{"id":4256,"date":"2022-05-25T07:00:00","date_gmt":"2022-05-25T07:00:00","guid":{"rendered":"https:\/\/www.buildsoft.eu\/les-bases-dun-modele-danalyse-structurelle-la-schematisation-est-un-art\/"},"modified":"2026-07-22T14:54:18","modified_gmt":"2026-07-22T14:54:18","slug":"les-bases-dun-modele-danalyse-structurelle-la-schematisation-est-un-art","status":"publish","type":"post","link":"https:\/\/www.buildsoft.eu\/fr\/les-bases-dun-modele-danalyse-structurelle-la-schematisation-est-un-art\/","title":{"rendered":"Les bases d\u2019un mod\u00e8le d\u2019analyse structurelle &#8211; la sch\u00e9matisation est un art"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">Tout commence par le mod\u00e8le architectural et la sch\u00e9matisation<\/h2>\n\n<p>La sch\u00e9matisation consiste \u00e0 simplifier un b\u00e2timent r\u00e9el (le mod\u00e8le architectural) en un mod\u00e8le d&rsquo;analyse structurelle, aussi appel\u00e9 mod\u00e8le filaire ou mod\u00e8le m\u00e9canique, que le logiciel peut effectivement calculer. Cela veut dire id\u00e9aliser trois choses : la g\u00e9om\u00e9trie (lignes et plans du syst\u00e8me plut\u00f4t que la forme r\u00e9elle), les appuis (comment la structure se connecte au sol) et les assemblages (comment les \u00e9l\u00e9ments se connectent entre eux). Une erreur dans ces trois id\u00e9alisations se r\u00e9percute sur chaque calcul en aval. Nous d\u00e9taillons chacune ci-dessous, puis les appliquons \u00e0 un portique r\u00e9el dans Diamonds.<\/p>\n\n<p>Nous allons donc simplifier le mod\u00e8le architectural jusqu\u2019\u00e0 ce qu\u2019il ne reste que la structure porteuse. La structure porteuse transf\u00e8re les charges appliqu\u00e9es au sol. Les charges possibles qui s\u2019appliquent sont le poids propre de la structure et le poids r\u00e9sultant de l\u2019utilisation de la structure (personnes, meubles, machines). Les facteurs comme le vent, la neige et les changements de temp\u00e9rature pouvant \u00e9galement provoquer des charges, il faut aussi en tenir compte.<\/p>\n\n<p>Pour rendre la structure porteuse adapt\u00e9e aux calculs, nous devons la sch\u00e9matiser en un mod\u00e8le d\u2019analyse (syn. mod\u00e8le filaire, mod\u00e8le m\u00e9canique). Cela va de pair avec des id\u00e9alisations et des simplifications n\u00e9cessaires. Les id\u00e9alisations portent sur :<\/p>\n\n<ul class=\"wp-block-list\">\n<li>La g\u00e9om\u00e9trie (la forme et les dimensions) de la structure<\/li>\n\n\n\n<li>Les appuis<\/li>\n\n\n\n<li>Les assemblages<\/li>\n<\/ul>\n\n<figure class=\"wp-block-image aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"386\" height=\"504\" src=\"https:\/\/www.buildsoft.eu\/wp-content\/uploads\/2022\/05\/Blog_EN_Artikel-1_figuur1.png\" alt=\"\" class=\"wp-image-4191\" srcset=\"https:\/\/www.buildsoft.eu\/wp-content\/uploads\/2022\/05\/Blog_EN_Artikel-1_figuur1.png 386w, https:\/\/www.buildsoft.eu\/wp-content\/uploads\/2022\/05\/Blog_EN_Artikel-1_figuur1-230x300.png 230w\" sizes=\"auto, (max-width: 386px) 100vw, 386px\" \/><figcaption class=\"wp-element-caption\"><em>Figure 1: Sch\u00e9matisation du mod\u00e8le architectural (a) pour cr\u00e9er le mod\u00e8le d\u2019analyse structurelle (b)<\/em><\/figcaption><\/figure>\n\n<h2 class=\"wp-block-heading\">Forme de la structure<\/h2>\n\n<p>Gr\u00e2ce \u00e0 la sch\u00e9matisation, les lignes du syst\u00e8me qui co\u00efncident avec les lignes d\u2019axe des sections transversales remplaceront les poutres et les colonnes. De m\u00eame, les plans du syst\u00e8me qui co\u00efncident avec le plan de l\u2019axe remplaceront les sols et les murs.