Steel beam strengthening 1

[xxpegasus11]

I am looking to strengthen an existing I section steel beam 10m long to carry a new additional load. Welding is not an option and the top of the flange is also inaccessible. Also depth that can be added below bottom flange is limited.
My thinking at the moment is for a C section bolted to underside of bottom flange, with C section flanges upright and work on increased z for increased moment needed, curtailing past point of reinfoncement required. Bolting worked out on shear flow etc. Any comments or points to be considered appreciated.
Builder suggests bolting two c sections, either side of web, at centre. My theory must be rusty and its been a while since i dealt with a lot of steel connections and I guess I keep thinking back to flanges carrying moments and webs carrying shear. The way I see it is that no shear flow at centre of web, so how is the composite action made?

 

[COEngineeer]

Is this flushed beam or dropped? I agree w/ u. Adding C on both sides wouldnt do the justice if you put the bolt it in the middle of the web. You are making it worse by addding dead load and reduce I due to the bolt holes. If you do use 2 C, you must use top and bottom bolts on the web. But his is out of my league. Got to be pretty complicated calc shear flow.


I got an idea! Add a column!

 

[xxpegasus11]

It supports a timber joist construction floor, not accessible, hence also why no welding. Column would have been nice but not possible

 

[youngstructural]

Unless I'm mistaken, with your contractor's suggestion there still is shear flow. In fact, there would be more shear flow. The amount of shear flow is proportional to the area above the fastening location. Remember your formulae for shear flow are V = VQ/I and Tau = VQ/It where the first is in terms of shear force and the second in terms of shear stress. Since your Q is the moment of area for the section above the fastening loaction, the resultant is higher the lower you fasten to make composite.

I asked a very similar question a few weeks ago, wondering about flitch beams. In the case of a flitch beam (vertical plies of varying materials fastening together, traditionally Wood-Steel-Wood), you do not require composite action because each of the materials must deflect with it's neighbour, as they are all loaded together. In your case you must acheive a composite section, since the Channels will not be receiving load directly, but rather through the fastening into the beam.

It's too bad you cannot weld. My favorite solution in these situations is to have reinforcing bars welded into the "nook" between the flange and web of a beam. Very clean, neat little solution, and so long as you're dealing with a well protected location, you can just calculate out the required stitch welding based on shear flow.

Have a read through my question and the answers it attracted:

http://www.eng-tips.com/viewthread.cfm?qid=167508&page=3

Bear in mind that this is a discussion of a flitch beam, not specifically your situation, which I believe to be distinct.

I would love for a more senior member to read through my post and back me up. I don't suppose JAE, UcfSE or SlideRuleEra are around?

Hope that helps,

YS

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

 

[youngstructural]

I totally forgot to list you COEng, hope that you're still willing to have a read through my thoughts and comment. It would be greatly appreciated!

As long as I haven't trip over some theory somewhere, I think that's sound...

Thanks,

YS

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

 

[JStephen]

Bolting a piece on to the bottom and calculating bending as a single piece assumes the bolting is adequate to prevent any relative movement at all. If this is not the case, the channel will be carrying very little of the load and the original section will carry most of it- and in that case, the channels on the sides might be better.

 

[xxpegasus11]

Young, thanks for the thread - I had in fact looked at it but didnt get all the answers there. Yes, there is ofcourse vertical shear in the web at centre which is in fact tmax based on the formula. And also, horizontal shear which can be calculated. I dont see the interface mechanism with the C section however for composite action.

For flitch beams, I agree. I design a lot of flitch beams. If wood/steel plate/wood I share the load based on EI of steel/wood and check each separately. Although I do take worst case on each member based on least favourable E. Plate is made a little shorter and I design bolts to transfer load to steel in span and back to timber at bearings.

 

[UcfSE]

Bolting channels to both sides of the center of the web would be an inefficient way to go. You wouldn't get much help for the amount of material you would be adding.

I had a situation recently where I could only add to the bottom flange and had only 3 inches to do it in. I ended up specifying a thick plate sized to meet the strength and deflection requirements needed.

You could try the same and see what you come up with. The shear flow calculation would be more straight forward this way. The hard part would be getting holes for bolts in the existing beam. Since you can't weld the other hard part would be getting a single continuous piece in place, but then you'll have that issue no matter what. You can try a tube also. That will have a little more area to help with your increase section properties. If you have room you can try attaching a WT shape to the bottom flange, stem up, or a smaller wide flange. That would use the added material more efficiently but if you have any reversal in load or uplift it could complicate your buckling analysis.

 

[xxpegasus11]

UcfSE - I agree- channels at centre is not very efficient way. Bottom piece could be cut off past point its needed and your suggestions are all possible options to be looked at. Theres no reversal of load or uplift so that helps.

JStephen has a point about bolting in clearance holes. I guess this makes HSFG bolts necessary no matter what?

I still not sure about the connection of the channels at centre. How would you go about the calculation for this?

 

[youngstructural]

Good points... Interesting to think about, but I'm still curious about the theory behind fastening channels to the flange, even if it is a poor (read: inefficient) way to go. There could be a situation that demands it, and I would hate to let the issue go without having it clear in my mind.

Have I outlined the procedure correctly above? Or does someone have another take...

And please don't just point out that it's inefficient. I get it, better is possible here, but might not be possible elsewhere.

Nice solution, by the way, UcfSE...

Regards all,

YS

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

 

[xxpegasus11]

Young,

I see no problem with your welding bars - doesnt apply to my case but its a solution all the same.
Bolting channel to bottom flange - again I dont see why that should be a problem. I see it similar to a crane girder, for example - albeit inverted. Slip in bolts as mentioned above maybe a factor.
Unless someone else can throw some more light on bolting channels at centre and either side of web however I cant see how that works. If i was supporting some cross members for example, and bolted a channel on the web for them to seat on I would just treat it as vertical load on the web. Dont see how that would increase z of the main beam. COeng I think stated the same.

