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Also I'm solving for the forces (Tab, Tc...

trial123 5
March 21 2013

Also I'm solving for the forces (Tab, Tcd, Tbc,HA,VA, etc.) in terms of the load, L, how do I do this?


Another problem that has arisen is I do not have an equation for the alpha angle. I'm not sure how to incorporate the alpha angle so do I just add the alpha angle and 45 degrees together? But how do I express that in maple?!

Recap Question...

trial123 5
March 21 2013

So as you can see, when I generate the equations and solve for the forces (Tab, Tcd, Tbc, etc.), its not giving me the right answers.

 

Note: "L" is not an unknown but I'm not sure how this is because I wasn't given any number for it. Do I just solve solve for L like this?

eqnE:=-Tce*upright+Tde*downright=-L*up;

 

 

FULL MWS FILE...

trial123 5
March 21 2013

 

> 

with(LinearAlgebra):
vecsys_to_scalarsys:=ve->map(op@veceqn_to_sys,ve):
veceqn_to_sys:=proc(ve) local i;
  RETURN([seq(lhs(ve)[i]=rhs(ve)[i],
      i=1..Dimension((lhs(ve))))]):
end:
> 

up:= < 0,1 >; right:= < 1,0 >; zero:= < 0,0 >;

up := Vector(2, {(1) = 0, (2) = 1})

right := Vector(2, {(1) = 1, (2) = 0})

zero := Vector(2, {(1) = 0, (2) = 0})

 (1)
> 

downright:=simplify(subs(theta=arctan(-1), < cos(theta),sin(theta) >));

downright := Vector(2, {(1) = (1/2)*sqrt(2), (2) = -(1/2)*sqrt(2)})

 (2)
> 

upright:=simplify(subs(theta=arctan(1), < cos(theta),sin(theta) >));

upright := Vector(2, {(1) = (1/2)*sqrt(2), (2) = (1/2)*sqrt(2)})

 (3)
> 

eqnA:=HA*right+VA*up+Tab*upright+Tac*upright=zero;

eqnA := (Vector(2, {(1) = HA+(1/2)*Tab*sqrt(2)+(1/2)*Tac*sqrt(2), (2) = VA+(1/2)*Tab*sqrt(2)+(1/2)*Tac*sqrt(2)})) = (Vector(2, {(1) = 0, (2) = 0}))

 (4)
> 

eqnB:=HB*right-Tab*upright-Tbc*downright+Tbd*upright=zero;
eqnC:=-Tac*upright+Tbc*downright+Tcd*upright+Tce*upright=zero;
eqnD:=-Tbd*upright-Tcd*upright-Tde*downright=zero;
eqnE:=-Tce*upright+Tde*downright-L*up=zero;

eqnB := (Vector(2, {(1) = HB-(1/2)*Tab*sqrt(2)-(1/2)*Tbc*sqrt(2)+(1/2)*Tbd*sqrt(2), (2) = -(1/2)*Tab*sqrt(2)+(1/2)*Tbc*sqrt(2)+(1/2)*Tbd*sqrt(2)})) = (Vector(2, {(1) = 0, (2) = 0}))

eqnC := (Vector(2, {(1) = -(1/2)*Tac*sqrt(2)+(1/2)*Tbc*sqrt(2)+(1/2)*Tcd*sqrt(2)+(1/2)*Tce*sqrt(2), (2) = -(1/2)*Tac*sqrt(2)-(1/2)*Tbc*sqrt(2)+(1/2)*Tcd*sqrt(2)+(1/2)*Tce*sqrt(2)})) = (Vector(2, {(1) = 0, (2) = 0}))

eqnD := (Vector(2, {(1) = -(1/2)*Tbd*sqrt(2)-(1/2)*Tcd*sqrt(2)-(1/2)*Tde*sqrt(2), (2) = -(1/2)*Tbd*sqrt(2)-(1/2)*Tcd*sqrt(2)+(1/2)*Tde*sqrt(2)})) = (Vector(2, {(1) = 0, (2) = 0}))

eqnE := (Vector(2, {(1) = -(1/2)*Tce*sqrt(2)+(1/2)*Tde*sqrt(2), (2) = -(1/2)*Tce*sqrt(2)-(1/2)*Tde*sqrt(2)-L})) = (Vector(2, {(1) = 0, (2) = 0}))

