Beam Reinforcement Calculation

[Nick6781]

Let's say I need to use a web plate instead of a flange cover plate (I know...) to reinforce a beam. How do I calculate the required weld to ensure the section acts compositely? The shear flow equation gives the shear along a horizontal plane, but in this case, the faying surface is vertical. I can't quite wrap my head around it.

 

[EngDM]

@BAretired is correct the definition of Q in VQ/I formula is the first moment of area above or below the shear plane being considered

This is how I've always understood it as well. You're only using the area past where you are trying to find the q value for.

 

[Celt83]

Giving it more thought VQ/I at the top and bottom of the reinforcement plates is 0, still would be curious to see the model with intermittent fasteners at the top and bottom of the plates rather than at the centroid.

 

[human909]

Giving it more thought VQ/I at the top and bottom of the reinforcement plates is 0, still would be curious to see the model with intermittent fasteners at the top and bottom of the plates rather than at the centroid.

Exactly. I have modelled it and it doesn't matter where the fasteners are located they are only transferring vertical shear. This is exactly as one would expect because there is no compound action. And no longitudinal shear demand on the fasteners. (To be pedantic if the fasteners are intermittent then you do have some extremely small longitudinal shear demand.)

Of course there is longitudinal shear flow in the plate and in the web of the beam but they are equal so there is no shear demand on longitudinal fasteners. (No shear flow between the plate and the web as I expressed earlier.)


If you have the time I would really suggest reading THIS thread.

Thread 'Welding on a Beam'

May 1, 2020

I have the below scenario: How do I resolve the force being applied to the welds given a max shear and a max moment (developed from shear-moment diagram).
The orange dots represent locations of the fillet welds. Channels are 15" deep. plate is 36" deep.

• JP20
• Replies: 111
• Forum: Structural engineering general discussion

@CANPRO argues the same point tirelessly. Against quite a few disputing including BARetired.

This post from KootK is another decent summary.

Post in thread 'Welding on a Beam'

May 4, 2020

I'm with CANPRO et al on:

1) The shear flow theory that applies (or doesn't apply) here and;

2) the value of a correct theoretical understanding even if a gross, overkill approach would do.

I'll tell my story the the long way let folks pick and choose which bits they might light to challenge.

THE TWO COMPONENTS OF COMPOSITE FLEXURAL FASTENING

3) All components of the cross section must be induced, by the fastening, to assume the same curvature along their independent axes. This is usually the low demand aspect of fastening demand.

4) Where the joining of the components would...

• KootK

 

[BAretired]

Giving it more thought VQ/I at the top and bottom of the reinforcement plates is 0, still would be curious to see the model with intermittent fasteners at the top and bottom of the plates rather than at the centroid.

VQ/I is zero at the top of the cross section, but not at the top and bottom of the plates.

 

[EngDM]

Perhaps a calculated example (not software) would clarify the difference between though processses here.

 

[human909]

VQ/I is zero at the top of the cross section, but not at the top and bottom of the plates.

View attachment 14767

I agree with this 100% this approach to the calculation IF we were trying to calculate the shear requirements of fixing that top T to the rest of the assembly. And my next step check whether that web is strong enough to transfer the shear which it is. Hence no welds required to transfer

Perhaps a calculated example (not software) would clarify the difference between though processses here.

It has been calculated. And that calculation has been denied. It has been explained in a dozen different ways using logic and that has been ignored. I've tried pointing to the other thread.

What matters here is that if in the absence of a connection there would be a discontinuity in the stress gradients. This discontinuity needs to be resolved if there was going to composite behaviour.

But in the case of members that have a common centroid there is no discontinuity in the stress gradients if they are simple 'sistered' together. stress and strain are identical. Thus there is no discontinuity.


YET ANOTHER EXAMPLE:

Consider a Square hollow section cut down its axis and calculate the shear and the weld required. Using VQ/I in the major axis we wouldn't required any weld as the resistance to bending is unchanged. The calculation unsurprisingly yields a ZERO result. Though calculate it for the minor axis and you have a completely difference result, again as expected. You'll find yourself needing to weld that cut back up to restore the strength stiffness in the minor direction.

 

[EngDM]

I agree with this 100% this approach to the calculation IF we were trying to calculate the shear requirements of fixing that top T to the rest of the assembly. And my next step check whether that web is strong enough to transfer the shear which it is. Hence no welds required to transfer


It has been calculated. And that calculation has been denied. It has been explained in a dozen different ways using logic and that has been ignored. I've tried pointing to the other thread.

What matters here is that if in the absence of a connection there would be a discontinuity in the stress gradients. This discontinuity needs to be resolved if there was going to composite behaviour.

But in the case of members that have a common centroid there is no discontinuity in the stress gradients if they are simple 'sistered' together. stress and strain are identical. Thus there is no discontinuity.


YET ANOTHER EXAMPLE:

Consider a Square hollow section cut down its axis and calculate the shear and the weld required. Using VQ/I in the major axis we wouldn't required any weld as the resistance to bending is unchanged. The calculation unsurprisingly yields a ZERO result. Though calculate it for the minor axis and you have a completely difference result, again as expected. You'll find yourself needing to weld that cut back up to restore the strength stiffness in the minor direction.

