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Truss Moment of Inertia

Truss Moment of Inertia

Truss Moment of Inertia

Do you have any formulae for truss moment of inertia / deflection etc.

I have been using I = Area of chord * 2 * (dist. to NA)^2. and once I get the I, I use it in beam formulae for deflection.


RE: Truss Moment of Inertia

This tye of deflection calculation is for beams and is not really suitable for trusses.

There is also shear deformation due to axial shortening/stretching of the truss diagonals and verticals.

The only real way to do it properly is by a full analysis.

RE: Truss Moment of Inertia

Are there any good references you would suggest for this? I am using ETABS to analyze, however, it does not do a composite truss design (or atleast I was told by tech support).

Hence, I was trying to estimate the truss MOI, and then do a composite top chord and use property modifiers to amplify stiffness due to composite action.


RE: Truss Moment of Inertia

If I recall correctly, the best way for you to analyze a truss would be by virtual work.

See if you can find any references about this. It is a bit tedious, but essentially you will end up setting up a spreadsheet. The critical info will be L, A and the angle of the web members.

Sorry I can't be more helpful, but I'm fairly certain you can get what you're looking for with virtual work.

RE: Truss Moment of Inertia

Yes, I was hoping to use virtual work. I also have a mathcad routine using direct stiffness method that I may use.

I was asking for references regarding shear deformations in trusses.

RE: Truss Moment of Inertia

The top chord and bottom chord are not usually the same size so the NA is not centered in the truss. I suggest finding the exact NA by normal methods and then using the more accurate moment of inertia.

Some engineers use a reduced moment of inertia of 85% to account for shear deformation.  

RE: Truss Moment of Inertia

Jike:  I have never heard of an empiracle reduction like 85%, but just looking at the two trusses I have analysed for deflection in the past an appropriate shear compensating term would have been 92% for one and 83% for the other.  Do you know of any papers/design procedure that would justify the 85%?

Oh, and just as a point of discussion: I only apply shear deformation to steel trusses, as in my opinion, timber is too brittle in tension to really experience much axial lengthening/shortening.  That said, I've always felt a bit uncomfortable simply making that assumption, and would probably worked through the numbers if I had ever been close.  I've only analysed half a dozen trusses though so it'll probably come up eventually.  Any thoughts?



B.Eng (Carleton)
Working in New Zealand, thinking of my snow covered home...

RE: Truss Moment of Inertia

I don't know where the 85% comes from, but it is an approximation that has been around a long time.

RE: Truss Moment of Inertia

i think csd's point is that trusses are (theoretically) axial elements.

if your truss elements react shear laods then they'll also have to react bending moments.

i think the 85% figure is an allowance for shear deflections", which implies a pretty large shear to me

RE: Truss Moment of Inertia

I'm confused..

Why take a reduced member moment of inertia for shear deformations in a truss?

Truss members (at least in theory) shouldn't have any significant shear stresses, lest they be flexural members.

I know..  "real-world" trusses are fabricated such that the members can see a little bit of flexure. I just don't see how that would impact deflection in any significant way. Even in flexural members, shear deformations don't even start to be significant until your L/d ratio drops below 3 or 4.

Please explain.

RE: Truss Moment of Inertia

The term shear deformation in the case of trusses is probably confusing and mis-leading. For parallel chord trusses the shear is carried by the diagonals and what we are talking about here is the component of axial deformation in the diagonals that add to the total deflection when the truss is looked at simply as a flexural member.

RE: Truss Moment of Inertia

I am using a W14x90 top chord/bottom chord with HSS diagonals. The distance between the centers of the chords is 6'. I am calculating an approximate moment of inertia of 2 * 26.5 * 36^2 = 68688 in^4. Is that right?

For a 72' truss with 1 klf, this would yield a deflection of (5/384)* (wl^4)/(EI) = 0.303 in.

However, the analysis program is giving me a deflection of 0.56 in. Can anyone throw some light into this?

RE: Truss Moment of Inertia

Thanks Jike-

Crystal clear!

RE: Truss Moment of Inertia


Did you try to use virtual work?  It doesn't require any calculation of moment of inertia.  Maybe I am misinterpreting what your restrictions are here.

RE: Truss Moment of Inertia


are you including self-weight in your program?

RE: Truss Moment of Inertia


Your top and bottom chords are generally continuous - the top chord with a pin at the ridge, and the bottom may have one or two pin splices.  The other connections of the T & B chords at the web members and verticals should be modeled as fixed, which will affect the overall truss deflection.

Also, try increasing the size of the diagonals and any vertical tension members to decrease the shear deflection component too.  

Mike McCann
MMC Engineering

RE: Truss Moment of Inertia

I was told in school to use a 15% reduction in the calculated moment of inertia for trusses, which is to approximate axial deformation of the web members.  This reduction can also be seen in the Appendix 2 of the AISC 13th edition as well as any joist catalogue (when calculating deflection of joist systems).

RE: Truss Moment of Inertia

from the weight point of view ... your two chords account for a weight of about 1000 lbs, which seems to be what you're applying as a UDL to calc deflection.  what about the weight of the webbing between the chords ?

RE: Truss Moment of Inertia

I think I figured it out. I was using a way stiffer truss than necessary (unrealistic). Once I use a truss I need, the hand calc values are within 4-5% of actual.

RE: Truss Moment of Inertia

Jike interpreted the meaning of my comment exactly.

I used the term shear to continue with the beam analogy.

If you think of the truss as a single beam member then it has a shear and a bending moment (overall).

If you think of it as a series of members then the shear becomes axial load in the diagonals and verticals and the bending becomes axial load in the chords.

RE: Truss Moment of Inertia

I may be seeing this simplistically but if you use virtual work, no moment of inertia would need to be worked out and no reduction of it to account for shear deformation would be necessary.

Now if you have a structural analysis program you would analyse for member actions and also obtain node diplacements right?  No need to use reductions for shear defs or moment of inertia right.

Slickdeals are you trying to do a quick and conservative calculation?

If you are it would be interesting to compare this to the more accurate one done by a full structural analysis.


RE: Truss Moment of Inertia

I have done a few test runs with trusses of different L/D ratios and I find that a 14-18% reduction will need to be applied for a truss to account for web deformations.

The reason I started this exercise was to account for composite action of the top chord of the truss. Hence, to account for amplification factors, I started studying the truss MOI.

Thanks for all your responses.

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