Calculating a beam

[MushCreek]

I'm wondering if there's a way to prescriptively calculate the carrier beam I need for my main floor. I'm attaching a drawing with the dimensions. I show two evenly spaced support posts, but could go with three if it would help. The lumber yard said I would need an LVL, but what did they do before those were around?

Specs- The floor joists will be 2X12's on 16" centers. They will be hung from ledgers at the edges, and the carrier beam in the middle. I don't have enough room to put them on top of the carrier beam, so they will be attached with hangers. Design load should be 40 psf minimum live load, and I want a L/480 stiffness. Materials available locally are #2 southern yellow pine- strong stuff.

My contractor (NOT an engineer) says a beam built up out of 3 or 4 2X12's will be 'plenty', but of course, the inspector has to believe that, too.

As an aside, my contractor builds such beams with all of the joints over the column. I always though it was better to stagger the joints to minimize a hinge effect over the column, but he says his way is correct.

[MountainDon]

Let's see what I can do...

Let's call that a 32 x 42 building; that = 1344 sq ft. 
Divide that into three parts = 448 sq ft per section
Let's call that 450 sq ft.
If we call the LL to be 40 PSF, let's call the DL out at 15 PSF.
That's a floor load total of 55 PSF
450 x 55 = 24750 on each floor segment.
Half of that will rest on the center beam and a quarter on each side wall.
24750 / 2 = 12375 on the center beam for each segment.

Using Don_P's simple beam calculator and the following data for SYP...
Modulus of Elasticity (E)   1600000 psi
Bending Strength (Fb)   1120
Shear Strength (Fv)   175 psi
(the calc is fixed to use a value of L/360 on floors)
But let's see what happens when we use...
a beam length of 13'4"
and 12500 lbs as the beam load

Hmmm. The calculator tells me that 4 layers of 2x12 (actual beam width of 6" and depth of 11.25" will FAIL the Fiberstress in bending test and the deflection test. Horizontal shear passes.



Using three columns across the length reduces the span for each to approximately 120" (10 ft)
And changes the segments to 4, giving...
1344 sq ft / 4 = 336 sq ft per segment
340 x 55 = 18700 PSF
18700 / 2 = 9350 lbs per beam segment
Call that 9500 lbs

Hmmm.
That still FAILS the fiberstress in bending test.

Perhaps you need some engineered wood, or steel.
Or yet another column? 
Or I did something wrong?


Hopefully Don_P will be along sometime soon and see if I have messed up or not.

[MountainDon]

An engineer could calculate the built up beams size with joints in mid span. But a set of 3 or 4 or more simple beams with all joints over supports is all that the IRC will recognize without engineering.


The planning department would likely want to see the calculations used to size the beam. They may not be happy with numbers that poured out of an online "home brewed" calculator.

[MushCreek]

Hmmm. My barn is spanning over 10' with three 2X10's, and that floor feels like concrete- very stiff. Not as big a span on the rafters, though. I'll have to try to figure out what the load is. It looks like about 5500 lbs, doing a rough guess.

The lumberyard ran a calc on it, and said a 3 ply 11-7/8" LVL meets my specs. By that, they mean 3 LVL nailed together. I don't know how thick that is. I do know it's expensive, and will require a crane to install that beast. The lumberyard will include engineering, though.

[MountainDon]

I was only counting a main floor too, no upstairs load coming down to the floor center.

I don't know how thick that is.

1  3/4"  I think

[Squirl]

Prescriptive?
Building Inspector?

ICC.
They have charts for girders and headers in the ICC.
http://publicecodes.citation.com/icod/irc/2009/icod_irc_2009_5_sec002_par021.htm

It sounds like the girders under the joists will be an "interior bearing wall" span supporting "one floor only." 
Your building is 32 ft wide, which is right in between the 28 and 36 foot columns of the chart. 

c. Building width is measured perpendicular to the ridge. For widths between those shown, spans are permitted to be interpolated.

