Deflection Limitations Question

[EngDYIGuy]

Hey guys,
Why are deflection limitations specified as a fraction of the span length, such as L/360 or L/240? I'm having a hard time picturing this criteria, it apears to be more of a deflection slope or gradient, rather than a maximum deflection limit, such as 1" or so. Can someone show a simple example how the total deflection is related mathmatically to this L/360 or L/240 criteria. Is this fraction the total deflection in the member (Delta) divided by the span length (L)?

 

[KootK]

I've always wondered the same thing. I've assumed that the issue was more curvature than displacement or slope. The limitations often seem to be tied to the finishes which have varying abilities to accommodate curvature without deleterious effects. That said, I've known more than one engineer to swear vehemently that the issue is really maximum slope for occupant comfort. Obviously, that wouldn't make much sense for roofs.

Is this fraction the total deflection in the member (Delta) divided by the span length (L)?

That's exactly right. Usually midspan deflection or something close to it.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[EngDYIGuy]

So essentially, one way to interprete the limitations is that the maximum deflection can not be greater than 1/360 of the span length? This is of coarse for L/360. Just reviewed my text book, and that's what the example problem is doing. Calculation of actural deflections, based on (Load, span length, E, and I) and then comparing the maximum deflection computed to the span length L divided by some fraction.

 

[JoshPlumSE]

AISC Design Guide 3: Serviceability Design Considerations for Steel Buildings is a decent place to start. As that document has a pretty good write up on the subject.

Most of the time, the design guide's recommendations are just related to span. But, other times (skylights, cladding, partitions, cranes) the recommendations may be a little different.

Also, ASCE-7 has appendix C: Serviceability considerations and the associated commentary. That's another good place to look.

There are other documents on the subject that are more technical. These two are just the ones that I'm most comfortable with.

If you're really interested in the subject, Larry Griffis has a book or paper on the subject of more rational drift restrictions where he defines a new "drift measurement index" and a "drift damage index". The only reason why I mention it is because it derives a new method (for lateral drift, not vertical deflection) for more rationally defining what is acceptable vs unacceptable drift.... Sort of the process you'd have to go through if you wanted to replace the simplistic span deflection ratios with something more rational.

 

[JoshPlumSE]

Oh, one other thing. It's not the TOTAL deflection of the member that you're comparing to the span. It's the RELATIVE deflection of the member.

So, if you're looking at a joist that spans between two girders. The girds may deflect 0.5" at the joist support points and the joist deflects another 0.125", for a total deflection of 0.625". Normally the deflection ratios for the joist are based on the 0.125" not the 0.625.

 

[EngDYIGuy]

Hey JoshPlum, can you expand on the relative deflection concept? I have access to the IBC, ASCE-7, and AISC Design Guide 3. I'll give those a read through.

My understanding of 2012 IBC 1604.3 is that you only look at the maximum deflection in each member, and then compare this calculated deflection to the deflection limits. You would need some 3D modeling of the structure to determine relative deflections. If you are using the relative deflection, than what L do you use (multiple members) for the limitations on deflections?

 

[KootK]

So essentially, one way to interprete the limitations is that the maximum deflection can not be greater than 1/360 of the span length?

The one, and only way, yes.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[rapt]

Yes, it is related to slope. This is logical for roofs (for drainage) as well as for visual deflection, the human feel factor and also brittle finishes. It is the rate of change of deflection or curvature that is being limited by codes, not the actual deflection. Some engineers (and design codes) also apply an overall deflection limit eg BS8110 limits incremental deflection for brittle finishes to 20mm. Some consultants try to limit total deflection to 25-30mm for visual effect reasons. This is normally very difficult in longer span members.

Re member deflection versus total deflection, the individual members deflection needs to be checked over its length and the total system deflection needs to be checked over its "length".
eg
- a flat slab needs to be checked for column line/strip deflection in each direction plus overall panel deflection based on the diagonal span length.
- in a structural steel system, each member needs to be checked individually for its own deflection and then each combination of members needs to be checked basically until you get back to a deflection between columns. Same for concrete transfer beam systems.

 

[JoshPlumSE]

Actually, relative deflections are really just that one members deflection. Easy to do with hand calcs. It's when people use software that they get confused. The software generally reports total deflection of the member. Then people start designing their beams overly conservatively. Or, they call up tech support (guys like me) and ask them why the L/y ratios the program reports don't match what they think it should be.... And, it's because they're accidentally using total deflection in their L/y calculation rather than accounting for end displacements of the member.

 

[EngDYIGuy]

Oh ok. I see what your saying now. I misconstrued your first response, and the terms "total" and "relative". I agree the code is written to look at the relative deflection of each member, and not the total deflection of the member under design + the deflection of the members that it's attached to. However, it is good to know what the total deflection is.

 

[XR250]

How about for a stud with a parapet (or beam with a cant. end)? I usually draw a secant from the tip of the parapet to the base of the stud and measure perpendicular off of that.