<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/5502e1cb-a069-41c0-937b-d1f856940370/bg1.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 lsb ws0"><span class="fc7 sc0">CY</span><span class="blank _0"></span><span class="fc7 sc0">AN</span></div><div class="t m1 x1 h3 y2 ff2 fs1 fc0 sc0 lsb ws8"><span class="fc7 sc0">VS Gráfica</span><span class="blank _1"> </span><span class="fc1"><span class="fc7 sc0">VS Gráfica</span></span></div><div class="t m0 x2 h2 y1 ff1 fs0 fc1 sc0 lsb"><span class="fc7 sc0">MAG</span></div><div class="t m1 x3 h3 y3 ff2 fs1 fc2 sc0 lsb ws8"><span class="fc7 sc0">VS Gráfica</span></div><div class="t m0 x4 h2 y4 ff1 fs0 fc2 sc0 lsb"><span class="fc7 sc0">YEL</span></div><div class="t m1 x5 h3 y5 ff2 fs1 fc3 sc0 lsb ws8"><span class="fc7 sc0">VS Gráfica</span></div><div class="t m2 x5 h2 y6 ff1 fs0 fc3 sc0 lsb"><span class="fc7 sc0">BLACK</span></div><div class="t m0 x6 h4 y7 ff3 fs2 fc4 sc0 lsb ws1"><span class="fc7 sc0">www</span><span class="blank _0"></span><span class="fc7 sc0">.grupoa.com.br</span></div><div class="t m0 x7 h5 y8 ff4 fs3 fc4 sc0 lsb ws8"><span class="fc7 sc0">0800 703 3444</span></div><div class="t m3 x8 h6 y9 ff5 fs4 fc5 sc0 ls0 ws8"><span class="fc7 sc0">EST</span><span class="blank _2"></span><span class="fc7 sc0">Á</span><span class="blank _2"></span><span class="fc7 sc0">TIC</span><span class="blank _0"></span><span class="fc7 sc0">A E MEC</span><span class="blank _0"></span><span class="fc7 sc0">ÂNIC</span><span class="blank _3"></span><span class="fc7 sc0">A</span><span class="blank _3"></span><span class="lsb"><span class="fc7 sc0"> </span></span></div><div class="t m3 x9 h6 ya ff5 fs4 fc5 sc0 ls0 ws8"><span class="fc7 sc0">DOS MA</span><span class="blank _2"></span><span class="fc7 sc0">TERIAIS</span></div><div class="t m3 xa h7 yb ff5 fs5 fc4 sc0 ls1 ws9"><span class="fc7 sc0">Beer </span><span class="ff6 fs6 ls2 ws8"><span class="fc7 sc0"> </span><span class="ff5 fc5 v1"><span class="fc7 sc0">|</span></span><span class="lsb wsa"><span class="fc7 sc0"> </span></span></span><span class="fc7 sc0">J</span><span class="fc7 sc0">ohnston </span><span class="ff6 fs6 ls2 ws8"><span class="fc7 sc0"> </span><span class="ff5 fc5 v1"><span class="fc7 sc0">|</span></span><span class="lsb wsa"><span class="fc7 sc0"> </span></span></span><span class="fc7 sc0">D</span><span class="fc7 sc0">eW</span><span class="blank _4"></span><span class="fc7 sc0">olf </span><span class="ff6 fs6 ls2 ws8"><span class="fc7 sc0"> </span><span class="ff5 fc5 v1"><span class="fc7 sc0">|</span></span><span class="lsb wsa"><span class="fc7 sc0"> </span></span></span><span class="fc7 sc0">M</span><span class="ws2"><span class="fc7 sc0">azur</span><span class="fc7 sc0">ek</span></span></div><div class="t m3 xb h8 yc ff5 fs7 fc5 sc0 ls3 ws8"><span class="fc7 sc0">EST</span><span class="blank _5"></span><span class="fc7 sc0">Á</span><span class="blank _5"></span><span class="fc7 sc0">TIC</span><span class="blank _3"></span><span class="fc7 sc0">A E MEC</span><span class="blank _0"></span><span class="fc7 sc0">ÂNIC</span><span class="blank _3"></span><span class="fc7 sc0">A</span><span class="blank _3"></span><span class="lsb"><span class="fc7 sc0"> </span></span></div><div class="t m3 xc h8 yd ff5 fs7 fc5 sc0 ls3 ws8"><span class="fc7 sc0">DOS MA</span><span class="blank _5"></span><span class="fc7 sc0">TERIAIS</span></div><div class="t m0 xd h9 ye ff5 fs8 fc5 sc0 ls4 ws8">EST<span class="blank _6"></span>Á<span class="blank _6"></span>TIC<span class="blank _4"></span>A E MEC<span class="blank _4"></span>ÂNIC<span class="blank _3"></span>A<span class="blank _4"></span><span class="lsb"> </span></div><div class="t m0 xe h9 yf ff5 fs8 fc5 sc0 ls4 ws8">DOS MA<span class="blank _6"></span>TERIAIS</div><div class="t m0 xf ha y10 ff5 fs9 fc4 sc0 ls5 wsb">Beer <span class="ff6 fsa ls6 ws8"> <span class="ff5 fc5 v2">|</span><span class="lsb wsc"> </span></span>J<span class="blank _0"></span>ohnston <span class="ff6 fsa ls6 ws8"> <span class="ff5 fc5 v2">|</span><span class="lsb wsc"> </span></span>DeW<span class="blank _2"></span>olf <span class="ff6 fsa ls6 ws8"> <span class="ff5 fc5 v2">|</span><span class="lsb wsc"> </span></span>M<span class="ws3">azurek</span></div><div class="t m0 x10 hb y11 ff5 fsb fc5 sc0 ls7 ws8"><span class="fc7 sc0">EST</span><span class="blank _5"></span><span class="fc7 sc0">Á</span><span class="blank _7"></span><span class="fc7 sc0">TIC</span><span class="blank _3"></span><span class="fc7 sc0">A E MEC</span><span class="blank _3"></span><span class="fc7 sc0">ÂNIC</span><span class="blank _3"></span><span class="fc7 sc0">A</span><span class="blank _3"></span><span class="lsb"><span class="fc7 sc0"> </span></span></div><div class="t m0 x11 hb y12 ff5 fsb fc5 sc0 ls7 ws8"><span class="fc7 sc0">DOS MA</span><span class="blank _7"></span><span class="fc7 sc0">TERIAIS</span></div><div class="t m0 x12 hc y13 ff5 fsc fc4 sc0 ls8 wsd"><span class="fc7 sc0">Beer </span><span class="ff6 fsd ls9 ws8"><span class="fc7 sc0"> </span><span class="ff5 fc5 v1"><span class="fc7 sc0">|</span></span><span class="lsb wse"><span class="fc7 sc0"> </span></span></span><span class="fc7 sc0">J</span><span class="fc7 sc0">ohnston </span><span class="ff6 fsd ls9 ws8"><span class="fc7 sc0"> </span><span class="ff5 fc5 v1"><span class="fc7 sc0">|</span></span><span class="lsb wse"><span class="fc7 sc0"> </span></span></span><span class="fc7 sc0">D</span><span class="fc7 sc0">eW</span><span class="blank _2"></span><span class="fc7 sc0">olf </span><span class="blank _8"> </span><span class="ff6 fsd ls9 ws8"><span class="fc7 sc0"> </span><span class="ff5 fc5 v1"><span class="fc7 sc0">|</span></span><span class="lsb wse"><span class="fc7 sc0"> </span></span></span><span class="fc7 sc0">M</span><span class="ws4"><span class="fc7 sc0">azur</span><span class="fc7 sc0">ek</span></span></div><div class="t m0 x13 hd y14 ff5 fse fc4 sc0 lsa"><span class="fc7 sc0">Beer</span></div><div class="t m0 x14 hd y15 ff5 fse fc4 sc0 lsa ws5"><span class="fc7 sc0">J</span><span class="blank _0"></span><span class="fc7 sc0">ohnston</span></div><div class="t m0 xc hd y16 ff5 fse fc4 sc0 lsa"><span class="fc7 sc0">D</span><span class="ws5"><span class="fc7 sc0">eW</span><span class="blank _4"></span><span class="fc7 sc0">olf</span></span></div><div class="t m0 x14 hd y17 ff5 fse fc4 sc0 lsa"><span class="fc7 sc0">M</span><span class="ws5"><span class="fc7 sc0">azur</span><span class="fc7 sc0">ek</span></span></div><div class="t m0 x15 he y18 ff6 fsf fc4 sc0 lsb ws10"><span class="fc7 sc0">Mantendo a metodologia de ensino tr</span><span class="fc7 sc0">adicional dos seus famosos livros-texto</span><span class="blank _3"></span><span class="fc7 sc0">,</span><span class="blank _0"></span><span class="fc7 sc0"> </span></div><div class="t m0 x15 he y19 ff6 fsf fc4 sc0 lsb ws11"><span class="fc7 sc0">Beer e Johnston unem nesta obr</span><span class="fc7 sc0">a conceitos e aplicações de duas importantes </span></div><div class="t m0 x15 he y1a ff6 fsf fc4 sc0 lsb ws12"><span class="fc7 sc0">áreas da engenharia \u2013 a </span><span class="fc7 sc0">estática e a mecânica dos materiais </span><span class="fc7 sc0">\u2013 permitindo que </span></div><div class="t m0 x15 he y1b ff6 fsf fc4 sc0 lsb ws13"><span class="fc7 sc0">os estudantes desen</span><span class="fc7 sc0">v</span><span class="blank _0"></span><span class="fc7 sc0">olv</span><span class="fc7 sc0">am a habilidade de compreender e solucionar um deter</span><span class="blank _4"></span><span class="fc7 sc0">-</span></div><div class="t m0 x15 he y1c ff6 fsf fc4 sc0 lsb ws8"><span class="fc7 sc0">minado problema de maneir</span><span class="fc7 sc0">a coesa,</span><span class="blank _3"></span><span class="fc7 sc0"> simples e lógica.</span></div><div class="t m0 x16 he y1d ff6 fsf fc4 sc0 lsb ws8"><span class="fc7 sc0"> </span><span class="blank _9"> </span><span class="fc7 sc0">Os capítulos têm início com exemplos reais e com um sumário resumido </span></div><div class="t m0 x17 he y1e ff6 fsf fc4 sc0 lsb ws8"><span class="fc7 sc0">dos conteúdos que serão trabalhados.</span></div><div class="t m0 x16 he y1f ff6 fsf fc4 sc0 lsb ws8"><span class="fc7 sc0"> </span><span class="blank _9"> </span><span class="fc7 sc0">Os conceitos são introduzidos passo a passo, de forma clara e objetiva.</span></div><div class="t m0 x16 he y20 ff6 fsf fc4 sc0 lsb ws8"><span class="fc7 sc0"> </span><span class="blank _9"> </span><span class="fc7 sc0">Seções opcionais oferecem tópicos avançados.</span></div><div class="t m0 x16 he y21 ff6 fsf fc4 sc0 lsb ws8"><span class="fc7 sc0"> </span><span class="blank _9"> </span><span class="fc7 sc0">As seções </span></div><div class="t m4 x18 hf y22 ff6 fs10 fc4 sc0 lsb ws8"><span class="fc7 sc0">Problemas resolvidos</span></div><div class="t m0 x19 he y22 ff6 fsf fc4 sc0 lsb ws8"><span class="fc7 sc0"> são apresentadas em uma única página, </span></div><div class="t m0 x17 he y23 ff6 fsf fc4 sc0 lsb ws8"><span class="fc7 sc0">o que proporciona melhor visualização dos problemas-chave.</span></div><div class="t m0 x16 he y24 ff6 fsf fc4 sc0 lsb ws8"><span class="fc7 sc0"> </span><span class="blank _9"> </span><span class="fc7 sc0">Todos os capítulos oferecem um conjunto de problemas que devem </span></div><div class="t m0 x17 he y25 ff6 fsf fc4 sc0 lsb ws8"><span class="fc7 sc0">ser resolvidos com o auxílio de programas computacionais.</span></div><div class="t m0 x1a he y26 ff6 fsf fc4 sc0 lsb ws14"><span class="fc7 sc0">V</span><span class="fc7 sc0">is</span><span class="fc7 sc0">i</span><span class="fc7 sc0">t</span><span class="fc7 sc0">e a Á</span><span class="fc7 sc0">r</span><span class="fc7 sc0">e</span><span class="fc7 sc0">a d</span><span class="fc7 sc0">o P</span><span class="fc7 sc0">r</span><span class="fc7 sc0">o</span><span class="fc7 sc0">f</span><span class="fc7 sc0">e</span><span class="fc7 sc0">s</span><span class="fc7 sc0">s</span><span class="fc7 sc0">o</span><span class="fc7 sc0">r n</span><span class="fc7 sc0">o n</span><span class="fc7 sc0">o</span><span class="fc7 sc0">s</span><span class="fc7 sc0">s</span><span class="fc7 sc0">o s</span><span class="fc7 sc0">i</span><span class="fc7 sc0">t</span><span class="fc7 sc0">e w</span><span class="fc7 sc0">w</span><span class="blank _8"> </span><span class="fc7 sc0">w</span><span class="blank _3"></span><span class="fc7 sc0">.</span><span class="fc7 sc0">g</span><span class="fc7 sc0">r</span><span class="fc7 sc0">u</span><span class="fc7 sc0">p</span><span class="fc7 sc0">o</span><span class="fc7 sc0">a</span><span class="fc7 sc0">.</span><span class="blank _0"></span><span class="fc7 sc0">c</span><span class="fc7 sc0">o</span><span class="fc7 sc0">m</span><span class="blank _0"></span><span class="fc7 sc0">.</span><span class="fc7 sc0">b</span><span class="fc7 sc0">r p</span><span class="fc7 sc0">a</span><span class="blank _0"></span><span class="fc7 sc0">r</span><span class="fc7 sc0">a </span></div><div class="t m0 x1a he y27 ff6 fsf fc4 sc0 lsb ws15"><span class="fc7 sc0">t</span><span class="fc7 sc0">e</span><span class="fc7 sc0">r </span><span class="fc7 sc0">l</span><span class="blank _0"></span><span class="fc7 sc0">i</span><span class="fc7 sc0">v</span><span class="fc7 sc0">r</span><span class="fc7 sc0">e a</span><span class="fc7 sc0">c</span><span class="fc7 sc0">e</span><span class="fc7 sc0">s</span><span class="fc7 sc0">s</span><span class="fc7 sc0">o </span><span class="fc7 sc0">a</span><span class="fc7 sc0">o m</span><span class="fc7 sc0">a</span><span class="blank _0"></span><span class="fc7 sc0">t</span><span class="fc7 sc0">e</span><span class="fc7 sc0">r</span><span class="fc7 sc0">i</span><span class="fc7 sc0">a</span><span class="blank _0"></span><span class="fc7 sc0">l e</span><span class="fc7 sc0">x</span><span class="fc7 sc0">c</span><span class="fc7 sc0">l</span><span class="fc7 sc0">u</span><span class="fc7 sc0">s</span><span class="blank _0"></span><span class="fc7 sc0">i</span><span class="fc7 sc0">v</span><span class="fc7 sc0">o</span><span class="blank _3"></span><span class="fc7 sc0">, e</span><span class="fc7 sc0">m i</span><span class="fc7 sc0">n</span><span class="fc7 sc0">g</span><span class="fc7 sc0">l</span><span class="blank _0"></span><span class="fc7 sc0">ê</span><span class="fc7 sc0">s e </span><span class="fc7 sc0">p</span><span class="fc7 sc0">o</span><span class="fc7 sc0">r</span><span class="blank _8"> </span><span class="fc7 sc0">t</span><span class="fc7 sc0">u</span><span class="fc7 sc0">g</span><span class="fc7 sc0">u</span><span class="fc7 sc0">ê</span><span class="fc7 sc0">s</span><span class="fc7 sc0">,</span><span class="ws8"><span class="fc7 sc0"> </span></span></div><div class="t m0 x1a he y28 ff6 fsf fc4 sc0 lsc ws16"><span class="fc7 sc0">d</span><span class="fc7 sc0">e</span><span class="fc7 sc0">s</span><span class="blank _8"> </span><span class="fc7 sc0">t</span><span class="fc7 sc0">e</span><span class="fc7 sc0"> liv</span><span class="fc7 sc0">r</span><span class="blank _8"> </span><span class="fc7 sc0">o</span><span class="fc7 sc0">.</span></div><div class="t m0 x1b h10 y29 ff7 fs11 fc4 sc0 lsd"><span class="fc7 sc0">engenharia</span></div><div class="t m0 x1b h11 y2a ff8 fs11 fc4 sc0 lsd ws6"><span class="fc7 sc0">www</span><span class="blank _0"></span><span class="fc7 sc0">.g</span><span class="fc7 sc0">rupoa.com.br</span></div><div class="t m3 x1c h12 y2b ff9 fs11 fc4 sc0 lsb ws18"><span class="fc7 sc0">Recorte aqui seu marcador de página.</span></div><div class="t m0 x1d h13 y2c ffa fs12 fc5 sc0 lsb"><span class="fc7 sc0">Engenharia</span></div><div class="t m0 x1d h14 y2d ffa fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">BEER, JOHNSTON, DEWOLF & MAZUREK</span></div><div class="t m0 x1d h14 y2e ffa fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">Estática e Mecânica dos Materiais</span></div><div class="t m0 x1d h15 y2f ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">BEER, JOHNSTON & CORNWELL</span></div><div class="t m0 x1d h15 y30 ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">Mecânica V</span><span class="fc7 sc0">etorial para Engenheiros: Dinâmica, 9.ed.</span></div><div class="t m0 x1d h15 y31 ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">BEER, JOHNSTON, MAZUREK & EISENBERG</span></div><div class="t m0 x1d h15 y32 ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">Mecânica V</span><span class="fc7 sc0">etorial para Engenheiros: Estática, 9.ed.</span></div><div class="t m0 x1d h15 y33 ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">BLANK & T</span><span class="blank _3"></span><span class="fc7 sc0">ARQUIN</span></div><div class="t m0 x1d h15 y34 ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">Engenharia Econômica, 6.ed.</span></div><div class="t m0 x1d h15 y35 ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">BUDYNAS & NISBETT</span></div><div class="t m0 x1d h15 y36 ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">Elementos de Máquinas de Shigley: Projeto de Engenharia Mecânica, 8.ed. </span></div><div class="t m0 x1d h15 y37 ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">*ÇENGEL & BOLES</span></div><div class="t m0 x1d h15 y38 ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">T</span><span class="blank _3"></span><span class="fc7 sc0">ermodinâmica: Uma Abordagem da Engenharia, 7.ed.</span></div><div class="t m0 x1d h15 y39 ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">ÇENGEL & CIMBALA</span></div><div class="t m0 x1d h15 y3a ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">Mecânica dos Fluidos </span></div><div class="t m0 x1d h15 y3b ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">ÇENGEL & GHAJAR</span></div><div class="t m0 x1d h15 y3c ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">T</span><span class="blank _3"></span><span class="fc7 sc0">ransferência de Calor e Massa, 4.ed.</span></div><div class="t m0 x1d h15 y3d ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">CHAPRA & CANALE</span></div><div class="t m0 x1d h15 y3e ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">Métodos Numéricos para Engenharia, 5.ed.</span></div><div class="t m0 x1d h15 y3f ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">CHAPRA, S.C.</span></div><div class="t m0 x1d h16 y40 ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">Métodos Numéricos Aplicados com MA</span><span class="blank _3"></span><span class="fc7 sc0">TLAB</span><span class="fs14 ws7 v2"><span class="fc7 sc0">®</span></span><span class="v0"><span class="fc7 sc0"> para Engenheiros e Cientistas, 3.ed.</span></span></div><div class="t m0 x1d h15 y41 ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">DYM & LITTLE</span></div><div class="t m0 x1d h15 y42 ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">Introdução à Engenharia: Uma Abordagem Baseada em Projeto, 3.ed.</span></div><div class="t m0 x1d h15 y43 ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">GILA</span><span class="blank _3"></span><span class="fc7 sc0">T</span><span class="blank _4"></span><span class="fc7 sc0">, A.</span></div><div class="t m0 x1d h15 y44 ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">MA</span><span class="blank _3"></span><span class="fc7 sc0">TLAB com Aplicações em Engenharia, 4.ed. </span></div><div class="t m0 x1d h15 y45 ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">HSU, H.P</span><span class="blank _2"></span><span class="fc7 sc0">.</span></div><div class="t m0 x1d h15 y46 ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">Sinais e Sistemas, 2.ed. (Coleção Schaum)</span></div><div class="t m0 x1d h15 y47 ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">LEET</span><span class="blank _4"></span><span class="fc7 sc0">, UANG & GILBER</span><span class="fc7 sc0">T</span></div><div class="t m0 x1d h15 y48 ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">Fundamentos da Análise Estrutural, 3.ed.</span></div><div class="t m0 x1d h15 y49 ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">NAHVI & EDMINISTER</span></div><div class="t m0 x1d h15 y4a ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">Cir</span><span class="fc7 sc0">cuitos Elétricos, 4.ed. (Coleção Schaum)</span></div><div class="t m0 x1d h15 y4b ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">NA</span><span class="blank _0"></span><span class="fc7 sc0">VIDI, W</span><span class="blank _4"></span><span class="fc7 sc0">.</span></div><div class="t m0 x1d h15 y4c ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">Probabilidade e Estatística para Ciências Exatas</span></div><div class="t m0 x1d h15 y4d ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">NOR</span><span class="fc7 sc0">TON, R.L.</span></div><div class="t m0 x1d h15 y4e ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">Cinemática e Dinâmica dos Mecanismos</span></div><div class="t m0 x1d h15 y4f ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">ROSA, E.S. </span></div><div class="t m0 x1d h15 y50 ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">Escoamento Multifásico Isotérmico </span></div><div class="t m0 x1d h15 y51 ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">SMITH & HASHEMI</span></div><div class="t m0 x1d h15 y52 ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">Fundamentos de Engenharia e Ciência dos Materiais, 5.ed.</span></div><div class="t m0 x1d h15 y53 ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">TREMBLA</span><span class="blank _3"></span><span class="fc7 sc0">Y</span><span class="blank _4"></span><span class="fc7 sc0">, T</span><span class="blank _4"></span><span class="fc7 sc0">.</span></div><div class="t m0 x1d h15 y54 ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">Autodesk Inventor 2012 e Inventor L</span><span class="blank _3"></span><span class="fc7 sc0">T 2012: Essencial </span></div><div class="t m0 x1d h15 y55 ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">WHITE, F</span><span class="blank _4"></span><span class="fc7 sc0">.M.</span></div><div class="t m0 x1d h15 y56 ff3 fs13 fc4 sc0 lsb ws8"><span class="fc7 sc0">Mecânica dos Fluidos, 6.ed.</span></div><div class="t m0 x1d h17 y57 ffb fs15 fc4 sc0 lsb ws8"><span class="fc7 sc0">* </span><span class="blank _a"> </span><span class="fc7 sc0">Livro em produção no momento de impressão desta obra, mas que muito </span></div><div class="t m0 x1e h17 y58 ffb fs15 fc4 sc0 lsb ws8"><span class="fc7 sc0">em breve estará à disposição dos leitores em língua portuguesa.</span></div><div class="t m0 x1f h18 y59 ff3 fs16 fc4 sc0 lse ws8"><span class="fc7 sc0">A Bookman Editora é parte do Grupo A,</span><span class="fc7 sc0"> </span></div><div class="t m0 x20 h18 y5a ff3 fs16 fc4 sc0 lsb ws8"><span class="fc7 sc0">uma empresa que engloba diversos </span></div><div class="t m0 x20 h18 y5b ff3 fs16 fc4 sc0 lsb ws8"><span class="fc7 sc0">selos editoriais e várias plataformas </span></div><div class="t m0 x21 h18 y5c ff3 fs16 fc4 sc0 lse ws8"><span class="fc7 sc0">de distribuição de conteúdo técnico,</span><span class="lsb"><span class="fc7 sc0"> </span></span></div><div class="t m0 x22 h18 y5d ff3 fs16 fc4 sc0 lsb ws8"><span class="fc7 sc0">científico e profissional, </span></div><div class="t m0 x23 h18 y5e ff3 fs16 fc4 sc0 lsb ws8"><span class="fc7 sc0">disponibilizando-o como, onde </span></div><div class="t m0 x22 h18 y5f ff3 fs16 fc4 sc0 lsb ws8"><span class="fc7 sc0">e quando você precisar.</span></div><div class="t m0 x1f h18 y60 ff3 fs16 fc4 sc0 lsb ws8"><span class="fc7 sc0">O Grupo A publica com exclusividade </span></div><div class="t m0 x23 h18 y61 ff3 fs16 fc4 sc0 lsb ws8"><span class="fc7 sc0">obras com o selo McGraw-Hill </span></div><div class="t m0 x24 h18 y62 ff3 fs16 fc4 sc0 lsb ws8"><span class="fc7 sc0">em língua portuguesa.</span></div><div class="t m0 x25 h19 y63 ffc fs17 fc6 sc0 lsb ws8"><span class="fc7 sc0">042376_Estatica_Mecanica_Materias.indd 2</span><span class="blank _b"> </span><span class="fc7 sc0">14/11/12 17:28</span></div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,-1219.730000,-43.355900]}"></div></div> <div id="pf2" class="pf w2 h1a" data-page-no="2"><div class="pc pc2 w2 h1a"><img class="bi x26 y64 w3 h1b" alt="" src="https://files.passeidireto.com/5502e1cb-a069-41c0-937b-d1f856940370/bg2.png"><div class="t m0 x27 h1c y65 ffd fs2 fc3 sc0 lsf ws1a">E79 <span class="blank _c"> </span>Est<span class="blank _8"> </span>át<span class="blank _8"> </span>ica e mec<span class="blank _8"> </span>ân<span class="blank _8"> </span>ica dos m<span class="blank _8"> </span>ate<span class="blank _8"> </span>r<span class="blank _8"> </span>iais / Ferd<span class="blank _8"> </span>in<span class="blank _8"> </span>and P<span class="blank _3"></span>. Bee<span class="blank _8"> </span>r ..<span class="blank _0"></span>. [<span class="blank _0"></span>et al.<span class="blank _3"></span>] ; </div><div class="t m0 x28 h1c y66 ffd fs2 fc3 sc0 ls10 ws1b">t<span class="blank _8"> </span>ra<span class="blank _8"> </span>duç<span class="blank _8"> </span>ão: Antô<span class="blank _8"> </span>nio Eu<span class="blank _8"> </span>st<span class="blank _8"> </span>áqu<span class="blank _8"> </span>io de Melo Per<span class="blank _8"> </span>te<span class="blank _8"> </span>nce; rev<span class="blank _8"> </span>isã<span class="blank _8"> </span>o </div><div class="t m0 x28 h1c y67 ffd fs2 fc3 sc0 ls11 ws1c">té<span class="blank _8"> </span>cn<span class="blank _8"> </span>ica: A<span class="blank _8"> </span>nton<span class="blank _8"> </span>io Per<span class="blank _8"> </span>t<span class="blank _8"> </span>ence Jú<span class="blank _8"> </span>n<span class="blank _8"> </span>ior<span class="blank _0"></span>. \u2013 Por<span class="blank _8"> </span>to A<span class="blank _8"> </span>leg<span class="blank _8"> </span>re : A<span class="blank _8"> </span>MGH, </div><div class="t m0 x28 h1c y68 ffd fs2 fc3 sc0 ls12 ws19">20<span class="blank _0"></span>1<span class="blank _0"></span>3<span class="blank _0"></span>.</div><div class="t m0 x28 h1c y69 ffd fs2 fc3 sc0 lsf ws1a">xv<span class="blank _8"> </span>iii<span class="blank _8"> </span>, 706 p. : il. color<span class="blank _0"></span>. ; 28 cm.</div><div class="t m0 x28 h1c y6a ffd fs2 fc3 sc0 ls13 ws1d">ISBN<span class="blank _0"></span> 978-85-8055-<span class="blank _3"></span>1<span class="blank _0"></span>64<span class="blank _8"> </span>-<span class="blank _8"> </span>8</div><div class="t m0 x28 h1c y6b ffd fs2 fc3 sc0 ls14 ws1e">1<span class="blank _0"></span>. Engen<span class="blank _8"> </span>ha<span class="blank _8"> </span>r<span class="blank _8"> </span>ia mec<span class="blank _8"> </span>ân<span class="blank _8"> </span>ica. 2<span class="blank _8"> </span>. Mecâ<span class="blank _8"> </span>nica d<span class="blank _8"> </span>os mat<span class="blank _8"> </span>er<span class="blank _8"> </span>iai<span class="blank _8"> </span>s. 3<span class="blank _0"></span>. Est<span class="blank _8"> </span>á-</div><div class="t m0 x29 h1c y6c ffd fs2 fc3 sc0 ls15 ws1f">tic<span class="blank _8"> </span>a. I. Bee<span class="blank _8"> </span>r, F<span class="blank _3"></span>e<span class="blank _8"> </span>rd<span class="blank _8"> </span>in<span class="blank _8"> </span>and P<span class="blank _3"></span>. </div><div class="t m0 x2a h1c y6d ffd fs2 fc3 sc0 lsb ws20"> CDU <span class="blank _d"></span>62<span class="blank _3"></span>1<span class="blank _0"></span>:5<span class="blank _3"></span>3<span class="blank _0"></span>1<span class="blank _3"></span>.