4-2x12's can span 9'-1" in a 36 foot wide building and 10'-2" in a 28 foot building, so to interpolate (split the difference), 4-2x12s should be able to span 9'-7" according to code. 

Since you have a 13'-6" between your posts you will need to cut down the span (more posts) or use an LVL.

You can think about it logically that you the beam will be supporting 20-2x12s (10, 16"o/c, 2 sides) in that 13'-6".  You would be trying to support those 20-2x12s with only 4-2x12s spanning a greater distance than the 20 (13'-6" vs 11').

Your contractor is correct. Code requires all splices to be supported by a stud or post.  Don_P frequently cites the code citation, I don't know it off the top of my head.  To get the splice at the right spot outside of over a post gets to more complicated engineering, so for ease, code is alway over a post.


Don_P might be able to run you through some better numbers.

[Squirl]

Also if you are going for 1/480 deflection, you a probably going to have to upsize from the chart.

If you compare the 4-2x12's on a 36ft wide floor (usually 40 p.s.f. per code) are allowed to span 9'-1" and the 4-2x12ss for a roof beam are allowed to span 9'-5" with a 50 p.s.f. snow load.  I would venture a guess the reason that 4-2x12s can span that 4 extra inches for a roof vs. a floor is that a roof is L/240 to code and a floor is L/360.  So if you are going with L/480 you might want to give yourself a few extra inches.

[Squirl]

Don got me thinking about the calculations.
I know the question was about a beam, so just takes this as rambling.

So each posts supports 50% of the weight to each of the four sides. That is 13'6" x 15'7" = aprx. 210 sq. ft x 55 p.s.f. = aprx 12,000 lbs per post. Be sure to have a big footing and/or very good soil for the posts. I have heavy clay soil (2000 psf).  I would need a 30" square footing for that kind of weight. 

I was just thinking about this because I did my center piers this last weekend.

[flyingvan]

  If I understand your original post, you're dropping your joists down with hangars.  Have you considered TJI's?  The hangars are great---once in place, the TJI's just snap in.  They are light and stiff, and perfectly straight.  I know nothing beats seing dimensional lumber all lined up pretty, but these will never show anyway

[Don_P]

Sorry guys, had a little setback this week. Done the ER bit and am whupped. I don't know who didn't wash his hands but I got strong suspicions. My head is still way too swimmy for higher math, y'all are making it spin 

LVL's are a good bit stronger (Fb ~2800 vs 1600) and stiffer (E2.1 million psi vs 1.6) than SYP. Increasing a span does a whole lot more than most folks realize. Double the span and the span doubled and so did the load, bending moment just quadrupled.

Yup the ol heeldrop test is qualitative in some ways but you are designing for 40psf uniformly distributed, pack everyone in there that'll fit and then start pushing a few more in. I know but people have more stuff than that, and thump in unison at parties.

Ilevel Forte free on the net does calcs for lvl's and some dimensional lumber. If your inspector will accept it. I can guarantee you he'll be impressed if you show him mine, it has been checked by several engineers, has shown up on their forums, but he don't know that and you could enter something wrong. WSDD... wood structural design data, I think it's on the AWC site has some beam span data that might help, free DL from the folks who write the code referenced nat'l design standard for wood construction (AF&PA's NDS). I'd call it prescriptive but have had that thrown back in my face before. I'd start with codebook, move to WSDD, Ilevel, then if he won't budge decide whether to spend the money on lvl's or an engineer to say SYP will squeek by. and it bites when you know it'll work.

[Davegmc]

Would it be possible to run a 8"x16" footing the length of the crawlspace and just frame a stub wall to provide the mid span floor support in lieu of a beam?

[MushCreek]

It's not a crawlspace; it's a full walk-out basement.

I'm getting quotes on a TJI system, but I'm afraid the cost will be too high. Time will tell.

