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									<p class="ds-markdown-paragraph">Le radier est une fondation superficielle qui permet de répartir les charges d’un bâtiment sur une large surface de sol. Utilisé lorsque la capacité portante du sol est faible ou lorsque les charges sont importantes, le radier constitue une solution économique et technique adaptée aux structures lourdes ou de grande emprise.</p>
<p class="ds-markdown-paragraph">Dans cet article, nous détaillons pas à pas la méthodologie de calcul d’un radier, depuis la descente de charge jusqu’au ferraillage, en nous appuyant sur un exemple concret issu d’un projet réel. Vous trouverez également un chapitre dédié au téléchargement du PDF complet contenant l’intégralité des calculs et des vérifications.</p>
<p><img class="image_Base_Génie_Civil_fondations_superstructures_matériaux_construction_PDF_débutants alignnone wp-image-8901 size-large" title="Base de Génie Civil : illustration des fondations, superstructures et matériaux de construction pour cours PDF débutants" src="https://cours-genie-civil.com/wp-content/uploads/2025/09/Base-de-Genie-Civil-Cours-Complet-pour-Debutants-en-PDF-2-683x1024.webp" alt="Schéma illustrant les composants d’un bâtiment en génie civil, avec légendes sur l’infrastructure, la superstructure et les matériaux de construction." width="683" height="1024" /></p>
<hr />
<h3><strong>1. Descente de Charge sur le Radier</strong></h3>
<p class="ds-markdown-paragraph">La première étape consiste à évaluer l’ensemble des charges permanentes et variables qui s’appliquent sur le radier.</p>
<h4><strong>Charges permanentes G</strong></h4>
<ul>
<li>
<p class="ds-markdown-paragraph"><strong>P1</strong> : Poids de la gaine<br /><span class="katex"><span class="katex-mathml">P1=A×h×25=1,7×13,90×25=590,75 kN</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord mathnormal">P</span><span class="mord">1</span><span class="mrel">=</span></span><span class="base"><span class="mord mathnormal">A</span><span class="mbin">×</span></span><span class="base"><span class="mord mathnormal">h</span><span class="mbin">×</span></span><span class="base"><span class="mord">25</span><span class="mrel">=</span></span><span class="base"><span class="mord">1</span><span class="mpunct">,</span><span class="mord">7</span><span class="mbin">×</span></span><span class="base"><span class="mord">13</span><span class="mpunct">,</span><span class="mord">90</span><span class="mbin">×</span></span><span class="base"><span class="mord">25</span><span class="mrel">=</span></span><span class="base"><span class="mord">590</span><span class="mpunct">,</span><span class="mord">75</span><span class="mord text"><span class="mord"> kN</span></span></span></span></span></p>
</li>
<li>
<p class="ds-markdown-paragraph"><strong>P2</strong> : Poids de l’édicule<br /><span class="katex"><span class="katex-mathml">P2=2×1,85×0,15×25=13,88 kN</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord mathnormal">P</span><span class="mord">2</span><span class="mrel">=</span></span><span class="base"><span class="mord">2</span><span class="mbin">×</span></span><span class="base"><span class="mord">1</span><span class="mpunct">,</span><span class="mord">85</span><span class="mbin">×</span></span><span class="base"><span class="mord">0</span><span class="mpunct">,</span><span class="mord">15</span><span class="mbin">×</span></span><span class="base"><span class="mord">25</span><span class="mrel">=</span></span><span class="base"><span class="mord">13</span><span class="mpunct">,</span><span class="mord">88</span><span class="mord text"><span class="mord"> kN</span></span></span></span></span></p>
</li>
<li>
<p class="ds-markdown-paragraph"><strong>P3</strong> : Poids de la cabine et équipements<br /><span class="katex"><span class="katex-mathml">P3=6,3+6,32=9,45 kN</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord mathnormal">P</span><span class="mord">3</span><span class="mrel">=</span></span><span class="base"><span class="mord">6</span><span class="mpunct">,</span><span class="mord">3</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"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">6<span class="mpunct mtight">,</span>3</span></span></span><span class="vlist-s">​</span></span></span></span></span><span class="mrel">=</span></span><span class="base"><span class="mord">9</span><span class="mpunct">,</span><span class="mord">45</span><span class="mord text"><span class="mord"> kN</span></span></span></span></span></p>
