# Calculating Bending & Deflection for 5" dia Pipe with 5000 lb Load

• dmurugan
In summary: I can help with that if you need. Welcome to the PF, dmurugan. Is this for homework or for a school project, or for a work project? If it's homework, I can move it to the Homework Help forums. We need to see your attempts at a solution (see Fred's question about beam theory), before we can offer tutorial help. If it's for a work project, you should have enough background to do the calculation if you have been tasked with it. The city inspectors will be checking your work, no?Yes, I want to go ahead with the calculations and I am quite sure about the theory...could you help me out..??

#### dmurugan

!kindly look at the attachment to better understand!

I have a project which has this configuration of
two 5" dia double E.H,25 ft long pipe separated by a web vertically of dimension 1x2x25 inches also simply supported at the ends.

If you could visualize by rotating the below thing by 90 degree clockwise you will see what i am saying,

" o-o "

A load of 5000 lb is acting on top of it at an equal interval of 3 ft . I should make sure that it could hold this load without any bending or deflection. I have no clue to go about calculating the bending or deflection for the given load. It would be great if anyone could help me in this.

!kindly look at the attachment to better understand!

Thank you,
dmurugan.

#### Attachments

• Configuration.doc
25 KB · Views: 280
Well, there will definitely be deflections in the pipes. There's no way around that. Do you still need to go through the calculations?

Are you familiar with classical beam theory?

dmurugan said:
!kindly look at the attachment to better understand!

I have a project which has this configuration of
two 5" dia double E.H,25 ft long pipe separated by a web vertically of dimension 1x2x25 inches also simply supported at the ends.

If you could visualize by rotating the below thing by 90 degree clockwise you will see what i am saying,

" o-o "

A load of 5000 lb is acting on top of it at an equal interval of 3 ft . I should make sure that it could hold this load without any bending or deflection. I have no clue to go about calculating the bending or deflection for the given load. It would be great if anyone could help me in this.

!kindly look at the attachment to better understand!

Thank you,
dmurugan.

Welcome to the PF, dmurugan. Is this for homework or for a school project, or for a work project? If it's homework, I can move it to the Homework Help forums. We need to see your attempts at a solution (see Fred's question about beam theory), before we can offer tutorial help.

If it's for a work project, you should have enough background to do the calculation if you have been tasked with it. The city inspectors will be checking your work, no?

yes i want to go ahead with the calculations and i am quite sure about the theory...could u help me out..??

FredGarvin said:
Well, there will definitely be deflections in the pipes. There's no way around that. Do you still need to go through the calculations?

Are you familiar with classical beam theory?

Hi Berkeman..Its a work project actually..I am student doing an Internship at a steel plant..My specialization is in component design and layout..but they came up with this project in which i haven't got any experience..All they ask for is a approximate value of how much load the new configuration would take..

so i calculated the total load which is a combination of pipes, water and the rails on the top with a safety factor of 2:1. I thought i could use some fundamentals of strength of materials which i studied in school..

I tried solving it as uniformly distributed load ( simply supported at the ends) , one point load seperately ( simply supported as well as cantilever beam) and i ended up getting some results. But the problem is the pipe that i add at the bottom with a web in the middle. I have no clue to approach this configuration itself.

Also this is a in house project no worries about the city inspectors.

berkeman said:
Welcome to the PF, dmurugan. Is this for homework or for a school project, or for a work project? If it's homework, I can move it to the Homework Help forums. We need to see your attempts at a solution (see Fred's question about beam theory), before we can offer tutorial help.

If it's for a work project, you should have enough background to do the calculation if you have been tasked with it. The city inspectors will be checking your work, no?

Couple questions:
- Can you put some dimensions on the web in between the pipes? You say 1x2x25 inches but I assume the 25 is supposed to be feet and that's the overall length, but what is the height and width? Also, how is the web attached to the pipe? If welded, the weld design would help as you should also consider transverse shear stress at this joint.

- Is the pipe a 5" XXS? (5.563" OD x .750" wall)?

- What are the materials of construction? ASTM spec, condition or temper would help or whatever else you know about the pipes and web.

- Is the beam cyclically loaded or static?

- How is the beam attached at the ends?

- What temperature range is this exposed to?

- Would you consider rust or other failure mechanisms for this? Is anything flowing through the pipe? If so, what pressure?

1. width is 1 inch , height is 2 inches and the length is 25 ft.
2. Yes it is 0.750'' thick
3. Web is made of a normal mild steel a 1018 or A-36 and the pipes are Seamless Welded pipes.
5. Beam are attached to a concrete wall at the ends.
6. The pipe carries water which is insulated with 1" thick lithochrome insulation..but the surrounding temperature is 2200 degree F and the pressure of water inside is 50 psi...

Responce attached.

#### Attachments

• Configuration[1].doc
28.5 KB · Views: 276
Thanks a lot..mean while i was tryin to figure how u got tat Moment of Inertia value..??..also I made very detail shear force and bending moment diagram from which i got the Mmax..through which i can substitute the value of sigma max of the web material and i could calculate section modulus of the web..from this value I can find the best safe dimensions for the web...also there are only 5 point loads acting..it is organised in such a way that 3.5 feet length of the pipes are hanging beyond the simply supported walls at the ends..do i sound reasonable..??

dmurugan said:
Thanks a lot..mean while i was tryin to figure how u got tat Moment of Inertia value..??..
I quoted a wiki page that has a table on it. That was the wrong page though. I see now that's a different type of moment of inertia. Just ignore that page.

