{"id":3236,"date":"2021-03-22T17:32:48","date_gmt":"2021-03-22T15:32:48","guid":{"rendered":"https:\/\/blog.federnshop.com\/schubspannung-berechnen-portugiesisch\/"},"modified":"2026-10-01T10:22:57","modified_gmt":"2026-10-01T08:22:57","slug":"schubspannung-berechnen-portugiesisch","status":"publish","type":"post","link":"https:\/\/blog.federnshop.com\/pt-pt\/schubspannung-berechnen-portugiesisch\/","title":{"rendered":"Calcular a tens\u00e3o de compress\u00e3o em molas de press\u00e3o e de tra\u00e7\u00e3o"},"content":{"rendered":"<p>Na conce\u00e7\u00e3o precisa de molas de compress\u00e3o e de tra\u00e7\u00e3o, o c\u00e1lculo da tens\u00e3o de cisalhamento \u00e9 uma parte essencial da <a href=\"https:\/\/blog.federnshop.com\/funktions-festigkeitsnachweis\/\" target=\"_blank\" rel=\"noopener\">verifica\u00e7\u00e3o da resist\u00eancia<\/a>. Esta mostra o grau de solicita\u00e7\u00e3o a que o material da mola \u00e9 submetido pelas for\u00e7as que atuam sobre ela, constituindo assim uma base importante para a resist\u00eancia mec\u00e2nica, a seguran\u00e7a de funcionamento e a vida \u00fatil da mola. No caso das molas de compress\u00e3o, a for\u00e7a de compress\u00e3o que atua axialmente no fio da mola \u00e9, essencialmente, convertida numa solicita\u00e7\u00e3o de tor\u00e7\u00e3o.<\/p>\n<p>&nbsp;<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_87 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/blog.federnshop.com\/pt-pt\/schubspannung-berechnen-portugiesisch\/#Tensao_de_cisalhamento_em_molas_de_compressao\" >Tens\u00e3o de cisalhamento em molas de compress\u00e3o<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/blog.federnshop.com\/pt-pt\/schubspannung-berechnen-portugiesisch\/#Tensao_de_compressao_da_mola_de_pressao_da_Kraft\" >Tens\u00e3o de compress\u00e3o da mola de press\u00e3o da Kraft:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/blog.federnshop.com\/pt-pt\/schubspannung-berechnen-portugiesisch\/#Tensao_de_compressao_da_mola_de_pressao_em_funcao_do_deslocamento\" >Tens\u00e3o de compress\u00e3o da mola de press\u00e3o em fun\u00e7\u00e3o do deslocamento:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/blog.federnshop.com\/pt-pt\/schubspannung-berechnen-portugiesisch\/#Tensao_de_cisalhamento_corrigida_da_mola_de_compressao\" >Tens\u00e3o de cisalhamento corrigida da mola de compress\u00e3o:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/blog.federnshop.com\/pt-pt\/schubspannung-berechnen-portugiesisch\/#Tensao_admissivel_da_mola_de_pressao\" >Tens\u00e3o admiss\u00edvel da mola de press\u00e3o:<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/blog.federnshop.com\/pt-pt\/schubspannung-berechnen-portugiesisch\/#Tensao_de_cisalhamento_para_molas_de_tracao\" >Tens\u00e3o de cisalhamento para molas de tra\u00e7\u00e3o<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/blog.federnshop.com\/pt-pt\/schubspannung-berechnen-portugiesisch\/#Tensao_de_cisalhamento\" >Tens\u00e3o de cisalhamento:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/blog.federnshop.com\/pt-pt\/schubspannung-berechnen-portugiesisch\/#Tensao_de_cisalhamento_corrigida\" >Tens\u00e3o de cisalhamento corrigida:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/blog.federnshop.com\/pt-pt\/schubspannung-berechnen-portugiesisch\/#Tensao_admissivel\" >Tens\u00e3o admiss\u00edvel:<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/blog.federnshop.com\/pt-pt\/schubspannung-berechnen-portugiesisch\/#Explicacao_dos_simbolos_da_formula\" >Explica\u00e7\u00e3o dos