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									<p>Guide pratique PDF pour le <strong>Calcul et Dimensionnement d’une Semelle Filante</strong> : méthodes, exemples et conseils pour des fondations solides et sûres.</p><p><img class="image_Illustration_calcul_dimensionnement_semelle_filante_guide_pratique_PDF alignnone wp-image-8731 size-large" title="Illustration du calcul et du dimensionnement d’une semelle filante pour guide pratique PDF en génie civil." src="https://cours-genie-civil.com/wp-content/uploads/2025/08/Calcul-et-Dimensionnement-dune-Semelle-Filante-Guide-pratique-PDF-683x1024.webp" alt="Diagramme illustrant le calcul et le dimensionnement d’une semelle filante, avec diagrammes de charges et de contraintes pour un guide pratique PDF." width="683" height="1024" /></p><p class="ds-markdown-paragraph">La semelle filante est un élément fondamental dans la construction des structures porteuses. Elle permet de répartir les charges des murs et des poteaux sur une surface suffisante du sol, garantissant ainsi la stabilité et la durabilité de l’ouvrage. Ce guide détaille les étapes essentielles pour le calcul et le dimensionnement d’une semelle filante, en intégrant les contraintes sismiques et les normes en vigueur.</p><hr /><h2><strong>Choix et Pré-dimensionnement Initial</strong></h2><h3><strong>Sélection du Type de Fondation</strong></h3><p class="ds-markdown-paragraph">Dans notre étude, le choix s’est porté sur une semelle filante suivant l’axe « B » de la structure. Cette décision est justifiée par la nécessité de supporter une série de poteaux et de voiles alignés sur une longueur de 17,00 mètres.</p><h3><strong>Calcul Préliminaire de la Largeur</strong></h3><p class="ds-markdown-paragraph">La largeur <span class="katex"><span class="katex-mathml">B</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord mathnormal">B</span></span></span></span> de la semelle est déterminée à partir des efforts normaux transmis par les éléments verticaux. Les formules utilisées sont les suivantes :</p><ul><li><p class="ds-markdown-paragraph"><strong>ELU</strong> : <span class="katex"><span class="katex-mathml">B≥ΣNi1.33×L×σsol</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord mathnormal">B</span><span class="mrel">≥</span></span><span class="base"><span class="mord"><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1.33<span class="mbin mtight">×</span><span class="mord mathnormal mtight">L</span><span class="mbin mtight">×</span><span class="mord mathnormal mtight">σ</span><span class="msupsub"><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">so</span><span class="mord mathnormal mtight">l</span></span><span class="vlist-s">​</span></span></span></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">Σ<span class="mord mathnormal mtight">N</span><span class="msupsub"><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">i</span></span><span class="vlist-s">​</span></span></span></span></span><span class="vlist-s">​</span></span></span></span></span></span></span></span></p></li><li><p class="ds-markdown-paragraph"><strong>ELS</strong> : <span class="katex"><span class="katex-mathml">B≥ΣNiL×σsol</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord mathnormal">B</span><span class="mrel">≥</span></span><span class="base"><span class="mord"><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">L</span><span class="mbin mtight">×</span><span class="mord mathnormal mtight">σ</span><span class="msupsub"><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">so</span><span class="mord mathnormal mtight">l</span></span><span class="vlist-s">​</span></span></span></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">Σ<span class="mord mathnormal mtight">N</span><span class="msupsub"><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">i</span></span><span class="vlist-s">​</span></span></span></span></span><span class="vlist-s">​</span></span></span></span></span></span></span></span></p></li></ul><p class="ds-markdown-paragraph">Avec <span class="katex"><span class="katex-mathml">σsol=200 KPa</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord"><span class="mord mathnormal">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">so</span><span class="mord mathnormal mtight">l</span></span></span></span><span class="vlist-s">​</span></span></span></span></span><span class="mrel">=</span></span><span class="base"><span class="mord">200</span><span class="mord text"><span class="mord">KPa</span></span></span></span></span> et <span class="katex"><span class="katex-mathml">L=17,00 m</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord mathnormal">L</span><span class="mrel">=</span></span><span class="base"><span class="mord">17</span><span class="mpunct">,</span><span class="mord">00</span><span class="mord text"><span class="mord">m</span></span></span></span></span>, les calculs donnent :</p><ul><li><p class="ds-markdown-paragraph"><span class="katex"><span class="katex-mathml">BELU≥0,79 m</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord"><span class="mord mathnormal">B</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight">ELU</span></span></span></span><span class="vlist-s">​</span></span></span></span></span><span class="mrel">≥</span></span><span class="base"><span class="mord">0</span><span class="mpunct">,</span><span class="mord">79</span><span class="mord text"><span class="mord">m</span></span></span></span></span></p></li><li><p class="ds-markdown-paragraph"><span class="katex"><span class="katex-mathml">BELS≥0,77 m</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord"><span class="mord mathnormal">B</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight">ELS</span></span></span></span><span class="vlist-s">​</span></span></span></span></span><span class="mrel">≥</span></span><span class="base"><span class="mord">0</span><span class="mpunct">,</span><span class="mord">77</span><span class="mord text"><span class="mord">m</span></span></span></span></span></p></li></ul><p class="ds-markdown-paragraph">La largeur retenue est de <strong>1,00 mètre</strong>, puis validée sous les combinaisons sismiques.</p><hr /><h2><strong>Vérification sous Combinaisons Sismiques</strong></h2><h3><strong>Combinaisons de Charges Utilisées</strong></h3><p class="ds-markdown-paragraph">Les vérifications sont réalisées sous les combinaisons sismiques suivantes :</p><ul><li><p class="ds-markdown-paragraph"><span class="katex"><span class="katex-mathml">G+Q±Ey</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord mathnormal">G</span><span class="mbin">+</span></span><span class="base"><span class="mord mathnormal">Q</span><span class="mbin">±</span></span><span class="base"><span class="mord"><span class="mord mathnormal">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">y</span></span></span><span class="vlist-s">​</span></span></span></span></span></span></span></span></p></li><li><p class="ds-markdown-paragraph"><span class="katex"><span class="katex-mathml">0,8G±Ey</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord">0</span><span class="mpunct">,</span><span class="mord">8</span><span class="mord mathnormal">G</span><span class="mbin">±</span></span><span class="base"><span class="mord"><span class="mord mathnormal">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">y</span></span></span><span class="vlist-s">​</span></span></span></span></span></span></span></span></p></li></ul><h3><strong>Étapes de Vérification des Contraintes</strong></h3><ol start="1"><li><p class="ds-markdown-paragraph"><strong>Calcul de la somme des efforts normaux</strong> <span class="katex"><span class="katex-mathml">ΣNi</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord">Σ</span><span class="mord"><span class="mord mathnormal">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span class="vlist-s">​</span></span></span></span></span></span></span></span></p></li><li><p class="ds-markdown-paragraph"><strong>Détermination des moments sismiques</strong> <span class="katex"><span class="katex-mathml">Mc</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord"><span class="mord mathnormal">M</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">c</span></span></span><span class="vlist-s">​</span></span></span></span></span></span></span></span> au niveau des appuis</p></li><li><p class="ds-markdown-paragraph"><strong>Calcul de l’excentricité</strong> <span class="katex"><span class="katex-mathml">e</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord mathnormal">e</span></span></span></span> de la résultante :</p><p><span class="katex-display ds-markdown-math"><span class="katex"><span class="katex-mathml">e=L2−Σ(Ni⋅xi)+ΣMcΣNi</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord mathnormal">e</span><span class="mrel">=</span></span><span class="base"><span class="mord"><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist">2<span class="mord mathnormal">L</span></span><span class="vlist-s">​</span></span></span></span></span><span