I hate it.

I hate my own game. How sad is that?

Update without a screenshot

No screenshot of the game today.

Yesterday I implemented collision detection between characters. This wasn't as complicated as I thought it'd be. But now the rat will chase the player around and stop near him and the player can't actually enter the rats area.

I also set the first action: attacking. There's currently a really terrible attack animation for the player that fires whenever the player presses the space bar. The scale of the "attack" and sword swinging is so off that I feel like I need to adjust the size of character sprites and/or use new textures for the character before continuing. It's distracting at the moment.

Once I get that taken care of I can add in dealing damage to the rat (and attack radius, etc). This will build on the methods I already developed for collision detection.

Then after that I need to start building an actual "level" with walls. That will allow me to do more complicated AI tasks such as LOS and path finding.

Update to project

There's now a not-so-cute rat that chases after the player. Cut me some slack, I'm not an artist.

Basic AI for chasing the player has been setup and works nicely. Now I just need to add the ability to attack (and more artwork showing this). I've also been completely unable to get this to work on anyone elses computer. I have a feeling it has something to do with the directX SDK.

New Project

It's a very simple game. The only buttons that do anything right now are WASD. And here's the download. It took me a year to figure out object oriented coding and the directx library. It took me about 5 hours to make this. The program needs directX and .NET 3.5 to run. Most windows installations should already have this.

Blog 2.0

This blog has been upgraded to the obligatory 2.0.

Woo.

Yea, I'm even less excited than you are. But I am happy with the nifty links section to the comics I read on the right.

An Open Letter

To Mr. Ross:

I haven’t done any debunking in about a year. But imagine my surprise when I visited your website recently and found that you had finally crafted a “response” to my refutation of your “Moment Transfer in WTC1” “paper”. Please note the words that I have in quotations: response and paper. This is because I hold these items in contempt, not because they’re imaginary. I also find your lack of testicular fortitude contemptible. When in a lively internet discussion such as the one that we have had, try to have necessary courage to actually inform your opponent that you’ve said something. Otherwise it would appear (as it does now) that you’re afraid of a real response. Let’s take a look at what you’ve written and I’ll respond to it paragraph by paragraph.

If only you could investigate 911 as thorough as you investigated my name.

A few people have written to me over the past few months regarding an article by Mr. Trevor Self, from Albuquerque I believe, styling himself Newton’s Bit. Rather than continue to answer these individually it will save time and effort if this reply is placed on the web and freely available. I have not previously bothered to answer this article because I did not believe that anyone would be taken in by his rubbish, riddled as it is with very basic errors, but for those who have not studied the subject it may prove beneficial to have some of these errors explained. Firstly I will deal with the arithmetical errors, then I will explain the engineering errors.

You’ve outed me! You have done a wonderful investigation and examined all the various clues I’ve left of myself over the internet and figured out my real name! I fear the massive unwashed hordes of Truthers hounding my every step. Or maybe I would, if I wasn’t sure that the hygiene-challenged Truthers were huddled in their parent’s basements playing the latest Halo game.

First of all the conversion from degrees to radians used by Mr Self is incorrect. There are pi (3.142) radians in 180 degrees, except apparently in New Mexico. This introduces an error of 200%.

You got me, an arithmetic error. I intended to use 30 degree angles (pi/6) but incorrectly used 15 degrees (pi/12). Unfortunately for you, 15 degrees still falls within the bounds of my “fudging”. You see, steel columns have ruptured by 8-12 degrees anyways. Let’s just call this one a wash. I made an error, but it doesn’t matter.

There are four rotations in a three point buckle except in the mind of Mr Self who believes there are only three. A further error of 133%.

Incorrect. This should be self-explanatory to an engineer, but I guess you didn’t have to take any Mechanics of Materials classes. Under an arbitrary amount of work, the top and bottom buckle points will rotate X degrees, however the middle one will rotate an angle of 2*X. Each buckle point absorbs the same amount of energy. Let me know if you need me to explain this further, it’s a tad bit complicated (I’m lying here: I’m trying to protect your feelings, it’s really not complicated at all).

Mr Self uses a slenderness ratio which assumes that the columns in the towers were fitted with hinges on every storey. A casual glance at the towers proves this false, and the very fact that they stood for many years would help to confirm the non existence of these hinges. The error in slenderness ratio is 200%.