s\u00edmbolos da f\u00f3rmula<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"Text\"><span class=\"ez-toc-section\" id=\"Tensao_de_cisalhamento_em_molas_de_compressao\"><\/span>Tens\u00e3o de cisalhamento em molas de compress\u00e3o<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Em molas de compress\u00e3o, a for\u00e7a compressiva axial que atua no fio da mola \u00e9 essencialmente convertida em uma tens\u00e3o de tor\u00e7\u00e3o. Sob uma carga est\u00e1tica ou quase est\u00e1tica em uma mola de compress\u00e3o, a tens\u00e3o de cisalhamento resultante \u03c4 \u00e9 calculada da seguinte forma.<\/p>\n<h4 class=\"Text\"><span class=\"ez-toc-section\" id=\"Tensao_de_compressao_da_mola_de_pressao_da_Kraft\"><\/span>Tens\u00e3o de compress\u00e3o da mola de press\u00e3o da Kraft:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\Large\\tau=\\frac{8DF}{\\pi d^{3}}<\/span>\n<h4 class=\"Text\"><span class=\"ez-toc-section\" id=\"Tensao_de_compressao_da_mola_de_pressao_em_funcao_do_deslocamento\"><\/span>Tens\u00e3o de compress\u00e3o da mola de press\u00e3o em fun\u00e7\u00e3o do deslocamento:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\Large\\tau=\\frac{Gds}{\\pi nD^{2}}<\/span>\n<p>&nbsp;<\/p>\n<p>Quando a mola de compress\u00e3o \u00e9 submetida a esfor\u00e7os din\u00e2micos, aplica-se a tens\u00e3o de cisalhamento corrigida<sub>\u03c4k. <\/sub> A distribui\u00e7\u00e3o da tens\u00e3o de cisalhamento na sec\u00e7\u00e3o transversal do fio de uma mola \u00e9 irregular; a tens\u00e3o mais elevada ocorre no di\u00e2metro interior da mola. Com o fator de corre\u00e7\u00e3o da tens\u00e3o k, que depende da rela\u00e7\u00e3o de enrolamento (rela\u00e7\u00e3o entre o di\u00e2metro m\u00e9dio e a espessura do fio) da mola, \u00e9 poss\u00edvel determinar aproximadamente a tens\u00e3o m\u00e1xima. Para molas submetidas a esfor\u00e7os din\u00e2micos, tem-se, portanto:<\/p>\n<h4 class=\"Text\"><span class=\"ez-toc-section\" id=\"Tensao_de_cisalhamento_corrigida_da_mola_de_compressao\"><\/span>Tens\u00e3o de cisalhamento corrigida da mola de compress\u00e3o:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\Large \\tau_{{\\kappa}}= \\kappa \\cdot \\tau  <\/span>\n<p class=\"Text\">sendo que, para k (segundo Bergstr\u00e4sser): <span class=\"katex-eq\" data-katex-display=\"false\"> \\Large \\kappa=\\frac{\\frac{D}{d}+0,5}{\\frac{D}{d}-0,75}<\/span><\/p>\n<p>&nbsp;<\/p>\n<p>Agora faz-se a compara\u00e7\u00e3o com a tens\u00e3o permitida.<\/p>\n<h4 class=\"Text\"><span class=\"ez-toc-section\" id=\"Tensao_admissivel_da_mola_de_pressao\"><\/span>Tens\u00e3o admiss\u00edvel da mola de press\u00e3o:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\Large \\tau_{{zul}}= 0,5 \\cdot R_{{m}}<\/span>\n<p>ou<\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\Large \\tau_{{czul}}= 0,56 \\cdot R_{{m}}<\/span>\n<p>&nbsp;<\/p>\n<p>Os valores da <a href=\"https:\/\/blog.federnshop.com\/zugfestigkeit-federwerkstoffe\/\" target=\"_blank\" rel=\"noopener noreferrer\">resist\u00eancia m\u00ednima \u00e0 tra\u00e7\u00e3o<sub>Rm<\/sub><\/a> dependem da espessura do fio e podem ser consultados nas normas relativas aos materiais em quest\u00e3o.<\/p>\n<p>Normalmente, as molas de compress\u00e3o t\u00eam de poder ser comprimidas at\u00e9 ao comprimento do bloco; por isso, \u00e9 preciso ter em conta a tens\u00e3o admiss\u00edvel para o comprimento do bloco<sub>tczul<\/sub>.