{"id":3219,"date":"2024-03-22T17:25:45","date_gmt":"2024-03-22T15:25:45","guid":{"rendered":"https:\/\/blog.federnshop.com\/schubspannung-berechnen-englisch\/"},"modified":"2026-10-01T10:18:36","modified_gmt":"2026-10-01T08:18:36","slug":"schubspannung-berechnen-englisch","status":"publish","type":"post","link":"https:\/\/blog.federnshop.com\/en\/schubspannung-berechnen-englisch\/","title":{"rendered":"Calculating Shear Stress in Compression and Tension Springs"},"content":{"rendered":"<p>In the precise design of compression springs and tension springs, the calculation of shear stress is a central component of <a href=\"https:\/\/blog.federnshop.com\/en\/function-and-strength-verification-for-compression-springs\/\" target=\"_blank\" rel=\"noopener\">the strength analysis<\/a>. It indicates the extent to which the spring material is stressed by the applied forces and thus forms an important basis for the spring\u2019s mechanical load-bearing capacity, operational reliability, and service life. In compression springs, the axially acting compressive force in the spring wire is essentially converted into torsional stress.<\/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\/en\/schubspannung-berechnen-englisch\/#Shear_stress_for_compression_springs\" >Shear stress for compression springs<\/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\/en\/schubspannung-berechnen-englisch\/#Shear_stress_compression_spring_from_force\" >Shear stress compression spring from force:<\/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\/en\/schubspannung-berechnen-englisch\/#Shear_stress_Compression_spring_from_displacement\" >Shear stress Compression spring from displacement:<\/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\/en\/schubspannung-berechnen-englisch\/#Corrected_shear_stress_compression_spring\" >Corrected shear stress compression spring:<\/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\/en\/schubspannung-berechnen-englisch\/#Permissible_tension_of_compression_spring\" >Permissible tension of compression spring:<\/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\/en\/schubspannung-berechnen-englisch\/#Shear_stress_for_tension_springs\" >Shear stress for tension springs<\/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\/en\/schubspannung-berechnen-englisch\/#Shear_stress\" >Shear stress:<\/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\/en\/schubspannung-berechnen-englisch\/#Corrected_shear_stress\" >Corrected shear stress:<\/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\/en\/schubspannung-berechnen-englisch\/#Allowable_stress\" >Allowable stress:<\/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\/en\/schubspannung-berechnen-englisch\/#Explanation_of_Formula_Symbols\" >Explanation of Formula Symbols<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"Text\"><span class=\"ez-toc-section\" id=\"Shear_stress_for_compression_springs\"><\/span>Shear stress for compression springs<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> In compression springs, the axially acting compressive force in the spring wire is essentially converted into a torsional stress. Under a static or quasi-static load on a compression spring, the resulting shear stress \u03c4 is calculated as follows.<\/p>\n<h4 class=\"Text\"><span class=\"ez-toc-section\" id=\"Shear_stress_compression_spring_from_force\"><\/span>Shear stress compression spring from force:<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=\"Shear_stress_Compression_spring_from_displacement\"><\/span>Shear stress Compression spring from displacement:<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>When a compression spring is subjected to dynamic loading<sub>, <\/sub> the corrected shear stress<sub>\u03c4k <\/sub> applies<sub>. <\/sub> The shear stress distribution across a spring\u2019s wire cross-section is uneven; the highest stress occurs at the spring\u2019s inner diameter. The maximum stress can be approximated using the stress correction factor k, which depends on the coil ratio (ratio of the mean diameter to the wire diameter) of the spring. For springs subjected to dynamic loading, the following applies:<\/p>\n<h4 class=\"Text\"><span class=\"ez-toc-section\" id=\"Corrected_shear_stress_compression_spring\"><\/span>Corrected shear stress compression spring:<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\">where the following holds for k (according to 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>Now the comparison is made with the permissible voltage.<\/p>\n<h4 class=\"Text\"><span class=\"ez-toc-section\" id=\"Permissible_tension_of_compression_spring\"><\/span>Permissible tension of compression spring:<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>or.<\/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>The values for the<a href=\"https:\/\/blog.federnshop.com\/zugfestigkeit-federwerkstoffe\/\" target=\"_blank\" rel=\"noopener noreferrer\">Minimum tensile strength R<sub> m<\/sub><\/a> are dependent on the wire thickness and can be found in the standards of the corresponding materials.<\/p>\n<p>As a rule, it must be possible to compress compression springs up to the block length, which is why the permissible stress for the block length is t czul to consider.