Analysis of Bazant & Zhou (2002)

[cmcaulif]

"overload" does not refer to what the building can take vs the dynamic load, it refers to the dynamic load vs the static load.

 

[rwguinn]

From B&Z:



It is very clear that they are talking about an overload ratio. You are talking out of your batooty.

and it just as clearly says:
Dynamic load due to falling distance H will exceed design load by a factor of 31.
This is an overload (over the design load). If design load is defined as 1, then the new load is 31.

This means Dynamic load is 31 times as high as design load.
So, the actual load is 31 times the design load.
design load is (Yield load)/(safety factor)


The implication there, if you had a clue of any kind:
Nothing is designed to a Safety Factor of 31.

dropping the design weight of the structure above the failure point causes a load of 31 times the design weight to be applied to the structure below the failure point.
This means that the structure below the failure has to support 31 times what it was designed to support.

t cannot do that

Is there any way to make it any clearer?
The reason for using design load is to demonstrate that a safe building, which suffers a fractured support system where a portion falls onto the lower structure will have to absorb a dynamic load many times the design weight.

 

[einsteen]

31 times ? That would certainly result in peak forces during each collision during a very short time, in order to account for the energy dissipation. Did you notice that in the homogeneous model the average resisting force
in the beginning of the collapse is 1/3 of the static force at that point for wtc1. Very interesting. This follows completely from the observation that it started with about a=(2/3)g

 

[GregoryUrich]

and it just as clearly says:
Dynamic load due to falling distance H will exceed design load by a factor of 31.
This is an overload (over the design load). If design load is defined as 1, then the new load is 31.

This means Dynamic load is 31 times as high as design load.
So, the actual load is 31 times the design load.
design load is (Yield load)/(safety factor)


The implication there, if you had a clue of any kind:
Nothing is designed to a Safety Factor of 31.

dropping the design weight of the structure above the failure point causes a load of 31 times the design weight to be applied to the structure below the failure point.
This means that the structure below the failure has to support 31 times what it was designed to support.

t cannot do that

Is there any way to make it any clearer?
The reason for using design load is to demonstrate that a safe building, which suffers a fractured support system where a portion falls onto the lower structure will have to absorb a dynamic load many times the design weight.

I redid that post...too late. Anyway this is what I said.

OK, now I see we are talking about two different things. You are following B&Z's argument and I am saying what they should have done. I see your point about the definitions. Please bear with me. This is not my area of expertise.

As cmcaulif mentions above, eq (1) does not govern failure. However, B&Z move on to plastic buckling without showing that failure will occur in the first impact. Plastic buckling will not occur unless the columns fail so eq (3) does not necessarily apply.

I thought they were trying to demonstrate failure in eq (1), which would be necessary for the rest of the paper to make sense. To prove column failure they would need to apply my version of the equation, with the correct values for C and m and use the yield capacity. They would also need to take the upper spring (which fails first) into account.

To prove collapse continuation they would first need to prove failure in the lower columns at the first impact and then eq(3) would have to hold, which it clearly would.

 

[cmcaulif]

No, eq 3 uses energy, eq 1 deals with force, there is no reason to juxtapose the two, and one is not needed for the other.

As newtons bit showed on his blog in his response to ross, the energy dissipated in compression a member is small compared to the energy dissipated through bending. Also, they are dealing with energy in eq. 3, and in Bazant and Verdure, they elaborate on this, the energy criterion for collapse trigger, and note that strength of the columns does not matter, and collapse will continue or be arrested based on the energy impacted to a floor vs the energy dissipated.

 

[beachnut]

I redid that post...too late. Anyway this is what I said.

OK, now I see we are talking about two different things. You are following B&Z's argument and I am saying what they should have done. I see your point about the definitions. Please bear with me. This is not my area of expertise.

As cmcaulif mentions above, eq (1) does not govern failure. However, B&Z move on to plastic buckling without showing that failure will occur in the first impact. Plastic buckling will not occur unless the columns fail so eq (3) does not necessarily apply.

I thought they were trying to demonstrate failure in eq (1), which would be necessary for the rest of the paper to make sense. To prove column failure they would need to apply my version of the equation, with the correct values for C and m and use the yield capacity. They would also need to take the upper spring (which fails first) into account.

To prove collapse continuation they would first need to prove failure in the lower columns at the first impact and then eq(3) would have to hold, which it clearly would.

If you use some of that engineering stink you claim to have, one day you will be disgusted you signed the petition of sham.

