Originally posted by Seymour Butz
All this got me looking at the NIST again.
Me too.
Here:
wtc.nist.gov...
Table 5-1 says DCR is roughly .75 for the ext columns. This means that they had about a 33% safety factor? Based on worst case scenario - 100 mph
hurricane?
DCR is confusing to equate factors of safety. Because to calculate DCR, you use the allowable stress. Which is already 60% of the ultimate stress.
Thus, you have already included a FOS of 40% reserve before we even begin to calculate DCR.
I could be wrong. As DCR is usually used for failure analysis and I don't analyse building failures. But, even in the equations given by NIST, they
use .6Fy which is 60% of the yield strength.
But, going on. This may be where people get the 20x reserve capacity for the exterior columns. And it's from NIST's own mouth.
The allowable stress design method has an inherent factor of safety for structural components. For example, the safety factor for yielding and
buckling is:
• 1.67 and 1.92 for core columns in the original design and SOP cases, and for all columns in refined NIST estimate case.
• 1.26 and 1.44 for perimeter columns in the original design and SOP case (discounting the 1/3 increase in allowable stress under wind
loads).
I'll break here for a second. 1.26 when discounting the 1/3 increase under wind loads. Counting for wind loads this number would increase to
1.59.
Going on:
• After reaching the yield strength, structural steel components continue to have significant reserve capacity, thus allowing for load
redistribution to other components that are still in the elastic range.
• On September 11, the towers were subjected to in-service live loads, which are considered to be approximately 25 percent of the design live
loads.
Break again. Notice that the live loads on 9/11 were estimated to be 25% of the design live load. Again, more redundancy.
• On September 11, the wind loads were minimal, thus allowing significantly more reserve capacity for the exterior walls (demand on exterior
columns was about 1/5 their capacity).
• The safety of the WTC towers on September 11 was most likely not affected by the fraction of members for which the demand exceeded allowable
capacity.
wtc.nist.gov...
And this I believe is where people get the 20x reserve capacity from.
1/5 is 20%. It is actually in error to use 20x but it does show that the reserve capacity of the exterior columns was 4/5 the design capacity. Which
is 80%.
So if the design capacity was say 100 kips, then the columns had a 80 kip reserve capacity.
Which would give a FOS of 4 not 20. But, still, 4 is a big enough number to wonder what caused the steel to initiate collapse when even the hottest
temperatures quoted (that NIST analysed and found to be at max. about 600C) wouldn't cause the strength to decrease to 25%.
So, again. The specs are needed to really determine this stuff.