[flyingvan]

16" TJI's will span 32'8" if you go 12" OC, then you wouldn't need any pillars

[MushCreek]

I think that span would be too bouncy. At L/480, it could move over 3/4" under load. My experience has been that a floor that wide has a trampoline effect, all else being equal. 16" would also reduce my ceiling height, which is 8' with 12" joists. I'd like to use this basement some day, and basements are dark enough without further reducing the ceiling height.

[Don_P]

Exactly, the solution on those floors is to add mass to dampen them and it still is a poor floor.
You're looking for perfomance of the joists to be l/480 but to get that "feel" the girders need to be l/600 or stiffer, its a sum of parts problem. Putting l/480 joist on an l/480 girder does not give an l/480 floor.

Lets wring out some numbers on the girders and see where we can get.
Step up to Select Structural SYP base design value Fb= 1900, you'll get a 15% increase for multiple member use, Fb=2185 psi, MOE=1.8x10⁶ psi, Fv=175 psi

Tributary load = 13.5' x 15.6' x (40+10 psf)= 10,530 lbs
Plugging it in to my calc it passes bending and shear handily, no problem strengthwise. deflection... performance, barely fails... on the calc. There is a cheat in the calc, I tried to foolproof it. Deflection is properly based on live load rather than total load. Backing out and re-entering just the LL 8424 lbs yields a deflection of .364"... l/445

There is one more grade up, dense SS @ 1.9E. We left the prescriptive farm long ago. LVL's start @ 1.9E and are typically 2.0. LVL's are easier to find, we're into a losing battle costwise, the LVL wins, you don't have to go with tji's to use lvl's solid sawn joists are ok. The real problem is the post spacing. What is driving that and can you tighten them up?

[Don_P]

You're looking for perfomance of the joists to be l/480 but to get that "feel" the girders need to be l/600 or stiffer, its a sum of parts problem. Putting l/480 joist on an l/480 girder does not give an l/480 floor.

The math for this came from Dr Woeste at VT, it gets into what I was trying to describe above.
http://www.timbertoolbox.com/Calcs/floorfreq.htm

Another way is a flitchplate, LVL's have largely replaced them but you might have some inside tracks on steel. This is an NAHB guide for them that an inspector may approve;
http://www.toolbase.org/PDF/DesignGuides/flitchplate.pdf

[MushCreek]

I have no problem going to 3 posts. I don't have sufficient egress windows to divide the basement up into rooms anyhow. I might enclose one back corner (with a window) to make a separate bedroom, but the rest would have to remain open.

The best lumber I can get around here is #2. I called every lumberyard, and they all said it is special order, and I would have to order a LOT more than I need to hit the minimum. I'll probably have to go LVL for the beam. Any idea what a 12" X 42' 3 ply LVL would weigh? I'm sure it's out of the reach of man power. I'm not even sure how I would get the 3 pieces down into the basement to assemble them. There's nowhere else that's flat enough to nail them together. The LVL's add up to almost $600; wonder what an equivalent steel I-beam would cost?

My reasoning for pricing TJI's is the dismal state of framing lumber these days. I don't know how builders can build a partition wall with this stuff; the bathroom walls in my barn are all over the place. I just drywalled it, and it's truly ugly. I'm looking into steel studs for my partition walls in the house.

[Don_P]

11-7/8 LVL weighs 5.5 lbs/ft... at 42' that's 231 lbs. Michelle and I have hauled 40'er's up and set them for hips by hand before... 20 years ago. I'm not sure 42's are readily available but probably not a big deal. But, I wouldn't set these as full length anyway. I would build them up a stick at a time and a ply at a time, weaving the joints and breaking them over posts. The supplier should be able to calc all of this and give you a printout. If the inspector requires I let the supplier know and he sends his calcs back to the home office and their engineer seals the design.

