>das </div><div class="t m0 x1 h7 y3b ff2 fs4 fc0 sc0 ls0 ws0">reações <span class="_4 blank"> </span>para <span class="_8 blank"> </span>a <span class="_4 blank"> </span>viga <span class="_8 blank"> </span>AB <span class="_4 blank"> </span>e, <span class="_4 blank"> </span>em <span class="_8 blank"> </span>seguida, <span class="_4 blank"> </span>as <span class="_8 blank"> </span>de <span class="_4 blank"> </span>BC. <span class="_8 blank"> </span>Como <span class="_4 blank"> </span>a <span class="_8 blank"> </span>viga <span class="_4 blank"> </span>AB <span class="_4 blank"> </span>está <span class="_8 blank"> </span>apoiada <span class="_4 blank"> </span>nela, </div><div class="t m0 x1 h7 y3c ff2 fs4 fc0 sc0 ls0 ws0">devemos <span class="_4 blank"> </span>incluir <span class="_4 blank"> </span>no <span class="_4 blank"> </span>ponto <span class="_4 blank"> </span>B <span class="_4 blank"> </span>a <span class="_4 blank"> </span>reação <span class="_a blank"> </span>obtida <span class="_4 blank"> </span>no <span class="_4 blank"> </span>cálculo <span class="_4 blank"> </span>anterior <span class="_4 blank"> </span>para <span class="_4 blank"> </span>esse <span class="_4 blank"> </span>ponto, <span class="_4 blank"> </span>de </div><div class="t m0 x1 h7 y3d ff2 fs4 fc0 sc0 ls0 ws0">mesmo módulo e direção, e de sentido oposto ao da reação calculada. </div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/0866faf6-6ca2-4fe6-bc14-45a600308a4f/bg3.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls0 ws0">3 </div><div class="c x1 y3 w2 h3"><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls0 ws0"> </div></div><div class="t m0 x17 h7 y3e ff2 fs4 fc0 sc0 ls0 ws0"> <span class="_10 blank"> </span> </div><div class="t m0 x18 h8 y3f ff4 fs4 fc0 sc0 ls0 ws7">\u2211\ue72f</div><div class="t m0 x13 h9 y40 ff4 fs5 fc0 sc0 ls2">\uebba<span class="fs4 ls0 ws8 v1">= 0 \u2192 \ue738</span></div><div class="t m0 x19 h9 y40 ff4 fs5 fc0 sc0 lsb">\uebbb<span class="fs4 ls0 ws0 v1"> .<span class="_2 blank"> </span>3\ue749<span class="_d blank"> </span>\u2212 2\ue747\ue730<span class="_1 blank"> </span>/\ue749<span class="_1 blank"> </span> .<span class="_2 blank"> </span>3\ue749<span class="_1 blank"> </span> .<span class="_2 blank"> </span>1,5\ue749<span class="_7 blank"> </span>=<span class="_7 blank"> </span>0<span class="_c blank"> </span>\u2192<span class="_7 blank"> </span>\ue738</span></div><div class="t m0 x1a ha y40 ff4 fs5 fc0 sc0 lsc">\uebbb<span class="fs4 ls0 ws6 v1">=<span class="_c blank"> </span>3\ue747\ue730 <span class="ff2 ws0"> </span></span></div><div class="t m0 xa h8 y41 ff4 fs4 fc0 sc0 ls0 ws7">\u2211\ue728</div><div class="t m0 x1b h9 y42 ff4 fs5 fc0 sc0 ls4">\uebec<span class="fs4 ls0 ws8 v1">= 0 \u2192 \ue738</span></div><div class="t m0 x1c h9 y42 ff4 fs5 fc0 sc0 ls5">\uebba<span class="fs4 ls0 ws9 v1">+ \ue738</span></div><div class="t m0 x1d h9 y42 ff4 fs5 fc0 sc0 lsd">\uebbb<span class="fs4 ls0 ws0 v1">\u2212 2\ue747\ue730<span class="_1 blank"> </span>/\ue749<span class="_1 blank"> </span> .