Total Building Collapse from a Single Column Failure

W14x730 properties:
A = 215in^2
Ix = 14,300
Iy = 4,720in^4

The properties of the two 2"x26" side plates as shown in JSanderO's pdf:
A = 104 in^2
Ix = 5,858in^4
Iy = 1/12bh^3 + Ad^2 = 34.667 + 10286in = 10320 in^4

The combined section:
A = 319in^2
Ix = 20,158 in^4
Iy = 15,040 in^4
rx = SQRT(I/A) = 7.3in
ry = SQRT(I/A) = 6.86in

The transition from inelastic to euler buckling occurs at KL/r > 4.71*SQRT(E/Fy)
E is the modulus of elasticity, or 29,000ksi at room temperature.
Fy is the yield stress, 36 ksi at room temperature.

Let's assume k = 1.0 (non-conservative, favorable to a non Euler collapse, because we have to give all the assumptions to the truthers or they'll cry foul)

1.0 * L / 6.86 > 4.71 * SQRT(29000/36)
L > 917in or 76.4ft.

Not sure where, or how, JSanderO is getting his numbers from...
 
Newtons Bit said:
W14x730 properties:
A = 215in^2
Ix = 14,300
Iy = 4,720in^4

The properties of the two 2"x26" side plates as shown in JSanderO's pdf:
A = 104 in^2
Ix = 5,858in^4
Iy = 1/12bh^3 + Ad^2 = 34.667 + 10286in = 10320 in^4

The combined section:
A = 319in^2
Ix = 20,158 in^4
Iy = 15,040 in^4
rx = SQRT(I/A) = 7.3in
ry = SQRT(I/A) = 6.86in

The transition from inelastic to euler buckling occurs at KL/r > 4.71*SQRT(E/Fy)
E is the modulus of elasticity, or 29,000ksi at room temperature.
Fy is the yield stress, 36 ksi at room temperature.

Let's assume k = 1.0 (non-conservative, favorable to a non Euler collapse, because we have to give all the assumptions to the truthers or they'll cry foul)

1.0 * L / 6.86 > 4.71 * SQRT(29000/36)
L > 917in or 76.4ft.

Not sure where, or how, JSanderO is getting his numbers from...
Click to expand...

Who you callin' truther?
FROM THIS:
 

Attachments

JSanderO said:
Who you callin' truther?
FROM THIS:
Click to expand...

Let's see your calcs. I don't even know what your pdf is supposed to be computing, or how. "Slenderness" can mean a number of different things, however it's never the point in which a column transitions from elastic buckling to inelastic buckling.
 
The calculations are trivial. CAD program computed areas.

That column config will not self buckle if it is 76 feet tall. You think so?
 
Last edited:
JSanderO said:
The calculations are trivial. CAD program computed areas.

That column config will not self buckle if it is 76 feet tall. You think so?
Click to expand...

I ran the numbers and posted them. The column transitions from inelastic to elastic (aka Euler) behavior at 76.4ft. Self buckling does not occur at this point.
 
All this is at room temperature though, correct? There is that detail of a 10-12 foot portion at several hundred degrees.
So if the column close to Euler buckling if calc'd at room temp, and a portion of the column is at ,let's say 350 degrees, would that be enough to push it to failure?
 
ozeco41 said:
Interesting idea. Maybe we need to tell Euler. Next time I meet him........
Click to expand...

He posts a link that shows Pe is a function of 1/(length^2) then says it varies linearly. He does't understand this stuff at all.
 
Newtons Bit said:
He posts a link that shows Pe is a function of 1/(length^2) then says it varies linearly. He does't understand this stuff at all.
Click to expand...

I corrected that error I meant it did not... it's a parabolic relationship No? See post 602 Mea Cupla

You haven't explained boo to me and I would imagine to others here. Give it a try.
 
JSanderO said:
I corrected that error I meant it did not... it's a parabolic relationship No? See post 602 Mea Cupla

You haven't explained boo to me and I would imagine to others here. Give it a try.
Click to expand...

