How do I analyze a body with a 14 kip force at a point?

[fayan77]

Homework Statement

Homework Equations

Using dimensional plane in the vertical y and horizontal x.
$\Sigma$F_x = 0
$\Sigma$F_y = 0
$\Sigma$M_z = 0

The Attempt at a Solution

I have detached the 2 members at B and analyze them both separately. The 14 kip force is throwing me off though. When I detach the body do I still include a Bx and By force at B, on top of the 14 kip force?

 

[haruspex]

Homework Statement

View attachment 238247

Homework Equations

Using dimensional plane in the vertical y and horizontal x.
$\Sigma$F_x = 0
$\Sigma$F_y = 0
$\Sigma$M_z = 0

The Attempt at a Solution

I have detached the 2 members at B and analyze them both separately. The 14 kip force is throwing me off though. When I detach the body do I still include a Bx and By force at B, on top of the 14 kip force?

In separating them, yes, you must include equal and opposite sets of Bx, By. For the X force, you just have to include it with one of them. If you need to answer for the values of Bx and By, it matters which you include it in. Looks like it is to be considered as applied to AB. But which you include it in does not affect any other reaction forces.

 

[fayan77]

But then I'm still left with 3 equations 4 unknowns. member AB x positive to the right y positive up moment positive counter clockwise.
$\Sigma$F_x=0: A_x+14-B_x = 0
$\Sigma$F_y=0: A_y-B_y = 0
$\Sigma$M_A=0: -14(12) + B_x(12) - B_y(9) = 0

same with other member

 

[haruspex]

same with other member

Yes, but how many unknowns do you have altogether?

 

[fayan77]

A_x
A_y
B_x
B_y
D_x
D_y
6 unknowns

 

[haruspex]

A_x
A_y
B_x
B_y
D_x
D_y
6 unknowns

And six equations altogether, right?

 

[fayan77]

the only ones I could combine are the ones at connection B. However, that 14 Kip force only act on member AB correct?
If so then from member BCD I use
$\Sigma$M_D = 0: 10(5)-B_y(10)-B_x(12) = 0
50 = 10B_y+12B_x from member BCD
168 = 12B_x-9B_y from member AB
solving for B_x and B_y and solve for the rest

 

[haruspex]

the only ones I could combine are the ones at connection B. However, that 14 Kip force only act on member AB correct?
If so then from member BCD I use
$\Sigma$M_D = 0: 10(5)-B_y(10)-B_x(12) = 0
50 = 10B_y+12B_x from member BCD
168 = 12B_x-9B_y from member AB
solving for B_x and B_y and solve for the rest

Looks right.

 

[fayan77]

Thank you