Homework Help: Statics: Internal forces at a point along a beam

1. Jul 15, 2013

yaro99

1. The problem statement, all variables and given/known data

2. Relevant equations
ƩFx=0
ƩFy=0
ƩM=0

3. The attempt at a solution

FBD of the entire thing:

ƩMB = 780(0.3) + (5/13)T*(0.72) - (12/13)T*(0.6) = 0
T = 845N

ƩFx = Bx + (5/13)*845 = 0
Bx = 325N ←
ƩFy = By + (12/13)*845 = 0
By = 780N ↓

Now here is where I tried 2 different methods for the forces at J:

Method 1:

FBD of CDJ:

ƩFx = (5/13)*845 - (12/13)V + (5/13)F = 0
ƩFy = (12/13)*845 - 780 + (5/13)V + (12/13)F = 0
θ = arctan(5/13) = 22.6°
F = 125N 67.4° down and to the left
V = 300N 22.6° up and to the left

horizontal distance from D to J = 0.24/tan(67.4°) = 0.1m
ƩMJ = (5/13)*845*(0.24) - (12/13)*845*(0.4) + 780*(0.1) + M = 0
M = 156 N*m counterclockwise

This method gives me the correct magnitudes, but the directions are supposed to be opposite of what I got, which I don't understand.

Method 2:

FBD of BJ:

ƩFx = (12/13)V - (5/13)F - 325 = 0
ƩFy = -(5/13)V - (12/13)F - 780 = 0

F = 845N 67.4° up and to the right
V = 0N

horizontal distance from J to B = 0.48/tan(67.4°) = 0.2m
ƩMJ = 325*(0.48) -780*(0.2) + M = 0
M = 144 N*m counterclockwise

I am not sure why this method gives me incorrect answers.

2. Jul 15, 2013

TSny

Did you leave out one of the vertical forces here?

Last edited: Jul 15, 2013
3. Jul 15, 2013

Maiq

There is no By force. The horizontal force in the AC rope is 780. It looks like your forgot to add that in on your Sum of y-direction forces.

4. Jul 15, 2013

yaro99

Oh yeah, thanks for the correction. I have the right numbers and directions now, using the second method.

Doing method 2 I get the "correct" directions according to the book, which are opposite those in method 1.

5. Jul 15, 2013

Maiq

Your answers for both methods should have opposite directions. If you were to put those two sections back together the forces at J would cancel out and the whole system would be in static equilibrium. I guess your book just used method two but either way would be correct.

6. Jul 16, 2013

yaro99

Ah, ok, this makes sense. Thanks!