For a tube or pipe the bending moment of inertia is:
I = pi/64(Do^4-Di^4)

Find the I for your pipe, then to find the moment of inertia around the neutral axis of the composite beam, use the parallel axis theorem (ie: add pipe's cross sectional area times distance from neutral axis of composite beam to neutral axis of pipe). The total I is twice that since you have two pipes plus the moment of inertia for the small, rectangular section between the two. Try going over it again and let me know if you still can't figure it out.

Regarding the total stress then, if you have the moment diagram, multiply the maximum moment times the distance from the neutral axis to the outer fiber (should be OD of pipe plus 1/2 the height of your rectangular piece) then divide by total inertia. What do you get?

Existing Setup in the plant:
Which has one 10" pipe, I got a M.I of 367.8056 and a total stress of 12,933.122 p.s.i..

New Configurations:

I did it for 3" size pipe.with O.D 3.5 " and I.D 2.3"..The moment of inertia that i got is 361.3455 and the total stress is 17,144.2566 p.s.i..
And also I tried for 4" inch with O.D 4.5" and I.D 3.152", the moment of inertia that i got is 558.6498 and the Total stress is 12,673.635 p.s.i...
And also I tried for 5" inch with O.D 5.563" and I.D 4.063", the moment of inertia that i got is 1102.30 and the Total stress is 7275 p.s.i...

2 Questions That I have is,
a. Which pipe size is safer 3" , 4" or the 5" ? ( I think 4")
b. Earlier we used a 10" pipe of wall thicknes 1 "..now if i change it to 3"(0.6") or 4"(0.674) or 5"(0.75) we have a reduced wall thickness..so will it bend or collase when loaded..??

Existing Setup in the plant:
Which has one 10" pipe, I got a M.I of 367.8056 and a total stress of 12,933.122 p.s.i..

New Configurations:

I did it for 3" size pipe.with O.D 3.5 " and I.D 2.3"..The Moment Of Inertia that i got is 361.3455 and the total stress is 17,144.2566 p.s.i..
And also I tried for 4" inch with O.D 4.5" and I.D 3.152", the moment of inertia that i got is 558.6498 and the Total stress is 12,673.635 p.s.i...
And also I tried for 5" inch with O.D 5.563" and I.D 4.063", the moment of inertia that i got is 1102.30 and the Total stress is 7275 p.s.i...

2 Questions That I have is,
a. Which pipe size is safer 3" , 4" or the 5" ? ( I think 4")
b. Earlier we used a 10" pipe of wall thicknes 1 "..now if i change it to 3"(0.6") or 4"(0.674) or 5"(0.75) we have a reduced wall thickness..so will it bend or collase when loaded..??

The safest installation is the one that has the lowest stress (everything else being equal).

Hi..Please find the report that i made in the attachment. Thank you.

#### Attachments

• REPLACEMENT OF CROSS OVER PIPES.doc
96 KB · Views: 265
Thanks for that. Responce attached. PDF file shows calculation of the moment of inertia for a composite beam. Think you're still missing this. The other big thing is stress allowable. See if you can find the exact material, condition, temper, etc... the various pipes or other materials will be made from. ASME B31.3 gives stress allowable of 17.8 ksi for A 36 up to 100 F, but this drops to 16.9 ksi up to 700 F. Knowing this is inside a furnace, you need to know what temperature the material will see. It shouldn't be used above 700 F. Note also, A 36 is for plate steel, not for pipe. You should locate the material spec for the pipe. Saying it is 1018 is insufficient. Don't forget to look at shear stress in any weld. Transverse shear is highest at the center of the beam and drops to 0 at top and bottom edges.

#### Attachments

• REPLACEMENT OF CROSS OVER PIPES.doc
95 KB · Views: 238
• Stress.pdf
25 KB · Views: 213
One more thing I forgot to mention. Normally, you should subtract off the manufacturing tolerance on the pipe wall or any other structural member. Assume that is, that the member was manufactured on the low end of the tolerance. For pipe, that means reducing wall thickness by 12% (typical). The actual value can be located in the ASTM code for the material.

## 1. What is the formula for calculating bending and deflection for a 5" diameter pipe with a 5000 lb load?

The formula for calculating bending and deflection for a 5" diameter pipe with a 5000 lb load is: Bending = (FL^3)/(48EI) and Deflection = (FL^3)/(3EI), where F is the load, L is the length of the pipe, E is the modulus of elasticity, and I is the moment of inertia.

## 2. How do I determine the modulus of elasticity for the pipe material?

The modulus of elasticity, E, can be found in material properties tables or by consulting with the manufacturer of the pipe. It is a measure of the pipe's ability to resist deformation under stress.

## 3. Can I use the same formula for calculating bending and deflection for pipes of different diameters?

Yes, the formula for calculating bending and deflection can be used for pipes of different diameters as long as the load and other variables remain the same. The only difference may be in the moment of inertia, as it takes into account the cross-sectional shape and size of the pipe.

## 4. What is the acceptable level of bending and deflection for a 5" diameter pipe with a 5000 lb load?

The acceptable level of bending and deflection for a 5" diameter pipe with a 5000 lb load may vary depending on the specific application and industry standards. It is important to consult with industry guidelines and codes to determine the acceptable levels for your specific project.

## 5. Are there any other factors that may affect the bending and deflection of the pipe under a 5000 lb load?

Yes, other factors such as the pipe's wall thickness, material properties, and external support or restraints may also affect the bending and deflection of the pipe. It is important to consider all of these variables when calculating and predicting the behavior of the pipe under a 5000 lb load.