Flexural strength as length shrinks

[princeyprince]

I'm currently compiling a report on the strength of balsa woods planks under a three point test.

Thus far i've found that maximum load shrinks as length does, upto a point, beyond which max load increases. This doesn't fit with the proscribed flex. strength = 3FL/2bd^2 formula.

Is there any concurrent formula that can make allowance for this?

 

[apsix]

Are you saying that total load capacity decreases as the span decreases? Or conversely, total load capacity increases as the span increases.

I think you are observing the natural variability of timber. We are a lot less certain about the strength of an individual piece of the timber than for steel say, which is why timber design uses greater safety factors.

I suggest you increase your sample size until the results follow logic.

 

[ishvaaag]

Also, very short spans won't be in accord with the formula, for this is in accord of Timoshenko's beam that supposes uniform behaviour along the length, what doesn't happen near the supports. Neither they will exactly be in accord with the formula if you use wide planks and narrow loads, you will be seeing some plate behaviour. As well, if laminated, the structural member have particular properties that are not neccesarily well represented by just ordinary beam theory; you may get safe designs with it but normally at high safety factors to be negligent with the actual setup in the section.

 

[JoshPlumSE]

What sort of lengths are we talking about? With what sort of deflection limits? How are you defining failure?

A steel cable has virtually zero flexural strength. But, catenary action allows it to take relatively signficant transverse load. That's becasue a tension in the cable (combined with the deflection of the cable) allows it to resist the load.

I'm not saying that is what's happening for your balsa wood. I'm just point out one case where 2nd order effects cause the behavior to deviate substantially from classic beam theory.

 

[rb1957]

if failure is defined by bending, then M = PL/4 ... as L decreases, P should increase; unless you're shearing the balsa (so it's not failing in bending)

 

[rb1957]

just checking ... when you say "balsa plank" you're not referring to a composite panel with a balsa core and face sheets of Al or kevlar or some other ?

 

[apsix]

PP hasn't returned to the forum since his first and only visit, when he posted this question.

It smells of student assignment.