I was looking through my college papers, it would take me a year or two to get up to solving the equations I could solve in an hour back then. You will find you should have studied for years before signing the petition which now makes you slow to understand the truth of your mistake.

 

[GregoryUrich]

No, eq 3 uses energy, eq 1 deals with force, there is no reason to juxtapose the two, and one is not needed for the other.

As newtons bit showed on his blog in his response to ross, the energy dissipated in compression a member is small compared to the energy dissipated through bending. Also, they are dealing with energy in eq. 3, and in Bazant and Verdure, they elaborate on this, the energy criterion for collapse trigger, and note that strength of the columns does not matter, and collapse will continue or be arrested based on the energy impacted to a floor vs the energy dissipated.

Yes, equation (3) assumes buckling. If there is no buckling, equation (3) is not applicable.

B&Z:

The basic question to answer is: Can the fall of the upper part
be arrested by energy dissipation during plastic buckling, which
follows the initial elastic deformation?

 

[cmcaulif]

right, and newtons bit showed there is plenty of energy to buckle the columns, with lots leftover to be dissipated by bending.

for easy comparison, when NB calculated the energy dissipated by a perimeter column, he found:

172.9kip in for compression
2436.6kip in for bending

thats about 14 times as much for bending. Clearly, there is more than enough energy to buckle the columns.

 

[GregoryUrich]

right, and newtons bit showed there is plenty of energy to buckle the columns, with lots leftover to be dissipated by bending.

for easy comparison, when NB calculated the energy dissipated by a perimeter column, he found:

172.9kip in for compression
2436.6kip in for bending

thats about 14 times as much for bending. Clearly, there is more than enough energy to buckle the columns.

Unless that energy goes into buckling columns in the upper part.

 

[cmcaulif]

that is another thing NB has calculated, and you surely know it too, since you posted on that thread

Elastic Strain Energy of the Lower Stories - 213MJ
Inelastic Strain Energy of the Lower Story - 171MJ
Elastic Strain Energy of the Upper Block - 71MJ
Inelastic Strain Energy of the Upper Story - 171MJ

 

[GregoryUrich]

that is another thing NB has calculated, and you surely know it too, since you posted on that thread

Elastic Strain Energy of the Lower Stories - 213MJ
Inelastic Strain Energy of the Lower Story - 171MJ
Elastic Strain Energy of the Upper Block - 71MJ
Inelastic Strain Energy of the Upper Story - 171MJ

I think the point is that B&Z haven't proven anything. I haven't taken the time to read all of Newton's post yet. He may very well be correct.

 

[cmcaulif]

I think the point is that B&Z haven't proven anything.

How do you figure that? 8.4 as an initial estimate for the lower bound for the Wg/Wp ratio says a great deal.

Though if you have the blueprints, this equation could be checked for accuracy by finding the plastic modulus for the various column sections used, and checking his Wp value, since you already have checked his Wg value with your mass paper.

 

[beachnut]

I think the point is that B&Z haven't proven anything.

You failed to prove that point. I have to think someone who has signed the 9/11 truth petition is just out to say things like you say and try to prove your CD ideas by discreting others. Your error ridden posts here are an example of just that. Blind support of 9/11 truth.

 

[Newtons Bit]

Bazant calculates the total energy for buckling 90 degrees at each plastic hinge at 500MJ. I calculate it at 171MJ, though I only allow 30 degrees of rotation before fracture at each plastic hinge. Multiply my number by 3 (from 30 degrees to 90 degrees) and you get 513MJ. He's using approximately the same plastic modulus and area of steel that I am.

 

[cmcaulif]

Thats interesting, I recall that you noted in your paper that 30 degrees was quite a lot as well, I wonder why Bazant uses three times as much. I suppose he was being very conservative.

 

[Newtons Bit]

Thats interesting, I recall that you noted in your paper that 30 degrees was quite a lot as well, I wonder why Bazant uses three times as much. I suppose he was being very conservative.

He was just showing that in the absolute upper limit, the column bending over until it reached the floor (through three bends), still is not a large portion of the total collapse energy.

 

[einsteen]

As far as I understand David B. Benson estimated about 400MJ based on the Bazant model and empirical data input, where the initial acceleration is used, that is about (2/3)g for wtc1.

 

[gumboot]

OMG! You Enjineer people think your so smart! Net Force = 0!!!1`11!!111!

Pwned!

-Gumboot

 

[cmcaulif]

As far as I understand David B. Benson estimated about 400MJ based on the Bazant model and empirical data input, where the initial acceleration is used, that is about (2/3)g for wtc1.

Do you know where I could find his work?