<\/p>\n\n<figure class=\"wp-block-image aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"444\" height=\"416\" src=\"https:\/\/www.buildsoft.eu\/wp-content\/uploads\/2022\/05\/Blog_EN_Artikel-1_figuur2.png\" alt=\"\" class=\"wp-image-4195\" srcset=\"https:\/\/www.buildsoft.eu\/wp-content\/uploads\/2022\/05\/Blog_EN_Artikel-1_figuur2.png 444w, https:\/\/www.buildsoft.eu\/wp-content\/uploads\/2022\/05\/Blog_EN_Artikel-1_figuur2-300x281.png 300w\" sizes=\"auto, (max-width: 444px) 100vw, 444px\" \/><figcaption class=\"wp-element-caption\"><em>Figure 2: Sch\u00e9matisation du poutre\/ collone (a) et d&rsquo;un dalle\/mur (b) respectivement aux lignes et aux plans du syst\u00e8me<\/em><\/figcaption><\/figure>\n\n<p>Comme nous travaillons avec des lignes et des plans du syst\u00e8me, la valeur calcul\u00e9e des port\u00e9es dans un mod\u00e8le d\u2019analyse est l\u00e9g\u00e8rement diff\u00e9rente des dimensions r\u00e9elles que nous trouvons dans la construction r\u00e9elle (= mod\u00e8le architectural). Dans la Figure 3 :<\/p>\n\n<ul class=\"wp-block-list\">\n<li>les barres du mod\u00e8le d\u2019analyse sont l\u00e9g\u00e8rement plus courtes que dans la r\u00e9alit\u00e9<\/li>\n\n\n\n<li>les colonnes sont un peu plus longues qu\u2019en r\u00e9alit\u00e9<\/li>\n<\/ul>\n\n<p>Lorsque la position des lignes et des plans du syst\u00e8me est d\u00e9termin\u00e9e, nous devons leur attribuer une section transversale. Plus ce choix initial est conforme \u00e0 la conception finale, moins le travail de calcul est important. \u00c0 titre indicatif, nous pouvons estimer la section initiale de chaque \u00e9l\u00e9ment en utilisant les r\u00e8gles empiriques du tableau ci-dessous.<\/p>\n\n<figure class=\"wp-block-image aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"419\" height=\"567\" src=\"https:\/\/www.buildsoft.eu\/wp-content\/uploads\/2022\/05\/Blog_EN_Artikel-1_figuur3.png\" alt=\"\" class=\"wp-image-4199\" srcset=\"https:\/\/www.buildsoft.eu\/wp-content\/uploads\/2022\/05\/Blog_EN_Artikel-1_figuur3.png 419w, https:\/\/www.buildsoft.eu\/wp-content\/uploads\/2022\/05\/Blog_EN_Artikel-1_figuur3-222x300.png 222w\" sizes=\"auto, (max-width: 419px) 100vw, 419px\" \/><figcaption class=\"wp-element-caption\"><em>Figure 3 : Influence de la sch\u00e9matisation sur les longueurs des \u00e9l\u00e9ments de construction<\/em><\/figcaption><\/figure>\n\n<figure class=\"wp-block-table aligncenter\"><table class=\"has-fixed-layout\"><tbody><tr><th class=\"has-text-align-left\" data-align=\"left\" colspan=\"3\"> Poutres de plancher<\/th><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\" rowspan=\"2\">B\u00e9ton<\/td><td>Sur place<\/td><td>\nL\/10 (port\u00e9e unique)<br\/>L\/14,5 (en continu)\n<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">Pr\u00e9contraint<\/td><td>L\/20<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\" colspan=\"2\">Acier<\/td><td>L\/15 \u00e0 L\/20<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\" rowspan=\"2\">Bois<\/td><td>Sci\u00e9<\/td><td>L\/20<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">Stratifi\u00e9<\/td><td>L\/17<\/td><\/tr><tr><th class=\"has-text-align-left\" data-align=\"left\" colspan=\"3\">Poutres de toit<\/th><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\" rowspan=\"2\">B\u00e9ton<\/td><td>Sur place<\/td><td>L\/20<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">Pr\u00e9contraint<\/td><td>L\/20<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\" colspan=\"2\">Acier<\/td><td>L\/30<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\" rowspan=\"2\">Bois<\/td><td>Sci\u00e9<\/td><td>L\/20<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">Stratifi\u00e9<\/td><td>L\/12<\/td><\/tr><tr><th class=\"has-text-align-left\" data-align=\"left\" colspan=\"3\">Colonnes<\/th><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\" rowspan=\"2\">B\u00e9ton<\/td><td>1 \u00e9tage (L<\/td><td>L\/12 \u00e0\u00a0L\/15<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">\u00c9tages multiples (L <\/td><td>L\/10 \u00e0 L\/12<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\" rowspan=\"2\">Acier<\/td><td>1 \u00e9tage (3m <\/td><td>L\/20 \u00e0 L\/25<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">\u00c9tages multiples (3m <\/td><td>L\/7 \u00e0 L\/8<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">Bois<\/td><td>1 \u00e9tage<\/td><td>L\/20<\/td><\/tr><tr><th class=\"has-text-align-left\" data-align=\"left\" colspan=\"3\">Sols en b\u00e9ton<\/th><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\" rowspan=\"2\">Appui lin\u00e9aire (jusqu\u2019\u00e0 7 m)<\/td><td>Champ unique<\/td><td>\n<p>L\/22<\/p><br\/>\n<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">Continu<\/td><td>L\/30<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\" colspan=\"2\">Appui ponctuel (jusqu\u2019\u00e0 7 m)<\/td><td>L\/25 \u00e0 L\/28<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\" colspan=\"2\">Plancher \u00e0 caissons, plancher creux, plancher nervur\u00e9 (jusqu\u2019\u00e0 20 m)<\/td><td>1\/20 \u00e0 1\/25 x la longueur diagonale<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\" colspan=\"2\">Dalles alv\u00e9ol\u00e9es (jusqu\u2019\u00e0 17 m)<\/td><td>L\/35<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\" colspan=\"2\">Double plancher en T (jusqu\u2019\u00e0 22 m)<\/td><td>L\/30<\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\"><em>Tableau 1 : R\u00e8gles empiriques pour estimer les dimensions des pi\u00e8ces structurelles (Source : [4])<\/em><\/figcaption><\/figure>\n\n<h2 class=\"wp-block-heading\">Appuis et assemblages<\/h2>\n\n<p>Une (partie d\u2019une) construction ne flotte pas librement dans l\u2019air. Les parties structurelles sont interconnect\u00e9es par des assemblages (syn. n\u0153uds). Et la structure est reli\u00e9e \u00e0 la terre par des appuiss qui d\u00e9vient les forces internes vers le sol.<\/p>\n\n<p>La sch\u00e9matisation des appuis\/n\u0153uds d\u00e9pend de leurs degr\u00e9s de libert\u00e9 possibles. Ces degr\u00e9s de libert\u00e9 se jouent \u00e0 deux niveaux :<\/p>\n\n<ul class=\"wp-block-list\">\n<li>D\u2019une part, la rigidit\u00e9 en translation mesure la r\u00e9sistance de l\u2019appui\/assemblage aux d\u00e9placements.<\/li>\n\n\n\n<li>D\u2019autre part, la rigidit\u00e9 en rotation mesure la r\u00e9sistance de l\u2019appui\/assemblage \u00e0 la rotation.<\/li>\n<\/ul>\n\n<p>Un appui\/assemblage limite toujours au moins un degr\u00e9 de libert\u00e9. Dans un plan plat \u00e0 deux dimensions[1], un appui\/assemblage a un maximum de 3 degr\u00e9s de libert\u00e9 : deux en translation et un en rotation (Figure 4).<\/p>\n\n<figure class=\"wp-block-image aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"379\" height=\"180\" src=\"https:\/\/www.buildsoft.eu\/wp-content\/uploads\/2022\/05\/Blog_EN_Artikel-1_figuur4.png\" alt=\"\" class=\"wp-image-4203\" style=\"object-fit:cover\" srcset=\"https:\/\/www.buildsoft.eu\/wp-content\/uploads\/2022\/05\/Blog_EN_Artikel-1_figuur4.png 379w, https:\/\/www.buildsoft.eu\/wp-content\/uploads\/2022\/05\/Blog_EN_Artikel-1_figuur4-300x142.png 300w\" sizes=\"auto, (max-width: 379px) 100vw, 379px\" \/><figcaption class=\"wp-element-caption\"><em>Figure 4: Les trois degr\u00e9s de libert\u00e9 dans un plan plat bidimensionnel illustr\u00e9 par un rectangle (Source: [5])<\/em><\/figcaption><\/figure>\n\n<p>En jouant sur la rigidit\u00e9 en translation et en rotation, nous pouvons distinguer diff\u00e9rents appuis\/assemblages (Figure 5).<\/p>\n\n<ul class=\"wp-block-list\">\n<li>Les appuis articul\u00e9s, roulants et retenus sont les plus utilis\u00e9s. La rigidit\u00e9 en translation et la rigidit\u00e9 en rotation sont toutes deux importantes ici.<\/li>\n\n\n\n<li>Pour cat\u00e9goriser les assemblages, on utilise g\u00e9n\u00e9ralement uniquement la rigidit\u00e9 en rotation.\n<ul class=\"wp-block-list\">\n<li>Les assemblages avec une rotation libre sont appel\u00e9s assemblages articul\u00e9s.<\/li>\n\n\n\n<li>Les assemblages dans lesquels la rotation est emp\u00each\u00e9e sont appel\u00e9s assemblages rigides, fixes ou continus.<\/li>\n\n\n\n<li>Les assemblages dont la rigidit\u00e9 en rotation est limit\u00e9e sont appel\u00e9s assemblages semi-rigides.