 (5)
> 

vecsys:=[eqnA,eqnB,eqnC,eqnD,eqnE];
sys:=vecsys_to_scalarsys(vecsys);

vecsys := [(Vector(2, {(1) = HA+(1/2)*Tab*sqrt(2)+(1/2)*Tac*sqrt(2), (2) = VA+(1/2)*Tab*sqrt(2)+(1/2)*Tac*sqrt(2)})) = (Vector(2, {(1) = 0, (2) = 0})), (Vector(2, {(1) = HB-(1/2)*Tab*sqrt(2)-(1/2)*Tbc*sqrt(2)+(1/2)*Tbd*sqrt(2), (2) = -(1/2)*Tab*sqrt(2)+(1/2)*Tbc*sqrt(2)+(1/2)*Tbd*sqrt(2)})) = (Vector(2, {(1) = 0, (2) = 0})), (Vector(2, {(1) = -(1/2)*Tac*sqrt(2)+(1/2)*Tbc*sqrt(2)+(1/2)*Tcd*sqrt(2)+(1/2)*Tce*sqrt(2), (2) = -(1/2)*Tac*sqrt(2)-(1/2)*Tbc*sqrt(2)+(1/2)*Tcd*sqrt(2)+(1/2)*Tce*sqrt(2)})) = (Vector(2, {(1) = 0, (2) = 0})), (Vector(2, {(1) = -(1/2)*Tbd*sqrt(2)-(1/2)*Tcd*sqrt(2)-(1/2)*Tde*sqrt(2), (2) = -(1/2)*Tbd*sqrt(2)-(1/2)*Tcd*sqrt(2)+(1/2)*Tde*sqrt(2)})) = (Vector(2, {(1) = 0, (2) = 0})), (Vector(2, {(1) = -(1/2)*Tce*sqrt(2)+(1/2)*Tde*sqrt(2), (2) = -(1/2)*Tce*sqrt(2)-(1/2)*Tde*sqrt(2)-L})) = (Vector(2, {(1) = 0, (2) = 0}))]

sys := [HA+Tab*2^(1/2)/2+Tac*2^(1/2)/2 = 0, VA+Tab*2^(1/2)/2+Tac*2^(1/2)/2 = 0, HB-Tab*2^(1/2)/2-Tbc*2^(1/2)/2+Tbd*2^(1/2)/2 = 0, -Tab*2^(1/2)/2+Tbc*2^(1/2)/2+Tbd*2^(1/2)/2 = 0, -Tac*2^(1/2)/2+Tbc*2^(1/2)/2+Tcd*2^(1/2)/2+Tce*2^(1/2)/2 = 0, -Tac*2^(1/2)/2-Tbc*2^(1/2)/2+Tcd*2^(1/2)/2+Tce*2^(1/2)/2 = 0, -Tbd*2^(1/2)/2-Tcd*2^(1/2)/2-Tde*2^(1/2)/2 = 0, -Tbd*2^(1/2)/2-Tcd*2^(1/2)/2+Tde*2^(1/2)/2 = 0, -Tce*2^(1/2)/2+Tde*2^(1/2)/2 = 0, -Tce*2^(1/2)/2-Tde*2^(1/2)/2-L = 0]

 (6)
> 

vars:=[Tab,Tac,Tbc,Tbd,Tcd,Tce,Tde,VA,HA,HB]:
augmat:=GenerateMatrix(sys,vars,augmented=true);

augmat := Vector(4, {(1) = ` 10 x 11 `*Matrix, (2) = `Data Type: `*anything, (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order})

 (7)
> 

evalm(augmat);

