Existing Beam - Added Shear Capacity

[PEinVA]

How do I add shear capacity to a reinforced concrete beam that looks what is shown on the attachment. I know you can use carbon-fiber on a typical rectangular beam, but I can't do it here due to existing geometry. I'd rather not add the cost of demo'ing the extra 4" overhang around the entire opening that is being infilled.

This beam is 20' long and is supported by beams on either end. The shear capacity is needed in the middle because the shear is greater than 50% of the Vc. The reinforcement is there but it is spaced at 10" oc. This does not meet the requirement of d/2 minimum spacing.

This area is getting infilled so that is why the beam does not have the required shear reinforcement, and I was wondering how we can reinforce this beam. Any suggestions? I don't have the head room to put a steel beam below this beam.

RC
All that is necessary for the triumph of evil is that good men do nothing.
Edmund Burke

 

[JAE]

RCraine -

I would normally provide expansion anchors or through-bolts at a uniform spacing to transfer 100% of the load from the concrete beam to the two channels. This would be a basic shear on the bolt per foot kind of thing.

Then at the ends, the channels must deliver the accumulated load back into the support somehow with a connection.

If the "flange" of your existing beam can successfully transfer that load via shear through the thickness of the slab, then the bolts aren't totally needed, but I'd be tempted to use them anyway.

youngstructual makes a good point to look at the relative stiffnesses of the concrete beam vs. the two channels. There are two issues here.

First, the safety/strength issue is satisfied if the two channels can indeed take 100% of the total load (ignoring the capacity of the concrete beam).

Second, if the concrete beam is much stiffer than the channels, then indeed the concrete would first take all the load until it is overstressed and begins to yield. At some point the channels, being bent right along with the beam, would begin taking load. If the beam fails first flexurally, the channels would simply deliver the needed strength as the bending progressed.

If the concrete fails in shear (which you indicate is the governing limit state) then the failure might be a bit abrupt and the channels would then immediately take the load and deflect according to their stiffness with zero stiffness supplied by the now cracked beam.

Hope this helps a bit.

 

[youngstructural]

Firstly; Ronster is quite right: The situation you have presented would be very rare indeed... Be certain your problem is what you believe it to be! You might be giving yourself head-aches for nothing. It would be much, much more common for the bending strength at the centre to be insufficient, along with the shear at the face of the supports. The reverse (in the case of shear) is something I have only seen once, and that was due to an added prop!

Assuming you are certain of your problem I think I see where you are getting confused, and I'll try to clarify the situation, as best as I understand it.

You have a concrete beam. It has a capacity (too little in shear, but only for say the middle third. Either way it is the middle you are trying to give increased shear capacity.

Although this all revolves around the same issue (P-delta) the problem can be broken into sub-parts for additional clarity. The difficulty in adding shear capacity to the centre of the beam is three fold:

1. The added section will only take load if you force it to do so. This is an issue of stiffness, and it does not matter what REACTION type (flexural, shear, axial) you are talking about, the section added must be sufficiently stiff to "pick up" the load. Thus if the section is a steel section, much less stiff than the existing section, you must fasten composite to FORCE load to transfer into the channels. The question of how often to fasten has come up in other threads and no-one has ever satisfied me, nor been able to provide design examples. Personally I fasten at varying distances for different situations, but typically d/2 minimum on a larger beam.

2. You are trying to increase the shear capacity of a section that is already sufficiently strong in bending. This means that you are dealing with a section that should not (theoretically, although you do need to check) deflect excessively, further complicating the load transfer. Again you really need to fasten composite, and I would recommend a check of double the bolting required for the shear load at any given point. As you transfer the shear load into the chanels from the concrete beam through the bolting you have a step function of shear reduction at each of those points. So where you had a ULD shear responce for the original beam, you need to superimpose your addition shear reductioin (due to point load supports where the shear capacity introduced by the bolts appears) and then remember to reverse this back into your main beam at the last bolt group (which is, in fact, the "end bearing" for your double channels. This last point is a faily uncommon, although not always avoidable, situation caused by having a beam which only requires additional capacity along a portion of the length. I often finds this is required for bending capacity or deflection, however as mentioned above, at the end of the day the reason why is irrelevant to the design and detailing of the channels: You must always deal with the total energy (load) in all of its forms (bending, shear, axial).

