{"id":2217,"date":"2026-04-27T12:31:02","date_gmt":"2026-04-27T12:31:02","guid":{"rendered":"https:\/\/protasoftware.com\/fr\/wiki\/effets-3d-d-un-element-sur-un-autre\/"},"modified":"2026-04-27T12:31:02","modified_gmt":"2026-04-27T12:31:02","slug":"effets-3d-d-un-element-sur-un-autre","status":"publish","type":"wiki","link":"https:\/\/protasoftware.com\/fr\/support\/manuels-techniques\/effets-3d-d-un-element-sur-un-autre\/","title":{"rendered":"Effets 3D d’un \u00e9l\u00e9ment sur un autre"},"content":{"rendered":"
\n L’effet 3D le plus probable est celui o\u00f9 les efforts de calcul des poutres g\u00e9n\u00e9r\u00e9s ne correspondent pas toujours \u00e0 ce que l’on attend d’une analyse 2D traditionnelle.
<\/span><\/span>
\n<\/span><\/div>\n


\n<\/span><\/p>\n

Ce type d’effet peut se produire de nombreuses fa\u00e7ons. Il devient plus probable quand la disposition structurelle se complique et devient irr\u00e9guli\u00e8re.<\/span><\/span><\/div>\n

\n<\/span><\/div>\n


\n<\/span><\/p>\n

Nous pouvons  d\u00e9montrer cet effet avec un mod\u00e8le tr\u00e8s simple, o\u00f9 plusieurs poutres de plancher sont assembl\u00e9es selon un angle aigu (inf\u00e9rieur \u00e0 90 %), comme illustr\u00e9 ci-dessous.<\/span><\/span><\/div>\n
\n
<\/span>\n<\/div>\n
\n
\n
\n \n<\/div>\n

<\/span><\/p>\n

<\/span><\/p>\n

\n Ce mod\u00e8le contient :
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\n<\/span><\/div>\n


\n<\/span><\/p>\n


    \n <\/span><\/p>\n
  1. 5 poutres de 250 mm x 500 mm
    <\/span><\/span><\/li>\n


    \n <\/span><\/p>\n

  2. 4 poteaux de 400 mm x 400 mm
    <\/span><\/span><\/li>\n


    \n <\/span><\/p>\n

  3. 2 dalles de 120 mm d’\u00e9paisseur.
    <\/span><\/span><\/li>\n


    \n<\/span><\/ol>\n


    \n<\/span><\/p>\n


    \n <\/span>Les diagrammes de charge, d’effort tranchant et de moment de la poutre diagonale 1B5 sont pr\u00e9sent\u00e9s ci-dessous :<\/span><\/span><\/div>\n
    \n \n<\/div>\n
    \n
    \n \n<\/div>\n
    \n \n<\/div>\n
    \n Comme les deux extr\u00e9mit\u00e9s de la poutre sont en assemblage encastr\u00e9 (support\u00e9es par des poteaux), un moment n\u00e9gatif approximativement sym\u00e9trique est attendu aux deux extr\u00e9mit\u00e9s. 
    <\/span><\/span>
    \n<\/span><\/div>\n


    \n<\/span><\/p>\n

    Cependant, le diagramme de moment de la poutre 1B3 diff\u00e8re nettement de celui de 1B5, bien qu’elle soit support\u00e9e par les m\u00eames poteaux aux deux extr\u00e9mit\u00e9s.<\/span><\/div>\n

    \n<\/span><\/div>\n


    \n<\/span><\/p>\n

    Les diagrammes de charge, d’effort tranchant et de moment de la poutre 1B3 sont pr\u00e9sent\u00e9s ci-dessous :<\/span><\/div>\n

    <\/span>\n<\/div>\n
    \n <\/span>
    \n \n<\/div>\n
    \n \n<\/div>\n
    \n Les charges sont l\u00e9g\u00e8rement d\u00e9cal\u00e9es en raison de la zone triangulaire de dalle support\u00e9e. Le diagramme de moment fl\u00e9chissant montre toutefois un moment positif \u00e0 l’appui gauche et un moment n\u00e9gatif \u00e0 l’appui droit. Ce r\u00e9sultat est inattendu, car le diagramme de moment fl\u00e9chissant n’est pas sym\u00e9trique.   <\/span>
    <\/span><\/span>
    \n<\/span><\/div>\n


    \n<\/span><\/p>\n


    \n <\/span>
    <\/span><\/span>
    \n<\/span><\/div>\n


    \n<\/span><\/p>\n


    \n <\/span>L’explication concerne la poutre diagonale du plancher. Lorsque la structure est \u00e9valu\u00e9e dans le post-processeur d’analyse du b\u00e2timent > Mod\u00e8le analytique<\/a>, le mod\u00e8le filaire analytique avec le moment fl\u00e9chissant d\u00fb au cas de charge ultime est pr\u00e9sent\u00e9 ci-dessous.<\/span><\/span><\/div>\n
    \n \n<\/div>\n
    \n
    \n \n<\/div>\n
    \n \n<\/div>\n
    \n Notez que l’option zone rigide (r\u00e9duite de 25 %) \u00e9tait activ\u00e9e. Des liens rigides automatiques (lignes bleu fonc\u00e9) ont donc \u00e9t\u00e9 cr\u00e9\u00e9s dans l’analyse pour simuler la rigidit\u00e9 de l’assemblage poutre-poteau. Les moments sont par cons\u00e9quent interpol\u00e9s et affich\u00e9s \u00e0 l’extr\u00e9mit\u00e9 de la zone rigide, soit approximativement au nu du poteau et \u00e0 la sous-face de la poutre. <\/span><\/span>
    \n
    \n<\/span><\/div>\n