<span class="blank _8"> </span>2 </div><div class="t m0 x2b h1c y6e ffd fs2 fc3 sc0 lsb ws8">Catalogação na publicação: <span class="blank _3"></span>A<span class="blank _8"> </span>n<span class="blank _8"> </span>a Paula M. Ma<span class="blank _8"> </span>g<span class="blank _8"> </span>nus \u2013 CR<span class="blank _e"> </span>B 1<span class="blank _0"></span>0/205<span class="blank _0"></span>2</div><div class="t m0 x2c h1d y6f ffe fs17 fc7 sc1 lsb ws8"><span class="fc7 sc0">iniciais_Beer.indd ii</span><span class="blank _f"></span><span class="fc3 sc0"><span class="fc7 sc0">iniciais_Beer.indd ii</span><span class="blank _10"> </span><span class="fc7 sc1"><span class="fc7 sc0">03/12/2012 19:05:03</span><span class="blank _11"></span><span class="fc3 sc0"><span class="fc7 sc0">03/12/2012 19:05:03</span></span></span></span></div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,-23.513400,-23.513400]}"></div></div> <div id="pf3" class="pf w2 h1a" data-page-no="3"><div class="pc pc3 w2 h1a"><img fetchpriority="low" loading="lazy" class="bi x2d y70 w4 h1e" alt="" src="https://files.passeidireto.com/5502e1cb-a069-41c0-937b-d1f856940370/bg3.png"><div class="t m0 x2d h1f y71 fff fs13 fc8 sc0 lsb ws21">574<span class="blank"> </span><span class="ff10 fs2 fc3 ws8 v0">Estática e mecânica dos materiais</span></div><div class="t m0 x2e h20 y72 fff fs18 fc7 sc2 lsb ws22">14<span class="blank"> </span><span class="fs19 fc8 sc0 ws8 v3">T<span class="blank _4"></span>ransformações de tensão</span></div><div class="t m0 x2f h21 y73 ff11 fs15 fc7 sc1 lsb ws23">\u4272<span class="blank _12"></span><span class="fc8 sc0">\u4272</span></div><div class="t m0 x2d h22 y74 ff12 fs15 fc8 sc0 lsb ws2a"> 14.1 <span class="blank _13"> </span><span class="ff10 fc3">Introdução</span></div><div class="t m0 x2d h22 y75 ff12 fs15 fc8 sc0 lsb ws2a"> 14.2 <span class="blank _13"> </span><span class="ff10 fc3 ws8">T<span class="blank _4"></span>ransformação do estado </span></div><div class="t m0 xf h22 y76 ff10 fs15 fc3 sc0 lsb ws8">plano de tensão</div><div class="t m0 x2d h22 y77 ff12 fs15 fc8 sc0 lsb ws2a"> 14.3 <span class="blank _13"> </span><span class="ff10 fc3 ws8">T<span class="blank _2"></span>ensões principais e tensão </span></div><div class="t m0 xf h22 y78 ff10 fs15 fc3 sc0 lsb ws8">de cisalhamento máxima</div><div class="t m0 x2d h22 y79 ff12 fs15 fc8 sc0 lsb ws2a"> 14.4 <span class="blank _13"> </span><span class="ff10 fc3 ws8">Círculo de Mohr para o </span></div><div class="t m0 xf h22 y7a ff10 fs15 fc3 sc0 lsb ws8">estado plano de tensão</div><div class="t m0 x2d h22 y7b ff12 fs15 fc8 sc0 lsb ws2a"> 14.5 <span class="blank _13"> </span><span class="ff10 fc3 ws8">T<span class="blank _2"></span>ensões em vasos de </span></div><div class="t m0 xf h22 y7c ff10 fs15 fc3 sc0 lsb ws8">pressão de paredes finas</div><div class="t m0 x2f h21 y7d ff11 fs15 fc7 sc1 lsb ws23">\u428f<span class="blank _12"></span><span class="fc8 sc0">\u428f</span></div><div class="t m0 x30 h23 y7e fff fs1a fc8 sc0 lsb ws2b">14.1 Introdução</div><div class="t m0 x30 h24 y7f ff13 fs1b fc3 sc0 ls16 ws2c">Na Seção 8.9<span class="blank _4"></span>, v<span class="blank _8"> </span>i<span class="blank _8"> </span>mos que o est<span class="blank _8"> </span>ado mais ger<span class="blank _8"> </span>al de te<span class="blank _8"> </span>nsão e<span class="blank _8"> </span>m u<span class="blank _8"> </span>m da<span class="blank _8"> </span>do ponto </div><div class="t m0 x30 h25 y80 ff14 fs1b fc3 sc0 lsb">Q<span class="ff13 ls17 ws2d"> pode ser re<span class="blank _8"> </span>present<span class="blank _8"> </span>ado por seis c<span class="blank _8"> </span>omponentes, dos qu<span class="blank _8"> </span>ais t<span class="blank _8"> </span>rês, <span class="ff15 ls18">\u03c3</span></span><span class="fs1c ls19 v4">x</span><span class="ff13 ws8 v0">, <span class="blank _8"> </span><span class="ff15 ls1a">\u03c3</span></span><span class="fs1c ws24 v4">y</span><span class="ff13 ws2e v0"> e <span class="ff15 ls1b">\u03c3</span></span><span class="fs1c ls1c v4">z</span><span class="ff13 ws8 v0">, </span></div><div class="t m0 x30 h24 y81 ff13 fs1b fc3 sc0 ls1d ws2f">def<span class="blank _8"> </span>ine<span class="blank _8"> </span>m as te<span class="blank _8"> </span>nsõe<span class="blank _8"> </span>s nor<span class="blank _8"> </span>mais que at<span class="blank _8"> </span>u<span class="blank _8"> </span>am n<span class="blank _8"> </span>as face<span class="blank _8"> </span>s de um p<span class="blank _8"> </span>equeno elemento </div><div class="t m0 x30 h26 y82 ff13 fs1b fc3 sc0 ls26 ws30">de volu<span class="blank _8"> </span>me c<span class="blank _8"> </span>ent<span class="blank _8"> </span>r<span class="blank _8"> </span>a<span class="blank _8"> </span>do e<span class="blank _8"> </span>m<span class="ff14 ls27 ws8"> Q<span class="blank _8"> </span></span><span class="ls28 ws31"> e com a mesma or<span class="blank _8"> </span>ient<span class="blank _8"> </span>ação dos ei<span class="blank _8"> </span>xos de coorde-</span></div><div class="t m0 x30 h26 y83 ff13 fs1b fc3 sc0 lsb ws32">nad<span class="blank _8"> </span>as (<span class="blank _8"> </span>Fi<span class="blank _0"></span>g. 1<span class="blank _4"></span>4.<span class="blank _3"></span>1<span class="blank _0"></span><span class="ff14 ws25">a<span class="blank _3"></span><span class="ff13 ls29 ws33">)<span class="blank _0"></span>.<span class="blank _0"></span> Os<span class="blank _3"></span> ou<span class="blank _3"></span>tro<span class="blank _3"></span>s tr<span class="blank _0"></span>ês<span class="blank _3"></span>, </span></span></div><div class="t m5 x31 h27 y84 ff16 fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 x32 h28 y85 ff14 fs1c fc3 sc0 ls2a">xy</div><div class="t m0 x33 h24 y84 ff13 fs1b fc3 sc0 lsb ws8">, </div><div class="t m5 x34 h27 y84 ff16 fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 x35 h28 y85 ff14 fs1c fc3 sc0 ls2b">yz</div><div class="t m0 x36 h24 y84 ff13 fs1b fc3 sc0 lsb ws32"> e </div><div class="t m5 x37 h27 y84 ff16 fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 x38 h29 y85 ff14 fs1c fc3 sc0 ls2c ws26">zx<span class="ff13 fs1b lsb v5">,</span></div><div class="t m0 x39 h2a y86 ff13 fs1c fc3 sc0 lsb ws24">*<span class="fs1b ls2d ws34 v6"> def<span class="blank _8"> </span>ine<span class="blank _8"> </span>m as compone<span class="blank _8"> </span>ntes d<span class="blank _8"> </span>as </span></div><div class="t m0 x30 h24 y87 ff13 fs1b fc3 sc0 ls2d ws35">ten<span class="blank _8"> </span>sões de cisal<span class="blank _8"> </span>ha<span class="blank _8"> </span>mento no mesmo elemento. Como já mencio<span class="blank _0"></span>na<span class="blank _8"> </span>mos, o </div><div class="t m0 x30 h24 y88 ff13 fs1b fc3 sc0 ls2e ws8">m<span class="blank _8"> </span>e<span class="blank _8"> </span>s<span class="blank _8"> </span>m<span class="blank _8"> </span>o<span class="blank _8"> </span> e<span class="blank _8"> </span>s<span class="blank _8"> </span>t<span class="blank _e"> </span>a<span class="blank _e"> </span>d<span class="blank _8"> </span>o<span class="blank _8"> </span> d<span class="blank _8"> </span>e<span class="blank _8"> </span> t<span class="blank _8"> </span>e<span class="blank _e"> </span>n<span class="blank _8"> </span>s<span class="blank _8"> </span>ã<span class="blank _e"> </span>o<span class="blank _8"> </span> p<span class="blank _8"> </span>o<span class="blank _8"> </span>d<span class="blank _8"> </span>e<span class="blank _e"> </span>r<span class="blank _8"> </span>á<span class="blank _8"> </span> s<span class="blank _e"> </span>e<span class="blank _8"> </span>r<span class="blank _8"> </span> r<span class="blank _8"> </span>e<span class="blank _e"> </span>p<span class="blank _8"> </span>r<span class="blank _8"> </span>e<span class="blank _8"> </span>s<span class="blank _e"> </span>e<span class="blank _8"> </span>n<span class="blank _8"> </span>t<span class="blank _e"> </span>a<span class="blank _8"> </span>d<span class="blank _8"> </span>o<span class="blank _8"> </span> p<span class="blank _e"> </span>o<span class="blank _8"> </span>r<span class="blank _8"> </span> u<span class="blank _e"> </span>m<span class="blank _8"> </span> c<span class="blank _8"> </span>o<span class="blank _8"> </span>nj<span class="blank _8"> </span>u<span class="blank _e"> </span>n<span class="blank _8"> </span>t<span class="blank _8"> </span>o<span class="blank _8"> </span> d<span class="blank _e"> </span>i<span class="blank _8"> </span>f<span class="blank _8"> </span>e<span class="blank _8"> </span>r<span class="blank _8"> </span>e<span class="blank _e"> </span>n<span class="blank _8"> </span>-</div><div class="t m0 x30 h24 y89 ff13 fs1b fc3 sc0 ls1e ws36">te de compone<span class="blank _8"> </span>ntes se os ei<span class="blank _8"> </span>x<span class="blank _0"></span>os de coorden<span class="blank _8"> </span>ad<span class="blank _8"> </span>as sofr<span class="blank _8"> </span>erem u<span class="blank _8"> </span>ma rot<span class="blank _8"> </span>ação e<span class="blank _8"> </span>m </div><div class="t m0 x30 h26 y8a ff13 fs1b fc3 sc0 ls2f ws37">relação aos pr<span class="blank _8"> </span>i<span class="blank _8"> </span>meiros (<span class="blank _8"> </span>F<span class="blank _0"></span>ig. 1<span class="blank _4"></span>4.<span class="blank _3"></span>1<span class="blank _0"></span><span class="ff14 lsb ws25">b<span class="blank _3"></span><span class="ff13 ls30 ws38">). N<span class="blank _0"></span>a pri<span class="blank _8"> </span>mei<span class="blank _8"> </span>ra par<span class="blank _e"> </span>te dest<span class="blank _8"> </span>e capí<span class="blank _0"></span>t<span class="blank _8"> </span>ulo, deter<span class="blank _0"></span>-</span></span></div><div class="t m0 x30 h24 y8b ff13 fs1b fc3 sc0 ls31 ws39">mi<span class="blank _8"> </span>na<span class="blank _8"> </span>remos como as c<span class="blank _8"> </span>omponentes de t<span class="blank _8"> </span>ensã<span class="blank _8"> </span>o são t<span class="blank _8"> </span>ra<span class="blank _8"> </span>nsforma<span class="blank _8"> </span>dos qua<span class="blank _8"> </span>ndo </div><div class="t m0 x30 h24 y8c ff13 fs1b fc3 sc0 ls17 ws3a">um<span class="blank _8"> </span>a rotaçã<span class="blank _8"> </span>o dos eixos de coordena<span class="blank _8"> </span>da<span class="blank _8"> </span>s é reali<span class="blank _8"> </span>za<span class="blank _8"> </span>da.</div><div class="t m6 x3a h2b y8d ff16 fs1e fc9 sc0 lsb">\ue602</div><div class="t m0 x3b h2c y8e ff17 fs17 fc9 sc0 ls32">yz</div><div class="t m6 x3c h2b y8f ff16 fs1e fc9 sc0 lsb">\ue602</div><div class="t m0 x3d h2c y90 ff17 fs17 fc9 sc0 ls33">yx</div><div class="t m6 x31 h2b y91 ff16 fs1e fc9 sc0 lsb">\ue602</div><div class="t m0 x3e h2c y92 ff17 fs17 fc9 sc0 ls34">xy</div><div class="t m6 x3f h2b y93 ff16 fs1e fc9 sc0 lsb">\ue602</div><div class="t m0 x40 h2c y94 ff17 fs17 fc9 sc0 ls32">xz</div><div class="t m6 x3a h2b y95 ff16 fs1e fc9 sc0 lsb">\ue602</div><div class="t m0 x3b h2c y96 ff17 fs17 fc9 sc0 ls35">zx</div><div class="t m6 x3a h2b y97 ff16 fs1e fc9 sc0 lsb">\ue602</div><div class="t m0 x3b h2c y98 ff17 fs17 fc9 sc0 ls36">zy</div><div class="t m6 x41 h2d y99 ff18 fs1e fc9 sc0 lsb">\u03c3</div><div class="t m0 x42 h2c y9a ff17 fs17 fc9 sc0 lsb">y</div><div class="t m6 x43 h2b y9b ff16 fs1e fc9 sc0 lsb">\ue602</div><div class="t m0 x44 h2e y9c ff17 fs17 fc9 sc0 lsb">y<span class="ff18">\u2032</span>z<span class="ff18">\u2032</span></div><div class="t m6 x45 h2b y9d ff16 fs1e fc9 sc0 lsb">\ue602</div><div class="t m0 x46 h2e y9e ff17 fs17 fc9 sc0 lsb">y<span class="ff18">\u2032</span>x<span class="ff18">\u2032</span></div><div class="t m6 x47 h2b y9f ff16 fs1e fc9 sc0 lsb">\ue602</div><div class="t m0 x48 h2e ya0 ff17 fs17 fc9 sc0 lsb">x<span class="ff18">\u2032</span>z<span class="ff18">\u2032</span></div><div class="t m6 x49 h2b ya1 ff16 fs1e fc9 sc0 lsb">\ue602</div><div class="t m0 x4a h2e ya2 ff17 fs17 fc9 sc0 lsb">z<span class="ff18">\u2032</span>x<span class="ff18">\u2032</span></div><div class="t m6 x4b h2b ya0 ff16 fs1e fc9 sc0 lsb">\ue602</div><div class="t m0 x4c h2e ya3 ff17 fs17 fc9 sc0 lsb">z<span class="ff18">\u2032</span>y<span class="ff18">\u2032</span></div><div class="t m6 x4d h2b ya4 ff16 fs1e fc9 sc0 lsb">\ue602</div><div class="t m0 x4e h2e ya5 ff17 fs17 fc9 sc0 lsb">x<span class="ff18">\u2032</span>y<span class="ff18">\u2032</span></div><div class="t m6 x4f h2d ya6 ff18 fs1e fc9 sc0 lsb">\u03c3</div><div class="t m0 x50 h2e ya7 ff17 fs17 fc9 sc0 lsb">y<span class="ff18">\u2032</span></div><div class="t m6 x4e h2d ya8 ff18 fs1e fc9 sc0 lsb">\u03c3</div><div class="t m0 x51 h2e ya9 ff17 fs17 fc9 sc0 lsb">x<span class="ff18">\u2032</span></div><div class="t m6 x52 h2d yaa ff18 fs1e fc9 sc0 lsb">\u03c3</div><div class="t m0 x53 h2c yab ff17 fs17 fc9 sc0 lsb">z</div><div class="t m6 x54 h2d yac ff18 fs1e fc9 sc0 lsb">\u03c3</div><div class="t m0 x55 h2c yad ff17 fs17 fc9 sc0 lsb">x</div><div class="t m0 x56 h2f yae ff17 fs11 fc3 sc0 lsb">Q</div><div class="t m0 x57 h2f yaf ff17 fs11 fc3 sc0 lsb">O</div><div class="t m0 x30 h2f yb0 ff17 fs11 fc3 sc0 lsb">z</div><div class="t m0 x58 h2f yb1 ff17 fs11 fc3 sc0 lsb">y</div><div class="t m0 x59 h2f yb2 ff17 fs11 fc3 sc0 lsb">x</div><div class="t m0 x5a h30 yb3 ff18 fs11 fc3 sc0 lsb">(<span class="ff17">a</span>)</div><div class="t m0 x5b h2f yb4 ff17 fs11 fc3 sc0 lsb">O</div><div class="t m0 x5c h2f yb5 ff17 fs11 fc3 sc0 lsb">z</div><div class="t m0 x5d h30 yb6 ff17 fs11 fc9 sc0 lsb">z<span class="ff18">\u2032</span></div><div class="t m0 x5e h31 yb7 ff17 fs11 fc9 sc0 lsb">y<span class="ff18 ls1f">\u2032</span><span class="fc3 v7">y</span></div><div class="t m0 x5f h2f yb8 ff17 fs11 fc3 sc0 lsb">x</div><div class="t m0 x5f h30 yb9 ff17 fs11 fc9 sc0 lsb">x<span class="ff18">\u2032</span></div><div class="t m0 x60 h30 yb3 ff18 fs11 fc3 sc0 lsb">(<span class="ff17">b</span>)</div><div class="t m6 x61 h2d y9f ff18 fs1e fc9 sc0 lsb">\u03c3</div><div class="t m0 x62 h2e ya0 ff17 fs17 fc9 sc0 lsb">z<span class="ff18">\u2032</span></div><div class="t m0 x63 h2f yba ff17 fs11 fc3 sc0 lsb">Q</div><div class="t m0 x30 h32 ybb fff fs16 fc8 sc0 ls20 ws3b">Figura 1<span class="blank _3"></span>4<span class="blank _8"> </span>.<span class="blank _3"></span>1</div><div class="t m0 x64 h24 ybc ff13 fs1b fc3 sc0 ls17 ws3c">Nossa discussã<span class="blank _8"> </span>o sobre a tr<span class="blank _8"> </span>an<span class="blank _8"> </span>sf<span class="blank _0"></span>or<span class="blank _8"> </span>maçã<span class="blank _8"> </span>o de ten<span class="blank _8"> </span>são t<span class="blank _8"> </span>rat<span class="blank _8"> </span>ar<span class="blank _8"> </span>á pr<span class="blank _8"> </span>incipal-</div><div class="t m0 x30 h26 ybd ff13 fs1b fc3 sc0 ls37 ws3d">mente do <span class="ff14 ls38 ws3e">estad<span class="blank _0"></span>o p<span class="blank _0"></span>lan<span class="blank _0"></span>o d<span class="blank _0"></span>e t<span class="blank _0"></span>ensão<span class="blank _3"></span><span class="ff13 ls39 ws3f">, is<span class="blank _0"></span>to é,<span class="blank _0"></span> de uma s<span class="blank _0"></span>i<span class="blank _0"></span>t<span class="blank _8"> </span>uação na q<span class="blank _0"></span>ual duas f<span class="blank _0"></span>a-</span></span></div><div class="t m0 x30 h26 ybe ff13 fs1b fc3 sc0 ls3a ws40">ces<span class="blank _8"> </span> do element<span class="blank _8"> </span>o de volume e<span class="blank _8"> </span>st<span class="blank _8"> </span>ão l<span class="blank _8"> </span>iv<span class="blank _8"> </span>res<span class="blank _8"> </span> de qu<span class="blank _8"> </span>alque<span class="blank _8"> </span>r te<span class="blank _8"> </span>ns<span class="blank _8"> </span>ão. Se o ei<span class="blank _8"> </span>xo<span class="ff14 ls3b ws8"> z</span><span class="ls3c ws41"> for<span class="blank _8"> </span> </span></div><div class="t m0 x30 h33 ybf ff13 fs1b fc3 sc0 ls2f ws42">escolh<span class="blank _8"> </span>ido como per<span class="blank _8"> </span>pe<span class="blank _8"> </span>ndicula<span class="blank _8"> </span>r a essas fa<span class="blank _8"> </span>ces, te<span class="blank _8"> </span>remos <span class="ff15 ls21">\u03c3<span class="ff14 fs1c ls22 v4">z</span></span><span class="lsb ws2c v0"> = </span></div><div class="t m5 x60 h27 yc0 ff16 fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 x4f h28 yc1 ff14 fs1c fc3 sc0 ls2c">zx</div><div class="t m0 x50 h24 yc0 ff13 fs1b fc3 sc0 lsb ws2c"> = </div><div class="t m5 x65 h27 yc0 ff16 fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 x66 h28 yc1 ff14 fs1c fc3 sc0 ls3d">zy</div><div class="t m0 x67 h24 yc0 ff13 fs1b fc3 sc0 lsb ws2c"> = 0, e as </div><div class="t m0 x30 h25 yc2 ff13 fs1b fc3 sc0 ls3e ws43">ún<span class="blank _8"> </span>i<span class="blank _0"></span>cas co<span class="blank _0"></span>mpon<span class="blank _0"></span>entes<span class="blank _0"></span> de tensão<span class="blank _0"></span> restantes s<span class="blank _0"></span>erão <span class="ff15 ls23">\u03c3<span class="ff14 fs1c ls19 v4">x</span></span><span class="lsb ws8 v0">, <span class="ff15 ls24">\u03c3</span><span class="ff14 fs1c ws24 v4">y</span><span class="ws44"> e </span></span></div><div class="t m5 x68 h27 yc3 ff16 fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 x69 h28 yc4 ff14 fs1c fc3 sc0 ls2a">xy</div><div class="t m0 x6a h24 yc3 ff13 fs1b fc3 sc0 ls3f ws45"> (Fi<span class="blank _0"></span>g. 1<span class="blank _4"></span>4.2<span class="blank _3"></span>). Uma </div><div class="t m0 x30 h24 yc5 ff13 fs1b fc3 sc0 ls1e ws46">situ<span class="blank _8"> </span>ação a<span class="blank _8"> </span>ssim oc<span class="blank _8"> </span>or<span class="blank _8"> </span>re em u<span class="blank _8"> </span>ma placa f<span class="blank _8"> </span>i<span class="blank _8"> </span>na submet<span class="blank _8"> </span>ida a forças que at<span class="blank _8"> </span>ua<span class="blank _8"> </span>m no </div><div class="t m0 x30 h24 yc6 ff13 fs1b fc3 sc0 ls40 ws47">plano médio d<span class="blank _8"> </span>a espessu<span class="blank _8"> </span>r<span class="blank _8"> </span>a da placa (<span class="blank _8"> </span>F<span class="blank _0"></span>ig<span class="blank _0"></span>. 1<span class="blank _3"></span>4.3<span class="blank _3"></span>). E<span class="blank _0"></span>la ocor<span class="blank _8"> </span>re t<span class="blank _8"> </span>ambé<span class="blank _8"> </span>m na su-</div><div class="t m0 x30 h24 yc7 ff13 fs1b fc3 sc0 ls41 ws48">pe<span class="blank _0"></span>rfí<span class="blank _3"></span>ci<span class="blank _3"></span>e l<span class="blank _0"></span>i<span class="blank _0"></span>vr<span class="blank _0"></span>e<span class="blank _0"></span> d<span class="blank _0"></span>e<span class="blank _0"></span> um<span class="blank _0"></span> e<span class="blank _0"></span>l<span class="blank _3"></span>em<span class="blank _0"></span>en<span class="blank _3"></span>to<span class="blank _3"></span> es<span class="blank _0"></span>trutur<span class="blank _0"></span>al<span class="blank _3"></span> ou<span class="blank _3"></span> co<span class="blank _0"></span>m<span class="blank _0"></span>p<span class="blank _0"></span>o<span class="blank _0"></span>n<span class="blank _0"></span>en<span class="blank _3"></span>te<span class="blank _0"></span> d<span class="blank _0"></span>e<span class="blank _0"></span> má<span class="blank _0"></span>q<span class="blank _0"></span>uin<span class="blank _0"></span>a,<span class="blank _3"></span> is<span class="blank _0"></span>t<span class="blank _0"></span>o<span class="blank _0"></span> </div><div class="t m0 x30 h24 yc8 ff13 fs1b fc3 sc0 ls42 ws8">é<span class="blank _3"></span>,<span class="blank _4"></span> e<span class="blank _0"></span>m<span class="blank _4"></span> q<span class="blank _3"></span>u<span class="blank _0"></span>a<span class="blank _3"></span>l<span class="blank _4"></span>q<span class="blank _3"></span>u<span class="blank _3"></span>e<span class="blank _3"></span>r<span class="blank _3"></span> p<span class="blank _3"></span>o<span class="blank _3"></span>n<span class="blank _4"></span>t<span class="blank _0"></span>o<span class="blank _4"></span> d<span class="blank _0"></span>a<span class="blank _3"></span> s<span class="blank _3"></span>u<span class="blank _3"></span>p<span class="blank _3"></span>e<span class="blank _3"></span>r<span class="blank _3"></span>fí<span class="blank _4"></span>c<span class="blank _3"></span>i<span class="blank _4"></span>e<span class="blank _3"></span> d<span class="blank _3"></span>o<span class="blank _3"></span> e<span class="blank _4"></span>l<span class="blank _3"></span>e<span class="blank _3"></span>m<span class="blank _3"></span>e<span class="blank _3"></span>n<span class="blank _4"></span>t<span class="blank _0"></span>o<span class="blank _4"></span> o<span class="blank _3"></span>u<span class="blank _3"></span> c<span class="blank _3"></span>o<span class="blank _3"></span>m<span class="blank _3"></span>p<span class="blank _3"></span>o<span class="blank _3"></span>n<span class="blank _4"></span>e<span class="blank _3"></span>n<span class="blank _3"></span>t<span class="blank _3"></span>e<span class="blank _3"></span> q<span class="blank _3"></span>u<span class="blank _3"></span>e<span class="blank _3"></span> n<span class="blank _3"></span>ã<span class="blank _3"></span>o<span class="blank _3"></span> </div><div class="t m0 x30 h24 yc9 ff13 fs1b fc3 sc0 ls25 ws49">esteja submetido a u<span class="blank _8"> </span>ma força exter<span class="blank _e"> </span>na (<span class="blank _8"> </span>F<span class="blank _0"></span>ig<span class="blank _0"></span>. 1<span class="blank _3"></span>4.<span class="blank _0"></span>4<span class="blank _0"></span>).</div><div class="t m0 x6b h34 yca ff19 fs11 fc9 sc0 lsb ws27">F<span class="ff18 fs17 v8">1</span></div><div class="t m0 x6c h34 ycb ff19 fs11 fc9 sc0 lsb ws27">F<span class="ff18 fs17 v8">2</span></div><div class="t m0 x52 h32 ycc fff fs16 fc8 sc0 ls20 ws3b">Figura 1<span class="blank _3"></span>4<span class="blank _8"> </span>.4</div><div class="t m0 x30 h35 ycd ff13 fs1f fc3 sc0 lsb ws28">*<span class="fs11 ws4a v4"> Le<span class="blank _8"> </span>mbr<span class="blank _8"> </span>amo<span class="blank _8"> </span>s <span class="blank _14"></span>que </span></div><div class="t m7 x6d h36 yce ff16 fs20 fc3 sc0 lsb">\ue602</div><div class="t m0 x6e h37 ycf ff14 fs1f fc3 sc0 ls43">yx</div><div class="t m0 x6f h38 yce ff13 fs11 fc3 sc0 lsb ws8"> = </div><div class="t m7 x70 h36 yce ff16 fs20 fc3 sc0 lsb">\ue602</div><div class="t m0 x71 h37 ycf ff14 fs1f fc3 sc0 ls44">xy</div><div class="t m0 x72 h38 yce ff13 fs11 fc3 sc0 lsb ws8">, </div><div class="t m7 x73 h36 yce ff16 fs20 fc3 sc0 lsb">\ue602</div><div class="t m0 x74 h37 ycf ff14 fs1f fc3 sc0 ls45">zy</div><div class="t m0 x75 h38 yce ff13 fs11 fc3 sc0 lsb ws8"> = </div><div class="t m7 x76 h36 yce ff16 fs20 fc3 sc0 lsb">\ue602</div><div class="t m0 x77 h37 ycf ff14 fs1f fc3 sc0 ls46">yz</div><div class="t m0 x78 h38 yce ff13 fs11 fc3 sc0 lsb ws8"> e </div><div class="t m7 x3c h36 yce ff16 fs20 fc3 sc0 lsb">\ue602</div><div class="t m0 x3d h37 ycf ff14 fs1f fc3 sc0 ls47">xz</div><div class="t m0 x79 h38 yce ff13 fs11 fc3 sc0 lsb ws8"> = </div><div class="t m7 x55 h36 yce ff16 fs20 fc3 sc0 lsb">\ue602</div><div class="t m0 x32 h39 ycf ff14 fs1f fc3 sc0 ls48 ws29">zx<span class="fs11 lsb v9">.