I'm not sure that Brent's math is as wrong as you may be suggesting. My assumption is that Brent is using something like an A572 which is a high-strength low alloy steel which has better corrosion properties and more strength than A36 which you mentioned, and which has a tensile yield strength in the 60,000 psi range.
Brent said,"That is 11,250 lbs per linear inch for 3/16th plate. Multiply that by the 96 inches in the side of one of my twin keels." And in that regard, something like A572-60 that was 3/16 thick would have a tensile yield strength around 11,250 lbs per linear inch. (60,000*3/16= 11,250) His arithmetic is essentually correct.
The problem is one of how the is applying that math relative to proper engineering principles contained in Brent's metaphoric description of:
"That is 1.08 million pounds per side, times four keels sides.
How are you going to break that with a boat under 20,000 lbs?"
This metaphor assumes that the loads are shared by both keels equally and that the loads are solely in tension. Neither is likely to be present or likely to relate to the actual failure mode of the keel.
The more probable failure modes for a frameless keel connection would more likely be some mix of buckling of the keel sides in compression (skinny column failure), sheer where the keel sides try to cut through the hull plate (as you noted in your comments), or bending of the hull skin perhaps coupled with lamellar tearing near where the hull meets the keel since the hull plate would be in bending due to the large lever arm formed by the depth of the keel and the narrower width of the keel root being resisted in bending by comparably thin plate.
But beyond that I also want to touch on Brent's Herreshoff reference.
I am not sure that its clear which Herreshoff Brent is referring to, but by and large all of the Herreshoffs were consumate engineers. Nat Herreshoff and Herreshoff Manufacturing developed their own formulas for many of the calculations involved in properly engineering a boat. At a time when boats were 'engineered' by rules of thumb, Nat did his own scientific research and developed his own formulas based on his research. And he used these formulas to design some of the most sohisticatedly engineered designs in that era. He later boiled those down into his own set of widely used rules of thumb, but these were heavily based on proper engineering based methodologies.
L. Francis began his carreer working with Nat as a designer at Herreshoff Manufacturing but did the majority of his apprenticeship working beside Starling Burgess and Frank Payne at Burgess, Swasey & Paine in Boston. Burgess was one of the most creative, multi-discipline, engineering-oriented designer/ inventors of his day. Burgess was a brilliant mathematician who was able to do high level scientific research, then develop mathematic equations to explain the observations and ultimately literally wrote the book on a wide range of early 20th aeronautical engineering applications.
In yacht design, Burgess literally developed sophisticated formulas that replaced the crude rules of thumb which preceeded his time. Starling Burgess working with Glenn Curtiss was key to the design of the first successful seaplane (only a few years after the Wright Bros first flight), he designed three America's Cup winning defenders, he designed the first successful aluminum masts, he designed many of Buckminster Fuller's so called Dymaxion inventions (car and house being most notable), (and designed 'Little Dipper' for Bucky, one of the most beautiful little cutters of all time), as a kid in the late 1800's he designed one of the first light weight machine guns, he also is thought to have possibly/probably designed the Times New Roman font, wrote poetry, and novels, and produced world class paintings.
And L. Francis learned his trade at Starling's side and along side of Frank Payne as well. And Frank Payne was no slouch either when it came to sophisticated engineering. There was nothing even slightly shoddy about L. Francis's math or engineering skills.
But of all the Herreshoffs', L. Francis would be the only one that I could imagine who might write negative comments about using engineering formulas. I can imagine that since L. Francis was known for writing things that he thought sounded good and doing just the opposite. (Like advising adult sailors that they had an obligation to take children sailing and teach them the ways of the sea, when L. Francis notoriously hated kids and hated being around them.) So, if L. Francis was dismissive of the crude formulae of the day, it was only because he and his close life long friends, Starling and Frank, were beyond the quick and dirty engineering methods that he decried.
Sidney Dewolf Herreshoff was a graduate from MIT in engineering. 'nuf said. He used the numbers. Halsey Herrshoff has an undergraduate degree from Webb Instutute and a masters from MIT, I have to figure that he uses the numbers as well.
Please, lets try to keep the historic references close to what is actually known about these people.
1.08 million pounds per side, times two, means 3.6 million pounds per keel, if you only hit one keel at a time. Sheer and tensile are the same at that point, as you are not talking about a sharp edge. Still not wooden boat numbers, nor plastic boat numbers. To buckle, plate has to buckles both ways, inward and outward . Kind of hard to for it to buckle inwards, if they have 4500 lbs of lead cast inside.
How do my 4 lengths of 3 by 3 by 1/2 inch angles across the tops of the keels, slotted and fully welded into them , let the plate take all the flexing?
How does running the 3/16th water tank top, fully welded in against the inside edge of the keel, a fully welded steel longitudinal bulkhead, a triangular shape, let the hull plate take all the flexing, when it gives you three curved, fully welded edges of steel coming together ? How do they allow the hull plate to bend at that point, like a simple flat piece of steel, when they are far more structurally complex?
I think the biggest problem some have in comprehending steel hull shapes and their structural factors, is they are incapable of seeing structural loads in three dimensions. They only look at a cross section in two dimensions, and make their conclusions on that basis. That is why some put a longitudinal right next to a cabin side, which is a super strong longitudinal in itself , then put a series of gussets along the sheer, when such an I beam structural equivalent needs only two supports anywhere along its length; any more being structurally irrelevant. That is why they suggest longitudinal stiffeners along the keel side, when the keel itself is the structural equivalent of a fully welded longitudinal steel 1/4 inch plate bulkhead.
Where they get really loonie tune, is when they talk about hogging and sagging in a 36 foot steel boat, which would take 12 1/2 feet of 1/8th inch deck and cabin side plate to stretch longitudinally, or more than 10 feet of 3/16th hull plate to stretch longitudinally . Racers have shortened the waterline of plastic racing boats for measuring, by putting a hydraulic backstay tensioner on and jacking it up til the boat bows and sags considerably, shortening the waterline considerably. When I tried to take some twist out of an origami 36 ft hull, by a 3 ton come along from the top corner of the transom to the opposite chine, I broke handle off the come along without changing it a 16th of an inch. The hydraulic back stay tensioner would break the back stay before shortening the waterline 1/16th of an inch. Implying that transverse frames will stop hogging and sagging is like saying that transverse frames will stop a camera bellows from lengthening or shortening, or sagging. You couldn't ask for a clearer demonstration of a complete inability to see reality in three dimensions.
As for L Francis Hereshoff, I suggest you read his book "The Common Sense of Yacht Design," in which he ridicules mathematical exhibitionists.
As he points out , if you add up the areas of sections in sq feet, and multiply it by the space between them, you get your displacement in cubic feet. Multiply this by the number of pounds of water per cubic ft and you have your displacement , exhibitionists Simpson's multipliers be damned. Compare this with a figure acquired by multiplying the area of your midships section by your waterline length, and you have your prismatic coeficient .
Its that simple , to the consternation of exhibitionists!