# Inclined Beam with UDL

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1. Dec 16, 2014

### MayZ91

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

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.

2. Relevant 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))

3. 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.

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2. Dec 18, 2014

### OldEngr63

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!

3. Dec 18, 2014

### 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).

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Last edited: Dec 18, 2014
4. Dec 19, 2014

### 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.

Last edited: Dec 19, 2014