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%this program is used to evaluate reaction force in hinged beam problem
syms Ra Rb Ma
%principle of statics
T1=Ra+Rb-F1-F2-F3-u1*(xe1-xb1);
Rb=solve(T1,Rb);
%Second bordary conditions;, M(L)=0
Ta=Ra*maccaulay(L,1)+Rb*maccaulay(L-xRb,1)+Ma*maccaulay(L,0)-F1*maccaulay((L-x1),1)-(u1/2)*maccaulay((L-xb1),2)+ (u2/2)*maccaulay((L-xe1),2)-(u2-u1)/(6*(div(xe1,xb1)))*maccaulay((L-xb1),3)+ (u2-u1)/(6*(div(xe1,xb1)))*maccaulay((L-xe1),3)+K1*maccaulay((L-xk1),0)+m1*maccaulay((L-xb2),1)-m2*maccaulay((L-xe2),1)+(m2-m1)/(2*(div(xe2,xb2)))*maccaulay((L-xb2),2)- (m2-m1)/(2*(div(xe2,xb2)))*maccaulay((L-xe2),2)-F2*maccaulay((L-x2),1)- F3*maccaulay((L-x3),1);
Ra=(solve(Ta,Ra));
% %Calculation of Bending moment
for i=1:1:n
M(i)=Ra*maccaulay(x(i),1)+Rb*maccaulay(x(i)-xRb,1)+Ma*maccaulay(x(i),0)-F1*maccaulay((x(i)-x1),1)-(u1/2)*maccaulay((x(i)-xb1),2)+(u2/2)*maccaulay((x(i)-xe1),2)-(u2-u1)/(6*(div(xe1,xb1)))*maccaulay((x(i)-xb1),3)+(u2-u1)/(6*(div(xe1,xb1)))*maccaulay((x(i)-xe1),3)+K1*maccaulay((x(i)-xk1),0)+m1*maccaulay((x(i)-xb2),1)-m2*maccaulay((x(i)-xe2),1)+(m2-m1)/(2*(div(xe2,xb2)))*maccaulay((x(i)-xb2),2)- (m2-m1)/(2*(div(xe2,xb2)))*maccaulay((x(i)-xe2),2)-F2*maccaulay((x(i)-x2),1)- F3*maccaulay((x(i)-x3),1);
end
%deflection
syms C1 C2
for i=1:1:n
W(i)=(Ra/2)*maccaulay(x(i),2)+(Rb/2)*maccaulay(x(i)-xRb,2)+(Ma)*maccaulay(x(i),1)-(F1/2)*maccaulay((x(i)-x1),2)-(u1/6)*maccaulay((x(i)-xb1),3)+ (u2/6)*maccaulay((x(i)-xe1),3)-(u2-u1)/(24*(div(xe1,xb1)))*maccaulay((x(i)-xb1),4)+ (u2-u1)/(24*(div(xe1,xb1)))*maccaulay((x(i)-xe1),4)+(K1)*maccaulay((x(i)-xk1),1)+(m1/2)*maccaulay((x(i)-xb2),2)-(m2/2)*maccaulay((x(i)-xe2),2)+(m2-m1)/(6*(div(xe2,xb2)))*maccaulay((x(i)-xb2),3)- (m2-m1)/(6*(div(xe2,xb2)))*maccaulay((x(i)-xe2),3)-(F2/2)*maccaulay((x(i)-x2),2)- (F3/2)*maccaulay((x(i)-x3),2)+C1;
end |
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