Resolving forces on a hydraulic frame - method of sections?

[Mech King]

Hi guys,

I want to check that I am going about this problem in the right way:

The attached image shows a parallelogram type frame with a hydraulic ram located from corner to corner as shown (E to C). There is a load applied to a platform in the far bottom right hand side of the drawing. This load is -4635N. The frame is pin supported and fixed at the base E.

I have worked out that the force on the ram must be 16141N. I have taken moments about the Pivot D. Since the ram is the only thing stopping the frame from collapsing once the load is applied, then the ram and the applied load are the only factors to take into account to determine the ram force:

Ram force = [(640+450)X (-4635)]/313 = -16141N.

Note that the 313 mm above is the perpendicular distance from the ram centreline to the pivot D.

I have then gone on to use the method of sections to resolve the forces in the beams.

The platform creates a normal reaction “Fr” just below A and also an X and Y force at A.
Fr= (-4635x450)/150 = 13905N

Summing forces in the X and Y direction will give the force components at A, these are:
FAx = -13905N, FAy = 4635N.

It is at this point where I get a bit confused. I could use the method of sections to resolve the forces along member ABC. I presume I am right in assuming that given that members EB, CD and the ram (EC) are all two force members. I am torn between this method or could I simply treat the parallelogram BCDE with the Ram EC as two triangles and resolve the forces and then apply these forces the member ABC.

Also, have i calculated the ram force correctly? Or, should i have used the method of section starting at where the load is applied and then worked my way through to determine the ram force etc?

I have got my self into a bit of a pickle, on what seemed like a straight forward problem. Could somebody please advise me on how to proceed and whether my current approach is correct?
This has been bugging me for days.
Any advice will be a life saver,

Many thanks

Amir

 

[LightHero]

The approach you have taken is correct, Amir. You have calculated the force on the ram correctly and the method of sections would be the best way to resolve the forces in the beams. The method of sections can be used to break the system down into two parts and then solve for the forces at each joint. The process would be to first calculate the forces at A, then calculate the forces along the beam ABC, then calculate the forces along the beam CD, and finally calculate the forces along the ram EC. After resolving the forces in the beams, the forces in the frame can be determined. The platform creates a normal reaction “Fr” just below A and also an X and Y force at A. Fr= (-4635x450)/150 = 13905N. Summing forces in the X and Y direction will give the force components at A, these are: FAx = -13905N, FAy = 4635N.Once all the forces have been resolved, it is easy to calculate moments and determine the reactions at the pin supports. All of this can be done using the method of sections. Hope this helps!

 

[Mene]

I would first commend you for taking the time to carefully assess and analyze the problem before proceeding with your calculations. It is always important to have a clear understanding of the forces at play in a system before attempting to solve for specific values.

Based on your description and calculations, it seems like you have correctly determined the force on the hydraulic ram and the forces at point A. Your approach of using the method of sections to resolve forces on member ABC is a valid one. However, as you mentioned, you could also treat the parallelogram BCDE as two triangles and use trigonometry to solve for the forces on member ABC.

In terms of calculating the ram force, it seems like you have used the correct approach by taking moments about pivot D. However, it is always a good idea to double check your calculations and assumptions to ensure accuracy.

Overall, it seems like your approach is correct and you are on the right track. Keep in mind that there may be multiple ways to solve a problem and it is important to choose the method that you are most comfortable with and that yields accurate results. If you are still unsure or have further questions, I would recommend seeking guidance from a mentor or colleague with expertise in this area. Good luck with your calculations!