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\" colspan=\"3\" rowspan=\"2\">\u00a0<\/td><td class=\"has-text-align-center\" data-align=\"center\" colspan=\"3\"><strong>RIGITIT\u00c9 EN ROTATION<\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>Libre<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>Limit\u00e9e<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">Fixe<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\" colspan=\"3\"><strong>ASSEMBLAGES<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" width=\"54\" height=\"54\" class=\"wp-image-3955\" style=\"width: 54px;\" src=\"https:\/\/structural-engineering-software.com\/wp-content\/uploads\/2022\/05\/blog_basicstructuralengineering-36.png\" alt=\"\"\/><br\/>Noeud articul\u00e9<\/td><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" width=\"54\" height=\"54\" class=\"wp-image-3963\" style=\"width: 54px;\" src=\"https:\/\/structural-engineering-software.com\/wp-content\/uploads\/2022\/05\/blog_basicstructuralengineering-38.png\" alt=\"\"\/><br\/>Noeud semi-rigide<\/td><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" width=\"54\" height=\"54\" class=\"wp-image-3959\" style=\"width: 54px;\" src=\"https:\/\/structural-engineering-software.com\/wp-content\/uploads\/2022\/05\/blog_basicstructuralengineering-37.png\" alt=\"\"\/><br\/>Noeud rigide<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\" rowspan=\"3\"><strong>APPUIS<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\" rowspan=\"2\">RIGIDIT\u00c9 EN TRANSLATION \u2194<\/td><td class=\"has-text-align-center\" data-align=\"center\">Libre<\/td><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" width=\"30\" height=\"90\" class=\"wp-image-3967\" style=\"width: 30px;\" src=\"https:\/\/structural-engineering-software.com\/wp-content\/uploads\/2022\/05\/blog_basicstructuralengineering-39.png\" alt=\"\"\/><br\/>Appui roulant<\/td><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" width=\"30\" height=\"90\" class=\"wp-image-3983\" style=\"width: 30px;\" src=\"https:\/\/structural-engineering-software.com\/wp-content\/uploads\/2022\/05\/blog_basicstructuralengineering-43.png\" alt=\"\"\/>\u00a0<\/td><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" width=\"30\" height=\"90\" class=\"wp-image-3983\" style=\"width: 30px;\" src=\"https:\/\/www.buildsoft.eu\/wp-content\/uploads\/2022\/05\/blog_basicstructuralengineering-43.png\" alt=\"\"\/>\u00a0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Empechee<\/td><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" width=\"30\" height=\"90\" class=\"wp-image-3971\" style=\"width: 30px;\" src=\"https:\/\/structural-engineering-software.com\/wp-content\/uploads\/2022\/05\/blog_basicstructuralengineering-40.png\" alt=\"\"\/><br\/>Appui articul\u00e9<\/td><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" width=\"30\" height=\"90\" class=\"wp-image-3979\" style=\"width: 30px;\" src=\"https:\/\/structural-engineering-software.com\/wp-content\/uploads\/2022\/05\/blog_basicstructuralengineering-42.png\" alt=\"\"\/><br\/>Semi-fixe<\/td><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" width=\"30\" height=\"89\" class=\"wp-image-3987\" style=\"width: 30px;\" src=\"https:\/\/structural-engineering-software.com\/wp-content\/uploads\/2022\/05\/blog_basicstructuralengineering-44.png\" alt=\"\"\/><br\/>Encastr\u00e9<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\" colspan=\"2\">RIGIDIT\u00c9 EN TRANSLATION \u2195<\/td><td class=\"has-text-align-center\" data-align=\"center\" colspan=\"3\">G\u00e9n\u00e9ralement \u00e9vit\u00e9e, mais LIMIT\u00c9E possible en appliquant un ressort dans la direction verticale.