Inclined Beam w/ UDL Homework Statement

[MayZ91]

Homework Statement

Hello all,

I am trying to find the deflection of a hydraulic cylinder at point A (refer the attached).
There are two hydraulic cylinders, with certain distance apart. On top of it is a beam that is inclined to the horizontal by 12 degrees. The piston is operated by two different pumps, which facilitates in extending and retracting of the pistons individually. I have captured the length of the piston after the guide in the hydraulic cylinder, as it is firmly fixed.
A UDL of 1.56 N/mm is acting on the beam perpendicular to the horizontal.
Please refer the attached to get the geometry of the system.

Homework Equations

I have calculated the moments at point A and B, by assuming these points as fixed. However, they are all rotary joints.
The reason to assume it to be fixed is to break the system into two sub-systems. One is the beam and other are the pistons.
After finding the moment at A and B from first subsystem, I transfer the moment into second sub system to obtain the deflection at A. (deflection = M(L^2)/(2EI))

The Attempt at a Solution

I have attached the excel sheet, where I have done my calculations.
I have ended up with 0.54mm as the deflection. But, this is by assuming the piston is a cantilever (deflection = M(L^2)/(2EI))
However, it is not a cantilever with a free end. The deflection obtained from FEA is 0.036mm.
Please help.

 

[OldEngr63]

I am trying to find the deflection of a hydraulic cylinder at point A

The deflection at A due to what? Bending? Isn't A the tip of one of your hydraulic cylinders? You have a given position for A (357.34), so what deflection are you thinking about here?

Is B the tip of the second hydraulic cylinder?

It is a bit flaky to take about a uniformly distributed load on an inclined beam if we have to think in terms of the angle of inclination as variable. If the 12 degree angle is decreased to say 8 deg, the horizontal length of the beam increases. Does the total load on the beam likewise increase, or does something else happen? This seems ill posed!

 

[MayZ91]

Hello,

Thank you very much for going through the post.

You're right, the tip B is the tip of the second cylinder.
Also, to maintain the distance between the cylinders constant, there is a sliding member on the beam CD at point B.
The actual scenario is this, the two hydraulic cylinders are screwed to 2 load beams respectively, these load beams are oriented in the direction of the paper(X-axis). The beam CD is mounted on top of these two load beams. The load beam on B has the sliding point, on which the beam CD slides when the hydraulic cylinder retracts.

The end condition here is the problem. Although the load beam has the sliding member and the rotary joint, the hydraulic cylinder gets tightly screwed to the load beams. Therefore, it may needs to be considered as simply supported with respect to beam CD(I think!)
If its simply supported, then I have to use the elastic beam deflection formula = M*(L^2)/(27*E*I)
What I am trying to find is the deflection of point A, due to bending in horizontal axis (Y-axis).

 

[MayZ91]

And the UDL is decided based on the test conditions. I do not know how that decision is made.
Also, to make it clear, i am not worried about the load beams or the beam CD. My concern is the bending of the piston of the hyd cylinder.

 

[rezeew]

Dear researcher,

Thank you for sharing your work on finding the deflection of the inclined beam with a UDL. It is clear that you have put a lot of effort into your calculations and have taken into consideration the complexities of the system.

It is important to note that in order to accurately calculate the deflection of a beam, the boundary conditions and loading conditions must be accurately represented. In this case, the hydraulic cylinder and pistons provide additional support and constraints to the beam, which may affect the deflection.

Additionally, using FEA can provide a more accurate representation of the deflection as it takes into account the material properties and structural behavior. However, it is always important to validate FEA results with experimental data.

I suggest considering the boundary conditions and loading conditions more carefully in your calculations and comparing your results with experimental data to ensure accuracy. It may also be helpful to consult with a structural engineer or conduct further research on similar systems to gain a better understanding of the behavior of the inclined beam with UDL.

Best of luck with your research.

Sincerely,