Do not put words into my mouth, HVAC designer. I never said that the tower was fitted with hinges. I can only surmise that you are making the same basic mistake that Tony Szamboti made regarding the effective length factor “K”. Please see my response to him, I’m really getting tired of having to correct this insanely basic concept of engineering. Here’s the link.

Educate yourself.

Mr Self chooses to call himself Newton’s bit for some reason but his refusal to accept Newton’s laws would have that famous man turning in his grave. Isaac Newton, or “whirling Isaac” as he is now known told us that each action has an equal and opposite reaction, but Mr Self chooses to ignore this fact conveniently allowing him to understate the energies involved by half. An error of 200%.

Hmm. I’m not sure how my handle has anything to do with what I write. Nor do I see where this “error” occurs as my paper only deals with recalculating things you did incorrectly.

Mr. Self ignores the strengthening and bracing effect of the spandrel plates, core bracing, etc. The error is more difficult to quantify but is clearly significant. Why else would they have been included in the original design?

The spandrel plates do not brace from buckling in a direction orthogonal to their length. They provide stiffness to in-plane forces (thus a moment frame) to deliver shear forces to the bottom of the structure. This is basic engineering mechanics. There is no excuse for not understanding this.

These errors when combined add up to ridiculous. It is easy to see therefore why I have previously dismissed this article without much comment. The only interesting part of this episode has been the manner in which supporters of the official story have latched onto it. There are those without the specialised knowledge to judge, who have betrayed their own unthinking bias by adopting Mr Self’s article without question. More importantly there are those who are or claim to be engineers and who do or should have that specialised knowledge and yet they have allowed the article to stand and allowed

Mr. Self to continue to embarrass himself, even when these most basic errors have been pointed out.
I hope that this clears up a few issues for some people, but if questions continue then please do not hesitate to contact me.

As an aside, I have always thought that the custom on the web of allowing everyone to choose their own nickname is a little bit strange. If this were the case in real life then all the Porkys and Kiffys of this world would be calling themselves Ace or Tiger. Mr Self, or Newton’s Bit, as he appears to prefer, is a definite case in point.

You managed to find an arithmetic error (that's posted on the JREF forums) that doesn't actually change any results.  You also showed how ignorant you are of structural design.  Anyhoo, this has been pretty dang entertaining for me.  When you have more “problems” (this quotation is both for contempt and because it’s imaginary), please actually grow a pair and let me know about them instead of hiding it on your website.

Cheers!

Trevor Self

P.S.  My middle name is Newton.  And my blog is my bit.  Hence: Newton's Bit.  Do you get it?

Why the columns bowed in

Update 9/20/08: Rephrased a couple of sentences, referenced reduction in modulus, fixed some weird formatting.

Why did the columns bow in? There’s been quite a bit of speculation and misinformed opinion about the mechanics of the structure that caused that, so I hope to do a little bit of enlightenment. The first thing that needs to be looked at is the problem. Figure 1 shows a typical building section through a building such as the WTC towers.

Figure 1

Everything here is fairly straight forward. The gravity load path can be seen very easily. The floor trusses deliver the vertical floor loads to the columns which deliver them to the foundations. But what happens when a core column is severed as in Figure 2?

Figure 2

Things start to get a little bit more complicated. The first thing that should dawn on most people is that the floor is no longer being supported by the middle column which is going to cause some problems. The middle column will drop unless there is a force that can resist it, see Figure 3.

Figure 3

As the column drops, the top chord of the floor truss develops tensile forces (it is quite literally stretched). This tensile force has two parts, a vertical portion that pulls the column up and a horizontal force that pulls the rest of the structure in. This can be seen in Figure 4.

Figure 4

The other things to note here is that the left column is still under its full axial loading (P2, which will be important in the analysis). The left column is already shown pulled in to some degree, however it is not to scale. Further modifying the problem, we know that the fires caused the trusses to sag to some degree. If the fire is hot enough, the truss will become a tension only member. This means that the top chord of the truss will act something like a rope and pull inwards at its connections. This can be seen in Figure 5. There is another condition as well (which I have no illustrated) that will cause the heated floor to expand outwards without losing its bending capacity and thus not sagging. It is a condition that likely proceeded that of the sagging floor trusses.

Figure 5

NIST (1-6D) estimates that the total pull-in force at the exterior columns is roughly 6 kips (6,000lbs) at each column. The truss to column connection consisted of (2) 5/8” diameter bolts. Even non-structural grade bolts of this size will have a shear capacity of over 5kips each, so it is reasonable to assume that the top chord of the truss will not pull off of the columns at the connections due to a 6kip load.