3. You cannot transfer load like this and only achieve one kind of load. If you transfer load into the beam to handle the shear, you must also handle the proportionate share of bending. Thus while you will size your webs for the shear force, your flanges must be sized for the corresponding bending.

Is that any more clear? If it is not, I would be pleased to walk you through a step by step analysis I have previously carried out. Would be nice to have another engineer (you would be the fourth by this point) review my procedure as, again, I have never found a published article or design recommendation for this situation.

One other point: With the transfer of the shear suddenly at the end (returning into the principle beam from the channels) you need to consider the additional deflection due to shear effects caused by this returning load if you have the connection relatively close to the support of the main beam. In any case you need to calculate the additional deflection caused by this returning load as a typical point load flexural deflection. This means that the deflection check is also now a problem of superposition.

Keep up the questions where there is a need, I'm very must enjoying the discussion and happy to help. I also hope no one comes up with a rationale contradiction to my recommendation, although appreciate the opportunity to air my design laundry!

Cheers,

YS

B.Eng (Carleton)
Working in New Zealand, thinking of my snow covered home...

 

[PEinVA]

Hey guys,
Thanks for your responses. I think the biggest issue I have is what youngstructural has covered in Items 1 and 2 of his post. Item 3 is a valid point, but how do you actually determine the force in this member?

If I attempt to frame the infill in another direction, I need to come up with pretty stiff steel beams to match stiffness of the concrete to limit differential deflection, etc, in case they want this exposed, we don't want any cracks or whatever. (At least a big concern of my boss)

Anyway, sorry also for any confusion about the stirrups in the beam. The stirrups are listed as follows: (and verified in field) 1@3, 8@6, R@10. The beam is ok in shear for the 6" stirrups, but when it goes to 10" they are pretty useless as this spacing is greater than the minimum required by code, d/2.

See attached sketch for some clarity about the framing.

RC
All that is necessary for the triumph of evil is that good men do nothing.
Edmund Burke

 

[youngstructural]

JAE: Beat me out by minutes... I was mid-post when you posted. Sorry for the overlap!

Speaking of which however, you have made a very good point: If it is only the Ultimate Limit State that is unfulfilled, who cares if the beam cracks since the load would immediately transfer to the channels!

Well thought out, however I would say that I would consider a dynamic load factor (say 1.2, similar to many crane rail codes) in addition to your live load factor to compensate for the sudden imput of the loading to the beam.

You'll keep the beam from falling down, but she'll look pretty nasty at the transition load!

As for my item 3, the added channels are a beam, with each shear load removed a point load along it... The ends where you terminate the channels and return the load to the concrete beam are thus the simple (pin) supports. So if you are trying to find the flexural demand on the channels, you are modelling a simple span with point loads (where you have the through bolting which removes load from the main concrete beam). This presumes you have forced load into the channels by jacking the beam up and installing the channels with a "precamber" which should be roughly equal to the anticipated deflection (again, stiffness issue).

Does that clarify the situation?

One quick question: You are calculating your deflections to unfactored (or otherwise appropriately factored) serviceability loads, right?

Cheers,

YS

B.Eng (Carleton)
Working in New Zealand, thinking of my snow covered home...

 

[Tomfh]

Are you sure you need to strengthen the middle of the beam?

As hokie66 said there are other ways of looking at it, e.g. a truss analogy model.

 

[PEinVA]

How do I review this as a strut and tie or truss analogy? I've never used this method, and I'm sure my boss wouldn't want to sit down with me and review it, just cause of time.

RC
All that is necessary for the triumph of evil is that good men do nothing.
Edmund Burke

 

[PEinVA]

Doesn't this only work for deep beams and corbels?

