Timber Mat Design/Shear

[CE520]

To All,

I am working on designing a false work/jacking system to support a multi-span steel bridge. The support system is so the replacement of the substructure pier may take place.

I have received my calculation package back from a state reviewing agency. See attached sheet.
The two main comments i am trying to understand/modify are:
1.) shear check must be done on the timber mat
2.) Only 3 out of the 5 timbers are being used but all timbers are being considered for distribution.
*Note* - All mats are to be placed on the ground, so full bearing occurs. The mats have 2 7/8" dia rods running through the timbers that have been impacted tight.

My comments on concern #1.

I do not feel shear plays any real control of the mat design. I feel the moment and the crushing the under mat control. The moment, I believe is the bigger of the concerns as if the mat becomes longer the moment will increase towards the ends. Thus forcing me to increase my plate size and/or increase my timber size.
Also with this point is, I am not sure exactly how to check the shear on this mat. I view the crushing check as my shear check.
Any help on this would be greatly appreciated.

My comments on concern #2

I feel that with the rods running through the mats they help force the load over the entire mat and not just the timbers that are loaded under the plate. Thus giving myself a larger distribution area. I am unable to show "correctly" this theory.
I understand possible solutions are to increase my distribution plate size or place a second layer of mats the full width of the bottom mat.
I am not looking to set this precedent of using a larger plate or second mat if i can avoid this.
Any help would be greatly appreciated.

I have check in NDS and AWC references, cannot find what i am looking for.

 

[dhengr]

CE520:
You have kinda a crazy problem here with your mat, and the plan checker was right to question you on it. There are 6 - 8x8x4' long timbers, not five of them, to make up the 4'x4' mat, right? In the long direction of the 8x8's, I would check the shear at d/2 beyond the steel plate, much like you would on a conc. footing, and that should probably be no problem, but I haven’t checked any of the math. In the other direction, across the timbers, the only thing that distributes loads out to the outer two plus timbers (one plus on each side) are the two tie-rods, and I suspect they really aren’t “2 7/8"” rods (rather 2 - 7/8" dia. rods), are they? The two rods act in bearing on the hole in the wood to apply the whole load to that timber. And, that would be a problem in really bringing those outer timbers into play, in soil bearing. Also, 6,000lb. soil bearing is really pretty good soil. Why not put three more 8x8x4' timbers under your 1.5" stl. plate and perpendicular to the bottom layer of timbers? Then you should have no issues. Do make a quick check of the steel pl. w.r.t. the 99k and the base area of the jack, for bending and crushing immediately under the jack base, making some effort to justify that. Compression perpendicular to the grain is not the same as shear. And, on wood members horiz. shear is what you really want to be checking.

 

[RHTPE]

I'm not sure that I agree with your approach.

The wood is strongest in one direction only. While your timbers may be clamped together with (2) 7/8" threaded rods, I doubt that the holes are 7/8" diameter, so bearing against the rod does not make the side-by-side timbers behave as if they were one member. While the friction between the timbers developed by the clamping force helps, it is impossible to quantify and may vary over time depending on the moisture content and condition of the wood.

You use a CD value of 1.25. which I feel is not applicable. You say this is for temporary support of a bridge superstructure so that the substructure can be replaced. The 2005 NDS, Appendix B, allows a CD value of 1.25 for a 7 day duration. In your case I doubt that the pier can be removed and replace in 7 days, so I would use a more conservative value - say 1.15 (2 month duration) or 1.00 (normal duration).

You have a beam bearing on an elastic continuous support, so I question the validity of using M = 0.5wl^2 to determine maximum bending moment at the edge of the plate and assuming no greater bending stress between the edges of the plate. Lets assume for a moment that this gives the worst-case bending:

tributary width = 12"
bearing load applied to soil = 42.92 psi
w = 12 * 42.92 = 515 #/in.
L = 24
M = 0.5wl^2 = 0.5 * 0.515 * 24 * 24 = 148 in-kip37.08
S = bd^2/6 = (12 * 8 * 8) / 6 = 128 in^3
fb = M / S = 148 / 128 = 1.156 ksi

Obviously this disagrees with your value, but I assumed L is from center of load to edge of mat for the first run.

So, if consider the steel plate to be inflexible (a lie), L becomes 12". Doing the math again I get fb = 0.29 ksi, which is pretty close to your number, BUT:

- The plate is not inflexible and will deflect, adding to the bending stress experienced by the timber.
- Your bearing load is the average over the entire mat area but your bending stress does not does not account for the bearing load applied outside of the footprint of the steel plate.