</li>
<li>
<p class="ds-markdown-paragraph"><strong>P4</strong> : Contrepoids<br /><span class="katex"><span class="katex-mathml">P4=6,3+45×6,3100=9,135 kN</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord mathnormal">P</span><span class="mord">4</span><span class="mrel">=</span></span><span class="base"><span class="mord">6</span><span class="mpunct">,</span><span class="mord">3</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"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">100</span></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">45<span class="mbin mtight">×</span>6<span class="mpunct mtight">,</span>3</span></span></span><span class="vlist-s">​</span></span></span></span></span><span class="mrel">=</span></span><span class="base"><span class="mord">9</span><span class="mpunct">,</span><span class="mord">135</span><span class="mord text"><span class="mord"> kN</span></span></span></span></span></p>
</li>
<li>
<p class="ds-markdown-paragraph"><strong>P5</strong> : Poids propre du radier (à déterminer ultérieurement)</p>
</li>
</ul>
<p class="ds-markdown-paragraph"><strong>Total des charges permanentes :</strong><br /><span class="katex"><span class="katex-mathml">G=P1+P2+P3+P4=623,215 kN</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord mathnormal">G</span><span class="mrel">=</span></span><span class="base"><span class="mord mathnormal">P</span><span class="mord">1</span><span class="mbin">+</span></span><span class="base"><span class="mord mathnormal">P</span><span class="mord">2</span><span class="mbin">+</span></span><span class="base"><span class="mord mathnormal">P</span><span class="mord">3</span><span class="mbin">+</span></span><span class="base"><span class="mord mathnormal">P</span><span class="mord">4</span><span class="mrel">=</span></span><span class="base"><span class="mord">623</span><span class="mpunct">,</span><span class="mord">215</span><span class="mord text"><span class="mord"> kN</span></span></span></span></span></p>
<h4><strong>Charges d’exploitation Q</strong></h4>
<p class="ds-markdown-paragraph"><span class="katex"><span class="katex-mathml">Q=1,5×2×1,85=5,55 kN</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">1</span><span class="mpunct">,</span><span class="mord">5</span><span class="mbin">×</span></span><span class="base"><span class="mord">2</span><span class="mbin">×</span></span><span class="base"><span class="mord">1</span><span class="mpunct">,</span><span class="mord">85</span><span class="mrel">=</span></span><span class="base"><span class="mord">5</span><span class="mpunct">,</span><span class="mord">55</span><span class="mord text"><span class="mord"> kN</span></span></span></span></span></p>
<h4><strong>Charges aux ELU et ELS</strong></h4>
<ul>
<li>
<p class="ds-markdown-paragraph"><strong>ELU</strong> : <span class="katex"><span class="katex-mathml">1,35G+1,5Q=849,67 kN</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord">1</span><span class="mpunct">,</span><span class="mord">35</span><span class="mord mathnormal">G</span><span class="mbin">+</span></span><span class="base"><span class="mord">1</span><span class="mpunct">,</span><span class="mord">5</span><span class="mord mathnormal">Q</span><span class="mrel">=</span></span><span class="base"><span class="mord">849</span><span class="mpunct">,</span><span class="mord">67</span><span class="mord text"><span class="mord"> kN</span></span></span></span></span></p>
</li>
<li>
<p class="ds-markdown-paragraph"><strong>ELS</strong> : <span class="katex"><span class="katex-mathml">G+Q=628,765 kN</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="mrel">=</span></span><span class="base"><span class="mord">628</span><span class="mpunct">,</span><span class="mord">765</span><span class="mord text"><span class="mord"> kN</span></span></span></span></span></p>
</li>
</ul>
<hr />
<h3><strong>2. Détermination de l’Épaisseur du Radier</strong></h3>
<p class="ds-markdown-paragraph">Plusieurs conditions régissent le choix de l’épaisseur du radier :</p>
<h4><strong>Formule empirique</strong></h4>