class="mbin">−</span></span><span class="base"><span class="mord"><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist">Σ<span class="mord mathnormal">N</span><span class="msupsub"><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span><span class="vlist-s">​</span></span>Σ<span class="mopen">(</span><span class="mord mathnormal">N</span><span class="msupsub"><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span><span class="vlist-s">​</span></span><span class="mbin">⋅</span><span class="mord mathnormal">x</span><span class="msupsub"><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span><span class="vlist-s">​</span></span><span class="mclose">)</span><span class="mbin">+</span>Σ<span class="mord mathnormal">M</span><span class="msupsub"><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">c</span></span><span class="vlist-s">​</span></span></span><span class="vlist-s">​</span></span></span></span></span></span></span></span></span></p></li><li><p class="ds-markdown-paragraph"><strong>Vérification des contraintes</strong> en fonction de <span class="katex"><span class="katex-mathml">e</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord mathnormal">e</span></span></span></span> :</p><ul><li><p class="ds-markdown-paragraph">Si <span class="katex"><span class="katex-mathml">e≤L6</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord mathnormal">e</span><span class="mrel">≤</span></span><span class="base"><span class="mord"><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">6</span></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">L</span></span></span></span><span class="vlist-s">​</span></span></span></span></span></span></span></span> : <span class="katex"><span class="katex-mathml">σ=ΣNiB⋅L(1+6eL)</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord mathnormal">σ</span><span class="mrel">=</span></span><span class="base"><span class="mord"><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">B</span><span class="mbin mtight">⋅</span><span class="mord mathnormal mtight">L</span></span></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">Σ<span class="mord mathnormal mtight">N</span><span class="msupsub"><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">i</span></span><span class="vlist-s">​</span></span></span></span></span><span class="vlist-s">​</span></span></span></span></span><span class="minner"><span class="mopen delimcenter"><span class="delimsizing size1">(</span></span><span class="mord">1</span><span class="mbin">+</span><span class="mord"><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">L</span></span></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">6<span class="mord mathnormal mtight">e</span></span></span></span><span class="vlist-s">​</span></span></span></span></span><span class="mclose delimcenter"><span class="delimsizing size1">)</span></span></span></span></span></span></p></li><li><p class="ds-markdown-paragraph">Si <span class="katex"><span class="katex-mathml">e>;L6</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord mathnormal">e</span><span class="mrel">>;</span></span><span class="base"><span class="mord"><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">6</span></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">L</span></span></span></span><span class="vlist-s">​</span></span></span></span></span></span></span></span> : <span class="katex"><span class="katex-mathml">σ=2ΣNi3B(L2−e)</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord mathnormal">σ</span><span class="mrel">=</span></span><span class="base"><span class="mord"><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3<span class="mord mathnormal mtight">B</span><span class="minner mtight"><span class="mopen sizing reset-size3 size6 mtight delimcenter"><span class="mtight">(</span></span><span class="sizing reset-size3 size1 mtight">2</span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">L</span></span><span class="vlist-s">​</span><span class="mbin mtight">−</span><span class="mord mathnormal mtight">e</span><span class="mclose sizing reset-size3 size6 mtight delimcenter"><span class="mtight">)</span></span></span></span></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2Σ<span class="mord mathnormal mtight">N</span><span class="msupsub"><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">i</span></span><span class="vlist-s">​</span></span></span></span></span><span class="vlist-s">​</span></span></span></span></span></span></span></span></p></li></ul></li></ol><p