Thanks for sharing that thread. Appreciate @CANPRO going all in for that discussion.
But while it remains a symmetric member about the neutral axis there still is no longitudinal shear flow, even for "side channels or other more substantial welded reinforcements".
I disagree. 'I' is not an "elastic property" it is a geometric property. And unless the geometry of the section changes then 'I' won't change (Any plastic deformation isn't going to change the geometry significantly). Thus VQ/I doesn't become inaccurate in the plastic range.
I'm not sure what you mean here. The shear flow formula for this example calculates out to ZERO as Q = 0.
Q is not unchanged, it is zero. As you measure the center of area of the plate to the centroid of the beam. This gives a value of 0.
Why do you assert this when it goes against the theory and shear flow formula and the previously explained points?
The section will behave in a combined manner purely on vertical shear transfer. Provide staggered bolts with horizontal slots and you'll have 'combined behaviour'. Both beams will deflect in unison and the added plates will provide resistance to bending.
You are wrong. There is shear flow for every beam, even a simple rectangular beam.
Again, you are bloody wrong! It is a geometric property which is used in the elastic range, not the plastic range.
It is exact within the elastic range. It is not exact in the plastic range.
Q is not zero at the neutral axis, it is not zero where the web meets the flange, and it is not zero anywhere in between. I suggest you read a strength of materials textbook for the definition of Q..
Well that is stating the obvious. Since we are being pedantic I should have said there is not longitudinal shear flow BETWEEN the members. In this case the beam and the plates.
It is a geometric property (have a look at any basic definition) that exists inside the elastic range and in the plastic range. It isn't a property that disappears if there is plastic deformation. If you are referring to the EI formula to determine stiffness it is the E that effectively changes. The 'I' remains the same as long as the section retains its geometric shape.
Again I'll refer to the first line from wikipedia. "The first moment of area is based on the mathematical construct moments in metric spaces. It is a measure of the spatial distribution of a shape in relation to an axis."
You keep asserting this without any explanation.
Yes there is.
My/I is not correct for stress in the plastic range.
Here are a few 'q' values for your amusement. Note that q at y=2 is unchanged by the presence of side plates.
The explanation is that moment of inertia is the wrong property to use in the plastic or partial plastic range.
It relates because it shows the shear flow between the plates and the beam which is exactly the original question. It shows no longitudinal shear flow. In the second image I offset the plates to check that the model behaves as theory would expect, which it does.
The strength of the connection, weld or otherwise, required to transfer shear force longitudinal to the beam is ZERO as described by myself and others and demonstrated mathematically and via computational analysis software. Naturally you also need to transfer the vertical shear which is simply the proportion of the load on the beam relative to the stiffnesses.
I didn't respond to this point earlier as I didn't know what or how your were calculating things. And I still don't. But it seems you have a non zero value for when y=0 which presumably is the at the centroid. But this flies in the face of the one of the definition of the centroid as the location where the first moment of are are equal to zero.
When you want to find horizontal shear, the formula which you have quoted is correct, but dA refers to the area above the level you are examining, not the total area.
If you are talking about the link to the 2020 thread, I don't think I participated in it at the time. I have scanned it briefly in the last couple of days, but I have not had time to read it carefully. It is pretty long winded.
Where is above? Where in that formula does it say above? In the wiki page you now linked back at me it even says:
When calculating the fixings required for the plate the Q in the formula VQ/I is the concerns the area of the entire plate, to which the second moment is zero. (To clarify I'm talking above the forces along the axis of the beam here, clearly some fixings are needed to transfer the shear in the direction of the load.)
Well the first moment of area is ZERO at the centroid which is the definition of the centroid. But since we can't agree on this fact then I think we'll struggle to find common ground.
