% Homework #5 Solutions
%%%
%%%
% Problem 4.6
Problem = 46
pause
L = 5 	% meters
E = 200*10^6 	% Pa
I = 96*10^(-6)	% m^4
ndof = 6
fdof = 3
Ksys = zeros(ndof)
%%
k = swfbeamstiff(L,E,I)
Xmap = [1 2 3 4]
X = swfgetX(Xmap,ndof)
Ksys = Ksys + X'*k*X
pause
%%
k = swfbeamstiff(L,E,I)
Xmap = [3 4 5 6]
X = swfgetX(Xmap,ndof)
Ksys = Ksys + X'*k*X
pause
%%%%
%%%%
% Reorder Ksys so 3 free dof are at top left
Xmap = [4 5 1 2 6 3]
X = swfgetX(Xmap,ndof)
Kffss = X'*Ksys*X
%
Kff = Kffss(1:fdof,1:fdof)
Kfs = Kffss(1:fdof,fdof+1:ndof)
Ksf = Kffss(fdof+1:ndof,1:fdof)
Kss = Kffss(fdof+1:ndof,fdof+1:ndof)
%
Ds = zeros(3,1)
Pf = [12 20 0]'
% member forces
Pfm = zeros(3,1)
Psm = zeros(3,1)
%
Df = inv(Kff)*(Pf - Kfs*Ds - Pfm)
Ps = Ksf*Df + Kss*Ds + Psm
%
EI = E*I;
Dsol = (L^2/EI)*[L 1 -2]
%
% member ab forces
Am1 = k*[Ds(1) Ds(2) Df(1) Df(2)]'
Am2 = k*[Df(1) Df(2) Ds(3) Df(3)]'
   
