{"id":1379,"date":"2024-09-23T14:58:53","date_gmt":"2024-09-23T12:58:53","guid":{"rendered":"https:\/\/solveredu.com\/?p=1379"},"modified":"2026-01-27T23:40:09","modified_gmt":"2026-01-27T22:40:09","slug":"truss-calculation-method-of-joints-example-solutions","status":"publish","type":"post","link":"https:\/\/solveredu.com\/en\/post\/kratownice-metoda-rownowazenia-wezlow-przykladowe-zadania\/","title":{"rendered":"Truss calculation method of joints - example solutions"},"content":{"rendered":"<p class=\"wp-block-paragraph\" id=\"foo\">In this article you will learn how to calculate the forces in the members of a statically determinate truss using the method of joints.<\/p>\n\n\n\n<ol id=\"iwmbp3uhy3fggp17945259\" class=\"wp-block-list\">\n<li><a href=\"#1qctj\">Method of joints<\/a><\/li>\n\n\n\n<li><a href=\"#xvw3h143749\">Truss solution manual<\/a><\/li>\n\n\n\n<li><a href=\"#igszs30304\">Method of Joints - example solution of the task<\/a><\/li>\n<\/ol>\n\n\n\n<h1 id=\"1qctj\" class=\"wp-block-heading has-large-font-size\">Method of joints<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"jkoif985\"><strong>Method of joints<\/strong> is one of the methods used to solve truss tasks. It is an analytical method considered by many to be the easiest, but at the same time it is labor-intensive with a lot of calculations, especially if the truss has a large number of nodes and members.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"9b0514675\">Other methods include:<\/p>\n\n\n\n<ul id=\"i6fzh3uhy3fggp17945268\" class=\"wp-block-list\">\n<li>Ritter's analytical-diagram method<\/li>\n\n\n\n<li>Cremona method - plotting<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"5bz3j6100\">The method involves calculating the normal forces in the bars of a truss by successively separating the nodes ( that is, the points at which the bars come together).<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>It is important that the node we calculate has a <strong>maximum two bars<\/strong> For which we do not know the normal forces. Since we have two equilibrium equations (horizontal forces and vertical forces), we can calculate up to two unknown forces from these equations.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 id=\"xvw3h143749\" class=\"wp-block-heading has-medium-font-size\">Truss solution manual<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"ya7my143661\">Below you will find the recipe, instructions in points for solving the truss:<\/p>\n\n\n\n<ol id=\"b0uhr3uhy3fggp17945292\" class=\"wp-block-list\">\n<li><em>Designation of nodes - consecutive numbers (1,2,3...) or letters of the alphabet (A,B,C...)<\/em><\/li>\n\n\n\n<li><em>Designation of bars - usually consecutive digits (1,2,3...)<\/em><\/li>\n\n\n\n<li><em>Determination of reaction in supports<\/em><\/li>\n\n\n\n<li><em>Calculation of support reactions from equilibrium equations (Fx, Fy, Mi)<\/em><\/li>\n\n\n\n<li><em>Separation of nodes and calculation of forces in rods from equilibrium equations (Fx, Fy)<\/em><\/li>\n\n\n\n<li><em>Check for the last node - optional<\/em><\/li>\n\n\n\n<li><em>Summary in the table (Rod No. -&gt; Normal force).<\/em><\/li>\n\n\n\n<li>Drawing of the truss diagram with the values of the forces in the bars plotted<\/li>\n<\/ol>\n\n\n\n<h2 id=\"igszs30304\" class=\"wp-block-heading has-medium-font-size\">Method of Joints - example solution of the task<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"g4vew31777\">Below I have included a diagram of the truss we will solve. The truss consists of 6 nodes and 9 bars. It is loaded with three concentrated forces P1=2 kN, P2=6 kN and P3=3 kN.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"t77wp31885\">I have labeled the nodes with the numbers 1 through 6. In the supports, I have added the support reaction forces R1 for the sliding pivot support at node 1. H4 and V4 for the non-sliding pivot support at node 4. As a reminder, you will find the types of supports and support reactions in this <a href=\"https:\/\/solveredu.com\/en\/post\/support-reactions\/\" rel=\"noreferrer noopener\" target=\"_blank\"><u>entry<\/u><\/a><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"944\" height=\"497\" data-attachment-id=\"1382\" data-permalink=\"https:\/\/solveredu.com\/en\/post\/kratownice-metoda-rownowazenia-wezlow-przykladowe-zadania\/przyklad-1\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-1-1.jpg?fit=944%2C497&amp;ssl=1\" data-orig-size=\"944,497\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"przyklad 1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-1-1.jpg?fit=944%2C497&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-1-1.jpg?resize=944%2C497&#038;ssl=1\" alt=\"Trusses method of balancing nodes-example tasks, SolverEdu\" class=\"wp-image-1382\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-1-1.jpg?w=944&amp;ssl=1 944w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-1-1.jpg?resize=300%2C158&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-1-1.jpg?resize=768%2C404&amp;ssl=1 768w\" sizes=\"auto, (max-width: 944px) 100vw, 944px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"jugqt33923\">In the next step, we will calculate the support reactions from the three equilibrium equations.