</span></div><div class="t m6 x7a h2b yd0 ff16 fs1e fc9 sc0 lsb">\ue602</div><div class="t m0 x7b h2c yd1 ff17 fs17 fc9 sc0 ls33">yx</div><div class="t m6 x29 h2b yd2 ff16 fs1e fc9 sc0 lsb">\ue602</div><div class="t m0 x7c h2c yd3 ff17 fs17 fc9 sc0 ls32">xy</div><div class="t m6 x7d h2d yd4 ff18 fs1e fc9 sc0 lsb">\u03c3</div><div class="t m0 x7e h2c yd5 ff17 fs17 fc9 sc0 lsb">y</div><div class="t m6 x28 h2d yd6 ff18 fs1e fc9 sc0 lsb">\u03c3</div><div class="t m0 x7f h2c yd7 ff17 fs17 fc9 sc0 lsb">x</div><div class="t m0 x80 h34 yd8 ff19 fs11 fc9 sc0 lsb ws27">F<span class="ff18 fs17 v8">1</span></div><div class="t m0 x81 h34 yd9 ff19 fs11 fc9 sc0 lsb ws27">F<span class="ff18 fs17 v8">2</span></div><div class="t m0 x82 h34 yda ff19 fs11 fc9 sc0 lsb ws27">F<span class="ff18 fs17 v8">3</span></div><div class="t m0 x28 h34 ydb ff19 fs11 fc9 sc0 lsb ws27">F<span class="ff18 fs17 v8">4</span></div><div class="t m0 x83 h34 ydc ff19 fs11 fc9 sc0 lsb ws27">F<span class="ff18 fs17 v8">5</span></div><div class="t m0 x84 h34 ydd ff19 fs11 fc9 sc0 lsb ws27">F<span class="ff18 fs17 v8">6</span></div><div class="t m0 x85 h32 yde fff fs16 fc8 sc0 ls20 ws3b">Figura 1<span class="blank _3"></span>4<span class="blank _8"> </span>.2</div><div class="t m0 x80 h32 ydf fff fs16 fc8 sc0 ls20 ws3b">Figura 1<span class="blank _3"></span>4<span class="blank _8"> </span>.3</div><div class="t m0 x2c h1d y6f ff1a fs17 fc7 sc1 lsb ws8"><span class="fc7 sc0">Cap.14_Beer.indd 574</span><span class="blank _15"></span><span class="fc3 sc0"><span class="fc7 sc0">Cap.14_Beer.indd 574</span><span class="blank _16"> </span><span class="fc7 sc1"><span class="fc7 sc0">03/12/2012 19:14:53</span><span class="blank _11"></span><span class="fc3 sc0"><span class="fc7 sc0">03/12/2012 19:14:53</span></span></span></span></div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,-23.513400,-23.513400]}"></div></div> <div id="pf4" class="pf w2 h1a" data-page-no="4"><div class="pc pc4 w2 h1a"><img fetchpriority="low" loading="lazy" class="bi x86 ye0 w4 h3a" alt="" src="https://files.passeidireto.com/5502e1cb-a069-41c0-937b-d1f856940370/bg4.png"><div class="t m0 x87 h1f ye1 ff1b fs13 fc8 sc0 lsb">575</div><div class="t m0 x77 h3b ye2 ff1c fs2 fc3 sc0 lsb ws8">Capítulo 14 <span class="blank _a"> </span><span class="ff1d fs21 ws4b">\u426c</span> <span class="blank _a"> </span>T<span class="blank _4"></span>ransformações de tensão</div><div class="t m0 x88 h24 ye3 ff1e fs1b fc3 sc0 ls31 ws52">Considera<span class="blank _8"> </span>ndo, na Seção 1<span class="blank _3"></span>4.2, que u<span class="blank _8"> </span>m est<span class="blank _8"> </span>ado plano de ten<span class="blank _8"> </span>são em u<span class="blank _8"> </span>m </div><div class="t m0 x86 h3c ye4 ff1e fs1b fc3 sc0 ls5e ws40">dado<span class="blank _0"></span> po<span class="blank _0"></span>n<span class="blank _0"></span>to<span class="blank _0"></span> <span class="ff1f lsb">Q</span><span class="ls50 ws53"> é car<span class="blank _8"> </span>acte<span class="blank _8"> </span>ri<span class="blank _8"> </span>za<span class="blank _8"> </span>do pelas componente<span class="blank _8"> </span>s de ten<span class="blank _8"> </span>são <span class="ff20 ls49">\u03c3<span class="ff1f fs1c ls4a v4">x</span></span><span class="lsb ws8 v0">, <span class="blank _8"> </span><span class="ff20 ls4b">\u03c3</span><span class="ff1f fs1c ws24 v4">y</span><span class="ws54"> e </span></span></span></div><div class="t m5 x89 h27 ye5 ff21 fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 x8a h28 ye6 ff1f fs1c fc3 sc0 ls2a">xy</div><div class="t m0 x3c h24 ye5 ff1e fs1b fc3 sc0 ls4c ws55"> as-</div><div class="t m0 x86 h26 ye7 ff1e fs1b fc3 sc0 ls5f ws8">s<span class="blank _0"></span>oc<span class="blank _3"></span>ia<span class="blank _0"></span>da<span class="blank _0"></span>s<span class="blank _0"></span> c<span class="blank _0"></span>o<span class="blank _0"></span>m<span class="blank _0"></span> o<span class="blank _0"></span> e<span class="blank _3"></span>le<span class="blank _0"></span>m<span class="blank _0"></span>e<span class="blank _0"></span>n<span class="blank _0"></span>t<span class="blank _0"></span>o<span class="blank _0"></span> m<span class="blank _0"></span>o<span class="blank _0"></span>s<span class="blank _0"></span>tra<span class="blank _0"></span>d<span class="blank _0"></span>o<span class="blank _0"></span> na<span class="blank _3"></span> F<span class="blank _3"></span>ig<span class="blank _3"></span>.<span class="blank _0"></span> 1<span class="blank _4"></span>4<span class="blank _3"></span>.5<span class="blank _3"></span><span class="ff1f ls2f">a<span class="ff1e ls4d ws56">, você aprender<span class="blank _8"> </span>á a deter<span class="blank _0"></span>-</span></span></div><div class="t m0 x86 h3d ye8 ff1e fs1b fc3 sc0 ls60 ws57">mi<span class="blank _8"> </span>na<span class="blank _8"> </span>r as comp<span class="blank _8"> </span>onentes <span class="ff20 ls4e">\u03c3<span class="ff1f fs1c ls61 ws4c v4">x'<span class="blank"> </span></span></span><span class="lsb ws8 v0">, <span class="ff20 ls4f">\u03c3<span class="ff1f fs1c ls62 ws4d v4">y'<span class="blank _0"></span><span class="ff1e fs1b lsb ws58 v5"> e </span></span></span></span></div><div class="t m5 x8b h27 ye9 ff21 fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 x83 h3e yea ff1f fs1c fc3 sc0 ls61 ws4e">x'y<span class="blank"> </span>'<span class="blank"> </span><span class="ff1e fs1b ls50 ws59 v5"> a<span class="blank _8"> </span>ssociados com e<span class="blank _8"> </span>sse elemento depois de </span></div><div class="t m0 x86 h33 yeb ff1e fs1b fc3 sc0 ls17 ws5a">el<span class="blank _0"></span>e sofre<span class="blank _8"> </span>r uma rot<span class="blank _8"> </span>açã<span class="blank _8"> </span>o de um â<span class="blank _8"> </span>ng<span class="blank _8"> </span>ulo <span class="ff20 lsb">\u03b8</span><span class="ls16 ws5b"> em tor<span class="blank _8"> </span>no do ei<span class="blank _8"> </span>xo<span class="blank _0"></span><span class="ff1f ls63 ws8"> z<span class="ff1e ls64 ws5c"> (F<span class="blank _3"></span>ig<span class="blank _0"></span>.<span class="blank _0"></span> 1<span class="blank _4"></span>4.<span class="blank _0"></span>5<span class="blank _3"></span><span class="ff1f lsb ws25">b<span class="blank _0"></span><span class="ff1e ls65 ws5d">). N<span class="blank _8"> </span>a </span></span></span></span></span></div><div class="t m0 x86 h3d yec ff1e fs1b fc3 sc0 ls25 ws46">Seção 1<span class="blank _3"></span>4.3, v<span class="blank _0"></span>ocê deter<span class="blank _8"> </span>m<span class="blank _8"> </span>i<span class="blank _8"> </span>na<span class="blank _8"> </span>rá o valor <span class="ff20 ls51">\u03b8<span class="ff1f fs1c lsb ws24 v4">p</span></span><span class="ls31 ws5e v0"> de <span class="ff20 lsb">\u03b8</span><span class="ls66 ws8"> pa<span class="blank _e"> </span>r<span class="blank _8"> </span>a o<span class="blank _8"> </span> q<span class="blank _8"> </span>u<span class="blank _8"> </span>a<span class="blank _8"> </span>l<span class="blank _8"> </span> a<span class="blank _8"> </span>s t<span class="blank _8"> </span>e<span class="blank _8"> </span>n<span class="blank _8"> </span>s<span class="blank _8"> </span>õ<span class="blank _8"> </span>e<span class="blank _8"> </span>s <span class="blank _8"> </span><span class="ff20 ls52">\u03c3<span class="ff1f fs1c ls53 v4">x<span class="ff22 lsb ws4f">\u02b9</span></span></span><span class="lsb ws5f"> e <span class="ff20 ls54">\u03c3<span class="ff1f fs1c ls55 v4">y<span class="ff22 lsb ws4f">\u02b9</span></span></span><span class="ws8"> </span></span></span></span></div><div class="t m0 x86 h24 yed ff1e fs1b fc3 sc0 ls67 ws60">são, respe<span class="blank _8"> </span>ctivame<span class="blank _8"> </span>nte, o máx<span class="blank _8"> </span>i<span class="blank _8"> </span>mo e o mí<span class="blank _8"> </span>ni<span class="blank _8"> </span>mo desse<span class="blank _8"> </span>s valores da te<span class="blank _8"> </span>nsão </div><div class="t m0 x86 h26 yee ff1e fs1b fc3 sc0 ls56 ws61">nor<span class="blank _e"> </span>mal que são a<span class="blank _8"> </span>s<span class="ff1f ls57"> tensõe<span class="blank _8"> </span>s principai<span class="blank _8"> </span>s</span><span class="ls68 ws62"> no pont<span class="blank _8"> </span>o<span class="ff1f ls69 ws8"> Q</span><span class="ls25 ws63">, e a<span class="blank _8"> </span>s faces cor<span class="blank _e"> </span>resp<span class="blank _8"> </span>onden-</span></span></div><div class="t m0 x86 h26 yef ff1e fs1b fc3 sc0 ls25 ws64">tes do elemento def<span class="blank _8"> </span>i<span class="blank _8"> </span>nem os<span class="ff1f ls6a ws8"> pl<span class="blank _8"> </span>a<span class="blank _8"> </span>n<span class="blank _8"> </span>os<span class="blank _8"> </span> p<span class="blank _8"> </span>r<span class="blank _8"> </span>in<span class="blank _8"> </span>c<span class="blank _8"> </span>ip<span class="blank _8"> </span>a<span class="blank _8"> </span>i<span class="blank _8"> </span>s d<span class="blank _8"> </span>e t<span class="blank _8"> </span>e<span class="blank _8"> </span>n<span class="blank _8"> </span>s<span class="blank _8"> </span>ão<span class="blank _8"> </span></span><span class="ls31 ws65"> nesse ponto. V<span class="blank _4"></span>ocê </span></div><div class="t m0 x86 h33 yf0 ff1e fs1b fc3 sc0 ls31 ws66">deter<span class="blank _e"> </span>mi<span class="blank _8"> </span>na<span class="blank _8"> </span>rá t<span class="blank _8"> </span>ambé<span class="blank _8"> </span>m o valor de <span class="ff20 ls58">\u03b8<span class="ff1f fs1c lsb ws24 v4">c</span></span><span class="ls59 ws67 v0"> do ângulo de rota<span class="blank _8"> </span>ção par<span class="blank _8"> </span>a o qual a te<span class="blank _8"> </span>n-</span></div><div class="t m0 x86 h24 yf1 ff1e fs1b fc3 sc0 ls31 ws68">são de cisal<span class="blank _8"> </span>hame<span class="blank _8"> </span>nto é máx<span class="blank _8"> </span>im<span class="blank _8"> </span>a, be<span class="blank _8"> </span>m como o valor desta.</div><div class="t m6 x8c h2b yf2 ff21 fs1e fc9 sc0 lsb">\ue602</div><div class="t m0 x26 h2c yf3 ff23 fs17 fc9 sc0 ls33">xy</div><div class="t m6 x8d h2b yf4 ff21 fs1e fc9 sc0 lsb">\ue602</div><div class="t m0 x8e h2c yf5 ff23 fs17 fc9 sc0 ls34">x'y'</div><div class="t m6 x8f h2d yf6 ff24 fs1e fc9 sc0 lsb">\u03c3</div><div class="t m0 x90 h2c yf7 ff23 fs17 fc9 sc0 lsb">y</div><div class="t m6 x91 h2d yf8 ff24 fs1e fc9 sc0 lsb">\u03c3</div><div class="t m0 x92 h2e yf9 ff23 fs17 fc9 sc0 lsb">y<span class="ff24">\u2032</span></div><div class="t m6 x93 h2d yfa ff24 fs1e fc9 sc0 lsb">\u03c3</div><div class="t m0 x27 h2c yfb ff23 fs17 fc9 sc0 lsb">x</div><div class="t m6 x3a h2d yfc ff24 fs1e fc9 sc0 lsb">\u03c3</div><div class="t m0 x3b h2c yfd ff23 fs17 fc9 sc0 ls34">x'</div><div class="t m0 x94 h2f yfe ff23 fs11 fc3 sc0 ls5a">Q<span class="lsb v4">Q</span></div><div class="t m0 x88 h2f yff ff23 fs11 fc3 sc0 lsb">z</div><div class="t m0 x95 h2f y100 ff23 fs11 fc3 sc0 ls6b">xx</div><div class="t m0 x78 h30 y101 ff23 fs11 fc9 sc0 lsb">x<span class="ff24">\u2032</span></div><div class="t m0 x90 h3f y102 ff23 fs11 fc3 sc0 ls5b">y<span class="fc9 lsb va">y<span class="ff24">\u2032</span></span></div><div class="t m0 x96 h30 y103 ff23 fs11 fc9 sc0 lsb">z<span class="ff24 ls6c ws69">\u2032 = </span>z</div><div class="t m0 x97 h2f y104 ff23 fs11 fc3 sc0 lsb">y</div><div class="t m8 x98 h40 y105 ff24 fs22 fc3 sc0 lsb">\u03b8</div><div class="t m8 x74 h40 y106 ff24 fs22 fc3 sc0 lsb">\u03b8</div><div class="t m0 x99 h30 y107 ff24 fs11 fc3 sc0 lsb">(<span class="ff23">a</span><span class="ls6d ws50">)(<span class="blank _17"></span><span class="ff23 lsb">b<span class="ff24">)</span></span></span></div><div class="t m0 x9a h32 y108 ff1b fs16 fc8 sc0 ls20 ws3b">Figura 1<span class="blank _3"></span>4<span class="blank _8"> </span>.5</div><div class="t m0 x88 h24 y109 ff1e fs1b fc3 sc0 ls17 ws6a">Na Seção 1<span class="blank _3"></span>4.<span class="blank _0"></span>4, será aprese<span class="blank _8"> </span>nta<span class="blank _8"> </span>do um mét<span class="blank _8"> </span>odo alter<span class="blank _8"> </span>nat<span class="blank _8"> </span>iv<span class="blank _0"></span>o par<span class="blank _8"> </span>a a sol<span class="blank _0"></span>ução </div><div class="t m0 x86 h24 y10a ff1e fs1b fc3 sc0 ls40 ws6b">de probl<span class="blank _0"></span>ema<span class="blank _8"> </span>s que env<span class="blank _0"></span>ol<span class="blank _0"></span>vem esta<span class="blank _8"> </span>do plano de ten<span class="blank _8"> </span>são, a t<span class="blank _8"> </span>ra<span class="blank _8"> </span>nsf<span class="blank _0"></span>or<span class="blank _8"> </span>ma<span class="blank _8"> </span>ção de </div><div class="t m0 x86 h26 y10b ff1e fs1b fc3 sc0 lsb ws8">ten<span class="blank _8"> </span>sões plan<span class="blank _8"> </span>as com base no u<span class="blank _8"> </span>so do<span class="ff1f ls5c ws6c"> círculo de Mohr.</span></div><div class="t m0 x88 h26 y10c ff1e fs1b fc3 sc0 ls6e ws51">Os<span class="ff1f ls6f ws6d"> vasos de pressão de parede<span class="blank _8"> </span>s f<span class="blank _8"> </span>ina<span class="blank _8"> </span>s</span><span class="ls70 ws6e"> proporcionam u<span class="blank _8"> </span>ma aplicação i<span class="blank _8"> </span>m-</span></div><div class="t m0 x86 h24 y10d ff1e fs1b fc3 sc0 ls70 ws6f">por<span class="blank _8"> </span>t<span class="blank _8"> </span>ante pa<span class="blank _8"> </span>ra a a<span class="blank _8"> </span>nálise do e<span class="blank _8"> </span>sta<span class="blank _8"> </span>do plano de ten<span class="blank _8"> </span>são. N<span class="blank _0"></span>a Seção 1<span class="blank _3"></span>4.5<span class="blank _0"></span>, discut<span class="blank _8"> </span>i<span class="blank _8"> </span>remos<span class="blank _8"> </span> </div><div class="t m0 x86 h24 y10e ff1e fs1b fc3 sc0 ls71 ws70">as te<span class="blank _8"> </span>nsõe<span class="blank _8"> </span>s em vasos de pre<span class="blank _8"> </span>ssão cil<span class="blank _8"> </span>índ<span class="blank _8"> </span>r<span class="blank _8"> </span>icos e esfér<span class="blank _8"> </span>icos (F<span class="blank _0"></span>otos 1<span class="blank _3"></span>4.<span class="blank _3"></span>1 e 1<span class="blank _3"></span>4.2<span class="blank _3"></span>).</div><div class="t m0 x86 h24 y10f ff1b fs16 fc8 sc0 ls72 ws71">Foto<span class="blank _0"></span> 1<span class="blank _3"></span>4.<span class="blank _0"></span>1<span class="ff1e fs1b fc3 ls5d ws8"> </span><span class="ls73 ws72">Fo<span class="blank _0"></span>to 1<span class="blank _4"></span>4<span class="blank _8"> </span>.2</span></div><div class="t m0 x2c h1d y6f ff25 fs17 fc7 sc1 lsb ws8"><span class="fc7 sc0">Cap.14_Beer.indd 575</span><span class="blank _15"></span><span class="fc3 sc0"><span class="fc7 sc0">Cap.14_Beer.indd 575</span><span class="blank _16"> </span><span class="fc7 sc1"><span class="fc7 sc0">03/12/2012 19:14:53</span><span class="blank _11"></span><span class="fc3 sc0"><span class="fc7 sc0">03/12/2012 19:14:53</span></span></span></span></div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,-23.513400,-23.513400]}"></div></div> <div id="pf5" class="pf w2 h1a" data-page-no="5"><div class="pc pc5 w2 h1a"><img fetchpriority="low" loading="lazy" class="bi x2d y110 w4 h41" alt="" src="https://files.passeidireto.com/5502e1cb-a069-41c0-937b-d1f856940370/bg5.png"><div class="t m0 x2d h1f y71 ff26 fs13 fc8 sc0 lsb ws21">576<span class="blank"> </span><span class="ff27 fs2 fc3 ws8 v3">Estática e mecânica dos materiais</span></div><div class="t m0 x30 h23 y7e ff26 fs1a fc8 sc0 lsb ws8">14.2 <span class="blank _13"> </span>T<span class="blank _4"></span>ransformação do estado plano de tensão</div><div class="t m0 x30 h26 y111 ff28 fs1b fc3 sc0 ls1d ws83">V<span class="blank _3"></span>amos con<span class="blank _8"> </span>si<span class="blank _0"></span>der<span class="blank _8"> </span>ar que ex<span class="blank _8"> </span>iste u<span class="blank _8"> </span>m est<span class="blank _8"> </span>ado plano de t<span class="blank _8"> </span>ensã<span class="blank _8"> </span>o par<span class="blank _8"> </span>a o ponto<span class="ff29 ls95 ws8"> Q<span class="blank _3"></span><span class="ff28 lsb"> </span></span></div><div class="t m0 x30 h33 y112 ff28 fs1b fc3 sc0 ls96 ws8">(c<span class="blank _e"> </span>o<span class="blank _e"> </span>m<span class="blank _e"> </span> <span class="blank _8"> </span><span class="ff2a ls74">\u03c3<span class="ff29 fs1c ls22 v4">z</span></span><span class="lsb ws84 v0"> = </span></div><div class="t m5 x9b h27 y113 ff2b fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 x9c h28 y114 ff29 fs1c fc3 sc0 ls2c">zx</div><div class="t m0 x9d h24 y113 ff28 fs1b fc3 sc0 lsb ws84"> = </div><div class="t m5 x9e h27 y113 ff2b fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 x9f h28 y114 ff29 fs1c fc3 sc0 ls3d">zy</div><div class="t m0 x6e h33 y113 ff28 fs1b fc3 sc0 ls16 ws85"> = 0<span class="blank _0"></span>) e que el<span class="blank _0"></span>e é def<span class="blank _8"> </span>in<span class="blank _8"> </span>ido pelas compone<span class="blank _8"> </span>ntes de ten<span class="blank _8"> </span>são <span class="ff2a ls75">\u03c3<span class="ff29 fs1c ls19 v4">x</span></span><span class="lsb ws8">, </span></div><div class="t m0 x30 h33 y115 ff2a fs1b fc3 sc0 ls76">\u03c3<span class="ff29 fs1c lsb ws24 v4">y</span><span class="ff28 lsb ws86 v0"> e </span></div><div class="t m5 x64 h27 y116 ff2b fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 xa0 h28 y117 ff29 fs1c fc3 sc0 ls2a">xy</div><div class="t m0 xa1 h26 y116 ff28 fs1b fc3 sc0 ls97 ws3a"> a<span class="blank _8"> </span>s<span class="blank _8"> </span>s<span class="blank _8"> </span>o<span class="blank _e"> </span>c<span class="blank _8"> </span>i<span class="blank _8"> </span>a<span class="blank _8"> </span>d<span class="blank _e"> </span>a<span class="blank _8"> </span>s<span class="blank _8"> </span> a<span class="blank _e"> </span>o<span class="blank _8"> </span> e<span class="blank _8"> </span>le<span class="blank _e"> </span>m<span class="blank _8"> </span>e<span class="blank _8"> </span>n<span class="blank _8"> </span>t<span class="blank _8"> </span>o<span class="blank _8"> </span> m<span class="blank _8"> </span>o<span class="blank _8"> </span>s<span class="blank _8"> </span>t<span class="blank _e"> </span>r<span class="blank _e"> </span>a<span class="blank _8"> </span>d<span class="blank _8"> </span>o<span class="blank _8"> </span> n<span class="blank _e"> </span>a<span class="blank _8"> </span> Fig<span class="blank _8"> </span>.<span class="blank _8"> </span><span class="ff29 lsb ws8"> </span><span class="ls98 ws73">14<span class="blank"> </span>.<span class="blank"> </span>5<span class="blank"> </span><span class="ff29 ls99 ws74">a.</span><span class="ls9a ws87"> Pr<span class="blank _0"></span>opo<span class="blank _0"></span>m<span class="blank _0"></span>os<span class="blank _0"></span> de<span class="blank _0"></span>termi-</span></span></div><div class="t m0 x30 h42 y118 ff28 fs1b fc3 sc0 ls28 ws88">na<span class="blank _8"> </span>r as compone<span class="blank _8"> </span>ntes de te<span class="blank _8"> </span>nsã<span class="blank _8"> </span>o <span class="ff2a ls77">\u03c3<span class="ff29 fs1c ls61 ws75 v4">x'</span></span><span class="lsb ws8 v0">, <span class="blank _8"> </span><span class="ff2a ls78">\u03c3<span class="ff29 fs1c ls62 ws4d v4">y'</span></span><span class="ws89"> e </span></span></div><div class="t m5 xa2 h27 y119 ff2b fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 xa3 h29 y11a ff29 fs1c fc3 sc0 ls61 ws4e">x'y<span class="blank"> </span>'<span class="ff28 fs1b ls9b ws8a v5"> associadas<span class="blank _0"></span> ao e<span class="blank _0"></span>lem<span class="blank _0"></span>ento<span class="blank _0"></span> depo<span class="blank _0"></span>is </span></div><div class="t m0 x30 h33 y11b ff28 fs1b fc3 sc0 ls5c ws8b">de el<span class="blank _0"></span>e sofre<span class="blank _8"> </span>r uma rot<span class="blank _8"> </span>açã<span class="blank _8"> </span>o de um â<span class="blank _8"> </span>ng<span class="blank _8"> </span>ulo <span class="ff2a lsb">\u03b8</span><span class="ls9c ws8"> em<span class="blank _0"></span> torno<span class="blank _0"></span> do<span class="blank _0"></span> eix<span class="blank _3"></span>o<span class="ff29"> z</span><span class="ls9d ws8c"> (F<span class="blank _3"></span>i<span class="blank _0"></span>g<span class="blank _0"></span>. 1<span class="blank _4"></span>4<span class="blank _0"></span>.5<span class="blank _3"></span><span class="ff29 lsb ws25">b<span class="blank _0"></span><span class="ff28 ls65 ws8">). </span></span></span></span></div><div class="t m0 x30 h25 y11c ff28 fs1b fc3 sc0 ls5c ws6c">Essas compone<span class="blank _8"> </span>ntes devem ser expressa<span class="blank _8"> </span>s em te<span class="blank _8"> </span>r<span class="blank _8"> </span>mos de <span class="ff2a ls79">\u03c3<span class="ff29 fs1c ls19 v4">x</span></span><span class="lsb ws8 v0">, <span class="ff2a ls7a">\u03c3</span><span class="ff29 fs1c ws24 v4">y</span> </span></div><div class="t m5 x49 h27 y11d ff2b fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 x4a h28 y11e ff29 fs1c fc3 sc0 ls2a">xy</div><div class="t m0 x45 h33 y11d ff28 fs1b fc3 sc0 lsb ws8"> e <span class="ff2a ws76">\u03b8<span class="blank _3"></span><span class="ff28">.</span></span></div><div class="t m6 xa4 h2b y11f ff2b fs1e fc9 sc0 lsb">\ue602</div><div class="t m0 x72 h2c y120 ff2c fs17 fc9 sc0 ls33">xy</div><div class="t m6 x43 h2b y121 ff2b fs1e fc9 sc0 lsb">\ue602</div><div class="t m0 x44 h2c y122 ff2c fs17 fc9 sc0 ls34">x'y'</div><div class="t m6 x8d h2d y123 ff2d fs1e fc9 sc0 lsb">\u03c3</div><div class="t m0 xa5 h2c y124 ff2c fs17 fc9 sc0 lsb">y</div><div class="t m6 xa6 h2d y125 ff2d fs1e fc9 sc0 lsb">\u03c3</div><div class="t m0 xa7 h2e y126 ff2c fs17 fc9 sc0 lsb">y<span class="ff2d">\u2032</span></div><div class="t m6 xa8 h2d y127 ff2d fs1e fc9 sc0 lsb">\u03c3</div><div class="t m0 xa9 h2c y128 ff2c fs17 fc9 sc0 lsb">x</div><div class="t m6 x4f h2d y129 ff2d fs1e fc9 sc0 lsb">\u03c3</div><div class="t m0 x50 h2c y12a ff2c fs17 fc9 sc0 ls34">x'</div><div class="t m0 x8e h2f y12b ff2c fs11 fc3 sc0 ls5a">Q<span class="lsb v4">Q</span></div><div class="t m0 x64 h2f y12c ff2c fs11 fc3 sc0 lsb">z</div><div class="t m0 x3e h2f y12d ff2c fs11 fc3 sc0 ls6b">xx</div><div class="t m0 x48 h30 y12e ff2c fs11 fc9 sc0 lsb">x<span class="ff2d">\u2032</span></div><div class="t m0 xa5 h3f y12f ff2c fs11 fc3 sc0 ls5b">y<span class="fc9 lsb va">y<span class="ff2d">\u2032</span></span></div><div class="t m0 xaa h30 y130 ff2c fs11 fc9 sc0 lsb">z<span class="ff2d ls9e ws8d">\u2032 = </span>z</div><div class="t m0 xab h2f y131 ff2c fs11 fc3 sc0 lsb">y</div><div class="t m8 x5b h40 y132 ff2d fs22 fc3 sc0 lsb">\u03b8</div><div class="t m8 x66 h40 y133 ff2d fs22 fc3 sc0 lsb">\u03b8</div><div class="t m0 xac h30 y134 ff2d fs11 fc3 sc0 lsb">(<span class="ff2c">a</span><span class="ls6d ws50">)(<span class="blank _17"></span><span class="ff2c lsb">b<span class="ff2d">)</span></span></span></div><div class="t m0 x64 h32 y135 ff26 fs16 fc8 sc0 ls9f ws8e">Figura 1<span class="blank _3"></span>4<span class="blank _8"> </span>.5 <span class="blank _a"> </span>(repetida)</div><div class="t m0 x64 h33 y136 ff28 fs1b fc3 sc0 ls16 ws8f">Para det<span class="blank _8"> </span>er<span class="blank _8"> </span>m<span class="blank _8"> </span>in<span class="blank _8"> </span>ar<span class="blank _8"> </span>mos a t<span class="blank _8"> </span>ens<span class="blank _8"> </span>ão nor<span class="blank _8"> </span>mal <span class="ff2a ls7b">\u03c3<span class="ff29 fs1c ls61 ws77 v4">x'<span class="blank _8"> </span></span></span><span class="ls30 ws90"> e a tens<span class="blank _8"> </span>ão de cisalh<span class="blank _8"> </span>amento </span></div><div class="t m5 x51 h27 y136 ff2b fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 xad h28 y137 ff29 fs1c fc3 sc0 ls61 ws4e">x'y<span class="blank"> </span>'<span class="ff28 lsb ws8"> </span></div><div class="t m0 x30 h26 y138 ff28 fs1b fc3 sc0 ls25 ws91">que at<span class="blank _8"> </span>ua<span class="blank _8"> </span>m na face p<span class="blank _8"> </span>er<span class="blank _8"> </span>p<span class="blank _8"> </span>endicula<span class="blank _8"> </span>r ao ei<span class="blank _8"> </span>xo <span class="ff29 lsa0 ws78">x'</span><span class="ls50 ws92">, considera<span class="blank _8"> </span>mos um elemento </span></div><div class="t m0 x30 h26 y139 ff28 fs1b fc3 sc0 ls50 ws93">pr<span class="blank _8"> </span>ismático com fa<span class="blank _8"> </span>ces respe<span class="blank _8"> </span>ctiva<span class="blank _8"> </span>mente per<span class="blank _e"> </span>pe<span class="blank _8"> </span>ndiculare<span class="blank _8"> </span>s aos ei<span class="blank _8"> </span>x<span class="blank _0"></span>os <span class="ff29 lsb ws25">x<span class="ff28 ws8">, <span class="blank _8"> </span></span>y<span class="ff28 ws94"> e </span><span class="lsa0 ws79">x'<span class="blank"> </span></span><span class="ff28 ws8"> </span></span></div><div class="t m0 x30 h26 y13a ff28 fs1b fc3 sc0 ls64 ws7a">(F<span class="blank _3"></span>ig<span class="blank _3"></span>.<span class="ff29 lsb ws8"> </span><span class="ls98 ws7b">14<span class="blank"> </span>.<span class="blank"> </span>6<span class="blank"> </span><span class="ff29 lsb ws25">a<span class="blank _0"></span><span class="ff28">)<span class="ff29">.</span><span class="lsa1 ws8"> Obse<span class="blank _8"> </span>r<span class="blank _e"> </span>va<span class="blank _8"> </span>m<span class="blank _8"> </span>os<span class="blank _8"> </span> qu<span class="blank _8"> </span>e, s<span class="blank _8"> </span>e a<span class="blank _8"> </span> á<span class="blank _8"> </span>re<span class="blank _8"> </span>a<span class="blank _8"> </span> d<span class="blank _8"> </span>a f<span class="blank _8"> </span>ac<span class="blank _8"> </span>e o<span class="blank _8"> </span>blíq<span class="blank _8"> </span>u<span class="blank _8"> </span>a é<span class="blank _8"> </span> r<span class="blank _8"> </span>ep<span class="blank _8"> </span>r<span class="blank _8"> </span>es<span class="blank _8"> </span>en<span class="blank _8"> </span>t<span class="blank _8"> </span>a<span class="blank _8"> </span>d<span class="blank _8"> </span>a p<span class="blank _8"> </span>or<span class="blank _8"> </span> </span></span></span></span></div><div class="t m0 x30 h43 y13b ff2e fs1b fc3 sc0 ls7c">\u2206<span class="ff29 lsb ws25">A<span class="ff28">,</span><span class="ls7d ws8"> </span></span><span class="ff28 ls1e ws95">as áre<span class="blank _8"> </span>as d<span class="blank _8"> </span>as face<span class="blank _8"> </span>s ver<span class="blank _8"> </span>tical e hor<span class="blank _8"> </span>izont<span class="blank _8"> </span>al são, respe<span class="blank _8"> </span>ctiva<span class="blank _8"> </span>mente, igu<span class="blank _8"> </span>ais a </span></div><div class="t m0 x30 h43 y13c ff2e fs1b fc3 sc0 ls7c">\u2206<span class="ff29 lsb ws8">A <span class="blank _8"> </span><span class="ff28 lsa2">cos <span class="blank _8"> </span></span><span class="ff2a">\u03b8<span class="ff28 lsa3"> e<span class="blank _0"></span><span class="ff29 ls7e"> <span class="ff2e ls7c">\u2206</span><span class="lsb">A <span class="blank _8"> </span><span class="ff28 ls31">sen <span class="blank _8"> </span></span><span class="ff2a ws76">\u03b8</span>.