Infer Vertical Loading on Wood Beam

[WickedJester]

I have a question regarding determining the ultimate vertical loading of a wood beam.

I have testing data to start. In the test its three planks of wood that are layed horizontally on top of each other. A balanced horizontal longitudinal load is applied simitaniously at 4 locations on the beam and the beam is fixed in the middle. The horizontal load performance and ultimate strength were determined.

Data is represented as pounds (load) and inches (deflection). The size per plank is 1.75"x7.25"x118".

I have not does these clacs for awhile and not sure where to start? Is it possible to infer my ultimate vertical loading strength from the ultimate horizontal loading strength?

 

[Guastavino]

I'd start with a good mechanics reference book to get deflection equations, etc. And get a copy of NDS

As for inferring ultimate load from horizontal strength, sure. If you can come up with a maximum bending stress, it's going to be similar for the other direction. Although, NDS usually has a flat-wise factor, and I think that it works out that horizontally loaded beams work better. Also, there are other factors that arise from turning it vertically, like the stability factor CL, etc.

In summary, get a good mechanics book and the NDS code.

 

[Triangled]

hmmmm... clever handle selection...

 

[WickedJester]

Ha, thanks.

Okay had open my materials book. Don't have a NDS book on hand right now.

Im not sure if I did the calcs correctly. Our maximum longitudinal force was 10578 pounds. In vertical loading we had 3641 pounds.

When I do the calculations to infer the vertical loading I get a force that is roughly 3 times what our testing came up with. Does this seem correct?

Would anyone mind taking a look at my work?

 

[WickedJester]

Calculations here

 

[BAretired]

Three planks laid one on top of the other, unless glued, act independently so your expression for I for the vertical loads is wrong.

I per plank = 7.25(1.75)[sup]3[/sup]/12 = 3.24 in[sup]4[/sup]

S per plank = bd[sup]2[/sup]/6 = 7.25(1.75)[sup]2[/sup]/6 = 3.7 in[sup]3[/sup]

The ultimate fiber stress for wood bent about its minor axis is greater than for its major axis. Your code should give a value for this.

If fu = 17,900 psi for horizontal loading and assuming the same value for vertical loading, then three planks should be capable of resisting a moment of M = f.S = 17,900(3 * 3.7) = 198,700 "#

This would be equivalent to P = M/78= 2548#

You found P = 3641# which suggests a factor of a little over 1.4 for minor axis bending. That sounds reasonable.

Edit: If you have just one load at 54", P = M/54 = 3680#, slightly higher than your value of 3641#.

BA