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RE: Wind load and pile depths for wooden fences (San Jose)

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Dmitri,

I don't believe there was any deliberate intent to hide so called safety
factors, it is more to do with subtle use of the English language.
Reliability is a statistical matter, and in statistics when carrying out an
hypothesis test, an hypothesis is never fully accepted, rather it is not
rejected. Thus we say: we do not reject the hypothesis that the mean yield
strength of the material is 300MPa, rather than conclude that the mean yield
strength is 300MPa.

Also in mechanical design, I had it hammered in, never to refer to factors
of safety, but to refer to design factors or factors of ignorance. A factor
of safety infers safety, when no such safety is provided. Reference to
factor of ignorance also not all that good, since multiplying by 100, may
still only get 1% of the real load, if have high level of ignorance of the
system being designed. We deal with uncertainty, and I believe those
advocating the limit state approach, here, believe we should deal more
directly with the risk and uncertainty, and not be misled by so called
safety factors in the codes. Codes do not produce safe designs, rather they
produce a design which some committee considers to have an acceptable risk
of failure: the designers and end-users may have a different view. If a
failure occurs the jury and coroner may also have a different view.
Complying with the codes doesn't get you off the hook. The designer needs
have some understanding of variability and uncertainty.

My understanding of the soft conversion to limit state relative to steel
structures is as follows:

Z = elastic section modulus
Fy = yield strength
M = applied moment

Permissible stress design
 M = 0.6 Fy*Z

Or 

M / (0.6Fy*Z) <= 1

Rearranging the equality gives:

1.67M = Fy*Z

Suggesting to some to declare that the structure is 67% stronger than it
needs to be. Which totally neglects the variation in Fy and Z. It also
declares that M is the actual value of the action-effect likely to be
experienced by the structure, or that its maximum value is certain.

Soft conversion to limit state is therefore to split the design factor, into
two components: capacity reduction factor, and load factor. To then give.

1.5M <= 0.9Fy*Z

Or 

0.9Fy*Z / 1.5M >= 1

Where for hard conversion, (0.9Z) should be replaced by the 5th percentile
estimate of the section property being considered, and 1.5M is replaced by
the 95th percentile estimate of the load. Other percentiles could be used,
and more rigorous consideration of reliability make more complex still. (as
you say wind, snow, and seismic have different return periods, or here
different annual probabilities of exceedence. Which suggests the most recent
change has invalidated the 5% probability of load exceedence.)

Our resistances and loads are all estimates. In some situations the standard
deviations on the resistances and the loads are low, in others they are
large. By improving control in manufacturing the standard deviation on the
resistance can be reduced so that the 5th percentile resistance is a lot
closer to the mean value. Not all structures are buildings, and for many
structures it is possible to have a high level of control over the loading
of the structure, so that 95th percentile load can be calculated and the
standard deviation kept low so that close to the mean or nominal value of
loading. The steel structures code may indicate that it primarily relates to
buildings but it is used for more than just buildings. Further more
increased control over the operating environment can eliminate the need to
increase required design loads. Thus research into crowds and panic
behaviour is leading to improved approaches for evacuating sports stadia,
without need to increase design loads on associated structures.

Since we largely use nominal values in design, we replace 0.9Z with phi*Z,
and 1.5M with chi*M (strictly our code only uses chi for serviceability load
reductions, but it is still a load factor, so for convenience I use as
such). The values of phi and chi, are then supposedly determined so that
nominal values are transformed into the required 5th and 95th percentile
values. And a load is not taken as the 95th percentile value if it has a
stabilising influence, or otherwise provides a resistance, then it needs to
be a 5th percentile value. In the soft conversion phi, may provide allowance
for other aspects of uncertainty other than variation in section properties.
For this purpose I think there should be additional capacity reduction
factors and load factors, and their purpose more explicitly identified. I
don't see any problem with doing so, the timber structures code has a
multitude of 'k' values to adjust resistance of a section.

Also there is nothing stopping anyone writing:

1) N = phi*Fy*Z / chi*M 
2) N >= 1

Or 

3)  n  = chi*M / phi*Fy*Z
4)  n <= 1
5)  n = 1/N
 
Where by the design factors (N,n) give an indication of efficiency relative
to the requirements of the code, not an indication of greater or lesser
safety. Equality is seldom achieved, for few sections are optimised for a
specific purpose.

As I indicated previously the advocates of risk based design, cite how
patients are comfortable with a life or death situation and making a
decision when doctor tells them operation has a 30% success rate.
Engineering tends to have a far better success rate.

The objective is not to obscure but to place in more familiar terms. It has
also been noted, that with increased emphasis on statistical process
control, and risk management requirements for occupational health and
safety, that a greater proportion of the population has understanding of the
problems of uncertainty, variability and risk. So explaining risk to the
public is not a major issue. 

For the advocates of risk based design, engineers who insist on quoting
safety factors of 2 and the likes, they are part of the problem, not the
solution. They are the ones who distort public perceptions, and generate a
public demanding safer structures. After all before building collapsed did
say it had a factor of safety of 2. If it collapsed it must have been less
than one. And therefore can engineers be relied on?

Know the storey of the USS Pueblo? Before probability of US Ship being
boarded zero. After increased to 1.

If there is a 5% probability that the design load will be exceeded and a 5%
probability the load will not be up to strength, then there is a risk that
the structure will fail. Can we prevent failure? Generally No. But we can
reduce the probability of over load and the probability of lack of
resistance, and exponentially increase the cost of supply. The requirements
in the code suddenly become that more preferable rather than excessive and
unnecessary cost. If it fails. We didn't say it wouldn't fail, nor at what
time it would fail. The question is should it have failed under the
conditions experienced? Sure may get that with a safety factor, but focus
then is on: the engineer failed not the structure failed: because engineer
implied it wouldn't. 

So I don't believe risk based design makes anything more complicated to the
public, nor does it hide anything. The numbers can be discarded and a purely
qualitative explanation of risks can be given to the public. So I guess I am
more advocate than opponent. Also from my perspective it fits in with
philosophical basis of Taguchi's methods, design of experiments and
principles of quality robust design. At its simplest: need to recognise
variation and allow for in design.

Quality robust design also tends to place a focus on the possibility of
failure, and the mode of failure, the behaviour of the system at failure. So
a single numerical factor of safety doesn't really inform about anything. As
you indicated there is buckling, yield, fracture, progressive collapse,
formation of plastic hinges, and more. These may lead to early failure, or
provide reserve and early warning of impending failure.

I don't believe a factor of safety would generate the better understanding
that you were wishing to promote. That understanding is not about the
numbers but qualitative awareness of the behaviour of the whole structure,
not just its component parts.



Regards
Conrad Harrison
B.Tech (mfg & mech), MIIE, gradTIEAust
mailto:sch.tectonic(--nospam--at)bigpond.com
Adelaide
South Australia

 



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