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francois |
941 |
clc;
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| 2 |
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disp('Solution exercice 1 du chapitre contraintes');
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| 3 |
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F=157000;
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T=200000;
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p=1.2e6;
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r=400e-3;
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t=20e-3;
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disp(' a) Contraintes dues a la pression interne');
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syms b teta ro
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Fteta=0.5*int(p*b*r*sin(teta),teta,0,pi);
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sigmatetaa=Fteta/b/t
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| 12 |
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sigmaxa=p*r/2/t
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disp(' b) Contraintes dues a la force axiale');
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sigmaxb=F/2/pi/r/t
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J=int(1,teta,0,2.*pi)*int(ro*ro*ro,ro,r-t/2,r+t/2);
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tauxtetac=T*r/J;
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| 17 |
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eval(tauxtetac)
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disp(' tenseur des contraintes en Pa');
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sigma=[sigmatetaa,tauxtetac,0;tauxtetac,sigmaxa+sigmaxb,0;0,0,0];
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eval(sigma)
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| 21 |
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disp(' Vecteurs et valeurs propores');
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[V,D]=eig(sigma);
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eval(V)
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eval(D)
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disp(' Angle de la direction 1 en degre');
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costeta1=V(1,3)/sqrt(V(1,3)*V(1,3)+V(2,3)*V(2,3));
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| 27 |
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sinteta1=V(2,3)/sqrt(V(1,3)*V(1,3)+V(2,3)*V(2,3));
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| 28 |
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teta1=sign(eval(sinteta1))*acos(costeta1);
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eval(teta1);
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| 30 |
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eval(teta1/pi*180)
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| 31 |
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disp(' Angle de la direction 2 en degre');
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costeta2=V(1,2)/sqrt(V(1,2)*V(1,2)+V(2,2)*V(2,2));
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| 33 |
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sinteta2=V(2,2)/sqrt(V(1,2)*V(1,2)+V(2,2)*V(2,2));
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| 34 |
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teta2=sign(eval(sinteta2))*acos(costeta2);
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| 35 |
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eval(teta2);
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| 36 |
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eval(teta2/pi*180)
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disp(' Cisaillement maximal en Pa');
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| 38 |
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taumax=0.5*(D(3,3)-D(2,2));
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| 39 |
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eval(taumax)
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| 40 |
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disp(' Direction du cisaillement maximal en degre');
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| 41 |
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eval(teta1/pi*180+45)
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| 42 |
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