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3D Structures
disp('')disp(' ** SPAN LENGTHS:')disp('')for j=1:ml(j)=0;
while l(j)
// stiffness from floor displacements// first floorr(1,1)=0;if n==1 then // first floor = last floor, one floor structure for j=1:m+1 // translation dof r(1,1)=r(1,1)+12*c(1,j)/h(1)^3; p=n+j; // rotational dof r(p,1)=-6*c(1,j)/h(1)^2;
endelse // first floor, more than one floor structurer(2,1)=0;for j=1:m+1
// translation dof r(1,1)=r(1,1)+12*(c(1,j)/h(1)^3+c(2,j)/h(2)^3); r(2,1)=r(2,1)-12*c(2,j)/h(2)^3; p=n+j; // rotational dof r(p,1)=6*(c(2,j)/h(2)^2-c(1,j)/h(1)^2); r(p+m+1,1)=6*c(2,j)/h(2)^2;
endend// stiffness from floor displacements// last floorif n~=1 then // last floor, more than one floor structurer(n,n)=0;r(n-1,n)=0;for j=1:m+1
// translation dof r(n,n)=r(n,n)+12*c(n,j)/h(n)^3; r(n-1,n)=r(n-1,n)-12*c(n,j)/h(n)^3; // rotational dof p=n+(n-1)*(m+1)+j; r(p,n)=-6*c(n,j)/h(n)^2; r(p-m-1,n)=-6*c(n,j)/h(n)^2;
endend // stiffness from floor displacements// current floorsfor i=2:n-1
r(i,i)=0; r(i-1,i)=0; r(i+1,i)=0; for j=1:m+1 // translation dof r(i,i)=r(i,i)+12*(c(i,j)/h(i)^3+c(i+1,j)/h(i+1)^3); r(i-1,i)=r(i-1,i)-12*c(i,j)/h(i)^3; r(i+1,i)=r(i+1,i)-12*c(i+1,j)/h(i+1)^3; p=n+(i-1)*(m+1)+j; // rotational dof r(p,i)=6*(c(i+1,j)/h(i+1)^2-c(i,j)/h(i)^2); r(p+m+1,i)=6*c(i+1,j)/h(i+1)^2; r(p-m-1,i)=-6*c(i,j)/h(i)^2; end
end
// stiffness from node rotation// first floorif n==1 then // first floor = last floor, one floor structure// left node, j=1
// translation dof r(1,2)=-6*c(1,1)/h(1)^2; // rotational dof r(2,2)=4*(c(1,1)/h(1)+b(1,1)/l(1)); r(3,2)=2*b(1,1)/l(1);
// right node, j=m+1 // translation dof p=m+2; r(1,p)=-6*c(1,m+1)/h(1)^2; // rotational dof r(p,p)=4*(c(1,m+1)/h(1)+b(1,m)/l(m)); r(p-1,p)=2*b(1,m)/l(m);
// current nodefor j=2:m
// translation dof p=n+j; r(1,p)=-6*c(1,j)/h(1)^2; // rotational dof r(p,p)=4*(c(1,j)/h(1)+b(1,j-1)/l(j-1)+b(1,j)/l(j)); r(p-1,p)=2*b(1,j-1)/l(j-1); r(p+1,p)=2*b(1,j)/l(j);
endelse // first floor, more than one floor structure// left node, j=1
// translation dof p=n+1; r(1,p)=6*(-c(1,1)/h(1)^2+c(2,1)/h(2)^2); r(2,p)=-6*c(2,1)/h(2)^2; // rotational dof r(p,p)=4*(c(1,1)/h(1)+c(2,1)/h(2)+b(1,1)/l(1)); r(p+1,p)=2*b(1,1)/l(1); r(p+m+1,p)=2*c(2,1)/h(2);
// right node, j=m+1 // translation dof p=n+m+1; r(1,p)=6*(-c(1,m+1)/h(1)^2+c(2,m+1)/h(2)^2); r(2,p)=-6*c(2,m+1)/h(2)^2; // rotational dof r(p,p)=4*(c(1,m+1)/h(1)+c(2,m+1)/h(2)+b(1,m)/l(m)); r(p-1,p)=2*b(1,m)/l(m); r(p+m+1,p)=2*c(2,m+1)/h(2);
