{"id":9218,"date":"2021-08-15T09:36:43","date_gmt":"2021-08-15T13:36:43","guid":{"rendered":"https:\/\/www.purdue.edu\/freeform\/me323\/?page_id=9218"},"modified":"2025-09-05T10:03:10","modified_gmt":"2025-09-05T14:03:10","slug":"torsion-shear-stress-strain-and-twist-angle","status":"publish","type":"page","link":"https:\/\/www.purdue.edu\/freeform\/me323\/animations-and-demonstrations\/torsion-shear-stress-strain-and-twist-angle\/","title":{"rendered":"Torsion: shear stress\/strain and twist angle"},"content":{"rendered":"

Circular shaft experiencing an axial torque<\/strong><\/em><\/span><\/p>\n

\"\"<\/p>\n

A solid, circular cross-sectioned shaft experiences an axial torque T<\/em>, as shown above.<\/p>\n

Angle of twist
\n<\/strong><\/em>The hypothesis used in developing the stress and strain in the shaft is that all points on a cross-section of the shaft experience the same angle of twist. The angle of twist for a section of length L is given by the equation shown below.<\/span><\/span><\/p>\n

<\/p>\n

The animation shown below demonstrates the geometry of deformation of the shaft under the load of the torque.<\/p>\n

<\/p>\n

A freeze-frame of the twisting of the shaft is shown below.<\/p>\n

<\/p>\n

 <\/p>\n

Stress distribution on the shaft cross-section<\/strong><\/em><\/span>
\nFor the solid cross-section shaft with material homogeneity on the cross-section, the both the shear strain and shear stress vary linearly with radial position on the cross-section, as shown below.<\/p>\n

<\/p>\n

 <\/p>\n

Stress element for points on the cross-section
\n<\/strong><\/em><\/span>For point “a” on the cross-section, the shear stress on the x<\/em>-face points in the positive z<\/em>-direction. For point “b” on the cross-section, the shear stress on the x<\/em>-face points in the negative\u00a0y<\/em>-direction. The corresponding stress elements for these two points are shown below.<\/span><\/span><\/p>\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

Circular shaft experiencing an axial torque A solid, circular cross-sectioned shaft experiences an axial torque T, as shown above. Angle of twist The hypothesis used in developing the stress and strain in the shaft is that all points on a cross-section of the shaft experience the same angle of twist. The angle of twist for … Continue reading Torsion: shear stress\/strain and twist angle<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":10,"featured_media":0,"parent":5074,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-9218","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.purdue.edu\/freeform\/me323\/wp-json\/wp\/v2\/pages\/9218","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.purdue.edu\/freeform\/me323\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.purdue.edu\/freeform\/me323\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/me323\/wp-json\/wp\/v2\/users\/10"}],"replies":[{"embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/me323\/wp-json\/wp\/v2\/comments?post=9218"}],"version-history":[{"count":6,"href":"https:\/\/www.purdue.edu\/freeform\/me323\/wp-json\/wp\/v2\/pages\/9218\/revisions"}],"predecessor-version":[{"id":16343,"href":"https:\/\/www.purdue.edu\/freeform\/me323\/wp-json\/wp\/v2\/pages\/9218\/revisions\/16343"}],"up":[{"embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/me323\/wp-json\/wp\/v2\/pages\/5074"}],"wp:attachment":[{"href":"https:\/\/www.purdue.edu\/freeform\/me323\/wp-json\/wp\/v2\/media?parent=9218"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}