<span class="ff28 lsa4 ws96"> Con<span class="blank _0"></span>clui-se que as<span class="ff29 lsa5 ws97"> forç<span class="blank _8"> </span>as<span class="blank _8"> </span> </span><span class="ls4d ws98">result<span class="blank _8"> </span>ante<span class="blank _8"> </span>s que at<span class="blank _8"> </span>ua<span class="blank _8"> </span>m nas </span></span></span></span></span></span></span></div><div class="t m0 x30 h26 y13d ff28 fs1b fc3 sc0 ls40 ws99">t<span class="blank _8"> </span>rês face<span class="blank _8"> </span>s são aq<span class="blank _8"> </span>uelas mostr<span class="blank _8"> </span>ad<span class="blank _8"> </span>as n<span class="blank _8"> </span>a F<span class="blank _0"></span>ig<span class="blank _0"></span>. 1<span class="blank _3"></span>4.<span class="blank _0"></span>6<span class="ff29 lsb ws25">b<span class="blank _0"></span><span class="ff28">.</span></span></div><div class="t m0 xae h2f y13e ff2c fs11 fc3 sc0 lsb">z</div><div class="t m0 xaf h2f y13f ff2c fs11 fc3 sc0 lsb">x</div><div class="t m0 x89 h30 y140 ff2c fs11 fc9 sc0 lsb">x<span class="ff2d">\u2032</span></div><div class="t m0 xb0 h30 y141 ff2c fs11 fc9 sc0 lsb">y<span class="ff2d ls7f">\u2032</span><span class="fc3 v3">y</span></div><div class="t m0 xb1 h30 y142 ff2d fs11 fc3 sc0 lsb">(<span class="ff2c">a</span>)</div><div class="t m0 xb2 h30 y143 ff2d fs11 fc3 sc0 lsb">\u2206<span class="ff2c">A</span><span class="ls6c ws69"> cos</span></div><div class="t m9 x97 h44 y143 ff2d fs23 fc3 sc0 ls80">\u03b8<span class="ls81 v1">\u03b8</span><span class="lsb vb">\u03b8</span></div><div class="t m0 x6d h30 y144 ff2d fs11 fc3 sc0 lsb">\u2206<span class="ff2c">A</span><span class="ws8"> sen</span></div><div class="t m9 x72 h45 y144 ff2d fs23 fc3 sc0 lsb">\u03b8</div><div class="t m0 x41 h30 y145 ff2d fs11 fc3 sc0 lsb">\u2206<span class="ff2c">A</span></div><div class="t m0 x87 h2f y146 ff2c fs11 fc3 sc0 lsb">x</div><div class="t m0 x47 h30 y147 ff2c fs11 fc9 sc0 lsb">x<span class="ff2d">\u2032</span></div><div class="t m0 xb3 h46 y148 ff2c fs11 fc9 sc0 lsb">y<span class="ff2d ls7f">\u2032</span><span class="fc3 vc">y</span></div><div class="t m0 x38 h30 y149 ff2d fs11 fc3 sc0 lsb">(<span class="ff2c">b</span>)</div><div class="t m0 xa2 h30 y14a ff2d fs11 fc9 sc0 lsb">(\u2206<span class="ff2c">A</span><span class="ls6c ws69"> cos<span class="blank _18"> </span>)</span></div><div class="t m8 xb4 h40 y14a ff2d fs22 fc9 sc0 lsb">\u03b8</div><div class="t m0 x5c h30 y14b ff2d fs11 fc9 sc0 lsb">(\u2206<span class="ff2c">A</span><span class="ls6c ws69"> cos<span class="blank _18"> </span>)</span></div><div class="t m8 xb5 h40 y14b ff2d fs22 fc9 sc0 lsb">\u03b8</div><div class="t m8 xb6 h40 y14c ff2d fs22 fc3 sc0 lsb">\u03b8</div><div class="t m6 x60 h2b y14d ff2b fs1e fc9 sc0 lsb">\ue602</div><div class="t m0 x4f h47 y14e ff2c fs17 fc9 sc0 lsb">x<span class="ff2d">\u2032</span>y<span class="ff2d ls11 ws8">\u2032 <span class="fs11 lsb v1">\u2206</span></span><span class="fs11 v1">A</span></div><div class="t m6 x36 h2b y14b ff2b fs1e fc9 sc0 lsb">\ue602</div><div class="t m0 xa3 h2c y14f ff2c fs17 fc9 sc0 ls34">xy</div><div class="t m0 xa6 h30 y150 ff2d fs11 fc9 sc0 lsb">(\u2206<span class="ff2c">A</span><span class="ws8"> sen<span class="blank _18"> </span>)</span></div><div class="t m8 xb7 h40 y150 ff2d fs22 fc9 sc0 lsb">\u03b8</div><div class="t m6 x5e h2b y150 ff2b fs1e fc9 sc0 lsb">\ue602</div><div class="t m0 x5c h2c y151 ff2c fs17 fc9 sc0 ls33">xy</div><div class="t m6 xb8 h2d y152 ff2d fs1e fc9 sc0 lsb">\u03c3</div><div class="t m0 x62 h47 y153 ff2c fs17 fc9 sc0 lsb">x<span class="ff2d ls34 ws8">\u2032 <span class="fs11 lsb v1">\u2206</span></span><span class="fs11 v1">A</span></div><div class="t m6 xaa h2d y14a ff2d fs1e fc9 sc0 lsb">\u03c3</div><div class="t m0 xb9 h2c y154 ff2c fs17 fc9 sc0 lsb">x</div><div class="t m0 x6b h30 y155 ff2d fs11 fc9 sc0 lsb">(\u2206<span class="ff2c">A</span><span class="ws8"> sen<span class="blank _19"> </span>)</span></div><div class="t m8 x4f h40 y155 ff2d fs22 fc9 sc0 lsb">\u03b8</div><div class="t m6 xba h2d y155 ff2d fs1e fc9 sc0 lsb">\u03c3</div><div class="t m0 x4b h2c y156 ff2c fs17 fc9 sc0 lsb">y</div><div class="t m0 x64 h32 y157 ff26 fs16 fc8 sc0 ls20 ws3b">Figura 1<span class="blank _3"></span>4<span class="blank _8"> </span>.6</div><div class="t m0 x30 h24 y158 ff28 fs1b fc3 sc0 ls25 ws9a">(<span class="blank _8"> </span>Não há forças aplicada<span class="blank _8"> </span>s nas fa<span class="blank _8"> </span>ces t<span class="blank _8"> </span>r<span class="blank _8"> </span>iang<span class="blank _8"> </span>u<span class="blank _8"> </span>lare<span class="blank _8"> </span>s do el<span class="blank _0"></span>emento, v<span class="blank _8"> </span>isto que as </div><div class="t m0 x30 h24 y159 ff28 fs1b fc3 sc0 ls40 ws9b">ten<span class="blank _8"> </span>sões nor<span class="blank _8"> </span>m<span class="blank _8"> </span>al e de cisalh<span class="blank _8"> </span>amento cor<span class="blank _e"> </span>resp<span class="blank _8"> </span>ondentes foram t<span class="blank _8"> </span>oda<span class="blank _8"> </span>s considera-</div><div class="t m0 x30 h26 y15a ff28 fs1b fc3 sc0 ls2d ws9c">da<span class="blank _8"> </span>s igu<span class="blank _8"> </span>ais a ze<span class="blank _8"> </span>ro<span class="blank _0"></span>.<span class="blank _3"></span>) Usando as compone<span class="blank _8"> </span>ntes a<span class="blank _8"> </span>o long<span class="blank _0"></span>o dos eixos <span class="ff29 lsa0 ws7c">x'<span class="blank"> </span></span><span class="lsb ws58"> e <span class="ff29 lsa6 ws7d">y'</span>, esc<span class="blank _8"> </span>re-</span></div><div class="t m0 x30 h24 y15b ff28 fs1b fc3 sc0 ls50 ws9d">vemos as segu<span class="blank _8"> </span>int<span class="blank _8"> </span>es equ<span class="blank _8"> </span>açõe<span class="blank _8"> </span>s de equi<span class="blank _8"> </span>líbr<span class="blank _8"> </span>io<span class="blank _0"></span>:</div><div class="t m0 xbb h48 y15c ff2d fs1b fc3 sc0 lsa7 ws8"> \u03a3<span class="blank _1a"> </span><span class="ff2c ls82">F<span class="fs24 ls83 v8">x<span class="ff2d ls84">\u2032</span></span></span><span class="lsa8 ws7e v0">=0<span class="blank _1b"></span>:<span class="blank"> </span><span class="ff2c ls85">\u03c3<span class="fs24 ls83 v8">x<span class="ff2d ls86">\u2032<span class="fs25 ls87 ws8 v0"> </span></span></span></span><span class="ls88">\u2206<span class="ff2c ls89">A</span><span class="ls8a">\u2013<span class="ff2c ls8b">\u03c3<span class="fs24 ls8c v8">x</span></span><span class="lsa9 ws7f">(\u2206<span class="blank"> </span><span class="ff2c ls8d">A</span><span class="ls8e ws9e"> cos <span class="ff2c ls8f">\u03b8</span><span class="lsaa ws9f">) c<span class="blank _8"> </span>o<span class="blank _8"> </span>s<span class="blank _e"> </span> <span class="ff2c ls90">\u03b8</span><span class="lsb">\u2013</span></span></span></span></span></span></span></div><div class="t m5 xab h27 y15d ff2b fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 x4c h49 y15e ff2c fs24 fc3 sc0 lsab ws80">xy<span class="blank"> </span><span class="ff2d fs1b lsa9 ws7f v1">(\u2206<span class="blank"> </span><span class="ff2c ls8d">A<span class="ff2d ls8e ws9e"> cos </span><span class="ls8f">\u03b8<span class="ff2d lsac wsa0">) s<span class="blank _8"> </span>e<span class="blank _8"> </span>n<span class="blank _e"> </span> </span></span></span></span></div><div class="c xbb y15f w5 h4a"><div class="t m0 x8d h4b y160 ff2c fs1b fc3 sc0 lsb">\u03b8</div></div><div class="t m0 xa4 h4c y161 ff2d fs1b fc3 sc0 ls91">\u2013<span class="ff2c ls92">\u03c3<span class="fs24 ls93 v8">y</span></span><span class="lsad ws81">(\u2206<span class="blank"> </span><span class="ff2c ls8d">A</span></span><span class="ls8e ws9e"> sen <span class="blank _3"></span><span class="ff2c ls8f">\u03b8<span class="ff2d lsaa ws9f">) s<span class="blank _8"> </span>e<span class="blank _e"> </span>n<span class="blank _8"> </span> <span class="blank _5"></span><span class="ff2c ls90">\u03b8<span class="ff2d lsb">\u2013</span></span></span></span></span></div><div class="t m5 xb4 h27 y162 ff2b fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 x5b h4d y163 ff2c fs24 fc3 sc0 lsae ws82">xy<span class="blank"> </span><span class="ff2d fs1b lsa9 ws7f v1">(\u2206<span class="blank"> </span><span class="ff2c ls8d">A<span class="ff2d ls8e ws9e"> sen <span class="blank _3"></span><span class="ff2c ls8f">\u03b8<span class="ff2d lsaa ws9f">) c<span class="blank _8"> </span>o<span class="blank _e"> </span>s<span class="blank _8"> </span> </span><span class="ls94">\u03b8<span class="ff2d lsaf">=0</span></span></span></span></span></span></div><div class="t m0 x2c h1d y6f ff2f fs17 fc7 sc1 lsb ws8"><span class="fc7 sc0">Cap.14_Beer.indd 576</span><span class="blank _15"></span><span class="fc3 sc0"><span class="fc7 sc0">Cap.14_Beer.indd 576</span><span class="blank _16"> </span><span class="fc7 sc1"><span class="fc7 sc0">03/12/2012 19:14:53</span><span class="blank _11"></span><span class="fc3 sc0"><span class="fc7 sc0">03/12/2012 19:14:53</span></span></span></span></div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,-23.513400,-23.513400]}"></div></div> <div id="pf6" class="pf w2 h1a" data-page-no="6"><div class="pc pc6 w2 h1a"><img fetchpriority="low" loading="lazy" class="bi x86 y164 w4 h4e" alt="" src="https://files.passeidireto.com/5502e1cb-a069-41c0-937b-d1f856940370/bg6.png"><div class="t m0 x87 h1f ye1 ff30 fs13 fc8 sc0 lsb">577</div><div class="t m0 x77 h3b ye2 ff31 fs2 fc3 sc0 lsb ws8">Capítulo 14 <span class="blank _a"> </span><span class="ff32 fs21 ws4b">\u426c</span> <span class="blank _a"> </span>T<span class="blank _4"></span>ransformações de tensão</div><div class="t m0 x80 h4c y165 ff33 fs1b fc3 sc0 ls108 ws8"> \u03a3<span class="blank _1c"> </span><span class="ff34 lsb0">F<span class="fs24 lsb1 v8">y<span class="ff33 lsb2">\u2032</span></span></span><span class="lsa8 wsa1">=0<span class="blank _1b"></span>:</span></div><div class="t m5 xbc h27 y166 ff35 fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 xbd h4f y167 ff34 fs24 fc3 sc0 ls83">x<span class="ff33 lsb3">\u2032</span><span class="lsb1">y<span class="ff33 lsb4">\u2032<span class="fs1b ls109 ws8 v1"> \u2206<span class="blank _e"> </span><span class="ff34 lsb5">A<span class="ff33 lsb6">+</span><span class="lsb7">\u03c3</span></span></span></span><span class="ls8c">x<span class="ff33 fs1b lsaa wsa2 v1">(\u2206<span class="blank"> </span><span class="ff34 ls8d">A<span class="ff33 lsb8 wsb3"> cos </span><span class="ls8f">\u03b8</span></span><span class="ws9f">) s<span class="blank _8"> </span>e<span class="blank _e"> </span>n<span class="blank _e"> </span> <span class="blank _3"></span><span class="ff34 ls94">\u03b8<span class="ff33 lsb">\u2013</span></span></span></span></span></span></div><div class="t m5 x97 h27 y166 ff35 fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 xbe h4f y167 ff34 fs24 fc3 sc0 ls10a wsa3">xy<span class="blank"> </span><span class="ff33 fs1b lsaa wsa2 v1">(\u2206<span class="blank"> </span><span class="ff34 ls8d">A<span class="ff33 ls8e ws9e"> cos </span><span class="ls8f">\u03b8</span></span><span class="ws9f">) c<span class="blank _8"> </span>o<span class="blank _8"> </span>s<span class="blank _e"> </span> </span></span></div><div class="c x80 y168 w6 h50"><div class="t m0 x8d h4b y169 ff34 fs1b fc3 sc0 lsb">\u03b8</div></div><div class="t m0 x26 h51 y16a ff33 fs1b fc3 sc0 lsb9">\u2013<span class="ff34 lsba">\u03c3<span class="fs24 lsbb v8">y</span></span><span class="lsad ws81 v0">(\u2206<span class="blank"> </span><span class="ff34 ls8d">A</span><span class="ls8e ws9e"> sen <span class="blank _3"></span><span class="ff34 ls8f">\u03b8<span class="ff33 lsaa ws9f">) c<span class="blank _8"> </span>o<span class="blank _e"> </span>s<span class="blank _8"> </span> </span><span class="ls94">\u03b8<span class="ff33 lsb">+</span></span></span></span></span></div><div class="t m5 x58 h27 y16b ff35 fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 xbf h4f y16c ff34 fs24 fc3 sc0 ls10a wsa3">xy<span class="blank"> </span><span class="ff33 fs1b ls10b wsa4 v1">(\u2206<span class="blank"> </span><span class="ff34 ls8d">A<span class="ff33 ls8e ws9e"> sen <span class="blank _3"></span><span class="ff34 ls8f">\u03b8<span class="ff33 lsaa ws9f">) s<span class="blank _8"> </span>e<span class="blank _e"> </span>n<span class="blank _8"> </span> <span class="blank _3"></span><span class="ff34 lsbc">\u03b8<span class="ff33 ls10c">=0</span></span></span></span></span></span></span></div><div class="t m0 x86 h33 y16d ff36 fs1b fc3 sc0 ls5c ws6c">Resol<span class="blank _0"></span>vendo a pri<span class="blank _8"> </span>meir<span class="blank _8"> </span>a equa<span class="blank _8"> </span>ção pa<span class="blank _8"> </span>ra <span class="ff37 lsbd">\u03c3<span class="ff38 fs1c ls61 ws77 v4">x'</span></span><span class="ls1d wsb4"> e a seg<span class="blank _8"> </span>u<span class="blank _8"> </span>nda pa<span class="blank _8"> </span>ra </span></div><div class="t m5 x6e h27 y16d ff35 fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 xac h29 y16e ff38 fs1c fc3 sc0 ls61 wsa5">x'y<span class="blank"> </span>'<span class="blank"> </span><span class="ff36 fs1b ls2d wsb5 v5">, t<span class="blank _8"> </span>emos</span></div><div class="t m0 x86 h52 y16f ff36 fs1b fc3 sc0 lsbe ws8"> <span class="ff34 lsbf vd">\u03c3<span class="fs24 ls83 v8">x<span class="ff33 lsc0">\u2032<span class="fs1b lsc1 v1">=<span class="ff34 lsc2">\u03c3</span></span><span class="ff34 lsb wsa6">x</span><span class="fs1b ls10d wsb6 v1"> cos</span></span></span></span></div><div class="t m0 x93 h53 y170 ff33 fs24 fc3 sc0 lsc3">2<span class="fs1b lsc4 ws8 ve"> <span class="ff34 ls94">\u03b8<span class="ff33 lsc5">+</span><span class="lsc6">\u03c3<span class="fs24 lsc7 v8">y</span><span class="ff33 ls10e wsb7"> sen</span></span></span></span></div><div class="t m0 xc0 h53 y170 ff33 fs24 fc3 sc0 lsc3">2<span class="fs1b lsc4 ws8 ve"> <span class="ff34 ls94">\u03b8<span class="ff33 ls10f">+2</span></span></span></div><div class="t m5 x92 h27 y171 ff35 fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 x57 h54 y172 ff34 fs24 fc3 sc0 lsae wsa7">xy<span class="blank"> </span><span class="ff33 fs1b ls8e ws9e v1"> sen <span class="blank _3"></span><span class="ff34 ls7d">\u03b8<span class="ff33 lsb8 wsb3"> cos </span>\u03b8<span class="ff33 lsb ws8"> <span class="ff36 lsc8 vf"> </span><span class="ff36 va">(14.1)</span></span></span></span></div><div class="t m0 x86 h24 y173 ff36 fs1b fc3 sc0 lsb ws8"> </div><div class="t m5 xc1 h27 y174 ff35 fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 xc2 h4f y175 ff34 fs24 fc3 sc0 ls83">x<span class="ff33 lsb3">\u2032</span><span class="lsb1">y<span class="ff33 lsc9">\u2032<span class="fs1b ls110 wsa8 v1">=\u2013<span class="blank _6"></span>(<span class="blank _1d"></span><span class="ff34 lsca">\u03c3<span class="fs24 lscb v8">x</span><span class="ff33 lscc">\u2013</span><span class="lscd">\u03c3<span class="fs24 lsce v8">y</span><span class="ff33 lsaa ws9f">) s<span class="blank _8"> </span>e<span class="blank _e"> </span>n<span class="blank _8"> </span> <span class="blank _3"></span><span class="ff34 ls7d">\u03b8<span class="ff33 ls8e ws9e"> cos </span><span class="ls90">\u03b8<span class="ff33 lsb">+</span></span></span></span></span></span></span></span></span></div><div class="t m5 xc3 h27 y174 ff35 fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 xbb h55 y175 ff34 fs24 fc3 sc0 ls111 wsa9">xy<span class="blank"> </span><span class="ff33 fs1b lsaa wsaa v1">(c<span class="blank"> </span>o<span class="blank"> </span>s<span class="blank"> </span></span><span class="ff33 lsc3 v10">2<span class="fs1b lsc4 ws8 ve"> <span class="ff34 ls94">\u03b8<span class="ff33 lscc wsab">\u2013s<span class="blank _1e"></span>e<span class="blank _1e"></span>n</span></span></span></span></div><div class="t m0 x3a h53 y176 ff33 fs24 fc3 sc0 lsc3">2<span class="fs1b lsc4 ws8 ve"> <span class="ff34 ls8f">\u03b8<span class="ff33 lsaa">) <span class="blank _8"> </span><span class="ff36 lscf vf"> <span class="lsb v11">(14.2)</span></span></span></span></span></div><div class="t m0 x86 h24 y177 ff36 fs1b fc3 sc0 ls40 ws99">Usando as relaçõe<span class="blank _8"> </span>s tr<span class="blank _8"> </span>igonométr<span class="blank _8"> </span>icas</div><div class="t m0 x86 h56 y178 ff36 fs1b fc3 sc0 lsd0 ws8"> <span class="ff33 ls8e ws9e v2">sen 2<span class="blank _8"> </span><span class="ff34 ls90">\u03b8<span class="ff33 ls112 wsb8">=2<span class="blank _1f"></span> s<span class="blank _1f"></span>e<span class="blank _1f"></span>n<span class="blank _1f"></span> <span class="blank _3"></span><span class="ff34 ls7d">\u03b8<span class="ff33 lsb8 wsb9"> cos </span><span class="lsd1">\u03b8<span class="ff33 ls8e ws9e">cos 2<span class="blank _0"></span><span class="ff34 ls90">\u03b8<span class="ff33 lsd2 wsac">=<span class="blank"> </span>cos</span></span></span></span></span></span></span></span></div><div class="t m0 x9b h53 y179 ff33 fs24 fc3 sc0 lsc3">2<span class="fs1b lsc4 ws8 ve"> <span class="ff34 ls90">\u03b8<span class="ff33 ls113 wsad">\u2013s<span class="blank _1d"></span>e<span class="blank _1f"></span>n</span></span></span></div><div class="t m0 x3b h57 y179 ff33 fs24 fc3 sc0 lsc3">2<span class="fs1b lsc4 ws8 ve"> <span class="ff34 ls7d">\u03b8<span class="ff33 lsd3"> <span class="ff36 lsd4 v6"> <span class="lsb v11">(14.3)</span></span></span></span></span></div><div class="t m0 x86 h24 y17a ff36 fs1b fc3 sc0 lsb">e</div><div class="t m0 x86 h58 y17b ff36 fs1b fc3 sc0 lsd5 ws8"> <span class="ff33 lsd2 v12">cos</span></div><div class="t m0 xc4 h59 y17c ff33 fs24 fc3 sc0 lsd6">2<span class="fs1b lsc4 ws8 ve"> <span class="ff34 ls94">\u03b8<span class="ff33 lsd7">=<span class="lsd8 wsba vb">1+c<span class="blank _20"></span>o<span class="blank _20"></span>s<span class="blank _20"></span> 2</span></span></span></span></div><div class="t m0 xc5 h4b y17d ff34 fs1b fc3 sc0 lsb">\u03b8</div><div class="t m0 xc6 h5a y17e ff33 fs1b fc3 sc0 lsd9">2<span class="ls114 vb">sen</span></div><div class="t m0 xc7 h59 y17c ff33 fs24 fc3 sc0 lsc3">2<span class="fs1b lsc4 ws8 ve"> <span class="ff34 ls94">\u03b8<span class="ff33 lsda">=<span class="ls115 wsbb vb">1\u2013<span class="blank _a"> </span>c<span class="blank _20"></span>o<span class="blank _20"></span>s<span class="blank _21"></span> 2</span></span></span></span></div><div class="t m0 xac h4b y17d ff34 fs1b fc3 sc0 lsb">\u03b8</div><div class="t m0 xb0 h4c y17e ff33 fs1b fc3 sc0 ls116 ws8">2 </div><div class="t m0 x53 h5b y17f ff36 fs1b fc3 sc0 lsdb ws8"> <span class="lsb v13">(14.4)</span></div><div class="t m0 x86 h24 y180 ff36 fs1b fc3 sc0 ls117 ws5a">esc<span class="blank _8"> </span>revemos a Eq. (<span class="blank _3"></span>1<span class="blank _3"></span>4.<span class="blank _3"></span>1<span class="blank _3"></span>) da seg<span class="blank _8"> </span>ui<span class="blank _8"> </span>nte m<span class="blank _8"> </span>anei<span class="blank _8"> </span>ra:</div><div class="t m0 xc2 h5a y181 ff33 fs1b fc3 sc0 lsb ws8"> <span class="blank _5"></span><span class="ff34 lsdc">\u03c3<span class="fs24 ls83 v8">x<span class="ff33 lsdd">\u2032</span></span><span class="ff33 lsb6">=</span><span class="lsde">\u03c3<span class="fs24 lsdf v8">x</span><span class="ff33 lse0"> <span class="lsd8 wsba vb">1+c<span class="blank _20"></span>o<span class="blank _20"></span>s<span class="blank _20"></span> 2</span></span></span></span></div><div class="t m0 x7b h4b y182 ff34 fs1b fc3 sc0 lsb">\u03b8</div><div class="t m0 xc8 h5c y183 ff33 fs1b fc3 sc0 lse1">2<span class="lsc1 vb">+<span class="ff34 lse2">\u03c3<span class="fs24 lse3 v8">y</span></span></span><span class="lse4 ws8 vb"> </span><span class="ls118 wsbc v14">1\u2013<span class="blank _e"> </span>c<span class="blank _1f"></span>o<span class="blank _1f"></span>s<span class="blank _1f"></span> 2</span></div><div class="t m0 xc9 h4b y182 ff34 fs1b fc3 sc0 lsb">\u03b8</div><div class="t m0 x91 h5a y183 ff33 fs1b fc3 sc0 lse1">2<span class="lsb vb">+</span></div><div class="t m5 x8e h27 y184 ff35 fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 x9e h49 y185 ff34 fs24 fc3 sc0 ls10a wsae">xy<span class="blank"> </span><span class="ff33 fs1b ls8e ws9e v1"> sen 2<span class="blank _8"> </span><span class="ff34 lsb">\u03b8</span></span></div><div class="t m0 x86 h24 y186 ff36 fs1b fc3 sc0 ls119">ou</div><div class="t m0 x86 h24 y187 ff36 fs1b fc3 sc0 lsb ws8"> </div><div class="t m0 xca h5d y188 ff34 fs1b fc3 sc0 lsbf">\u03c3<span class="fs24 ls83 v8">x<span class="ff33 ls11a ws8">\u2032 <span class="blank _22"> </span></span></span><span class="ff33 lsda">=</span><span class="lse5 v15">\u03c3</span><span class="fs24 lscb v16">x</span><span class="ff33 lsb6 v15">+</span><span class="lsde v15">\u03c3</span><span class="fs24 lsb v16">y</span></div><div class="t m0 x26 h5e y189 ff33 fs1b fc3 sc0 lse6">2<span class="fs24 lse7 ws8 v17"> </span><span class="lsd7 vb">+</span><span class="ff34 lsc2 v18">\u03c3<span class="fs24 lse8 v8">x</span></span><span class="lscc v18">\u2013<span class="ff34 lse9">\u03c3<span class="fs24 lsb v8">y</span></span></span></div><div class="t m0 xcb h5a y189 ff33 fs1b fc3 sc0 lsea">2<span class="ls8e ws9e vb"> cos 2<span class="ff34 ls94">\u03b8<span class="ff33 lsb">+</span></span></span></div><div class="t m5 x97 h27 y18a ff35 fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 xbe h5f y18b ff34 fs24 fc3 sc0 ls10a wsae">xy<span class="blank"> </span><span class="ff33 fs1b lsb8 wsb3 v1"> sen 2<span class="blank _8"> </span><span class="ff34 lsb">\u03b8</span></span></div><div class="t m0 x70 h4c y18c ff33 fs1b fc3 sc0 lseb ws8"> <span class="ff36 lsb v19"> </span></div><div class="t m0 x77 h24 y18d ff36 fs1b fc3 sc0 lsb">(14.5)</div><div class="t m0 x86 h24 y18e ff36 fs1b fc3 sc0 lsb ws8">Usando as relaçõe<span class="blank _8"> </span>s (<span class="blank _3"></span>1<span class="blank _3"></span>4.3<span class="blank _3"></span>), escrevemos a Eq. (<span class="blank _3"></span>1<span class="blank _3"></span>4.2<span class="blank _0"></span>) como</div><div class="t m0 x86 h24 y18f ff36 fs1b fc3 sc0 lsb ws8"> </div><div class="t m5 x82 h27 y190 ff35 fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 xcc h60 y191 ff34 fs24 fc3 sc0 ls83">x<span class="ff33 lsb3">\u2032</span><span class="lsb1">y<span class="ff33 lsec">\u2032<span class="fs1b ls11b wsaf v1">=\u2013<span class="blank"> </span></span></span><span class="lsed v15">x</span><span class="ff33 fs1b lsee v1a">\u2013</span><span class="lsb v15">y</span></span></div><div class="t m0 x7a h5a y192 ff33 fs1b fc3 sc0 lsef">2<span class="ls8e ws9e vb"> sen 2<span class="blank _8"> </span><span class="ff34 ls94">\u03b8<span class="ff33 lsb">+</span></span></span></div><div class="t m5 xb2 h27 y190 ff35 fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 x58 h49 y191 ff34 fs24 fc3 sc0 lsae wsa7">xy<span class="blank"> </span><span class="ff33 fs1b ls8e ws9e v1"> cos 2<span class="ff34 lsf0">\u03b8<span class="ff33 lsb ws8 v1b"> </span></span></span></div><div class="t ma x2a h61 y193 ff34 fs26 fc3 sc0 lsf1">\u03c3<span class="lsb v0">\u03c3</span></div><div class="t m0 x6e h24 y194 ff36 fs1b fc3 sc0 lsb ws8"> </div><div class="t m0 x77 h24 y195 ff36 fs1b fc3 sc0 lsb">(14.6)</div><div class="t m0 x86 h62 y196 ff36 fs1b fc3 sc0 lsa6 wsbd">A expressã<span class="blank _8"> </span>o par<span class="blank _8"> </span>a a tens<span class="blank _8"> </span>ão nor<span class="blank _8"> </span>mal <span class="ff37 lsf2">\u03c3<span class="ff38 fs1c ls11c wsb0 v4">y'</span></span><span class="ls11d wsbe v0"> é o<span class="blank _0"></span>b<span class="blank _0"></span>ti<span class="blank _0"></span>da s<span class="blank _0"></span>ub<span class="blank _0"></span>sti<span class="blank _3"></span>t<span class="blank _8"> </span>uin<span class="blank _0"></span>do<span class="blank _0"></span> <span class="ff37 lsb ws76">\u03b8</span><span class="ls11e wsbf"> na Eq<span class="blank _0"></span>. (<span class="blank _3"></span>1<span class="blank _3"></span>4.5) </span></span></div><div class="t m0 x86 h33 y197 ff36 fs1b fc3 sc0 ls11f wsc0">pelo<span class="blank _8"> </span> â<span class="blank _8"> </span>ng<span class="blank _8"> </span>u<span class="blank _8"> </span>lo <span class="ff37 lsb">\u03b8</span><span class="ls120 ws8"> +<span class="blank _2"></span> 9<span class="blank _4"></span>0<span class="blank _4"></span>º<span class="blank _5"></span>,<span class="blank _2"></span> f<span class="blank _5"></span>o<span class="blank _2"></span>r<span class="blank _3"></span>m<span class="blank _2"></span>a<span class="blank _4"></span>d<span class="blank _2"></span>o<span class="blank _2"></span> p<span class="blank _4"></span>e<span class="blank _5"></span>l<span class="blank _4"></span>a<span class="blank _2"></span> a<span class="blank _2"></span>s<span class="blank _4"></span>s<span class="blank _2"></span>o<span class="blank _4"></span>c<span class="blank _2"></span>i<span class="blank _2"></span>a<span class="blank _2"></span>ç<span class="blank _4"></span>ã<span class="blank _2"></span>o<span class="blank _2"></span> d<span class="blank _4"></span>o<span class="blank _2"></span> e<span class="blank _2"></span>i<span class="blank _4"></span>x<span class="blank _5"></span>o<span class="blank _2"></span> <span class="ff38 lsa6 ws7d">y'<span class="blank _8"> </span></span><span class="ls117 wsc1"> com o eixo <span class="ff38 lsb ws25">x</span></span><span class="lsb">. </span></span></div><div class="t m0 x86 h33 y198 ff36 fs1b fc3 sc0 ls28 ws3f">Como cos (<span class="blank _0"></span>2<span class="ff37 lsb">\u03b8</span><span class="ls16 wsc2"> + 1<span class="blank _3"></span>80<span class="blank _8"> </span>º) = \u2013<span class="blank _8"> </span>cos 2<span class="ff37 lsb">\u03b8</span><span class="ls1e ws70"> e sen (2<span class="ff37 lsb">\u03b8<span class="ff36 ws8"> + 1<span class="blank _4"></span>80<span class="blank _8"> </span>º) = \u2013<span class="blank _8"> </span>sen 2<span class="ff37 ws76">\u03b8<span class="blank _3"></span><span class="ff36 ls2d wsb5">, t<span class="blank _8"> </span>emos</span></span></span></span></span></span></div><div class="t m0 x86 h24 y199 ff36 fs1b fc3 sc0 lsb ws8"> </div><div class="t m0 xca h63 y19a ff34 fs1b fc3 sc0 lsf3">\u03c3<span class="fs24 lsf4 v8">y<span class="ff33 lsf5">\u2032<span class="fs1b lsda v1">=</span></span></span><span class="lse5 v15">\u03c3</span><span class="fs24 lsf6 v16">x</span><span class="ff33 lsb6 v15">+</span><span class="lsf7 v15">\u03c3</span><span class="fs24 lsb v16">y</span></div><div class="t m0 xcd h5e y19b ff33 fs1b fc3 sc0 lsf8">2<span class="lsf9 vb">\u2013</span><span class="ff34 lsfa v18">\u03c3<span class="fs24 lsfb v8">x</span></span><span class="ls8a v18">\u2013<span class="ff34 lsc6">\u03c3<span class="fs24 lsb v8">y</span></span></span></div><div class="t m0 x95 h5a y19b ff33 fs1b fc3 sc0 lsea">2<span class="ls8e ws9e vb"> cos 2<span class="ff34 ls90">\u03b8<span class="ff33 lsb">\u2013</span></span></span></div><div class="t m5 x9b h27 y19c ff35 fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 xce h64 y19d ff34 fs24 fc3 sc0 ls111 wsb1">xy<span class="blank"> </span><span class="ff33 fs1b ls8e ws9e v1"> sen 2<span class="blank _8"> </span><span class="ff34 lsb">\u03b8</span></span></div><div class="t m0 x53 h4c y19e ff33 fs1b fc3 sc0 lsfc ws8"> <span class="ff36 lsb v1c"> </span></div><div class="t m0 x77 h24 y19f ff36 fs1b fc3 sc0 lsb">(14.7)</div><div class="t m0 x88 h24 y1a0 ff36 fs1b fc3 sc0 ls37 wsc3">Soma<span class="blank _8"> </span>ndo as Eqs. (<span class="blank _0"></span>1<span class="blank _3"></span>4.5) e (<span class="blank _3"></span>1<span class="blank _3"></span>4.