User:Eml4500.f08.team.Bengtson/teamHw2

Meeting 8-3 to 8-4
Continued from P 7-5 in Compact notation

[kij]{dj] = {fij}

6x6

More generally nxn

kijdj=fij    i=1,……,6

knxn=[kij]

nxn=global stiffness matrix

d={dj}

nx1=global displacement matrix

F=global force matrix

d5=d3(2) { node (3)

d6=d4(2)

Conceptual step of the assembly:

(Topology of K)



Meeting 11
Element 1

K(1)*d(1)=f(1)

$$\begin{bmatrix} k & -k \\ -k & k \\ \end{bmatrix} $$ $$\begin{bmatrix} d_1 \\ d_2 \\ \end{bmatrix} $$ = $$\begin{bmatrix} F_1 \\ F_2 \\ \end{bmatrix} $$

$$\begin{bmatrix} 0.5625 & 0.32476 & .... & ....\\ .... & .... & .... & ....\\ .... & ....& .... & ....\\ .... & ....& .... & ....\\ \end{bmatrix} $$ = $$\begin{bmatrix} 0\\ 0\\ 4.52\\ 6.1271\\ \end{bmatrix} $$

4x4 matrix multiplied by a 1x4 matrix

Since the top two numbers for d(1) are zero it means you can reduce the 4x4 matrix into a 2x2 matrix.

=$$\begin{bmatrix}

0.5625 & 0.3247\\ .... & ....\\

\end{bmatrix} $$ $$\begin{bmatrix} 4.52\\ 6.1271\\ \end{bmatrix} $$ =$$\begin{bmatrix} -4.4378\\ -2.5622\\ 4.4378\\ 2.5622\\ \end{bmatrix} $$ Obs Element 1 is inequal

ΣFx=F1(1) + F3(1)= 0

ΣFy=F3(1) + F4(1)= 0





P1(1) = [(F1(2))2+ (F2(1)2]1/2

Method 2: Solve for 2 Bar Truss using Statics Method

Statics Method



Other Method