class="ds-markdown-paragraph">La contrainte maximale obtenue est de <strong>245 KPa</strong>, inférieure à <span class="katex"><span class="katex-mathml">1,33×σsol=266 KPa</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord">1</span><span class="mpunct">,</span><span class="mord">33</span><span class="mbin">×</span></span><span class="base"><span class="mord"><span class="mord mathnormal">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">so</span><span class="mord mathnormal mtight">l</span></span></span></span><span class="vlist-s">​</span></span></span></span></span><span class="mrel">=</span></span><span class="base"><span class="mord">266</span><span class="mord text"><span class="mord">KPa</span></span></span></span></span>. La largeur finale est donc validée à <strong>1,50 mètres</strong>.</p><hr /><h2><strong>Détermination de la Hauteur de la Semelle</strong></h2><h3><strong>Hauteur Minimale</strong></h3><p class="ds-markdown-paragraph">La hauteur <span class="katex"><span class="katex-mathml">h</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord mathnormal">h</span></span></span></span> de la semelle est déterminée par :</p><p><span class="katex-display ds-markdown-math"><span class="katex"><span class="katex-mathml">h≥B−b4+5 cm</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord mathnormal">h</span><span class="mrel">≥</span></span><span class="base"><span class="mord"><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist">4<span class="mord mathnormal">B</span><span class="mbin">−</span><span class="mord mathnormal">b</span></span><span class="vlist-s">​</span></span></span></span></span><span class="mbin">+</span></span><span class="base"><span class="mord">5</span><span class="mord text"><span class="mord">cm</span></span></span></span></span></span></p><p class="ds-markdown-paragraph">Avec <span class="katex"><span class="katex-mathml">b=0,45 m</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord mathnormal">b</span><span class="mrel">=</span></span><span class="base"><span class="mord">0</span><span class="mpunct">,</span><span class="mord">45</span><span class="mord text"><span class="mord">m</span></span></span></span></span> (côté du poteau), on obtient <span class="katex"><span class="katex-mathml">h≥31,25 cm</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord mathnormal">h</span><span class="mrel">≥</span></span><span class="base"><span class="mord">31</span><span class="mpunct">,</span><span class="mord">25</span><span class="mord text"><span class="mord">cm</span></span></span></span></span>. La hauteur retenue est de <strong>35 cm</strong>.</p><h3><strong>Hauteur de la Nervure</strong></h3><p class="ds-markdown-paragraph">La hauteur de la nervure <span class="katex"><span class="katex-mathml">ht</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord"><span class="mord mathnormal">h</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">t</span></span></span><span class="vlist-s">​</span></span></span></span></span></span></span></span> doit satisfaire trois conditions :</p><ol start="1"><li><p class="ds-markdown-paragraph"><strong>Condition forfaitaire de coffrage</strong> :</p><p><span class="katex-display ds-markdown-math"><span class="katex"><span class="katex-mathml">Lmax8≤ht≤Lmax5</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord"><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist">8<span class="mord mathnormal">L</span><span class="msupsub"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight">max</span></span></span><span class="vlist-s">​</span></span></span><span class="vlist-s">​</span></span></span></span></span><span class="mrel">≤</span></span><span class="base"><span class="mord"><span class="mord mathnormal">h</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">t</span></span></span><span class="vlist-s">​</span></span></span></span></span><span class="mrel">≤</span></span><span class="base"><span class="mord"><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist">5<span class="mord mathnormal">L</span><span class="msupsub"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight">max</span></span></span><span class="vlist-s">​</span></span></span><span class="vlist-s">​</span></span></span></span></span></span></span></span></span></p><p class="ds-markdown-paragraph">Avec <span class="katex"><span class="katex-mathml">Lmax=4,15 m</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight">max</span></span></span></span><span