In torsion, you have a neutral axis, not a plane. The very center of a solid bar experiences zero force in torsion, which is why we have tubes. All that weight down the middle would be doing nothing. I don’t remember the math well enough to prove it myself, but it’s well-proven that a thinwall tube is the best possible shape for resisting torsion, per a given amount of weight.
Tubes aren’t as good as, say an I-beam against bending that’s always in one plane, but a tube is the best shape against bending when it can come from any direction.
For some particular combo of torsion and bending, there might be some other shape that’s better, but a round (cylindrical) thinwall tube is quite good, and also easy to make, which explains why they’re so popular.
At the head tube, the bending that TT and DT feel is all in the central plane, so the neutral plane is on the sides of the tube. The sides feel just as much force as anywhere else on the tube from torsion, but the bending forces are significant, so the sides are less loaded overall.
Cycletourer, are you still looking for more explanation here?
You can think of the bike’s down tube as the bridge in the diagram I posted before. If you drill a hole in the top of the tube, it’ll get compressed when the rider sits on the bike. And if you put the hole in the bottom of the tube, it’ll get stretched when the rider sits on the bike.
And because the hole is a stress riser (a weak point in the tube), it’s likely to fail at the hole if the tube gets loaded enough.
But like I was pointing out, and as bulgie alluded to as well - the sum of forces acting on any one tube in the bike can be complex. (This is true of any real-world object really)
The weight of the rider sitting on the bike really isn’t the primary thing to design around.
The bike is under much more load when the rider is pedaling hard.
And even more force when they’re hard on the brakes.
And maybe the highest force (short of a crash) is hitting something a pothole when traveling at high speed.
That pothole case will cause a massive backward and upward force from the front wheel, counteracted by forward and downward force from the rider’s hands on the bars and feet on the bottom bracket. This is still a similar case to the bridge diagram I posted earlier - the two supports are at the handlebars and bottom bracket, and the force is coming in from the front wheel.
The result is that the head tube and down tube will experience compression on their forward/lower faces and tension on their upper/rearward faces.
And any weak points in the frame on the upper and lower surfaces of that down tube will cause frame failures in the worst case, or possibly some fatigue that might cause a future failure.
The reinforcement I add around the wiring hole helps bear the load and reduces the chance of failure. And something like a water bottle boss would bear even more of the load and further reduce the chance of failure.