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francois |
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clc;
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| 2 |
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disp('Solution exercice 2 du chapitre introduction');
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disp('Resolution du probleme statique');
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A=[0,0,0];
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B=[2,0,0];
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C=[4,0,0];
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D=[6,0,0];
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Pb=[0,-1250,0];
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Pd=[0,-500,0];
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syms Ray Rcy;
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Ra=[0,Ray,0];
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Rc=[0,Rcy,0];
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eq1=Ra(2)+Rc(2)+Pb(2)+Pd(2);
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AB=B-A;
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AC=C-A;
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AD=D-A;
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eq2=Pb(2)*norm(AB,2)+Rc(2)*norm(AC,2)+Pd(2)*norm(AD,2);
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R=solve(eq1,eq2);
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disp(sprintf('Ray=%d N',eval(R.Ray)));
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disp(sprintf('Rcy=%d N',eval(R.Rcy)));
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disp('Calcul des diagrammes V et M');
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syms x y
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Vab=-R.Ray;
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Mab=R.Ray*x;
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Vbc=Vab-Pb(2);
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Mbc=Mab+Pb(2)*(x-2);
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Vcd=Vbc-R.Rcy;
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Mcd=Mbc+R.Rcy*(x-4);
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ezplot(Vab,[0 2]);
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hold on;
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ezplot(Vbc,[2 4]);
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ezplot(Vcd,[4 6]);
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p2=ezplot(Mab,[0 2]);
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set(p2,'Color','red');
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p2=ezplot(Mbc,[2 4]);
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set(p2,'Color','red');
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p2=ezplot(Mcd,[4 6]);
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set(p2,'Color','red');
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xlim('auto');
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ylim('auto');
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title('Diagramme V et M');
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disp('entre A et B');
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Vab
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Mab
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disp('entre B et C');
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Vbc
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Mbc
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disp('entre C et D');
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Vcd
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Mcd
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disp('Calcul de la contrainte normale maximale');
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l=40e-3;
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L=60e-3;
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I=int(1,x,-l/2,l/2) * int(y*y,y,-L/2,L/2);
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sigmamaxsup=-Mbc*L/2/I;
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sigmamaxinf=-Mbc*(-L)/2/I;
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disp(sprintf(' sur la fibre superieure en x=4 sigma=%d Pa',eval(limit(sigmamaxsup,4))));
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disp(sprintf(' sur la fibre inferieure en x=4 sigma=%d Pa',eval(limit(sigmamaxinf,4))));
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disp('Calcul de la contrainte tangeantielle maximale');
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Q=int(1,x,-l/2,l/2)*int(y,y,0,L/2);
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Tmax=Vbc*Q/I/l;
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disp(sprintf(' sur la fibre neutre entre B et C superieure tau=%d Pa',eval(Tmax)));
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