Maths equation assistance

[HOJ]

For my own curiosity I am trying to rationalise these equations for the strength of a bolted timber to timber connection.



My questions are probably simple for some, but would like to seek some clarity as to the actual number values I am dealing with and which should be allocated to the expressions outlined below:




For the value of "ti timber or board thickness or penetration depth, i = (1, 2)." is this just the timber thickness, i.e, 44mm?

What does this ask for:"fh,i,k = characteristic embedment strength in wood member i."

And the therefore the value of "β"

For the "ratio between embedment strengths of members." I am assuming that I need a value for individual timber section thicknesses, more so if they are different, i.e, 44mm and 38mm, but on the basis they are C24, I cant see how the number will be different.

Values for C24:



I was going to use a value for a 4.6, 12mm bolt to apply to the equation, & the basis my 2 timbers are 44 x 195 C24

Hope this makes some sense TIA.

 

[ChaiLatte]

Yes. The equations are formed to give you an answer for fastening anything to anything.

It could be a thin piece of oak to a thick piece of balsa wood. It could be two identical parallel 3" x 2" (be wary if the members cross at 90 degrees as the 'along the grain' and 'across the grain' numbers differ*). In the former case the i=1 values will be considerably different to the i=2 values. In the latter case, i=1=2 and both sides of the joint use the same values.

In principle, you have to specify the geometrical characteristics of the two pieces and also the strength/engineering characteristics. If you were building a formula 1 car with such a joint, you would adjust thicknesses or materials such that both sides of the joint fail at the same load.

There are six possible failure modes and the governing one is the lowest (common sense).

From what document do the spider squiggles originate? If you are lucky, you might search for 'BSxx online calculator', and find something where you just fill in numbers and it works out the 1-6 results for you.

* you get bonus maths points for joints where members cross at a random angle.

 

[Spectric]

Use a spreadsheat and find a worked example, get your calculations to correctly work out the example and now you can use any input data you want knowing the output will be correct providing the worked wexample was correct. In my world "And the therefore the value of "β" " that B is magnetic field density.

Can you really have precise calculations when dealing with wood, or is it a case of " perfect wood with no defects " so there are allowances to be made.

 

[ChaiLatte]

Can you really have precise calculations when dealing with wood...

In the above, they are using "characteristic" in quite a specialised, technical manner. This is quite good on where and how it fits into the overall design process:

https://strongtie.co.nz/news/characteristic-and-design-capacities

 

[HOJ]

From what document do the spider squiggles originate?

I was in book 2 page 36 from here: Timber structures which is written as Eurocode 5.

* you get bonus maths points for joints where members cross at a random angle.

That's the next problem!

Use a spreadsheat and find a worked example, get your calculations to correctly

I've been all over the web, I can find lots of answered equations and the same formulas, but not clarity and detail of the workings, I am also working them in SMath rather than a spread sheet, so that's another learning curve, all probably a waste of my time but worth understanding.

Thanks

 

[Spectric]

I am also working them in SMath

I used to use Mathcad until PTC brought them out and now charge too much on a subscription basis and before that a program called derive which was really fantastic as a symbolic equation solver but looking for something similar so what is Smath like ?

 

[ChaiLatte]

I've been all over the web, I can find lots of answered equations and the same formulas, but not clarity and detail of the working

This popped up in my search. It has a downloadable demo. I do not know if it would help or hinder:

https://www.apfstructuralsoftware.com/en/portfolio-item/timber-joint/

Reading around very briefly, it appears Eurocode 5 has a simplified method of joint design as well as the calculation-intense version above. It might be worth using that as a sanity check.

 

[paulrbarnard]

I used to use Mathcad until PTC brought them out and now charge too much on a subscription basis and before that a program called derive which was really fantastic as a symbolic equation solver but looking for something similar so what is Smath like ?

Give Octave a try. It’s comparable to Matlab so pretty much the ultimate math solving solution. It’s GNU so free but doesn’t run as fast.
I’ve used MathType on a Mac for writing equations

 

[Adam W.]

Phew!

That bakes my noodle.

I think I'll stick to working out how to build fan vaults with a stick and some string.

 

[HOJ]

Can someone give me sanity check and look at these 2 equations, I can't get the same answers as they show:



This one is slightly different, for nails:



I'm clearly not understanding how the 6 over the 4 sqrd is applied, I presumed its just a power to convert by 1000.

 

[Essex Barn Workshop]

My understanding of those equations, if it helps at all, is that whatever you were going to use, you need a bigger bolt.

 

[ChaiLatte]

Can someone give me sanity check and look at these 2 equations, I can't get the same answers as they show:

Original equations are in Vol. 1 page 92.

One is for a nail. One is for a bolt of diameter > 8mm.

It looks like the nail is 4mm diameter and has 600N/mm^2 ultimate strength.

It looks like the bolt is 16mm diameter with a strength of 360N/mm^2.

The 2,6 is the diameter raised to the power of 2.6. The Europeans like using a comma where we use a decimal point.

The maths is correct if you read the units correctly (bolt is Nm; nail is Nmm).

0.3 x 360 x 16^2.6 = 145927

(600/600) x 270 x 4^2.6 = 9925

 

[HOJ]

@ChaiLatte thanks, I had just sussed it, it is Swedish!



I can carry on with my learning curve.

 

[paulrbarnard]

@ChaiLatte thanks, I had just sussed it, it is Swedish!

View attachment 179744

I can carry on with my learning curve.

As its Swedish the average temperature at which this applies is probably -20C

 

[woodieallen]

The Physics forum is excellent for these sort of questions. https://www.physicsforums.com/

Warning: If you have any interest in physics whatsoever do not go to this site as you will not have any more spare time left since your entire day will be spent reading all the fascinating topics.