To be conservative and a bit more realistic, I would add a layer of (3) timbers on top of and running perpendicular to those in the 4' x 4' mat and bear the 24" square plate on top of those.

Ralph
Structures Consulting
Northeast USA

 

[oldrunner]

I haven't designed a set of mats in a number of years, but I remember that we had more than 2 rods holding the timbers together. We also used split rings to assist in allowing the whole of the mat to work as one unit. Maybe the spacing of the rods are about 4' on center. Used them to roll a 500 ton reactor from a barge on Lake Michigan up a hill to a storage area. Think the mats were 20 feet x 4 feet.

 

[CE520]

I thank you for all your responses. I feel I do need to clear some things up.
It was supposed to be - 3 of 6 mats.
Yes it is 2- 7/8" diameter rods - The holes they are drilled in are ~1 1/8" dia. The rods are placed on 2' centers

RHTPE - I think your explanation of the mats using the friction and the moisture comment, is very good, it is something i will have to take note on for the future.
Also thank you for the catch on CD, you are correct that i should reduce that to 1.15 or 1.

dhenger - yes 6 ksf is a large bearing pressure but I have been given permission to go up to 6.5 ksf at this location. Some other locations on this job, I need to be below 2.5 ksf. I also have already check the steel plate, I have no concerns there. Also thank you for the reference of checking as a concrete footing, that was something I found before posting but was unsure if that was the best way to look at it.

So in closing both of you have recommend the second layer of timbers to be used under the plate, I will readjust my calcs to show the second layer of timbers.

On a side note if i was to reduce the rod spacing from 2' on center to 1' on center, or also increase rod size, do you believe i would be able to show the mats as one unit? or due to the oversize holes used in construction of the mats will a single mat be able to achieve full bearing with a reduced size plate on it?

 

[Splitrings]

You need to transfer shear between the faces of adjoining members. What you are proposing is very similar to a stress laminated bridge deck. I would check into AASHTO or the attached document. I am assuming these documents transfer the shear by friction between the members alone, without considering the shear capacity of the stressing rod. Considerable slippage would have to occur, especially in your case with oversized holes, to engage the rods in shear. If you were to pretension your rods to a set level you could calculate the frictional force between the piles you might expect to develop.

 

[dik]

...and just when things were nearly resolved...

Is the load applied continuously for 2 months or only applied for a few hours/days? then the 1.15 may be OK...

You may be further ahead to use split rings... the largest ones I've encountered are '4" maleable iron/steel' and they are available for a max 7/8" dia rod... shear rings 'really' connect and should be considered. Hole oversize has little or no influence on the split rings.

Dik

 

[dhengr]

CE520:
You’ve kinda got to think about these problems in a slightly different way..., do the 3 extra - 8"x8"x4' timbers cost more than anything you would do with more rods in the bottom layer? The extra timbers certainly distribute the load in a more defined/effective way, no guess-work about it. In making matts, the drilling of holes and the through rods, are really rough fabrication. The holes are somewhere near the center of the timber/member and they may be fairly square and true, a function of the hangover of the guy with the drill that morning. The 7/8" rod vs. the 1&1/8" hole is to make this all start to fit together. The friction btwn. the timbers is there, but we have no way of really accounting for that, due to expansion/contraction of the timbers and steel due to moisture and temps., etc. We just can’t count on this; it is part of our safety factor, not a guaranteed value. We can’t tighten the rods enough, due to compression perpendicular to the grain, under too small a washer, to bring timber friction into play. Split rings or some such would work, but they are very expensive to install in this application. The value of the bolt/rod bearing in the hole is more likely something we can count on, and design around, but there may be more movement and deflection, btwn. timbers than you want, to bring this into play. In making a timber mat, there is a big difference btwn. a 4'x4' mat under a 10"x10" base under a 50ton jack, and a 1.5" thick base pl., vs. a group of 10'x20' mats under the crawlers of a large crane. The way that the load is applied, the settlement/deflection which can be tolerated, etc. Mostly, the through rods are there to facilitated mat handling, not load distrib. which happens through another means.

 

[Splitrings]

The dapping tool to cut the correct size slot for a splitring is nearly a $1000. I am guessing the extra timbers are a lot less money.

 

[oldrunner]

Actually you can probably rent the dapping tools, but you might have to teach the workers how to use them.