{"id":342,"date":"2021-04-18T22:30:12","date_gmt":"2021-04-19T02:30:12","guid":{"rendered":"http:\/\/pressbooks.library.upei.ca\/statics\/?post_type=chapter&p=342"},"modified":"2025-07-17T11:56:18","modified_gmt":"2025-07-17T15:56:18","slug":"5-4-zero-force-members","status":"publish","type":"chapter","link":"https:\/\/pressbooks.library.upei.ca\/statics\/chapter\/5-4-zero-force-members\/","title":{"raw":"5.4 Zero-Force Members","rendered":"5.4 Zero-Force Members"},"content":{"raw":"This is a special case that is especially useful for the method of joints and the method of sections. These special types of members, called zero-force members, ensure the truss stays in a particular shape as a rigid body, but carries no load.\r\n\r\nZero-force members are members that you can tell just by inspection carry no load. They are important to the structure to ensure it stays in a rigid shape.\r\n\r\nZero-force members can be found by considering the equilibrium equations. Look at the joint E below. In the y direction, there is only 1 force: Feh<\/sub>. So if the sum of the forces in the y direction [latex]\r\n\\sum F_{y}\r\n[\/latex]= 0, then Feh<\/sub> = 0. Similarly, Fmk <\/sub>and Fcp<\/sub> are zero-force members (if you look at joint m and c). Note that if you looked at joint k or p, you couldn't tell that Fmk <\/sub>and Fcp<\/sub> are zero-force members.\r\n\r\n \r\n\r\n[caption id=\"attachment_1383\" align=\"aligncenter\" width=\"489\"]\"Labeled Adapted from original source: https:\/\/demo.webwork.rochester.edu\/webwork2_files\/tmp\/daemon_course\/images\/4cbba3a2-d72c-3d22-bba6-f6856747dafd___50b8ddcf-dab2-3209-b817-0ab27426a1d4.png[\/caption]\r\n\r\nThere isn't a huge problem if you can't find zero-force members just from inspection, but you might find that certain joints are not able to be solved as easily. (Zero-force members let you have one less unknown.)\r\n\r\nAlso, see that L and G have no zero-force members because the externally applied loads balance the members.\r\n\r\nHere are some examples to practice on:\r\n

Example 1<\/h4>\r\n[caption id=\"attachment_1384\" align=\"aligncenter\" width=\"1024\"]\"Camelback Source: https:\/\/commons.wikimedia.org\/wiki\/File:Camelback-truss.svg[\/caption]\r\n\r\n \r\n\r\n(I count 3 zero-force members, assuming there are no loads on the bridge at the joints).\r\n

Example 2<\/h4>\r\n[caption id=\"attachment_1385\" align=\"aligncenter\" width=\"640\"]\"Bowstring Source: https:\/\/commons.wikimedia.org\/wiki\/File:Bowstring-truss.svg[\/caption]\r\n\r\n(I count 1 zero-force member, assuming there are no loads on the bridge at the joints.)\r\n

Example 3<\/h4>\r\n[caption id=\"attachment_1386\" align=\"aligncenter\" width=\"1024\"]\"Train Source: https:\/\/pxhere.com\/en\/photo\/995729[\/caption]\r\n\r\n(Looking at only 1 side of the bridge, in theory there are 7 zero-force members, but because there is a load on the deck it is more likely that all of them would be carrying a load).\r\n\r\nAdmittedly, zero-force members are more theoretical than actual.\r\n
\r\n

Key Takeaways<\/p>\r\n\r\n<\/header>\r\n

\r\n\r\nBasically<\/em>: Zero-force members are two-force members that do not carry any load but help keep the structure into a certain shape.\r\n\r\nApplication:<\/em> In trusses.\r\n\r\nLooking ahead: <\/em>We will talk about this again in sections 1.3 on vectors and in section 1.4 and 1.5 on dot products and cross products.\r\n\r\n<\/div>\r\n<\/div>","rendered":"

This is a special case that is especially useful for the method of joints and the method of sections. These special types of members, called zero-force members, ensure the truss stays in a particular shape as a rigid body, but carries no load.<\/p>\n

Zero-force members are members that you can tell just by inspection carry no load. They are important to the structure to ensure it stays in a rigid shape.<\/p>\n

