Absolute Maximum Allowable Deflection 2

[SlideRuleEra]

First of All - I have been particiapating in this forum for 3 months and just want to tell all of you that the quality of both questions and answers is impressive - Thank You.

I'm familiar with use of typical deflection/span limits for a steel member (1/360, 1/240, 1/180, etc.) but have not come across an answer to the following:
If the amount of defection is not a concern, what is the deflection/span ratio that would, by itself, be a limiting factor; that is greater deflection would cause permanent beam deformation?
I hope that I have state this clearly.

 

[ishvaaag]

If there are no other things than the structure to be damaged by the deflection, as you hint only the status of the structure would be of concern. If your understanding is that the preservation of the good servicebility of the structure alone is represented by it never (by design) going outside the elastic state, you are in reality stating your own goal: the onset of yield (as long no other more limiting factor such stress concentration, second order effects, fatigue, vibration, resonance, ponding etc is more limiting) would signify your limit deflection, to be calculated in the pertaining way.

But the question is that going up to the limit elastic capacity of a structure has not been seen sound policy by most structural designers, that always preferred -and not just as s measure in order to safety, but also to serviceability- to use working stresses below the limit of proportionality or elasticity, this ensuring more reserve strength and longer life.

Hence, whichever your structure surely the serviceability of the same will suggest some practical limit to the deflection. Serviceability on the other hand is misunderstood if taken in general as to not be a life safety standard. There are plenty of examples that may prove the contrary, be it by the risks derived (remember for example how sagging of an electrical line is blamed for the last big blackout) or directly because the need of its intrinsical consideration to prevent failure, such when limits to the absolute lateral deflection in buildings is imposed.

 

[steve111]

Where displacements are small and gross distortions to the geometry of the structure don't apply it can be reasonable assumed that the equilibrium equations based on original directions and positions of the external forces and the members are still valid. Where this may not be the case then the structure may behave in a non-linear manner even though the stress-strain relation of the material still remains linear. The geometry of displacements is of considerable importance in structural analysis, compatability of displacements is essential. besides angular rotations at a node and its effect on connection assumptions and design are essential.

 

[steve111]

sorry back, stupid viruses. We have an internet dedicated computer, firewalls, latestest and greatest anti-virus, live update etc., etc., but still ...
so yes ishvaag concur totally on structure vs. member however do need to consider individual member and effects large deformations can have on its ends and even the member itself. Plates and large deformations being an example and a whole different thing in any case. It really goes back to the fundamental assumptions of Linear Elasticity as you state.

 

[DJHaley]

I see nothing wrong with the earlier responses to your question, however, I would like to point out some other reasons for the various values. As mentioned, you choose the ratio, but, the applicable code or engineering judgement dictates which you choose. The smallest deflection (1/360) is typically used for the interior of structures and relates to applied finishing materials (ie plaster, dry wall) and visual perception. The 1/240 value is suitable for floor joists in a crawl space which is not typically seen and no finishing is usually done. The 1/180 value is suitable for industrial or large open space spans where cost is more important than looks. I have found that in most beam conditions, maximum allowable deflection is reached long before maximum allowable stress.

 

[IFRs]

Your question was, what is the highest deflection to span ratio before further deflection overstresses the member.

The answer, I think, is that you would calculate the load that results in the stress level equalling the maximum allowable stress, then calculate the deflection from that load, and ratio it to the span.

Note that for relatively large high deflections to occur, your structure has to mimic your calculation assumptions and boundary conditions, including secondary members picking up portions of the load.

In some of my structure designs, deflection is not an issue and the members are designed to allowable stress levels. We don't even calculate the deflection. These are very simple structures used in industrial applications where there is no human occupancy.

 

[SlideRuleEra]

Thanks to all for your input. The situation that I often see are similar to those described by IFRs.

 

[steve111]

Masonry always screws up the l/360 assumption as being the 'Smallest' deflection under LL permitted. All these deflection criteria are based on limiting crack apperances in finishes, read masonry in this case, or human perception read sloping floors etc., and vibration. Agree with IFRs if the game is to max out fy and who cares about defl'n., then i would sure take a look at connecting members and the assumed boundry conditions of the member itself as stated. Besides what is a live load anyways?, and when does it become dead? after you pour the concrete, after the product is in the bin?, is my cup 1/2 full? and if it is then exactly which 1/2 is full? it's my hope that it is always the bottom half. Industrial applications.... lets talk to the process engineer and see about piping. There is no rule here only guidelines and engineering judgement.

 

[letrab]

Plastic analysis and design would give you an upper bound value for loads a structure can carry when deflection is no concern. i.e. in a lab setting. Buckling checks would however rule out many sections