class="vlist-s">​</span></span></span></span></span><span class="mrel">=</span></span><span class="base"><span class="mord">4</span><span class="mpunct">,</span><span class="mord">15</span><span class="mord text"><span class="mord">m</span></span></span></span></span>, on a <span class="katex"><span class="katex-mathml">51,88 cm≤ht≤83 cm</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord">51</span><span class="mpunct">,</span><span class="mord">88</span><span class="mord text"><span class="mord">cm</span></span><span class="mrel">≤</span></span><span class="base"><span class="mord"><span class="mord mathnormal">h</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">t</span></span></span><span class="vlist-s">​</span></span></span></span></span><span class="mrel">≤</span></span><span class="base"><span class="mord">83</span><span class="mord text"><span class="mord">cm</span></span></span></span></span>.</p></li><li><p class="ds-markdown-paragraph"><strong>Condition de non-cisaillement</strong> :</p><p><span class="katex-display ds-markdown-math"><span class="katex"><span class="katex-mathml">ht≥Vu,max⋅γb0,9⋅d⋅fc28</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord"><span class="mord mathnormal">h</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">t</span></span></span><span class="vlist-s">​</span></span></span></span></span><span class="mrel">≥</span></span><span class="base"><span class="mord"><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist">0<span class="mpunct">,</span>9<span class="mbin">⋅</span><span class="mord mathnormal">d</span><span class="mbin">⋅</span><span class="mord mathnormal">f</span><span class="msupsub"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">c</span>28</span></span><span class="vlist-s">​</span></span><span class="mord mathnormal">V</span><span class="msupsub"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">u</span><span class="mpunct mtight">,</span><span class="mord text mtight">max</span></span></span><span class="vlist-s">​</span></span><span class="mbin">⋅</span><span class="mord mathnormal">γ</span><span class="msupsub"><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">b</span></span><span class="vlist-s">​</span></span></span><span class="vlist-s">​</span></span></span></span></span></span></span></span></span></p></li><li><p class="ds-markdown-paragraph"><strong>Condition de rigidité</strong> :</p><p><span class="katex-display ds-markdown-math"><span class="katex"><span class="katex-mathml">ht≥12⋅K⋅b⋅Lmax44E⋅π43</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord"><span class="mord mathnormal">h</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">t</span></span></span><span class="vlist-s">​</span></span></span></span></span><span class="mrel">≥</span></span><span class="base"><span class="mord sqrt"><span class="root"><span class="vlist-t"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size1 mtight"><span class="mord mtight">3</span></span></span></span></span></span><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="svg-align"><span class="mord"><span class="mfrac">4<span class="mord mathnormal">E</span><span class="mbin">⋅</span><span class="mord mathnormal">π</span><span class="msupsub"><span class="vlist-t"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span>12<span class="mbin">⋅</span><span class="mord mathnormal">K</span><span class="mbin">⋅</span><span class="mord mathnormal">b</span><span class="mbin">⋅</span><span class="mord mathnormal">L</span><span class="msupsub"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight">max</span></span></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span><span class="vlist-s">​</span></span><span class="vlist-s">​</span></span></span></span></span><span class="vlist-s">​</span></span></span></span></span></span></span></span></p><p class="ds-markdown-paragraph">Avec <span class="katex"><span class="katex-mathml">K=40 MN/m3</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord mathnormal">K</span><span class="mrel">=</span></span><span class="base"><span class="mord">40</span><span class="mord"><span class="mord text">MN/m</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span></span></span></span></span></span></span>, <span class="katex"><span class="katex-mathml">E=32164195 MPa</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord mathnormal">E</span><span class="mrel">=</span></span><span class="base"><span class="mord">32164195</span><span class="mord text"><span class="mord">MPa</span></span></span></span></span>, et <span class="katex"><span class="katex-mathml">b=0,45 m</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord mathnormal">b</span><span class="mrel">=</span></span><span class="base"><span class="mord">0</span><span class="mpunct">,</span><span class="mord">45</span><span class="mord text"><span class="mord">m</span></span></span></span></span>, on trouve <span class="katex"><span class="katex-mathml">ht≥57 cm</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord"><span class="mord mathnormal">h</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">t</span></span></span><span class="vlist-s">​</span></span></span></span></span><span class="mrel">≥</span></span><span class="base"><span class="mord">57</span><span class="mord text"><span class="mord">cm</span></span></span></span></span>.</p></li></ol><p class="ds-markdown-paragraph">La hauteur finale de la nervure est fixée à <strong>65 cm</strong>.</p><hr /><h2><strong>Calcul du Ferraillage</strong></h2><h3><strong>Modélisation et Moments Fléchissants</strong></h3><p class="ds-markdown-paragraph">La semelle est modélisée comme une poutre continue soumise à une charge linéique <span class="katex"><span class="katex-mathml">q=σ×B=367,5 kN/ml</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord mathnormal">q</span><span class="mrel">=</span></span><span class="base"><span class="mord mathnormal">σ</span><span class="mbin">×</span></span><span class="base"><span class="mord mathnormal">B</span><span class="mrel">=</span></span><span class="base"><span class="mord">367</span><span class="mpunct">,</span><span class="mord">5</span><span class="mord text"><span class="mord">kN/ml</span></span></span></span></span>. Les moments maximaux en travée et sur appui sont :</p><ul><li><p class="ds-markdown-paragraph"><span class="katex"><span class="katex-mathml">MtraveËe=−365,64 kNm</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord"><span class="mord mathnormal">M</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight">trav<span class="mord accent mtight"><span class="vlist-t">e<span class="accent-body">Ë</span></span></span>e</span></span></span></span><span class="vlist-s">​</span></span></span></span></span><span class="mrel">=</span></span><span class="base"><span class="mord">−</span><span class="mord">365</span><span class="mpunct">,</span><span class="mord">64</span><span class="mord text"><span class="mord">kNm</span></span></span></span></span></p></li><li><p class="ds-markdown-paragraph"><span class="katex"><span class="katex-mathml">Mappui=707,37 kNm</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord"><span class="mord mathnormal">M</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight">appui</span></span></span></span><span class="vlist-s">​</span></span></span></span></span><span class="mrel">=</span></span><span class="base"><span class="mord">707</span><span class="mpunct">,</span><span class="mord">37</span><span class="mord text"><span class="mord">kNm</span></span></span></span></span></p></li></ul><h3><strong>Ferraillage en Travée</strong></h3><p class="ds-markdown-paragraph">Le moment négatif implique une traction en partie supérieure. La section d’acier requise est :</p><p><span class="katex-display ds-markdown-math"><span class="katex"><span class="katex-mathml">As,traveËe=15,95 cm2</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">s</span><span class="mpunct mtight">,</span><span class="mord text mtight">trav<span class="mord accent mtight"><span class="vlist-t">e<span class="accent-body">Ë</span></span></span>e</span></span></span></span><span class="vlist-s">​</span></span></span></span></span><span class="mrel">=</span></span><span class="base"><span class="mord">15</span><span class="mpunct">,</span><span class="mord">95</span><span class="mord"><span class="mord text">cm</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></p><p class="ds-markdown-paragraph">Disposition : <strong>4â20 + 4â12</strong> (17,09 cm²)</p><h3><strong>Ferraillage sur Appui</strong></h3><p class="ds-markdown-paragraph">Le moment positif implique une traction en partie inférieure. La section d’acier requise est :</p><p><span class="katex-display ds-markdown-math"><span class="katex"><span class="katex-mathml">As,appui=34,15 cm2</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">s</span><span class="mpunct mtight">,</span><span class="mord text mtight">appui</span></span></span></span><span class="vlist-s">​</span></span></span></span></span><span