<span class="blank _4"></span>7<span class="blank _8"> </span>) membro a membro, obtemos</div><div class="t m0 x86 h65 y1a1 ff36 fs1b fc3 sc0 lsfd ws8"> <span class="ff34 lsfe vd">\u03c3<span class="fs24 ls83 v8">x<span class="ff33 lsff">\u2032<span class="fs1b lsb6 v1">+</span></span></span><span class="lsde">\u03c3<span class="fs24 lsf4 v8">y<span class="ff33 ls100">\u2032</span></span><span class="ff33 lsb6">=</span>\u03c3<span class="fs24 lsf6 v8">x</span><span class="ff33 lsb6">+</span><span class="ls101">\u03c3<span class="fs24 ls102 v8">y</span><span class="ff33 ls103"> </span></span></span></span><span class="ls104 v0"> <span class="lsb v11">(14.8)</span></span></div><div class="t m0 x86 h62 y1a2 ff36 fs1b fc3 sc0 ls121 ws8">Como <span class="ff37 ls105">\u03c3<span class="ff38 fs1c ls22 v4">z</span></span><span class="lsb wsc4 v0"> = <span class="ff37 ls106">\u03c3<span class="ff38 fs1c ls122 wsb2 v4">z'</span></span><span class="ls50 wsc5"> = 0, v<span class="blank _0"></span>er<span class="blank _8"> </span>if<span class="blank _8"> </span>icamos e<span class="blank _8"> </span>ntão que, no ca<span class="blank _8"> </span>so de est<span class="blank _8"> </span>ado plano de te<span class="blank _8"> </span>n-</span></span></div><div class="t m0 x86 h24 y1a3 ff36 fs1b fc3 sc0 lsb wsc6">são, a soma d<span class="blank _8"> </span>as te<span class="blank _8"> </span>nsõe<span class="blank _8"> </span>s nor<span class="blank _8"> </span>mais que at<span class="blank _8"> </span>u<span class="blank _8"> </span>am no elemento de vol<span class="blank _0"></span>u<span class="blank _8"> </span>me do </div><div class="t m0 x86 h24 y1a4 ff36 fs1b fc3 sc0 ls50 ws9d">mate<span class="blank _8"> </span>rial é i<span class="blank _8"> </span>ndepe<span class="blank _8"> </span>ndente d<span class="blank _8"> </span>a or<span class="blank _8"> </span>ientaçã<span class="blank _8"> </span>o desse elemento<span class="blank _0"></span>.</div><div class="t m0 x86 h23 y1a5 ff30 fs1a fc8 sc0 lsb ws8">14.3 <span class="blank _13"> </span>T<span class="blank _4"></span>ensões principais e tensão de cisalhamento </div><div class="t m0 xf h23 y1a6 ff30 fs1a fc8 sc0 lsb">máxima</div><div class="t m0 x86 h24 y1a7 ff36 fs1b fc3 sc0 ls1e wsc7">As Eqs. (<span class="blank _0"></span>1<span class="blank _3"></span>4.5) e (<span class="blank _4"></span>1<span class="blank _3"></span>4.6) obtidas n<span class="blank _8"> </span>a seção a<span class="blank _8"> </span>nter<span class="blank _8"> </span>ior são as e<span class="blank _8"> </span>qua<span class="blank _8"> </span>ções pa<span class="blank _8"> </span>ra<span class="blank _8"> </span>mé-</div><div class="t m0 x86 h24 y1a8 ff36 fs1b fc3 sc0 ls50 wsc8">t<span class="blank _8"> </span>r<span class="blank _8"> </span>icas de um<span class="blank _8"> </span>a circu<span class="blank _8"> </span>n<span class="blank _8"> </span>ferência. Isso sign<span class="blank _8"> </span>if<span class="blank _8"> </span>ica que, se escolhe<span class="blank _8"> </span>r<span class="blank _8"> </span>mos u<span class="blank _8"> </span>m siste-</div><div class="t m0 x86 h26 y1a9 ff36 fs1b fc3 sc0 ls40 wsc9">ma de ei<span class="blank _8"> </span>x<span class="blank _0"></span>os car<span class="blank _e"> </span>tesia<span class="blank _8"> </span>nos or<span class="blank _8"> </span>togonais e represe<span class="blank _8"> </span>nta<span class="blank _8"> </span>r<span class="blank _8"> </span>mos u<span class="blank _8"> </span>m ponto <span class="ff38 lsb">M</span><span class="ls63 wsca"> de abs-</span></div><div class="t m0 x86 h33 y1aa ff36 fs1b fc3 sc0 ls16 ws8">cissa <span class="blank _0"></span><span class="ff37 ls107">\u03c3<span class="ff38 fs1c ls61 ws77 v4">x'</span><span class="ff36 ls16 wscb v0"> e ordena<span class="blank _8"> </span>da </span></span></div><div class="t m5 xcf h27 y1ab ff35 fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 xd0 h66 y1ac ff38 fs1c fc3 sc0 ls61 ws4e">x'y<span class="blank"> </span>'<span class="blank"> </span><span class="ff36 fs1b ls123 ws8 v5"> p<span class="blank _e"> </span>a<span class="blank _e"> </span>r<span class="blank _e"> </span>a<span class="blank _e"> </span> u<span class="blank _e"> </span>m<span class="blank _e"> </span> d<span class="blank _e"> </span>a<span class="blank _e"> </span>d<span class="blank _e"> </span>o<span class="blank _8"> </span> v<span class="blank _e"> </span>a<span class="blank _8"> </span>l<span class="blank _e"> </span>o<span class="blank _8"> </span>r<span class="blank _e"> </span> d<span class="blank _8"> </span>o<span class="blank _e"> </span> p<span class="blank _8"> </span>a<span class="blank _1a"> </span>r<span class="blank _e"> </span>â<span class="blank _e"> </span>m<span class="blank _8"> </span>e<span class="blank _e"> </span>t<span class="blank _1a"> </span>r<span class="blank _8"> </span>o<span class="blank _e"> </span> <span class="ff37 lsb ws76">\u03b8<span class="blank _3"></span><span class="ff36 ls5c wscc">, t<span class="blank _8"> </span>odos os pontos </span></span></span></div><div class="t m0 x2c h1d y6f ff39 fs17 fc7 sc1 lsb ws8"><span class="fc7 sc0">Cap.14_Beer.indd 577</span><span class="blank _15"></span><span class="fc3 sc0"><span class="fc7 sc0">Cap.14_Beer.indd 577</span><span class="blank _16"> </span><span class="fc7 sc1"><span class="fc7 sc0">03/12/2012 19:14:53</span><span class="blank _11"></span><span class="fc3 sc0"><span class="fc7 sc0">03/12/2012 19:14:53</span></span></span></span></div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,-23.513400,-23.513400]}"></div></div> <div id="pf7" class="pf w2 h1a" data-page-no="7"><div class="pc pc7 w2 h1a"><img fetchpriority="low" loading="lazy" class="bi x2d y1ad w4 h67" alt="" src="https://files.passeidireto.com/5502e1cb-a069-41c0-937b-d1f856940370/bg7.png"><div class="t m0 x2d h1f y71 ff3a fs13 fc8 sc0 lsb ws21">578<span class="blank"> </span><span class="ff3b fs2 fc3 ws8 v3">Estática e mecânica dos materiais</span></div><div class="t m0 x30 h24 ye3 ff3c fs1b fc3 sc0 ls2f wsd7">assim obt<span class="blank _8"> </span>idos per<span class="blank _8"> </span>te<span class="blank _8"> </span>ncerão a u<span class="blank _8"> </span>ma ci<span class="blank _8"> </span>rcu<span class="blank _8"> </span>nferência<span class="blank _8"> </span>. Para est<span class="blank _8"> </span>abelecer<span class="blank _8"> </span>mos es<span class="blank _8"> </span>sa </div><div class="t m0 x30 h33 ye4 ff3c fs1b fc3 sc0 ls2f wsd8">propr<span class="blank _8"> </span>iedade, eli<span class="blank _8"> </span>mi<span class="blank _8"> </span>na<span class="blank _8"> </span>mos <span class="ff3d lsb">\u03b8</span><span class="ls50 wsd9"> da<span class="blank _8"> </span>s Eqs. (<span class="blank _3"></span>1<span class="blank _3"></span>4.5) e (<span class="blank _3"></span>1<span class="blank _3"></span>4.6)<span class="blank _0"></span>; isso é fe<span class="blank _0"></span>ito passa<span class="blank _8"> </span>ndo </span></div><div class="t m0 x30 h68 y1ae ff3c fs1b fc3 sc0 ls50 wsda">pr<span class="blank _8"> </span>imei<span class="blank _8"> </span>ro (<span class="blank _3"></span><span class="ff3d ls124">\u03c3<span class="ff3e fs1c lsb ws24 v4">x</span><span class="ff3c lsb wsdb v0"> + <span class="ff3d ls7a">\u03c3</span><span class="ff3e fs1c v4">y</span></span></span></div><div class="t m0 x6e h24 y1af ff3c fs1b fc3 sc0 ls60 wsdc">)/2 par<span class="blank _8"> </span>a o pr<span class="blank _8"> </span>imei<span class="blank _8"> </span>ro membro d<span class="blank _8"> </span>a Eq. (<span class="blank _3"></span>1<span class="blank _3"></span>4.5) e elevando ao </div><div class="t m0 x30 h24 y1b0 ff3c fs1b fc3 sc0 ls176 ws8">q<span class="blank _4"></span>u<span class="blank _4"></span>a<span class="blank _3"></span>d<span class="blank _3"></span>r<span class="blank _4"></span>a<span class="blank _3"></span>d<span class="blank _4"></span>o<span class="blank _4"></span> a<span class="blank _4"></span>m<span class="blank _4"></span>b<span class="blank _4"></span>o<span class="blank _4"></span>s<span class="blank _4"></span> o<span class="blank _4"></span>s<span class="blank _4"></span> m<span class="blank _4"></span>e<span class="blank _4"></span>m<span class="blank _4"></span>b<span class="blank _4"></span>r<span class="blank _4"></span>o<span class="blank _4"></span>s<span class="blank _4"></span> d<span class="blank _3"></span>a<span class="blank _4"></span> e<span class="blank _4"></span>q<span class="blank _4"></span>u<span class="blank _3"></span>a<span class="blank _4"></span>ç<span class="blank _4"></span>ã<span class="blank _3"></span>o<span class="blank _2"></span>,<span class="blank _4"></span> d<span class="blank _4"></span>e<span class="blank _3"></span>p<span class="blank _4"></span>o<span class="blank _4"></span>i<span class="blank _4"></span>s<span class="blank _4"></span> e<span class="blank _2"></span>l<span class="blank _4"></span>e<span class="blank _4"></span>v<span class="blank _4"></span>a<span class="blank _4"></span>n<span class="blank _4"></span>d<span class="blank _4"></span>o<span class="blank _4"></span> a<span class="blank _3"></span>o<span class="blank _4"></span> q<span class="blank _4"></span>u<span class="blank _4"></span>a<span class="blank _3"></span>d<span class="blank _4"></span>r<span class="blank _3"></span>a<span class="blank _4"></span>d<span class="blank _4"></span>o<span class="blank _4"></span> </div><div class="t m0 x30 h24 y1b1 ff3c fs1b fc3 sc0 lsb wsdd">ambos os me<span class="blank _8"> </span>mbros da E<span class="blank _8"> </span>q. (<span class="blank _3"></span>1<span class="blank _3"></span>4.<span class="blank _0"></span>6), e f<span class="blank _8"> </span>ina<span class="blank _8"> </span>lme<span class="blank _8"> </span>nte somando me<span class="blank _8"> </span>mbro a mem-</div><div class="t m0 x30 h24 y1b2 ff3c fs1b fc3 sc0 ls4d wsde">bro as du<span class="blank _8"> </span>as equ<span class="blank _8"> </span>açõe<span class="blank _8"> </span>s obtidas de<span class="blank _8"> </span>ssa fo<span class="blank _0"></span>r<span class="blank _8"> </span>ma<span class="blank _8"> </span>. T<span class="blank _4"></span>emos</div><div class="t m0 x30 h69 y1b3 ff3c fs1b fc3 sc0 ls125 ws8"> <span class="ff3f ls126 v1d">\u03c3<span class="fs24 ls83 v8">x<span class="ff40 lsc0">\u2032<span class="fs1b lsf9 v1">\u2013</span></span></span><span class="ls127 v15">\u03c3<span class="fs24 ls128 v8">x</span></span></span><span class="ff40 lsc5 v1e">+<span class="ff3f ls129">\u03c3<span class="fs24 lsb v8">y</span></span></span></div><div class="t m0 x72 h4c y1b4 ff40 fs1b fc3 sc0 lsb">2</div><div class="t m0 xd1 h53 y1b5 ff40 fs24 fc3 sc0 lsb">2</div><div class="t m0 x3c h4c y1b6 ff40 fs1b fc3 sc0 lsb">+</div><div class="t m5 x54 h27 y1b7 ff41 fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 x3e h53 y1b8 ff3f fs24 fc3 sc0 ls83">x<span class="ff40 lsb3">\u2032</span><span class="lsb1">y<span class="ff40 lsb">\u2032</span></span></div><div class="t m0 x3e h6a y1b9 ff40 fs24 fc3 sc0 ls12a">2<span class="fs1b ls12b ve">=<span class="ff3f ls12c v15">\u03c3</span></span><span class="ff3f ls12d v2">x</span><span class="fs1b lscc v11">\u2013<span class="ff3f ls12e">\u03c3<span class="fs24 lsb v8">y</span></span></span></div><div class="t m0 xd2 h4c y1b4 ff40 fs1b fc3 sc0 lsb">2</div><div class="t m0 xd3 h53 y1b5 ff40 fs24 fc3 sc0 lsb">2</div><div class="t m0 xd4 h4c y1b6 ff40 fs1b fc3 sc0 lsb">+</div><div class="t m5 xd5 h27 y1b7 ff41 fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 x60 h6b y1b8 ff3f fs24 fc3 sc0 lsae">xy</div><div class="t m0 x60 h53 y1b9 ff40 fs24 fc3 sc0 lsb">2</div><div class="t m0 x63 h6c y1b4 ff40 fs1b fc3 sc0 lsb ws8"> <span class="ff3c ls12f v1f"> </span><span class="ff3c vb">(14.9)</span></div><div class="t m0 x30 h24 y1ba ff3c fs1b fc3 sc0 ls166 wscd">Defi<span class="blank"> </span>n<span class="blank"> </span>i<span class="blank"> </span>ndo</div><div class="t m0 x30 h24 y1bb ff3c fs1b fc3 sc0 lsb ws8"> </div><div class="t m0 xd6 h5d y1bc ff3f fs1b fc3 sc0 ls130">\u03c3<span class="ff40 fs24 lsae wsce v8">méd<span class="blank"> </span></span><span class="ff40 lsd7">=</span><span class="lsc2 v15">\u03c3</span><span class="fs24 ls131 v16">x</span><span class="ff40 lsb6 v15">+</span><span class="ls132 v15">\u03c3</span><span class="fs24 lsb v16">y</span></div><div class="t m0 x3b h5a y1bd ff40 fs1b fc3 sc0 ls133">2<span class="ls2d wsdf v20"> e <span class="blank _23"> </span></span><span class="ff3f ls134 vb">R</span><span class="ls135 vb">=</span><span class="lsb va">\u221a</span></div><div class="t m0 xb4 h6d y1be ff3f fs1b fc3 sc0 ls136">\u03c3<span class="fs24 lse8 v8">x</span><span class="ff40 ls137 v0">\u2013<span class="ff3f ls138">\u03c3<span class="fs24 lsb v8">y</span></span></span></div><div class="t m0 xb3 h4c y1bd ff40 fs1b fc3 sc0 lsb">2</div><div class="t m0 xd7 h53 y1bf ff40 fs24 fc3 sc0 lsb">2</div><div class="t m0 x61 h4c y1bc ff40 fs1b fc3 sc0 lsb">+</div><div class="t m5 xd8 h27 y1c0 ff41 fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 x4a h6b y1c1 ff3f fs24 fc3 sc0 lsae">xy</div><div class="t m0 x4a h53 y1c2 ff40 fs24 fc3 sc0 lsb">2</div><div class="t m0 x45 h4c y1bd ff40 fs1b fc3 sc0 ls139 ws8"> <span class="ff3c lsb v21"> </span></div><div class="t m0 xd9 h24 y1c3 ff3c fs1b fc3 sc0 lsb">(14.10)</div><div class="t m0 x30 h24 y1c4 ff3c fs1b fc3 sc0 lsb ws8">escr<span class="blank _8"> </span>evemos a i<span class="blank _0"></span>dent<span class="blank _8"> </span>idade (<span class="blank _0"></span>1<span class="blank _3"></span>4.<span class="blank _0"></span>9<span class="blank _3"></span>) na for<span class="blank _8"> </span>ma</div><div class="t m0 x30 h6e y1c5 ff3c fs1b fc3 sc0 ls13a ws8"> <span class="ff40 lsb ws25 vd">(<span class="blank _0"></span><span class="ff3f ls13b">\u03c3<span class="fs24 ls83 v8">x<span class="ff40 ls13c">\u2032</span></span><span class="ff40 ls13d">\u2013</span><span class="ls13e">\u03c3<span class="ff40 fs24 lsae wscf v8">méd</span><span class="ff40 lsb">)</span></span></span></span></div><div class="t m0 x55 h53 y1c6 ff40 fs24 fc3 sc0 ls13f">2<span class="fs1b lsb ve">+</span></div><div class="t m5 xb9 h27 y1c7 ff41 fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 xda h53 y1c8 ff3f fs24 fc3 sc0 ls83">x<span class="ff40 lsb3">\u2032</span><span class="lsf4">y<span class="ff40 lsb">\u2032</span></span></div><div class="t m0 xda h6f y1c9 ff40 fs24 fc3 sc0 ls140">2<span class="fs1b lsb6 ve">=<span class="ff3f ls141">R</span></span><span class="ls142 v0">2<span class="fs1b lsb ws8 ve"> <span class="ff3c ls143 vf"> <span class="lsb ws25 v11">(14.1<span class="blank _0"></span>1)</span></span></span></span></div><div class="t m0 x30 h70 y1ca ff3c fs1b fc3 sc0 ls31 ws88">que é a equ<span class="blank _8"> </span>ação de u<span class="blank _8"> </span>ma ci<span class="blank _8"> </span>rcu<span class="blank _8"> </span>nferência de r<span class="blank _8"> </span>aio<span class="ff3e fs2 ls144 ws8 v0"> <span class="fs1b lsb">R<span class="ff3c ls177 wse0"> cent<span class="blank _8"> </span>r<span class="blank _8"> </span>a<span class="blank _8"> </span>do no p<span class="blank _8"> </span>onto<span class="blank _8"> </span> </span>C</span></span><span class="v0"> de </span></div><div class="t m0 x30 h33 y1cb ff3c fs1b fc3 sc0 ls145 ws8">abscissa <span class="blank _0"></span><span class="ff3d ls146">\u03c3<span class="ff3c fs1c ls147 wsd0 v4">méd</span></span></div><div class="t m0 xb0 h24 y1cc ff3c fs1b fc3 sc0 ls40 wse1"> e ordena<span class="blank _8"> </span>da 0 (<span class="blank _8"> </span>F<span class="blank _0"></span>ig. 1<span class="blank _4"></span>4.<span class="blank _3"></span>7). P<span class="blank _3"></span>o<span class="blank _8"> </span>de-se obse<span class="blank _8"> </span>r<span class="blank _8"> </span>var que, em v<span class="blank _8"> </span>i<span class="blank _8"> </span>r<span class="blank _8"> </span>t<span class="blank _8"> </span>ude da </div><div class="t m0 x30 h24 y1cd ff3c fs1b fc3 sc0 ls40 ws9a">simet<span class="blank _8"> </span>r<span class="blank _8"> </span>ia da ci<span class="blank _8"> </span>rcu<span class="blank _8"> </span>nferê<span class="blank _8"> </span>ncia em relação ao ei<span class="blank _8"> </span>xo horiz<span class="blank _8"> </span>ontal, o mesmo re<span class="blank _8"> </span>sul-</div><div class="t m0 x30 h71 y1ce ff3c fs1b fc3 sc0 ls5c wse2">ta<span class="blank _8"> </span>do ter<span class="blank _8"> </span>ia sido obtido se, em v<span class="blank _0"></span>ez de repre<span class="blank _8"> </span>senta<span class="blank _8"> </span>r<span class="blank _8"> </span>mos o ponto<span class="ff3e fs2 lsb ws8 v0"> <span class="fs1b ws25">M<span class="ff3c ls148 wse3">, tiv<span class="blank _0"></span>éssemos </span></span></span></div><div class="t m0 x30 h72 y1cf ff3c fs1b fc3 sc0 ls14f wse4">representa<span class="blank _8"> </span>do um ponto<span class="ff3e fs2 ls149 ws8 v0"> <span class="fs1b lsb">N<span class="ff3c ls14a wse5"> de abscissa <span class="ff3d ls18">\u03c3</span></span><span class="fs1c ls61 ws77 v4">x'</span><span class="ff3c ls16 wse6"> e ordena<span class="blank _8"> </span>da \u2013</span></span></span></div><div class="t m5 x44 h27 y1d0 ff41 fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 xd7 h29 y1d1 ff3e fs1c fc3 sc0 ls61 ws4e">x'y<span class="blank"> </span>'<span class="blank"> </span><span class="ff3c fs1b lsa4 wse7 v5"> (<span class="blank _8"> </span>F<span class="blank _0"></span>ig<span class="blank _0"></span>. 1<span class="blank _3"></span>4.<span class="blank _0"></span>8<span class="blank _0"></span>)<span class="blank _0"></span>. Essa </span></div><div class="t m0 x30 h24 y1d2 ff3c fs1b fc3 sc0 ls40 ws99">propr<span class="blank _8"> </span>ieda<span class="blank _8"> </span>de será u<span class="blank _8"> </span>sad<span class="blank _8"> </span>a na Seçã<span class="blank _8"> </span>o 1<span class="blank _3"></span>4.<span class="blank _0"></span>4.</div><div class="t m0 x64 h73 y1d3 ff3c fs1b fc3 sc0 ls178 wse8">Os do<span class="blank _0"></span>is po<span class="blank _0"></span>ntos<span class="ff3e fs2 ls14b ws8 v0"> <span class="fs1b ls14c">A<span class="ff3c ls179"> e<span class="blank _3"></span><span class="ff3e"> B<span class="ff3c ls17a ws48"> e<span class="blank _0"></span>m<span class="blank _0"></span> q<span class="blank _0"></span>u<span class="blank _0"></span>e a<span class="blank _3"></span> cir<span class="blank _3"></span>cunf<span class="blank _3"></span>er<span class="blank _0"></span>ên<span class="blank _3"></span>ci<span class="blank _3"></span>a da<span class="blank _3"></span> F<span class="blank _0"></span>i<span class="blank _3"></span>g.<span class="blank _3"></span> 1<span class="blank _4"></span>4<span class="blank _0"></span>.