<p><span class="katex-display ds-markdown-math"><span class="katex"><span class="katex-mathml">h≥Lmax10=20010=20 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">10<span class="mord mathnormal">L</span><span class="msupsub"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">ma</span><span class="mord mathnormal mtight">x</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="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist">10200</span><span class="vlist-s">​</span></span></span></span></span><span class="mrel">=</span></span><span class="base"><span class="mord">20</span><span class="mord text"><span class="mord"> cm</span></span></span></span></span></span></p>
<h4><strong>Condition minimale</strong></h4>
<p><span class="katex-display ds-markdown-math"><span class="katex"><span class="katex-mathml">hmin≥25 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 mtight"><span class="mord mathnormal mtight">min</span></span></span></span><span class="vlist-s">​</span></span></span></span></span><span class="mrel">≥</span></span><span class="base"><span class="mord">25</span><span class="mord text"><span class="mord"> cm</span></span></span></span></span></span></p>
<h4><strong>Condition forfaitaire</strong></h4>
<p><span class="katex-display ds-markdown-math"><span class="katex"><span class="katex-mathml">Lmax8≤hr≤Lmax5⇒25≤hr≤40 cm</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 mathnormal mtight">ma</span><span class="mord mathnormal mtight">x</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">r</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 mathnormal mtight">ma</span><span class="mord mathnormal mtight">x</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">25</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">r</span></span></span><span class="vlist-s">​</span></span></span></span></span><span class="mrel">≤</span></span><span class="base"><span class="mord">40</span><span class="mord text"><span class="mord"> cm</span></span></span></span></span></span></p>
<h4><strong>Condition de longueur élastique</strong></h4>
<p><span class="katex-display ds-markdown-math"><span class="katex"><span class="katex-mathml">hr≥[(2×200π)4⋅3×4010819]1/3=142,89 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">r</span></span></span><span class="vlist-s">​</span></span></span></span></span><span class="mrel">≥</span></span><span class="base"><span class="minner"><span class="mopen delimcenter"><span class="delimsizing size4">[</span></span><span class="mopen delimcenter"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="mord mathnormal">π</span>2<span class="mbin">×</span>200</span><span class="vlist-s">​</span></span></span></span></span><span class="mclose delimcenter"><span class="delimsizing size3">)</span></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">4</span></span></span></span></span></span><span class="mbin">⋅</span><span class="mord"><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist">108193<span class="mbin">×</span>40</span><span class="vlist-s">​</span></span></span></span></span><span class="mclose delimcenter"><span class="delimsizing size4">]</span></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">1/3</span></span></span></span></span></span></span><span class="mrel">=</span></span><span class="base"><span class="mord">142</span><span class="mpunct">,</span><span class="mord">89</span><span class="mord text"><span class="mord"> cm</span></span></span></span></span></span></p>
<p class="ds-markdown-paragraph">Cependant, pour des raisons pratiques et normatives, on retient une épaisseur de <strong>25 cm</strong>.</p>
<hr />
<h3><strong>3. Épaisseur de la Dalle du Radier</strong></h3>
<p class="ds-markdown-paragraph">La dalle doit satisfaire :</p>
<p><span class="katex-display ds-markdown-math"><span class="katex"><span class="katex-mathml">h≥Lmax20=22020=11 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">20<span class="mord mathnormal">L</span><span class="msupsub"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">ma</span><span class="mord mathnormal mtight">x</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="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist">20220</span><span class="vlist-s">​</span></span></span></span></span><span class="mrel">=</span></span><span class="base"><span class="mord">11</span><span class="mord text"><span class="mord"> cm</span></span></span></span></span></span></p>
<p class="ds-markdown-paragraph">On choisit une épaisseur de <strong>20 cm</strong> pour des raisons de rigidité et de sécurité.</p>
<hr />