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"614\" height=\"285\" data-attachment-id=\"1384\" data-permalink=\"https:\/\/solveredu.com\/en\/post\/kratownice-metoda-rownowazenia-wezlow-przykladowe-zadania\/przyklad-2-2\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-2.jpg?fit=614%2C285&amp;ssl=1\" data-orig-size=\"614,285\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1721933118&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"przyklad 2\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-2.jpg?fit=614%2C285&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-2.jpg?resize=614%2C285&#038;ssl=1\" alt=\"Reactions,Trusses method of balancing nodes-example tasks, SolverEdu\" class=\"wp-image-1384\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-2.jpg?w=614&amp;ssl=1 614w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-2.jpg?resize=300%2C139&amp;ssl=1 300w\" sizes=\"auto, (max-width: 614px) 100vw, 614px\" \/><\/figure>\n\n\n\n<figure style=\"font-size:clamp(14px, 0.875rem + ((1vw - 3.2px) * 0.536), 20px);\" class=\"wp-block-table\"><table class=\"has-theme-5-background-color has-text-color has-background has-link-color has-fixed-layout\" style=\"color:#ffffff\"><tbody><tr><td>All examples used in this post were created in my <a href=\"https:\/\/solveredu.com\/en\/truss-calculator\/\" target=\"_blank\" rel=\"noreferrer noopener\"><u>Truss Calculator<\/u><\/a>. In this application you will determine support reactions and normal forces in truss members. Step-by-step calculations, drawings of forces at each node and analytical calculation. Try it !<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"4wl6557584\">Once we have calculated the values of the support reactions, we can proceed to the next step, which is to separate the nodes. In our case, we will start with node No. 1. In this node we have two unknown bars bar N1-5 and N1-2. The angle of 45 degrees is due to the geometry of the bar system.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Node 1<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"472\" height=\"736\" data-attachment-id=\"1386\" data-permalink=\"https:\/\/solveredu.com\/en\/post\/kratownice-metoda-rownowazenia-wezlow-przykladowe-zadania\/przyklad-3\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-3.jpg?fit=472%2C736&amp;ssl=1\" data-orig-size=\"472,736\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1721933137&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"przyklad 3\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-3.jpg?fit=472%2C736&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-3.jpg?resize=472%2C736&#038;ssl=1\" alt=\"Node , Trusses method of balancing nodes-example tasks, SolverEdu\" class=\"wp-image-1386\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-3.jpg?w=472&amp;ssl=1 472w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-3.jpg?resize=192%2C300&amp;ssl=1 192w\" sizes=\"auto, (max-width: 472px) 100vw, 472px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"ld1za72837\">The figure above shows the drawing of forces for node 1 and the calculation of forces in bars 1-2 and 1-5. These forces are calculated from the equilibrium conditions <strong>sum of horizontal force projections<\/strong> and <strong>sum of vertical force projections<\/strong> must be zero. Bar 1-2 is stretched because the value of the force is positive. On the other hand, bar 1-5 is compressed because the value of the force is negative.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"ok96296824\">The next node we will deal with is node 4. At this node we also have two unknown forces for bar 4-3 and 4-6. Also we use the equilibrium conditions sum of the projections of horizontal forces and sum of the projections of vertical forces.