<span class="_2 blank"> </span>3\ue749<span class="_7 blank"> </span>=<span class="_7 blank"> </span>0<span class="_c blank"> </span>\u2192<span class="_c blank"> </span>\ue738</span></div><div class="t m0 x1e ha y42 ff4 fs5 fc0 sc0 lse">\uebbb<span class="fs4 ls0 ws2 v1">= 6\ue747\ue730<span class="_d blank"> </span>\u2212<span class="_f blank"> </span>3\ue747\ue730<span class="_7 blank"> </span>= 3\ue747\ue730<span class="_1 blank"> </span><span class="ff2 ws0"> </span></span></div><div class="t m0 x1f h8 y43 ff4 fs4 fc0 sc0 ls0">\ue72f</div><div class="t m0 xd h9 y44 ff4 fs5 fc0 sc0 ls8">\uebbc<span class="fs4 ls0 ws0 v1">=<span class="_c blank"> </span>0<span class="_7 blank"> </span>\u2192<span class="_c blank"> </span>3\ue747\ue730<span class="_1 blank"> </span> .<span class="_2 blank"> </span>2\ue749<span class="_d blank"> </span>+ 2\ue747\ue730<span class="_6 blank"> </span>/\ue749<span class="_1 blank"> </span> .<span class="_2 blank"> </span>2\ue749<span class="_1 blank"> </span> .<span class="_2 blank"> </span>1\ue749<span class="_d blank"> </span>+ \ue72f</span></div><div class="t m0 x20 h9 y44 ff4 fs5 fc0 sc0 ls9">\uebbc<span class="fs4 ls0 ws8 v1">= 0 \u2192 \ue72f</span></div><div class="t m0 x21 h9 y44 ff4 fs5 fc0 sc0 ls8">\uebbc<span class="fs4 ls0 ws6 v1">=<span class="_c blank"> </span>\u22126\ue747\ue730 .<span class="_2 blank"> </span>\ue749<span class="_d blank"> </span>\u2212<span class="_f blank"> </span>4\ue747\ue730 .<span class="_2 blank"> </span>\ue749</span></div><div class="t m0 xf h7 y45 ff4 fs4 fc0 sc0 ls0 wsa">=<span class="_c blank"> </span>\u221210\ue747\ue730<span class="_1 blank"> </span>.<span class="_e blank"> </span>\ue749<span class="ff2 ws0"> </span></div><div class="t m0 x22 h8 y46 ff4 fs4 fc0 sc0 ls0 ws7">\u2211\ue728</div><div class="t m0 x23 h9 y47 ff4 fs5 fc0 sc0 ls4">\uebec<span class="fs4 ls0 wsb v1">= 0 \u2192 \ue738</span></div><div class="t m0 x24 h9 y47 ff4 fs5 fc0 sc0 ls6">\uebbc<span class="fs4 ls0 ws0 v1">\u2212 3\ue747\ue730<span class="_d blank"> </span>\u2212 2\ue747\ue730<span class="_1 blank"> </span>/\ue749<span class="_1 blank"> </span> .<span class="_2 blank"> </span>2\ue749<span class="_7 blank"> </span>=<span class="_7 blank"> </span>0<span class="_c blank"> </span>\u2192<span class="_7 blank"> </span>\ue738</span></div><div class="t m0 x25 ha y47 ff4 fs5 fc0 sc0 ls9">\uebbc<span class="fs4 ls0 ws2 v1">= 3\ue747\ue730<span class="_d blank"> </span>+<span class="_f blank"> </span>4\ue747\ue730<span class="_7 blank"> </span>= 7\ue747\ue730<span class="_1 blank"> </span><span class="ff2 ws0"> </span></span></div><div class="t m0 x1 h7 y48 ff2 fs4 fc1 sc0 ls0 ws0">Traçado dos diagramas </div><div class="t m0 x1 h7 y49 ff2 fs4 fc0 sc0 ls0 ws0"> <span class="_0 blank"> </span>Nesse <span class="_3 blank"></span>exemplo, <span class="_5 blank"></span>como não <span class="_5 blank"></span>há forças <span class="_5 blank"></span>horizontais, <span class="_3 blank"></span>não <span class="_5 blank"></span>teremos esforços <span class="_5 blank"></span>normais. </div><div class="t m0 x1 h7 y4a ff2 fs4 fc0 sc0 ls0 ws0">É <span class="_1 blank"> </span>possível <span class="_1 blank"> </span>pensar <span class="_1 blank"> </span>no <span class="_1 blank"> </span>traçado <span class="_1 blank"> </span>de <span class="_1 blank"> </span>cada <span class="_1 blank"> </span>viga <span class="_1 blank"> </span>decomposta <span class="_1 blank"> </span>de <span class="_1 blank"> </span>forma <span class="_1 blank"> </span>independente, já <span class="_1 blank"> </span>que </div><div class="t m0 x1 h7 y4b