Shear Flow with a Uniform Moment
Shear Flow with a Uniform Moment
(OP)
If a composite member has a uniform moment along it's length (dM=0), how do I calculate the required shear flow capacity between it's bonded components for composite behavior?
I understand this is a little academic for these boards, but separating the theory conversation from the application should keep the discussion on topic.
I understand this is a little academic for these boards, but separating the theory conversation from the application should keep the discussion on topic.
Structural, Alberta






RE: Shear Flow with a Uniform Moment
Interesting question... Although it feels intuitive to think there should be some longitudinal stress to resolve, I think the answer is as the formula would suggest - zero.
RE: Shear Flow with a Uniform Moment
If you have a simple span member with two concentrated loads at the 1/3 points, the moment is constant between the two loads but the shear varies from load to load in a "bowtie" pattern.
q = VQ/I right? So per the V there would be some type of shear that would have to be some bonding between the components.
If you have a member with two concentrated end moments - perhaps no shear along the member and no bonding required?
Check out Eng-Tips Forum's Policies here:
FAQ731-376: Eng-Tips.com Forum Policies
RE: Shear Flow with a Uniform Moment
RE: Shear Flow with a Uniform Moment
RE: Shear Flow with a Uniform Moment
I think this too.
I believe that the trick to this is recognizing that, at the ends of the member, the moment has to be applied in such a way that it instantaneously creates a strain profile common to both materials. That's a pretty tall order for any real world loading situation other than where the "member" is really just a segment of consideration within a larger member. Especially so if one or more of the materials is a thing that cracks and creeps and generally behaves in a complex, non-linear manner.
Where the instantaneous development of a common strain profile is not realistic, shear flow capacity would need to be provided needed near the ends of the member to bring things in line, so to speak. In a lot of practical situations, I think that it would be prudent and conservative to assume that the moment originates in one of the materials and has to migrate to the other via localized shear flow.
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
RE: Shear Flow with a Uniform Moment
Pfft. Get the attention of the right cadre here and we'll bury you alive in esoteric voodoo.
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
RE: Shear Flow with a Uniform Moment
RE: Shear Flow with a Uniform Moment
Opposing end moments. It's a rare thing but not unheard of. The central segment of JAE's 1/3 point loaded beam is a good example. A column assumed to be loaded, and supported, eccentrically by the same amount is another.
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
RE: Shear Flow with a Uniform Moment
RE: Shear Flow with a Uniform Moment
RE: Shear Flow with a Uniform Moment
Check out Eng-Tips Forum's Policies here:
FAQ731-376: Eng-Tips.com Forum Policies
RE: Shear Flow with a Uniform Moment
The moments would have to be applied as a bunch of independent, linearly varying axial stresses that, when summed, would simulate the stress and strain profile of a composite member. Like I said, that's a tall order but, if it can be accomplished, there is no VQ/I demand between plies. Really, the end result would be a bunch of disconnected layers with linearly varying, mostly axial loads applied to them such that the aggregate condition would simulate the strain profile of a composite member.
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
RE: Shear Flow with a Uniform Moment
So with a symmetrical profile or a profile proportioned to the load shape the local dP/dA = Axial Stress. But with a non-symmetrical member that is not the same shape as the load profile, dP/dA =/= Axial Stress. So some sort of composite behavior is required.
Structural, Alberta
RE: Shear Flow with a Uniform Moment
I don't believe it is.
Consider this;
- A rigid clamp that matches the member cross-section (any shape) is installed at each end of the beam
- It rotates about a perfect pin at the neutral axis of the member
- By applying a uniform moment at each end without shear, you are effectively dialing in a certain final rotation of the clamps. That rotation is governed by the stiffness of the axial compression and tension of each longitudinal fibre - which doesn't depend on I.
I can't say I understand your sketch though... The 'load' you are applying is not that of a uniform moment?
RE: Shear Flow with a Uniform Moment
This statement is only true when shear flow is required. That, of course, is the overwhelming majority of the time. When shear flow is not required, Ix is identical for members with and without laminar shear connection. This recent thread is highly related to your question and may well resolve this for you: Concentric Tube Bending
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
RE: Shear Flow with a Uniform Moment
When I apply my eccentric tension to the member (triangle load distribution in the above sketch), convert the eccentric load to a Force and Moment at the centroid, and calculate the stress in the extreme fibers (P/A + My/I); I get a different stress result at any given location than I get when I slice the member and load into small slices and distribute a fraction of the load over the corresponding fraction of the member area.
