Question of calculating Q for Horiz. Shear

[JAE]

In-office debate about the attached sketch.

The top section is a wide flange with a channel cap on top with welds at the WF flange tips.

The bottom section is a wide flange with the same channel - but the connection is at the WF neutral axis via two figuratively thin
plates and a small gap between WF top flange and channel web. Assume the two connector plates in the second option are very small/thin.

It appears that both would have the same value of Q for determining horizontal shear for the weld attachment calculation.

However it doesn't seem intuitively correct that the welds would carry the same shear as the flexural behavior of the two sections seem very different.



Any thoughts?

 

[PMR06]

It seems to me the moment of inertias would not be equal... I just dont have time today to rigorously look at it though.

Interesting thought experiment!

 

[rb1957]

wouldn't the bending behaviour of the two beams be very different ?

the first section is obviously a "proper" beam, all the elements are connected together well enough.

the 2nd section the upper channel is quite separated from the I beam. if down load is applied to the I-beam, i see it separating from the channel, so that the I-beam would be bending, but the channel wouldn't (or not as much).

 

[flight7]

Agree with rb1957. The thin plates will buckle under load, which leads to flexural behavior very different from the first case. Thus the weld design becomes moot.

 

[JAE]

Hey guys - ignore the little connector plates. The question is about calculating the second moment - Q for horizontal shear.

Both cases shown have identical Q values from what we understand how Q is calculated.
(Q - area above the connection plane times the distance from channel centroid to total section neutral axis).

But it seems very obvious intuitively that the horizontal shear on the welds would be quite different.

 

[rb1957]

if the two piecws of the section are not well connected together (as they are in the 1st section) then i don't see them bending as one.

the top Channel could be lying on top of the I-beam. down loads would have them reasonably working together. up loads applied to the channel would cause the Channel to separate from the I-beam ... no? similarly down loads applied to the I-beam would have less effect on teh Channel.

 

[chrislaope]

From purely theoretical view, Q for 2 cases are identical. Realistically, they are different.

 

[rowingengineer]

I think JAE means the plates while being very thin it is however strong enough to ensure that load is transferred from the beam to the channel.

My thoughts are that the welds will have the same longitudinal shear stress. The forces in the channel should be the same for both, hence the same transfer of forces is required.

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[tclat]

Before you get into shear flow, doesn't the built up section need to act compositely? It would seem unlikely that the second section is a composite member.

 

[chrislaope]

Please see attached modification of JAE's sketch, assume the legs flanges, and web of the C-Channel cross section are rigid enough, then no matter where the weld is on top or bottom, it will have same result. However in reality, there is no such thing as theoretical "rigid", therefore they will be different.

 

[JAE]

chrislaope's sketch is a good alternative to my question.

Even though some of the welds in that alternative sketch can't be physically done, the theory is what we are after.

The Q value for both appear to be identical so it seems that the welds for both would have similar horizontal shear values.

 

[haynewp]

The same weld should theoretically be required and I would use that for the design. The equation doesn't have a factor for where the attachment is made on the compound section and assumes the entire channel area is equally effective in bending. I expect testing would show the difference in weld stress due to variations in the way the shear is actually flowing into the channel and engaging it along the length of the beam for each case.

 

[BAretired]

I don't believe that Q = A_CH(d) is the correct expression on the upper sketch because the channel flange tips are below the centroid of the combined section. If the top of the beam is in compression, the channel flange tips will be in tension and vice versa.

In the second sketch, the two shapes will tend to perform almost independently, taking load more or less in proportion to their separate EI values.

BA

 

[haynewp]

I should have put "effective" instead of "equally effective".

The "d" is getting smaller the more of the channel is extending below the compound N.A. As "d" goes to zero the shear flow required to be resisted is zero. I don't know if that invalidates the shear flow the top weld is required to resist or not per that equation, I have to think about that.

In the second sketch that was posted, the bottom case would seem to me to go through the same deflection as a compound section as in the top case and I don't see the WF and channel theoretically performing independently just because of the weld location.

 

[BAretired]

I don't believe that Q = A_CH(d) is the correct expression on the upper sketch because the channel flange tips are below the centroid of the combined section.

That is incorrect! Q = A_CH(d) is the correct expression. The fact that the channel flange tips are below the centroid is irrelevant.

In the second sketch, the two shapes will tend to perform almost independently, taking load more or less in proportion to their separate EI values.

That is also incorrect! The channel and WF will act as a combined section if the thin plates can (a) carry the shear without excessive shear deformation and (b) are stiff enough to prevent the channel and WF from separating vertically.

If the channel flanges extend down and are welded to an enlarged bottom flange of the WF, Q = A_CH(d). Alternatively, Q = A_WF(d_W) where d_W is the distance from the cg of the WF to the cg of the combined section.

My earlier post was wrong and should be disregarded.

BA

 

[kylesito]

JAE - Just curious...what is the application of this? Existing structure you are retrofitting...new design...just for kicks and giggles?

By the way, you have a post on the Civil Board directed to you...not sure if you saw it.

PE, SE
Eastern United States

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[rb1957]

Q is the first moment of area of the cross-section above the section cut being analyzed.

looking at chris's sketches, I'd assume the cross-sections are fully effective and calc bending stress dist'n. from this i'd calc the change in load in the channel (per inch length). in both versions i'd expect this load to be off-set from the welds so either ...
1) the welds are transferring moment (yech) or
2) the wlds transfer axial (shear) load into the channel. now i have a different load distribution ...
a) the I-beam reacts the applied moment by bending and by transferring load into the channel, and
b) the channel reacts the load transferred from the I-beam.
to find out the proportions (how much bending, how much axial load) derive displacements and match the channel and I-beam at the weld location.

i think chris's sketches are quite different to JAE's

 

[ToadJones]

The general premise for shear flow is that the force transfer takes place at the contact surface. I understand that there is a "small gap" between the two for the second example, so the force transfer is still at the welds.
'Q' still needs to be calculated as the first moment of inertia of the cross sectional area above (or below I suppose) the combined N.A.
I think that this is analogous to shear flow, or complete lack thereof, for two beams side by side (as is say (2)2x10s) or shear flow for plates welded across the flange tips of a wideflange beam (boxing it in). There is no shear flow. The beams take load according to their EI.

 

[ToadJones]

"I think that this is analogous to shear flow, or complete lack thereof, for two beams side by side (as is say (2)2x10s) or shear flow for plates welded across the flange tips of a wideflange beam (boxing it in). There is no shear flow. The beams take load according to their EI."

I meant this for the second modified sketch where the plates were thickened. That extra material will bring the N.A.'s of the two individual parts closer together and reduce the shear flow.

 

[RWW0002]

My understanding of horizonral shear flow that is is stress introduced to prevent relative movement betwween the two parts. If the parts are indeed consitdered to act compositely (which may be a generous assumption depending on loading), and plane sections remain plane, it seems to me that the relative displacement between the two parts would be constant along the cross section of the channel(see attached sketch). The displacement would be dependant only on the location of the shear plane between parts and the section properties of the members, both of which remain constant.

If shear flow is induced in order to restrain this displacement, it would make sense to me that it would be independant of the weld location along the cross section. Therefore the calculation as presented by JAE seems correct.