<h3><strong>4. Surface du Radier et Débord</strong></h3>
<h4><strong>Surface minimale à l’ELS</strong></h4>
<p><span class="katex-display ds-markdown-math"><span class="katex"><span class="katex-mathml">Sradier≥Nserσsol=628,765130=4,84 m2</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord"><span class="mord mathnormal">S</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">r</span><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">d</span><span class="mord mathnormal mtight">i</span><span class="mord mathnormal mtight">er</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 class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="mord mathnormal">σ</span><span class="msupsub"><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 class="vlist-s">​</span></span><span class="mord mathnormal">N</span><span class="msupsub"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">ser</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="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist">130628<span class="mpunct">,</span>765</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">84</span><span class="mord"><span class="mord text"> 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">2</span></span></span></span></span></span></span></span></span></span></span></p>
<p class="ds-markdown-paragraph">La surface du bâtiment est de <span class="katex"><span class="katex-mathml">2,40×2,25=5,40 m2</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord">2</span><span class="mpunct">,</span><span class="mord">40</span><span class="mbin">×</span></span><span class="base"><span class="mord">2</span><span class="mpunct">,</span><span class="mord">25</span><span class="mrel">=</span></span><span class="base"><span class="mord">5</span><span class="mpunct">,</span><span class="mord">40</span><span class="mord"><span class="mord text"> 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">2</span></span></span></span></span></span></span></span></span></span>. Un débord est donc prévu :</p>
<ul>
<li>
<p class="ds-markdown-paragraph">Largeur de débord : <span class="katex"><span class="katex-mathml">LD=max⁡(h2;30 cm)=30 cm</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 mathnormal mtight">D</span></span></span><span class="vlist-s">​</span></span></span></span></span><span class="mrel">=</span></span><span class="base"><span class="mop">max</span><span class="minner"><span class="mopen delimcenter"><span class="delimsizing size1">(</span></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">2</span></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">h</span></span></span></span><span class="vlist-s">​</span></span></span></span></span><span class="mpunct">;</span><span class="mord">30</span><span class="mord text"><span class="mord"> cm</span></span><span class="mclose delimcenter"><span class="delimsizing size1">)</span></span></span><span class="mrel">=</span></span><span class="base"><span class="mord">30</span><span class="mord text"><span class="mord"> cm</span></span></span></span></span></p>
</li>
<li>
<p class="ds-markdown-paragraph">Surface totale :</p>
<p><span class="katex-display ds-markdown-math"><span class="katex"><span class="katex-mathml">Sradier=2,40×2,25+(3×2,85−2,40×2,25)=8,55 m2</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord"><span class="mord mathnormal">S</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">r</span><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">d</span><span class="mord mathnormal mtight">i</span><span class="mord mathnormal mtight">er</span></span></span></span><span class="vlist-s">​</span></span></span></span></span><span class="mrel">=</span></span><span class="base"><span class="mord">2</span><span class="mpunct">,</span><span class="mord">40</span><span class="mbin">×</span></span><span class="base"><span class="mord">2</span><span class="mpunct">,</span><span class="mord">25</span><span class="mbin">+</span></span><span class="base"><span class="mopen">(</span><span class="mord">3</span><span class="mbin">×</span></span><span class="base"><span class="mord">2</span><span class="mpunct">,</span><span class="mord">85</span><span class="mbin">−</span></span><span class="base"><span class="mord">2</span><span class="mpunct">,</span><span class="mord">40</span><span class="mbin">×</span></span><span class="base"><span class="mord">2</span><span class="mpunct">,</span><span class="mord">25</span><span class="mclose">)</span><span class="mrel">=</span></span><span class="base"><span class="mord">8</span><span class="mpunct">,</span><span class="mord">55</span><span class="mord"><span class="mord text"> 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">2</span></span></span></span></span></span></span></span></span></span></span></p>
