Guidance sought on 2D vs. 3D truss design 1

[Brett88]

Good afternoon,

I appreciate the opportunity to be able to post this request for guidance on your site.

I am of a mechanical background, thus my exposure to structural design has been limited to Strength of Material courses covered in university and some fairly extensive reading in the calculation of axial forces, moments and deflections in simple 2D truss structures. I would like to expand my knowledge of first order force and deflection analysis of 2D trusses to 3D spatial trusses.

If possible, I'd like some guidance.

1. Many books cover the analysis of 2D trusses in much detail. Since 2D trusses are often only a section through a greater 3D truss, is it appropriate that the single 2D truss be analysed in isolation? How accurate can an engineer be by only considering the 2D analysis? My gut feel is that the stiffening supplied by beams in the z-direction needs to be taken into account, and hence 3D truss analysis is necessary.

2. I have considered a number of text books on the subject of 3D truss design. Can someone recommend a text that considers 3D truss analysis from fist principles, and that presents the mathematics in a manner that is clear and understandable.

I'd appreciate any help I can get before I wander off on the wrong path.

Regards,

Brett

 

[rb1957]

not sure i get your question ... a 2D truss solves with 2 force and 1 moment equilibrium equations; a 3D solves with 3 force and 3 moment equiilibrium equations. the implicit assumption is that force in the members of a truss is axial, and the joints are pinned. i don't see why you'd need a special textbook/reference for 3D trusses ...

 

[Qshake]

Years ago, before we had the computational power and numerical methods that we have at our fingertips now, we simplifed trusses that were more or less planar in behavior to a simple 2D analysis. The main assumption with that is that the greater percentage of all load acting on the truss would be acting in the plane of the truss members, i.e., no out of plane forces. Typically this can be said of nearly all bridge trusses. the in-planse forces are typically magnitudes higher than any out of plane forces and that axial forces are several orders of magnitude higher than any bending, shear or torsional forces on the actual truss members.

To analyze a truss structure, such as a bridge, for wind loads, the structure is simply analyzed as a frame with the appropriate bracing to resist the wind. This is more or less orthogonal and independent of the actual trusses themselves...another simplifying assumption.

3D spatial trusses are quite a different structure altogether from simple trusses that are joined with bracing members such as most bridges. Such structures are typically used in geodesic domes and the like. And one of the differences is that all members are typically of the same size rather than the bridge whose longitudinal trusses are far larger than the bracing inbetween them.

Back to appropriate analysis of typical trusses today. A 2D analysis of a truss will not show redundancy no matter how small it may be. A 3D analysis will show a more representative behavior of a full truss/bracing system. And as a consequence you will see that there are alternate load paths should a truss member fail. That does not mean that a single alternate load path is all that is necessary to keep a truss from failing. So as the industry sees a focus on redundancy and elimating fracture critical members in trusses, a step to 3D analysis is necessary. And always should be reviewed by an experienced engineer.

An explanation plus a bit of opinion!

Good Luck.

Regards,
Qshake

Eng-Tips Forums:Real Solutions for Real Problems Really Quick.

 

[Brett88]

@ rb1957,

Thank you for the response.

Perhaps I can be more specific about my needs. I am a materials handling engineer, concerned primarily with the design of mechanical aspects of conveyors. The structures on which conveyors are supported are made up of gantries that typically span distances up to 36m. These structures, which are truss/lattice structures, often need to be designed both for strength and for pre-determined deflection under load.

I am interested in studying the design of these conveyor structures in more detail, and have started doing so by reading up on truss design. I get a lot of detail on 2D truss analysis, and in principle I agree that the conversion to 3D truss analysis is merely a matter of "sloging" through a bit more math to define the forces acting on the structure. But what I was asking in my first question was whether or not a 2D-analysis would prove sufficient in the analysis of these structures or whether one would need to consider the structures in 3D to fully understand their loading and deflection characteristics?

It could be that my question is a lot simpler than some of the postings I have considered on this forum and, therefore, causing some confusion.

 

[Brett88]

@Qshake,

Thank you for the posting.

Based on your explanation, is there a solid introductory text to 3D truss analysis that you could recommend. Perhaps my second posting could give you some insight into my needs.

 

[vcueto80]

Structural Analysis by RC Hibbeler has a simple Space Truss Analysis example. Also, has truss analysis using the stiffness method. But only has very little information of Space-Truss Analysis using the stiffness method.

 

[paddingtongreen]

Brett88, although, if properly performed, 3D analysis is a little more accurate than superimposing the results of two or three 2D analyses, the differences on something like a conveyor gantry are pretty much negligible. It is much easier to build a 2D model than a 3D, and it is a great deal easier to debug the 2D model. The results are easier to read as well.

A word of warning, if you go the 3D route on a box gantry, and look at a load case with only vertical load, you may be surprised to find some significant horizontal effects at the supports if you put the occasional diagonal cross braces from the top chord of one truss to the bottom chord of the other truss. These effects are real and the magnitude has to do with the whether the horizontal bracing at the top chord and that at the bottom chord look the same in plan or opposite.



Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[Qshake]

Brett88 - Hibbeler is good as noted above but may be too basic so I'd recommend Ronald Sack as well. Between them you'll get what you need.

Based on your description I see the members in all planes of the truss to be of similar dimensions and would conclude that a 3D analysis is more applicable as you will need to consider the participation of the out-of-plane members on the in-plane trusses.

I have also seen a lot of conveyor systems made up of three sided trusses.

Regards,
Qshake

Eng-Tips Forums:Real Solutions for Real Problems Really Quick.

 

[MiketheEngineer]

You might want to look into some 3D software to verify your calcs. RISA comes to mind. There are a number of good ones.

BUT I suggest you start doing it by hand first. Pick smaller ones. I have engineers walk in here everyday with the most outlandish computer results thinking they have either found the Holy Grail or telling me there is no way it will work.

The Holy Grail "find" is usually because they used the wrong units or intermixed them.

The ones that say it can't be done - I refer them to the competition down the road - who do it everday.

Just remember - Junk In - Junk Out - JI-JO

 

[BAretired]

Personally, I would use a 2D analysis because I believe the results from that are more accurate than the input data.

If you want to treat it as a 3D project, the principles are exactly the same as a 2D analysis. Every node has three co-ordinates and six degrees of freedom.

In the end, you would have 6N linear equations where N is the number of nodes. These can be solved by matrix inversion if the matrix is not too large or by a variety of other techniques.

One book called "Matrix Structural Analysis" by William McGuire, Richard H. Gallagher and Ronald D. Ziemian describes the method quite well. There are probably many other good references as well.

BA

 

[Brett88]

@paddingtongreen, Qshake, MiketheEngineer and BAretired,

Thanks for the time you took to respond. I have come away with three good references and I intend to have a look into these. Hopefully they can guide me to where I need to go.

Much appreciated.