In a member without laminar connections the method of slicing (dP/dA) should get the same result as any other method but if you calculate the bending stresses as a composite member (P/A + My/I) you get slightly different stresses. See the sketch, I'm afraid my notation is very rust, sorry.
Sorry about the unclear sketch earlier. The right most diagram is a simplification of my problem, the left and center sketches were my brainstorms on the rigid clamping approach, circumstances where I get the same stress result for shapes with or without laminar connection.
I'm not trying to be stubborn here, just this problem has me doubting.
Structural, Alberta
RE: Shear Flow with a Uniform Moment
My view would be this - based on nothing but intuition;
- Take the same member supported on perfect rotational pins, and supported vertically.
- Take the same rigid clamp and apply your moment, giving you a certain rotation and curvature of member
- Now apply your axial load (its concurrent but meh)
- I would guess that due to the curvature of the member, the axial load you are applying would either try 'straighten' the member (tension) or curve it further due to eccentric load (compression).
- This 'straightening' or 'additional curving' would result in some tangible vertical shear force at the support.
- This shear force is what you would use to calculate the required shear flow
Pure speculation
PS - I still dun get your sketch. calculus is beyond me now.
RE: Shear Flow with a Uniform Moment
RE: Shear Flow with a Uniform Moment
Consider the absurdly trivial yet altogether salient analog of an axially loaded member. Say, 2-2x6 that you'd like to resist an axial load of 1000 lb compositely. Don't sweat buckling or the moments due to eccentricity. Neither is germane to the example. You've got three possibilities:
1) Put all 1000 lb on one of the 2x and do not nail the plies. One ply resists, the other does not, the axial strain profiles of the two sticks do not match, and you have the analog of the non-composite case.
2) Put all 1000 lb on one of the 2x and do nail the plies. Load transfers between plies, each ply resists 500 lb, the axial strain profiles of the two stick match, and you have the analog of the composite case where shear transfer between plies is required.
3) Put 500 lb on each of the 2x and do not nail the plies. No load needs to be transferred between plies, each ply resists 500 lb, the axial strain profiles of the two stick match without any interconnection, and you have the analog of the composite case where shear transfer between plies is not required.
The uniform moment example here is very much like #3.
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
RE: Shear Flow with a Uniform Moment
BA
RE: Shear Flow with a Uniform Moment
RE: Shear Flow with a Uniform Moment
I think that we're probably speaking to the same phenomenon here. I've explored it a bit below for the case of a rectangular section with a load eccentricity of B/6. I think that it's worth noting that this shear would be of a different, and lesser, order of magnitude that one would expect from a true flexural application.
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
RE: Shear Flow with a Uniform Moment
I agree with the phone book analogy but feel that it is missing an important feature in this instance. Namely, it's missing little axial loads at the end of each page that increase linearly towards the outside edges of the phone book and simulate the linearly varying stress that would normally produce linearly varying strain.
At the end of the day, all you need to make use of composite section properties is for all of the cross section to flex according to a common strain diagram. One way to achieve that is to force them to strain together via shear flow. Another is to load them in such a way that their strains match at the boundaries without the need for shear flow capacity.
I made the sketch below to study your phone book analogy as I see it. The pages are separated by by rolling pins and each page is loaded independently. Not sure if this will clarify things or further confuse them. Let me know if I've made things worse.
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
RE: Shear Flow with a Uniform Moment
I also believe that three additional things are producing that flexibility:
1) the pages in compression are buckling.
2) the pages are not held together vertically.
3) your hands are not providing perfect shear slip restraint at the ends to apply the moment as I've described.
Obviously, I've never seen you bend a telephone book. You might be the hulk and doing an incredible job of it.
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
RE: Shear Flow with a Uniform Moment
BA
RE: Shear Flow with a Uniform Moment
BA
RE: Shear Flow with a Uniform Moment
Keeping our phone book analogy - we'd need to transfer the resultant axial loads due to the end moments for each page - I figure dipping the edges into 1/2" of glue. I can't think of away to keep the compression pages from buckling though.
RE: Shear Flow with a Uniform Moment
RE: Shear Flow with a Uniform Moment
RE: Shear Flow with a Uniform Moment
This member should behave the same if you glue the plies together, or if you just nail the the last 1' of each end together with no shear connections along the center span.
I was barking up the wrong tree with my problem. Looks like my problem is a local shear flow issue as the loading distributes across the member profile, well shown in KootK's vertical load sketch (edit: and in Dozer's FEA). I'm going back to the drawing board: seeing if I can find any literature on the shear load on the connections between atmospheric tank shells of different thicknesses under hydro-static stress.
Structural, Alberta