Calc moment of a hydraulic piston?

[sf2k]

Homework Statement

Working through 5.17 problem in Bedford 5th edition (Engineering Statics) p214

"The hydraulic piston AB exerts a 2000 N force on the ladder at B in the direction parallel to the piston. Determine the weight of the ladder and the reactions at C."

piston between A and B on an angle theta.
point C is further away from A and B by 1 metre along the base.

1m height from A->B or C->B
2m distance between base A->B
1m distance between base B->C
2m distance between the centre Weight of the ladder and the end point C

Homework Equations

Tan -1(opp/adj) gives the angle of force for C(x) and C(y).
forces on the x plane are cos theta
forces on the y plane are sin theta
F = ma using 9.81 m/s^2

The Attempt at a Solution

Sum of F(x) = C(x) + (2000/9.81) cos theta = 0

since base between A and B is 2 and height is 1 thus tan -1 (1/2) = 26.57 degrees

Sum of F(x) = C(x) + 203.87 cos 26.57 = 0
C(x) + 182.34 = 0
C(x) = -182.34 kgSum of F(y) = C(y) + 203.87 sin 26.57 - W = 0

The W force counters the C(y) force so I subtracted.
Don't know how to calculate C(y).

Sum of M(c) = ??

not sure how to calculate the moment at C nor solve for W.So I"m missing concepts from class in terms of when to solve for what and why. I have seen the answers for it so it's not a question of getting an answer. But I'm not following what to do for myself and I want to understand what is going on, what the moment is at C, and how to calculate it out.

Thanks for any advice or attempts at improving my understanding.

 

[nvn]

sf2k: Can you post a diagram, or give the (x, y) coordinates of each point? Make up a letter for all points that do not already have a label. Let's call the centroid of the ladder point D, and the lower end of the ladder point E (?). E.g., if point B is arbitrarily chosen as the origin, let me see if I understand your diagram. In units of metres, the coordinates would be B(0, 0), C(1, 1), A(-2, -1), D(-1, -1)? But what are the coordinates of point E? And what is touching points A, C, and E? I.e., what are the boundary conditions, meaning what are the supports around your structure, which apply the reaction forces?

 

[sf2k]

Here's the ladder problem with image attached. Also another problem with just image. (Solve for moment at B). Oddly the ladder prob is more complex but the second problem shows I don't really know the process.

I don't know what is is about Moment that I keep forgetting. I think we can flush it out though between these two examples and figure our where the holes are in my understanding. This could then help others in similar straits.

 

[pongo38]

For your second problem, could you define what you think the "bending moment at a section" is?

 

[sf2k]

Not sure. It's confusing since it looks like at C the pole is compressing upwards and outwards since the force it at an angle upwards at 40N and outwards at 48N. So I'll guess the component at B(y) of (1.2)(40)sin45 up and B(x) of 48N to match C(x).

 

[nvn]

sf2k: For your second problem, your answer for Bx is correct. Your answer for By is currently incorrect. One thing that appears to be missing is a free-body diagram. You posted a diagram of the given structure; but any time you need to solve for forces and moments at a support or at an internal section cut, you must draw a free-body diagram, which means you must draw the unknown reaction forces, or unknown forces and moments at the section cut. Then you use equilibrium equations to solve for the unknown forces and moments.

E.g., make a section cut at point B, and analyze only member BC. At the section cut, draw the unknown forces and moment acting on the section cut. Go ahead and do it. After you draw it, write the equilibrium equations only for the sectioned-off structure, member BC. Now solve the equilibrium equations, and it will give you the forces and moment at the section cut at point B. Use the right-hand rule for moments, and say anticlockwise moments are positive. Show your work, and someone can check your math. Also, see the last paragraph of post https://www.physicsforums.com/showpost.php?p=2946515".