<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/b33ede67-33c6-461b-ad6c-9c5c2708e824/bg1.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls3 ws4"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls3 ws4">1 </div><div class="c x1 y3 w2 h3"><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls3 ws4"> </div></div><div class="t m0 x1 h4 y5 ff2 fs1 fc1 sc0 ls3 ws4">Análise de Estruturas I - Resumo </div><div class="t m0 x1 h4 y6 ff2 fs1 fc1 sc0 ls3 ws4"> </div><div class="t m0 x1 h5 y7 ff3 fs2 fc0 sc0 ls3 ws4">PÓRTICOS I </div><div class="t m0 x1 h6 y8 ff3 fs3 fc1 sc0 ls3 ws4"> </div><div class="t m0 x1 h6 y9 ff3 fs3 fc1 sc0 ls3 ws4">Introdução </div><div class="t m0 x1 h7 ya ff2 fs4 fc0 sc0 ls3 ws4"> <span class="_0 blank"> </span>Na últi<span class="_1 blank"></span>ma aula <span class="_1 blank"></span>fizemos <span class="_1 blank"></span>uma revisão <span class="_1 blank"></span>geral <span class="_1 blank"></span>do <span class="_1 blank"></span>estudo de <span class="_1 blank"></span>vigas. <span class="_1 blank"></span>Trabalhamos com </div><div class="t m0 x1 h7 yb ff2 fs4 fc0 sc0 ls3 ws4">vigas Gerber <span class="_1 blank"></span>(rotuladas), v<span class="_1 blank"></span>igas engastadas <span class="_1 blank"></span>e livres, <span class="_1 blank"></span>vigas e<span class="_1 blank"></span>m balan<span class="_1 blank"></span>ço e vi<span class="_1 blank"></span>gas incli<span class="_1 blank"></span>nadas.<span class="_2 blank"> </span> </div><div class="t m0 x1 h7 yc ff2 fs4 fc0 sc0 ls3 ws4"> <span class="_0 blank"> </span>No <span class="_3 blank"> </span>entanto, <span class="_3 blank"> </span>em <span class="_3 blank"> </span>um <span class="_3 blank"> </span>projeto <span class="_3 blank"> </span>de <span class="_3 blank"> </span>estruturas <span class="_3 blank"> </span>nem <span class="_3 blank"> </span>sempre <span class="_3 blank"> </span>conseguimos <span class="_3 blank"> </span>trabalhar </div><div class="t m0 x1 h7 yd ff2 fs4 fc0 sc0 ls3 ws4">com <span class="_4 blank"> </span>vigas <span class="_4 blank"> </span>isoladamente. <span class="_4 blank"> </span>Pelo <span class="_4 blank"> </span>contrário, <span class="_4 blank"> </span>usualmente <span class="_4 blank"> </span>p<span class="_1 blank"></span>recisamos <span class="_4 blank"> </span>analisar <span class="_4 blank"> </span>estruturas </div><div class="t m0 x1 h7 ye ff2 fs4 fc0 sc0 ls3 ws4">planas <span class="_5 blank"> </span>que <span class="_5 blank"> </span>são <span class="_5 blank"> </span>compostas <span class="_5 blank"> </span>por <span class="_5 blank"> </span>diversos <span class="_5 blank"> </span>elementos <span class="_5 blank"> </span>lineares. <span class="_5 blank"> </span>Estamos <span class="_5 blank"> </span>falando <span class="_5 blank"> </span>dos </div><div class="t m0 x1 h7 yf ff2 fs4 fc0 sc0 ls3 ws4">pórticos. </div><div class="t m0 x1 h7 y10 ff2 fs4 fc0 sc0 ls3 ws4"> <span class="_0 blank"> </span>Nessa <span class="_6 blank"> </span>aula <span class="_6 blank"> </span>e <span class="_6 blank"> </span>na <span class="_6 blank"> </span>próxima <span class="_6 blank"> </span>vamos <span class="_6 blank"> </span>estudar <span class="_6 blank"> </span>como <span class="_6 blank"> </span>podemos <span class="_6 blank"> </span>analisar <span class="_6 blank"> </span>os <span class="_6 blank"> </span>pórticos, </div><div class="t m0 x1 h7 y11 ff2 fs4 fc0 sc0 ls3 ws4">trabalhando com quadros biapoiados, engastados e livres e triart<span class="_1 blank"></span>iculados. </div><div class="t m0 x1 h6 y12 ff3 fs3 fc1 sc0 ls3 ws4">Pórticos simples e engastados e livres </div><div class="t m0 x1 h7 y13 ff2 fs4 fc0 sc0 ls3 ws4"> <span class="_0 blank"> </span>Chamamos <span class="_6 blank"> </span>de <span class="_6 blank"> </span>pórtico <span class="_6 blank"> </span>(ou <span class="_7 blank"> </span>quadro) <span class="_7 blank"> </span>simples, <span class="_6 blank"> </span>uma <span class="_7 blank"> </span>estrutura <span class="_6 blank"> </span>bidimensional <span class="_6 blank"> </span>que </div><div class="t m0 x1 h7 y14 ff2 fs4 fc0 sc0 ls3 ws4">possua cargas no plano da estrutura. </div><div class="t m0 x1 h7 y15 ff2 fs4 fc0 sc0 ls3 ws4"> <span class="_0 blank"> </span>Considere, por <span class="_2 blank"> </span>exemplo, <span class="_2 blank"> </span>o <span class="_2 blank"> </span>pórtico abaixo. <span class="_2 blank"> </span>Como <span class="_2 blank"> </span>temos três <span class="_2 blank"> </span>reações <span class="_2 blank"> </span>de apoio <span class="_2 blank"> </span>e </div><div class="t m0 x1 h7 y16 ff2 fs4 fc0 sc0 ls3 ws4">três equações <span class="_5 blank"> </span>de equilíbrio, trata-se <span class="_8 blank"> </span>de um <span class="_8 blank"> </span>pórtico isostático, e<span class="_2 blank"> </span>ntão <span class="_8 blank"> </span>conseguimos </div><div class="t m0 x1 h7 y17 ff2 fs4 fc0 sc0 ls3 ws4">determinar as reações sem problemas. </div><div class="t m0 x3 h7 y18 ff2 fs4 fc0 sc0 ls3 ws4"> </div><div class="t m0 x4 h8 y19 ff4 fs4 fc0 sc0 ls3 ws0">\u2211\ue72f</div><div class="t m0 x5 h9 y1a ff4 fs5 fc0 sc0 ls0">\uebba<span class="fs4 ls3 ws4 v1">=<span class="_9 blank"> </span>0<span class="_9 blank"> </span>\u2192<span class="_9 blank"> </span>4\ue749 .<span class="_a blank"> </span>\ue738</span></div><div class="t m0 x6 h9 y1a ff4 fs5 fc0 sc0 ls1">\uebbd<span class="fs4 ls3 ws4 v1">\u2212 4\ue747\ue730<span class="_2 blank"> </span>/\ue749 .<span class="_a blank"> </span>4\ue749<span class="_2 blank"> </span> .<span class="_4 blank"> </span>2\ue749<span class="_5 blank"> </span>\u2212 20\ue747\ue730<span class="_2 blank"> </span> .<span class="_a blank"> </span>2\ue749<span class="_9 blank"> </span>=<span class="_9 blank"> </span>0<span class="_9 blank"> </span>\u2192<span class="_9 blank"> </span>\ue738</span></div><div class="t m0 x7 ha y1a ff4 fs5 fc0 sc0 ls3">\uebbd</div><div class="t m0 x8 hb y1b ff4 fs4 fc0 sc0 ls2">=<span class="ls3 ws1 v2">32\ue747\ue730 .<span class="_4 blank"> </span>\ue749<span class="_5 blank"> </span>+<span class="_8 blank"> </span>40\ue747\ue730 .<span class="_4 blank"> </span>\ue749</span></div><div class="t m0 x9 hc y1c ff4 fs4 fc0 sc0 ls3 ws2">4\ue749 <span class="ws3 v3">=<span class="_9 blank"> </span>18\ue747\ue730 <span class="ff2 ws4"> </span></span></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/b33ede67-33c6-461b-ad6c-9c5c2708e824/bg2.