<\/p>\n<p class=\"Text\">Under <a href=\"https:\/\/blog.federnshop.com\/en\/fatigue-strength\/\">dynamic loading<\/a>, the lower and upper stresses (<sub>tk1<\/sub>and<sub>tk2<\/sub>) of the corresponding stroke must be determined. The difference is the stroke stress. Neither the upper stress nor the stroke stress may exceed the corresponding allowable values. These values can be found in the <a href=\"https:\/\/www.beuth.de\/de\/norm\/din-en-13906-1\/189797622\" target=\"_blank\" rel=\"noopener noreferrer\">fatigue strength diagrams of EN 13906-1:2002<\/a>. If the stresses satisfy this comparison, the spring is fatigue-resistant with a limit load cycle of<sup>10\u2077<\/sup>.<\/p>\n<p>&nbsp;<\/p>\n<h2 class=\"Text\"><span class=\"ez-toc-section\" id=\"Shear_stress_for_tension_springs\"><\/span>Shear stress for tension springs<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> When a tension spring is subjected to a static or quasi-static load, the existing shear stress \u03c4 is calculated as follows.<\/p>\n<h4 class=\"Text\"><span class=\"ez-toc-section\" id=\"Shear_stress\"><\/span>Shear stress:<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>When a tension spring is subjected to dynamic loading, no universally applicable fatigue strength values can be specified, as additional stresses may occur at the bends of the eyes, some of which may exceed the permissible stress levels. <a href=\"https:\/\/blog.federnshop.com\/en\/types-of-stress-extension-springs\/\">Tension springs should therefore be subjected to static loads whenever possible<\/a>. If dynamic loading cannot be avoided, bent-on <a href=\"https:\/\/blog.federnshop.com\/en\/eyelet-shapes-extension-springs\/\">eyes<\/a> should be avoided, and rolled or screwed-in end pieces should be used instead. It is advisable to conduct a service life test under the intended operating conditions. <a href=\"https:\/\/blog.federnshop.com\/en\/ball-blasting-of-metal-springs\/\">Surface hardening by shot peening<\/a> is not feasible due to the closely spaced coils.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Corrected_shear_stress\"><\/span>Corrected shear stress:<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=\"Allowable_stress\"><\/span>Allowable stress:<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>The existing maximum stress<sub>tn<\/sub> at the maximum spring travel<sub>sn<\/sub> is set equal to the allowable stress. However, to avoid <a href=\"https:\/\/blog.federnshop.com\/en\/relaxation-for-springs\/\">relaxation<\/a>, only 80% of this spring travel should be utilized in practice.<\/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=\"Explanation_of_Formula_Symbols\"><\/span>Explanation of Formula Symbols<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>d = Wire diameter (mm)<br \/>\nD = Mean coil diameter (mm)<br \/>\nF = Spring force (N)<br \/>\nG = Shear modulus (N\/mm\u00b2)<br \/>\nn = Number of active coils (units)<br \/>\nRm = Minimum tensile strength (N\/mm\u00b2)<br \/>\ns = Spring travel (mm)<br \/>\n\u03c4 = Shear stress (N\/mm\u00b2)<br \/>\n\u03c4zul = Allowable shear stress (N\/mm\u00b2)<br \/>\n\u03c4czul = Allowable shear stress at block length (N\/mm\u00b2)<\/p>\n<p>&nbsp;<\/p>\n<p><em>For more information:<\/em><\/p>\n<ul>\n<li><a href=\"https:\/\/www.federnshop.com\/de\/produkte\/druckfedern\/berechnung.html\" target=\"_blank\" rel=\"noopener noreferrer\">Compression spring calculation online<\/a><\/li>\n<\/ul>\n<ul>\n<li><a href=\"https:\/\/www.federnshop.com\/de\/berechnung\/zugfedern.html\" target=\"_blank\" rel=\"noopener noreferrer\">Online Tension Spring Calculator<\/a><\/li>\n<\/ul>\n<ul>\n<li><a href=\"https:\/\/blog.federnshop.com\/neues-federnberechnungsprogramm\/\">WinFSB 8 Spring Calculation Program<\/a><\/li>\n<\/ul>\n<ul>\n<li><a href=\"https:\/\/blog.federnshop.com\/zugfestigkeit-federwerkstoffe\/\">Tensile Strength of Spring Materials<\/a><\/li>\n<\/ul>\n<p>&nbsp;<\/p>","protected":false},"excerpt":{"rendered":"<p>In the precise design of compression springs and tension springs, the calculation of shear stress is a central component of the strength analysis. It indicates the extent to which the spring material is stressed by the applied forces and thus<\/p>\n","protected":false},"author":4,"featured_media":3220,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[550,457,857],"tags":[555,551,553,552,556,557,554],"class_list":["post-3219","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-industry-en","category-knowledge","category-wire-springs","tag-bergstraesser-en","tag-festigkeitsnachweis-en","tag-korrigierte-schubspannung-en","tag-schubspannung-en","tag-schubspannung-druckfedern-en","tag-schubspannung-zugfedern-en","tag-zulaessige-spannung-en"],"_links":{"self":[{"href":"https:\/\/blog.federnshop.com\/en\/wp-json\/wp\/v2\/posts\/3219","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.federnshop.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.federnshop.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.federnshop.com\/en\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.federnshop.com\/en\/wp-json\/wp\/v2\/comments?post=3219"}],"version-history":[{"count":13,"href":"https:\/\/blog.federnshop.com\/en\/wp-json\/wp\/v2\/posts\/3219\/revisions"}],"predecessor-version":[{"id":12724,"href":"https:\/\/blog.federnshop.com\/en\/wp-json\/wp\/v2\/posts\/3219\/revisions\/12724"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/blog.federnshop.com\/en\/wp-json\/wp\/v2\/media\/3220"}],"wp:attachment":[{"href":"https:\/\/blog.federnshop.com\/en\/wp-json\/wp\/v2\/media?parent=3219"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.federnshop.com\/en\/wp-json\/wp\/v2\/categories?post=3219"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.federnshop.com\/en\/wp-json\/wp\/v2\/tags?post=3219"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}