[Solved] 3 Dimensional Equlibirum - Statics (Astar, plz help)

[SGVaibhav]

Resolved

Need help out here, mostly in finding moment about an axis.

1. The problem statement, all variables and given/known data
The member is supported by a pin at A and a cable BC. If the load at D is 300, determine the x, y, z components of reaction at these supports.
i.e Find the reactions at A and the tension in the cable BC

2. Relevant equations
Since it is in equilbrium.



3. The attempt at a solution
The most confusing part for me, is moment about an axis. (If possible, please tell me, how to find moment about an axis - the direct method and through the vector matrix).

Correct me, if i am wrong.

rBC = 0.3i - 0.6j + 0.2k
|rBC| = 0.7
uBC = 1/0.7 (0.3 i - 0.6j + 0.2k)

TBC = |TBC|/0.7 (0.3i - 0.6j + 0.2k)

Now


Az is unknown, so to determine Az - we find moment about the x axis of B.
This will give, Az = 0


TBC = 1050 N.


Ax + 1050(0.3/0.7) = 0
Ax = -450 N


Ay - 1050(0.6/0.7) = 0
Ay = 900N

Thats what i could do max (i think im right), now only moment about Y-axis w.r.t a  and moment about Z-axis is left, w.r.t a again. (May and Maz).
Please tell me how to get this part, with 2-3 methods to get moment about an axis (Direct and through matrix).

Thanks a lot =)

[elemis]

May God help you with this question, because I certainly cant

[SGVaibhav]

May God help you with this question, because I certainly cant

i just notified the topic.
if u see astar, plz tell him to solve the moments part with explanation.
im off for now..

[elemis]

Send him a PM, if you havent already

[SGVaibhav]

sent..... but he has not come online from long time.

[SGVaibhav]

i got it.....
but where is astar

[elemis]

He was online a few hours ago.

[astarmathsandphysics]

I am here now. Am looking at question

[astarmathsandphysics]

moments about A for tension in BC
0.6j*-300k=Tx(-0.1i+0.2k)
Tx(-0.1i+0.2k)=-180i
T=-180i.180i/((-0.1i+0.2k).(-180i)) =-32400/-36j=-900j

[astarmathsandphysics]

The diagram is difficult to make out. is BC paralell to the y axis?

[SGVaibhav]

erm no...

rBC = 0.3i - 0.6j + 0.2k
|rBC| = 0.7

Since there is no reaction Max  (M_Ax)


(-300 x 0.6) + (0.2 / 0.7 x Tbc) = 0
Therefore Tbc = 1050 N
I did not understand the part in bold.   Why is only the k component considered in this equation?

[astarmathsandphysics]

I cant make out the diagram properly. Is the bar holding the weight at z=0

[SGVaibhav]

I cant make out the diagram properly. Is the bar holding the weight at z=0

yep =)
see my calculations
its all correct, but there is one part in the bold, which i dont understand.
lol i edited it like 5 times to put sigma properly

[astarmathsandphysics]

is BC paralell with y axis?

[SGVaibhav]

is BC paralell with y axis?

nop
the position vector rBC describes it path from B to C.