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls3 ws4"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls3 ws4">2 </div><div class="c x1 y3 w2 h3"><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls3 ws4"> </div></div><div class="t m0 xa h8 y1d ff4 fs4 fc0 sc0 ls3 ws0">\u2211\ue728</div><div class="t m0 xb h9 y1e ff4 fs5 fc0 sc0 ls4">\uebec<span class="fs4 ls3 ws5 v1">= 0 \u2192 \ue738</span></div><div class="t m0 xc h9 y1e ff4 fs5 fc0 sc0 ls5">\uebba<span class="fs4 ls3 ws6 v1">+ \ue738</span></div><div class="t m0 xd h9 y1e ff4 fs5 fc0 sc0 ls1">\uebbd<span class="fs4 ls3 ws4 v1">\u2212 4\ue747\ue730<span class="_2 blank"> </span>/\ue749 .<span class="_a blank"> </span>4\ue749<span class="_9 blank"> </span>=<span class="_9 blank"> </span>0<span class="_9 blank"> </span>\u2192<span class="_9 blank"> </span>\ue738</span></div><div class="t m0 xe hd y1e ff4 fs5 fc0 sc0 ls6">\uebba<span class="fs4 ls3 ws3 v1">=<span class="_9 blank"> </span>\u22122\ue747\ue730 <span class="ff2 ws4"> </span></span></div><div class="t m0 xf h8 y1f ff4 fs4 fc0 sc0 ls3 ws0">\u2211\ue728</div><div class="t m0 x10 h9 y20 ff4 fs5 fc0 sc0 ls7">\uebeb<span class="fs4 ls3 ws6 v1">=<span class="_9 blank"> </span>0<span class="_9 blank"> </span>\u2192<span class="_9 blank"> </span>20\ue747\ue730<span class="_5 blank"> </span>+ \ue72a</span></div><div class="t m0 x11 h9 y20 ff4 fs5 fc0 sc0 ls0">\uebba<span class="fs4 ls3 ws5 v1">= 0 \u2192 \ue72a</span></div><div class="t m0 x12 hd y20 ff4 fs5 fc0 sc0 ls0">\uebba<span class="fs4 ls3 ws1 v1">=<span class="_9 blank"> </span>\u221220\ue747\ue730 <span class="ff2 ws4"> </span></span></div><div class="t m0 x1 h7 y21 ff2 fs4 fc0 sc0 ls3 ws4"> <span class="_0 blank"> </span>Vamos <span class="_7 blank"> </span>começar <span class="_6 blank"> </span>o <span class="_7 blank"> </span>traçado <span class="_6 blank"> </span>dos <span class="_6 blank"> </span>diagramas <span class="_6 blank"> </span>pelo <span class="_7 blank"> </span>DEN. <span class="_6 blank"> </span>Analisando <span class="_6 blank"> </span>da <span class="_7 blank"> </span>esquerda </div><div class="t m0 x1 h7 y22 ff2 fs4 fc0 sc0 ls3 ws4">para a direita, <span class="_1 blank"></span>vemos que a <span class="_1 blank"></span>reação V<span class="fs6 ws7 v4">A</span> <span class="_1 blank"></span>faz um esforço d<span class="_1 blank"></span>e tração na <span class="_1 blank"></span>barra AB de <span class="_1 blank"></span>2kN. Em </div><div class="t m0 x1 h7 y23 ff2 fs4 fc0 sc0 ls3 ws4">seguida, observando <span class="_2 blank"> </span>o <span class="_2 blank"> </span>ponto B, <span class="_2 blank"> </span>vemos <span class="_2 blank"> </span>que <span class="_2 blank"> </span>o total <span class="_2 blank"> </span>de <span class="_2 blank"> </span>forças horizontais <span class="_2 blank"> </span>é <span class="_2 blank"> </span>igual a <span class="_2 blank"> </span>zero. </div><div class="t m0 x1 h7 y24 ff2 fs4 fc0 sc0 ls3 ws4">Neste <span class="_7 blank"> </span>caso, <span