</li>
</ul>
<hr />
<h3><strong>5. Vérification au Cisaillement</strong></h3>
<p><span class="katex-display ds-markdown-math"><span class="katex"><span class="katex-mathml">τu=Vub⋅d=921,768,55=107,81 kN/m2=0,108 MPa</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord"><span class="mord mathnormal">τ</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">u</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"><span class="mord mathnormal">b</span><span class="mbin">⋅</span><span class="mord mathnormal">d</span><span class="mord mathnormal">V</span><span class="msupsub"><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">u</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="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist">8<span class="mpunct">,</span>55921<span class="mpunct">,</span>76</span><span class="vlist-s">​</span></span></span></span></span><span class="mrel">=</span></span><span class="base"><span class="mord">107</span><span class="mpunct">,</span><span class="mord">81</span><span class="mord"><span class="mord text"> kN/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">2</span></span></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">108</span><span class="mord text"><span class="mord"> MPa</span></span></span></span></span></span></p>
<p class="ds-markdown-paragraph">À comparer à <span class="katex"><span class="katex-mathml">0,05⋅fc28=1,25 MPa</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord">0</span><span class="mpunct">,</span><span class="mord">05</span><span class="mbin">⋅</span></span><span class="base"><span class="mord"><span class="mord mathnormal">f</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">c</span>28</span></span></span><span class="vlist-s">​</span></span></span></span></span><span class="mrel">=</span></span><span class="base"><span class="mord">1</span><span class="mpunct">,</span><span class="mord">25</span><span class="mord text"><span class="mord"> MPa</span></span></span></span></span>. La condition est vérifiée.</p>
<hr />
<h3><strong>6. Vérification au Poinçonnement</strong></h3>
<p><span class="katex-display ds-markdown-math"><span class="katex"><span class="katex-mathml">Nu≤0,07⋅μC⋅h⋅fc28γb=3,4 MN</span><span class="katex-html" aria-hidden="true"><span class="base"><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">u</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"><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>0<span class="mpunct">,</span>07<span class="mbin">⋅</span><span class="mord mathnormal">μ</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 class="mbin">⋅</span><span class="mord mathnormal">h</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><span class="vlist-s">​</span></span></span></span></span><span class="mrel">=</span></span><span class="base"><span class="mord">3</span><span class="mpunct">,</span><span class="mord">4</span><span class="mord text"><span class="mord"> MN</span></span></span></span></span></span></p>
<p class="ds-markdown-paragraph">Avec <span class="katex"><span class="katex-mathml">Nu=0,3 MN</span><span class="katex-html" aria-hidden="true"><span class="base"><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">u</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">3</span><span class="mord text"><span class="mord"> MN</span></span></span></span></span>, la condition est largement satisfaite.</p>
<hr />
<h3><strong>7. Calcul des Ferraillages</strong></h3>
<h4><strong>Ferraillage de la dalle</strong></h4>
<p class="ds-markdown-paragraph">La dalle est calculée comme un plancher renversé appuyé sur 4 côtés, soumis à la réaction du sol.</p>
<ul>
<li>
<p class="ds-markdown-paragraph">Charge ultime :</p>