<\/p>\n<p class=\"Text\">Em caso de <a href=\"https:\/\/blog.federnshop.com\/dauerfestigkeit\/\">solicita\u00e7\u00e3o din\u00e2mica<\/a>, \u00e9 preciso determinar a tens\u00e3o m\u00ednima e a tens\u00e3o m\u00e1xima (<sub>tk1<\/sub>e<sub>tk2<\/sub>) da respectiva amplitude de curso. A diferen\u00e7a entre elas \u00e9 a tens\u00e3o de curso. Tanto a tens\u00e3o m\u00e1xima como a tens\u00e3o de curso n\u00e3o podem ultrapassar os valores admiss\u00edveis correspondentes. Estes valores podem ser consultados nos <a href=\"https:\/\/www.beuth.de\/de\/norm\/din-en-13906-1\/189797622\" target=\"_blank\" rel=\"noopener noreferrer\">gr\u00e1ficos de resist\u00eancia \u00e0 fadiga da norma EN 13906-1:2002<\/a>. Se as tens\u00f5es cumprirem estes requisitos, a mola \u00e9 resistente \u00e0 fadiga com um \u00edndice de ciclos de carga-descarga de<sup>10\u2077<\/sup>.<\/p>\n<p>&nbsp;<\/p>\n<h2 class=\"Text\"><span class=\"ez-toc-section\" id=\"Tensao_de_cisalhamento_para_molas_de_tracao\"><\/span>Tens\u00e3o de cisalhamento para molas de tra\u00e7\u00e3o<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>No caso de uma carga est\u00e1tica ou quase est\u00e1tica numa mola de tra\u00e7\u00e3o, a tens\u00e3o de cisalhamento \u03c4 \u00e9 calculada da seguinte forma.<\/p>\n<h4 class=\"Text\"><span class=\"ez-toc-section\" id=\"Tensao_de_cisalhamento\"><\/span>Tens\u00e3o de cisalhamento:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\Large \\tau=\\frac{8DF}{\\pi d^{3}}<\/span>\n<p>&nbsp;<\/p>\n<p>No caso de uma carga din\u00e2mica na mola de tra\u00e7\u00e3o, n\u00e3o \u00e9 poss\u00edvel indicar valores gerais de resist\u00eancia \u00e0 fadiga, uma vez que podem surgir tens\u00f5es adicionais nos pontos de dobragem dos olhais, que, em alguns casos, podem exceder as tens\u00f5es admiss\u00edveis. <a href=\"https:\/\/blog.federnshop.com\/beanspruchung-zugfedern\/\">Por isso, as molas de tra\u00e7\u00e3o devem, na medida do poss\u00edvel, ser submetidas apenas a cargas est\u00e1ticas<\/a>. Se a solicita\u00e7\u00e3o din\u00e2mica for inevit\u00e1vel, deve evitar-se a utiliza\u00e7\u00e3o de <a href=\"https:\/\/blog.federnshop.com\/oesenformen-zugfedern\/\">olhais<\/a> dobrados e optar-se por extremidades enroladas ou aparafusadas. \u00c9 aconselh\u00e1vel realizar um teste de vida \u00fatil nas condi\u00e7\u00f5es de utiliza\u00e7\u00e3o futuras. N\u00e3o \u00e9 poss\u00edvel realizar um <a href=\"https:\/\/blog.federnshop.com\/kugelstrahlen-metallfedern\/\">endurecimento superficial por jateamento de esferas<\/a> devido \u00e0s espiras muito pr\u00f3ximas umas das outras.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Tensao_de_cisalhamento_corrigida\"><\/span>Tens\u00e3o de cisalhamento corrigida:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\Large \\tau_{{\\kappa}}=\\kappa\\cdot\\tau<\/span>\n<h4><span class=\"ez-toc-section\" id=\"Tensao_admissivel\"><\/span>Tens\u00e3o admiss\u00edvel:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\Large \\tau_{{zul}}=0,45 \\cdot R_{{m}}<\/span>\n<p>&nbsp;<\/p>\n<p>A tens\u00e3o m\u00e1xima existente<sub>tn<\/sub>, correspondente ao curso m\u00e1ximo da mola<sub>sn<\/sub>, \u00e9 considerada igual \u00e0 tens\u00e3o admiss\u00edvel. No entanto, para evitar <a href=\"https:\/\/blog.federnshop.com\/pt-pt\/relaxamento-para-molas\/\">a relaxa\u00e7\u00e3o<\/a>, na pr\u00e1tica s\u00f3 se deve utilizar 80 % desse curso da mola.