class="_6 blank"> </span>não <span class="_7 blank"> </span>há <span class="_6 blank"> </span>esforços <span class="_6 blank"> </span>normais <span class="_7 blank"> </span>na <span class="_6 blank"> </span>barra <span class="_6 blank"> </span>BC. <span class="_6 blank"> </span>Por <span class="_7 blank"> </span>último, <span class="_6 blank"> </span>analisando <span class="_7 blank"> </span>o <span class="_6 blank"> </span>ponto <span class="_6 blank"> </span>C </div><div class="t m0 x1 h7 y25 ff2 fs4 fc0 sc0 ls3 ws4">observamos <span class="_b blank"> </span>que <span class="_b blank"> </span>o <span class="_b blank"> </span>total <span class="_b blank"> </span>de <span class="_b blank"> </span>carga <span class="_b blank"> </span>será <span class="_b blank"> </span>(<span class="_2 blank"> </span><span class="ff4">\u22122\ue747\ue730<span class="_8 blank"> </span>\u2212<span class="_8 blank"> </span>4\ue747\ue730<span class="_2 blank"> </span>/<span class="_2 blank"> </span>\ue749 .<span class="_a blank"> </span>4\ue749<span class="_9 blank"> </span>=<span class="_9 blank"> </span>\u221218\ue747\ue730<span class="_2 blank"> </span></span>). <span class="_b blank"> </span>Como </div><div class="t m0 x1 h7 y26 ff2 fs4 fc0 sc0 ls3 ws4">estamos analisando a barra CD pelo ponto C, esta carga estará comprimin<span class="_1 blank"></span>do a barra. </div><div class="t m0 x1 h7 y27 ff2 fs4 fc0 sc0 ls3 ws4"> <span class="_0 blank"> </span>No DEN, <span class="_1 blank"></span>não <span class="_1 blank"></span>é i<span class="_1 blank"></span>mportante <span class="_1 blank"></span>o lad<span class="_1 blank"></span>o da <span class="_1 blank"></span>barra <span class="_1 blank"></span>que r<span class="_1 blank"></span>epresentamos o <span class="_1 blank"></span>esforço. <span class="_1 blank"></span>O sinal </div><div class="t m0 x1 h7 y28 ff2 fs4 fc0 sc0 ls3 ws4">do <span class="_c blank"></span>esforço <span class="_c blank"></span>já <span class="_c blank"></span>indica <span class="_c blank"></span>se <span class="_c blank"></span>a <span class="_c blank"></span>barra <span class="_c blank"></span>está <span class="_c blank"></span>comprimida <span class="_c blank"></span>(normal <span class="_c blank"></span>negativa) <span class="_c blank"></span>ou <span class="_c blank"></span>tracionada <span class="_c blank"></span>(normal </div><div class="t m0 x1 h7 y29 ff2 fs4 fc0 sc0 ls3 ws4">positiva). </div><div class="t m0 x13 h7 y2a ff2 fs4 fc0 sc0 ls3 ws4"> </div><div class="t m0 x1 h7 y2b ff2 fs4 fc0 sc0 ls3 ws4"> <span class="_0 blank"> </span>Vamos <span class="_3 blank"> </span>agora <span class="_3 blank"> </span>seguir <span class="_2 blank"> </span>para <span class="_3 blank"> </span>o <span class="_3 blank"> </span>traçado <span class="_3 blank"> </span>do <span class="_3 blank"> </span>DEC. <span class="_2 blank"> </span>A <span class="_3 blank"> </span>ideia <span class="_3 blank"> </span>é <span class="_3 blank"> </span>a <span class="_3 blank"> </span>mesma <span class="_2 blank"> </span>do <span class="_3 blank"> </span>traçado <span class="_3 blank"> </span>em </div><div class="t m0 x1 h7 y2c ff2 