Zero-force members can be found by considering the equilibrium equations. Look at the joint E below. In the y direction, there is only 1 force: Feh<\/sub>. So if the sum of the forces in the y direction [latex]\\sum F_{y}[\/latex]= 0, then Feh<\/sub> = 0. Similarly, Fmk <\/sub>and Fcp<\/sub> are zero-force members (if you look at joint m and c). Note that if you looked at joint k or p, you couldn’t tell that Fmk <\/sub>and Fcp<\/sub> are zero-force members.<\/p>\n

 <\/p>\n

\"Labeled
Adapted from original source: https:\/\/demo.webwork.rochester.edu\/webwork2_files\/tmp\/daemon_course\/images\/4cbba3a2-d72c-3d22-bba6-f6856747dafd___50b8ddcf-dab2-3209-b817-0ab27426a1d4.png<\/figcaption><\/figure>\n

There isn’t a huge problem if you can’t find zero-force members just from inspection, but you might find that certain joints are not able to be solved as easily. (Zero-force members let you have one less unknown.)<\/p>\n

Also, see that L and G have no zero-force members because the externally applied loads balance the members.<\/p>\n

Here are some examples to practice on:<\/p>\n

Example 1<\/h4>\n
\"Camelback
Source: https:\/\/commons.wikimedia.org\/wiki\/File:Camelback-truss.svg<\/figcaption><\/figure>\n

 <\/p>\n

(I count 3 zero-force members, assuming there are no loads on the bridge at the joints).<\/p>\n

Example 2<\/h4>\n
\"Bowstring
Source: https:\/\/commons.wikimedia.org\/wiki\/File:Bowstring-truss.svg<\/figcaption><\/figure>\n

(I count 1 zero-force member, assuming there are no loads on the bridge at the joints.)<\/p>\n

Example 3<\/h4>\n
\"Train
Source: https:\/\/pxhere.com\/en\/photo\/995729<\/figcaption><\/figure>\n

(Looking at only 1 side of the bridge, in theory there are 7 zero-force members, but because there is a load on the deck it is more likely that all of them would be carrying a load).<\/p>\n

Admittedly, zero-force members are more theoretical than actual.<\/p>\n

\n
\n

Key Takeaways<\/p>\n<\/header>\n

\n

Basically<\/em>: Zero-force members are two-force members that do not carry any load but help keep the structure into a certain shape.<\/p>\n

Application:<\/em> In trusses.<\/p>\n

Looking ahead: <\/em>We will talk about this again in sections 1.3 on vectors and in section 1.4 and 1.5 on dot products and cross products.<\/p>\n<\/div>\n<\/div>\n","protected":false},"author":60,"menu_order":4,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-342","chapter","type-chapter","status-publish","hentry"],"part":58,"_links":{"self":[{"href":"https:\/\/pressbooks.library.upei.ca\/statics\/wp-json\/pressbooks\/v2\/chapters\/342","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.library.upei.ca\/statics\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.library.upei.ca\/statics\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.library.upei.ca\/statics\/wp-json\/wp\/v2\/users\/60"}],"version-history":[{"count":9,"href":"https:\/\/pressbooks.library.upei.ca\/statics\/wp-json\/pressbooks\/v2\/chapters\/342\/revisions"}],"predecessor-version":[{"id":2762,"href":"https:\/\/pressbooks.library.upei.ca\/statics\/wp-json\/pressbooks\/v2\/chapters\/342\/revisions\/2762"}],"part":[{"href":"https:\/\/pressbooks.library.upei.ca\/statics\/wp-json\/pressbooks\/v2\/parts\/58"}],"metadata":[{"href":"https:\/\/pressbooks.library.upei.ca\/statics\/wp-json\/pressbooks\/v2\/chapters\/342\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.library.upei.ca\/statics\/wp-json\/wp\/v2\/media?parent=342"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.library.upei.ca\/statics\/wp-json\/pressbooks\/v2\/chapter-type?post=342"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.library.upei.ca\/statics\/wp-json\/wp\/v2\/contributor?post=342"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.library.upei.ca\/statics\/wp-json\/wp\/v2\/license?post=342"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}