class="mrel">=</span></span><span class="base"><span class="mord">34</span><span class="mpunct">,</span><span class="mord">15</span><span class="mord"><span class="mord text">cm</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></p><p class="ds-markdown-paragraph">Cette section inclut :</p><ul><li><p class="ds-markdown-paragraph">Aciers de la semelle : <strong>10â14</strong> (15,39 cm²)</p></li><li><p class="ds-markdown-paragraph">Aciers de la nervure : <span class="katex"><span class="katex-mathml">34,15−15,39=18,76 cm2</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord">34</span><span class="mpunct">,</span><span class="mord">15</span><span class="mbin">−</span></span><span class="base"><span class="mord">15</span><span class="mpunct">,</span><span class="mord">39</span><span class="mrel">=</span></span><span class="base"><span class="mord">18</span><span class="mpunct">,</span><span class="mord">76</span><span class="mord"><span class="mord text">cm</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span> → <strong>4â20 + 4â16</strong> (20,61 cm²)</p></li></ul><h3><strong>Dispositions Constructives</strong></h3><ul><li><p class="ds-markdown-paragraph"><strong>Semelle</strong> : Aciers longitudinaux <strong>10â14</strong> et transversaux <strong>â12/15cm</strong>.</p></li><li><p class="ds-markdown-paragraph"><strong>Nervure</strong> :</p><ul><li><p class="ds-markdown-paragraph">Partie inférieure : <strong>4â20 (filants) + 4â16 (renforts)</strong></p></li><li><p class="ds-markdown-paragraph">Partie supérieure : <strong>4â20 + 4â12</strong></p></li></ul></li></ul><hr /><h2><strong>Schémas de Ferraillage</strong></h2><h3><strong>En Travée</strong></h3><ul><li><p class="ds-markdown-paragraph">Aciers supérieurs : 4â20 (filants) + 4â12 (renforts)</p></li></ul><h3><strong>Sur Appui</strong></h3><ul><li><p class="ds-markdown-paragraph">Aciers inférieurs : 10â14 (semelle) + 4â20 (filants) + 4â16 (renforts)</p></li><li><p class="ds-markdown-paragraph">Aciers transversaux : â12 espacés de 15 cm</p></li></ul><hr /><h2><strong>Télécharger le Guide Complet PDF</strong></h2><p class="ds-markdown-paragraph">Découvrez notre guide pratique PDF sur le <strong>Calcul et Dimensionnement d’une Semelle Filante</strong> pour maîtriser toutes les étapes essentielles. Ce document détaillé vous accompagne dans l’analyse structurelle, les calculs de charge, la sélection des dimensions optimales, et le respect des normes en vigueur. Que vous soyez étudiant ou professionnel en génie civil, ce guide complet vous permet de réaliser efficacement le dimensionnement d’une semelle filante, en intégrant les principes fondamentaux de résistance des matériaux, d’architecture et de stabilité. Accédez à des méthodes éprouvées, des exemples pratiques et des conseils pour obtenir une conception sûre et économique. Téléchargez ce PDF pour approfondir vos connaissances, faciliter vos calculs et garantir la réussite de vos projets de fondations en toute confiance. Simplifiez votre travail avec ce référence indispensable pour le <strong>Calcul et Dimensionnement d’une Semelle Filante</strong>.</p><p class="ds-markdown-paragraph">Pour consulter l’intégralité des calculs, des schémas détaillés et des explications techniques, vous pouvez télécharger le document PDF complet :</p><p><span style="font-size: 2em;"><strong><a href="https://cours-genie-civil.com/wp-content/uploads/2025/08/817829948-Calcul-et-dimensionnement-de-Semelle-Filante_watermark.pdf" target="_blank" rel="noopener">ðððð¥ Télécharger le PDF : Calcul et Dimensionnement d’une Semelle Filante</a></strong></span></p><h2>Chapitre des liens utiles</h2><h3><a class="ng-star-inserted" href="https://cours-genie-civil.com/techniques-de-construction-et-de-fondation-guide-complet-en-pdf/" target="_blank" rel="noopener">Guide PDF sur les techniques de construction et de fondation</a></h3><p>Ce document complet est un <b><a class="ng-star-inserted" href="https://cours-genie-civil.com/techniques-de-construction-et-de-fondation-guide-complet-en-pdf/" target="_blank" rel="noopener">guide de référence en PDF</a></b> sur les <b>techniques de construction</b> et la mise en œuvre des <b>fondations</b>. Il est conçu pour les professionnels et les étudiants cherchant des informations détaillées et précises sur ces sujets.