fs4 fc0 sc0 ls3 ws4">vigas retas, onde vamos <span class="_2 blank"> </span>\u201ccaminhando\u201d pela estrutura, sempre <span class="_2 blank"> </span>de <span class="_2 blank"> </span>cima para baixo e <span class="_2 blank"> </span>da </div><div class="t m0 x1 h7 y2d ff2 fs4 fc0 sc0 ls3 ws4">esquerda <span class="_a blank"> </span>para <span class="_4 blank"> </span>a direita, <span class="_4 blank"> </span>adicionando ou <span class="_a blank"> </span>subtrain<span class="_1 blank"></span>do <span class="_a blank"> </span>os <span class="_a blank"> </span>esforços <span class="_4 blank"> </span>cortantes em <span class="_4 blank"> </span>c<span class="_2 blank"> </span>ada </div><div class="t m0 x1 h7 y2e ff2 fs4 fc0 sc0 ls3 ws4">trecho. </div><div class="t m0 x14 h7 y2f ff2 fs4 fc0 sc0 ls3 ws4"> </div><div class="t m0 x1 h7 y30 ff2 fs4 fc0 sc0 ls3 ws4"> <span class="_0 blank"> </span>Por <span class="_c blank"></span>último, <span class="_c blank"></span>devemos <span class="_1 blank"></span>calcular <span class="_c blank"></span>o <span class="_c blank"></span>diagrama <span class="_c blank"></span>de <span class="_c blank"></span>momentos <span class="_1 blank"></span>fletores. <span class="_c blank"></span>Para <span class="_c blank"></span>isso, <span class="_c blank"></span>basta </div><div class="t m0 x1 h7 y31 ff2 fs4 fc0 sc0 ls3 ws4">calcularmos <span class="_7 blank"> </span>os <span class="_7 blank"> </span>momentos <span class="_7 blank"> </span>em <span class="_7 blank"> </span>cada <span class="_7 blank"> </span>ponto <span class="_7 blank"> </span>de <span class="_7 blank"> </span>aplicação <span class="_7 blank"> </span>de <span class="_7 blank"> </span>carga <span class="_7 blank"> </span>o<span class="_2 blank"> </span>u <span class="_7 blank"> </span>ao <span class="_7 blank"> </span>final <span class="_7 blank"> </span>de <span class="_7 blank"> </span>cada </div><div class="t m0 x1 h7 y32 ff2 fs4 fc0 sc0 ls3 ws4">barra. Um p<span class="_1 blank"></span>onto importan<span class="_1 blank"></span>te que <span class="_1 blank"></span>devemos sem<span class="_1 blank"></span>pre levar <span class="_1 blank"></span>em consid<span class="_1 blank"></span>eração é <span class="_1 blank"></span>o equi<span class="_1 blank"></span>líbrio </div><div class="t m0 x1 h7 y33 ff2 fs4 fc0 sc0 ls3 ws4">nos <span class="_3 blank"> </span>momentos <span class="_3 blank"> </span>em <span class="_3 blank"> </span>cada <span class="_3 blank"> </span>nó. <span class="_3 blank"> </span>Tome, <span class="_3 blank"> </span>por <span class="_3 blank"> </span>exemplo, <span class="_3 blank"> </span>o <span class="_3 blank"> </span>momento <span class="_3 blank"> </span>no <span class="_3 blank"> </span>nó <span class="_3 blank"> </span>B, <span class="_3 blank"> </span>analisado <span class="_3 blank"> </span>pela </div><div class="t m0 x1 h7 y34 ff2 fs4 fc0 sc0 ls3 ws4">barra AB (ou seja, pelo lado esquerdo). Temos: </div><div class="t m0 xb h8 y35 ff4 fs4 fc0 sc0 ls3">\ue72f</div><div class="t m0 x15 hd y36 ff4 fs5 fc0 sc0 ls3 ws8">\uebbb ,\uebd8\uebe6\uebe4<span class="_d blank"> </span><span class="fs4 ws4 v1">=<span class="_9 blank"> </span>\u221220\ue747\ue730<span class="_2 blank"> </span> .