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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              <s xml:id="echoid-s6767" xml:space="preserve">
                <pb o="21" file="0305" n="316" rhead="LIVRE IV. DES EDIFICES MILITAIRES."/>
              en quarré, & </s>
              <s xml:id="echoid-s6768" xml:space="preserve">la baſe de l’autre 6. </s>
              <s xml:id="echoid-s6769" xml:space="preserve">pouces auſſi en quarré, leur for-
                <lb/>
              ce ſera dans le raport des cubes des côtés de leur baſes: </s>
              <s xml:id="echoid-s6770" xml:space="preserve">par con-
                <lb/>
              ſequent comme un eſt à 216. </s>
              <s xml:id="echoid-s6771" xml:space="preserve">ainſi la Solive d’un pouce en quarré
                <lb/>
              & </s>
              <s xml:id="echoid-s6772" xml:space="preserve">de 3. </s>
              <s xml:id="echoid-s6773" xml:space="preserve">pieds de longueur portant 300. </s>
              <s xml:id="echoid-s6774" xml:space="preserve">livres, arrêtée par les
                <lb/>
              deux bouts, celle qui auroit 3. </s>
              <s xml:id="echoid-s6775" xml:space="preserve">pieds en longueur & </s>
              <s xml:id="echoid-s6776" xml:space="preserve">6. </s>
              <s xml:id="echoid-s6777" xml:space="preserve">pouces
                <lb/>
              en quarré portera donc 64800. </s>
              <s xml:id="echoid-s6778" xml:space="preserve">mais comme cette derniere Solive
                <lb/>
              eſt très commode, pour ſervir de modêle dans la maniere de con-
                <lb/>
              noître la force du bois, nous nous en ſervirons préférablement
                <lb/>
              à toute autre, pour les operations ſuivantes; </s>
              <s xml:id="echoid-s6779" xml:space="preserve">c’eſt-à-dire, que nous
                <lb/>
              regarderons comme indubitable, qu’une Solive de 3. </s>
              <s xml:id="echoid-s6780" xml:space="preserve">pieds de
                <lb/>
              longueur & </s>
              <s xml:id="echoid-s6781" xml:space="preserve">de 6. </s>
              <s xml:id="echoid-s6782" xml:space="preserve">pouces en quarré porte dans ſon milieu 64800
                <lb/>
              avant l’inſtant de ſe rompre, lors qu’elle eſt parfaitement ſerrée
                <lb/>
              par les deux bouts.</s>
              <s xml:id="echoid-s6783" xml:space="preserve"/>
            </p>
            <p>
              <s xml:id="echoid-s6784" xml:space="preserve">Preſentement, ſi l’on avoit une poutre de 30. </s>
              <s xml:id="echoid-s6785" xml:space="preserve">pieds de lon-
                <lb/>
              gueur entre ſes deux apuis, & </s>
              <s xml:id="echoid-s6786" xml:space="preserve">de 12. </s>
              <s xml:id="echoid-s6787" xml:space="preserve">pouces en quarré, dont les
                <lb/>
              extrêmités ſeroient bien engagées & </s>
              <s xml:id="echoid-s6788" xml:space="preserve">ſerrées dans deux murs, & </s>
              <s xml:id="echoid-s6789" xml:space="preserve">
                <lb/>
              qu’on voulut ſavoir qu’elle eſt la charge que peut porter cette
                <lb/>
              poutre dans ſon milieu, avant l’inſtant de ſe rompre; </s>
              <s xml:id="echoid-s6790" xml:space="preserve">il faut com-
                <lb/>
              mencer par diviſer 216. </s>
              <s xml:id="echoid-s6791" xml:space="preserve">par 3. </s>
              <s xml:id="echoid-s6792" xml:space="preserve">c’eſt-à-dire, le cube de la hauteur de
                <lb/>
              la Solive, qui doit ſervir de modele par ſa longueur, & </s>
              <s xml:id="echoid-s6793" xml:space="preserve">le quo-
                <lb/>
              tient ſera 72. </s>
              <s xml:id="echoid-s6794" xml:space="preserve">qui doit ſervir de premier terme à une regle de pro-
                <lb/>
              portion, dont le ſecond ſera le poids que peut porter cette ſolive,
                <lb/>
              c’eſt-à-dire, 64800. </s>
              <s xml:id="echoid-s6795" xml:space="preserve">pour avoir le troiſiéme terme, il faut quarrer
                <lb/>
              la hauteur de la poutre dont il eſt queſtion, multiplier ce quarré
                <lb/>
              par la largeur de la baſe, diviſer enſuite le produit qui eſt ici 1728.
                <lb/>
              </s>
              <s xml:id="echoid-s6796" xml:space="preserve">par la longueur de la poutre, qu’on ſupoſe être de 30. </s>
              <s xml:id="echoid-s6797" xml:space="preserve">pieds,
                <lb/>
              & </s>
              <s xml:id="echoid-s6798" xml:space="preserve">en prendre le quotient; </s>
              <s xml:id="echoid-s6799" xml:space="preserve">faiſant la regle comme à l’ordinaire,
                <lb/>
              le quatriéme terme donnera le poids que doit porter la poutre,
                <lb/>
              qui ſe trouvera de 51840.</s>
              <s xml:id="echoid-s6800" xml:space="preserve">, on aura de même la force de toute au-
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              tre poutre, dont les dimenſions ſeroient telles qu’on voudra.</s>
              <s xml:id="echoid-s6801" xml:space="preserve"/>
            </p>
            <p>
              <s xml:id="echoid-s6802" xml:space="preserve">Si la poutre, dont on demande la force, n’étoit point ſerrée par
                <lb/>
              ſes deux bouts, mais ſeulement poſée ſur deux apuis; </s>
              <s xml:id="echoid-s6803" xml:space="preserve">on pourra
                <lb/>
              faire la même regle que ci-deſſus, & </s>
              <s xml:id="echoid-s6804" xml:space="preserve">prendre les deux tiers du
                <lb/>
              poids que le calcul aura donné, puiſque l’on ſait qu’une poutre
                <lb/>
              dans cette ſituation porte un tiers moins que la précédente.</s>
              <s xml:id="echoid-s6805" xml:space="preserve"/>
            </p>
            <p>
              <s xml:id="echoid-s6806" xml:space="preserve">Nous avons ſupoſé juſqu’ici, que le poids étoit toûjours poſé
                <lb/>
              dans le milieu; </s>
              <s xml:id="echoid-s6807" xml:space="preserve">ce pendant, comme il peut ſe rencontrer dans d’au-
                <lb/>
              tres endroits, voici une maniere de connoître la charge que por-
                <lb/>
              tera une poutre, à tel point qu’on voudra de ſa longueur, pour
                <lb/>
              qu’elle reſiſte autant qu’elle le feroit ſi elle étoit chargée dans le
                <lb/>
              milieu.</s>
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