 

[WillisV]

Adding channels to both sides of the beam web WOULD be beneficial, however (sorry but I must say it) very inefficient.

If the channels are bolted at the exact neutral axis of the beam the shear flow will be...0. Nadda. Shear flow is calculated based on the first moment of the CONNECTED part. Q for the channels about the neutral axis in this case is zero. Young is correct in saying that shear flow would be maximum at towards the middle of the wide flange -if you were trying to weld the wide flange together at that point. But if you are just slapping channels on the sides that is not the case.

This is really a question of deformation compatibility. If you assume that the channel and wide flange must deform together to pick up the load, then you can calculate a "composite" moment of intertia for the beam plus channel system. Add the load and see what the deflections of the system are. Once you know the deflections of the system together - then you know the deflections of the channels themselves (hence the compatibility term of deformation compatibility ;-).

Once you know the deflection of the channels you can calculate the load (shear) and moment that must be introduced into them using (for a simple uniformly loaded case) Delta=5wl^4/384EI - where delta is the deformation between the end and center of the channels, l is the length of the channel, E is known, and I of the channels is known - the only missing term is w which can therefore be back-calculated. Once w on the channels is known the bolts can be sized to transmit that w, and the channel moment capacity can be checked for M=wl^2/8.

 

[rb1957]

shear flow between the reinforcement and the existing I-beam is a critical piece of the design. it should be easy enough to calculate the flexural shear flow across the interface.

i'd start with a plate. as UcfSE pointed out, you'll probably have issues with the size of part that you can maneouvre around the site. with a plate i can calc ebnding stresses. then the flexural shear (q=VQ/It). i'd put in as tight a fit bolts as i can manage, 'cause you don't want any relative motion. maybe drilling holes in the I-beam flange isn't that big a problem; start the holes in the plate, copy them onto the I-beam flange, lick of paint.

if a straigght forward plate doesn't do it for you , you could add flanges (making the plate a C channel, flanged upwards). maybe you could use CSK bolts, to increase the plate thickness. both increase the shear flow.

you're also right about extending this someways beyond the section that needs reinforcing. i'd go beyond where the I-beam is critical ... you know the section of the I-beam is down on strength. you could, if you wanted to get fancy, use a couple of plates ... one long one and a shorter one doubling up at the critical section.

i guess you're adding a new load into this I-beam. do you need to add stiffeners on the beam web, to help shear the load into the I-beam ?

 

[COEngineeer]

I still think adding 2 C on both sides with 2 rows of bolts will work(all the way on the top and bottom of web).

 

[jike]

Two channels with two rows of bolts or plug welds should work. This is not normally my first choice as others have stated, it is not as efficient as other options. Often my first choice is to add a single(upside down)tee to the bottom flange. The tee reinforcement sometimes will not work because of headroom requirements. Second choice would be to try to balance out the reinforcement on the top and bottom flanges with plates or rods.

 

[UcfSE]

You can try adding channels if you want. You have all the loads to do so. I would put them as far from the existing neutral axis as you can. At least that will help more. It all come down to the loads you have. We can say channels are inefficient all day long, but we don't know if your beam only needs a little help or a lot. If you need to double your moment of inertia, channels probably won't do it. If you need 10% more moment of inertia or section modulus, well maybe they'll do. You just have to check and see.

I wouldn't want to add a channel to the bottom of the bottom flange with the legs up. That would leave a gap for your bolts to cross. I think you could have some issues with getting the bolts not to slip or bend/tilt across that gap.

 

[ntpe]

One thing to consider; when reinforcing an existing beam, you need to account for the stress in the beam before reinforcing. If the dead load is not removed before reinforcing, than it won't be transfered to the reinforcement. The best eay to reinforce an existing beam is to jack the member up and support it while the reinforcement is being added. If that is not possible, than assume that the capacity of the origional shape of built-up section is reduced by whatever the stress was prior to the addition of the reinf.

 

[lkjh345]

Maybe a crazy idea:

Any chance you could create a kingpost truss with tendon(s)? You would need to have some way to resolve the thrusts at each end, and you would need to have a way to preload the tendon(s).

Might be a way more expensive idea that the situation calls for, but just throwing it out as a theoretical solution.

 

[xxpegasus11]

Thanks everyone for all the feedback.
I think everyone agrees that welding a T, or failing that plates etc is most efficient, and the theory and shear flow etc is quite clear. I dont have much headroom to play with, and probably no welding, so I ll have to go with something bolted, but principle is same.
Ucfse -your points agreed -not sure I undersand the bolt gap or I didnt describe it adequately before. Channel would be wider that bottom flange,i.e. bolting inside channel web to outside flange surface.
We are rechecking loading and will have to see if channels to side of web make up the strength needed. ll have to see if channels work.
Willis - yes i agree this becomes a load sharing issue basically on EI of the parts connected.
Thnks all for your input - good to discuss the various options

 

[jec67]

Regarding bolting of Channels on each side of the web: The bolts will need to transfer the proportional amount of total load that will be carried by each channel. For instance, if the channels will assume 40% of the total load, then the bolts need to be sized to transfer 40% of the total load out of the web of the I section and into the channels.

the amount of load that will be transferred into the channels can be determined as follows:

% load in channels = (monemt of inertia of channels)/(moment of inertia of combined section)

as the deflections in the channels must equal the deflection of the combined section.

One additional note: the bolts will need to be slip critical, to ensuer composite action is obtained without deflections having to occur to engage the bolts.