<span class="blank _4"></span>7 in<span class="blank _3"></span>te<span class="blank _0"></span>rc<span class="blank _3"></span>ep<span class="blank _0"></span>ta<span class="blank _0"></span> </span></span></span></span></span></div><div class="t m0 x30 h26 y1d4 ff3c fs1b fc3 sc0 ls14d wse9">o eixo hori<span class="blank _8"> </span>zontal sã<span class="blank _8"> </span>o de espe<span class="blank _8"> </span>cial inte<span class="blank _8"> </span>resse<span class="blank _0"></span>: o ponto <span class="ff3e ls14c">A</span><span class="ls17b ws3a"> cor<span class="blank _8"> </span>respond<span class="blank _0"></span>e ao va<span class="blank _0"></span>-</span></div><div class="t m0 x30 h33 y1d5 ff3c fs1b fc3 sc0 ls17c ws8">l<span class="blank _3"></span>o<span class="blank _3"></span>r<span class="blank _3"></span> m<span class="blank _3"></span>á<span class="blank _0"></span>x<span class="blank _3"></span>i<span class="blank _0"></span>m<span class="blank _3"></span>o<span class="blank _3"></span> d<span class="blank _0"></span>a<span class="blank _3"></span> t<span class="blank _3"></span>e<span class="blank _0"></span>n<span class="blank _3"></span>s<span class="blank _3"></span>ã<span class="blank _0"></span>o<span class="blank _3"></span> n<span class="blank _3"></span>o<span class="blank _3"></span>r<span class="blank _0"></span>m<span class="blank _3"></span>a<span class="blank _0"></span>l<span class="blank _3"></span> <span class="ff3d ls14e">\u03c3<span class="ff3e fs1c ls17d wsd1 v4">x'</span></span><span class="ls161 wsea v0"> enqua<span class="blank _8"> </span>nto o ponto <span class="ff3e ls14c">B</span><span class="ls14f wseb"> cor<span class="blank _8"> </span>r<span class="blank _8"> </span>esponde a seu </span></span></div><div class="t m0 x30 h24 y1d6 ff3c fs1b fc3 sc0 ls17e wsec">valor mí<span class="blank _8"> </span>ni<span class="blank _8"> </span>mo. Além disso, ambo<span class="blank _8"> </span>s os pontos cor<span class="blank _8"> </span>re<span class="blank _8"> </span>spondem a u<span class="blank _8"> </span>m valor </div><div class="t m0 x30 h24 y1d7 ff3c fs1b fc3 sc0 ls17f ws8">ze<span class="blank _0"></span>r<span class="blank _0"></span>o<span class="blank _0"></span> da<span class="blank _0"></span> t<span class="blank _0"></span>en<span class="blank _0"></span>sã<span class="blank _0"></span>o<span class="blank _0"></span> d<span class="blank _0"></span>e<span class="blank _0"></span> c<span class="blank _0"></span>is<span class="blank _3"></span>alh<span class="blank _0"></span>am<span class="blank _3"></span>en<span class="blank _0"></span>to<span class="blank _3"></span> </div><div class="t m5 x54 h27 y1d8 ff41 fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 x31 h66 y1d9 ff3e fs1c fc3 sc0 ls17d wsd2">x'y<span class="blank"> </span>'<span class="ff3c fs1b ls15c wsed v5">. A<span class="blank _8"> </span>ssim, os valores</span><span class="fs2 ls150 ws8 v5"> <span class="ff3d fs1b ls151">\u03b8</span></span><span class="ls152">p<span class="ff3c fs1b ls153 wsee v5"> do par<span class="blank _8"> </span>âmet<span class="blank _8"> </span>ro <span class="ff3d lsb">\u03b8<span class="ff3c ws8"> </span></span></span></span></div><div class="t m0 x30 h26 y1da ff3c fs1b fc3 sc0 ls154 ws46">que cor<span class="blank _8"> </span>res<span class="blank _8"> </span>pondem aos p<span class="blank _8"> </span>ontos <span class="ff3e ls14c">A<span class="ff3c ws5f"> e </span><span class="ls121">B</span></span> podem se<span class="blank _8"> </span>r obtidos faze<span class="blank _8"> </span>ndo-<span class="blank _8"> </span>se </div><div class="t m5 xdb h27 y1db ff41 fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 x87 h29 y1dc ff3e fs1c fc3 sc0 ls17d wsd2">x'y<span class="blank"> </span>'<span class="blank"> </span><span class="ff3c fs1b ls180 wsef v5"> = 0 </span></div><div class="t m0 x30 h24 y1dd ff3c fs1b fc3 sc0 ls181 ws68">na Eq. (<span class="blank _3"></span>1<span class="blank _3"></span>4.6)<span class="blank _0"></span>. Escrevemos</div><div class="t m0 xdc h74 y1de ff3c fs1c fc3 sc0 lsb">*</div><div class="t m0 x30 h24 y1df ff3c fs1b fc3 sc0 lsb ws8"> </div><div class="t m0 xdd h75 y1e0 ff40 fs1b fc3 sc0 ls182 wsf0">tg 2<span class="ff3f ls155">\u03b8<span class="fs24 ls156 v8">p</span></span><span class="ls157 v0">=<span class="lsb v15">2</span></span></div><div class="t m5 xa3 h27 y1e1 ff41 fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 xde h6b y1e2 ff3f fs24 fc3 sc0 lsb wsa6">xy</div><div class="t m0 xdf h4c y1e3 ff3f fs1b fc3 sc0 lsfe">\u03c3<span class="fs24 ls158 v8">x</span><span class="ff40 lscc">\u2013</span><span class="ls159">\u03c3<span class="fs24 ls15a v8">y</span><span class="ff40 ls15b ws8 v22"> </span><span class="ff3c lsb ws8 v23"> </span></span></div><div class="t m0 xd9 h24 y1e4 ff3c fs1b fc3 sc0 lsb">(14.12)</div><div class="t m0 x30 h33 y1e5 ff3c fs1b fc3 sc0 ls15c wsf1">Essa equ<span class="blank _8"> </span>ação def<span class="blank _8"> </span>i<span class="blank _8"> </span>ne dois v<span class="blank _0"></span>alores de 2<span class="ff3d ls15d">\u03b8<span class="ff3e fs1c ls152 v4">p</span></span><span class="ls15e wsf2 v0"> que est<span class="blank _8"> </span>ão defasados e<span class="blank _8"> </span>m 1<span class="blank _3"></span>80º e, </span></div><div class="t m0 x30 h33 y1e6 ff3c fs1b fc3 sc0 ls15f wsf3">por<span class="blank _8"> </span>t<span class="blank _8"> </span>anto, dois valo<span class="blank _0"></span>res de <span class="ff3d ls160">\u03b8<span class="ff3e fs1c ls152 v4">p</span></span><span class="ls15c wsf4 v0"> que est<span class="blank _8"> </span>ão defasa<span class="blank _8"> </span>dos em 90<span class="blank _8"> </span>º<span class="blank _3"></span>. Q<span class="blank _8"> </span>ualquer u<span class="blank _8"> </span>m </span></div><div class="t m0 x30 h24 y1e7 ff3c fs1b fc3 sc0 ls181 wsf5">desses valores pode se<span class="blank _8"> </span>r uti<span class="blank _8"> </span>liz<span class="blank _8"> </span>ado pa<span class="blank _8"> </span>ra dete<span class="blank _8"> </span>r<span class="blank _8"> </span>mi<span class="blank _8"> </span>na<span class="blank _8"> </span>r a or<span class="blank _8"> </span>ientaçã<span class="blank _8"> </span>o do el<span class="blank _0"></span>emen-</div><div class="t m0 x30 h24 y1e8 ff3c fs1b fc3 sc0 ls183 wsb4">to<span class="blank _8"> </span> c<span class="blank _8"> </span>or<span class="blank _e"> </span>re<span class="blank _8"> </span>s<span class="blank _8"> </span>po<span class="blank _8"> </span>nd<span class="blank _8"> </span>en<span class="blank _8"> </span>te<span class="blank _8"> </span> (<span class="blank _8"> </span>Fig. 1<span class="blank _3"></span>4.9<span class="blank _0"></span>). O<span class="blank _8"> </span>s pl<span class="blank _8"> </span>an<span class="blank _8"> </span>os<span class="blank _8"> </span> qu<span class="blank _8"> </span>e c<span class="blank _8"> </span>ont<span class="blank _8"> </span>ê<span class="blank _8"> </span>m a<span class="blank _8"> </span>s<span class="blank _8"> </span> fa<span class="blank _8"> </span>ce<span class="blank _8"> </span>s d<span class="blank _8"> </span>o ele<span class="blank _8"> </span>me<span class="blank _8"> </span>nt<span class="blank _8"> </span>o </div><div class="t m0 x30 h26 y1e9 ff3c fs1b fc3 sc0 ls161 wsf6">obtido dessa manei<span class="blank _8"> </span>r<span class="blank _8"> </span>a são chama<span class="blank _8"> </span>dos de<span class="ff3e ls184 ws8"> p<span class="blank _2"></span>l<span class="blank _4"></span>a<span class="blank _2"></span>n<span class="blank _4"></span>o<span class="blank _4"></span>s<span class="blank _2"></span> p<span class="blank _4"></span>r<span class="blank _4"></span>i<span class="blank _4"></span>n<span class="blank _2"></span>c<span class="blank _4"></span>i<span class="blank _2"></span>p<span class="blank _4"></span>a<span class="blank _4"></span>i<span class="blank _4"></span>s<span class="blank _2"></span> d<span class="blank _4"></span>e<span class="blank _2"></span> t<span class="blank _4"></span>e<span class="blank _2"></span>n<span class="blank _4"></span>s<span class="blank _4"></span>ã<span class="blank _4"></span>o<span class="blank _2"></span><span class="ff3c ls2f wsf7"> no </span></span></div><div class="t m0 x30 h33 y1ea ff3c fs1b fc3 sc0 ls185 wsd3">pon<span class="blank _0"></span>to<span class="ff3e ls186 ws8"> Q</span><span class="ls153 wsf8">, e os valores cor<span class="blank _8"> </span>responde<span class="blank _8"> </span>ntes <span class="ff3d ls162">\u03c3</span><span class="fs1c ls163 wsd4 v4">máx</span></span></div><div class="t m0 xe0 h33 y1eb ff3c fs1b fc3 sc0 ls14c wsf9"> e <span class="ff3d ls164">\u03c3</span><span class="fs1c ls187 v4">mín</span></div><div class="t m0 xe1 h24 y1eb ff3c fs1b fc3 sc0 ls165 wse3"> da<span class="blank _8"> </span>s te<span class="blank _8"> </span>nsõe<span class="blank _8"> </span>s nor<span class="blank _8"> </span>mais que </div><div class="t m0 x30 h26 y1ec ff3c fs1b fc3 sc0 ls166 wsfa">at<span class="blank _8"> </span>ua<span class="blank _8"> </span>m nesses planos sã<span class="blank _8"> </span>o chama<span class="blank _8"> </span>dos de<span class="ff3e ls188 wsfb"> ten<span class="blank _8"> </span>sões pr<span class="blank _8"> </span>incipai<span class="blank _8"> </span>s</span><span class="ls167 wsfc"> em<span class="ff3e ls189 wsfd"> Q.</span><span class="ls168 wsfe"> Como os<span class="blank _0"></span> </span></span></div><div class="t m0 x30 h33 y1ed ff3c fs1b fc3 sc0 ls18a wsff">dois val<span class="blank _0"></span>ores<span class="ff3e lsb ws8"> <span class="blank _0"></span><span class="ff3d ls169">\u03b8<span class="ff3e fs1c ls16a v4">p</span><span class="ff3c ls18b ws100 v0"> def<span class="blank _8"> </span>in<span class="blank _8"> </span>idos pela Eq. (<span class="blank _3"></span>1<span class="blank _3"></span>4.<span class="blank _3"></span>1<span class="blank _0"></span>2<span class="blank _0"></span>) f<span class="blank _0"></span>ora<span class="blank _8"> </span>m obtidos faze<span class="blank _8"> </span>ndo </span></span></span></div><div class="t m5 x46 h27 y1ee ff41 fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 x67 h29 y1ef ff3e fs1c fc3 sc0 ls17d wsd2">x'y<span class="blank"> </span>'<span class="blank"> </span><span class="ff3c fs1b ls14c ws101 v5"> = 0 na </span></div><div class="t m0 x30 h24 y1f0 ff3c fs1b fc3 sc0 ls154 ws89">Eq. (<span class="blank _3"></span>1<span class="blank _3"></span>4.6)<span class="blank _0"></span>, est<span class="blank _8"> </span>á claro que nen<span class="blank _8"> </span>hu<span class="blank _8"> </span>ma ten<span class="blank _8"> </span>são de cisal<span class="blank _8"> </span>ha<span class="blank _8"> </span>mento at<span class="blank _8"> </span>ua nos pla-</div><div class="t m0 x30 h24 y1f1 ff3c fs1b fc3 sc0 ls18c ws102">nos pr<span class="blank _8"> </span>i<span class="blank _8"> </span>ncipais.</div><div class="t m0 x64 h24 y1f2 ff3c fs1b fc3 sc0 ls40 ws99">Obser<span class="blank _8"> </span>va<span class="blank _8"> </span>mos da Fi<span class="blank _0"></span>g. 1<span class="blank _4"></span>4.<span class="blank _3"></span>7 que</div><div class="t m0 x30 h76 y1f3 ff3c fs1b fc3 sc0 ls16b ws8"> <span class="ff3f lsfe v24">\u03c3</span><span class="ff40 fs24 lsb v5">m</span></div><div class="c xbe y1f4 w7 h77"><div class="t m0 xe2 h53 y1f5 ff40 fs24 fc3 sc0 lsb">á</div></div><div class="t m0 xe3 h78 y1f6 ff40 fs24 fc3 sc0 ls16c">x<span class="fs1b lsc1 v1">=<span class="ff3f lsc2">\u03c3</span></span><span class="lsb">m</span></div><div class="c xbe y1f4 w7 h77"><div class="t m0 xe4 h53 y1f5 ff40 fs24 fc3 sc0 ls10a">éd</div></div><div class="t m0 xa9 h4c y1f7 ff40 fs1b fc3 sc0 lsc5">+<span class="ff3f ls16d">R</span><span class="ls16e">e<span class="ff3f ls16f">\u03c3</span><span class="fs24 ls18d wsd5 v8">mí<span class="blank _3"></span>n<span class="blank"> </span><span class="fs1b lsc1 v1">=<span class="ff3f ls12c">\u03c3</span></span><span class="lsb">m</span></span></span></div><div class="c xbe y1f4 w7 h77"><div class="t m0 xe5 h53 y1f5 ff40 fs24 fc3 sc0 ls10a">éd</div></div><div class="t m0 x68 h79 y1f7 ff40 fs1b fc3 sc0 lscc">\u2013<span class="ff3f ls8d">R</span><span class="lsb ws8"> <span class="ff3c ls170 ve"> </span><span class="ff3c v25">(14.13)</span></span></div><div class="t m0 x30 h7a y1f8 ff3c fs1f fc3 sc0 lsb ws28">*<span class="fs11 ls18e ws103 v4"> <span class="blank _24"> </span>Essa relação pode também ser obtida quando se deter<span class="blank _8"> </span>min<span class="blank _8"> </span>a que<span class="blank _0"></span> a derivad<span class="blank _8"> </span>a de <span class="ff3d ls171">\u03c3<span class="ff3e fs1f ls18f wsd6 v8">x'</span><span class="ff3c ls190 ws104"> na Eq. (1<span class="blank _3"></span>4.5<span class="blank _8"> </span>) </span></span></span></div><div class="t m0 x91 h7b yce ff3c fs11 fc3 sc0 ls191 ws105">é ig<span class="blank _8"> </span>ua<span class="blank _8"> </span>l a ze<span class="blank _8"> </span>ro:<span class="ff3e lsb ws8"> d<span class="ff3d ls172">\u03c3</span><span class="fs1f ls18f v8">x' </span>/ d<span class="ff3d">\u03b8</span> = </span><span class="ls192">0.</span></div><div class="t mb xe6 h7c y1f9 ff40 fs27 fc9 sc0 lsb">\u03c3</div><div class="t m0 xe7 h7d y1fa ff40 fs28 fc9 sc0 ls193">mín</div><div class="t mb xe8 h7c y1fb ff40 fs27 fc9 sc0 lsb">\u03c3</div><div class="t m0 xe9 h7d y1fc ff40 fs28 fc9 sc0 ls193">mín</div><div class="t mb x88 h7c y1fd ff40 fs27 fc9 sc0 lsb">\u03c3</div><div class="t m0 x81 h7d y1fe ff40 fs28 fc9 sc0 ls193">máx</div><div class="t mb x2a h7c y1ff ff40 fs27 fc9 sc0 lsb">\u03c3</div><div class="t m0 xe5 h7d y200 ff40 fs28 fc9 sc0 ls193">máx</div><div class="t mc xea h7e y201 ff40 fs29 fc3 sc0 lsb">\u03b8</div><div class="t m0 xeb h7f y202 ff3f fs28 fc3 sc0 lsb">p</div><div class="t mc xec h7e y203 ff40 fs29 fc3 sc0 lsb">\u03b8</div><div class="t m0 x2b h7f y204 ff3f fs28 fc3 sc0 lsb">p</div><div class="t m0 x2f h80 y205 ff3f fs2a fc3 sc0 lsb">y</div><div class="t m0 xe h81 y206 ff3f fs2a fc3 sc0 ls173">Q<span class="lsb vc">x</span></div><div class="t m0 xca h82 y207 ff3f fs2a fc9 sc0 lsb">y<span class="ff40">\u2032</span></div><div class="t m0 xed h82 y208 ff3f fs2a fc9 sc0 lsb">x<span class="ff40">\u2032</span></div><div class="t m0 xee h32 y209 ff3a fs16 fc8 sc0 ls20 ws3b">Figura 1<span class="blank _3"></span>4<span class="blank _8"> </span>.<span class="blank _0"></span>9</div><div class="t md x80 h83 y20a ff41 fs2b fc3 sc0 lsb">\ue602</div><div class="t m0 xef h2e y20b ff3f fs17 fc3 sc0 lsb">x<span class="ff40">\u2032</span>y<span class="ff40">\u2032</span></div><div class="t md xc5 h83 y20c ff41 fs2b fc3 sc0 lsb">\ue602</div><div class="t m0 x83 h2e y20d ff3f fs17 fc3 sc0 lsb">x<span class="ff40">\u2032</span>y<span class="ff40">\u2032</span></div><div class="t md x90 h84 y20e ff40 fs2b fc3 sc0 lsb">\u03c3</div><div class="t m0 xf0 h2e y20f ff3f fs17 fc3 sc0 lsb">x<span class="ff40">\u2032</span></div><div class="t md xf1 h84 y210 ff40 fs2b fc3 sc0 lsb">\u03c3</div><div class="t m0 x28 h2e y211 ff3f fs17 fc3 sc0 lsb">x<span class="ff40">\u2032</span></div><div class="t md x9a h84 y212 ff40 fs2b fc9 sc0 lsb">\u03c3</div><div class="t m0 xf2 h2e y213 ff40 fs17 fc9 sc0 ls34">mín</div><div class="t md xc4 h84 y214 ff40 fs2b fc9 sc0 lsb">\u03c3</div><div class="t m0 xe h2e y215 ff40 fs17 fc9 sc0 ls34">máx</div><div class="t md xca h84 y216 ff40 fs2b fc9 sc0 lsb">\u03c3</div><div class="t m0 x85 h2e y217 ff40 fs17 fc9 sc0 ls34">méd</div><div class="t m0 x2f h2f y218 ff3f fs11 fc9 sc0 lsb">D</div><div class="t m0 x2f h2f y219 ff3f fs11 fc9 sc0 lsb">E</div><div class="t m0 x84 h2f y21a ff3f fs11 fc9 sc0 lsb">C</div><div class="t m0 xc1 h85 y21b ff3f fs11 fc9 sc0 ls174">B<span class="lsb va">A</span></div><div class="t m0 xf3 h2f y21c ff3f fs11 fc3 sc0 lsb">O</div><div class="t m0 xec h2f y21d ff3f fs11 fc9 sc0 lsb">M</div><div class="t m0 x26 h2f y21e ff3f fs11 fc9 sc0 lsb">R</div><div class="t md x80 h83 y21f ff41 fs2b fc3 sc0 lsb">\ue602</div><div class="t m0 xef h2e y220 ff3f fs17 fc3 sc0 lsb">x<span class="ff40">\u2032</span>y<span class="ff40">\u2032</span></div><div class="t md x7c h83 y221 ff41 fs2b fc3 sc0 lsb">\ue602</div><div class="t m0 xf4 h2e y222 ff3f fs17 fc3 sc0 lsb">x<span class="ff40">\u2032</span>y<span class="ff40">\u2032</span></div><div class="t m0 xf5 h30 y223 ff40 fs11 fc3 sc0 lsb">\u2013</div><div class="t md xcb h84 y224 ff40 fs2b fc3 sc0 lsb">\u03c3</div><div class="t m0 xed h2e y225 ff3f fs17 fc3 sc0 lsb">x<span class="ff40">\u2032</span></div><div class="t md xc4 h84 y226 ff40 fs2b fc3 sc0 lsb">\u03c3</div><div class="t m0 xf6 h2e y227 ff3f fs17 fc3 sc0 lsb">x<span class="ff40">\u2032</span></div><div class="t md xe7 h84 y228 ff40 fs2b fc9 sc0 lsb">\u03c3</div><div class="t m0 x85 h2e y229 ff40 fs17 fc9 sc0 ls34">méd</div><div class="t m0 xe9 h2f y22a ff3f fs11 fc9 sc0 lsb">C</div><div class="t m0 xf3 h2f y22b ff3f fs11 fc3 sc0 lsb">O</div><div class="t m0 xea h2f y22c ff3f fs11 fc9 sc0 ls175">R<span class="fc3 lsb v1c">N</span></div><div class="t m0 x2d h32 y22d ff3a fs16 fc8 sc0 ls20 ws3b">Figura 1<span class="blank _3"></span>4<span class="blank _8"> </span>.7</div><div class="t m0 x2d h32 y22e ff3a fs16 fc8 sc0 ls20 ws3b">Figura 1<span class="blank _3"></span>4<span class="blank _8"> </span>.8</div><div class="t m0 x2c h1d y6f ff42 fs17 fc7 sc1 lsb ws8"><span class="fc7 sc0">Cap.14_Beer.indd 578</span><span class="blank _15"></span><span class="fc3 sc0"><span class="fc7 sc0">Cap.14_Beer.indd 578</span><span class="blank _16"> </span><span class="fc7 sc1"><span class="fc7 sc0">03/12/2012 19:14:53</span><span class="blank _11"></span><span class="fc3 sc0"><span class="fc7 sc0">03/12/2012 19:14:53</span></span></span></span></div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,-23.513400,-23.513400]}"></div></div> <div id="pf8" class="pf w2 h1a" data-page-no="8"><div class="pc pc8 w2 h1a"><img fetchpriority="low" loading="lazy" class="bi x86 y1ad w4 h67" alt="" src="https://files.passeidireto.com/5502e1cb-a069-41c0-937b-d1f856940370/bg8.png"><div class="t m0 x87 h1f ye1 ff43 fs13 fc8 sc0 lsb">579</div><div class="t m0 x77 h3b ye2 ff44 fs2 fc3 sc0 lsb ws8">Capítulo 14 <span class="blank _a"> </span><span class="ff45 fs21 ws4b">\u426c</span> <span class="blank _a"> </span>T<span class="blank _4"></span>ransformações de tensão</div><div class="t m0 x86 h33 y22f ff46 fs1b fc3 sc0 ls1be ws8">Subs<span class="blank _8"> </span>tit<span class="blank _e"> </span>u<span class="blank _8"> </span>in<span class="blank _8"> </span>do <span class="ff47 ls194">\u03c3</span><span class="fs1c ls147 wsd0 v4">mé<span class="blank _8"> </span>d</span></div><div class="t m0 xcc h26 y22f ff46 fs1b fc3 sc0 lsb ws8"> e<span class="ff48"> R</span><span class="ls1d wsb4"> da E<span class="blank _8"> </span>q. (<span class="blank _3"></span>1<span class="blank _3"></span>4.<span class="blank _3"></span>1<span class="blank _3"></span>0<span class="blank _0"></span>), escrevemos</span></div><div class="t m0 x86 h24 y230 ff46 fs1b fc3 sc0 lsb ws8"> </div><div class="t m0 xf7 h86 y231 ff49 fs1b fc3 sc0 ls126">\u03c3<span class="ff4a fs24 ls1bf ws10f v8">máx,<span class="blank _0"></span> mí<span class="blank _0"></span>n<span class="blank _25"> </span><span class="fs1b lsd7 v1">=<span class="ff49 ls12c v15">\u03c3<span class="fs24 lscb v8">x</span></span><span class="lsc5 v15">+<span class="ff49 ls195">\u03c3<span class="fs24 lsb v8">y</span></span></span></span></span></div><div class="t m0 xec h87 y232 ff4a fs1b fc3 sc0 ls196">2<span class="ff4b ls197 vb">\ue603</span><span class="lsb va">\u221a</span></div><div class="t m0 xf8 h88 y233 ff49 fs1b fc3 sc0 ls198">\u03c3<span class="fs24 ls199 v8">x</span><span class="ff4a lscc v0">\u2013<span class="ff49 lse9">\u03c3<span class="fs24 lsb v8">y</span></span></span></div><div class="t m0 x64 h4c y232 ff4a fs1b fc3 sc0 lsb">2</div><div class="t m0 x9b h53 y234 ff4a fs24 fc3 sc0 lsb">2</div><div class="t m0 xbe h4c y231 ff4a fs1b fc3 sc0 lsb">+</div><div class="t m5 x5a h27 y235 ff4b fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 x9f h6b y236 ff49 fs24 fc3 sc0 lsab">xy</div><div class="t m0 x9f h53 y237 ff4a fs24 fc3 sc0 lsb">2</div><div class="t m0 xac h4c y232 ff4a fs1b fc3 sc0 lsb ws8"> </div><div class="t m0 x71 h24 y238 ff46 fs1b fc3 sc0 lsb ws8"> </div><div class="t m0 xdc h24 y239 ff46 fs1b fc3 sc0 lsb">(14.14)</div><div class="t m0 x86 h24 y23a ff46 fs1b fc3 sc0 ls148 ws110">A menos que seja possív<span class="blank _0"></span>el<span class="blank _0"></span> di<span class="blank _8"> </span>zer p<span class="blank _8"> </span>or ins<span class="blank _8"> </span>peção qu<span class="blank _8"> </span>al dos dois p<span class="blank _0"></span>lanos pr<span class="blank _8"> </span>i<span class="blank _8"> </span>nci-</div><div class="t m0 x86 h33 y23b ff46 fs1b fc3 sc0 ls148 ws111">pais est<span class="blank _8"> </span>á submetido a <span class="ff47 ls19a">\u03c3</span><span class="fs1c ls19b ws106 v4">máx</span></div><div class="t m0 x2a h33 y23c ff46 fs1b fc3 sc0 lsb ws2e"> e a <span class="ff47 ls19c">\u03c3</span><span class="fs1c ls19d ws107 v4">mín</span><span class="ls63 ws112">, é necessá<span class="blank _8"> </span>rio subst<span class="blank _8"> </span>itu<span class="blank _8"> </span>ir u<span class="blank _8"> </span>m dos valores </span></div><div class="t m0 x86 h33 y23d ff46 fs1b fc3 sc0 ls31 ws8">de <span class="blank _e"> </span><span class="ff47 ls19e">\u03b8<span class="ff48 fs1c lsb ws24 v4">p</span></span><span class="ls1c0 v0"> n<span class="blank _3"></span>a<span class="blank _3"></span> E<span class="blank _3"></span>q<span class="blank _3"></span>.<span class="blank _3"></span> (<span class="blank _2"></span>1<span class="blank _2"></span>4<span class="blank _4"></span>.<span class="blank _3"></span>5<span class="blank _3"></span>)<span class="blank _3"></span> p<span class="blank _3"></span>a<span class="blank _3"></span>r<span class="blank _0"></span>a<span class="blank _4"></span> d<span class="blank _3"></span>e<span class="blank _3"></span>t<span class="blank _3"></span>e<span class="blank _0"></span>r<span class="blank _0"></span>m<span class="blank _3"></span>i<span class="blank _0"></span>n<span class="blank _3"></span>a<span class="blank _3"></span>r<span class="blank _3"></span> q<span class="blank _3"></span>u<span class="blank _3"></span>a<span class="blank _3"></span>l<span class="blank _3"></span> d<span class="blank _3"></span>o<span class="blank _3"></span>s<span class="blank _3"></span> d<span class="blank _3"></span>o<span class="blank _4"></span>i<span class="blank _3"></span>s<span class="blank _3"></span> p<span class="blank _3"></span>l<span class="blank _4"></span>a<span class="blank _0"></span>n<span class="blank _4"></span>o<span class="blank _3"></span>s<span class="blank _3"></span> c<span class="blank _3"></span>o<span class="blank _3"></span>rr<span class="blank _4"></span>e<span class="blank _3"></span>s<span class="blank _3"></span>p<span class="blank _0"></span>o<span class="blank _4"></span>n<span class="blank _3"></span>d<span class="blank _3"></span>e<span class="blank _3"></span> a<span class="blank _3"></span>o<span class="blank _3"></span> </span></div><div class="t m0 x86 h24 y23e ff46 fs1b fc3 sc0 ls117 ws5a">valor máx<span class="blank _8"> </span>imo d<span class="blank _8"> </span>a te<span class="blank _8"> </span>nsão nor<span class="blank _e"> </span>mal.</div><div class="t m0 x88 h24 y23f ff46 fs1b fc3 sc0 ls60 ws113">V<span class="blank _4"></span>olta<span class="blank _8"> </span>ndo no<span class="blank _0"></span>vame<span class="blank _8"> </span>nte à ci<span class="blank _8"> </span>rcun<span class="blank _8"> </span>ferência d<span class="blank _8"> </span>a F<span class="blank _0"></span>ig. 1<span class="blank _4"></span>4.<span class="blank _3"></span>7<span class="blank _3"></span>, nota<span class="blank _8"> </span>mos que os </div><div class="t m0 x86 h26 y240 ff46 fs1b fc3 sc0 ls1c1 ws8">pon<span class="blank _0"></span>tos <span class="blank _1a"> </span><span class="ff48 lsb">D</span><span class="ls1c2"> e<span class="blank _4"></span><span class="ff48"> E<span class="blank _4"></span><span class="ff46"> l<span class="blank _4"></span>o<span class="blank _4"></span>c<span class="blank _4"></span>a<span class="blank _4"></span>l<span class="blank _3"></span>i<span class="blank _4"></span>z<span class="blank _3"></span>a<span class="blank _4"></span>d<span class="blank _4"></span>o<span class="blank _3"></span>s<span class="blank _4"></span> n<span class="blank _4"></span>o<span class="blank _4"></span> d<span class="blank _4"></span>i<span class="blank _4"></span>â<span class="blank _3"></span>m<span class="blank _4"></span>e<span class="blank _4"></span>t<span class="blank _3"></span>r<span class="blank _3"></span>o<span class="blank _4"></span> v<span class="blank _2"></span>e<span class="blank _3"></span>r<span class="blank _3"></span>t<span class="blank _3"></span>i<span class="blank _4"></span>c<span class="blank _4"></span>a<span class="blank _4"></span>l<span class="blank _4"></span> d<span class="blank _3"></span>a<span class="blank _4"></span> c<span class="blank _4"></span>i<span class="blank _3"></span>r<span class="blank _4"></span>c<span class="blank _4"></span>u<span class="blank _3"></span>n<span class="blank _3"></span>f<span class="blank _2"></span>e<span class="blank _3"></span>r<span class="blank _4"></span>ê<span class="blank _3"></span>n<span class="blank _4"></span>c<span class="blank _4"></span>i<span class="blank _4"></span>a<span class="blank _4"></span> c<span class="blank _4"></span>o<span class="blank _4"></span>r<span class="blank _3"></span>r<span class="blank _3"></span>e<span class="blank _4"></span>s<span class="blank _4"></span>-</span></span></span></div><div class="t m0 x86 h24 y241 ff46 fs1b fc3 sc0 ls1c3 ws8">p<span class="blank _0"></span>o<span class="blank _0"></span>n<span class="blank _3"></span>de<span class="blank _3"></span>m a<span class="blank _3"></span>o m<span class="blank _3"></span>ai<span class="blank _3"></span>o<span class="blank _0"></span>r<span class="blank _0"></span> v<span class="blank _3"></span>al<span class="blank _3"></span>o<span class="blank _0"></span>r<span class="blank _0"></span> n<span class="blank _3"></span>um<span class="blank _0"></span>é<span class="blank _0"></span>ri<span class="blank _3"></span>c<span class="blank _0"></span>o<span class="blank _0"></span> da<span class="blank _3"></span> te<span class="blank _3"></span>ns<span class="blank _0"></span>ã<span class="blank _0"></span>o<span class="blank _0"></span> d<span class="blank _3"></span>e c<span class="blank _3"></span>is<span class="blank _3"></span>al<span class="blank _0"></span>h<span class="blank _0"></span>a<span class="blank _0"></span>m<span class="blank _0"></span>e<span class="blank _0"></span>n<span class="blank _3"></span>to<span class="blank _3"></span> </div><div class="t m5 xf9 h27 y242 ff4b fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 x56 h89 y243 ff48 fs1c fc3 sc0 ls61 ws4e">x'y<span class="blank"> </span>'<span class="ff46 fs1b ls28 ws114 v5">. Como a </span></div><div class="t m0 x86 h33 y244 ff46 fs1b fc3 sc0 ls56 ws115">abscissa dos pontos<span class="ff48 ls1c4 ws8"> D<span class="blank _8"> </span><span class="ff46"> e<span class="blank _8"> </span></span> E<span class="blank _8"> </span></span><span class="lsb ws116"> é <span class="ff47 ls19f">\u03c3</span><span class="fs1c ls147 wsd0 v4">méd</span></span></div><div class="t m0 xf5 h33 y245 ff46 fs1b fc3 sc0 lsb ws116"> = (<span class="blank _3"></span><span class="ff47 ls1a0">\u03c3<span class="ff48 fs1c lsb ws24 v4">x</span><span class="ff46 lsb"> + </span><span class="ls1a1">\u03c3<span class="ff48 fs1c lsb v4">y</span></span></span></div><div class="t m0 xf8 h33 y245 ff46 fs1b fc3 sc0 ls1c5 ws117">)/2, os valore<span class="blank _8"> </span>s de<span class="ff48 lsb ws8"> <span class="blank _0"></span><span class="ff47 ls1a2">\u03b8<span class="ff48 fs1c lsb ws24 v4">c</span><span class="ff46 ls17 ws118"> do parâ<span class="blank _8"> </span>met<span class="blank _8"> </span>ro</span><span class="ff48 lsb"> </span></span></span></div><div class="t m0 x86 h72 y246 ff47 fs1b fc3 sc0 lsb">\u03b8<span class="ff46 ls1e ws119"> cor<span class="blank _8"> </span>res<span class="blank _8"> </span>pondentes a e<span class="blank _8"> </span>sses