02-06-2011, 03:19 AM
The safety factor is for AXIAL loads... the weight of the building and contents - all dead and live loads will factor into the safety factor.
The steel strength is determined by its cross sectional area and the TYPE of steel used. In the base of the twin towers the steel was A36 which means it can support 36,000 #/in before failing. This is called the "yield strength".
To determine the total load the steel in the towers' columns can support you sum up the cross sectional area at the base and multiply it by the type of steel which in this case was A36.
Based on the areas I computed the tower's A36 steel columns (core plus facade) could support 825,708 tons. The factor of safety for AXIAL loads would be the ratio of the ACTUAL building weight to the 825,708 tons. If the building weighs 825,708 the factor of safety = 1. If the building weighs 412,854 the FOS = 2. It's that simple.
But we need to know how much DID the buildings weigh? The popular commonly expressed weight is 500,000 tons giving a 1.65 FOS.
But what if there was LESS steel in the facade... less cross sectional area? The ACTUAL load distribution between the core and the facade columns was about ~52% of the weight was carried by the facade and ~48%. Since we DO know the area of the core columns and if we assume this load distribution and the area of steel to support the loads.. the facade steel would be about 1/10 more cross sectional area than the core steel. The core steel area was 122.17 sq ft at the base so the facade would have to be 122.7 x 110% = 135 sq ft. so the total area would be 257.17 sq ft. This could support 666,507 tons.
If the building weighed 500,000 tons the FOS would THEN be 1.33. If it weighed 400,000 tons the FOS would be 1.66
So we have two variables: weight of building and total area of facade columns. However we can see that the FOS falls within a range from 1.33 - 1.66. The average being 1.5. The typical steel frame highrise has a FOS of 1.42 so the twin towers appears to be a bit "stronger" than your average highrise by about 5% as far as AXIAL loads are concerned.
It should be noted that this is the AVERAGE FOS of ALL the columns at the base. Some columns may have higher FOS and some lower depending on the loads they carry in proportion to their cross sectional area.
We've heard numbers for FOS of 4, 5 and even 20. This is simply nonsense and not based in reality. The steel would have had to have been 3 to 12 times heavier or the building 3-12 times lighter. And you can see that the numbers don't add up.
Of course this FOS discussion is moot, because the failure was NOT the columns, but the floors!
The steel strength is determined by its cross sectional area and the TYPE of steel used. In the base of the twin towers the steel was A36 which means it can support 36,000 #/in before failing. This is called the "yield strength".
To determine the total load the steel in the towers' columns can support you sum up the cross sectional area at the base and multiply it by the type of steel which in this case was A36.
Based on the areas I computed the tower's A36 steel columns (core plus facade) could support 825,708 tons. The factor of safety for AXIAL loads would be the ratio of the ACTUAL building weight to the 825,708 tons. If the building weighs 825,708 the factor of safety = 1. If the building weighs 412,854 the FOS = 2. It's that simple.
But we need to know how much DID the buildings weigh? The popular commonly expressed weight is 500,000 tons giving a 1.65 FOS.
But what if there was LESS steel in the facade... less cross sectional area? The ACTUAL load distribution between the core and the facade columns was about ~52% of the weight was carried by the facade and ~48%. Since we DO know the area of the core columns and if we assume this load distribution and the area of steel to support the loads.. the facade steel would be about 1/10 more cross sectional area than the core steel. The core steel area was 122.17 sq ft at the base so the facade would have to be 122.7 x 110% = 135 sq ft. so the total area would be 257.17 sq ft. This could support 666,507 tons.
If the building weighed 500,000 tons the FOS would THEN be 1.33. If it weighed 400,000 tons the FOS would be 1.66
So we have two variables: weight of building and total area of facade columns. However we can see that the FOS falls within a range from 1.33 - 1.66. The average being 1.5. The typical steel frame highrise has a FOS of 1.42 so the twin towers appears to be a bit "stronger" than your average highrise by about 5% as far as AXIAL loads are concerned.
It should be noted that this is the AVERAGE FOS of ALL the columns at the base. Some columns may have higher FOS and some lower depending on the loads they carry in proportion to their cross sectional area.
We've heard numbers for FOS of 4, 5 and even 20. This is simply nonsense and not based in reality. The steel would have had to have been 3 to 12 times heavier or the building 3-12 times lighter. And you can see that the numbers don't add up.
Of course this FOS discussion is moot, because the failure was NOT the columns, but the floors!