</p><h3><a class="ng-star-inserted" href="https://cours-genie-civil.com/cours-gros-oeuvre-detaille-techniques-fondations-muraille-et-securite-sur-chantier-pdf/" target="_blank" rel="noopener">Cours de gros œuvre détaillé : fondations, murailles et sécurité</a></h3><p>Ce cours en format <b><a class="ng-star-inserted" href="https://cours-genie-civil.com/cours-gros-oeuvre-detaille-techniques-fondations-muraille-et-securite-sur-chantier-pdf/" target="_blank" rel="noopener">PDF sur le gros œuvre</a></b> aborde en profondeur les <b>techniques</b> de construction des <b>fondations</b> et des murailles, tout en intégrant des aspects cruciaux de <b>sécurité sur chantier</b>.</p><h3><a class="ng-star-inserted" href="https://www.4geniecivil.com/2022/10/semelle-filante-ferraillage-cours-pdf.html" target="_blank" rel="noopener">Cours et ferraillage des semelles filantes en PDF</a></h3><p>Cet article propose un <b><a class="ng-star-inserted" href="https://www.4geniecivil.com/2022/10/semelle-filante-ferraillage-cours-pdf.html" target="_blank" rel="noopener">cours détaillé</a></b> sur les <b>semelles filantes</b>, en se concentrant spécifiquement sur leur <b>ferraillage</b>. Un guide pratique pour comprendre le dimensionnement et la mise en œuvre de ces éléments de fondation.</p><h3><a class="ng-star-inserted" href="https://www.4geniecivil.com/2018/11/calcul-de-semelles-organigramme.html" target="_blank" rel="noopener">Organigramme de calcul des semelles</a></h3><p>Découvrez une approche structurée pour le <b><a class="ng-star-inserted" href="https://www.4geniecivil.com/2018/11/calcul-de-semelles-organigramme.html" target="_blank" rel="noopener">calcul des semelles</a></b> grâce à cet <b>organigramme</b>. Un outil visuel pour simplifier les étapes du <b>dimensionnement des fondations</b> et garantir la conformité des calculs.</p><h3><a class="ng-star-inserted" href="https://www.4geniecivil.com/2021/11/semelle-filante-definition-et-calcul.html" target="_blank" rel="noopener">Définition et calcul des semelles filantes</a></h3><p>Ce document fournit une <b><a class="ng-star-inserted" href="https://www.4geniecivil.com/2021/11/semelle-filante-definition-et-calcul.html" target="_blank" rel="noopener">définition claire</a></b> et des méthodes de <b>calcul</b> pour les <b>semelles filantes</b>. Il constitue une ressource essentielle pour les étudiants et les professionnels qui souhaitent approfondir leur compréhension de ces éléments.</p><h3><a class="ng-star-inserted" href="https://www.4geniecivil.com/2017/09/semelles-filante-cours-special.html" target="_blank" rel="noopener">Cours spécial sur les semelles filantes</a></h3><p>Consultez ce <b><a class="ng-star-inserted" href="https://www.4geniecivil.com/2017/09/semelles-filante-cours-special.html" target="_blank" rel="noopener">cours spécial</a></b> qui offre un aperçu approfondi des <b>semelles filantes</b>. Ce guide est idéal pour une <b>révision</b> ou pour assimiler les concepts fondamentaux liés à la conception de ces fondations.</p><p>Feuille Excel en action : <a href="https://cours-genie-civil.com/2-notes-de-calcul-de-semelle-isolee-et-semelle-filante-sur-feuille-excel/">calculs de semelle isolée et filante</a> avec zones de saisie, formules automatisées et résultats structurés pour projets de fondation. </p><p>Guide de <a href="https://cours-genie-civil.com/guide-conception-immeuble-beton-arme-pfe/">Dimensionnement Immeuble R+8 Béton Armé</a>. Projet de fin d&rsquo;étude Génie Civil PDF offert en téléchargement. Maîtrisez le calcul des structures </p><h2><strong>Conclusion</strong></h2><p class="ds-markdown-paragraph">Le dimensionnement d’une semelle filante nécessite une approche méthodique, intégrant les charges permanentes, variables et sismiques. Les étapes de vérification des contraintes, de détermination des hauteurs et de calcul des sections d’acier sont essentielles pour garantir la stabilité et la sécurité de l’ouvrage. Ce guide offre un cadre technique robuste pour la conception de semelles filantes nervurées, conformément aux normes en vigueur.</p><div id="ag-popper-container-1756198521085"> </div><p><script src="chrome-extension://lopnbnfpjmgpbppclhclehhgafnifija/aiscripts/script-main.js"></script></p><div class="simg-pop-btn" style="position: absolute; z-index: 1000; top: 84px; left: 14px; display: none;"> </div><div id="ag-popper-container-1756984954359" class="ag-translate-popper-host"> </div><p><script src="chrome-extension://lopnbnfpjmgpbppclhclehhgafnifija/aiscripts/script-main.js"></script></p><div class="host-lopnbnfpjmgpbppclhclehhgafnifija" style="position: relative; z-index: 2147483647;"> </div>								</div>
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Calcul et Dimensionnement d’une Semelle Filante – Guide pratique PDF
