# Any Engineers here to determine something for me..?

Joined: 12:41 AM - Feb 27, 2005
How much weight would this beam (glued and screwed together) would this thing hold if it were 26ft long by itself?

Joined: 2:15 AM - Jan 28, 2008
Not an engineer, but I deal with engineered wood products a lot like LVL and Versa-Lam beams.  I can safely say it wouldn't carry much.  How much would depend on the grade and species of both the solid sawn lumber and plywood along with the number and type of fasteners and how it was loaded. A beam that long would also want to rotate unless it was laterally braced.

As a comparison a 2-ply 1.75" x 9.5" x 26' long LVL beam can only carry 54 pounds per linear foot when used in a floor system.  Here's a specifier guide for one manufacturer:  https://p.widencdn.net/pclohu

Dave
Dave
Portland, ME

Joined: 12:41 AM - Feb 27, 2005
It will be braced.  Glued and screwed together with 3" and 3.5" decking screws.  The wood will be your usual pine lumber found at Lowe's, Home Depot, etc.  It will just be holding up part of the roof and ceiling in my garage no other floors above it.

Joined: 2:15 AM - Jan 28, 2008
I sent you a private message, but I'm struggling with the new process.  It's in my Outbox, but not in my Sent items.  Let me know if you got it or not.

Dave
Dave
Portland, ME

Joined: 1:28 AM - Aug 24, 2017
dgcantrell wrote: How much weight would this beam (glued and screwed together) would this thing hold if it were 26ft long by itself?  beam.JPG
I calculate a total moment of inertia of 632 inch^4 ( = 263E6 mm4 )

In a book on construction / building materials I found an allowable tensile stress for pine of only 5 MPa (725 psi), which I found amazingly low. Maybe it accounts for the large knots that pine sometimes has. Lacking better information I will use it.

Length 26 feet = 312" (= 7925 mm)

For a point load in the middle, the maximum tensile and compressive stresses in the extreme fibers are M*y/I = 1/2*F*1/2*L*y/I. Reordered for the force this gives:

F = 4*stress*I/(L*y) = 4 * 725 * 632 / (312 * 10.5/2) = 1120 pounds

For a distributed load, the maximum tensile and compressive stresses in the extreme fibers are 1/2*F*1/4*L*y/I. Reordered for the distributed load this gives:

F = 8*stress*I/(L*y) = 8 * 725 * 632 / (312 * 10.5/2) = 2239 pounds (or 86 pounds per feet)

You'll have to deduct the weight of the beam itself, which is around 380 pounds I think, leaving 1859 pounds (or 72 pounds per feet)

The above assumes:
- perfect assembly, as if it was one solid piece
- all pieces continuous for 26 ft (quite unlikely)
- no check of the loads on the screws/nails/glue
- no safety factor
- the calculation is for pure bending stresses only
- no buckling analysis

Rob

- - -

Calculation of the moment of inertia:

three vertical webs
height 7.5", width 1.5"
I = 1/12*w*h^3 = 1/12*1.5*7.5^3 = 52.73 inch^4
three of them makes I = 158.20 inch^4

two vertical plywood webs
height 8.5", width 0.75".
The effective width for this calculation is half, since only half the fibers run like those of the solid wood pieces
I = 1/12*w*h^3 = 1/12*0.375*8.5^3 = 19.19 inch^4
two of them makes I = 38.38 inch^4

girder:
height 1.5" width 7.5", distance from neutral axis 4.5"
I = 1/12*w*h^3 + A*d^2 = 1/12*7.5*1.5^3 + 7.5*1.5*4.5^2 = 2.11 + 227.81 = 229.92 inch^4
two of them makes I = 459.85 inch^4

girder cut-out:
height 0.5" width 0.75", distance from neutral axis 4"
I = 1/12*w*h^3 + A*d^2 = 1/12*0.75*0.5^3 + 0.5*0.75*4^2 = 6.00 inch^4
for of them makes I = 24.00 inch^4 (to be subtracted)

Total moment of inertia: 158.20 + 38.38 + 459.85 - 24.00 = 632.43 inch^4 ( = 263.09E6 mm4 )
Last edited by Rob_de_Bie on 12:41 PM - Jun 12, 2018, edited 1 time in total.

Joined: 1:28 AM - Aug 24, 2017
Rob_de_Bie wrote:In a book on construction / building materials I found an allowable tensile stress for pine of only 5 MPa (725 psi), which I found amazingly low. Maybe it accounts for the large knots that pine sometimes has. Lacking better information I will use it.
That low stress value puzzled me, so I found some more data. In Europe (or the Netherlands) pine is classed as C18 if judged to be 'standard building wood' (class C), or C24 if it's 'construction wood' (class B) of 'fine wood' (class A). If I take the lowest grade, C18, then the allowable tensile stress is 11 MPa, compressive 18 MPa. If that's correct, then the stress value I used in my calculation can be raised to 1595 psi. That would give a distributed load of 4923 pounds, minus its own weight 4546 pounds, or 175 pounds per linear feet.

Moving away from construction to aircraft design, the good old ANC-18 'Design of wood aircraft structures' lists for various pines a yield stress in bending of 4600 to 7000 psi. I really can't explain the huge differences between these sources. Of course in aircraft manufacturing the quality criteria would be much more strict, but a factor of 3 to 4 cannot be explained by just that. If anyway knows, I'm all ears.

Rob

Joined: 12:41 AM - Feb 27, 2005
Just to clarify, this thing is not going to be hanging out there like a wet noodle. LOL  Two of these beams spaced parallel about 10ft apart and 10 ft away from the end walls of a 30'x26' block/brick building.  2x4x10's on 16" (maybe 24") centers filling the spaces on both sides to mount 3/8' plywood for a ceiling.  Typical roof framing with 2x4 or 2x6 rafters and 5/4" furring strips to mount 36" wide metal roofing.  The metal roofing structure and metal itself is half the weight of traditional 1/2" plywood and asphalt shingle covering  A few sheets of 3/8 and 5/8' plywood over the ceiling for storage area insulated with lightweight foam board.  No heavy items though.  Mostly plastic storage totes full of plastic and resin (my stash)...  However, I may have a couple of leads on some 8" steel I-beams that will more than fit the bill.

Joined: 1:28 AM - Aug 24, 2017
dgcantrell wrote:Just to clarify, this thing is not going to be hanging out there like a wet noodle. LOL  Two of these beams spaced parallel about 10ft apart and 10 ft away from the end walls of a 30'x26' block/brick building.  2x4x10's on 16" (maybe 24") centers filling the spaces on both sides to mount 3/8' plywood for a ceiling.  Typical roof framing with 2x4 or 2x6 rafters and 5/4" furring strips to mount 36" wide metal roofing.  The metal roofing structure and metal itself is half the weight of traditional 1/2" plywood and asphalt shingle covering  A few sheets of 3/8 and 5/8' plywood over the ceiling for storage area insulated with lightweight foam board.  No heavy items though.  Mostly plastic storage totes full of plastic and resin (my stash)...  However, I may have a couple of leads on some 8" steel I-beams that will more than fit the bill.
Do you know the stress levels that US building codes allow for pine? That would give you a better answer. And would a strength of 175 pounds per linear feet be enough? It would be nice to know whether the calculation gave you an answer.

Rob

Joined: 12:41 AM - Feb 27, 2005
I don't know but I'm trying to find out.  Most, it not all wooden construction in the US utilizes pine.