{"id":2973,"date":"2018-07-02T14:19:50","date_gmt":"2018-07-02T14:19:50","guid":{"rendered":"http:\/\/buildsoftsupport.com\/?post_type=ht_kb&#038;p=2973"},"modified":"2025-09-04T09:45:27","modified_gmt":"2025-09-04T09:45:27","slug":"what-is-the-difference-between-a-1st-and-a-2nd-order-calculation","status":"publish","type":"ht_kb","link":"https:\/\/support.buildsoft.eu\/es\/knowledge-base\/what-is-the-difference-between-a-1st-and-a-2nd-order-calculation\/","title":{"rendered":"What is the difference between a 1st and a 2nd order calculation"},"content":{"rendered":"<p>We perfer to explain the difference using an example:<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"size-large wp-image-3009 aligncenter\" src=\"http:\/\/buildsoftsupport.com\/wp-content\/uploads\/2018\/07\/12order.jpg\" alt=\"\" width=\"643\" height=\"313\" \/><\/p>\n<ul>\n<li>Figure A = <strong>intitial<\/strong> <strong>state<br \/>\n<\/strong>A column loaded with a bending moment M and a point load P needs to be calculated.<\/li>\n<li>Figure B = <strong>iteration<\/strong> <strong>1<br \/>\n<\/strong>Using the geometry and supports, the reactions M<sub>0<\/sub> and deformation\u00a0\u03b4<sub>0<\/sub> can be calculated.<\/li>\n<li>Figure C= <strong>iteration<\/strong> <strong>2<br \/>\n<\/strong>You could stop the calculations at this point, but because of the deformation \u03b4<sub>0<\/sub>, the load P has an eccentricity of \u03b4<sub>0<\/sub>.<br \/>\nResulting in an additional moment \u0394M<sub>1<\/sub>. Increasing the total moment M<sub>1<\/sub>\u00a0=\u00a0M<sub>0<\/sub>\u00a0+\u00a0\u0394M<sub>1<\/sub>.<br \/>\nResulting in additional deformation \u0394\u03b4<sub>1<\/sub>. Increasing the total deformation \u03b4<sub>1<\/sub>\u00a0=\u00a0\u03b4<sub>0<\/sub>\u00a0+\u00a0\u0394\u03b4<sub>1<\/sub>.<\/li>\n<li>Figure D = <strong>iteration 3<br \/>\n<\/strong>Again you could stop the calculation but because of the additional deformation \u0394\u03b4<sub>1<\/sub>, the load P has an additional eccentricity ().<br \/>\nResulting in an additional moment \u0394M<sub>2<\/sub>. Increasing the total moment M<sub>2<\/sub>\u00a0=\u00a0M<sub>1<\/sub>\u00a0+\u00a0\u0394M<sub>2<\/sub>.<br \/>\nResulting in additional deformation \u0394\u03b4<sub>2<\/sub>. Increasing the total deformation \u03b4<sub>2<\/sub>\u00a0=\u00a0\u03b4<sub>1<\/sub>\u00a0+\u00a0\u0394\u03b4<sub>2<\/sub>.<\/li>\n<li>You could continue the calculation and do an additional iteration, but it will almost not affect the final result.\u00a0\u0394\u03b4<sub>2<\/sub>\u00a0has become quite small during iteration 3, that the affect of\u00a0\u0394\u03b4<sub>2<\/sub> will be neglectable. You stop the calculations.<\/li>\n<\/ul>\n<p>Conclusions:<\/p>\n<ul>\n<li>The calculation in &#8216;Iteration 1&#8217; is called a <span style=\"text-decoration: underline;\"><strong>first order calculation<\/strong>.<\/span><br \/>\nEquilibrium expressed as function of the\u00a0<b>initial geometry<\/b>.<br \/>\nIf the boundary conditions are adequately defined (= you didn&#8217;t make a mechanism), <strong>a solution\/ equilibrium will always be found<\/strong>.<br \/>\nBecause of the simplicity, this type of calculation is used in <strong>hand calculations<\/strong>.<\/li>\n<li>The calculation from &#8216;Iteration 1&#8217; to &#8216;Iteration 3) is called <span style=\"text-decoration: underline;\"><strong>a second order calculation<\/strong>.<\/span><br \/>\nEquilibrium expressed as function of the <b>a priori unknown deformation state.<br \/>\n<\/b>Results in larger internal forces and additional deformations relative to a 1st order calculation. The additional effects are called \u2018<a href=\"https:\/\/support.buildsoft.eu\/knowledge-base\/what-are-second-order-effects\/\" target=\"_blank\" rel=\"noopener\"><strong>second order effects<\/strong><\/a>\u2019.<b><br \/>\n<\/b>Even if the boundary conditions are adequately defined, <b><b>a solution\/ equilibrium might not always be found. <\/b><\/b>For some structures the deformations and internal forces will keep increasing until it collapses.<b><br \/>\n<\/b>Because of its complexity, this type of calculation is done<b> by software.<br \/>\n<\/b><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>We perfer to explain the difference using an example: Figure A = intitial state A column loaded with a bending moment M and a point load P needs to be calculated. Figure B = iteration 1 Using the geometry and supports, the reactions M0 and deformation\u00a0\u03b40 can be calculated. Figure&#8230;<\/p>\n","protected":false},"author":3,"comment_status":"closed","ping_status":"closed","template":"","format":"standard","meta":[],"ht-kb-category":[62],"ht-kb-tag":[],"_links":{"self":[{"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/ht-kb\/2973"}],"collection":[{"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/ht-kb"}],"about":[{"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/types\/ht_kb"}],"author":[{"embeddable":true,"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/comments?post=2973"}],"version-history":[{"count":3,"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/ht-kb\/2973\/revisions"}],"predecessor-version":[{"id":23873,"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/ht-kb\/2973\/revisions\/23873"}],"wp:attachment":[{"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/media?parent=2973"}],"wp:term":[{"taxonomy":"ht_kb_category","embeddable":true,"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/ht-kb-category?post=2973"},{"taxonomy":"ht_kb_tag","embeddable":true,"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/ht-kb-tag?post=2973"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}