ff2 fs4 fc0 sc0 ls0 ws0">todas elas são estáveis e com condições de contorno bem definidas. </div><div class="t m0 x26 h7 y4c ff2 fs4 fc0 sc0 ls0 ws0">DEC <span class="_11 blank"> </span>DMF </div><div class="t m0 x4 hf y4d ff2 fs4 fc0 sc0 lsf ws0"> <span class="ls0 v1"> </span></div><div class="t m0 x1 h6 y4e ff3 fs3 fc1 sc0 ls0 ws0">Vigas inclinadas </div><div class="t m0 x1 h7 y4f ff2 fs4 fc0 sc0 ls0 ws0"> <span class="_0 blank"> </span>Teremos, com <span class="_f blank"> </span>frequência, esfo<span class="_1 blank"> </span>rços normais <span class="_f blank"> </span>nas barras. <span class="_f blank"> </span>Portanto, <span class="_f blank"> </span>devemos </div><div class="t m0 x1 h7 y50 ff2 fs4 fc0 sc0 ls0 ws0">traçar <span class="_9 blank"> </span>os <span class="_12 blank"> </span>diagramas <span class="_12 blank"> </span>de <span class="_12 blank"> </span>esforços <span class="_12 blank"> </span>normais <span class="_9 blank"> </span>(DEN), <span class="_12 blank"> </span>além <span class="_12 blank"> </span>do <span class="_9 blank"> </span>DEC <span class="_12 blank"> </span>e <span class="_9 blank"> </span>do <span class="_12 blank"> </span>DMF <span class="_12 blank"> </span>que </div><div class="t m0 x1 h7 y51 ff2 fs4 fc0 sc0 ls0 ws0">normalmente traçamos. </div><div class="t m0 x1 h7 y52 ff2 fs4 fc1 sc0 ls0 ws0">Exemplo </div><div class="t m0 x1 h7 y53 ff2 fs4 fc0 sc0 ls0 ws0"> <span class="_0 blank"> </span>Observe <span class="_4 blank"> </span>que <span class="_8 blank"> </span>o <span class="_4 blank"> </span>total <span class="_4 blank"> </span>de <span class="_4 blank"> </span>carregament<span class="_3 blank"></span>o <span class="_4 blank"> </span>sobre <span class="_8 blank"> </span>a <span class="_4 blank"> </span>viga <span class="_4 blank"> </span>inclinada <span class="_8 blank"> </span>é <span class="_4 blank"> </span>(6kN/m <span class="_4 blank"> </span>. <span class="_8 blank"> </span>5m <span class="_4 blank"> </span>= </div><div class="t m0 x1 h7 y54 ff2 fs4 fc0 sc0 ls0 ws0">30kN), <span class="_8 blank"> </span>uma <span class="_8 blank"> </span>vez <span class="_8 blank"> </span>que <span class="_6 blank"> </span>ela <span class="_8 blank"> </span>está <span class="_8 blank"> </span>distribuída <span class="_8 blank"> </span>sobre <span class="_8 blank"> </span>a <span class="_8 blank"> </span>hipotenusa <span class="_8 blank"> </span>de <span class="_8 blank"> </span>um <span class="_8 blank"> </span>triângulo <span class="_6 blank"> </span>de <span class="_8 blank"> </span>lados </div><div class="t m0 x1 h7 y55 ff2 fs4 fc0 sc0 ls0 ws0">3m, 4m e 5m. </div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/0866faf6-6ca2-4fe6-bc14-45a600308a4f/bg4.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls0 ws0">4 </div><div class="c x1 y3 w2 h3"><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls0 ws0"> </div></div><div class="t m0 x27 h7 y56 ff2 fs4 fc0 sc0 ls0 ws0"> </div><div class="t m0 x6 h8 y57 ff4 fs4 fc0 sc0 ls0 ws7">\u2211\ue728</div><div class="t m0 x28 h9 y58 ff4 fs5 fc0 sc0 ls10">\uebeb<span class="fs4 ls0 ws8 v1">= 0 \u2192 \ue72a</span></div><div class="t m0 x29 ha y58 ff4 fs5 fc0 sc0 ls11">\uebba<span class="fs4 ls0 ws2 v1">= 0<span class="ff2 ws0"> </span></span></div><div class="t m0 x2a h8 y59 ff4 fs4 fc0 sc0 ls0 ws7">\u2211\ue72f</div><div class="t m0 x2b h9 y5a ff4 fs5 fc0 sc0 ls11">\uebba<span class="fs4 ls0 ws0 v1">=<span class="_c blank"> </span>0<span class="_7 blank"> </span>\u2192<span class="_c blank"> </span>4\ue749<span class="_1 blank"> </span> .