As an aside I did check the WSDD manual and our calcs were agreeing with it, very high grade material at that original span. If you're reworking spans we can visit dimensional lumber girders again with a new drawing. Do not casually pick long girder spans, if you can take more posts, do it, many hands make light work. The house will be better for it and you'll get back into prescriptive, the easy path. I do like LVL beams, do check that the original quote was looking at l/600 or stiffer if you want that stiff feel. We can investigate steel but it won't be as easy to work with.

This is an interesting exercise if we think about it. It is showing why the prescriptive tables are what they are. The limits in the tables are not arbitrary they reflect the strength of commonly available materials. We were getting into hard to find materials and falling off the edge, then investigating the next strength classes which come with their premium. We have been working through why it is what it is.

On lumber quality. You're in the heart of where the trouble is coming from in the SYP industry. The worst problems appear to be in the upper part of the range at this point. If the framing getting to you is SYP I can see a couple of things to try. If the problem is studs, stop buying stud grade and look for #2, a stud is a #3 with #1 edges. If it is all crap see if you can switch species but SYP is the king strengthwise... at the moment on paper. Although the SYP belt extends to the Carolina piedmont right below me I have to order SYP when I need the strength, we bring in SPF from the west coast and Canada as stock framing, and there is a healthy amount of that I'm not bragging on. We certainly are paying the price for growing fiber instead of lumber. Avoid european lumber SP (scots pine) and NS (norway spruce), inferior in every way.

[Roy_M]

Hmmm. My barn is spanning over 10' with three 2X10's, and that floor feels like concrete- very stiff. Not as big a span on the rafters, though. I'll have to try to figure out what the load is. It looks like about 5500 lbs, doing a rough guess.

The lumberyard ran a calc on it, and said a 3 ply 11-7/8" LVL meets my specs. By that, they mean 3 LVL nailed together. I don't know how thick that is. I do know it's expensive, and will require a crane to install that beast. The lumberyard will include engineering, though.

Not necessarily a crane. I installed three 26 foot X 14 inch LVLs bolted together in my garage with the help of two friends. Before they arrived I built 4 temporary supports for the LVLs to sit on. I predrilled the bolt holes in the first LVL so they are evenly staggered or offset from each other (2 feet apart, which gave us roughly 14 inches of space between each bolt diagonally) to ensure the holes would be drilled straight. The floor the LVLs support is 9 feet above the garage floor. We placed them one at a time applying adhesive between each layer and strapped them together. Using the holes drilled in the first LVL as a template, we drilled through the other 2 LVLs and bolted them all together. Once we got the LVLs tight against the upstairs floor, I placed two large support posts at each end and a heavy duty house jack in the middle. All of which are bolted solid to 12 inch diameter concrete columns that sit on a 24"X24"X24" concrete footings as well as the beam, and then nail the LVLs together with columns of four pole barn nails spaced 2 feet apart. I added cleats  every 2 feet to help resist twisting and bending. The beam has been in place for 8 years and has never sagged even in the slightest or anything else even under the heaviest load of snow. And it wasn't nearly as hard to install as we thought it would be.

[MushCreek]

I don't know why this got bumped up, but the house is done! I went with the lumberyard engineer's numbers. I used a triple 11-7/8" LVL, full length. I assembled it, and we placed it with a crane. It sits in a pocket in the concrete on each end, wrapped in membrane to protect it from the concrete. The floor joists are 12" I-Joists on 16" centers. I could have gone 24" centers, but it didn't cost that much more to go 16. I glued and nailed 3/4" Advantech for subfloor.

The floors certainly feel very solid. Once I did the 3/4" finished floors, that stiffened it up even more. The system got tested during drywall when they stacked 4400 lbs. of drywall in one spot, essentially supported by only two I-Joists. In a panic, I went down to the basement and measured the deflection, but it was less than 1/8".

My only disappointment is the two 6X6 wood columns I used; one of them is bowed about an inch. I plan to replace them with 4" square steel posts when I get around to it. Sorry it took so long to post a follow-up, and thanks to those who helped me sort this out!