<\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\"><em>Figure 5 : repr\u00e9sentation m\u00e9canique de diff\u00e9rents appuis\/assemblages en fonction de leur rigidit\u00e9 en translation et en rotation (Source : [3])<\/em><\/figcaption><\/figure>\n\n<p>Lors de la r\u00e9alisation d\u2019un mod\u00e8le d\u2019analyse structurelle, nous devons donc sch\u00e9matiser les appuis et les assemblages de mani\u00e8re \u00e0 ce qu\u2019ils se rapprochent le plus possible du comportement r\u00e9el. Dans la Figure 6, vous pouvez voir la m\u00eame construction que dans la Figure 1, mais cette fois les appuis et les assemblages sont pr\u00e9sent\u00e9s avec leur sch\u00e9matisation respective. Par exemple, l\u2019appui gauche du mod\u00e8le architectural est traduit en un appui roulant dans le mod\u00e8le d\u2019analyse. Ou la connexion de la plaque de base de la colonne flexible en un appui semi-rigide, etc.<\/p>\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"414\" height=\"512\" src=\"https:\/\/www.buildsoft.eu\/wp-content\/uploads\/2022\/05\/Blog_EN_Artikel-1_figuur6.png\" alt=\"\" class=\"wp-image-4187\" style=\"width:808px;height:auto\" srcset=\"https:\/\/www.buildsoft.eu\/wp-content\/uploads\/2022\/05\/Blog_EN_Artikel-1_figuur6.png 414w, https:\/\/www.buildsoft.eu\/wp-content\/uploads\/2022\/05\/Blog_EN_Artikel-1_figuur6-243x300.png 243w\" sizes=\"auto, (max-width: 414px) 100vw, 414px\" \/><figcaption class=\"wp-element-caption\"><em>Figure 6: Sch\u00e9ma des supports et des joints dans une structure<\/em><\/figcaption><\/figure>\n\n<p>Photos de appuis\/assemblages r\u00e9els et leurs sch\u00e9mas associ\u00e9s.<\/p>\n\n<figure class=\"wp-block-table aligncenter\"><table class=\"has-fixed-layout\"><thead><tr><th class=\"has-text-align-center\" data-align=\"center\" colspan=\"2\">Exemples d\u2019appuis<\/th><th colspan=\"2\">Exemples de assemblages<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" alt=\"A neoprene strip is placed between a pre-slab and a load-bearing wall\" height=\"140\" src=\"https:\/\/www.buildsoft.eu\/sites\/default\/files\/inline-images\/Picture1.png\" width=\"114\"\/>\u00a0<\/td><td>Une bande de n\u00e9opr\u00e8ne est plac\u00e9e entre une pr\u00e9dalle et un mur porteur. La bande de n\u00e9opr\u00e8ne garantit que la pr\u00e9dalle peut subir de petits mouvements horizontaux.<\/td><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" alt=\"Classic bolted beam-column connection with a haunch\" height=\"125\" src=\"https:\/\/www.buildsoft.eu\/sites\/default\/files\/inline-images\/Picture9.png\" width=\"114\"\/><\/td><td>Assemblage classique boulonn\u00e9 poutre-colonne avec un jarret. Le jarret apporte une rigidit\u00e9 suppl\u00e9mentaire en rotation.<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" alt=\"Schematization: roller support\" height=\"50\" src=\"https:\/\/www.buildsoft.eu\/sites\/default\/files\/inline-images\/Picture2.png\" width=\"86\"\/><\/td><td>Sch\u00e9matisation : appui roulant<\/td><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" alt=\"Schematization: rigid node\" height=\"51\" src=\"https:\/\/www.buildsoft.eu\/sites\/default\/files\/inline-images\/Picture10.png\" width=\"49\"\/><\/td><td>Sch\u00e9matisation : n\u0153ud rigide<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" alt=\"Both translational and rotational displacements are prevented in this support\" height=\"136\" src=\"https:\/\/www.buildsoft.eu\/sites\/default\/files\/inline-images\/Picture3.png\" width=\"136\"\/><\/td><td>Cet appui permet d\u2019\u00e9viter les d\u00e9placements en translation et en rotation<\/td><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" alt=\"Beam-column connection in concrete where a console supports the beam.\" height=\"129\" src=\"https:\/\/www.buildsoft.eu\/sites\/default\/files\/inline-images\/Picture11.png\" width=\"129\"\/><\/td><td>Liaison poutre-colonne en b\u00e9ton o\u00f9 une console e la poutre. En g\u00e9n\u00e9ral, ce assemblage ne peut pas transf\u00e9rer de moments.<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" alt=\"Schematization: built-in \" height=\"96\" src=\"https:\/\/www.buildsoft.eu\/sites\/default\/files\/inline-images\/Picture4.png\" width=\"32\"\/><\/td><td>Sch\u00e9matisation : int\u00e9gr\u00e9e<\/td><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" alt=\"Schematization: hinged node\" src=\"https:\/\/www.buildsoft.eu\/sites\/default\/files\/inline-images\/Picture12.png\" width=\"59\" height=\"63\"\/><\/td><td>Sch\u00e9matisation : n\u0153ud articul\u00e9<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" alt=\"The four bolts ensure that this support can develop a specific moment resistance.