<span class="_4 blank"> </span>4\ue749<span class="_5 blank"> </span>+ 20\ue747\ue730<span class="_2 blank"> </span> .<span class="_a blank"> </span>2\ue749<span class="_9 blank"> </span>=<span class="_9 blank"> </span>\u221240\ue747\ue730<span class="_2 blank"> </span>.<span class="_a blank"> </span>\ue749<span class="ff2"> </span></span></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/b33ede67-33c6-461b-ad6c-9c5c2708e824/bg3.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls3 ws4"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls3 ws4">3 </div><div class="c x1 y3 w2 h3"><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls3 ws4"> </div></div><div class="t m0 x1 h7 y1d ff2 fs4 fc0 sc0 ls3 ws4"> <span class="_0 blank"> </span>O <span class="_c blank"></span>sina<span class="_2 blank"> </span>l <span class="_c blank"></span>negativo indica <span class="_c blank"></span>que <span class="_1 blank"></span>este <span class="_1 blank"></span>momento <span class="_c blank"></span>está <span class="_1 blank"></span>no <span class="_c blank"></span>se<span class="_2 blank"> </span>ntido <span class="_c blank"></span>horário. Temos <span class="_c blank"></span>então </div><div class="t m0 x1 h7 y37 ff2 fs4 fc0 sc0 ls3 ws4">a seguinte representação: </div><div class="t m0 x16 h7 y38 ff2 fs4 fc0 sc0 ls3 ws4"> </div><div class="t m0 x1 h7 y39 ff2 fs4 fc0 sc0 ls3 ws4"> <span class="_0 blank"> </span>O somatório dos momentos em torno de um nó sempre será igual a zero: </div><div class="t m0 x17 h8 y3a ff4 fs4 fc0 sc0 ls3">\ue72f</div><div class="t m0 x18 h9 y3b ff4 fs5 fc0 sc0 ls3 ws9">\uebbb,\uebd8\uebe6\uebe4<span class="_e blank"> </span><span class="fs4 wsa v1">+ \ue72f</span></div><div class="t m0 xf h9 y3b ff4 fs5 fc0 sc0 ls3 ws8">\uebbb ,\uebd7\uebdc\uebe5<span class="_d blank"> </span><span class="fs4 ws5 v1">= 0 \u2192 \ue72f</span></div><div class="t m0 x19 h9 y3b ff4 fs5 fc0 sc0 ls3 ws9">\uebbb,\uebd7\uebdc\uebe5<span class="_e blank"> </span><span class="fs4 ws3 v1">\u2212<span class="_8 blank"> </span>40\ue747\ue730 .<span class="_4 blank"> </span>\ue749<span class="_e blank"> </span>=<span class="_9 blank"> </span>0<span class="_9 blank"> </span>\u2192<span class="_9 blank"> </span>\ue72f</span></div><div class="t m0 x1a hd y3b ff4 fs5 fc0 sc0 ls3 ws8">\uebbb ,\uebd7\uebdc\uebe5<span class="_d blank"> </span><span class="fs4 wsb v1">=<span class="_9 blank"> </span>40\ue747\ue730 .<span class="_a blank"> </span>\ue749<span class="ff2 ws4"> </span></span></div><div class="t m0 x1 h7 y3c ff2 fs4 fc0 sc0 ls3 ws4"> <span class="_0 blank"> </span>De forma simplificada, sempre que tivermos um <span class="_2 blank"> </span>nó conectado por apenas duas </div><div class="t m0 x1 h7 y3d ff2 fs4 fc0 sc0 ls3 ws4">barras, <span class="_7 blank"> </span>os <span class="_7 blank"> </span>momentos <span class="_7 blank"> </span>em <span class="_6 blank"> </span>cada <span class="_7 blank"> </span>barra <span class="_7 blank"> </span>serão <span class="_6 blank"> </span>iguais <span class="_7 blank"> </span>e <span