Steel Plate to increase Concrete Beam Capacity 2

[youngstructural]

Hello All;

I'm looking at adding a steel plate to the underside of an existing concrete beam. I've done this before, and am pretty sure I know what to do, but have not liked the numbers I'm getting...

I want to add a 25mm thick plate to the underside of a 250 wide, 430 deep section spanning 10m. The shear load is 98 kN. My calculations using VQ/It show that the horizontal shear is around 0.6 kN when fastening at 250 crs..... Thi is quite surprising and I'm worried I've done someting rong...

What you do you all think,
Thanks in advace!

Cheers,

YS

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

 

[miecz]

It would help to have more information, i.e., plate width, tensile reinforcing area, concrete compressive strength, and what are you getting for t, Q and I?

 

[hokie66]

YS,

I'm not sure how you arrived at that number, which is obviously low, and I won't try to calculate the horizontal shear in your case without knowing more, but some things to consider:

How wide is the plate? If the full width of the beam, the beam may be overreinforced. But maybe not if it has a flange.

Shear flow is VQ/I, which will give you a force in kN/m or N/mm. The t in your equation is for calculating shear stress across a width, but that would not be applicable in determining bolt forces. If you used the width of the plate as t, then there is your answer.

I would worry about using such a thick plate, as irregularity in the beam soffit may make installing the plate in uniform contact problematic.

 

[youngstructural]

Okay, so I've made a small error in the formula I presented to you all... I should have said I was using

Tau = VQ(Delta X)/I

where V = Maximum shear at any point where I am adding plate
Q = Area of added plate times distance between centroid of plate and the composite section neutral axis (1st moment of area)
Delta X = Distance between fasteners
I = Composite section moment of inertial (second moment of area)

Where I am getting lost is the first moment of area calculation (Q); I know that I need to consider the ratio of Esteel/Econcrete and use the transformed section when calculating the composite section neutral axis, but do I use this again when calculating the first moment of area?

Oh, and although it has been a while, I have done this before... So I'm a little embarrassed, but not above putting my hand up for a bit of help! *smiles*

Hokie: Good point, and I do address this with my detailing. Not a worry; I'm just getting befuddled by a calculation I've done dozens of times. Can't see the forest for the trees and really need some logging assistance...

Cheers all,
Thanks for the replies,

YS

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

 

[hokie66]

YS,

Yes, you would use the transformed plate width in calculating Q and I.

You also have to provide enough connectors to develop the plate in tension on each side of the maximum moment.

 

[Tomfh]

Each fastener's capacity must exceed:

p * V * s / d

p = proportion of tensile bending force carried by plate
V = shear force
s = fastener spacing
d = beam depth

You need to factor according to your code of course.

As a side note, how do you make sure the plate doesn't slip at all?

 

[youngstructural]

Hokie: Was pretty sure that was the case, and that is what I have done, but the result is such a small load I'm still quite nervous. I'm going to have to review a few of my old jobs, as well as take a magnifying glass to my maths.

I really wanted to confirm my procedure prior to carrying forward. As with all jobs, there will be a comprehensive QA/Verification internally prior to construction... But I prefer to make sure my procedure is correct whenever I am designing, and minize/prevent any errors in my work.

Tomf: Where does that formula come from? I mean, I can see some logic in it, but would really like a reference. Any chance this is available in a design procedure or textbook?

Do I need to satisfy both of these formulae? Is this another one of those cases like composite steel beam/concrete floor design where VQ/I is not the force required at the welded studs?

Still not 100% sorted; Maybe I need to step back and work on a few other problems before taking another look at this. Really frustrating and making me feel a wee bit inadequate!

Thanks again for the support,
Looking forward to your replies,

YS

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

 

[hokie66]

Yes, it is composite design. I think your connectors will be governed by developing the tension in the plate.

Tom's question about slip is a good one. Use plate as template, install drive fit bolts? Sounds like a lot of trouble to me. Would providing channels each side be a better solution?

 

[youngstructural]

Channels on both sides would need to take the whole load on their own, given the relatively shallow depth of the beam involved. Also, I typically find you need a lot less steel, and only a moderately greater amount of fastening, given the effective depth to the new plate when you install the plate beneath the sofit. You can also pack the plate away from the existing beam using grout between the existing soffit and the new plate if needed. Shear becomes a concern near the far supports, however that's a wholly different problem...

Actually I have previously used drive fit bolts, or alternatively I have used an oversized hole with epoxied bolting, with the gap around the hole being filled with epoxy, or dry packed grout. My preference is for drive fit bolting, or Hilti HSL-3-M_ bolts through 0.5mm oversized holes in the steel plate. I have the contractor jack the beam up for an amount equal to the calculated dead load deflection and install the plate in the jacked position. When the jacks are removed, the plate takes the tension and the beam typically hardly drops at all. I did one job with an existing beam that I needed to jacket the full length (deflection controlled, but only just) and the beam did not deflect back down appreciably when the props were removed (read: deflection could be detected as a few millimeters, but was not noticeable). Normally the beam does deflect back down, but never as much as you would expect.

One further point: Given that the beam must not be over reinforced, you'd be surprised how little additional steel is needed to increase the strength of the beam. The exception to the rule (as is the case for this one I am currently doing) is when you're removing a column, where the tension steel does not continue through the columnn being removed.

Eventually I'm certain I'll have to get the contractor to run a diamond blade through the existing beam in order to ensure that the resulting section is not over reinforced; I have just been lucky enough not to require it yet.

Thanks again,

YS

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

 

[youngstructural]

Okay, So I have found the issue, and feel COMPLETELY embarassed!

Watch: Tau = VQ/I = kN·mm^3/mm^4 = kN/mm

So my 0.6 kN at 250 centres is actually 0.6 kN/mm, which works out to be approx 45kN per anchor. I think you'll agree that is a much more realistic number!

Thanks again,

YS

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

 

[hokie66]

Yep, 10^3 sometimes can get you. But let me get this straight. .6kN/mm x 250 mm = 150 kN, so you are using 45 kN as a working load? Then, assuming the load is uniform, you have about 900 kN working force on the plate?

 

[PEinVA]

Have you thought of carbon fibre for added flexural capacity?

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

 

[ali07]

Check if this could help, although it gives procedure for slab but you can workout for beams:

 

[StructLin]

YS,

I have calculated the shear force for you based on 250mm center. My result is 57.1 kN at 250mm center. Please see attached pdf file see if there is any mistake.

 

[youngstructural]

Thank you all for your posts and advice...

Just a few points:

- Hokie: Close, but I'm not looking to get my numbers confirmed in any case. We'll do that in house, and the geometry as well as loading has changed twice since I started this thread. I really wanted to be confident in my procedure... You have given a great deal of assistance on this one, and I appreciate it very much. A star for your help!

- I don't believe carbon fibre would be economical; I an doing only one beam, in a fairly remote location, and FPR is all about experienced contractors and economy of scale. I can't imagine having to get contractors trained up, or worse specifically brought in, for a single beam.

- Ali07's link is a fantastic resource, with a good design example at the end. A star for you.

- StructLin: As I said for Hokie, the geometry has changed. There has been a 100mm packing added between the beam soffit and the plate, and further our Es/Ec ratios differ. This is likely due to the code, but just for your information I get 9.71.

Thanks again everyone,
Looking forward to the next one,

YS

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