\" height=\"130\" src=\"https:\/\/www.buildsoft.eu\/sites\/default\/files\/inline-images\/Picture5.png\" width=\"130\"\/><\/td><td>Les quatre boulons permettent \u00e0 cet appui de d\u00e9velopper un moment de r\u00e9sistance sp\u00e9cifique. Malheureusement, cette r\u00e9sistance n\u2019est pas de la m\u00eame ampleur qu\u2019un appui int\u00e9gr\u00e9.<\/td><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" alt=\"A beam-beam connection in concrete. Also called a corbel.\" height=\"127\" src=\"https:\/\/www.buildsoft.eu\/sites\/default\/files\/inline-images\/Picture13.png\" width=\"127\"\/><\/td><td>Une connexion poutre-poutre en b\u00e9ton. \u00c9galement appel\u00e9 corbeau. Ce assemblage ne peut pas transf\u00e9rer de moments.<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" alt=\"Schematization: semi-fixed support\" height=\"96\" src=\"https:\/\/www.buildsoft.eu\/sites\/default\/files\/inline-images\/Picture6.png\" width=\"33\"\/><\/td><td>Sch\u00e9matisation : appui semi-fixe<\/td><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" alt=\"Schematization: hinged node\" src=\"https:\/\/www.buildsoft.eu\/sites\/default\/files\/inline-images\/Picture14.png\" width=\"114\" height=\"18\"\/><\/td><td>Sch\u00e9matisation : n\u0153ud articul\u00e9<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" alt=\"Only in bridges, you can encounter supports in their purest form. This example is a pinned support. \" height=\"128\" src=\"https:\/\/www.buildsoft.eu\/sites\/default\/files\/inline-images\/Picture7.png\" width=\"128\"\/><\/td><td>Il n\u2019y a que dans les ponts que vous pouvez rencontrer les appuis dans leur forme la plus pure. Cet exemple est un appui articul\u00e9. Les d\u00e9placements sont emp\u00each\u00e9s, mais la barre reli\u00e9e \u00e0 l\u2019appui peut tourner sans interruption.<\/td><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" alt=\"A bolted beam-column-beam connection without haunches.\" height=\"123\" src=\"https:\/\/www.buildsoft.eu\/sites\/default\/files\/inline-images\/Picture15.png\" width=\"123\"\/><\/td><td>Un assemblage boulonn\u00e9 poutre-colonne-poutre sans jarret. Cet assemblage a une rigidit\u00e9 en rotation sp\u00e9cifique, mais pas la m\u00eame magnitude que si des jarrets \u00e9taient pr\u00e9sentes.<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" alt=\"schematization\" src=\"https:\/\/www.buildsoft.eu\/sites\/default\/files\/inline-images\/Picture8.png\" width=\"36\" height=\"90\"\/><\/td><td>Sch\u00e9matisation : appui simple<\/td><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" alt=\"Schematization: semi-rigid node\" src=\"https:\/\/www.buildsoft.eu\/sites\/default\/files\/inline-images\/Picture16.png\" width=\"105\" height=\"60\"\/><\/td><td>Sch\u00e9matisation : n\u0153ud semi-rigide<\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\"><em>Tableau 1 : R\u00e8gles empiriques pour estimer les dimensions des pi\u00e8ces structurelles (Source : [4])<\/em><\/figcaption><\/figure>\n\n<p>Si un certain degr\u00e9 de libert\u00e9 (translationnelle ou rotative) est libre ou fixe, le mod\u00e8le d\u2019analyse structurelle de l\u2019appui\/assemblage est rapidement d\u00e9termin\u00e9. C\u2019est tout ou rien. Mais avec les ressorts de translation et les ressorts de rotation, c\u2019est une autre histoire. Il existe plusieurs fa\u00e7ons de d\u00e9terminer la valeur de ces ressorts de translation et de rotation dans le cadre de l\u2019analyse structurelle. Toutefois, cette question ne rel\u00e8ve pas du champ d\u2019application de cet article.