# Bending Calculation

## Main Question or Discussion Point

!!!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 seperated 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

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FredGarvin
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?

berkeman
Mentor
!!!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 seperated 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..??

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 havent 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.

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?

Q_Goest
Homework Helper
Gold Member
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...

Q_Goest
Homework Helper
Gold Member
Responce attached.

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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..??

Q_Goest
Homework Helper
Gold Member
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..??

Q_Goest
Homework Helper
Gold Member

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.

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Q_Goest
Homework Helper
Gold Member
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.

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Q_Goest