% Aufgabe 19-10a
clear all
a = 500 ; b = 700 ; EI1 = 6e9 ;
EI2 = 8e10 ; M = 800000 ; c = 800 ; q = 10 ;
A = [ 0 0 0 1 0 0 0 0 ;
0 0 1 0 0 0 0 0 ;
a^3/6 a^2/2 a 1 0 0 0 -1 ;
a^2/2 a 1 0 0 0 -1 0 ;
a 1 0 0 0 -EI2/EI1 0 0 ;
-1 0 0 0 EI2/EI1 0 0 c/EI1 ;
0 0 0 0 -b -1 0 0 ;
0 0 0 0 b^3/6 b^2/2 b 1 ] ;
B = [0 ; 0 ; 0 ; 0 ; 0 ; 0 ; (M+q*b^2/6)/EI2 ; -q*b^4/(120*EI2)] ;
C = A \ B ;
n = 1200 ; z = 0 : (a+b)/n : a+b ; v = zeros(n+1,1) ; Mb = zeros(n+1,1) ; FQ = zeros(n+1,1) ;
for i=1:n+1 if z(i) <= a
v(i) = C(1)*z(i)^3/6+C(2)*z(i)^2/2+C(3)*z(i)+C(4) ; Mb(i) = -EI1*(C(1)*z(i)+C(2)) ; FQ(i) = -EI1*C(1) ;
else z2 = z(i)-a ; v(i) = q*z2^5/(120*EI2*b)+C(5)*z2^3/6+C(6)*z2^2/2+C(7)*z2+C(8) ;
Mb(i) = -EI2*(q*z2^3/(6*EI2*b)+C(5)*z2+C(6)) ; FQ(i) = -EI2*(q*z2^2/(2*EI2*b)+C(5)) ; end end
subplot (3,1,1) ; plot (z , v) , grid on , title ('Biegelinie') , axis ij subplot (3,1,2) ; plot (z , Mb) , grid on , title ('Biegemoment') subplot (3,1,3) ; plot (z , FQ) , grid on , title ('Querkraft')
iFeder = round(n*a/(a+b)+1) ; vFeder = v(iFeder) MbLinks = Mb(1) MbFeder = Mb(iFeder) Mbmax = max(abs(Mb))
FQLinks = FQ(1) Federkraft = c*vFeder
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