RC
All that is necessary for the triumph of evil is that good men do nothing.
Edmund Burke

 

[frv]

No.

Strut and tie models MAY be used for any situation, and MUST be used for deep beams and corbels.

In fact, there is bit of a movement within ACI to have all design provisions reflect strut and tie modeling.

 

[PEinVA]

I want to make it clear, that the beam doesn't actually fail in shear, but the shear (Vu) after the spacing of stirrups goes from 6" to 10" is greater than 1/2 of Vc. So I need to provide minimum stirrups at a minimum spacing. If they are greater than that spacing, I cannot count on them correct? Are there limits to the strut and tie method?

Any help is appreciated.
Thanks

RC

RC
All that is necessary for the triumph of evil is that good men do nothing.
Edmund Burke

 

[mh2000]

in my opinion, you could either:

1. try to justify the links as they are. a 10' link spacing in the middle of the span, where shear is at its lowest, would probably work in most cases, if you take a 'first principles' approach. This would save the time/expense of remedial work.
2. if you do not wish to take the above approach, potentially you could temporarily prop the beam either side of the zone where you want increased shear capacity, then break out the concrete in this zone, retaining the main reinforcement. Add in new links, 'scabble' the exposed ends, then re-pour the beam.

 

[youngstructural]

Destructive renovation of beams can cause a great deal of problems in my experience... I've seen it done three times, each of which the contractor damaged the principle reinforcement in some way. It's not a cheap or easy solution, but done correctly mh2000's suggestion would work.

Cheers,

YS

B.Eng (Carleton)
Working in New Zealand, thinking of my snow covered home...

 

[PEinVA]

Right now I'm comparing the relative stiffness of the L beam to the MC channel, then distributing the % of load to the steel channel and making sure I give the shear load a path. Then based on that design and maximum (worst case) load path, I will design the channel for flexure. As long as I carry it back to the part of the beam where stirrup spacing is not an issue, I should be ok.

I'm only applying the new DL + LL and I'm applying any LL from the slab/beams from the original construction to the channel. I'm leaving the rest on the concrete beam.

How's that sound?

Thanks for all your input.

RC
All that is necessary for the triumph of evil is that good men do nothing.
Edmund Burke

 

[JAE]

RC,

That sounds rational. I would suggest that since you are only "violating" the d/2 spacing requirement, then keeping it simple, conservative, and somewhat redundant (channels take all the load and beam can still take most as well), then you get your structure to a point where you as the engineer know it is safe and yet didn't spend 100 hours trying to satisfy d/2 using complex or costly solutions that are exact.

 

[JAE]

youngstructural:

Impact factor of 1.2 - sounds fine - but with channels AND concrete beam both supplementing each other would you think it might be a bit of overkill? Shear failure is abrupt, but is it really impact? But I'd have no problem with it presuming I could still get an 8" channel to work - otherwise a 10" channel might get me second guessing whether the 1.2 was too much.

Deflections: yes at service level, not factored.

 

[PEinVA]

JAE and youngstructural,
Thanks for all your responses. JAE, I definitely agree about the d/2 requirement, and I wanted to come to a simple, conservative assumption .The strut and tie method seems a bit exhaustive for this small infill job, but it was interesting to mess around with.

I did not use a factor of 1.2. I am using a MC10 on a single face and was able to get it to "absorb" about 30% of the new imposed loads. I plan on epoxying the channel to the beam to try to avoid any of those impact loads as described above. Deflections were checked at service.

Thanks for all the help.

RC
All that is necessary for the triumph of evil is that good men do nothing.
Edmund Burke

 

[hokie66]

RC,

I have been away for a while, but see that others have addressed my suggestion of using a truss analogy.

I think your approach of using a channel is appropriate, although I would probably have tried harder to justify the existing.

As to gluing your channel to the side of the concrete beam, I don't know of any precedent or standard that would support that. I would use bolts.

 

[JAE]

yes...bolts