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Node 4<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"501\" height=\"717\" data-attachment-id=\"1387\" data-permalink=\"https:\/\/solveredu.com\/en\/post\/kratownice-metoda-rownowazenia-wezlow-przykladowe-zadania\/przyklad-4\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-4.jpg?fit=501%2C717&amp;ssl=1\" data-orig-size=\"501,717\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1721933161&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"przyklad 4\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-4.jpg?fit=501%2C717&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-4.jpg?resize=501%2C717&#038;ssl=1\" alt=\"Node , Trusses method of balancing nodes-example tasks, SolverEdu\" class=\"wp-image-1387\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-4.jpg?w=501&amp;ssl=1 501w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-4.jpg?resize=210%2C300&amp;ssl=1 210w\" sizes=\"auto, (max-width: 501px) 100vw, 501px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>When drawing the forces for subsequent nodes, remember the reactions or external forces applied to the node. A common mistake in node balancing solutions is to omit these forces.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"68m4b112645\">We proceed in the same way with the next nodes, remembering that the maximum number of unknown forces in the bar is two.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Node 3<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"447\" height=\"616\" data-attachment-id=\"1388\" data-permalink=\"https:\/\/solveredu.com\/en\/post\/kratownice-metoda-rownowazenia-wezlow-przykladowe-zadania\/przyklad-5\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-5.jpg?fit=447%2C616&amp;ssl=1\" data-orig-size=\"447,616\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1721933182&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"przyklad 5\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-5.jpg?fit=447%2C616&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-5.jpg?resize=447%2C616&#038;ssl=1\" alt=\"Node , Trusses method of balancing nodes-example tasks, SolverEdu\" class=\"wp-image-1388\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-5.jpg?w=447&amp;ssl=1 447w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-5.jpg?resize=218%2C300&amp;ssl=1 218w\" sizes=\"auto, (max-width: 447px) 100vw, 447px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Node 2<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"504\" height=\"626\" data-attachment-id=\"1390\" data-permalink=\"https:\/\/solveredu.com\/en\/post\/kratownice-metoda-rownowazenia-wezlow-przykladowe-zadania\/przyklad-6\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-6.jpg?fit=504%2C626&amp;ssl=1\" data-orig-size=\"504,626\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1721933204&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"przyklad 6\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-6.jpg?fit=504%2C626&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-6.jpg?resize=504%2C626&#038;ssl=1\" alt=\"Node , Trusses method of balancing nodes-example tasks, SolverEdu\" class=\"wp-image-1390\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-6.jpg?w=504&amp;ssl=1 504w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-6.jpg?resize=242%2C300&amp;ssl=1 242w\" sizes=\"auto, (max-width: 504px) 100vw, 504px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Node 5<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"684\" height=\"753\" data-attachment-id=\"1392\" data-permalink=\"https:\/\/solveredu.com\/en\/post\/kratownice-metoda-rownowazenia-wezlow-przykladowe-zadania\/przyklad-7\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-7.jpg?fit=684%2C753&amp;ssl=1\" data-orig-size=\"684,753\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1721933283&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"przyklad 7\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-7.jpg?fit=684%2C753&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-7.jpg?resize=684%2C753&#038;ssl=1\" alt=\"Node , Trusses method of balancing nodes-example tasks, SolverEdu\" class=\"wp-image-1392\" style=\"width:499px;height:auto\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-7.jpg?w=684&amp;ssl=1 684w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-7.jpg?resize=273%2C300&amp;ssl=1 273w\" sizes=\"auto, (max-width: 684px) 100vw, 684px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"h0gos72632\">After calculating all the normal forces in the bars, we prepare tables with the bar-force combination in the bar - the mode of work tension\/compression.