Calculate Section Modulus for an Irregular Section - (using X, Y Cordinates) 7

[DimzK]

Hi all,

I have a simple mechanics of solids type question which I have been googling, but I have not been able to find an answer.
I have an irregular shaped section with bending moments imposed about its X axis as shown below.

The centroid of the shape coincide with the x=0 aand y = 0 of the co-ordinate system.

Now for me to check my bending stresses at point 1 , 2 and 3, I need calculate my section modulus about Section X for each of these points.
If this was a simple rectangle, we could simply use B * H^2/6.

Is there any formular which would let me calculate the corresponding section modulus for these three points if I provide co-ordinates and Ix, Iy and Ixy values which I cam get of Autocad.

For context, I am trying model a deteriorated timber pile to check load capacity.

Any help would be appreciated.

Cheers,
Dimuth

 

[Celt83]

also can't have one of these threads without mentioning Handofthelion's impressive program:
Github Link
Original Eng-Tips thread where they announce it

My Personal Open Source Structural Applications:

https://github.com/buddyd16/Structural-Engineering

Open Source Structural GitHub Group:

https://github.com/open-struct-engineer

 

[dik]

A good link, Bookmarked, thanks.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[DimzK]

Hi Guys thank you very much for the input, and Dik I am going to install Smath and have a look at what you did.
I have never used Smath before.

 

[dik]

It's an excellent program... with a few little hiccups, but generally very good. I've written hundreds of programs using it... almost anything I have to design more than a couple of times, I'll do it up. Getting the hang of writing the formula is difficult to start with but after a while I can do formulae almost as fast as writing them. It keeps track of units, very well. I've attached a snapshot of my current program on lagscrews to show the complexity of the formulae. The text in blue are the units and the program takes care of them, too. Only downside to the program is that it was written by a Russian dude and that my have political fallout... I'm not concerned about such stuff. Larger programs can be written by cutting and pasting parts of other programs. Most of my programs are over 10 pages.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[IDS]

Here are my stress calculations. Using the same section as before, all in inch and lbf units:

First find the offsets from the points where stresses are required to the principal axes (points 1-3 are the corners, point 4 is the point used in Celt's calcs:

Then calculate stresses using the principal axes then the global XY axes:

So the results are consistent and also agrees with Celts results.

Having worked through the process I now think it is simplest to use the original axes with the full bending stress formulas:
Sigy =( (Mx Iy - My Ixy) / ( Ix Iy - Ixy^2) ) * dy
Sigx =( (My Ix - Mx Ixy) / ( Ix Iy - Ixy^2) ) * dx

The spreadsheet is attached below.


Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/