Calculating load per unit length

In summary, the conversation discusses the process of calculating q, the load per unit length, for a cylinder filled with water and fixed at both ends. The suggested method involves finding the total volume and mass of the cylinder and water, and using the deflection equation for a cylinder fixed at both ends. The conversation also mentions the possibility of replacing the distributed load with a point load to help find the vertical reactions at the supports.
  • #1
roldy
237
2
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.
5) Add the masses together.
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?
 

Attachments

  • Chill Roller.PDF
    18.1 KB · Views: 552
Engineering news on Phys.org
  • #2
roldy said:
I am having the hardest time calculating q, the load per unit length.
[...]
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.
[..]
7. Looks like it will calculate a distributed load.
8. Are you working with a solid circle?
 
  • #3
jackwhirl said:
7. Looks like it will calculate a distributed load.
8. Are you working with a solid circle?

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
roldy said:
What is the correct way to calculate the load per unit length?
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:
  • #5
jackwhirl said:
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, a distributed load can be replaced with an equivalent resultant load placed at the centroid of the distributed load.

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
That is what you wrote there. You had it right. No need to do it twice.
 
  • #7
jackwhirl said:
That is what you wrote there. You had it right. No need to do it twice.

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
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.
 
  • Like
Likes jackwhirl
  • #9
greentlc said:
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.
I see that you are right and will correct myself. Thank you.
 

1. How do you calculate load per unit length?

Load per unit length is calculated by dividing the total load by the length of the object. This gives you the amount of force per unit length that is being applied to the object.

2. What units are used for load per unit length?

Load per unit length is typically measured in units of force (such as Newtons or pounds) per unit of length (such as meters or feet).

3. What factors influence the load per unit length of an object?

The load per unit length of an object can be influenced by various factors such as the material of the object, its shape and dimensions, the type of load being applied, and any external forces acting on the object.

4. How does load per unit length affect the strength of an object?

The load per unit length is a measure of the amount of stress that an object can withstand before breaking. The higher the load per unit length, the greater the force that is being applied to the object and the more likely it is to fail.

5. Are there any safety considerations when calculating load per unit length?

Yes, it is important to ensure that the load per unit length does not exceed the maximum load capacity of the object. It is also important to consider any potential risks or hazards that may arise from the object being under high levels of stress.

Similar threads

  • Mechanical Engineering
Replies
2
Views
2K
  • Mechanical Engineering
Replies
1
Views
962
Replies
15
Views
2K
Replies
7
Views
542
  • Mechanical Engineering
Replies
8
Views
1K
  • Mechanical Engineering
Replies
4
Views
1K
  • Mechanical Engineering
Replies
5
Views
3K
  • Mechanical Engineering
Replies
8
Views
1K
  • Mechanical Engineering
Replies
20
Views
2K
Replies
1
Views
2K
Back
Top