<\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\Large s_{{2}}= 0,8 \\cdot s_{{n}}<\/span>\n<p>&nbsp;<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Explicacao_dos_simbolos_da_formula\"><\/span>Explica\u00e7\u00e3o dos s\u00edmbolos da f\u00f3rmula<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>d = di\u00e2metro do fio (mm)<br \/>\nD = di\u00e2metro m\u00e9dio da espira (mm)<br \/>\nF = for\u00e7a da mola (N)<br \/>\nG = m\u00f3dulo de cisalhamento (N\/mm\u00b2)<br \/>\nn = n\u00famero de espiras el\u00e1sticas (unidades)<br \/>\nRm = Resist\u00eancia m\u00ednima \u00e0 tra\u00e7\u00e3o (N\/mm\u00b2)<br \/>\ns = Curso da mola (mm)<br \/>\n\u03c4 = Tens\u00e3o de cisalhamento (N\/mm\u00b2)<br \/>\n\u03c4zul = Tens\u00e3o de cisalhamento admiss\u00edvel (N\/mm\u00b2)<br \/>\n\u03c4czul = Tens\u00e3o de cisalhamento admiss\u00edvel para o comprimento do bloco (N\/mm\u00b2)<\/p>\n<p>&nbsp;<\/p>\n<p><em>Mais informa\u00e7\u00f5es:<\/em><\/p>\n<ul>\n<li><a href=\"https:\/\/www.federnshop.com\/de\/produkte\/druckfedern\/berechnung.html\" target=\"_blank\" rel=\"noopener noreferrer\">C\u00e1lculo online de molas de compress\u00e3o<\/a><\/li>\n<\/ul>\n<ul>\n<li><a href=\"https:\/\/www.federnshop.com\/de\/berechnung\/zugfedern.html\" target=\"_blank\" rel=\"noopener noreferrer\">C\u00e1lculo de molas de tra\u00e7\u00e3o online<\/a><\/li>\n<\/ul>\n<ul>\n<li><a href=\"https:\/\/blog.federnshop.com\/neues-federnberechnungsprogramm\/\">Programa de c\u00e1lculo de molas WinFSB 8<\/a><\/li>\n<\/ul>\n<ul>\n<li><a href=\"https:\/\/blog.federnshop.com\/zugfestigkeit-federwerkstoffe\/\">Resist\u00eancia \u00e0 tra\u00e7\u00e3o dos materiais das molas<\/a><\/li>\n<\/ul>\n<p>&nbsp;<\/p>","protected":false},"excerpt":{"rendered":"<p>Na conce\u00e7\u00e3o precisa de molas de compress\u00e3o e de tra\u00e7\u00e3o, o c\u00e1lculo da tens\u00e3o de cisalhamento \u00e9 uma parte essencial da verifica\u00e7\u00e3o da resist\u00eancia. Esta mostra o grau de solicita\u00e7\u00e3o a que o material da mola \u00e9 submetido pelas for\u00e7as<\/p>\n","protected":false},"author":4,"featured_media":3228,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[482,766,907],"tags":[598,594,596,595,599,600,597],"class_list":["post-3236","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-conhecimento","category-industria-pt","category-molas-de-arame","tag-bergstraesser-pt-pt","tag-festigkeitsnachweis-pt-pt","tag-korrigierte-schubspannung-pt-pt","tag-schubspannung-pt-pt","tag-schubspannung-druckfedern-pt-pt","tag-schubspannung-zugfedern-pt-pt","tag-zulaessige-spannung-pt-pt"],"_links":{"self":[{"href":"https:\/\/blog.federnshop.com\/pt-pt\/wp-json\/wp\/v2\/posts\/3236","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.federnshop.com\/pt-pt\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.federnshop.com\/pt-pt\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.federnshop.com\/pt-pt\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.federnshop.com\/pt-pt\/wp-json\/wp\/v2\/comments?post=3236"}],"version-history":[{"count":6,"href":"https:\/\/blog.federnshop.com\/pt-pt\/wp-json\/wp\/v2\/posts\/3236\/revisions"}],"predecessor-version":[{"id":12730,"href":"https:\/\/blog.federnshop.com\/pt-pt\/wp-json\/wp\/v2\/posts\/3236\/revisions\/12730"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/blog.federnshop.com\/pt-pt\/wp-json\/wp\/v2\/media\/3228"}],"wp:attachment":[{"href":"https:\/\/blog.federnshop.com\/pt-pt\/wp-json\/wp\/v2\/media?parent=3236"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.federnshop.com\/pt-pt\/wp-json\/wp\/v2\/categories?post=3236"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.federnshop.com\/pt-pt\/wp-json\/wp\/v2\/tags?post=3236"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}