pontos sã<span class="blank _8"> </span>o obtidos faze<span class="blank _8"> </span>ndo </span><span class="ls1a3">\u03c3<span class="ff48 fs1c ls61 ws77 v4">x'</span></span><span class="ff46 ws11a v0"> = (<span class="blank _3"></span><span class="ff47 ls1a4">\u03c3<span class="ff48 fs1c lsb ws24 v4">x</span><span class="ff46 lsb"> + </span><span class="ls1a5">\u03c3<span class="ff48 fs1c lsb v4">y</span></span></span></span></div><div class="t m0 x89 h24 y247 ff46 fs1b fc3 sc0 ls1c6 ws11b">)/2 na </div><div class="t m0 x86 h24 y248 ff46 fs1b fc3 sc0 ls25 ws11c">Eq. (<span class="blank _3"></span>1<span class="blank _3"></span>4.5)<span class="blank _0"></span>. Conclui-se que a soma dos dois últi<span class="blank _8"> </span>mos ter<span class="blank _8"> </span>mos n<span class="blank _8"> </span>a equ<span class="blank _8"> </span>ação deve </div><div class="t m0 x86 h33 y249 ff46 fs1b fc3 sc0 ls2f ws11d">ser ze<span class="blank _8"> </span>ro<span class="blank _0"></span>. Assim<span class="blank _8"> </span>, par<span class="blank _8"> </span>a<span class="ff48 lsb ws8"> <span class="ff47">\u03b8<span class="ff46"> =</span></span> <span class="ff47 ls1a6">\u03b8</span><span class="fs1c ls1a7 v4">c</span></span><span class="ls1d wsb4 v0">, escr<span class="blank _8"> </span>ev<span class="blank _0"></span>emos</span></div><div class="t m0 x30 h74 y24a ff46 fs1c fc3 sc0 lsb">*</div><div class="t m0 xcf h8a y24b ff49 fs1b fc3 sc0 lsbf">\u03c3<span class="fs24 lsed v8">x</span><span class="ff4a ls8a v0">\u2013<span class="ff49 lsf7">\u03c3<span class="fs24 lsb v8">y</span></span></span></div><div class="t m0 x7d h8b y24c ff4a fs1b fc3 sc0 lsea">2<span class="ls8e ws9e vb"> cos 2<span class="ff49 ls1a8">\u03b8<span class="fs24 ls1a9 v8">c</span></span></span><span class="lsb vb">+</span></div><div class="t m5 xfa h27 y24d ff4b fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 xf8 h4f y24e ff49 fs24 fc3 sc0 ls10a ws108">xy<span class="blank"> </span><span class="ff4a fs1b ls8e ws9e v1"> sen 2<span class="blank _8"> </span><span class="ff49 ls1aa">\u03b8</span></span><span class="ls1ab">c<span class="ff4a fs1b ls10c v1">=0</span></span></div><div class="t m0 x86 h24 y24f ff46 fs1b fc3 sc0 ls119">ou</div><div class="t m0 x86 h24 y250 ff46 fs1b fc3 sc0 lsb ws8"> </div><div class="t m0 xc6 h4c y251 ff4a fs1b fc3 sc0 ls182 wsf0">tg 2<span class="ff49 ls1ac">\u03b8<span class="fs24 ls1ab v8">c</span></span><span class="ls11b ws109">=\u2013<span class="blank _4"></span><span class="fs2c lsb ws8"> </span></span></div><div class="t m0 x96 h4c y252 ff49 fs1b fc3 sc0 lse2">\u03c3<span class="fs24 lsfb v8">x</span><span class="ff4a ls13d">\u2013</span><span class="ls1ad">\u03c3<span class="fs24 lsb v8">y</span></span></div><div class="t m0 xfa h4c y253 ff4a fs1b fc3 sc0 lsb">2</div><div class="t m5 xf8 h27 y253 ff4b fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 xc3 h6b y254 ff49 fs24 fc3 sc0 ls10a">xy</div><div class="t m0 xb1 h4c y251 ff4a fs1b fc3 sc0 lsb ws8"> </div><div class="t m0 xc9 h24 y255 ff46 fs1b fc3 sc0 lsb ws8"> </div><div class="t m0 xdc h24 y256 ff46 fs1b fc3 sc0 lsb">(14.15)</div><div class="t m0 x86 h33 y257 ff46 fs1b fc3 sc0 ls56 ws11e">Essa equ<span class="blank _8"> </span>ação def<span class="blank _8"> </span>ine dois valores<span class="ff48 ls1ae ws8"> </span><span class="lsb ws25">2<span class="ff47 ls1af">\u03b8</span><span class="ff48 fs1c ws24 v4">c</span><span class="ls5c ws11f v0"> defasados em 1<span class="blank _3"></span>80<span class="blank _8"> </span>º e, por<span class="blank _8"> </span>t<span class="blank _8"> </span>anto, dois </span></span></div><div class="t m0 x86 h33 y258 ff46 fs1b fc3 sc0 ls1c7 ws8">valores <span class="ff47 ls1b0">\u03b8<span class="ff48 fs1c lsb ws24 v4">c</span></span><span class="ls63 wsde v0"> defasa<span class="blank _8"> </span>dos em 90<span class="blank _8"> </span>º<span class="blank _3"></span>. Q<span class="blank _8"> </span>ualquer u<span class="blank _8"> </span>m desses valores pode ser ut<span class="blank _8"> </span>il<span class="blank _8"> </span>iza-</span></div><div class="t m0 x86 h24 y259 ff46 fs1b fc3 sc0 ls1c8 ws120">do p<span class="blank _0"></span>ara determ<span class="blank _8"> </span>inar a orien<span class="blank _0"></span>tação do e<span class="blank _3"></span>lemen<span class="blank _0"></span>to corresponden<span class="blank _0"></span>te à<span class="blank _0"></span> tensão de </div><div class="t m0 x86 h24 y25a ff46 fs1b fc3 sc0 ls50 ws121">cisalh<span class="blank _8"> </span>amento m<span class="blank _8"> </span>áxi<span class="blank _8"> </span>ma (<span class="blank _8"> </span>Fi<span class="blank _0"></span>g. 1<span class="blank _4"></span>4.<span class="blank _3"></span>1<span class="blank _3"></span>0)<span class="blank _0"></span>. Obser<span class="blank _8"> </span>vando na Fi<span class="blank _0"></span>g. 1<span class="blank _3"></span>4.<span class="blank _4"></span>7 que o valor </div><div class="t m0 x86 h26 y25b ff46 fs1b fc3 sc0 ls1c9 ws122">máxi<span class="blank _8"> </span>mo<span class="blank _0"></span> da tensão de c<span class="blank _0"></span>isalhamento é<span class="blank _0"></span> igual ao rai<span class="blank _0"></span>o<span class="ff48 ls1ca ws8"> R<span class="blank _4"></span><span class="ff46"> da<span class="blank _4"></span> c<span class="blank _3"></span>ir<span class="blank _3"></span>c<span class="blank _3"></span>u<span class="blank _0"></span>n<span class="blank _0"></span>f<span class="blank _4"></span>e<span class="blank _0"></span>r<span class="blank _3"></span>ê<span class="blank _3"></span>n<span class="blank _0"></span>c<span class="blank _3"></span>i<span class="blank _3"></span>a<span class="blank _3"></span> e<span class="blank _3"></span> </span></span></div><div class="t m0 x86 h24 y25c ff46 fs1b fc3 sc0 ls1cb ws123">lembra<span class="blank _8"> </span>ndo a segu<span class="blank _8"> </span>nd<span class="blank _8"> </span>a d<span class="blank _8"> </span>as Eqs. (<span class="blank _0"></span>1<span class="blank _3"></span>4.<span class="blank _3"></span>1<span class="blank _3"></span>0<span class="blank _0"></span>), escrevemos</div><div class="t m0 x86 h24 y25d ff46 fs1b fc3 sc0 lsb ws8"> </div><div class="t m5 x8c h27 y25e ff4b fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 xea h8c y25f ff4a fs24 fc3 sc0 ls1bf ws10a">máx<span class="blank"> </span><span class="fs1b lsb6 v1">=<span class="lsb v26">\u221a</span></span></div><div class="t m0 xfb h8d y260 ff49 fs1b fc3 sc0 ls1b1">\u03c3<span class="fs24 lsed v8">x</span><span class="ff4a lscc v0">\u2013<span class="ff49 ls195">\u03c3<span class="fs24 lsb v8">y</span></span></span></div><div class="t m0 xed h4c y261 ff4a fs1b fc3 sc0 lsb">2</div><div class="t m0 xfc h53 y262 ff4a fs24 fc3 sc0 lsb">2</div><div class="t m0 xbb h4c y263 ff4a fs1b fc3 sc0 lsb">+</div><div class="t m5 xa0 h27 y263 ff4b fs1d fc3 sc0 lsb">\ue602</div><div class="t m0 x98 h6b y25f ff49 fs24 fc3 sc0 lsae">xy</div><div class="t m0 x98 h53 y264 ff4a fs24 fc3 sc0 lsb">2</div><div class="t m0 x9b h4c y261 ff4a fs1b fc3 sc0 ls1b2 ws8"> <span class="ff46 lsb v27"> </span></div><div class="t m0 xdc h24 y265 ff46 fs1b fc3 sc0 lsb">(14.16)</div><div class="t m0 x86 h24 y266 ff46 fs1b fc3 sc0 ls11d ws124">Conf<span class="blank _0"></span>orme ob<span class="blank _0"></span>ser<span class="blank _8"> </span>vamo<span class="blank _0"></span>s anterio<span class="blank _0"></span>r<span class="blank _8"> </span>men<span class="blank _0"></span>te, a<span class="blank _0"></span> tensão no<span class="blank _0"></span>r<span class="blank _8"> </span>mal co<span class="blank _0"></span>r<span class="blank _8"> </span>respon<span class="blank _0"></span>dente<span class="blank _0"></span> à </div><div class="t m0 x86 h24 y267 ff46 fs1b fc3 sc0 ls1e ws70">condição de t<span class="blank _8"> </span>ensã<span class="blank _8"> </span>o de cisalh<span class="blank _8"> </span>amento m<span class="blank _8"> </span>áx<span class="blank _8"> </span>ima é</div><div class="t m0 x86 h8e y268 ff46 fs1b fc3 sc0 ls1b3 ws8"> <span class="ff49 ls1b4 v12">\u03c3<span class="ff4a ls1cc ws10b">\u2032=<span class="blank"> </span><span class="ff49 ls1b5">\u03c3</span><span class="fs24 lsae ws10c v8">méd<span class="blank"> </span></span><span class="lsda v0">=<span class="ff49 lse5 v15">\u03c3<span class="fs24 lscb v8">x</span></span><span class="lsc5 v15">+<span class="ff49 ls195">\u03c3<span class="fs24 lsb v8">y</span></span></span></span></span></span></div><div class="t m0 xfc h4c y269 ff4a fs1b fc3 sc0 ls1cd ws8">2 </div><div class="t m0 x98 h5b y26a ff46 fs1b fc3 sc0 ls1b6 ws8"> <span class="lsb v13">(14.17)</span></div><div class="t m0 x88 h33 y26b ff46 fs1b fc3 sc0 ls16 ws125">Qu<span class="blank _8"> </span>ando compa<span class="blank _8"> </span>ra<span class="blank _8"> </span>mos as E<span class="blank _8"> </span>qs. (<span class="blank _3"></span>1<span class="blank _3"></span>4.<span class="blank _3"></span>1<span class="blank _0"></span>2<span class="blank _3"></span>) e (<span class="blank _0"></span>1<span class="blank _3"></span>4.<span class="blank _3"></span>1<span class="blank _3"></span>5), nota<span class="blank _8"> </span>mos que tg<span class="ff48 ls1b7 ws8"> </span><span class="lsb ws25">2<span class="ff47 ls58">\u03b8</span><span class="ff48 fs1c ws24 v4">c</span><span class="ws126 v0"> é o </span></span></div><div class="t m0 x86 h72 y26c ff46 fs1b fc3 sc0 ls1ce ws127">in<span class="blank _0"></span>v<span class="blank _0"></span>ers<span class="blank _0"></span>o<span class="blank _0"></span> ne<span class="blank _3"></span>gati<span class="blank _3"></span>vo<span class="blank _0"></span> d<span class="blank _0"></span>e t<span class="blank _0"></span>g<span class="ff48 ls1b8 ws8"> </span><span class="lsb ws25">2<span class="ff47 ls1b9">\u03b8</span><span class="ff48 fs1c ws24 v4">p</span><span class="ls30 ws128 v0"> Isso s<span class="blank _0"></span>ign<span class="blank _8"> </span>if<span class="blank _8"> </span>ica que os âng<span class="blank _8"> </span>ulos<span class="ff48 ls1ba ws8"> </span><span class="lsb ws25">2<span class="ff47 ls1a6">\u03b8</span><span class="ff48 fs1c ws24 v4">c</span><span class="ls1cf ws8"> e<span class="blank _4"></span><span class="ff48 ls1b8"> <span class="ff46 lsb ws25">2<span class="ff47 ls1bb">\u03b8</span><span class="ff48 fs1c ws24 v4">p</span><span class="ls11d ws129"> estão </span></span></span></span></span></span></span></div><div class="t m0 x86 h72 y26d ff46 fs1b fc3 sc0 ls31 ws119">defasados em 9<span class="blank _8"> </span>0º e, p<span class="blank _8"> </span>or<span class="blank _8"> </span>ta<span class="blank _8"> </span>nto, que os âng<span class="blank _8"> </span>ulos <span class="ff47 ls162">\u03b8<span class="ff48 fs1c lsb ws24 v4">c</span></span><span class="lsb ws12a v0"> e <span class="ff47 ls1bc">\u03b8</span><span class="ff48 fs1c ws24 v4">p</span><span class="ls2f ws12b"> est<span class="blank _8"> </span>ão defasados e<span class="blank _8"> </span>m </span></span></div><div class="t m0 x86 h26 y26e ff46 fs1b fc3 sc0 ls5c ws12c">4<span class="blank _0"></span>5º<span class="blank _4"></span>. Concluí<span class="blank _8"> </span>mos então que<span class="ff48 ls1d0 ws8"> o<span class="blank _0"></span>s<span class="blank _3"></span> p<span class="blank _0"></span>l<span class="blank _3"></span>a<span class="blank _0"></span>n<span class="blank _3"></span>o<span class="blank _0"></span>s<span class="blank _3"></span> d<span class="blank _3"></span>e<span class="blank _0"></span> t<span class="blank _3"></span>e<span class="blank _0"></span>n<span class="blank _0"></span>s<span class="blank _3"></span>ã<span class="blank _3"></span>o<span class="blank _0"></span> d<span class="blank _3"></span>e<span class="blank _0"></span> c<span class="blank _3"></span>i<span class="blank _0"></span>s<span class="blank _3"></span>a<span class="blank _3"></span>l<span class="blank _0"></span>h<span class="blank _3"></span>a<span class="blank _0"></span>m<span class="blank _3"></span>e<span class="blank _0"></span>n<span class="blank _3"></span>t<span class="blank _0"></span>o<span class="blank _3"></span> m<span class="blank _0"></span>á<span class="blank _0"></span>x<span class="blank _3"></span>i<span class="blank _0"></span>m<span class="blank _3"></span>a<span class="blank _3"></span> </span></div><div class="t m0 x86 h26 y26f ff48 fs1b fc3 sc0 ls3f ws12d">estão defasa<span class="blank _8"> </span>dos em 45<span class="ff46 lsb">º</span><span class="ls154 ws12e"> dos pl<span class="blank _0"></span>anos principais<span class="ff46 ls56 ws12f">, o que conf<span class="blank _8"> </span>i<span class="blank _8"> </span>r<span class="blank _8"> </span>ma os resu<span class="blank _8"> </span>lta-</span></span></div><div class="t m0 x86 h24 y270 ff46 fs1b fc3 sc0 ls25 ws130">dos obtidos ante<span class="blank _8"> </span>rior<span class="blank _8"> </span>ment<span class="blank _8"> </span>e na Seção 8.9<span class="blank _3"></span>, no caso de u<span class="blank _8"> </span>m ca<span class="blank _8"> </span>r<span class="blank _8"> </span>regame<span class="blank _8"> </span>nto ax<span class="blank _8"> </span>ial </div><div class="t m0 x86 h24 y271 ff46 fs1b fc3 sc0 ls1d1 ws5a">cen<span class="blank _0"></span>trado (F<span class="blank _0"></span>i<span class="blank _0"></span>g.<span class="blank _0"></span> 8.<span class="blank _0"></span>3<span class="blank _3"></span>7), e<span class="blank _0"></span> na S<span class="blank _0"></span>eção 1<span class="blank _4"></span>0.<span class="blank _0"></span>4<span class="blank _0"></span>, no<span class="blank _0"></span> caso<span class="blank _0"></span> de um carregam<span class="blank _0"></span>en<span class="blank _0"></span>to de<span class="blank _0"></span> tor<span class="blank _3"></span>-</div><div class="t m0 x86 h24 y272 ff46 fs1b fc3 sc0 ls5c ws6c">ção (<span class="blank _8"> </span>F<span class="blank _0"></span>ig<span class="blank _0"></span>. 1<span class="blank _3"></span>0.<span class="blank _3"></span>1<span class="blank _0"></span>9<span class="blank _3"></span>).</div><div class="t m0 x86 h35 y273 ff46 fs1f fc3 sc0 lsb ws28">*<span class="fs11 ls1d2 ws131 v4"> <span class="blank _24"> </span>Essa<span class="blank _0"></span> relação pode também ser obtida quando se deter<span class="blank _8"> </span>mi<span class="blank _8"> </span>na que a derivada de </span></div><div class="t m7 xa4 h36 y274 ff4b fs20 fc3 sc0 lsb">\ue602</div><div class="t m0 x72 h8f y275 ff48 fs1f fc3 sc0 ls1d3 ws10d">x'y'<span class="blank"> </span><span class="ff46 fs11 ls1d4 ws132 v9"> na Eq.<span class="blank _0"></span> (<span class="blank _0"></span>1<span class="blank _3"></span>4.6) </span></div><div class="t m0 xef h90 yce ff46 fs11 fc3 sc0 ls191 ws105">é ig<span class="blank _8"> </span>ua<span class="blank _8"> </span>l a ze<span class="blank _8"> </span>ro:<span class="ff48 lsb ws8"> d</span></div><div class="t m7 xf6 h36 yce ff4b fs20 fc3 sc0 lsb">\ue602</div><div class="t m0 xbc h91 ycf ff48 fs1f fc3 sc0 ls18f ws8">x'y'<span class="blank _8"> </span> <span class="fs11 ls1d5 ws10e v9">/d<span class="blank"> </span><span class="ff47 lsb">\u03b8<span class="ff48 ws8"> =<span class="ff46"> 0</span></span></span></span></div><div class="t m6 x43 h2b y276 ff4b fs1e fc9 sc0 lsb">\ue602</div><div class="t m0 xd4 h2e y277 ff4a fs17 fc9 sc0 ls34">máx</div><div class="t m6 x34 h2b y278 ff4b fs1e fc9 sc0 lsb">\ue602</div><div class="t m0 x35 h2e y279 ff4a fs17 fc9 sc0 ls34">máx</div><div class="t mc x4b h92 y27a ff4a fs2d fc3 sc0 lsb">\u03b8</div><div class="t m0 x4c h2c y27b ff49 fs17 fc3 sc0 lsb">c</div><div class="t mc xd7 h92 y27c ff4a fs2d fc3 sc0 lsb">\u03b8</div><div class="t m0 xfd h2c y27d ff49 fs17 fc3 sc0 lsb">c</div><div class="t m0 xd2 h2f y27e ff49 fs11 fc3 sc0 lsb">y</div><div class="t m0 xfe h93 y27f ff49 fs11 fc3 sc0 ls1bd">Q<span class="lsb v25">x</span></div><div class="t m0 x45 h30 y280 ff49 fs11 fc9 sc0 lsb">x<span class="ff4a">\u2032</span></div><div class="t m0 xd7 h30 y281 ff49 fs11 fc9 sc0 lsb">y<span class="ff4a">\u2032</span></div><div class="t m0 x43 h30 y282 ff4a fs11 fc9 sc0 lsb">\u2032</div><div class="t m0 xb9 h30 y283 ff4a fs11 fc9 sc0 lsb">\u2032</div><div class="t m0 xd7 h30 y284 ff4a fs11 fc9 sc0 lsb">\u2032</div><div class="t m0 x38 h30 y285 ff4a fs11 fc9 sc0 lsb">\u2032</div><div class="t me xdf h94 y286 ff49 fs2e fc9 sc0 lsb">\u03c3</div><div class="t me xff h94 y287 ff49 fs2e fc9 sc0 lsb">\u03c3</div><div class="t me xd4 h94 y288 ff49 fs2e fc9 sc0 lsb">\u03c3</div><div class="t me x5e h94 y289 ff49 fs2e fc9 sc0 lsb">\u03c3</div><div class="t m0 x34 h32 y28a ff43 fs16 fc8 sc0 ls20 ws3b">Figura 1<span class="blank _3"></span>4<span class="blank _8"> </span>.<span class="blank _3"></span>10</div><div class="t m0 x2c h1d y6f ff4c fs17 fc7 sc1 lsb ws8"><span class="fc7 sc0">Cap.14_Beer.indd 579</span><span class="blank _15"></span><span class="fc3 sc0"><span class="fc7 sc0">Cap.14_Beer.indd 579</span><span class="blank _16"> </span><span class="fc7 sc1"><span class="fc7 sc0">03/12/2012 19:14:54</span><span class="blank _11"></span><span class="fc3 sc0"><span class="fc7 sc0">03/12/2012 19:14:54</span></span></span></span></div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,-23.513400,-23.513400]}"></div></div> <div id="pf9" class="pf w2 h1a" data-page-no="9"><div class="pc pc9 w2 h1a"><img fetchpriority="low" loading="lazy" class="bi x2d y28b w4 h95" alt="" src="https://files.passeidireto.com/5502e1cb-a069-41c0-937b-d1f856940370/bg9.png"><div class="t m0 x2d h1f y71 ff4d fs13 fc8 sc0 lsb ws21">580<span class="blank"> </span><span class="ff4e fs2 fc3 ws8 v3">Estática e mecânica dos materiais</span></div><div class="t m0 x64 h24 ye3 ff4f fs1b fc3 sc0 ls5c ws14e">Devemos esta<span class="blank _8"> </span>r cientes de que nossa a<span class="blank _8"> </span>nálise d<span class="blank _8"> </span>a t<span class="blank _8"> </span>ra<span class="blank _8"> </span>nsf<span class="blank _0"></span>or<span class="blank _8"> </span>ma<span class="blank _8"> </span>ção da t<span class="blank _8"> </span>en-</div><div class="t m0 x30 h26 ye4 ff4f fs1b fc3 sc0 ls21c ws8">s<span class="blank _8"> </span>ã<span class="blank _8"> </span>o<span class="blank _8"> </span> n<span class="blank _8"> </span>o<span class="blank _8"> </span> e<span class="blank _e"> </span>s<span class="blank _8"> </span>t<span class="blank _e"> </span>a<span class="blank _8"> </span>d<span class="blank _e"> </span>o<span class="blank _8"> </span> pl<span class="blank _8"> </span>a<span class="blank _e"> </span>n<span class="blank _8"> </span>o<span class="blank _8"> </span> d<span class="blank _8"> </span>e<span class="blank _8"> </span> t<span class="blank _e"> </span>e<span class="blank _8"> </span>n<span class="blank _e"> </span>s<span class="blank _8"> </span>ã<span class="blank _e"> </span>o<span class="blank _8"> </span> e<span class="blank _8"> </span>s<span class="blank _8"> </span>t<span class="blank _e"> </span>e<span class="blank _8"> </span>ve<span class="blank _8"> </span> l<span class="blank _e"> </span>i<span class="blank _e"> </span>m<span class="blank _e"> </span>i<span class="blank _8"> </span>t<span class="blank _8"> </span>a<span class="blank _e"> </span>d<span class="blank _e"> </span>a<span class="blank _8"> </span> a<span class="blank _8"> </span> r<span class="blank _8"> </span>o<span class="blank _8"> </span>t<span class="blank _e"> </span>a<span class="blank _8"> </span>ç<span class="blank _e"> </span>õ<span class="blank _8"> </span>e<span class="blank _8"> </span>s<span class="blank _8"> </span><span class="ff50"> n<span class="blank _e"> </span>o<span class="blank _8"> </span> p<span class="blank _8"> </span>l<span class="blank _8"> </span>a<span class="blank _8"> </span>n<span class="blank _8"> </span>o<span class="blank _e"> </span> d<span class="blank _8"> </span>a<span class="blank _8"> </span> t<span class="blank _8"> </span>e<span class="blank _e"> </span>n<span class="blank _8"> </span>s<span class="blank _e"> </span>ã<span class="blank _8"> </span>o<span class="blank _e"> </span>.<span class="blank _8"> </span></span><span class="lsb"> </span></div><div class="t m0 x30 h24 y1ae ff4f fs1b fc3 sc0 lsa6 wsb5">Se o<span class="blank _8"> </span> eleme<span class="blank _8"> </span>nt<span class="blank _8"> </span>o de<span class="blank _8"> </span> vo<span class="blank _0"></span>lu<span class="blank _8"> </span>me d<span class="blank _8"> </span>a<span class="blank _8"> </span> Fi<span class="blank _0"></span>g. 1<span class="blank _0"></span>4.5 sof<span class="blank _8"> </span>re<span class="blank _8"> </span>r r<span class="blank _8"> </span>ot<span class="blank _8"> </span>aç<span class="blank _8"> </span>õe<span class="blank _8"> </span>s e<span class="blank _8"> </span>m t<span class="blank _8"> </span>or<span class="blank _e"> </span>no d<span class="blank _8"> </span>e u<span class="blank _8"> </span>m e<span class="blank _8"> </span>ixo </div><div class="t m0 x30 h26 y28c ff4f fs1b fc3 sc0 ls28 ws14f">que não seja o ei<span class="blank _8"> </span>x<span class="blank _0"></span>o<span class="ff50 ls21d ws8"> z<span class="blank _4"></span><span class="ff4f ls2f ws150">, suas fa<span class="blank _8"> </span>ces pode<span class="blank _8"> </span>rão e<span class="blank _8"> </span>sta<span class="blank _8"> </span>r submetid<span class="blank _8"> </span>as a te<span class="blank _8"> </span>nsões de </span></span></div><div class="t m0 x30 h24 y28d ff4f fs1b fc3 sc0 ls2f ws151">cisalh<span class="blank _8"> </span>amento ma<span class="blank _8"> </span>iores do que a tensã<span class="blank _8"> </span>o def<span class="blank _8"> </span>in<span class="blank _8"> </span>ida pela Eq. (<span class="blank _3"></span>1<span class="blank _3"></span>4.<span class="blank _3"></span>1<span class="blank _3"></span>6). Em tais </div><div class="t m0 x30 h24 y28e ff4f fs1b fc3 sc0 ls31 ws152">casos, o valor da<span class="blank _8"> </span>do pela Eq. (<span class="blank _3"></span>1<span class="blank _3"></span>4.<span class="blank _3"></span>1<span class="blank _3"></span>6) é cham<span class="blank _8"> </span>ado de te<span class="blank _8"> </span>nsão de cisal<span class="blank _8"> </span>ha<span class="blank _8"> </span>mento </div><div class="t m0 x30 h26 y28f ff4f fs1b fc3 sc0 ls1c1 ws133">máxi<span class="blank"> </span>ma<span class="ff50 ls1d6 wsfe"> no plano<span class="blank _0"></span>.</span></div><div class="t m0 x30 h96 y290 ff51 fs15 fc9 sc0 ls21e ws153">Exempl<span class="blank _8"> </span>o 1<span class="blank _3"></span>4.<span class="blank _3"></span>1. <span class="blank _26"> </span><span class="ff4f fc3 ls21f ws154">Para o e<span class="blank _8"> </span>st<span class="blank _8"> </span>ado plano de t<span class="blank _8"> </span>ens<span class="blank _8"> </span>ão most<span class="blank _8"> </span>r<span class="blank _8"> </span>ado na Fig. 1<span class="blank _4"></span>4.<span class="blank _0"></span>1<span class="blank _4"></span>1, deter<span class="blank _8"> </span>m<span class="blank _8"> </span>i-</span></div><div class="t m0 x30 h97 y291 ff4f fs15 fc3 sc0 ls1d7 ws155">ne (<span class="blank _3"></span><span class="ff50 lsb ws134">a<span class="blank _0"></span><span class="ff4f ls181 ws156">) os pl<span class="blank _0"></span>anos pr<span class="blank _8"> </span>incipais, (<span class="blank _0"></span><span class="ff50 lsb ws134">b<span class="blank _0"></span><span class="ff4f ls220 ws157">) as te<span class="blank _8"> </span>nsõ<span class="blank _8"> </span>es pr<span class="blank _8"> </span>i<span class="blank _8"> </span>ncipai<span class="blank _8"> </span>s e (<span class="blank _3"></span><span class="ff50 lsb ws134">c<span class="blank _0"></span><span class="ff4f ls221 ws158">) a te<span class="blank _8"> </span>nsã<span class="blank _8"> </span>o de cisal<span class="blank _8"> </span>ha<span class="blank _8"> </span>ment<span class="blank _8"> </span>o </span></span></span></span></span></span></div><div class="t m0 x30 h98 y292 ff4f fs15 fc3 sc0 ls222 ws154">má<span class="blank _8"> </span>xi<span class="blank _8"> </span>ma e a te<span class="blank _8"> </span>ns<span class="blank _8"> </span>ão nor<span class="blank _8"> </span>ma<span class="blank _8"> </span>l cor<span class="blank _8"> </span>re<span class="blank _8"> </span>spond<span class="blank _8"> </span>ente.</div><div class="t m0 x30 h99 y293 ff4d fs15 fc8 sc0 ls1d8 ws159">a. Planos principais.