<span class="_2 blank"> </span>\ue738</span></div><div class="t m0 x2c h9 y5a ff4 fs5 fc0 sc0 lsd">\uebbb<span class="fs4 ls0 ws0 v1">\u2212 6\ue747\ue730<span class="_1 blank"> </span>/\ue749<span class="_1 blank"> </span> .<span class="_2 blank"> </span>5\ue749<span class="_1 blank"> </span> .<span class="_2 blank"> </span>2\ue749<span class="_7 blank"> </span>=<span class="_7 blank"> </span>0<span class="_c blank"> </span>\u2192<span class="_7 blank"> </span>\ue738</span></div><div class="t m0 x2d ha y5a ff4 fs5 fc0 sc0 lsc">\uebbb<span class="fs4 ls0 ws6 v1">=<span class="_c blank"> </span>15\ue747\ue730 <span class="ff2 ws0"> </span></span></div><div class="t m0 x2e h8 y5b ff4 fs4 fc0 sc0 ls0 ws7">\u2211\ue728</div><div class="t m0 x2f h9 y5c ff4 fs5 fc0 sc0 ls4">\uebec<span class="fs4 ls0 wsb v1">= 0 \u2192 \ue738</span></div><div class="t m0 x30 h9 y5c ff4 fs5 fc0 sc0 ls12">\uebba<span class="fs4 ls0 ws9 v1">+ \ue738</span></div><div class="t m0 x31 h9 y5c ff4 fs5 fc0 sc0 ls13">\uebbb<span class="fs4 ls0 ws0 v1">\u2212 6\ue747\ue730<span class="_1 blank"> </span>/\ue749<span class="_1 blank"> </span> .<span class="_2 blank"> </span>5\ue749<span class="_7 blank"> </span>=<span class="_7 blank"> </span>0<span class="_c blank"> </span>\u2192<span class="_c blank"> </span>\ue738</span></div><div class="t m0 x32 ha y5c ff4 fs5 fc0 sc0 ls2">\uebba<span class="fs4 ls0 ws4 v1">=<span class="_c blank"> </span>15\ue747\ue730 <span class="ff2 ws0"> </span></span></div><div class="t m0 x1 h7 y5d ff2 fs4 fc0 sc0 ls0 ws0"> <span class="_0 blank"> </span>O <span class="_2 blank"> </span>traçado <span class="_a blank"> </span>do <span class="_2 blank"> </span>diagrama <span class="_2 blank"> </span>de <span class="_2 blank"> </span>momentos <span class="_a blank"> </span>fletores <span class="_2 blank"> </span>é <span class="_2 blank"> </span>imediato <span class="_a blank"> </span>e <span class="_2 blank"> </span>análogo <span class="_2 blank"> </span>ao <span class="_2 blank"> </span>que </div><div class="t m0 x1 h7 y5e ff2 fs4 fc0 sc0 ls0 ws0">temos <span class="_4 blank"> </span>estudado <span class="_a blank"> </span>até <span class="_4 blank"> </span>o <span class="_a blank"> </span>momento. <span class="_4 blank"> </span>Nossa <span class="_a blank"> </span>representação <span class="_4 blank"> </span>sempre <span class="_4 blank"> </span>se<span class="_1 blank"> </span>rá <span class="_4 blank"> </span>perpendicular <span class="_a blank"> </span>à </div><div class="t m0 x1 h7 y5f ff2 fs4 fc0 sc0 ls0 ws0">viga. A parábola a ser pendurada no diagrama, devido à distribuição <span class="_f blank"> </span>inclinada do </div><div class="t m0 x1 h7 y60 ff2 fs4 fc0 sc0 ls0 ws0">carregamento, será de momento igual a: </div><div class="t m0 x31 h8 y61 ff4 fs4 fc0 sc0 ls0">\ue72f</div><div class="t m0 x28 hc y62 ff4 fs5 fc0 sc0 ls0 wsc">\uebe3\uebd4\uebe5 <span class="fs4 ls3 v1">=</span><span class="fs4 ws0 v5">\ue74d<span class="_1 blank"> </span> .<span class="_2 blank"> </span>\ue748</span><span class="wsd v2">\uebd7\uebdc\uebe6\uebe7 </span><span class="fs4 ws0 v5"> .