<p><span class="katex-display ds-markdown-math"><span class="katex"><span class="katex-mathml">qu=1,35G+1,5QSradier=849,678,55=99,38 kN/m2</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord"><span class="mord mathnormal">q</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">u</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"><span class="mord mathnormal">S</span><span class="msupsub"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">r</span><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">d</span><span class="mord mathnormal mtight">i</span><span class="mord mathnormal mtight">er</span></span></span><span class="vlist-s">​</span></span>1<span class="mpunct">,</span>35<span class="mord mathnormal">G</span><span class="mbin">+</span>1<span class="mpunct">,</span>5<span class="mord mathnormal">Q</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">8<span class="mpunct">,</span>55849<span class="mpunct">,</span>67</span><span class="vlist-s">​</span></span></span></span></span><span class="mrel">=</span></span><span class="base"><span class="mord">99</span><span class="mpunct">,</span><span class="mord">38</span><span class="mord"><span class="mord text"> kN/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">2</span></span></span></span></span></span></span></span></span></span></span></p>
</li>
<li>
<p class="ds-markdown-paragraph">Charge de service :</p>
<p><span class="katex-display ds-markdown-math"><span class="katex"><span class="katex-mathml">qser=G+QSradier=628,7658,55=73,56 kN/m2</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord"><span class="mord mathnormal">q</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">ser</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 class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="mord mathnormal">S</span><span class="msupsub"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">r</span><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">d</span><span class="mord mathnormal mtight">i</span><span class="mord mathnormal mtight">er</span></span></span><span class="vlist-s">​</span></span><span class="mord mathnormal">G</span><span class="mbin">+</span><span class="mord mathnormal">Q</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">8<span class="mpunct">,</span>55628<span class="mpunct">,</span>765</span><span class="vlist-s">​</span></span></span></span></span><span class="mrel">=</span></span><span class="base"><span class="mord">73</span><span class="mpunct">,</span><span class="mord">56</span><span class="mord"><span class="mord text"> kN/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">2</span></span></span></span></span></span></span></span></span></span></span></p>
</li>
</ul>
<h4><strong>Ferraillage des nervures</strong></h4>
<p class="ds-markdown-paragraph">Les nervures sont calculées comme des poutres doublement encastrées, soumises aux charges réparties <span class="katex"><span class="katex-mathml">qu</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord"><span class="mord mathnormal">q</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">u</span></span></span><span class="vlist-s">​</span></span></span></span></span></span></span></span> et <span class="katex"><span class="katex-mathml">qser</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord"><span class="mord mathnormal">q</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">ser</span></span></span></span><span class="vlist-s">​</span></span></span></span></span></span></span></span>.</p>
<hr />
<h3><strong>Télécharger le PDF Complet sur le Calcul du Radier</strong></h3>
<p class="ds-markdown-paragraph">Vous souhaitez consulter l’intégralité des calculs, formules détaillées, et les plans de ferraillage ?<br />ð¥ <strong>Téléchargez gratuitement le PDF complet</strong> :<br />Lien de téléchargement du document :</p>
<p><span style="font-size: 2em;"><b>ð</b><b>ð</b><strong><a href="https://cours-genie-civil.com/wp-content/uploads/2025/09/420598144-Calcul-Du-Radier-1-0_watermark.pdf">Calcul-Du-Radier.pdf</a></strong></span></p>
<p class="ds-markdown-paragraph">Ce document inclut :</p>
<ul>
<li>
<p class="ds-markdown-paragraph">Les calculs complets de descente de charge</p>
</li>
<li>
<p class="ds-markdown-paragraph">Les vérifications techniques détaillées</p>
</li>
<li>
<p class="ds-markdown-paragraph">Les schémas de ferraillage</p>
</li>
<li>
<p class="ds-markdown-paragraph">Les références aux normes BAEL 91</p>
</li>
</ul>
<hr />
<h3><strong>Conclusion</strong></h3>
<p class="ds-markdown-paragraph">Le calcul d’un radier requiert une approche méthodique et normée, intégrant à la fois les charges structurelles, les caractéristiques du sol, et les exigences de sécurité. Les vérifications au cisaillement, au poinçonnement, et le dimensionnement des ferraillages sont essentiels pour garantir la stabilité et la durabilité de l’ouvrage.</p>
