Glu Lam failing in deflection, How to design steel plate connection

[smokiibear]

I have a glu lam beam that is failing in deflection. Our best option, I believe, is to add steel plate to the bottom of the beam.

I am unsure how to design the shear tranfer between the plate and the beam. I've used the transformed method to obtain the stress in the steel. but not sure how to convert the stress to a shear force.


Thanks for your feedback.

 

[RARWOOD]

You may want to check to see if the beam is in upside down. In general single span glulam beams are laid up, with a upward camber. When they are installed upside down the camber adds to the deflection.

 

[RockEngineer]

With the transformed area the shear you have to transfer through the connection is VQ/I for the steel.

 

[smokiibear]

Rock...does VQ/I yeild plf?

 

[RockEngineer]

V= Shear (lb)
Q= first moment of area beyond connection (in^3) Area of steel plate times distance from center of steel plate to neutral axis
I= Moment of Inertia (in^4)

Result in lb/in. This is the shear flow that must be resisted by your connection of the plate to the beam. I usually pick the maximum shear and use that connection along the entire beam to be conservative.

 

[miecz]

Seeing you've got two different materials, I believe you need to transform the area of the steel or the wood by the ratio of the elastic moduli (moduluses?) to get your I and Q.

 

[smokiibear]

Re-looking your (rock's) response, isn't VQ/I only the force per inch caused by shear?

Where I need the added steel plate is in the center of the beam, where there is "no shear" due to running load. However, i do have have force per inch due to Moment at the center of the simply supported beam.

Would I then use MYn/I to get max stress in the steel, then multiply times the Area to get the max force to transfer the plat to the beam?

n = the Es/Ec
I = transformed moment of inertia

 

[Whodapookie]

Wow, this is confusing. Smokiibear, are you trying to add a steel plate to the bottom of the beam (flat) or to the side of the beam (Vertical)? I don't understand what you are talking about with the "center of the beam".

If plate is in Vertical orientation, get a transformed moment of inertia and then calculate your stress (fb = Mc/I)
I normally "transform" the steel to wood (Es / Ew). Use the transformed I in calculating your deflection. The attachment of the steel to wood is a ratio of the amount the steel plate is carrying verses the wood beam. Remember this force is input throughout the member and must be accouted for at the end of the beam.

If you are really worried about horizontal shear in a steel plate (cough cough) use fv = 1.5*V/A compare %force in each material to their respective allowable Fv.

If you are trying to add a plate to the bottom of the beam in a flat orientation, then use simple mechanics to generate a "T" force for the steel plate and provide the proper amount of connectors to the wood to get the force back to the wood beam at the ends. (similar to using shear studs on composite steel / concrete beams).
Moment = Force*Distance ---> Force (shear) = Moment / Distance
where Moment = max beam moment
Distance = center of compression to center of tension

Notes:

1) Are you using the true or apparent "E" of the glulam beam? I would reccommend apparent and then you can ignore the shear deflection of the beam.

2) The glulam beam should be jacked to initial shape first if you want the steel plate to take any of the load.

3) I have never seen horizontal shear control for "Flitch plates" in conjunction with wood beams. I have seen it control the design of steel beams many times.

4) The devil is in the "Details"! Make sure you connect the steel plate properly to the Glulam beam or all your work will be for naught. Pay attention especially to the compression edge of the steel plate (vertical orientation).

Good luck! I hope this makes sense. If not, I'll try again.

 

[smokiibear]

Sorry for the confusion.

I have an existing building where a simple supported glu lam is barely failing in deflection. If the beam was one foot shorter, it would be okay. So, the best option was to put a steel plate on the bottom of the beam (horizontally, not vertically). However, as all can see, I wasn't sure how to design the plate and its connections. Also, the beam has running loads and no point loads.

My opinion: The beam is failing in deflection in the middle of the beam, not at the supports. So, I need to provide added support from the steel plate to the center of the beam. I do not know how far from the center the plate should extend...so I was going to be conservative and apply it to 14' of the 16' beam. I aslo didn't know how to connect the plate to the beam.

I believe the first thing i do is find the transformed area, find the nuetral axis, and the transformed moment of inertia.

I then calculate the moment of inertia that is required to limit deflection:

5wL^4/(584EI)<L/360

This is how I find the size of the steel plate.

At this point, I do not know how to find the force at the connection of the plate to the beam.

Rock suggested using VQ/I, but at the center of the beam, where the deflection is the maximum, shear is zero. So there is no shear force betweeen the plate and the beam due to shear at the center.

However, if i use Mcn/I, this would provide me the strees in the steel plate at distance c. However, I do not know how to resolve a force from this strees. Do I just take the stress and multiply by the width of the plate to get a pounds/inch?

Should I be taking the maximum shear in the beam (at the supports) and use that for the VQ/I, even though it is not that shear force causing the beam to deflect in the middle?

Is my understanding of mechanics pretty messed up?

I've spent a lot of time going through books, but I don't think I have a good resource for strength of materials.

Anyhow...thanks for everyone's interest and help.

 

[miecz]

True that the shear at the mid span is zero for a uniform load. However, you said you plan to extend the beam 14 feet of the 16 foot span. The shear at the end of the plate is the V in the VQ/I formula.

 

[smokiibear]

jmiec...would I be desinging for the deflection at the center of the beam from shear incured 2' from the end, and thus use the VQ/I?

 

[miecz]

Yes. You are going to use an increased moment of inertia for the 14 foot zone, so you need to be able to transfer the shear at any point in that zone. The shear is maximum at the end of the reinforcing plate, so that's the "V".

Curiously, this would seem to be the way one would handle shear studs in composite beams. But it's not. Honestly, I forget why not.

 

[smokiibear]

maybe i should be asing the question...how far do i need to extend the plate from center to limit deflecton. as i described above, i only solved for mimimum moment of inertia, not length of plate needed?

if i could use a shorter plate, v would be smaller, and connections would be fewer.

 

[Whodapookie]

...and deflection would be greater.

 

[smokiibear]

it seems like my point is getting missed?

Can I possibly build up just the center beam section with the plate...without have to build up the section for the entire length, and still minimize deflection...or am i mistaken?

 

[miecz]

You can reduce your deflection by reinforcing a section of the beam. As you say, V would be smaller, and the required connections would be fewer.

The problem is, the calculation of the resulting deflection is not easy, as you now have a beam with a variable moment of inertia. It's too long a solution to present here, and I know of no reference that provides the solution.

If you do find a solution that gives a theoretical cut-off point, you may need to extend your reinforcing plate (and connections) beyond that point so as to develop the plate.

 

[CJJS]

You could use a finite element software and model the beam with three different segments. The two segments at each end would be the original beam. The center section would be the composite beam (beam with steel attached). I would make sure the connection between the segments are rigid. This model, with the appropriate material characteristics of each member should give you an accurate deflection under the load.
As far as the shear connection goes, I would design for the shear at the termination point of the steel. You could conservatively use that value along the 14 ft. length of the steel.

 

[smokiibear]

that's a good point.

 

[bjb]

You might be able to use the moment-area method to either calculate deflections or at least check any computer model you make.

In Design of Welded Structures by Omer Bodgett there is an example where an estimated deflection of a tapered steel beam (variable moment of inertia)is calculated. I know that you're not dealing with a pure steel beam, but the basic approach would probably be applicable. If you have this book look at page 2.5-11. If you don't have this book I highly recommend it despite its age. As I remember when I bought it the price was very reasonable.