<span class="_2 blank"> </span>\ue748</span></div><div class="t m0 x33 hd y63 ff4 fs4 fc0 sc0 ls14">8<span class="ff2 ls0 ws0 v3"> </span></div><div class="t m0 x1 h7 y64 ff2 fs4 fc0 sc0 ls0 ws0"> <span class="_0 blank"> </span>Onde <span class="_3 blank"></span><span class="ff4 ws7">\ue748<span class="fs5 wse v6">\uebd7\uebdc\uebe6\uebe7 </span><span class="ff2 ws0"> é <span class="_5 blank"></span>o c<span class="_3 blank"></span>omprimento <span class="_5 blank"></span>da viga <span class="_5 blank"></span>e <span class="ff4 ls15">\ue748</span> <span class="_3 blank"></span>é <span class="_3 blank"></span>a <span class="_5 blank"></span>projeção do <span class="_5 blank"></span>carregamento. Portanto, </span></span></div><div class="t m0 x1 h7 y65 ff2 fs4 fc0 sc0 ls0 ws0">o DMF da estrutura é representado abaixo: </div><div class="t m0 x34 h7 y66 ff2 fs4 fc0 sc0 ls0 ws0"> </div><div class="t m0 x1 h7 y67 ff2 fs4 fc0 sc0 ls0 ws0"> <span class="_0 blank"> </span>Para <span class="_8 blank"> </span>o <span class="_8 blank"> </span>traçado <span class="_6 blank"> </span>dos <span class="_8 blank"> </span>diagramas <span class="_8 blank"> </span>de <span class="_6 blank"> </span>esforço <span class="_8 blank"> </span>cortante <span class="_8 blank"> </span>e <span class="_6 blank"> </span>esforço <span class="_8 blank"> </span>normal, <span class="_8 blank"> </span>d<span class="_1 blank"> </span>evemos </div><div class="t m0 x1 h7 y68 ff2 fs4 fc0 sc0 ls0 ws0">projetar <span class="_5 blank"></span>os <span class="_3 blank"></span>esforços <span class="_5 blank"></span>em <span class="_5 blank"></span>cada seção <span class="_b blank"></span>relevante <span class="_5 blank"></span>da estrutura <span class="_5 blank"></span>para <span class="_5 blank"></span>analisar <span class="_5 blank"></span>o seu <span class="_b blank"></span>diagrama.<span class="_1 blank"> </span> </div><div class="t m0 x1 h7 y69 ff2 fs4 fc0 sc0 ls0 ws0"> <span class="_0 blank"> </span>Admitindo <span class="_a blank"> </span>que <span class="_2 blank"> </span><span class="ff4 ls16">\ue7d9</span> <span class="_2 blank"> </span>seja <span class="_2 blank"> </span>o <span class="_a blank"> </span>ângulo <span class="_2 blank"> </span>de <span class="_2 blank"> </span>inclinação <span class="_2 blank"> </span>formado <span class="_a blank"> </span>pela <span class="_2 blank"> </span>viga <span class="_2 blank"> </span>com <span class="_a blank"> </span>o <span class="_2 blank"> </span>eixo </div><div class="t m0 x1 h7 y6a ff2 fs4 fc0 sc0 ls0 ws0">horizontal: </div><div class="t m0 x1 h7 y6b ff2 fs4 fc0 sc0 ls0 ws0"> <span class="_0 blank"> </span>- Apoio A: </div><div class="t m0 x35 h8 y6c ff4 fs4 fc0 sc0 ls0 ws2">\ue730<span class="_7 blank"> </span>= \u2212\ue738</div><div class="t m0 x36 ha y6d ff4 fs5 fc0 sc0 lsa">\uebba<span class="fs4 ls0 ws0 v1"> .<span class="_2 blank"> </span>\ue74f\ue741\ue74a<span class="_1 blank"> </span> \ue7d9<span class="_7 blank"> </span>=<span class="_7 blank"> </span>\u221215\ue747\ue730<span class="_1 blank"> </span> .<span class="_2 blank"> </span>0,6<span class="_7 blank"> </span>=<span class="_c blank"> </span>\u22129\ue747\ue730<span class="_1 blank"> </span><span class="ff2"> </span></span></div><div class="t m0 x37 h8 y6e ff4 fs4 fc0 sc0 ls0 ws2">\ue733<span class="_7 blank"> </span>= \ue738</div><div class="t m0 x17 ha y6f ff4 fs5 fc0 sc0 lsa">\uebba<span class="fs4 ls0 ws0 v1"> .