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# Moment of Inertia for built-up Beams

## Moment of Inertia for built-up Beams

(OP)
Question:

If I have an I-Beam and a C-channel stacked and welded as one, to find the "I" of the "built-up" member can I just add the two "I" values together, or is there some other method of finding the combined "I."

Thanks

Steve Mackie, Product/Applications Engineer
Apical Conveyor Systems, Inc.
Tavistock, Ontario

### RE: Moment of Inertia for built-up Beams

This can be found in many text or exam review manuals.

As a quick summary for obtaining I for "two members"

1. get neutral axis of combined section.
y_bar = sum(Ay)/A = (A1y1 + A2y2)/(A1+A2)

2. Iy = I1 + A1 d1^2 + I2 + A2 d2^2
where d1 = distance to center of A1 from y_bar
and d2 = distance to center of A2 from y_bar

This is as simple as I can explain it.  Good luck.

### RE: Moment of Inertia for built-up Beams

one more thing,  C channel should be oriented horizontally, thus use the I value for the weak axis.  Iy.

also, isnt there a table of section properties for I beam and a challel in the AISC steel manual?  Unless it is a bizarre combination, you should be able to find the values you need from the steel manual.

### RE: Moment of Inertia for built-up Beams

(OP)
Thanks guys, I don't have an AISC steel manual, I have a few books from Lincoln and my text books, but never really did that much structure so I just needed a little quick refresher and fast. There are a lot of smart people here that remember and do things on a daily basis that I don't.

Thanks Again

Steve Mackie, Product/Applications Engineer
Apical Conveyor Systems, Inc.
Tavistock, Ontario

### RE: Moment of Inertia for built-up Beams

packie,
Your question about structures (acutally its about section  properties - aka deformable bodies) makes me wonder what you are using this built up seciton for?  Finding the capacity of an I section with an attached channel is more than just finding the I.  Could you tell us what this is used for? Thanks

### RE: Moment of Inertia for built-up Beams

(OP)
Sure, the channel is a track for a roller to run in, and it is sitting on top of the i-beam. The S6x17.25 is in the usual position and the 7x12.25 channel is in the "I" position on top. There are two of these parallel about 48" apart and the wheels of a horizontal scrap conveyor run inside the channel.

Steve Mackie, Product/Applications Engineer
Apical Conveyor Systems, Inc.
Tavistock, Ontario

### RE: Moment of Inertia for built-up Beams

Hi Packie81,

You don't mention how the channel is attached to the I beam.  Horizontal shear connectors at intervals are required to utilize the composite section for bending.

Regards

VOD

### RE: Moment of Inertia for built-up Beams

My mistake, you mentioned it is welded as one.:)

VOD

### RE: Moment of Inertia for built-up Beams

VoyageofDiscovery,  i think your point is very well made.  Two pieces being welded as one, I am guessing, is a continuous fillet welds along each side.  My question is:  Is that necessary?

Only connection you need is to be able to resist the amount of shear flow between the two pieces so they act compositely.  Like VoyageofDiscovery sugggested, intermittent welds or even bolting at certain spacing may suffice.

### RE: Moment of Inertia for built-up Beams

(OP)
Hrm, I find some of these answers going much deeper than I expected.

Whyun: No, we wouldn't do a continuous weld over the 40', probably wouldn't be much more than a 1-12 1/4" fillet.

Steve Mackie, Product/Applications Engineer
Apical Conveyor Systems, Inc.
Tavistock, Ontario

### RE: Moment of Inertia for built-up Beams

Just as I thought.  VoyageofDiscovery and I were trying to interpret what you meant when you said "I-Beam and a C-channel stacked and welded as one".  If welded as one implies just enough intermittent connection to carry the shear flow, it is perfectly fine.

If 1" long 1/4" fillets at 12" spacing can carry the shear flow.  That's all you need.  If two rows of bolting is cheaper you can also go that route.

Of course, continuous weld entire length works designwise, but its a waste of money.

### RE: Moment of Inertia for built-up Beams

whyun,
In all of built-up sections, I prefer welding to bolting as if I go for bolting, the codal provisions eat up the effective area of the sections. I have to made deductions for holes and moment of inertia of the section decreases. This proves too be much more expensive and makes me hate bolts in such cases. Even continuous weld is not a very bad idea as compared to bolts.

### RE: Moment of Inertia for built-up Beams

welds are much stronger than bolts.  also it eats up part of the sections of the members attached.

bolts on the other hand are cheaper and installers need not have certifications.  in many jurisdictions, you may also be able to avoid inspection.

all in all, i also prefer welds over bolts (in the case of attaching channel to a WF beam)

### RE: Moment of Inertia for built-up Beams

it was late... when i posted my last...  obviously the one that eats up the member section is the bolt holes and not welds.  i must have been spooked.  sorry about that.

### RE: Moment of Inertia for built-up Beams

(OP)
lol, i was wondering about that...

Steve Mackie, Product/Applications Engineer
Apical Conveyor Systems, Inc.
Tavistock, Ontario

### RE: Moment of Inertia for built-up Beams

Packie,
The reason for my quesiton was to ask if you are trying to design this as a beam, or just determine the deflection.  There are a lot more things going on.  The connection between members is one thing, the lateral stability of the beam, if the beam is continuous, is the support designed for the load, what about fatigue, what about vibration.
I just wanted to make sure you weren't simplifying things to much, or making assumptions.
Just trying to be careful.
-Doug

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