Bélidor, Bernard Forest de, La science des ingenieurs dans la conduite des travaux de fortification et d' architecture civile

Table of Notes

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            <pb o="16" file="0124" n="127" rhead="LA SCIENCE DES INGENIEURS,"/>
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          <div xml:id="echoid-div160" type="section" level="2" n="13">
            <head xml:id="echoid-head123" style="it" xml:space="preserve">Remarque ſeconde.</head>
            <p>
              <s xml:id="echoid-s2305" xml:space="preserve">13. </s>
              <s xml:id="echoid-s2306" xml:space="preserve">Nous venons de ſupoſer que l’extradoſe de la Voûte, ſur la-
                <lb/>
              quelle nous avons operé, étoit circulaire, parce qu’il s’en rencontre
                <lb/>
              qui ont cette figure; </s>
              <s xml:id="echoid-s2307" xml:space="preserve">mais comme dans les Places de Guerre les
                <lb/>
              Voûtes des ſouterrains & </s>
              <s xml:id="echoid-s2308" xml:space="preserve">celles des Magaſins à poudre ont toûjours
                <lb/>
              leurs extradoſes terminés en dos d’âne, pour l’écoulement des eaux de
                <lb/>
                <note position="left" xlink:label="note-0124-01" xlink:href="note-0124-01a" xml:space="preserve">
                  <emph style="sc">Fig</emph>
                . 10.</note>
              pluye, & </s>
              <s xml:id="echoid-s2309" xml:space="preserve">pour qu’elles réſiſtent mieux en tems de Siége au choc
                <lb/>
              des bombes, il eſt bon de nous arrêter ici un moment pour faire
                <lb/>
              voir qu’on trouvera l’épaiſſeur des piés-droits de ces ſortes de Voûtes
                <lb/>
              de la même maniere que dans le Probléme précédent.</s>
              <s xml:id="echoid-s2310" xml:space="preserve"/>
            </p>
            <p>
              <s xml:id="echoid-s2311" xml:space="preserve">Prenant pour exemple le Profil d’un Magaſin à Poudre, il faut
                <lb/>
              être prévenu que pour mettre ces ſortes d’édifices à l’épreuve de
                <lb/>
              la Bombe, on donne ordinairement à la Voûte 3 pieds d’épaiſſeur
                <lb/>
              au milieu des reins; </s>
              <s xml:id="echoid-s2312" xml:space="preserve">c’eſt-à-dire, qu’ayant diviſé le quart de cercle
                <lb/>
              BD, en deux également au point C, on prolonge le rayon AC, juſ-
                <lb/>
              qu’en F, enſorte que CF, ſoit de 3 pieds: </s>
              <s xml:id="echoid-s2313" xml:space="preserve">& </s>
              <s xml:id="echoid-s2314" xml:space="preserve">afin de bien diriger
                <lb/>
              les pantes GH, & </s>
              <s xml:id="echoid-s2315" xml:space="preserve">GI, on les fait perpendiculaires ſur le rayon AF,
                <lb/>
              & </s>
              <s xml:id="echoid-s2316" xml:space="preserve">alors elles forment un angle droit HGI, au ſommet, qui eſt l’an-
                <lb/>
              gle qui convient le mieux pour ne point rendre le Magaſin trop
                <lb/>
              élevé ni trop écraſé.</s>
              <s xml:id="echoid-s2317" xml:space="preserve"/>
            </p>
            <p>
              <s xml:id="echoid-s2318" xml:space="preserve">Cela poſé, ſi l’on ſupoſe le rayon AB, de 12 pieds; </s>
              <s xml:id="echoid-s2319" xml:space="preserve">la ligne AF,
                <lb/>
              de 15; </s>
              <s xml:id="echoid-s2320" xml:space="preserve">& </s>
              <s xml:id="echoid-s2321" xml:space="preserve">la hauteur du pié-droit ZP auſſi de 15, nous aurons les
                <lb/>
              mêmes lignes que ci-devant, & </s>
              <s xml:id="echoid-s2322" xml:space="preserve">chacune ſera exprimée par les mê-
                <lb/>
              mes lettres & </s>
              <s xml:id="echoid-s2323" xml:space="preserve">les mêmes nombres, & </s>
              <s xml:id="echoid-s2324" xml:space="preserve">il n’y aura que les deux parties
                <lb/>
              égales CFGD & </s>
              <s xml:id="echoid-s2325" xml:space="preserve">CFHB de la Voûte qui ſeront differentes, étant
                <lb/>
              beaucoup plus conſidérables: </s>
              <s xml:id="echoid-s2326" xml:space="preserve">ce qui changera la valeur de nn.</s>
              <s xml:id="echoid-s2327" xml:space="preserve"/>
            </p>
            <p>
              <s xml:id="echoid-s2328" xml:space="preserve">Les triangles LKA & </s>
              <s xml:id="echoid-s2329" xml:space="preserve">NOP, étant enſemble, l’on aura LA (b)
                <lb/>
              LK (a) : </s>
              <s xml:id="echoid-s2330" xml:space="preserve">: </s>
              <s xml:id="echoid-s2331" xml:space="preserve">NP (f-y). </s>
              <s xml:id="echoid-s2332" xml:space="preserve">PO ({af-ay/b)} & </s>
              <s xml:id="echoid-s2333" xml:space="preserve">comme la partie CFGD
                <lb/>
              de la Voûte agit toûjours ſur le joint FC ou ſur la puiſſance O, dont
                <lb/>
              la direction OL eſt perpendiculaire ſur le milieu du joint FC, l’ex-
                <lb/>
              preſſion de cette puiſſance ſera encore {nnb/a}, laquelle étant multi-
                <lb/>
              pliée par ſon bras de lévier PO, il vient nnf-nny pour la pouſſée
                <lb/>
              de la Voûte par raport au point d’apui P.</s>
              <s xml:id="echoid-s2334" xml:space="preserve"/>
            </p>
            <p>
              <s xml:id="echoid-s2335" xml:space="preserve">D’un autre côté la réſiſtance du pié-droit ſera le produit de ſa ſu-
                <lb/>
              perficie par la moitié de la baſe PS, qui donne {dyy/2}, à quoi ajoûtant
                <lb/>
              le produit de la ſuperficie de la partie CFHB par ſon bras de lévier
                <lb/>
              PR (y-g) l’on aura {dyy/2}+nny-nng pour l’expreſſion de la </s>
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