class="_7 blank"> </span>de <span class="_7 blank"> </span>sentido <span class="_7 blank"> </span>contr<span class="_2 blank"> </span>ário <span class="_7 blank"> </span>(a <span class="_7 blank"> </span>menos, <span class="_7 blank"> </span>é </div><div class="t m0 x1 h7 y3e ff2 fs4 fc0 sc0 ls3 ws4">claro, <span class="_9 blank"> </span>que <span class="_9 blank"> </span>haja <span class="_9 blank"> </span>uma <span class="_9 blank"> </span>carga-momento <span class="_9 blank"> </span>aplicada <span class="_9 blank"> </span>no <span class="_9 blank"> </span>nó). <span class="_9 blank"> </span>Perceba, <span class="_9 blank"> </span>também, <span class="_9 blank"> </span>que <span class="_9 blank"> </span>os </div><div class="t m0 x1 h7 y3f ff2 fs4 fc0 sc0 ls3 ws4">momentos <span class="_c blank"></span>são <span class="_c blank"></span>tais <span class="_c blank"></span>que <span class="_c blank"></span>tracionam <span class="_c blank"></span>a <span class="_c blank"></span>mesma <span class="_c blank"></span>região <span class="_c blank"></span>das <span class="_c blank"></span>barras. <span class="_c blank"></span>No <span class="_c blank"></span>exemplo <span class="_c blank"></span>que <span class="_c blank"></span>estamos </div><div class="t m0 x1 h7 y40 ff2 fs4 fc0 sc0 ls3 ws4">discutindo, ambos os momentos tracionam as fibras interiores das barras. </div><div class="t m0 x1 h7 y41 ff2 fs4 fc0 sc0 ls3 ws4"> <span class="_0 blank"> </span>Devemos <span class="_3 blank"> </span>continuar <span class="_2 blank"> </span>com <span class="_3 blank"> </span>o <span class="_3 blank"> </span>cálculo <span class="_3 blank"> </span>dos <span class="_3 blank"> </span>momentos <span class="_2 blank"> </span>em <span class="_3 blank"> </span>cada <span class="_3 blank"> </span>ponto <span class="_3 blank"> </span>de <span class="_2 blank"> </span>aplicação<span class="_2 blank"> </span> </div><div class="t m0 x1 h7 y42 ff2 fs4 fc0 sc0 ls3 ws4">de carga ou nas extremidades das barras. Portanto: </div><div class="t m0 x1b h7 y43 ff5 fs4 fc0 sc0 ls3 wsc">\uf0b7<span class="ff6 ls8 ws4"> <span class="ff2 ls3">Momento <span class="_2 blank"> </span>no <span class="_3 blank"> </span>ponto <span class="_3 blank"> </span>da <span class="_2 blank"> </span>carga <span class="_3 blank"> </span>de <span class="_2 blank"> </span>20kN <span class="_3 blank"> </span>da <span class="_2 blank"> </span>barra <span class="_3 blank"> </span>AB <span class="_2 blank"> </span>(analisando <span class="_3 blank"> </span>pela <span class="_2 blank"> </span>esq<span class="_2 blank"> </span>uerda): </span></span></div><div class="t m0 x1c h7 y44 ff4 fs4 fc0 sc0 ls3 ws4">\ue72f<span class="_e blank"> </span>=<span class="_9 blank"> </span>\u221220\ue747\ue730 .<span class="_a blank"> </span>2\ue749<span class="_9 blank"> </span>=<span class="_9 blank"> </span>\u221240\ue747\ue730<span class="_3 blank"> </span>.