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"650\" height=\"479\" data-attachment-id=\"1393\" data-permalink=\"https:\/\/solveredu.com\/en\/post\/kratownice-metoda-rownowazenia-wezlow-przykladowe-zadania\/przyklad-8\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-8.jpg?fit=650%2C479&amp;ssl=1\" data-orig-size=\"650,479\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"przyklad 8\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-8.jpg?fit=650%2C479&amp;ssl=1\" src=\"https:\/\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-8_en.jpg\" alt=\"summary , Trusses method of balancing nodes-example tasks, SolverEdu\" class=\"wp-image-1393\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-8_en.jpg?w=642&ssl=1 642w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-8_en.jpg?resize=300%2C223&ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-8_en.jpg?resize=16%2C12&ssl=1 16w\" sizes=\"auto, (max-width: 650px) 100vw, 650px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">In addition, it is useful to draw the entire truss diagram with the values of the forces in the bars plotted. The red color denotes tension bars and the blue color denotes compression bars. The black color is zero bars - if they exist.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"823\" height=\"523\" data-attachment-id=\"2943\" data-permalink=\"https:\/\/solveredu.com\/en\/post\/kratownice-metoda-rownowazenia-wezlow-przykladowe-zadania\/rys\/\" data-orig-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/rys.jpg?fit=823%2C523&amp;ssl=1\" data-orig-size=\"823,523\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"rys\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/rys.jpg?fit=823%2C523&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/rys.jpg?resize=823%2C523&#038;ssl=1\" alt=\"Truss calculation, forces in bars on scjhemata, solveredu\" class=\"wp-image-2943\" srcset=\"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/rys.jpg?w=823&amp;ssl=1 823w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/rys.jpg?resize=300%2C191&amp;ssl=1 300w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/rys.jpg?resize=768%2C488&amp;ssl=1 768w, https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/rys.jpg?resize=18%2C12&amp;ssl=1 18w\" sizes=\"auto, (max-width: 823px) 100vw, 823px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"1pncc72034\">Here we will end the entry trusses method of balancing nodes- tasks<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"vx3iv149586\">Thank you.<\/p>","protected":false},"excerpt":{"rendered":"<p>W tym artykule dowiecie si\u0119, jak za pomoc\u0105 metody r\u00f3wnowa\u017cenia w\u0119z\u0142\u00f3w obliczy\u0107 si\u0142y w pr\u0119tach kratownicy statycznie wyznaczalnej. Metoda r\u00f3wnowa\u017cenia w\u0119z\u0142\u00f3w Metoda r\u00f3wnowa\u017cenia (wydzielania) w\u0119z\u0142\u00f3w jest jedn\u0105 z metod stosowanych do rozwi\u0105zywania zada\u0144 z zakresu kratownic. Jest to metoda analityczna przez wiele os\u00f3b uwa\u017cana za naj\u0142atwiejsz\u0105, ale przy tym pracoch\u0142onn\u0105, przy kt\u00f3rej jest du\u017co oblicze\u0144, [&hellip;]<\/p>\n","protected":false},"author":255930052,"featured_media":1488,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"_wpas_customize_per_network":false,"jetpack_post_was_ever_published":false},"categories":[14815],"tags":[14863,14864,14865],"class_list":["post-1379","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mechanika","tag-kratownica","tag-metoda-rownowazenia-wezlow","tag-sily-w-pretach-kratownicy"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/solveredu.com\/wp-content\/uploads\/2024\/09\/przyklad-1-2.jpg?fit=944%2C497&ssl=1","jetpack_shortlink":"https:\/\/wp.me\/pg3flK-mf","jetpack-related-posts":[],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/solveredu.com\/en\/wp-json\/wp\/v2\/posts\/1379","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/solveredu.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/solveredu.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/solveredu.com\/en\/wp-json\/wp\/v2\/users\/255930052"}],"replies":[{"embeddable":true,"href":"https:\/\/solveredu.com\/en\/wp-json\/wp\/v2\/comments?post=1379"}],"version-history":[{"count":12,"href":"https:\/\/solveredu.com\/en\/wp-json\/wp\/v2\/posts\/1379\/revisions"}],"predecessor-version":[{"id":3070,"href":"https:\/\/solveredu.com\/en\/wp-json\/wp\/v2\/posts\/1379\/revisions\/3070"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/solveredu.com\/en\/wp-json\/wp\/v2\/media\/1488"}],"wp:attachment":[{"href":"https:\/\/solveredu.com\/en\/wp-json\/wp\/v2\/media?parent=1379"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/solveredu.com\/en\/wp-json\/wp\/v2\/categories?post=1379"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/solveredu.com\/en\/wp-json\/wp\/v2\/tags?post=1379"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}