<span class="_2 blank"> </span>cos<span class="_2 blank"> </span>\ue7d9<span class="_12 blank"> </span>=<span class="_c blank"> </span>15\ue747\ue730<span class="_1 blank"> </span> .<span class="_2 blank"> </span>0,8<span class="_7 blank"> </span>=<span class="_c blank"> </span>12\ue747\ue730<span class="_1 blank"> </span><span class="ff2"> </span></span></div><div class="t m0 x1 h7 y70 ff2 fs4 fc0 sc0 ls0 ws0"> <span class="_0 blank"> </span>- Ponto B: </div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf5" class="pf w0 h0" data-page-no="5"><div class="pc pc5 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/0866faf6-6ca2-4fe6-bc14-45a600308a4f/bg5.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls0 ws0">5 </div><div class="c x1 y3 w2 h3"><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls0 ws0"> </div></div><div class="t m0 x38 h10 y71 ff4 fs4 fc0 sc0 ls0 ws2">\ue730<span class="_7 blank"> </span>= \u2212<span class="ws7 v4">(</span>\ue738</div><div class="t m0 x39 ha y72 ff4 fs5 fc0 sc0 ls5">\uebba<span class="fs4 ls0 ws0 v1">\u2212 6\ue747\ue730<span class="_1 blank"> </span>/\ue749<span class="_1 blank"> </span> .<span class="_2 blank"> </span>5\ue749<span class="_1 blank"> </span><span class="ws7 v4">)</span>.<span class="_2 blank"> </span>\ue74f\ue741\ue74a<span class="_1 blank"> </span> \ue7d9<span class="_7 blank"> </span>=<span class="_7 blank"> </span>\u2212<span class="ws7 v4">(<span class="v7">\u221215</span>)</span> .<span class="_2 blank"> </span>0,6<span class="_7 blank"> </span>=<span class="_c blank"> </span>9\ue747\ue730<span class="_1 blank"> </span><span class="ff2"> </span></span></div><div class="t m0 x3a h10 y73 ff4 fs4 fc0 sc0 ls0 ws2">\ue733<span class="_7 blank"> </span>= <span class="ws7 v4">(</span>\ue738</div><div class="t m0 x35 ha y74 ff4 fs5 fc0 sc0 ls5">\uebba<span class="fs4 ls0 ws0 v1">\u2212 6\ue747\ue730<span class="_1 blank"> </span>/\ue749<span class="_1 blank"> </span> .<span class="_2 blank"> </span>5\ue749<span class="_1 blank"> </span><span class="ws7 v4">)</span> .<span class="_2 blank"> </span>cos<span class="_2 blank"> </span>\ue7d9<span class="_12 blank"> </span>=<span class="_c blank"> </span>\u221215 .<span class="_2 blank"> </span>0,8<span class="_c blank"> </span>=<span class="_2 blank"> </span> <span class="_a blank"> </span>\u221212\ue747\ue730<span class="_1 blank"> </span><span class="ff2"> </span></span></div><div class="t m0 x1 h7 y75 ff2 fs4 fc0 sc0 ls0 ws0"> <span class="_0 blank"> </span>Portanto, seguimos <span class="_2 blank"> </span>os esforços calculados <span class="_2 blank"> </span>acima e traç<span class="_3 blank"></span>amos os <span class="_2 blank"> </span>diagramas, </div><div class="t m0 x1 h7 y76 ff2 fs4 fc0 sc0 ls0 ws0">conforme apresentado a seguir: </div><div class="t m0 x26 h7 y77 ff2 fs4 fc0 sc0 ls0 ws0">DEN <span class="_13 blank"> </span>DEC </div><div class="t m0 x31 h7 y78 ff2 fs4 fc0 sc0 ls0 ws0"> <span class="_14 blank"> </span> </div><div class="t m0 x1 h7 y79 ff2 fs4 fc0 sc0 ls0 ws0"> </div><div class="t m0 x1 h6 y7a ff3 fs3 fc1 sc0 ls0 ws0"> </div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div>
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