<p class="ds-markdown-paragraph">Que vous soyez ingénieur, étudiant en génie civil, ou maître d’œuvre, ce guide et le PDF associé vous offrent une ressource complète pour concevoir et vérifier un radier de fondation en toute confiance.</p>
<h2>Chapitre des liens utiles</h2>
<p>Voici un chapitre de liens utiles, détaillant les titres et intégrant les liens dans les mots-clés principaux pour une meilleure compréhension des fondations de type radier et semelle.</p>
<hr />
<p><b>Cours complet sur les radiers et les fondations</b> Ce lien propose un guide détaillé sur les <b><a class="ng-star-inserted" href="https://cours-genie-civil.com/cours-sur-les-radiers-telecharger-le-pdf-complet/" target="_blank" rel="noopener" data-hveid="0" data-ved="0CAAQ_4QMahcKEwiRg47P8MGPAxUAAAAAHQAAAAAQUA">radiers</a></b>, une solution de fondation adaptée aux sols de faible portance. Vous y apprendrez la définition du radier, ses avantages, les critères de choix, ainsi que les différents types, tels que le radier plat, nervuré ou champignon. Le document couvre également la conception et la mise en œuvre, en insistant sur le rôle crucial du ferraillage pour la stabilité de la structure.</p>
<hr />
<p><b>Notes de calcul pour semelles isolées et filantes</b> Cette page fournit des <b><a class="ng-star-inserted" href="https://cours-genie-civil.com/2-notes-de-calcul-de-semelle-isolee-et-semelle-filante-sur-feuille-excel/" target="_blank" rel="noopener" data-hveid="0" data-ved="0CAAQ_4QMahcKEwiRg47P8MGPAxUAAAAAHQAAAAAQUQ">notes de calcul</a></b> pour les semelles de fondation, éléments essentiels pour transmettre les charges d&rsquo;un ouvrage au sol. Vous y trouverez des exemples de calcul pour les semelles isolées et les semelles filantes, basés sur les normes BAEL, avec la possibilité de télécharger des fichiers Excel pour simplifier le processus de conception et réduire les erreurs.</p>
<hr />
<p><b>Définition et construction des radiers de fondation</b> Découvrez la définition et les étapes de construction d&rsquo;un <b><a class="ng-star-inserted" href="https://www.4geniecivil.com/2020/02/definition-du-radier-fondation-genie.html" target="_blank" rel="noopener" data-hveid="0" data-ved="0CAAQ_4QMahcKEwiRg47P8MGPAxUAAAAAHQAAAAAQUg">radier de fondation</a></b>, une dalle en béton armé qui répartit les charges d&rsquo;un bâtiment sur toute sa surface. L&rsquo;article explique pourquoi cette fondation est choisie pour les sols instables et détaille les différentes phases de sa mise en place, de la préparation du sol au coulage du béton, en passant par l&rsquo;armature en acier.</p>
<hr />
<p><b>Note de calcul de radier sur Excel</b> Téléchargez une <b><a class="ng-star-inserted" href="https://www.4geniecivil.com/2018/07/note-de-calcul-radier-en-excel.html" target="_blank" rel="noopener" data-hveid="0" data-ved="0CAAQ_4QMahcKEwiRg47P8MGPAxUAAAAAHQAAAAAQUw">note de calcul de radier</a></b> au format Excel. Cette ressource est idéale pour les étudiants et les professionnels qui souhaitent un exemple pratique de calcul basé sur la norme BAEL. Elle propose également une présentation PowerPoint pour mieux comprendre les méthodes de calcul et des liens vers d&rsquo;autres ressources pour le dimensionnement et le ferraillage des radiers.</p>
<hr />
<p><b>Calcul du radier en béton armé selon les normes</b> Ce document propose un cours détaillé sur le <b><a class="ng-star-inserted" href="https://www.4geniecivil.com/2016/11/calcul-radier-beton-arme.html" target="_blank" rel="noopener" data-hveid="0" data-ved="0CAAQ_4QMahcKEwiRg47P8MGPAxUAAAAAHQAAAAAQVA">calcul du radier</a></b> en béton armé, destiné à ceux qui veulent approfondir leurs connaissances. Il aborde les généralités sur les fondations, les types de radiers et leurs pathologies, ainsi que les méthodes de calcul statique et numérique, notamment avec le logiciel Robot Millinium pour la modélisation et l&rsquo;analyse.</p>
<p>Découvrez <a href="https://www.4geniecivil.com/2025/09/differents-types-fondations-pdf.html">les différents types de fondations</a> en construction : superficielles, profondes et spéciales. Téléchargez gratuitement le cours PDF pour tout.</p>
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Calcul Radier PDF pour Débutants : Fondations en Radier, Étapes Techniques et Cas Concret à Télécharger