<span class="ff4f fc3 ls21f ws15a"> <span class="blank _13"> </span>Com base na c<span class="blank _8"> </span>onvenção us<span class="blank _8"> </span>ual<span class="fs11 lsb ws8 v0"> <span class="fs15 ls223 ws15b">de si<span class="blank _8"> </span>na<span class="blank _8"> </span>is, es<span class="blank _8"> </span>crevemo<span class="blank _8"> </span>s as </span></span></span></div><div class="t m0 x30 h98 y294 ff4f fs15 fc3 sc0 ls224 ws15c">compo<span class="blank _0"></span>nentes<span class="blank _0"></span> de tensão<span class="blank _0"></span> como</div><div class="t m0 xae h9a y295 ff52 fs1b fc3 sc0 ls1d9">\u03c3<span class="fs2f ls1da v1f">x</span><span class="ff53 fs15 ls1ed ws15d v0">=<span class="blank _25"> </span>+<span class="blank _a"> </span>50 MPa<span class="blank _27"> </span></span><span class="ls1db v0">\u03c3<span class="fs2f ls1dc v1f">y</span><span class="ff53 fs15 ls1ed ws15d">=<span class="blank _22"> </span>\u2013<span class="blank _1a"> </span>10 M<span class="blank _8"> </span>Pa</span></span></div><div class="t mf x100 h9b y296 ff54 fs30 fc3 sc0 lsb">\ue602</div><div class="t m0 xab h9c y297 ff52 fs2f fc3 sc0 ls225 ws135">xy<span class="blank"> </span><span class="ff53 fs15 ls226 ws15e vc">=+<span class="blank _5"></span>4<span class="blank _21"></span>0<span class="blank _21"></span> M<span class="blank _6"></span>P<span class="blank _21"></span>a</span></div><div class="t m0 x30 h98 y298 ff4f fs15 fc3 sc0 lsb ws8">Subst<span class="blank _8"> </span>it<span class="blank _8"> </span>ui<span class="blank _8"> </span>ndo na E<span class="blank _8"> </span>q. (<span class="blank _3"></span>1<span class="blank _0"></span>4.<span class="blank _3"></span>12<span class="blank _3"></span>), temo<span class="blank _8"> </span>s</div><div class="t m0 x3a h9d y299 ff53 fs15 fc3 sc0 ls1dd ws15f"> tg 2<span class="blank _8"> </span><span class="ff52 ls1de">\u03b8<span class="fs2f ls1df v1f">p</span></span><span class="ls1e0 v0">=<span class="lsb v1d">2</span></span></div><div class="t mf x3f h9b y29a ff54 fs30 fc3 sc0 lsb">\ue602</div><div class="t m0 x40 h9e y29b ff52 fs2f fc3 sc0 lsb ws136">xy</div><div class="t m0 x78 h9f y29c ff52 fs15 fc3 sc0 ls1e1">\u03c3<span class="fs2f ls1e2 v1f">x</span><span class="ff53 ls1e3">\u2013</span><span class="ls1e4">\u03c3<span class="fs2f lsb v1f">y</span></span></div><div class="t m0 x34 ha0 y29d ff53 fs15 fc3 sc0 ls1e5">=<span class="ls227 ws137 v16">2(<span class="blank"> </span>+<span class="blank"> </span>4<span class="blank _0"></span>0<span class="lsb v0">)</span></span></div><div class="t m0 x101 ha1 y29e ff53 fs15 fc3 sc0 ls228 ws138">50<span class="blank _23"> </span>\u2013<span class="blank _28"> </span>(<span class="blank"> </span>\u2013<span class="blank _9"> </span>10<span class="blank"> </span>)<span class="blank _29"> </span><span class="ls1e6 v10">=</span><span class="ls1e7 v28">8</span><span class="lsb v28">0</span></div><div class="t m0 x68 h9f y29f ff53 fs15 fc3 sc0 ls228">60</div><div class="t m0 x8e h9f y2a0 ff53 fs15 fc3 sc0 ls1e8">2<span class="ff52 ls1e9">\u03b8<span class="fs2f ls1ea v1f">p</span></span><span class="ls1ed ws139 v0">=<span class="blank _2a"> </span>53,1<span class="blank _0"></span>º<span class="blank _2b"> </span>e<span class="blank _2c"> </span>180º<span class="blank"> </span>+<span class="blank"> </span>53,1<span class="blank _0"></span>º<span class="blank _23"> </span>=<span class="blank"> </span>233,1<span class="blank _0"></span>º</span></div><div class="t m0 x102 h9f y2a1 ff53 fs15 fc3 sc0 lsb ws8"> <span class="blank _7"></span><span class="ff52 ls1eb">\u03b8<span class="fs2f ls1ec v1f">p</span><span class="ff53 ls1ed ws13a v0">=<span class="blank"> </span>26,<span class="blank _0"></span>6º<span class="blank _2b"> </span>e<span class="blank _2c"> </span>116,<span class="blank _0"></span>6º</span></span></div><div class="t m0 x30 ha2 y2a2 ff4d fs15 fc8 sc0 ls1ee ws160">b. T<span class="blank _3"></span>ensões pri<span class="blank _0"></span>ncipais.<span class="fs1b ls1ef ws8"> <span class="ff4f fs15 fc3 lsb">A Eq. (<span class="blank _3"></span>1<span class="blank _3"></span>4.<span class="blank _0"></span>1<span class="blank _3"></span>4) indica</span></span></div><div class="t m0 x9f ha3 y2a3 ff52 fs15 fc3 sc0 ls1f0">\u03c3<span class="ff53 fs2f ls208 ws161 v1f">máx,<span class="blank _0"></span> mín<span class="blank _28"> </span><span class="fs15 ls1f1 vc">=<span class="ff52 ls1f2 v1d">\u03c3<span class="fs2f ls1f3 v1f">x</span></span><span class="ls1f4 v1d">+<span class="ff52 ls1f5">\u03c3<span class="fs2f lsb v1f">y</span></span></span></span></span></div><div class="t m0 x3c ha4 y2a4 ff53 fs15 fc3 sc0 ls1f6">2<span class="ff54 ls1f7 v10">\ue603</span><span class="lsb va">\u221a</span></div><div class="t m0 xe0 ha5 y2a5 ff52 fs15 fc3 sc0 ls1f8">\u03c3<span class="fs2f ls1e2 v1f">x</span><span class="ff53 ls1e3 v0">\u2013<span class="ff52 ls1f9">\u03c3<span class="fs2f lsb v1f">y</span></span></span></div><div class="t m0 xb4 h9f y2a4 ff53 fs15 fc3 sc0 lsb">2</div><div class="t m0 x4b ha6 y2a6 ff53 fs2f fc3 sc0 lsb">2</div><div class="t m0 x103 h9f y2a3 ff53 fs15 fc3 sc0 lsb">+</div><div class="t mf x104 h9b y2a7 ff54 fs30 fc3 sc0 lsb">\ue602</div><div class="t m0 xfd h9e y2a8 ff52 fs2f fc3 sc0 ls225">xy</div><div class="t m0 xfd ha6 y2a9 ff53 fs2f fc3 sc0 lsb">2</div><div class="t m0 x105 h9f y2aa ff53 fs15 fc3 sc0 ls229 ws162"> =2<span class="blank _2d"></span>0<span class="blank _2"></span><span class="ff54 ls1fa">\ue603<span class="ff53 ls22a ws13b">\u221a(<span class="blank _4"></span>3<span class="blank _0"></span>0)</span></span></div><div class="t m0 xa2 ha6 y2ab ff53 fs2f fc3 sc0 ls1fb">2<span class="fs15 ls22b ws13c vf">+(<span class="blank _1d"></span>4<span class="blank _6"></span>0<span class="blank _2e"></span>)</span></div><div class="t m0 x5b ha6 y2ab ff53 fs2f fc3 sc0 lsb">2</div><div class="t m0 x52 h9f y2ac ff53 fs15 fc3 sc0 lsb ws8"> <span class="blank _2e"></span><span class="ff52 ls1fc">\u03c3<span class="ff53 fs2f ls22c ws13d v1f">máx<span class="blank"> </span></span><span class="ff53 ls1ed ws15d">=<span class="blank _2a"> </span>20<span class="blank _28"> </span>+<span class="blank _2f"> </span>50<span class="blank _22"> </span>=<span class="blank _28"> </span>70 MPa</span></span></div><div class="t m0 x106 h9f y2ad ff53 fs15 fc3 sc0 lsb ws8"> <span class="blank _2e"></span><span class="ff52 ls1fd">\u03c3<span class="ff53 fs2f ls208 ws13e v1f">mín<span class="blank"> </span></span><span class="ff53 ls1ed ws15d v0">=<span class="blank _2a"> </span>20<span class="blank _2f"> </span>\u2013<span class="blank _30"> </span>50<span class="blank _22"> </span>=<span class="blank _22"> </span>\u2013<span class="blank _1a"> </span>30 MP<span class="blank _8"> </span>a</span></span></div><div class="t m0 x30 ha7 y2ae ff4f fs15 fc3 sc0 ls22d ws163">Os planos e a<span class="blank _8"> </span>s te<span class="blank _8"> </span>nsõe<span class="blank _8"> </span>s pr<span class="blank _8"> </span>i<span class="blank _8"> </span>ncipais es<span class="blank _8"> </span>tã<span class="blank _8"> </span>o esbo<span class="blank _8"> </span>çados n<span class="blank _8"> </span>a F<span class="blank _0"></span>ig. 1<span class="blank _3"></span>4.<span class="blank _3"></span>12. F<span class="blank _3"></span>a<span class="blank _8"> </span>zendo<span class="ff50 lsb ws8"> <span class="ff55">\u03b8</span></span><span class="ls22e ws164"> = 26,6º </span></div><div class="t m0 x30 h97 y2af ff4f fs15 fc3 sc0 ls221 ws15a">na Eq. (<span class="blank _0"></span>1<span class="blank _3"></span>4.5), veri<span class="blank _8"> </span>f<span class="blank _8"> </span>icamo<span class="blank _8"> </span>s que a te<span class="blank _8"> </span>nsã<span class="blank _8"> </span>o nor<span class="blank _8"> </span>mal q<span class="blank _8"> </span>ue at<span class="blank _8"> </span>ua n<span class="blank _8"> </span>a face<span class="ff50 ls22f ws165"> BC</span><span class="ls230 ws8"> d<span class="blank _8"> </span>o e<span class="blank _8"> </span>le<span class="blank _8"> </span>m<span class="blank _8"> </span>en<span class="blank _8"> </span>t<span class="blank _8"> </span>o é<span class="blank _8"> </span> </span></div><div class="t m0 x30 h98 y2b0 ff4f fs15 fc3 sc0 ls1ee ws160">a tensão máxima:</div><div class="t m0 x107 ha8 y2b1 ff52 fs15 fc3 sc0 ls1fe">\u03c3<span class="fs2f ls1ff v1f">x<span class="ff53 ls200">\u2032</span></span><span class="ff53 ls201">=<span class="ls1ed ws13f v10">50<span class="blank"> </span>\u2013<span class="blank _25"> </span>1</span><span class="lsb v10">0</span></span></div><div class="t m0 x6f ha1 y2b2 ff53 fs15 fc3 sc0 ls202">2<span class="ls203 v10">+</span><span class="ls1ed ws140 v28">50<span class="blank _22"> </span>+<span class="blank"> </span>1<span class="lsb">0</span></span></div><div class="t m0 x3c ha9 y2b2 ff53 fs15 fc3 sc0 ls204">2<span class="ls205 ws166 v10"> cos 53,1<span class="blank _0"></span>º<span class="blank _28"> </span>+<span class="blank _2a"> </span>40 sen 53,1<span class="blank _0"></span>º</span></div><div class="t m0 xce h9f y2b3 ff53 fs15 fc3 sc0 ls206 ws167"> <span class="blank _8"> </span>=<span class="blank _2a"> </span>20<span class="blank _29"> </span>+<span class="blank _30"> </span>30 cos 53,1º<span class="blank _2f"> </span>+<span class="blank _30"> </span>40 sen 53,1<span class="blank _0"></span>º<span class="blank _25"> </span>=<span class="blank _2f"> </span>70 MP<span class="blank _8"> </span>a<span class="blank _28"> </span>=<span class="blank _2a"> </span><span class="ff52 ls207">\u03c3</span><span class="fs2f ls208 ws141 v1f">máx</span></div><div class="t m0 x30 h99 y2b4 ff4d fs15 fc8 sc0 ls22d ws168">(c) T<span class="blank _3"></span>ens<span class="blank _8"> </span>ão de c<span class="blank _8"> </span>isalha<span class="blank _8"> </span>ment<span class="blank _8"> </span>o máx<span class="blank _8"> </span>ima.<span class="blank _8"> </span><span class="ff4f fc3 lsb ws8"> <span class="blank _18"> </span>A E<span class="blank _8"> </span>q. (<span class="blank _3"></span>1<span class="blank _0"></span>4.<span class="blank _3"></span>1<span class="blank _3"></span>6<span class="blank _8"> </span>) ind<span class="blank _8"> </span>ica</span></div><div class="t mf x107 h9b y2b5 ff54 fs30 fc3 sc0 lsb">\ue602</div><div class="t m0 x108 haa y2b6 ff53 fs2f fc3 sc0 ls231 ws142">máx<span class="blank"> </span><span class="fs15 ls209 vc">=<span class="lsb v29">\u221a</span></span></div><div class="t m0 x3b hab y2b7 ff52 fs15 fc3 sc0 ls20a">\u03c3<span class="fs2f ls1e2 v1f">x</span><span class="ff53 ls1e3 v0">\u2013<span class="ff52 ls20b">\u03c3<span class="fs2f lsb v1f">y</span></span></span></div><div class="t m0 x56 h9f y2b8 ff53 fs15 fc3 sc0 lsb">2</div><div class="t m0 xd1 ha6 y2b9 ff53 fs2f fc3 sc0 lsb">2</div><div class="t m0 x3c h9f y2b5 ff53 fs15 fc3 sc0 lsb">+</div><div class="t mf x109 h9b y2b5 ff54 fs30 fc3 sc0 lsb">\ue602</div><div class="t m0 x31 h9e y2b6 ff52 fs2f fc3 sc0 ls225">xy</div><div class="t m0 x31 ha6 y2ba ff53 fs2f fc3 sc0 ls20c">2<span class="fs15 ls232 ws143 vf">=\u221a<span class="blank _31"></span>(<span class="blank _12"></span>3<span class="blank _32"></span>0<span class="blank _31"></span>)</span></div><div class="t m0 x10a ha6 y2ba ff53 fs2f fc3 sc0 ls1fb">2<span class="fs15 ls233 ws144 vf">+(<span class="blank _1d"></span>4<span class="blank _6"></span>0<span class="blank _2e"></span>)</span></div><div class="t m0 x103 ha6 y2ba ff53 fs2f fc3 sc0 ls20d">2<span class="fs15 ls234 ws169 vf">=5<span class="blank _33"></span>0<span class="blank _33"></span> M<span class="blank _33"></span>P<span class="blank _1f"></span>a</span></div><div class="t m0 x64 ha7 y2bb ff4f fs15 fc3 sc0 ls235 ws16a">Com o <span class="blank _34"> </span><span class="ff55 lsb ws145">\u03c3</span><span class="fs31 ls20e ws146 v2a">máx</span></div><div class="t m0 x8e ha7 y2bb ff4f fs15 fc3 sc0 ls236 ws16b"> e <span class="ff55 lsb ws145">\u03c3</span><span class="fs31 ls237 v2a">mín</span></div><div class="t m0 x52 h98 y2bb ff4f fs15 fc3 sc0 ls238 ws16c"> tê<span class="blank _8"> </span>m sin<span class="blank _8"> </span>ais opo<span class="blank _8"> </span>stos<span class="blank _8"> </span>, o valor obtido pa<span class="blank _8"> </span>r<span class="blank _8"> </span>a </div><div class="t mf xd7 h9b y2bb ff54 fs30 fc3 sc0 lsb">\ue602</div><div class="t m0 x10b hac y2bc ff4f fs31 fc3 sc0 ls20e ws146">máx</div><div class="t m0 x62 h98 y2bb ff4f fs15 fc3 sc0 ls239 ws16d"> realmente repre-</div><div class="t m0 x30 h98 y2bd ff4f fs15 fc3 sc0 ls23a ws16e">sent<span class="blank _8"> </span>a o valor m<span class="blank _8"> </span>áx<span class="blank _8"> </span>imo d<span class="blank _8"> </span>a t<span class="blank _8"> </span>ens<span class="blank _8"> </span>ão de cis<span class="blank _8"> </span>al<span class="blank _8"> </span>ha<span class="blank _8"> </span>mento no p<span class="blank _8"> </span>onto c<span class="blank _8"> </span>onsider<span class="blank _8"> </span>ad<span class="blank _8"> </span>o. A orient<span class="blank _8"> </span>a-</div><div class="t m0 x30 h98 y2be ff4f fs15 fc3 sc0 ls23b ws16f">ção dos pla<span class="blank _8"> </span>nos de te<span class="blank _8"> </span>nsã<span class="blank _8"> </span>o de cisa<span class="blank _8"> </span>lh<span class="blank _8"> </span>ame<span class="blank _8"> </span>nto má<span class="blank _8"> </span>xi<span class="blank _8"> </span>ma e o se<span class="blank _8"> </span>ntido d<span class="blank _8"> </span>as t<span class="blank _8"> </span>en<span class="blank _8"> </span>sões d<span class="blank _8"> </span>e cisa-</div><div class="t m0 x30 h98 y2bf ff4f fs15 fc3 sc0 ls23c wse2">lh<span class="blank _8"> </span>ame<span class="blank _8"> </span>nto sã<span class="blank _8"> </span>o mais b<span class="blank _8"> </span>em det<span class="blank _8"> </span>er<span class="blank _8"> </span>m<span class="blank _8"> </span>i<span class="blank _8"> </span>na<span class="blank _8"> </span>dos cor<span class="blank _8"> </span>t<span class="blank _8"> </span>a<span class="blank _8"> </span>ndo o elemento p<span class="blank _8"> </span>or u<span class="blank _8"> </span>ma seç<span class="blank _8"> </span>ão ao longo </div><div class="t m0 x30 h97 y2c0 ff4f fs15 fc3 sc0 ls23d ws170">do plano diagonal<span class="ff50 ls23e ws171"> AC</span><span class="ls23f ws8"> d<span class="blank _e"> </span>o<span class="blank _8"> </span> e<span class="blank _8"> </span>le<span class="blank _e"> </span>m<span class="blank _8"> </span>e<span class="blank _8"> </span>n<span class="blank _8"> </span>t<span class="blank _e"> </span>o<span class="blank _8"> </span> d<span class="blank _8"> </span>a<span class="blank _8"> </span> F<span class="blank _8"> </span>ig<span class="blank _8"> </span>.<span class="blank _8"> </span> 14.12<span class="blank _8"> </span>.<span class="blank _8"> </span> C<span class="blank _8"> </span>o<span class="blank _8"> </span>m<span class="blank _8"> </span>o<span class="blank _8"> </span> a<span class="blank _e"> </span>s<span class="blank _8"> </span> f<span class="blank _8"> </span>a<span class="blank _e"> </span>c<span class="blank _8"> </span>e<span class="blank _8"> </span>s<span class="blank _8"> </span><span class="ff50 ls20f ws172"> AB</span> e<span class="blank _8"> </span><span class="ff50 ls240 ws173"> BC</span><span class="ls241 ws174"> do elemen-</span></span></div><div class="t m0 x30 h97 y2c1 ff4f fs15 fc3 sc0 ls242 ws175">to es<span class="blank _8"> </span>tã<span class="blank _8"> </span>o cont<span class="blank _8"> </span>ida<span class="blank _8"> </span>s nos plano<span class="blank _8"> </span>s pr<span class="blank _8"> </span>incip<span class="blank _8"> </span>ais, o pla<span class="blank _8"> </span>no dia<span class="blank _8"> </span>gonal<span class="ff50 ls243 ws176"> AC<span class="blank _8"> </span></span><span class="ls244 ws177"> deve<span class="blank _0"></span> ser u<span class="blank _8"> </span>m dos p<span class="blank _0"></span>lanos </span></div><div class="t m0 x30 h98 y2c2 ff4f fs15 fc3 sc0 ls245 ws8">de<span class="blank _8"> </span> t<span class="blank _8"> </span>e<span class="blank _8"> </span>n<span class="blank _8"> </span>sã<span class="blank _8"> </span>o<span class="blank _8"> </span> de<span class="blank _8"> </span> ci<span class="blank _8"> </span>s<span class="blank _8"> </span>a<span class="blank _8"> </span>l<span class="blank _8"> </span>h<span class="blank _8"> </span>a<span class="blank _8"> </span>me<span class="blank _8"> </span>nt<span class="blank _8"> </span>o<span class="blank _8"> </span> m<span class="blank _8"> </span>á<span class="blank _8"> </span>x<span class="blank _8"> </span>i<span class="blank _8"> </span>m<span class="blank _8"> </span>a (<span class="blank _8"> </span>Fig<span class="blank _8"> </span>. 1<span class="blank _0"></span>4.1<span class="blank _0"></span>3<span class="blank _0"></span>). A<span class="blank _8"> </span>l<span class="blank _8"> </span>ém<span class="blank _8"> </span> d<span class="blank _8"> </span>i<span class="blank _8"> </span>ss<span class="blank _8"> </span>o,<span class="blank _8"> </span> a<span class="blank _8"> </span>s c<span class="blank _8"> </span>o<span class="blank _8"> </span>nd<span class="blank _8"> </span>iç<span class="blank _8"> </span>õ<span class="blank _8"> </span>e<span class="blank _8"> </span>s d<span class="blank _8"> </span>e<span class="blank _8"> </span> eq<span class="blank _8"> </span>u<span class="blank _8"> </span>i<span class="blank _8"> </span>l<span class="blank _8"> </span>í-</div><div class="t m0 x30 h97 y2c3 ff4f fs15 fc3 sc0 ls246 ws178">br<span class="blank _8"> </span>io<span class="blank _8"> </span> pa<span class="blank _8"> </span>r<span class="blank _8"> </span>a o ele<span class="blank _8"> </span>men<span class="blank _8"> </span>to p<span class="blank _8"> </span>r<span class="blank _8"> </span>is<span class="blank _8"> </span>má<span class="blank _8"> </span>t<span class="blank _8"> </span>ico<span class="ff50 ls20f ws179"> ABC</span><span class="ls247 ws17a"> requerem que a tensão de cisalha<span class="blank _8"> </span>mento que </span></div><div class="t m0 x30 h97 y2c4 ff4f fs15 fc3 sc0 ls248 ws17b">at<span class="blank _8"> </span>ua em <span class="ff50 ls23e ws147">AC<span class="blank"> </span></span><span class="ls249 ws17c"> se<span class="blank _8"> </span>ja dir<span class="blank _8"> </span>eciona<span class="blank _8"> </span>da con<span class="blank _8"> </span>for<span class="blank _8"> </span>me most<span class="blank _8"> </span>ra a f<span class="blank _e"> </span>igu<span class="blank _8"> </span>r<span class="blank _8"> </span>a. O elemento d<span class="blank _8"> </span>e vo<span class="blank _0"></span>lume<span class="blank _8"> </span> </span></div><div class="t m0 x30 h98 y2c5 ff4f fs15 fc3 sc0 ls24a ws17d">co<span class="blank _0"></span>rres<span class="blank _0"></span>pon<span class="blank _3"></span>den<span class="blank _0"></span>te<span class="blank _0"></span> à t<span class="blank _0"></span>ens<span class="blank _0"></span>ão<span class="blank _0"></span> de<span class="blank _0"></span> c<span class="blank _0"></span>is<span class="blank _0"></span>alham<span class="blank _0"></span>en<span class="blank _3"></span>to má<span class="blank _0"></span>xima<span class="blank _0"></span> é m<span class="blank _3"></span>ostrad<span class="blank _0"></span>o n<span class="blank _0"></span>a<span class="blank _0"></span> F<span class="blank _0"></span>i<span class="blank _0"></span>g<span class="blank _0"></span>.<span class="blank _0"></span> 1<span class="blank _3"></span>4<span class="blank _0"></span>.<span class="blank _3"></span>1<span class="blank _4"></span>4.<span class="blank _0"></span> A<span class="blank _0"></span> ten<span class="blank _0"></span>-</div><div class="t m0 x30 h98 y2c6 ff4f fs15 fc3 sc0 ls24b ws17e">são nor<span class="blank _e"> </span>mal e<span class="blank _8"> </span>m cad<span class="blank _8"> </span>a u<span class="blank _8"> </span>ma d<span class="blank _8"> </span>as qu<span class="blank _8"> </span>at<span class="blank _8"> </span>ro face<span class="blank _8"> </span>s do elemento é d<span class="blank _8"> </span>ad<span class="blank _8"> </span>a pela E<span class="blank _8"> </span>q. (<span class="blank _3"></span>1<span class="blank _3"></span>4.<span class="blank _0"></span>1<span class="blank _3"></span>7)</div><div class="t m0 x8e had y2c7 ff52 fs15 fc3 sc0 ls210">\u03c3<span class="ff53 ls24c ws148">\u2032=<span class="blank"> </span></span><span class="ls211">\u03c3<span class="ff53 fs2f ls212 ws149 v1f">méd<span class="blank"> </span></span><span class="ff53 ls1f1">=</span><span class="ls213 v1d">\u03c3</span><span class="fs2f ls1f3 vb">x</span><span class="ff53 ls214 v1d">+</span><span class="ls215 v1d">\u03c3</span><span class="fs2f lsb vb">y</span></span></div><div class="t m0 x59 ha1 y2c8 ff53 fs15 fc3 sc0 ls216">2<span class="ls217 v10">=</span><span class="ls1ed ws14a v28">50<span class="blank _29"> </span>\u2013<span class="blank"> </span>1</span><span class="lsb v28">0</span></div><div class="t m0 x5c hae y2c9 ff53 fs15 fc3 sc0 ls202">2<span class="ls1ed ws15d v10">=<span class="blank _28"> </span>20 MP<span class="blank _8"> </span>a<span class="blank _e"> </span></span><span class="ls218 ws8 v20"> </span><span class="ff4f lsb ws8 v3"> <span class="ff56 fc9 v20">\u25a0</span></span></div><div class="t m0 x26 h30 y2ca ff53 fs11 fc9 sc0 ls24d ws17f">10 MPa</div><div class="t m0 x10c h30 y2cb ff53 fs11 fc9 sc0 ls24d ws17f">40 MPa</div><div class="t m0 xc5 h30 y2cc ff53 fs11 fc9 sc0 ls24d ws17f">50 MPa</div><div class="t mc x10d h92 y2cd ff53 fs2d fc9 sc0 lsb">\u03c3</div><div class="t m0 x10e haf y2ce ff53 fs17 fc9 sc0 ls34 ws14b">mín<span class="blank"> </span><span class="fs11 ls24d ws17f v1">= 30 MPa</span></div><div class="t mc x27 h92 y2cf ff53 fs2d fc9 sc0 lsb">\u03c3</div><div class="t m0 xc6 hb0 y2d0 ff53 fs17 fc9 sc0 ls34 ws14c">máx<span class="blank"> </span><span class="fs11 ls24d ws17f v1">= 70 MPa</span></div><div class="t mc xe5 h92 y2d1 ff53 fs2d fc3 sc0 lsb">\u03b8</div><div class="t m0 x10f h2c y2d2 ff52 fs17 fc3 sc0 ls219">p<span class="fs11 lsb v2b">x</span></div><div class="t m0 x7a h30 y2d3 ff53 fs11 fc3 sc0 lsb ws8">= 26,6º</div><div class="t m0 x110 h2f y2d4 ff52 fs11 fc3 sc0 lsb">A</div><div class="t m0 x8c h2f y2d5 ff52 fs11 fc3 sc0 lsb">B</div><div class="t m0 x27 h2f y2d6 ff52 fs11 fc3 sc0 lsb">C</div><div class="t mc xf2 h92 y2d7 ff53 fs2d fc9 sc0 lsb">\u03c3</div><div class="t mc xc2 h92 y2d8 ff53 fs2d fc9 sc0 lsb">\u03c3</div><div class="t m0 x111 h2e y2d9 ff53 fs17 fc9 sc0 ls34">mín</div><div class="t mc x112 h92 y2da ff53 fs2d fc9 sc0 lsb">\u03c3</div><div class="t m0 x8c h2e y2db ff53 fs17 fc9 sc0 ls34">máx</div><div class="t m0 xca h30 y2dc ff53 fs11 fc9 sc0 lsb">'</div><div class="t mc x113 hb1 y2dd ff54 fs2d fc9 sc0 lsb">\ue602</div><div class="t m0 x114 h2e y2de ff53 fs17 fc9 sc0 ls34">máx</div><div class="t mc x93 h92 y2df ff53 fs2d fc3 sc0 lsb">\u03b8</div><div class="t m0 x27 hb0 y2e0 ff52 fs17 fc3 sc0 ls21a">p<span class="ff53 fs11 lsb ws8 v1">= 26,6º</span></div><div class="t mc x115 h92 y2e1 ff53 fs2d fc3 sc0 lsb">\u03b8</div><div class="t m0 xe9 h2c y2e2 ff52 fs17 fc3 sc0 lsb">c</div><div class="t mc x7d h92 y2e1 ff53 fs2d fc3 sc0 lsb">\u03b8</div><div class="t m0 x7e h2c y2e2 ff52 fs17 fc3 sc0 lsb">p</div><div class="t m0 x8c h30 y2e3 ff53 fs11 fc3 sc0 ls24e ws14d">==<span class="blank _35"></span><span class="lsb ws8">\u2013 45º</span></div><div class="t m0 x110 h30 y2e4 ff53 fs11 fc3 sc0 lsb">45º</div><div class="t m0 x29 h30 y2e3 ff53 fs11 fc3 sc0 lsb">\u201318,4º</div><div class="c x81 y2e5 w8 hb2"><div class="t m0 x0 h2f y2e6 ff52 fs11 fc3 sc0 lsb">A</div></div><div class="t m0 x115 h2f y2e7 ff52 fs11 fc3 sc0 lsb">C</div><div class="t m0 x90 h2f y2e8 ff52 fs11 fc3 sc0 lsb">B</div><div class="t m0 xe h30 y2e9 ff53 fs11 fc9 sc0 lsb">'</div><div class="t mc x90 h92 y2e9 ff53 fs2d fc9 sc0 lsb">\u03c3</div><div class="t mc xd0 hb1 y2ea ff54 fs2d fc9 sc0 lsb">\ue602</div><div class="t m0 xcd h2e y2eb ff53 fs17 fc9 sc0 ls34">máx</div><div class="t m0 xfb h2f y2ec ff52 fs11 fc3 sc0 lsb">x</div><div class="t mc x2b h92 y2ed ff53 fs2d fc3 sc0 lsb">\u03b8</div><div class="t m0 x116 haf y2ee ff52 fs17 fc3 sc0 ls21b">p<span class="ff53 fs11 lsb ws8 v1">= \u201318,4º</span></div><div class="t m0 x82 h30 y2ef ff53 fs11 fc9 sc0 ls24d ws17f">= 20 MPa</div><div class="t m0 xd0 h30 y2f0 ff53 fs11 fc9 sc0 lsb">'</div><div class="t mc xcf h92 y2f1 ff53 fs2d fc9 sc0 lsb">\u03c3</div><div class="t m0 x8c h30 y2f1 ff53 fs11 fc9 sc0 ls24d ws17f">= 20 MPa</div><div class="t m0 x117 h30 y2f2 ff53 fs11 fc9 sc0 ls24d ws17f">= 50 MPa</div><div class="t m0 x94 h32 y2f3 ff4d fs16 fc8 sc0 ls20 ws3b">Figura 1<span class="blank _3"></span>4<span class="blank _8"> </span>.<span class="blank _3"></span>1<span class="blank _3"></span>1</div><div class="t m0 xc1 h32 y2f4 ff4d fs16 fc8 sc0 ls20 ws3b">Figura 1<span class="blank _3"></span>4<span class="blank _8"> </span>.<span class="blank _3"></span>1<span class="blank _0"></span>2</div><div class="t m0 x81 h32 y2f5 ff4d fs16 fc8 sc0 ls20 ws3b">Figura 1<span class="blank _3"></span>4<span class="blank _8"> </span>.<span class="blank _3"></span>1<span class="blank _0"></span>3</div><div class="t m0 xee h32 y2f6 ff4d fs16 fc8 sc0 ls20 ws3b">Figura 1<span class="blank _3"></span>4<span class="blank _8"> </span>.<span class="blank _3"></span>1<span class="blank _0"></span>4</div><div class="t m0 x2c h1d y6f ff57 fs17 fc7 sc1 lsb ws8"><span class="fc7 sc0">Cap.14_Beer.indd 580</span><span class="blank _15"></span><span class="fc3 sc0"><span class="fc7 sc0">Cap.14_Beer.indd 580</span><span class="blank _16"> </span><span class="fc7 sc1"><span class="fc7 sc0">03/12/2012 19:14:54</span><span class="blank _11"></span><span class="fc3 sc0"><span class="fc7 sc0">03/12/2012 19:14:54</span></span></span></span></div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,-23.513400,-23.513400]}"></div></div>
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