// current nodefor j=2:m
// translation dof p=n+j; r(1,p)=6*(-c(1,j)/h(1)^2+c(2,j)/h(2)^2); r(2,p)=-6*c(2,j)/h(2)^2; // rotational dof r(p,p)=4*(c(1,j)/h(1)+c(2,j)/h(2)+b(1,j-1)/l(j-1)+b(1,j)/l(j)); r(p-1,p)=2*b(1,j-1)/l(j-1); r(p+1,p)=2*b(1,j)/l(j); r(p+m+1,p)=2*c(2,j)/h(2);
end
end// stiffness from node rotation// last floorif n~=1 then // last floor, more than one floor structure// left node, j=1p=n+(n-1)*(m+1)+1;
// translation dofr(n,p)= -6*c(n,1)/h(n)^2;r(n-1,p)= 6*c(n,1)/h(n)^2;
// rotational dofr(p,p)=4*(c(n,1)/h(n)+b(n,1)/l(1));r(p+1,p)=2*b(n,1)/l(1);r(p-m-1,p)=2*c(n,1)/h(n);// right node, j=m+1
// translation dofp=n*(m+2);r(n,p)= -6*c(n,m+1)/h(n)^2;r(n-1,p)= 6*c(n,m+1)/h(n)^2;
// rotational dofr(p,p)=4*(c(n,m+1)/h(n)+b(n,m)/l(m));r(p-1,p)=2*b(n,m)/l(m);r(p-m-1,p)=2*c(n,m+1)/h(n);// right node, j=m+1for j=2:m
p=n+(n-1)*(m+1)+j; // translation dof r(n,p)= -6*c(n,j)/h(n)^2; r(n-1,p)= 6*c(n,j)/h(n)^2; // rotational dof r(p,p)=4*(c(n,j)/h(n)+b(n,j-1)/l(j-1)+b(n,j)/l(j)); r(p-1,p)=2*b(n,j-1)/l(j-1); r(p+1,p)=2*b(n,j)/l(j); r(p-m-1,p)=2*c(n,j)/h(n);
end end // stiffness from node rotation// current floorfor i=2:n-1// left node, j=1p=n+(i-1)*(m+1)+1;
// lateral dofr(i,p)=6*(-c(i,1)/h(i)^2+c(i+1,1)/h(i+1)^2);r(i+1,p)=-6*c(i+1,1)/h(i+1)^2;r(i-1,p)=6*c(i,1)/h(i)^2;
// rotational dofr(p,p)=4*(c(i,1)/h(i)+c(i+1,1)/h(i+1)+b(i,1)/l(1));r(p+1,p)=2*b(i,1)/l(1);r(p-m-1,p)=2*c(i,1)/h(i);r(p+m+1,p)=2*c(i+1,1)/h(i+1);// right node, j=m+1p=n+i*(m+1);
// lateral dofr(i,p)=6*(-c(i,m+1)/h(i)^2+c(i+1,m+1)/h(i+1)^2);r(i+1,p)=-6*c(i+1,m+1)/h(i+1)^2;r(i-1,p)=6*c(i,m+1)/h(i)^2;
// rotational dofr(p,p)=4*(c(i,m+1)/h(i)+c(i+1,m+1)/h(i+1)+b(i,m)/l(m));
r(p-1,p)=2*b(i,m)/l(m);r(p-m-1,p)=2*c(i,m+1)/h(i);r(p+m+1,p)=2*c(i+1,m+1)/h(i+1);//current nodefor j=2:m
p=n+(i-1)*(m+1)+j; // lateral dof r(i,p)=6*(-c(i,j)/h(i)^2+c(i+1,j)/h(i+1)^2); r(i+1,p)=-6*c(i+1,j)/h(i+1)^2; r(i-1,p)= 6*c(i,j)/h(i)^2; // rotational dof r(p,p)=4*(c(i,j)/h(i)+c(i+1,j)/h(i+1)+b(i,j-1)/l(j-1)+b(i,j)/l(j)); r(p-1,p)=2*b(i,j-1)/l(j-1); r(p+1,p)=2*b(i,j)/l(j); r(p-m-1,p)=2*c(i,j)/h(i); r(p+m+1,p)=2*c(i+1,j)/h(i+1);
endend// verifying the symmetryv=r-r';vm=max(max(abs(v)));disp(['maximum of the difference between simmetrical elements is ' + string(vm)])// calculation of the stiffness matrixR11=r(1:n,1:n);R12=r(1:n,(n+1):(n*(m+2)));R21=r((n+1):(n*(m+2)),1:n);R22=r((n+1):(n*(m+2)),(n+1):(n*(m+2)));K=(R11-R12*inv(R22)*R21)*EI
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