Acceptable failure rate for glass

[Yao1989]

Does anyone know if there any codes that gives clear guidance on this?

in Canada I use CGSB 12.20-M89 and ASTM E1300, for application of windows the typical acceptable probability of failure is 8 in 1000 once design load exceeds capacity, both codes give vague indication in the commentary that this is intended for window, and if the consequence of failure is more severe, the acceptable prob.fail should be adjusted. GANA glazing manual says it is common to use 1 in 1000 for more critical structural elements. My questions is are there code prescription/requirement on probability of failure for different application, or is this is a judgement call on the engineer of record?

For example, if I design a glass floor with failure rate that is same as those of window, but I have calculated a reasonable post-breakage design resistance (e.g. can resist 50% service load once glass breaks), then I would argue the post-breakage failure is not serious, therefore the 8 in 1000 probability is appropriate. Can anyone weigh in on this with their knowledge

 

[bob33]

See ASTM 2751-17 Standard Practice for Design and Performance of Supported Laminated Glass Walkways. I doubt people will use a glass walkway that has a high probability of cracking even if there is no danger of collapse.

 

[NorthCivil]

When designing structural glass elements that must account for post-breakage life safety, I always design to allow for %100 resistance of load post breakage.

ex: glass floor - I assume you will have a laminated unit - either side of the laminated sheet must be able to withstand full loading, with either side broken.

 

[catsndogs]

I think you're looking at the problem in reverse. Glass design for windows has always been based on breakage rate. But structural design of everything else is based on reliability. For example, you wouldn't say that steel has a 1% chance of yielding; you'd say that it has a yield strength that is 99% reliable. And there's lots of information available about reliability-based design.

You'll find in CGSB-12.20 that the reliability index of window glass is about 3.0 when designed according to that standard. If you're not designing a window, you need to target a higher reliability index. Glass failure can initiate anywhere, even areas of very low stress, resulting in sudden collapse. What reliability index is appropriate for that kind of material? You might be able to argue that the brittle failure of a weld is analogous. The target reliability index of a weld is about 4.5. (I would argue that glass is even more brittle than a weld, and rates a much higher reliability index. Maybe you can find a recommended index in relevant technical literature.)

To make the leap from windows to structures, it looks like the reliability of the glass needs to increase by a factor of about 400! Flip that around again, and the breakage rate would be reduced by a factor of about 400.

It sounds huge, but there's a logarithmic relationship between the breakage rate and the stress level, so it's not that bad. It will certainly increase the importance factor for glass breakage quite noticeably. If there are no redundant load paths, you'll have to push the importance factor even higher.

When designing glass guards without a top rail, some folks hope for relief from the CSA A500 standard (not yet adopted). But that standard will require the same importance factor for glass breakage, and will add the requirement to design or test for significant impact energy. IBC 2018 sets a high safety factor (load factor multiplied by importance factor) for all glass guards and requires testing for impact and static load when there is no top rail, to ensure a redundant load path. So the prescriptive requirements are there for you to follow.

(BTW, I don't think even the most generous interpretation of relevant standards would suggest that it's okay if the post-breakage strength of a floor is as low as you suggest. The floor needs to resist at least the full service load until that load is removed.)

 

[IRstuff]

When you say "break" do you mean crack? I typically think of "break" as in disintegration, i.e., the floor "breaks" into a bunch of pieces and falls down to the next floor. Actually, one would think that such a floor is laminated so that the pieces are at least held in place, so as to not kill or injure the people on the floor below.

However, if it's cracked and there's a rated load of people standing on the floor, then I'd hope and expect that the floor would support the weight of the people long enough to evacuate the floor be repaired or replaced.

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[catsndogs]

For a glass structure without redundant load paths, "crack" means "break", and "break" means "collapse".

For a laminated glass floor, the failure of one glass ply under static load will create a shock load in the remaining ply (or plies). Canadian codes identify an analogous problem in lightly reinforced concrete members: a flexural member must be reinforced to resist a moment greater than the cracking moment of the gross section, to account for the shock load at the moment the member cracks and the load is suddenly transferred fully to the reinforcement. Similarly, the remaining glass ply (or plies) must be able to survive this sudden spike in load after one ply fails. [The same requirement applies to design of a glass guard for static load, if a top rail is not provided. And there are adequate examples in the literature to indicate that it is sufficient to design the remaining ply (or plies) to resist the full factored load after failure of one ply. But I doubt whether that approach is adequate for impact loads in all cases.]

In other words, redundancy in glass structures does not come for free. You don't achieve redundancy the moment you choose laminated glass instead of monolithic glass. Redundancy has to be designed in, and it comes at a cost. But then you have an argument for the reliability of your design. Hopefully the glass breakage rate is addressed at the same time. But even that won't happen by accident.

 

[glass99]

Glass floors per ASTM E2751 are designed to 8:1000 with one ply broken.

Its worthy of note that 8:1000 probability of breakage is wildly conservative in terms of actual breakage probability. Its closer to 8 in a million.

 

[catsndogs]

Designed for the full factored load with one ply broken?

How have you established such a low breakage rate for glass on your projects? (ie 8 in 1,000,000) Based on tests of glass from a specific supplier, with specific glass flaw parameters, m and k? Based tests of prototype assemblies? Others types of tests?

 

[glass99]

Yes full load with one ply broken and 8:1000 at 10 minute load duration is the E2751 criteria for glass floors

If you take a piece of FT glass and put 10600psi edge stress in bending on it, it has effectively zero chance of breakage bc the tension stress is less than the surface pre compression. Failure is literally mechanically impossible, even this its the "8:1000" stress. The 8:1000 comes from the simplistic Weibull math, which basically smooshes together the AN and FT material models. AN glass is the only glass which is really statistical in nature. I understand from the academic folks that even for AN glass, the 8:1000 stresses are more like 8:1,000,000. It might be related to the weathering procedures, not sure.

 

[catsndogs]

Isn't that the trap that designers fall into? Designing for the maximum stress at the extreme fibre of the glass section, like it's steel. Aren't the glass flaw parameters (m and k) exactly what their name suggests? An indication of the surface flaws that initiate glass failure, even in areas of very low stress, despite pre-compression due to tempering. You could design a bolted connection that functions as intended, despite high localized stress, but then have the glass shatter because of a micro-flaw nowhere near the connection. The glass failure prediction model (FPM) accounts for that behaviour in glass plates. But applying the FPM to structural applications - rather than windows - make me shudder. Designing for the full factored load with one ply broken seems to be the consensus approach to deal with structural applications.

 

[glass99]

but then have the glass shatter because of a micro-flaw nowhere near the connection

Yes technically glass is a statistical material and could have a crack initiation at any point with stress, but at 50% of the stress, the probability of failure is ~200x lower. In tests of bolted connections for example, it almost always breaks at the bolt. Or more often, the bolt breaks.

 

[catsndogs]

It depends what values of m and k you use in the glass failure prediction model, of course. In the Canadian standard, the relationship between stress and breakage rate is prescribed, and is evidently based on different m and k values than you have used.