Reverse engineering section properties 2

[4thorns]

Hi All.

According to a third party report I have, an 8x12 beam notched both sides @ 24" o.c. for 4x8 timber floor joists has the following remaining
section properties. (It's basically an inverted "T" at each joist location with the space between the joists acting as solid blocking)


Area = 62.28

Section Modulus = 107.08

Moment Of Inertia = 700.71


My question is, can I reverse engineer these properties into a simple rectangular section with the same properties that I
can plug into any software?

It's not a priority here but if you can find a few minutes to point me in the right direction I'd greatly appreciate it.

Thanks,

Doug

 

[JoshPlumSE]

Your description is a little tricky for me. So, I'm going to restate it to make sure I understand. Your beam is an 8x12. But, every 24" there is a 4x8 section notched out of the top where the floor joists frame in.

My thoughts on this one....
1) On the tension side, you can calculate the allowable tension stress the normal way and compare it to the actual tension stress in your Tee section (based on the section properties you calculated).

2) On the compression side, use the properties of a rectangular beam that would exist if the notches existed on both top and bottom. My rational is that a) this is conservative, b) The extra width at the bottom of the Tee probably isn't helping that much for lateral stability, c) since this beam is laterally braced every 24" the tension stress should govern anyway.

There is probably a way to go back to first principals (used to derive the wood buckling equations) and figure out how to apply those to this situation. But, I don't know how to do it. And, since it's unlikely to control, I'm not sure why you'd want to.

 

[Ron247]

I do not think you can. Solve Area for d in terms of b. A = bd d=62.28/b Substitute b and 62.28/b into Sx = 107.08 equation and solve for actual value of b. Calculate d now based on a real value of b and you plug those b & d in to Ix you do not get 700.71. I think. At least I did not.

Your structural analysis requires the correct A and Ix, but does not need Sx at all. Later when your program checks your allowables, it needs Sx to be correct. But since you are using a fictitious b and d, all of your wood check formulas will be wrong. Le, l/d, la/b etc will be wrong. You can get your structural analysis correct, but not your allowables.

 

[CANPRO]

If the beam was symmetrical on the x-axis, you might have been able to get away with an equivalent width, keeping the depth the same. But with a T section, your neutral axis is offset and I feel like going to an equivalent rectangular section is a little off base. And in either case, your fictitious rectangular section with equivalent Ix/Sx will not have the same area (volume of member), which will effect the size factor in the strength calculation. Maybe you can do this, but you probably shouldn't.

 

[BAretired]

The depth of notch was not specified. Why would anyone take the trouble to notch each side of the beam to receive a joist? And how precise is the cut? The actual size of an 8x12 beam is 7.25 x 11.25 (Area 81.56 in^2). The area of two notches is 81.56 - 62.28 = 19.28 in^2 (7.25 x 2.66). The notches appear to be 1.33" deep with 4.59" between them.

If a rectangular beam of 4.59 x 11.25 is assumed, A = 51.64 in^2 (83% of 62.28), S = 96.8 in^3 (90% of 107.08) and I = 544.61 in^4 (78% of 700.7). I believe it would be conservative to use b of 4.59, d of 11.25 and E/0.78 or 1.28E for Young's Modulus. No reason to use less than the full value of EI for deflection calculations.

Note that this is contingent on notches being cut precisely as specified.

BA

 

[rb1957]

notching the beam makes it behave as separate spans between joist cut-outs. So assume SS, so the notched section supports shear. To replace a Tee section with a rectangle sounds troubling, since you can't match the Tee NA and the Tee remote fiber distances with a rectangle shape.

I assume that "8x12" is an I beam (from describing the notched sections as "tee"). and I assume that the upper cap is cut away (inverted tee).

another day in paradise, or is paradise one day closer ?