   pause
   pause
   
   %%%
% Problem 4.10
Problem = 410
pause
L = 20*12 	% in
E = 29*10^3 	% ksi
I = 862	% in^4
ndof = 4
fdof = 2
Ksys = zeros(ndof)
%%
k = swfbeamstiff(L,E,I)
Xmap = [1 2 3 4]
X = swfgetX(Xmap,ndof)
Ksys = Ksys + X'*k*X
pause
%%
%%%%
% Reorder Ksys so 2 free dof are at top left
Xmap = [3 1 4 2]
X = swfgetX(Xmap,ndof)
Kffss = X'*Ksys*X
%
Kff = Kffss(1:fdof,1:fdof)
Kfs = Kffss(1:fdof,fdof+1:ndof)
Ksf = Kffss(fdof+1:ndof,1:fdof)
Kss = Kffss(fdof+1:ndof,fdof+1:ndof)
%
Ds = zeros(2,1)
Pf = [-60*12 72*12]'
% member forces
Pfm = zeros(2,1)
Psm = zeros(2,1)
%
Df = inv(Kff)*(Pf - Kfs*Ds - Pfm)
Ps = Ksf*Df + Kss*Ds + Psm
%
% member ab forces
Am1 = k*[Ds(1) Df(1) Ds(2) Df(2)]'
%
pause
pause
%%%%%
%%%%%
% Problem 4.11
Problem = 411
pause
L = 12*12 	% in
E = 29*10^3 	% ksi
I = 776	% in^4
ndof = 8
fdof = 2
Ksys = zeros(ndof)
%%
% element 1
k = swfbeamstiff(L,E,I)
Xmap = [1 2 3 4]
X = swfgetX(Xmap,ndof)
Ksys = Ksys + X'*k*X
pause
%%
% element 2
k = swfbeamstiff(L,E,I)
Xmap = [3 4 5 6]
X = swfgetX(Xmap,ndof)
Ksys = Ksys + X'*k*X
pause
%%
% element 3
k = swfbeamstiff(L,E,I)
Xmap = [5 6 7 8]
X = swfgetX(Xmap,ndof)
Ksys = Ksys + X'*k*X
pause
%%%%
%%%%
% Reorder Ksys so 2 free dof are at top left
Xmap = [3 4 5 1 6 2 7 8]
X = swfgetX(Xmap,ndof)
Kffss = X'*Ksys*X
%
Kff = Kffss(1:fdof,1:fdof)
Kfs = Kffss(1:fdof,fdof+1:ndof)
Ksf = Kffss(fdof+1:ndof,1:fdof)
Kss = Kffss(fdof+1:ndof,fdof+1:ndof)
%
Ds = zeros(ndof-fdof,1)
Pf = [100*12 -100*12]'
% member forces
Pfm = zeros(fdof,1)
Psm = zeros(ndof-fdof,1)
%
% coordinate displacements
Df = inv(Kff)*(Pf - Kfs*Ds - Pfm)
%
% reaction forces
Ps = Ksf*Df + Kss*Ds + Psm
%
% member ab forces
Am1 = k*[Ds(1) Ds(2) Ds(3) Df(1)]'
Am2 = k*[Ds(3) Df(1) Ds(4) Df(2)]'
Am3 = k*[Ds(4) Df(1) Ds(5) Ds(6)]'
%
pause
pause
%%%%%
%%%%%
% Problem 4.12
Problem = 412
pause
Lab = 5 	% m
Lbc = 2*Lab
E = 200*10^6 % Pa
Iab = 200*10^-6 % m^4
Ibc = 1.5*Iab % m^4
ndof = 6
fdof = 2
Ksys = zeros(ndof)
%%
% element 1
kab = swfbeamstiff(Lab,E,Iab)
Xmap = [1 2 3 4]
X = swfgetX(Xmap,ndof)
Ksys = Ksys + X'*kab*X
pause
%%
% element 2
kbc = swfbeamstiff(Lbc,E,Ibc)
Xmap = [3 4 5 6]
X = swfgetX(Xmap,ndof)
Ksys = Ksys + X'*kbc*X
pause
%%
%%%%
%%%%
% Reorder Ksys so 2 free dof are at top left
Xmap = [3 4 1 2 5 6]
X = swfgetX(Xmap,ndof)
Kffss = X'*Ksys*X
%
Kff = Kffss(1:fdof,1:fdof)
Kfs = Kffss(1:fdof,fdof+1:ndof)
Ksf = Kffss(fdof+1:ndof,1:fdof)
Kss = Kffss(fdof+1:ndof,fdof+1:ndof)
%
Ds = zeros(ndof-fdof,1)
Pf = [-100 0]'
% member forces
Pfm = zeros(fdof,1)
Psm = zeros(ndof-fdof,1)
%
% coordinate displacements
Df = inv(Kff)*(Pf - Kfs*Ds - Pfm)
%
% reaction forces
Ps = Ksf*Df + Kss*Ds + Psm
%
% member ab forces
Am1 = kab*[Ds(1) Ds(2) Df(1) Df(2)]'
Am2 = kbc*[Df(1) Df(2) Ds(3) Ds(4)]'
   
   pause
   pause
   %%%%%%%%%%%
   %%%%%%%%%%%
   %%%%%%%%%%%
   %%%%%
%%%%%
% Problem 4.13
Problem = 413
pause
Lab = 1 	
Lbc = Lab
E = 1 
I = 1
Iab = 2*I 
Ibc = I 
ndof = 6
fdof = 2
Ksys = zeros(ndof)
%%
% element 1
kab = swfbeamstiff(Lab,E,Iab)
Xmap = [1 2 3 4]
X = swfgetX(Xmap,ndof)
Ksys = Ksys + X'*kab*X
pause
%%
% element 2
kbc = swfbeamstiff(Lbc,E,Ibc)
Xmap = [3 4 5 6]
X = swfgetX(Xmap,ndof)
Ksys = Ksys + X'*kbc*X
pause
%%
%%%%
%%%%
% Reorder Ksys so 2 free dof are at top left
Xmap = [3 4 5 1 6 2]
X = swfgetX(Xmap,ndof)
Kffss = X'*Ksys*X
%
Kff = Kffss(1:fdof,1:fdof)
Kfs = Kffss(1:fdof,fdof+1:ndof)
Ksf = Kffss(fdof+1:ndof,1:fdof)
Kss = Kffss(fdof+1:ndof,fdof+1:ndof)
%
Ds = zeros(ndof-fdof,1)
Pf = [50 0]'
% member forces
Pfm = zeros(fdof,1)
Psm = zeros(ndof-fdof,1)
%
% coordinate displacements
Df = inv(Kff)*(Pf - Kfs*Ds - Pfm)
%
% reaction forces
Ps = Ksf*Df + Kss*Ds + Psm
%
% member ab forces
Am1 = kab*[Ds(1) Ds(2) Ds(3) Df(1)]'
Am2 = kbc*[Ds(3) Df(1) Ds(4) Df(2)]'
   