You posted a pdf with some numbers on it. I asked you where the calculations for it are. Multiple times. You're ignoring that request. I can't explain what you get wrong until you actually explain how you're doing it.

By the way, a parabola is y = ax^2 + bx + c. Elastic compressive stress is Fe = pi^2*E/[(KL/r)^2] or Fe = a / (L^2).
 
Last edited:
Newtons Bit said:
You posted a pdf with some numbers on it. I asked you where the calculations for it are. Multiple times. You're ignoring that request. I can't explain what you get wrong until you actually explain how you're doing it.

By the way, a parabola is y = ax^2 + bx + c. Elastic compressive stress is Fe = pi^2*E/[(KL/r)^2] or Fe = a / (L^2).
Click to expand...

the calculations are done in the cad program... areas. what's the mystery.

the SR limit for a slender column is 150.. more than that and the column is unstable...less than 150 it is stable. Color me dumb.
 
Newtons Bit said:
ozeco41 said:
Interesting idea. Maybe we need to tell Euler. Next time I meet him........
Click to expand...
He posts a link that shows Pe is a function of 1/(length^2) then says it varies linearly. He does't understand this stuff at all.
Click to expand...
Maybe - but keep it in context. I've been trying to help Sander understand - not prove him wrong.

Seymour B asked a simple question but he confused exponential/linear and said "Correct me if I'm wrong" I did and explained that buckling - Euler version specifically - varies inversely with L squared.

Sander fumbled his response which disagreed with me on the engineering basics whilst posting two links which agreed with me, Euler, all the engineering profession including you. ;)

Hence my light hearted offer to let Euler know that he had been wrong...and Sanders hasty correction.

So it's partly my fault that this rabbit burrowing detailed derail has occurred.

Col 79 failed wherever/however and that is a known fact of collapse initiation for WTC7 - wherever that fact fits in the OP.
 
JSanderO said:
the calculations are done in the cad program... areas. what's the mystery.
Click to expand...

The mystery is the numbers you've posted make no sense.

the SR limit for a slender column is 150.. more than that and the column is unstable...less than 150 it is stable. Color me dumb.
Click to expand...

1) The transition between a inelastic and elastic buckling compressive strength happens at a slenderness ratio of 4.71 * SQRT(E/Fy) [AISC 360-10 E3]. This corresponds to a slenderness ratio of 133.7 for a compact A36 column.
2) The column does not magically become unstable at this point. The compressive strength calculations change to classical Euler buckling formulas.
3) A "slender column" is a column that has elements that are not fully loaded before the columns buckles. See AISC B4.
4) Your pdf multiplies some numbers together in a completely useless fashion. I can't tell where the numbers come from or what you're trying to do with them. The conclusion you derive from them is very wrong.
 
Newtons Bit said:
The mystery is the numbers you've posted make no sense.



1) The transition between a inelastic and elastic buckling compressive strength happens at a slenderness ratio of 4.71 * SQRT(E/Fy) [AISC 360-10 E3]. This corresponds to a slenderness ratio of 133.7 for a compact A36 column.
2) The column does not magically become unstable at this point. The compressive strength calculations change to classical Euler buckling formulas.
3) A "slender column" is a column that has elements that are not fully loaded before the columns buckles. See AISC B4.
4) Your pdf multiplies some numbers together in a completely useless fashion. I can't tell where the numbers come from or what you're trying to do with them. The conclusion you derive from them is very wrong.
Click to expand...

The information about steel columns for Euler buckling is a slender column can not exceed SR 150 the ratio of the radius of gyration - the x or y axis of the column plan to the length.

the numbers are the x and y axis dimension X 150 to find the upper limit (SR) for each axis of the column.

There is no dispute that unbraced columns bear less axial load than braced. The assertion is that so much of the bracing was removed that the column lost capacity and buckled.

I don't see that failure mode .. or even as you assert 70 something feet were unbraced and the column buckled. Your numbers don't sell me. Try a different approach...

Content in the link is not viewable for non ASCE members.
 
Last edited:
You must log in or register to reply here.

Back
Top Bottom