Is this 6 kips enough to pull the column in several feet as seen in the photos of the tower?

Figure 6

Math is needed here. First some assumptions need to be made. For the purpose of this analysis, let the exterior column be HSS14x14x5/16 tubes at 25% of the maximum axial load prior to any damage. The column has the following properties: Similar to HSS 14x14x5/16
A = 15.7in^2
I = 739 in^4
S = 92.3 in ^3
Pn = 557k (from AISC LRFD 3rd, table 4-6 with an unbraced length, KL = 12’-4”)
Pu = ¼* 557k = 139k
Mn = 92.3in^3*46ksi = 4645 kip*in (Mn = maximum bending capacity)

The column itself will bend inwardly until it snaps if the column itself ever becomes inelastic. This can be defined by the ratio (I’ve simplified this a bit): Mu/Mn + Pu/Pn <>

Figure 7

CALCULATION 1: DIAPHRAGM DAMAGE, NO FIRE EFFECTS
Unbraced length = 37’-0”
Pu = 139k
Pn = 465k (from AISC LRFD 3rd, table 4-6 with an unbraced length, KL = 37’-0”)
Mn = 4645 kip*in
Mu = P*a
Mu = 6kip*1/3*37ft
Mu = 74kip*ft or 888 kip*in

Deflection = P*a *(3L^2 – 4*a^2)/(24*E*I) (Formula from AISC LRFD 3rd)
a = 1/3*L
= P * 1/3L *(3L^2 – 4/9*L^2)/(24*E*I)
= 23*P*L^3/(1296*E*I)
= 23*6k*(37ft*12in/ft)^3/(1296*29000ksi*739in) = 0.435in

Additional moment due to P-delta
Mu+ = 0.435in*139k = 61.02 kip*in

Additional Deflection
=Mu+*L^2 / (4*EI)
= 61.02kip*in*(37 * 12ft\in)^2 / (4*29000ksi*739in^3)
= 0.140in

Additional moment due to P-delta2
Mu++ = (0.435+0.140)in*139k = 79.93 kip*in

Additional Deflection
= Mu++*L^2 / (4*EI) = 79.93kip*in*(37 * 12ft\in)^2 / (4*29000ksi*739in^3) = 0.184in

As seen, the first p-delta iteration results in an increased deflection of 0.140in. The second results in a deflection of only 0.184in. We can thus conclude that p-delta will eventually converge and that no further iterations are necessary. The 6kip pull-in force with no effect of fire will not result in the column becoming unstable. At 600C, the Modulus of Elasticity will have reduced to approximately 0.3 of its original value (see Figure 8), and the yield strength to 0.5 of its original value. The effect of the Modulus of Elasticity being so greatly lowered is of far greater important than the yield strength, however.

Figure 8
From AISC Facts for Steel Buildings

CALCULATION 2: DIAPHRAGM DAMAGE, 600C TEMP

Unbraced length = 37’-0”
E = 0.3*29000ksi = 8700ksi
Pu = 139k
Pn = 465k*0.5 = 233k
Mn = 4645 kip*in *0.5 = 2323kip*in Mu = P*a
Mu = 6kip*1/3*37ft
Mu = 74kip*ft or 888 kip*in

Deflection = P*a *(3L^2 – 4*a^2)/(24*E*I) (Formula from AISC LRFD 3rd)
a = 1/3*L
= P * 1/3L *(3L^2 – 4/9*L^2)/(24*E*I)
= 23*P*L^3/(1296*E*I)
= 23*6k*(37ft*12in/ft)^3/(1296*8700ksi*739in)
= 1.45in

Additional moment due to P-delta
Mu+ = 1.45in*139k = 201.6 kip*in

Additional Deflection
= Mu+*L^2 / (4*EI)
= 201.6kip*in*(37 * 12ft\in)^2 / (4*8700ksi*739in^3) = 1.55in

Additional moment due to P-delta2
Mu++ = (1.45+1.55)in*139k = 417 kip*in

Additional Deflection
= Mu++*L^2 / (4*EI)
= 417kip*in*(37 * 12ft\in)^2 / (4*8700ksi*739in^3) = 3.20in

This results in the column becoming unstable due to p-delta. This can easily be seen in that the deflection due to P-delta2 is double that of P-delta1. It can therefore be concluded that it was necessary for both fire and damage to result in the collapse of the towers.