Question

Using MATLAB PLease

For scaffolding system shown, assume P1-50 lbf and P2-20 lbf. Perform force and momentum equilibrium balances for each bar to find 4 equations. Then show how to set them up as one system of linear equations ( Ax-b)and solve in MATLAB to determine tension forces T.Ty.TC and To. Hint: write ΣFy-Oand ΣΜ-Ofor each bar to find the equations. Bar 1

Answer 1

P→

Bar 1:

$\small \sum F_y = 0\Rightarrow T_A+T_B = P_1+T_C+T_D$

$\small \Rightarrow T_A+T_B - T_C-T_D = 50$

Moment about A:

$\small \sum M = 0 \Rightarrow 9*T_B-1* T_C-4*T_D -5*P_1 = 0$

$\small \Rightarrow 9T_B - T_C-4T_D = 5*50 = 250$

Bar 2:

$\small \sum F_y = 0\Rightarrow -P_2+T_C+T_D = 0$

$\small \Rightarrow T_C+T_D = 20$

Moment about C:

$\small \sum M = 0 \Rightarrow P_2*1-T_D*3 = 0$

$\small \Rightarrow 3T_D = 20$

Equations are:

$\small T_A+T_B - T_C-T_D = 50$

$\small 9T_B - T_C-4T_D = 5*50 = 250$

$\small T_C+T_D = 20$

$\small 3T_D = 20$

Putting the four equation in matrix form:

$\small \begin{bmatrix} 1 & 1 &-1 & -1\\ 0 & 9 & -1 &-4 \\ 0 &0 &1 &1 \\ 0 & 0 & 0 & 3 \end{bmatrix}*\begin{bmatrix} T_A\\ T_B\\ T_C\\ T_D \end{bmatrix}= \begin{bmatrix} 50\\ 250\\ 20\\ 20 \end{bmatrix}$

Matlab:

>>A=[1 1-1-1:09-1-4;0 0 1 1;0 0 0 31: B = [50 250 20 20]'; >> T = inv (A) *B T= 37.7778 32.2222 13.3333 6.6667