# Calculating load per unit length

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1. Oct 22, 2015

### roldy

I am having the hardest time calculating q, the load per unit length. This question is in relation to my previous question I posted here.

I have a cylinder laying horizontally that is fixed on its ends. The cylinder is filled with water. To calculate the deflection I am simplifying the problem by combining the volume of the cylinder and the volume of the shaft.

1) Find the total volume of the cylinder with the end shafts.
2) Find the volume of the water inside the cylinder.
3) Find the mass of the value in 1) using the density of the cylinder material.
4) Find the mass of the value in 2) using the density of water.
6) Calculate the total mass and find the weight by multiplying by 9.81.
7) Take this weight (load) and divide by the entire length (from end of shaft to end of shaft).
8) Use the deflection equation for a cylinder fixed at both ends using I for a solid circle and E for the cylinder material.

Essentially what I am doing is lumping all the masses into one mass which is represented by the shaft end to end measurement with a diameter of the shaft.

Is this procedure good enough for a rough estimate for the deflection?

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2. Oct 23, 2015

### jackwhirl

7. Looks like it will calculate a distributed load.
8. Are you working with a solid circle?

3. Oct 23, 2015

### roldy

What is the correct way to calculate the load per unit length? I had a typo in 8). The shaft is hollow as the drawing shows.

4. Oct 23, 2015

### jackwhirl

That would be simply the load (weight of water + beam, as in your post above) divided by the length.
My mechanics of materials book was kind enough to remind me that, if you're trying to calculate beam deflection reactions, a distributed load can be replaced with an equivalent resultant load placed at the centroid of the distributed load.

Last edited: Oct 23, 2015
5. Oct 23, 2015

### roldy

isn't that what I wrote in step 7? Take the load (the weight) and divide by the length to get q. Or do I need to divide by the length again?

6. Oct 23, 2015

### jackwhirl

That is what you wrote there. You had it right. No need to do it twice.

7. Oct 23, 2015

### roldy

Ok, thanks. I will post the excel spreadsheet I made for the calculations as I believe the result is not as expected. I have something else to try on it before I do that.

8. Oct 23, 2015

### greentlc

You can't replace the distributed load with a point load to find the deflection, those are separate load cases and must be treated so as such. You can replace the distributed load with a point load to help find the vertical reactions at the supports.

9. Oct 23, 2015

### jackwhirl

I see that you are right and will correct myself. Thank you.