Matrix(10, 11, {(1, 1) = (1/2)*sqrt(2), (1, 2) = (1/2)*sqrt(2), (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (1, 6) = 0, (1, 7) = 0, (1, 8) = 0, (1, 9) = 1, (1, 10) = 0, (1, 11) = 0, (2, 1) = (1/2)*sqrt(2), (2, 2) = (1/2)*sqrt(2), (2, 3) = 0, (2, 4) = 0, (2, 5) = 0, (2, 6) = 0, (2, 7) = 0, (2, 8) = 1, (2, 9) = 0, (2, 10) = 0, (2, 11) = 0, (3, 1) = -(1/2)*sqrt(2), (3, 2) = 0, (3, 3) = -(1/2)*sqrt(2), (3, 4) = (1/2)*sqrt(2), (3, 5) = 0, (3, 6) = 0, (3, 7) = 0, (3, 8) = 0, (3, 9) = 0, (3, 10) = 1, (3, 11) = 0, (4, 1) = -(1/2)*sqrt(2), (4, 2) = 0, (4, 3) = (1/2)*sqrt(2), (4, 4) = (1/2)*sqrt(2), (4, 5) = 0, (4, 6) = 0, (4, 7) = 0, (4, 8) = 0, (4, 9) = 0, (4, 10) = 0, (4, 11) = 0, (5, 1) = 0, (5, 2) = -(1/2)*sqrt(2), (5, 3) = (1/2)*sqrt(2), (5, 4) = 0, (5, 5) = (1/2)*sqrt(2), (5, 6) = (1/2)*sqrt(2), (5, 7) = 0, (5, 8) = 0, (5, 9) = 0, (5, 10) = 0, (5, 11) = 0, (6, 1) = 0, (6, 2) = -(1/2)*sqrt(2), (6, 3) = -(1/2)*sqrt(2), (6, 4) = 0, (6, 5) = (1/2)*sqrt(2), (6, 6) = (1/2)*sqrt(2), (6, 7) = 0, (6, 8) = 0, (6, 9) = 0, (6, 10) = 0, (6, 11) = 0, (7, 1) = 0, (7, 2) = 0, (7, 3) = 0, (7, 4) = -(1/2)*sqrt(2), (7, 5) = -(1/2)*sqrt(2), (7, 6) = 0, (7, 7) = -(1/2)*sqrt(2), (7, 8) = 0, (7, 9) = 0, (7, 10) = 0, (7, 11) = 0, (8, 1) = 0, (8, 2) = 0, (8, 3) = 0, (8, 4) = -(1/2)*sqrt(2), (8, 5) = -(1/2)*sqrt(2), (8, 6) = 0, (8, 7) = (1/2)*sqrt(2), (8, 8) = 0, (8, 9) = 0, (8, 10) = 0, (8, 11) = 0, (9, 1) = 0, (9, 2) = 0, (9, 3) = 0, (9, 4) = 0, (9, 5) = 0, (9, 6) = -(1/2)*sqrt(2), (9, 7) = (1/2)*sqrt(2), (9, 8) = 0, (9, 9) = 0, (9, 10) = 0, (9, 11) = 0, (10, 1) = 0, (10, 2) = 0, (10, 3) = 0, (10, 4) = 0, (10, 5) = 0, (10, 6) = -(1/2)*sqrt(2), (10, 7) = -(1/2)*sqrt(2), (10, 8) = 0, (10, 9) = 0, (10, 10) = 0, (10, 11) = L})

 (8)
> 

reducedmat:=ReducedRowEchelonForm(augmat);

reducedmat := Vector(4, {(1) = ` 10 x 11 `*Matrix, (2) = `Data Type: `*anything, (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order})

 (9)
> 

GenerateEquations(reducedmat,vars);

[Tab+Tcd = 0, Tac-Tcd = 0, Tbc = 0, Tbd+Tcd = 0, Tce = 0, Tde = 0, VA = 0, HA = 0, HB = 0, 0 = 1]

 (10)

 [Editted due to drop-outs caused of the infamous angle-bracket bug.---Carl Love]

Diagram...

trial123 5
March 21 2013

 

Here's what I've done in maple:(I just...

trial123 5
March 21 2013

Here's what I've done in maple:

(I just printscreened my maple because I don't know how to put my codes in here, they are all in order)

 

http://postimage.org/image/m3efaop3f/

http://postimage.org/image/g6lnvwax9/

http://postimage.org/image/98ctjnl4b/

http://postimage.org/image/qn1beut0h/

 

As you can see, when I evalute my matrix, the forces (unknown) are not even giving me a proper answer. Please help me!

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