<\/p>\n\n<h2 class=\"wp-block-heading\">Application pratique : mod\u00e8le d\u2019analyse structurelle dans Diamonds<\/h2>\n\n<p>Appliquons ces connaissances dans\u00a0<a tabindex=\"-1\" title=\"Diamonds\" href=\"https:\/\/www.buildsoft.eu\/fr\/product\/diamonds\/\">Diamonds<\/a>, notre principal logiciel de calcul de structure. Nous cr\u00e9ons le mod\u00e8le d\u2019analyse structurelle pour la deuxi\u00e8me ossature dans le hall ci-dessous.<\/p>\n\n<div class=\"wp-block-uagb-image aligncenter uagb-block-a5bcbbad wp-block-uagb-image--layout-default wp-block-uagb-image--effect-static wp-block-uagb-image--align-center\"><figure class=\"wp-block-uagb-image__figure\"><img decoding=\"async\" srcset=\"https:\/\/www.buildsoft.eu\/wp-content\/uploads\/2022\/05\/Picture17_0-1024x692.png ,https:\/\/www.buildsoft.eu\/wp-content\/uploads\/2022\/05\/Picture17_0.png 780w, https:\/\/www.buildsoft.eu\/wp-content\/uploads\/2022\/05\/Picture17_0.png 360w\" sizes=\"auto, (max-width: 480px) 150px\" src=\"https:\/\/www.buildsoft.eu\/wp-content\/uploads\/2022\/05\/Picture17_0-1024x692.png\" alt=\"\" class=\"uag-image-3999\" width=\"1024\" height=\"692\" title=\"Picture17_0\" loading=\"lazy\" role=\"img\"\/><\/figure><\/div><br>\n\n<p>Les dimensions des axes du syst\u00e8me sont les suivantes :<\/p>\n\n<ul class=\"wp-block-list\">\n<li>Largeur : 12 m<\/li>\n\n\n\n<li>Hauteur de la colonne : 6 m<\/li>\n\n\n\n<li>Pente du toit : 15\u00b0<\/li>\n<\/ul>\n\n<p>Pour mieux comprendre o\u00f9 se trouvent exactement les axes du syst\u00e8me, nous les dessinons sur l\u2019image :<\/p>\n\n<div class=\"wp-block-uagb-image aligncenter uagb-block-95e4dea9 wp-block-uagb-image--layout-default wp-block-uagb-image--effect-static wp-block-uagb-image--align-center\"><figure class=\"wp-block-uagb-image__figure\"><img decoding=\"async\" srcset=\"https:\/\/www.buildsoft.eu\/wp-content\/uploads\/2022\/05\/Picture18.png ,https:\/\/www.buildsoft.eu\/wp-content\/uploads\/2022\/05\/Picture18.png 780w, https:\/\/www.buildsoft.eu\/wp-content\/uploads\/2022\/05\/Picture18.png 360w\" sizes=\"auto, (max-width: 480px) 150px\" src=\"https:\/\/www.buildsoft.eu\/wp-content\/uploads\/2022\/05\/Picture18.png\" alt=\"\" class=\"uag-image-3995\" width=\"1024\" height=\"326\" title=\"Picture18\" loading=\"lazy\" role=\"img\"\/><\/figure><\/div><br>\n\n<p>Ensuite, nous devons affecter des sections aux axes du syst\u00e8me. Sur la base du Tableau 1, nous pouvons faire une premi\u00e8re estimation :<\/p>\n\n<ul class=\"wp-block-list\">\n<li>Colonnes : 6 000 mm\/20 = 300 mm &gt; HEA 300<\/li>\n\n\n\n<li>Poutres : 6 000 mm\/20 = 300 mm &gt; IPE 300<\/li>\n\n\n\n<li>Jarret : longueur 1 m, hauteur \u00e9gale \u00e0 la hauteur de l\u2019IPE \u00e0 laquelle le jarret est attach\u00e9e<\/li>\n\n\n\n<li>Appuis : articul\u00e9s par hypoth\u00e8se<\/li>\n\n\n\n<li>Assemblages : assemblages fixes (en raison de la pr\u00e9sence du jarret). Les assemblages sont fixes par d\u00e9faut dans Diamonds.<\/li>\n<\/ul>\n\n<p>Pour g\u00e9n\u00e9rer rapidement une ossature de portail, nous utilisons l\u2019assistant de structure.<\/p>\n\n<p class=\"has-text-align-center\"><img loading=\"lazy\" decoding=\"async\" height=\"274\" width=\"476\" src=\"https:\/\/www.buildsoft.eu\/sites\/default\/files\/inline-images\/Picture19.png\" alt=\"structure wizard\"\/><img loading=\"lazy\" decoding=\"async\" width=\"480\" height=\"400\" src=\"https:\/\/www.buildsoft.eu\/sites\/default\/files\/inline-images\/Picture20.png\" alt=\"buildsoft diamonds (wizard: portal frame)\"\/><img loading=\"lazy\" decoding=\"async\" width=\"480\" height=\"383\" src=\"https:\/\/www.buildsoft.eu\/sites\/default\/files\/inline-images\/Picture21.png\" alt=\"buildsoft diamonds (releases at bar ends)\"\/><img loading=\"lazy\" decoding=\"async\" height=\"401\" width=\"747\" src=\"https:\/\/www.buildsoft.eu\/sites\/default\/files\/inline-images\/Picture22.png\" alt=\"diamonds software\"\/><\/p>\n\n<p>L\u2019ossature est repr\u00e9sent\u00e9e sous forme de fil dans l\u2019image ci-dessus : seules les lignes du syst\u00e8me sont visibles. Si vous demandez une repr\u00e9sentation solide, les dimensions de la section sont g\u00e9n\u00e9r\u00e9es et coll\u00e9es sur les lignes du syst\u00e8me. Par cons\u00e9quent, cette repr\u00e9sentation ne ressemble pas \u00e0 la construction r\u00e9elle (= mod\u00e8le architectural) :<\/p>\n\n<ul class=\"wp-block-list\">\n<li>Les poutres et les colonnes ne semblent pas s\u2019aligner correctement.