Question for the engineers

[Marcel R. Cyr]

Right on Robert, but I had fun and learned a few formulas.

What the hell, we all know that it does not pertain to HI., but you have to be open to a few challenges of the track side once in awhile. ha. ha.

Marcel

[Robert J. OConnor]

I could show you guys the formulas for calculating equivalent section modulus, arch cord compression stresses, and curved frame member deflection if ya would really like to have some fun and make your head spin ...

(P.S. Would prob have to scan in a few pages from the AISC manual, tube steel properties tables, and a bunch of pages from Rourke's Formulas for Stress and Strain ... but you will probably get a headache if ya don't know what you are looking at ... and that would probably be after a few days of pulling your hair out trying to figure out what the he!! they mean ... )

[Marcel R. Cyr]

Hi. Robert;

Let's play a game. ha. ha.

If I can not solve it, my friends will. ha.\

Marcel

[pdickerson]

The moment of inertia of a circle varies with the 4th power of its diameter (it is a cubed function for a rectangle). So the answer is (((2.375)^4)/2)^-4 or approximately 1.997".

[Robert J. OConnor]

Moment of Inertia (I) relates to a members stiffness ... for things such as compression, buckling and deflections. For bending only from the original question (if only bending is involved, which does not appear to be the case), then the correct property to compare would the Section Modulus (S).

Also consider that it's for structural pipe, which is hollow inside ... that complicates things, and a straight comparison of circular sections wouldn't be correct.

For Pipe, some of the parameters you will need/compare are:
I = 0.0491 x (D^4 - d^4)
S = 0.0982 x (D^4 - d^4) / D
r = (D^2 + d^2)^0.5 / 4
Where D = outside diameter and d = inside diameter

Without even considering that it's an arch which complicates things (including possibly curved members, stability/buckling issues, compression and bending combination, and eccentric loading) you will probably also need some of the formulas from the AISC Manual and some of the formulas here ... http://www.ce-ref.com/steel.htm ... that is assuming the members are steel, and not aluminum or some other material.

This is for educational purposes only! ... so have fun Marcel ...

[Marcel R. Cyr]

Thanks Robert, that will keep me busy for a while. ha.ha.

Marcel

[Brian E. Kelly]

Originally Posted by roconnor

Moment of Inertia (I) relates to a members stiffness ... for things such as compression, buckling and deflections. For bending only from the original question (if only bending is involved, which does not appear to be the case), then the correct property to compare would the Section Modulus (S).

Also consider that it's for structural pipe, which is hollow inside ... that complicates things, and a straight comparison of circular sections wouldn't be correct.

For Pipe, some of the parameters you will need/compare are:
I = 0.0491 x (D^4 - d^4)
S = 0.0982 x (D^4 - d^4) / D
r = (D^2 + d^2)^0.5 / 4
Where D = outside diameter and d = inside diameter

Without even considering that it's an arch which complicates things (including possibly curved members, stability/buckling issues, compression and bending combination, and eccentric loading) you will probably also need some of the formulas from the AISC Manual and some of the formulas here ... http://www.ce-ref.com/steel.htm ... that is assuming the members are steel, and not aluminum or some other material.

This is for educational purposes only! ... so have fun Marcel ...

Ya, good luck Marcel. Ouch Robert, what did we ever do to you?

[Robert J. OConnor]

Originally Posted by bkelly2

Ya, good luck Marcel. Ouch Robert, what did we ever do to you?

Well ... normally I wouldn't even scratch the surface of those issues, and would try to keep it in practial terms that would relate to home inspections. But, Marcel asked for it, so he got it ...

[Marcel R. Cyr]

Hi. Robert;
Since you are the expert, I guess you need to help me with this one. ha. ha.

(W) Load... The amount of pressure or force applied to a body to make it move or bend.
(d) Deflection... The distance a part will move or bend when (W) is applied to it.
(I) Moment of Inertia... Standard formulas for calculating the actions of material particles of area or mass using their locations from a reference axis.
(E) Modulus of Elasticity... The ratio of stress to strain within proportional limits of a material, usually in tension or compression.
Elastic Limit... The maximum point at which a material can be bent and then return to normal shape.
Yield Point... The point on a stress-strain curve at which a material will no longer return to normal and instead, will stay deformed or break.
(L) Length of beam The length of the beam being used for the calculation. In our case, a pole for martin housing. Convert this dimension to inches, since the result we want to know is inches.
Geometric shape... Round... Square... Triangular...
Size... Large... Small...
Material... Steel... Aluminum... PVC... Wood...


