Deflection Calculation of Flitch Beam 1

[Lake06]

I am designing a flitch beam consisting of two wood members and a steel plate. One wood member on each side of the plate. The beam is a composite member. I have determined the percentage of load contributing to the plate and wood. How do I calculate the deflection?

Is it correct to use the calculated percentage of load for the steel and wood independently to calculate the deflection? Calculate the deflection based on their respective E and I^4. Add the two deflections together to achieve the total deflection?

 

[Agent666]

No they are constrained to the same deflection if they are composite and sharing the load and placed so the plate is central horizontally and vertically on the timber, so definitely don't add the deflections together.

Work out the properties in one material (i.e. second moment of area) using the conversion of one to the other using their modular ratio (ratio of youngs moduli). Then work out the deflection like you would normally under the total load and added I's with the E of the material you are working in/converted to. If you've worked out the load distribution you've already sort of done the relative stiffness of one with respect to the other. To confirm you have it right you can apply your percentage of load to each material, and you should end up with the same deflection.

Keep in mind you need to allow for longer term effects in the timber (creep), i.e. modify the E by whatever this factor is.

At the strength limit state you also need to determine which of the two material is the limiting one, one will achieve its full strength at failure, but the other only come percentage based on the mechanics and assumptions around being under the same strain due to being composite.

 

[CANPRO]

When you proportioned the load each material is supporting, did you not do this based on a ratio of their stiffness (EI)? The load is split based on the fact that both materials deflect equally as noted by Agent666. You can take the procedure outlined to by Agent666 to get the answer - that is the correct way to solve for deflection. But, you should also take the stiffness of each material and the load supported by each material and calculate the deflection that way as well - if you split the load correctly you should get the exact same deflection with all three methods (stiffness of steel with just the steel load, stiffness of wood with just the wood load, and the combined stiffness with total load)

 

[Settingsun]

You won't use I^4 in this calculation. It's just E*I.

 

[Lake06]

Thank you for the insight, this makes sense to me now. When I proportioned the loads and calculated the deflections of the two different member properties independently they came out with the same deflection values.

When you are speaking of creep, are you referring to section 3.5.2 of the NDS with applying the 1.5 factor to the deadload? When should you be adjusting the value of E? Besides using E’.

Also, is there any good references on designing a flitch beam? I was wondering if there is a percentage you should be trying to obtain.

 

[Agent666]

Not familiar with NDS, but every code has a different way of doing it. For a composite section the only way is to factor down E or use a long term E if that's the way your code deals with it and then proportion the load if one of the elements is subject to creep, and the other isn't. The timber will still creep, and shed load to the steel plate over time until it reaches the long term equilibrium state. So you might need to look at the ultimate load being applied with long and short term as the loading percentages will differ obviously depending on when the ultimate load is applied. Least that's what I do.

There was a few freely available articles I found in Structure Magazine when I was researching this a while back.

My own timber code has a factor of 2 applied to calculate the long term deflection for example. Depending on the relative stiffnesses you start with it can alter the percentages of load carried by steel and timber by a reasonable margin.

Another important aspect to consider is how the load is applied, usually this is to the timber, so any fixing between the plies needs to transfer the portion of the load carried by the steel into the steel along the lemgth, then transfer the load in the steel back out of the steel at the ends (generally this means more concentration of fixings at the ends).

 

[Agent666]

On your last question, the percentages of load sharing doesn't really matter as long as it works for strength and deflections.

Take a look at this which I found helpful a while back.

 

[CANPRO]

I think the percentage of load sharing is still relevant. It should factor in when you size the fasteners between the steel and wood - especially in that design example where the steel plates are only partial length.

 

[Agent666]

What I meant was you don't need to necessarily be aiming for a particular percentage. There is no correct value so to speak as long as the numbers work out (including connections as you note).

 

[trackman417]

This is mainly for time savings. I would assume only the steel plate resists deflection(and forget about the contribution of wood).

If the steel itself passes deflection requirements, the steel and wood will pass indefinitely.

 

[Agent666]

That's true, I used to just do this, and this is fine for the absolute maximums possible. But I went away from this as often depending on what the beam is supporting you want to know the longer term creep component in isolation to ensure that the movement is ok for say a brittle claddings or glazing in going from short term instantaneous self load being applied immediately after construction (no relative movement experienced by the claddings), to the longer term deflection with this load being applied for several years causing creep. This extra incremental movement is what can cause distress in brittle claddings or glazing if the deflections are fairly high, and you might want to demonstrate say a span/600 deflection under the longer term component.

Depending on the percentages you can get a reasonable benefit though from using the wood as well as a composite member and its not that hard to work out correctly.

The way I see it to correctly allow for the connections to get the wood/steel plies working together and to work out the relative strengths of timber/steel at the strength limit state and which one governs, then you need to work out the percentages anyway for this. Then doing the deflections after this point is but a simple followup check (if the loading is simple at least).