Ron Hamberger delivered a thorough talk on
LRFD methodology, which is one of the design methodologies commonly used in
structural engineering in which we amplify our expected loads and reduce our
expected capacities. When we do so, an
acceptable design requires the amplified demand to be less than the reduced
capacities. Otherwise, we say the member
fails.
But what does this really mean? Is it sure to fail if this value is greater
than 1? Turns out that the load and
resistance factors are calibrated such that a demand/capacity ratio (DCR) = 1
provides a target probability of failure.
ASCE 7 has selected target probabilities of failure that it deems
sufficiently safe (See Table C1.3-1 in ASCE 7-10 for target annual probabilities of failure). So the meat of his presentation was to pose
the question, is your structure still safe if you have a DCR > 1, say
1.05? Turns out, using lognormal
distributions (implemented painlessly in Excel), you can calculate the probability
of failure for your DCR and use your engineering judgement (or better yet, owner’s
risk tolerance) to determine whether this calculate probability of failure is
satisfactory.
Now keep in mind, this will never fly with new construction (or really anything for which you are submitting for a building permit). After all, the building department’s job is to enforce the building codes and if DCR > 1, then you are not in compliance with the codes. But you might use this in a case if an owner wants to make a change of usage of the building that increases the live load or perhaps the owner is replacing their air conditioner with a larger unit or perhaps the owner wishes to install roof mounted solar panels and they have asked you to determine whether doing so would require structural upgrades to the building. In this case, you may calculate a number slightly greater than 1, but given the associated probability of failure (which you can calculate), you deem it sufficiently safe and do not recommend potentially costly repairs.
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