<span class="_4 blank"> </span>\ue749<span class="ff2"> (tracionando as fibras interiores); </span></div><div class="t m0 x1b h7 y45 ff5 fs4 fc0 sc0 ls3 wsc">\uf0b7<span class="ff6 ls8 ws4"> <span class="ff2 ls3">Momento no ponto C (analisando pela direita): <span class="ff4 wsd">\ue72f<span class="_e blank"> </span>= 0</span>; </span></span></div><div class="t m0 x1b he y46 ff5 fs4 fc0 sc0 ls3 wsc">\uf0b7<span class="ff6 ls8 ws4"> <span class="ff2 ls3">Momento <span class="_3 blank"> </span>da <span class="_7 blank"> </span>parábola <span class="_3 blank"> </span>a <span class="_3 blank"> </span>se<span class="_2 blank"> </span>r <span class="_3 blank"> </span>pendurada <span class="_7 blank"> </span>na <span class="_3 blank"> </span>barra <span class="_3 blank"> </span>BC: <span class="_7 blank"> </span><span class="ff4 wsd">\ue72f<span class="_e blank"> </span>= <span class="fs5 wse v5">\uebe4 \uebdf </span><span class="fs7 v6">\uec2e</span></span></span></span></div><div class="t m0 x1d hf y47 ff4 fs5 fc0 sc0 ls9">\ueb3c<span class="fs4 lsa v7">=</span><span class="ls3 ws4 v8">\ueb38\uebde\uebc7/\uebe0<span class="_2 blank"> </span> .(\ueb38\uebe0)<span class="fs7 v9">\uec2e</span></span></div><div class="t m0 x1e h10 y47 ff4 fs5 fc0 sc0 lsb">\ueb3c<span class="fs4 ls3 v7">=</span></div><div class="t m0 x1c h7 y48 ff4 fs4 fc0 sc0 ls3 wsb">8\ue747\ue730 .<span class="_a blank"> </span>\ue749<span class="ff2 ws4">. </span></div><div class="t m0 x1 h7 y49 ff2 fs4 fc0 sc0 ls3 ws4"> </div><div class="t m0 x1f h7 y4a ff2 fs4 fc0 sc0 ls3 ws4"> </div><div class="t m0 x1 h6 y4b ff3 fs3 fc1 sc0 ls3 ws4">Pórticos triarticulados </div><div class="t m0 x1 h7 y4c ff2 fs4 fc0 sc0 ls3 ws4"> <span class="_0 blank"> </span>Os pórticos triarticulados, assim como as vigas Gerber, são compostos por uma </div><div class="t m0 x1 h7 y4d ff2 fs4 fc0 sc0 ls3 ws4">articulação <span class="_3 blank"> </span>(rótula) <span class="_7 blank"> </span>a <span class="_3 blank"> </span>mais, <span class="_3 blank"> </span>além <span class="_7 blank"> </span>do<span class="_1 blank"></span>s <span class="_3 blank"> </span>dois <span class="_7 blank"> </span>apoios <span class="_3 blank"> </span>rotulados. <span class="_3 blank"> </span>O <span class="_3 blank"> </span>traçado <span class="_7 blank"> </span>dos <span class="_3 blank"> </span>diagramas </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/b33ede67-33c6-461b-ad6c-9c5c2708e824/bg4.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls3 ws4"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls3 ws4">4 </div><div class="c x1 y3 w2 h3"><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls3 ws4"> </div></div><div class="t m0 x1 h7 y1d ff2 fs4 fc0 sc0 ls3 ws4">segue <span class="_4 blank"> </span>as <span class="_6 blank"> </span>mesmas <span class="_4 blank"> </span>orientações <span class="_4 blank"> </span>dos <span class="_4 blank"> </span>pórticos <span class="_6 blank"> </span>anteriores, <span class="_4 blank"> </span>sabendo <span class="_4 blank"> </span>que <span class="_6 blank"> </span>o <span class="_4 blank"> </span>momento <span class="_4 blank"> </span>na </div><div class="t m0 x1 h7 y37 ff2 fs4 fc0 sc0 ls3 ws4">rótula deve ser zero. </div><div class="t m0 x1 h6 y4e ff3 fs3 fc1 sc0 ls3 ws4"> </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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