View attachment 14778

If the beam is being loaded by UDL applied to the top flange, doesn't the weld from top and bottom of the reinforcing plates need to be sized for Q, similar to how you'd do it if you were reinforcing with a T as BA drew? Otherwise how does the side plate go along for the ride if it's not designed for the stress to act compositely?

If the load were applied such that the plate and beam both got engaged, say with screws into the side (just as an example) then I'd get that they both get loaded, but otherwise how does any load make it into the plate without sizing for Q?

 

[human909]

If the beam is being loaded by UDL applied to the top flange, doesn't the weld from top and bottom of the reinforcing plates need to be sized for Q, similar to how you'd do it if you were reinforcing with a T as BA drew? Otherwise how does the side plate go along for the ride if it's not designed for the stress to act compositely?

If the load were applied such that the plate and beam both got engaged, say with screws into the side (just as an example) then I'd get that they both get loaded, but otherwise how does any load make it into the plate without sizing for Q?

Good question.

The side plate goes along for the ride by providing sufficient fixings to transfer the vertical load. This could be screw, bolts, welds, or whatever regularly spaced. Those fixing would need to be designed for the proportion of the UDL load transferred which could be calculated by the ratio of plate stiffness to I beam stiffness. It would be very low and much lower than an incorrectly applied QV/I shear calculation. The load also acts in a direction perpendicular to the shear value that is calculated by QV/I.

Otherwise how does the side plate go along for the ride if it's not designed for the stress to act compositely?

People keep talking about this member acting compositely. When it really isn't. It is acting in tandem, as though it three sistered sections, not compositely. If you doubt this just calculate the I value for the 'composite' member and the I value for the sistered member. They are identical. You are not getting composite action.


When designing for connections for a composite beam you need to allow for shear in two direction. Longitudinal and in the direction of the load (down for a normally loaded beam). QV/I is only half the story. In this case it equals zero, but the other half doesn't which I've pointed out repeatedly.

 

[BAretired]

Horizontal shear in the web and side plates must be resisted by welds top and bottom of side plates. The value of Q is shown below in two places, at the top of plates and at the neutral axis. Horizontal shear stress is VQ/It where t is the material thickness at the position under consideration. At the neutral axis, it would be the web plus side plates. That is true and cannot be dismissed by using faulty arguments.

In this case, little is gained because the side plates are only about half the depth of the beam. Much more effective would be to beef up one or both of the beam flanges, but this is the problem we were asked to address.

 

[canwesteng]

The horizontal shear at the top of the side plates is zero. The only area where shear can be anything but zero is at the corner of the side plate and existing web - but in any case this is the same amount of shear in the web as was there before the plating.

 

[BAretired]

The horizontal shear at the top of the side plates is zero. The only area where shear can be anything but zero is at the corner of the side plate and existing web - but in any case this is the same amount of shear in the web as was there before the plating.

Just above the welds, the horizontal shear is in the beam web, not the side plates. Just below the welds, shear is shared by the side plates, although there could be a bit of shear lag, so the shear stress needs to build up. I agree that Q above the welds is unchanged by the presence of side plates, but it starts to increase to a maximum at the neutral axis. Depending on the thickness of side plates, shear stress may actually decrease at the neutral axis.

 

[jhnblgr]

Wouldn’t the shear stress be concentrated and uneven with the proposed concept. Also isn’t welding that near to the flange web interface weaker the beam.

AISC recommended strengthening methods

 

[jerseyshore]

I see where BA is coming from thanks to that visual. He is looking at it based on just half the beam. So the top weld is based on the top half of the beam and the bottom weld is based on the bottom half of the beam.

But here the plates are one piece with equal amounts above and below the centroid of the whole section.

So to simplify it seems like the main discussion point is checking top half and bottom half separate vs VQ/I for the whole built-up section. Is that right?

 

[human909]

BAretired you really should be more professional in your discussion on this topic. I appreciate your engagement but I haven't appreciated your lack of respect or engagement on this topic.

Please do us all a favor and review your textbook on Strength of Materials.

That is true and cannot be dismissed by using faulty arguments.

The topic is nuanced. As I've repeatedly indicated. And when designing welds or fastenings you don't actually care about the shear flow in the area A, you care about the difference in shear flow between two areas. AKA the shear flow gradient. Or more accurate the stress/strain gradient induced by the shear flow...

If you calculate the shear flow in section A, B and C in the absence of a weld then you will find that you have identical longitudinal stresses/strains. (To do so you'll need to allocation V suitably and use different I values for A,C and B.

Thus you can throw all the weld there you want or none of the weld there and the result will be the same. There is no force flow across the boundaries between A, B and C. (If we include shear lag AND if the beam is top loaded then you can get some small difference if we want to be pedantic.)

 

[BAretired]

BAretired you really should be more professional in your discussion on this topic. I appreciate your engagement but I haven't appreciated your lack of respect or engagement on this topic.

Guilty as charged...I apologize for my unprofessional remarks.