    \n<\/span><\/p>\n


    \n <\/span>\"\"
    \n <\/span><\/p>\n

    \n <\/span><\/p>\n

    \n Dans cet exemple, la zone rigide est appliqu\u00e9e pour accentuer la raideur de l’assemblage, afin de mieux illustrer ce comportement 3D. 
    \n
    \n <\/span><\/div>\n


    \n <\/span><\/div>\n


    \n <\/span><\/p>\n


    \n Pour en savoir plus sur la zone rigide, consultez cet article :<\/span> 
    \n Interpr\u00e9tations de la zone rigide<\/span><\/a>
    \n \n <\/div>\n

    <\/span>\n<\/div>\n

    \n \n<\/div>\n
    \n
    \n Pour mieux visualiser la d\u00e9form\u00e9e, l’animation de la d\u00e9form\u00e9e est pr\u00e9sent\u00e9e ci-dessous.<\/span>
    <\/span>\n <\/div>\n
    \n
    \n \n <\/div>\n
    \n \n <\/div>\n
    \n
    \n La poutre diagonale fortement charg\u00e9e g\u00e9n\u00e8re un moment n\u00e9gatif important dans les poteaux porteurs, et l’assemblage tourne clairement. Cette rotation entra\u00eene n\u00e9cessairement des effets sur les autres poutres connect\u00e9es, en particulier les \u00e9l\u00e9ments assembl\u00e9s \u00e0 moins de 90 degr\u00e9s (perpendiculaire).<\/span><\/span>
    \n <\/span>
    <\/span>
    \n <\/span><\/div>\n


    \n <\/span><\/p>\n


    \n <\/span>
    <\/span>
    \n <\/span><\/div>\n


    \n <\/span><\/p>\n


    \n <\/span>Dans ce cas, la poutre diagonale impose \u00e0 l’assemblage une rotation dans le sens horaire au niveau du poteau, c’est-\u00e0-dire \u00e0 l’appui gauche de la poutre 1B3. Cela \u00e9quivaut \u00e0 un moment horaire appliqu\u00e9 de l’ext\u00e9rieur \u00e0 l’appui gauche de 1B3, qui annule ou neutralise tout moment n\u00e9gatif interne.<\/span><\/span>
    \n <\/span>
    <\/span>
    \n <\/span><\/div>\n


    \n <\/span><\/p>\n


    \n <\/span>En conclusion, les moments de calcul de 1B3 sont corrects dans le contexte d’une analyse 3D. Si le m\u00eame mod\u00e8le est analys\u00e9 dans un autre logiciel g\u00e9n\u00e9ral d’analyse 3D (par exemple SAP), le r\u00e9sultat sera identique. <\/span><\/span>
    \n \n <\/div>\n
    \n \n <\/div>\n
    \n
    \n \"\"
    \n <\/span><\/p>\n

    \n <\/span>On pourrait d\u00e9velopper d’innombrables exemples de ce type. Le point essentiel est le suivant : un effort de calcul qui semble incorrect dans un \u00e9l\u00e9ment ne signifie pas que l’analyse est fausse. Il faut examiner les r\u00e9sultats avec attention, et observer en particulier la nature des fl\u00e8ches de tous les \u00e9l\u00e9ments connect\u00e9s au n\u0153ud commun, car la fl\u00e8che refl\u00e8te les efforts internes de l’\u00e9l\u00e9ment.<\/span><\/span>
    \n \n <\/div>\n

    <\/span>\n <\/div>\n<\/div>\n<\/div>\n

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

    L’effet 3D le plus probable est celui o\u00f9 les efforts de calcul des poutres g\u00e9n\u00e9r\u00e9s ne correspondent pas toujours \u00e0 ce que l’on attend d’une…<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"template":"","meta":{"_whitepaper_youtube_videos":"","_whitepaper_youtube_url":"","_whitepaper_youtube_thumbnail":"","footnotes":""},"categories":[23],"whitepaper_topic":[],"whitepaper_product":[],"whitepaper_type":[],"class_list":["post-2217","wiki","type-wiki","status-publish","hentry","category-frequently-asked-questions"],"yoast_head":"\nEffets 3D d'un \u00e9l\u00e9ment sur un autre<\/title>\n<meta name=\"description\" content=\"D\u00e9couvrez comment ProtaStructure calcule les effets 3D d'un \u00e9l\u00e9ment sur un autre dans le mod\u00e8le, pour une analyse structurelle pr\u00e9cise et fiable.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link 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