   pause
   pause
   %%%%%%%%%%%
   %%%%%%%%%%%
   %%%%%%%%%%%
   %%%%%
%%%%%
% Problem 4.14a
Problem = 414
Part = ['a']
pause
L = 1 	
E = 1 
I = 1
ndof = 6
fdof = 3
Ksys = zeros(ndof)
%%
% element 1
kab = swfbeamstiff(L,E,I)
Xmap = [1 2 3 4]
X = swfgetX(Xmap,ndof)
Ksys = Ksys + X'*kab*X
pause
%%
% element 2
kbc = swfbeamstiff(L,E,I)
Xmap = [3 4 5 6]
X = swfgetX(Xmap,ndof)
Ksys = Ksys + X'*kbc*X
pause
%%
% take care of spring
Ksys(3,3) = Ksys(3,3) + 12*E*I/L
%%%%
%%%%
% Reorder Ksys so 2 free dof are at top left
Xmap = [4 5 1 2 6 3]
X = swfgetX(Xmap,ndof)
Kffss = X'*Ksys*X
%
Kff = Kffss(1:fdof,1:fdof)
Kfs = Kffss(1:fdof,fdof+1:ndof)
Ksf = Kffss(fdof+1:ndof,1:fdof)
Kss = Kffss(fdof+1:ndof,fdof+1:ndof)
%
Ds = zeros(ndof-fdof,1)
Pf = [-1 0 0]'
% member forces
Pfm = zeros(fdof,1)
Psm = zeros(ndof-fdof,1)
%
% coordinate displacements
Df = inv(Kff)*(Pf - Kfs*Ds - Pfm)
%
% reaction forces
Ps = Ksf*Df + Kss*Ds + Psm
%
% member ab forces
Am1 = kab*[Ds(1) Ds(2) Df(1) Df(2)]'
Am2 = kbc*[Df(1) Df(2) Ds(3) Df(3)]'
   
   pause
   pause
   
Part = ['b']
pause
L = 1 	
E = 1 
I = 1
ndof = 6
fdof = 3
Ksys = zeros(ndof)
%%
% element 1
kab = swfbeamstiff(L,E,I)
Xmap = [1 2 3 4]
X = swfgetX(Xmap,ndof)
Ksys = Ksys + X'*kab*X
pause
%%
% element 2
kbc = swfbeamstiff(L,E,2*I)
Xmap = [3 4 5 6]
X = swfgetX(Xmap,ndof)
Ksys = Ksys + X'*kbc*X
pause
%%
% take care of spring
Ksys(3,3) = Ksys(3,3) + 12*E*I/L
%%%%
%%%%
% Reorder Ksys so 2 free dof are at top left
Xmap = [4 5 1 2 6 3]
X = swfgetX(Xmap,ndof)
Kffss = X'*Ksys*X
%
Kff = Kffss(1:fdof,1:fdof)
Kfs = Kffss(1:fdof,fdof+1:ndof)
Ksf = Kffss(fdof+1:ndof,1:fdof)
Kss = Kffss(fdof+1:ndof,fdof+1:ndof)
%
Ds = zeros(ndof-fdof,1)
Pf = [-1 0 0]'
% member forces
Pfm = zeros(fdof,1)
Psm = zeros(ndof-fdof,1)
%
% coordinate displacements
Df = inv(Kff)*(Pf - Kfs*Ds - Pfm)
%
% reaction forces
Ps = Ksf*Df + Kss*Ds + Psm
%
% member ab forces
Am1 = kab*[Ds(1) Ds(2) Df(1) Df(2)]'
Am2 = kbc*[Df(1) Df(2) Ds(3) Df(3)]'
   
   pause
   pause