<\/li>\n\n\n\n<li>L\u2019assemblage poutre-poutre du fa\u00eete ne semble pas non plus bien raccord\u00e9.<\/li>\n\n\n\n<li>Les nervures se chevauchent au niveau du fa\u00eete (on peut m\u00eame le voir sur l\u2019image filaire).<\/li>\n<\/ul>\n\n<p>Mais c\u2019est normal. Ces ph\u00e9nom\u00e8nes r\u00e9sultent de la sch\u00e9matisation d\u2019un mod\u00e8le architectural (qui ne se pr\u00eate pas aux calculs) en un mod\u00e8le d\u2019analyse structurelle (qui se pr\u00eate aux calculs).<\/p>\n\n<p>Bibliographie:<\/p>\n\n<ol class=\"wp-block-list\">\n<li>Braam, R., &amp; Lagendijk, P. (2010). Constructieleer gewapend beton (7de editie). Vrije Uitgevers, de.<\/li>\n\n\n\n<li>Stark, J., &amp; Wardenier, J. (2014). Knopen (1ste editie). Bouwen Met Staal.<\/li>\n\n\n\n<li>Dicke, D. (1991). Stabiliteit voor ontwerpers (2e druk). Delftse U.M.<\/li>\n\n\n\n<li>Vuistregels voor het ontwerpen van een draagconstructie. (2013, 20 november). Wiki BK TU Delft. Geraadpleegd op 19 januari 2021, van http:\/\/wiki.bk.tudelft.nl\/mw_bk-wiki\/images\/1\/12\/Vuistregels.pdf<\/li>\n\n\n\n<li>Hanaor, A. (1998). Principles of Structures. Blackwell Publishing.<\/li>\n<\/ol>\n\n<h2 class=\"wp-block-heading\">FAQ<\/h2>\n\n<p><strong>Qu&rsquo;est-ce que la sch\u00e9matisation en analyse structurelle ?<\/strong><br\/>La sch\u00e9matisation consiste \u00e0 simplifier un mod\u00e8le architectural, \u00e0 quoi ressemble r\u00e9ellement un b\u00e2timent, en un mod\u00e8le d&rsquo;analyse que le logiciel peut calculer : les poutres et colonnes sont remplac\u00e9es par des lignes de syst\u00e8me, les sols et murs par des plans de syst\u00e8me, puis on attribue des appuis et des assemblages qui approchent le comportement r\u00e9el<\/p>\n\n<p><strong>Quelle est la diff\u00e9rence entre un appui et une condition limite dans un mod\u00e8le structurel ?<\/strong><br\/>Un appui connecte la structure au sol et y d\u00e9vie les efforts internes. Une condition limite s&rsquo;applique aux extr\u00e9mit\u00e9s d&rsquo;une barre, donc dans un n\u0153ud, qui connecte deux \u00e9l\u00e9ments de la structure entre eux. Les deux sont class\u00e9s de la m\u00eame fa\u00e7on, selon leur rigidit\u00e9 en translation et en rotation, allant de totalement libre (articul\u00e9) \u00e0 totalement fixe (rigide), avec des options semi-rigides entre les deux.<\/p>\n\n<p><strong>Pourquoi le mod\u00e8le sch\u00e9matis\u00e9 diff\u00e8re-t-il l\u00e9g\u00e8rement de la structure r\u00e9elle ?<\/strong><br\/>Parce que les lignes et plans du syst\u00e8me passent par l&rsquo;axe de chaque section transversale, et non par son bord, les port\u00e9es calcul\u00e9es dans le mod\u00e8le d&rsquo;analyse sont l\u00e9g\u00e8rement plus courtes pour les poutres et l\u00e9g\u00e8rement plus longues pour les colonnes que les dimensions r\u00e9elles. C&rsquo;est normal et ne signale pas une erreur.<br\/><\/p>\n\n<h2 class=\"wp-block-heading\">Prochaine \u00e9tape<\/h2>\n\n<p>Envie de voir la sch\u00e9matisation appliqu\u00e9e \u00e0 votre propre structure ? <a href=\"https:\/\/www.buildsoft.eu\/fr\/trial\">Essayez Diamonds gratuitement pendant 30 jours<\/a>, pleinement fonctionnel, sans engagement.<br\/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tout commence par le mod\u00e8le architectural et la sch\u00e9matisation La sch\u00e9matisation consiste \u00e0 simplifier un b\u00e2timent r\u00e9el (le mod\u00e8le architectural) [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":3230,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_uag_custom_page_level_css":"","site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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