After the reading the Va threads of my past questions, I found a
wonderful way to confuse myself. I notice that I've become quite good
at confusing myself and making things complicated. To give myself
some credit, I did search old messages but found no resolution. So
here we go...

I am sure most know the typical textbook definition of Va...goes
like..."the minimum speed at which the wing can produce lift equal to
the design load limit" or "the speed at which the pilot can use full
control deflections without over-stressing the airplane".

Essentially, it's the minimum airspeed that, coupled with a control
deflection to give you the critical angle of attack and CLmax, will
result in + 3.8 g's. Pulling any harder won't help since you'll stall
the airplane. Pulling with all your might as speeds below Va will
result in the airplane stalling without reaching the limit load factor
+ 3.8 g's. In essence, Va is the stall speed at the design load
factor of + 3.8 g's.

Now, the above seems to be what's commonly accepted.

Here's my question for this thread: Idealize the wing as a
cantilevered Euler beam representative of the wing spar ("the wing").
Assume the lift load to be a distributed elliptical spanwise,
transverse load, acting at the centroid of the section. Further
assume no other external loading such as drag loads.

The predominant stresses are bending (axial) stresses at the outer
regions of the spar caps and shear stresses in the spar web. Assume
that the failure mode is via the former.

Alright, so here, clearly, the failure of the wing is due to excessive
loading. The distributed load, expressed in X number of pounds per
inch, was too great. In fact, for the sake of simplicity, let's make
the distributed load a point load in pounds.

Now, we can say that the failure of the wing was due to excessive
FORCE which induced excessive stresses in the structure.

Consider that a certain airplane weighed at maximum takeoff weight is
designed to withstand + 3.8 g's (its design load). Actually,
airliners that I am familiar with are tested to ultimate load, or
1.5*design load (+ 5.7 g's before permanent deformation). For now,
we'll assume that at + 3.8 g, the plane's wings break off. That would
equal to a total force on both wings of 3.8 x 2550 lb or almost 10,000
lbs.

The thing that bothers me about Va is that it equates to a number of
g's ("design load") AND that Va is being rescaled for weight. By
doing so, Va becomes more of an acceleration criterion rather than a
structural criterion. It appears as though Va limits positive g
acceleration to + 3.8 g, not load itself.

In other words, Va adjusted for say, a lower weight, tells the pilot
"You will not exceed 3.8 g for your current weight, as you will stall
first". If the current weight was 2,000 lbs, the total load on the
wings would only equate to 7,600 lbs at + 3.8 g's, lower than the
design limit of 10,000 lbs of + 3.8 g's at max. takeoff weight. The
acceleration on the airplane would be a "limit load acceleration" but
would not produce a limit load condition, per se, structurally.

If Va was truly a structural consideration, it would not change
(regardless of weight), since no airspeed below Va coupled with any
non-stalled AOA, could produce limit loads of + 3.8 g as tested at max
takeoff weight of 2,550 lbs.

There may be severe flaws in my reasoning...please no flames and be
nice. It's a holiday.

Alex