Example:

11/2” Schedule 40 pipe.
Wall thickness = .145
I.D.= 1.21
Lbs. Per/sq.ft. = 2.71

Annullus Area = Pi(R1 + R2)(R2-R1)

0.049(D^4-d^4)

(E) for Cold Rolled Steel is 30x10^6 (30,000,000psi)



Pi (D^4 - d^4) or 0.049(D^4-d^4) Where D is the outside diameter and d is the inside diameter.
64

If you do the formula for a square pole, you have to measure the pole across the flats. Then use the following equation:

(A^4 - a^4) Where A is the outside 'flat' dimension and a is the inside 'flat' dimension.
12

The generic formula for the calculation of deflection (d) at the end of a beam, rigidly mounted at one end is:

d = W (L^3)
3 E I

Am I on the right track or not? Man, this is hard. No wonder they have computer progams to figure out this crap. ha. ha.

Marcel

[Robert J. OConnor]

They look like similar formulas for the stiffness/deflection part of the example topic related to moment of inertia (I) - see above. Only one piece of the puzzle. And the defelection calculation are not for what I assumed was a simply supported member ... but then again if it's part of a frame the you would need the Rourke's Formulas for Stress and Strain equations, or a computer program. You could assume simple end conditions for an example ... even though that wouldn't be correct for a space frame/arch.

[Marcel R. Cyr]

Boy, thanks alot Robert, your not making too easy on me, you know that don't you. ??

You have all the computers and the books, I only have common sense. I'm losing before I start, but I am not a quitter. Might take me some time, but I'll get there.

Marcel

[Robert J. OConnor]

Originally Posted by roconnor

I could show you guys the formulas for calculating equivalent section modulus, arch cord compression stresses, and curved frame member deflection if ya would really like to have some fun and make your head spin ...

I warned you ...

It's really not possible to walk someone through the mechanics of material and frame analysis portions of this issue on a web thread. And the original question was intended for the engineers on the board, so I gave my opinions on that.

It really doesn't have anything to do with home inspections, or something a home inspector needs to know. If it's a real world problem then an engineer should get involved.

JMO & 2-nickels ...
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[Marcel R. Cyr]

Originally Posted by roconnor

I warned you ...

It's really not possible to walk someone through the mechanics of material and frame analysis portions of this issue on a web thread. And the original question was intended for the engineers on the board, so I gave my opinions on that.

It really doesn't have anything to do with home inspections, or something a home inspector needs to know. If it's a real world problem then an engineer should get involved.

JMO & 2-nickels ...
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Very true Robert and agree with you.

In my case I am a heavy Commercial Builder full time, and work with Architects and Engineers on a daily basis, and this type of information keeps me abreast of what, how and when things get to where they are at a point.
I like to know all aspects of how it is achieved, and toying with structural analysis is interesting for me.

Thanks for your Patience.

Marcel


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[dchew]

A part of good sound engineering is understanding how to do the number crunching. However, many engineers forget that once you have the numbers, you need to do also do an analsysis with the proper failure criteria.

Not everything are simple beams with continous loading on them. You have short beams that are primarily loaded in shear, off-center loading, etc. A good engineer will crunch the numbers to get the estimated stress and deflection diagrams, then compare it to the proper design criteria, and then make his judgement.

[Marcel R. Cyr]

Dwight; your point is well taken and appreciate your input to this debate if you want to call it that. If, anything, I am learning.

Your thesis of the computations, stress and everything else reminds me of a school building of four floors I built about 12 years ago where I poured the second floor on deck and a few days later was going to pour the third floor on deck and the mezzanine supported by the third floor.

When I poured the second floor on deck and saw these beams sagging about an inch to 1 1/4", I called the Engineer. He said that was normal and to not worry, he had run his stress calculations and was comfortable with the sag.

The night before I poured the third floor in conjunction with the mezzanine floor supported by the same, I had a bad dream about a callapse.

The next morning I called the Engineer and told him I was concerned with pouring both at the same time. He said, no no no you can't do that, I did not figure nor calculated that you would pour both at the same time. I said, well you better come up with some figures fast, because I have some serious cancellations and co-ordination to do to make changes.

His numbers came back later and come to find out, that if I would not have questioned the design, a callapse was eminent. I said to him, thanks for flagging out your design based on assumptions on how the work gets executed.
I did not sleep to good that night just thinking of the consequences of what could of happened.

Marcel
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