Free-Body Diagram for Statics of a Crane

[unscientific]

]1. Homework Statement [/b]

The problem is attached in the picture

The Attempt at a Solution

The free-body diagram is in the second picture. However, when I try to do

1)Sum of horizontal forces = 0
2)Sum of Vertical forces = 0
3)Moments about A, B, C, = 0

I get nonsensical answers...

Could it be that at the pins my forces are in the wrong direction?

 

[voko]

Why do you compute moments about A, B and C? You should compute moments about ONE point.

 

[unscientific]

Why do you compute moments about A, B and C? You should compute moments about ONE point.

What I meant was, form 3 equations, like do it 3 times.

 

[CWatters]

Perhaps show us the working that gave you non-sensical answers so we can try and find the mistake.

In your second diagram you appear to have omitted forces on the winch.

Are you assuming T is vertical?

 

[voko]

Again, you don't need to compute the moments about different points. Choose just one, and the sum of the moments of all the forces about this one point must be zero.

 

[unscientific]

I'm trying to solve the forces on the crane first..Letting the joint A horizontal and vertical forces be F₁ and F₂, joint D F₃ and F₄, we have:

Sum of forces in x-direction

F₁ = F₃

Sum of forces in y-direction

T + 800 = F₂ + F₄

Moments about A

T(1) + 1600 = F₃ (1)
T + 1600 = F₃

Moments about B

800 + F₂ + F₄ = F₃

Moments about C

T + 2F₃ = 2F₂ + 2F₄

 

[unscientific]

Perhaps show us the working that gave you non-sensical answers so we can try and find the mistake.

In your second diagram you appear to have omitted forces on the winch.

Are you assuming T is vertical?

Yes, I'm doing it by the simplistic approach first before considering T tilted at 30 deg..

 

[unscientific]

any input would be appreciated!

 

[ehild]

Yes, I'm doing it by the simplistic approach first before considering T tilted at 30 deg..

Do not do it. Write up the horizontal (x ) and vertical (y) components of all forces acting at crucial points. You have the load first. What forces act on it? What about the pulley in the middle?
What are their torques acting on the beams?
I suppose the beams are considered massless, so the tension is the same in them along their length.

ehild

 

[CWatters]

What he said.

This bit...

Sum of forces in x-direction
F1 = F3

is missing forces because of the approach you took ignoring the winch.

 

[unscientific]

What he said.

This bit...



is missing forces because of the approach you took ignoring the winch.

Ok how about this now...

I am only considering all the forces acting on the crane...hence the free-body diagram is only of the crane and not inclusive of the winch

 

[cake of doom]

I think you'd find it easier in the long run to consider all forces now rather than having to back-track and recalculate. Trust me, looking at things too simply is a hard habit to break and can lead to things being overlooked.

 

[CWatters]

T1 acts at an angle so it has components in both x and y. If you show it verticaly you will (and did) forget about the x component.

Take a look at the forces on pulley C. There will also be T2 acting to the left there.

In short by ignoring the winch you appear to have forgoten some of the forces acting on the crane.

 

[unscientific]

T1 acts at an angle so it has components in both x and y. If you show it verticaly you will (and did) forget about the x component.

Take a look at the forces on pulley C. There will also be T2 acting to the left there.

In short by ignoring the winch you appear to have forgoten some of the forces acting on the crane.

is the horizontal component at B the same as the horizontal component at C?? In my opinion I don't think so..

Then the result would be too many unknowns and too little equations..

 

[CWatters]

is the horizontal component at B the same as the horizontal component at C?? In my opinion I don't think so..

Not clear what you mean by "the horizontal component at B".

Pulley B has two forces acting it. Neither are vertical.

 

[unscientific]

Not clear what you mean by "the horizontal component at B".

Pulley B has two forces acting it. Neither are vertical.

Ok, I still can't see what's wrong with my free-body diagram. Point B has a vertical and horizontal component. Point C I shall assume only vertical component for simplicity. Point A and D are shown in the picture.