Combing 2x8 Sawn Lumber with 1.75"x7.25" LVL Member

[echobs]

Hi all,

I am wondering what the best process is to determine the strength of combined section with different properties.

I currently have an existing building with 2x8 SPF No. 2 joists at 1'-4" o.c. … This existing building is very under designed and I need to reinforce these joists with something else.

Adding another 2x8 SPF No. 2 joist won't work here, so I would like to reinforce these joists with 1.75"x7.25" LVL joists. This way I can keep the same height for the ceiling.

My current moment on these joists is 2600 lb-ft. (15.125 feet span w/ DL = 34 PLF and LL = 54 PLF)
I am thinking maybe taking the average value of F'b for both the SPF and LVL and figuring out the combined Sx section of the combined section, however this process doesn't seem correct to me.

I'm not exactly sure the process on combining to members with different sections is, but any input would be fantastic.

Thanks in advance.

 

[dik]

If connected, the loading would be shared based on the EI values... assuming they would be sharing the load combined...

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[skeletron]

I would be inclined to estimate it by finding how much over capacity the stiffest member becomes by taking all the load. Design the nailing to transfer enough of this load to the second member. Then repeat vice versa and your solution should be in those bounds. If your area is wide enough, the redundancy should be acceptable.

Could check this answer by assuming 50-50 split of the load, although it would be more likely a relationship based on their stiffness values.

 

[dik]

a little more conservative, but would work well... and I would attach the two, using glue (LePage's PL Premium or something of that ilk) and nails...

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[phamENG]

I also vote stiffness values.

Don't forget, though, that your existing is already carrying all of the dead load and has already deflected that amount. So it skews your values a little. And if it is as underdesigned as you say, then its probably already deflecting quite a bit and installing the new joist may be tough. You may want to consider installing a shallower LVL to give the contractor room to work within the existing deflected shape of the floor.

 

[dik]

that's why I suggested EI...

Don't forget, though, that your existing is already carrying all of the dead load and has already deflected that amount. So it skews your values a little.

That's why I really like limit states...

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[XR250]

Your moment is actually 3,350 ft-lbs. With those loads, deflection will be your challenge - even with the LVL. Might have to sister with multiple LVL's or a steel channel.

EDIT - sorry, just noticed PLF not PSF - so you are correct.

 

[BridgeSmith]

If you can match the E*I for the joists, you should be able to calculate the stresses on the combined section. The 2x8's are presumably the same depth, or slightly deeper, than the LVL, and presumably have a lower allowable stress, so they would control the bending moment limit.

It you can't get the E*I close between the 2, you'd probably need to do some kind of a strain-based approach, e.g. calculate the loads on each joist at the same deflection and design for the one with the lower capacity vs. demand. I believe a shortcut to this would be to compare f*S / E*I.

This assumes the new LVL joists are 'sistered' to the existing joists, or the subfloor is very stiff. If the LVLs are placed out in between the existing ones, and the subfloor is fairly flexible, you could gain a slight advantage in capacity by considering the amount of differential deflection between the joists allowed by the subfloor, but that would be very complicated, and I expect the gains would be very small unless the subfloor is far more flexible than typical.

Edit: Now that I've read the other responses, there's one more assumption I should mention - that the LVL or the floor is jacked up so that the ends of the new joists are tight to the subfloor at the ends. Otherwise, as was mentioned, you're starting with locked-in stress in the existing joists, which would have to be subtracted from the capacity of those joists when calculating the capacity of the combined system.

Rod Smith, P.E., The artist formerly known as HotRod10

 

[echobs]

I went with the E*I method.

I determined the load required for the LVL and the 2x8 joist to deflect the same using the deflection equation. 5wl^4/384EI
Doing so I come up with the following relationship ->

W LVL /EI = W2x8/EI = WLVL / 111,140,000 = W2x8 / 66682000
WLVL=1.667W2x8 telling me that the LVL = 1.667 2x8s
Therefore the total section is 1.667 2x8 + 1 2x8 = 2.667 2x8s

I am able to run the rest of my calculations from here.

Thanks for all your help.

-Eric