Weld Stress Calculations

[TravisMcC]

Hi, I'm trying to use some calculations from Shigley's Mechanical Engineering design text, and run into a snag. While I understand how to apply the formulas, It requires that my weld grouping meets one of the diagrams in the book (

http://www.roymech.co.uk/Useful_Tables/Form/Weld_strength.html

basically the same table is shown here for considering weld groups as lines).

I am working with the welds in bending, as they are on the end of a structural section loaded as a cantilever.

Where i have run into trouble is trying to figure out exactly how to determine Iu (Unit second moment of area) for the weld groups as lines. This may seem odd because lines have no area, but the formulas in the text remove weld throat area in deriving the calculations. You add this in later.
I am trying to use the parallel axis theroem Sum of individual(Io+ad^2) where a = area, Io = moment of inertia of individual weld, d=distance from group centroid.
I cannot seem to get an answer for even some of the more complex groups in the table that agrees. I would like to figure out how those shapes were figured before i try figuring a shape i have no reference to what is correct.
If anyone can point me to some examples of or shed some light on this it would be appreciated.
Thanks
Travis

 

[desertfox]

Hi TravisMcC

On the roymech site it shows how to work out those values toward the bottom of the page of the link you give.
Can you post a picture of your welded component and we might be able to help further.

desertfox

 

[TravisMcC]

Here is the basic idea,
I did fudge up the drawing abit, as the welds do not fill the corners as shown, but in terms of figuring out how to get rid of the h(weld leg) values it should be the same.
Looking at the royal mech website again, i see how the got their answer, however what i'm missing is the steps between values with h, and the value below without.
I expect it is the long time since i have done the basic factoring and algebra operations required to get there, but what exactly to i do with the h values? set them = to 1 ie just remove them.

To highlight the exact place i am having trouble with i will quote the website here,

Ixx = 2[(bd^3/12)+bd(h+0.5d)^2] - This part i understand perfectly. Parallel axis theroem.
now the part i dont get.
how does the above, become this;
Ixx = 2bdh^2 ? if we are removing the weld leg, then why is there still a d in here?
Also the shigley formula for this exact group is
Ixx = b(2h)^2/2 (2h is given as d in the book, and equal to the distance between welds. or 2h as in the royal mech drawing).

 

[TravisMcC]

Also if you look further down the page to the table, the same arrangment of welds has a different value for Ixx, this value agrees with shigley.

 

[desertfox]

Hi TravisMcC

Well the 2bdh^2 as been concluded from the assumption that d is small compared to b and h, without going through the maths I can't say offhand how they got there but what I would do to prove whether its right or not is put values in the first formula and calculate a value and then use their assumption and see how close the figures are.

desertfox

 

[desertfox]

Hi TravisMcC

I have done the maths for the assumption and uploaded a file for your reference, you will see the assumption is valid.

desertfox

 

[weab]

I cannot speak for your reference and why it is so confusing. Try to find this reference: "Design of Welded Structures" by Omer Blodgett. Very clear. Sorry I don't have it with me right now.

Good luck.

 

[TravisMcC]

Could someone please look this over and see if I'm on the right track? What really gets me is unstated assumptions.

Using these same numbers it appears the shigley formula, and the roymech formula supply the same numbers (after adding the weld height to the shigly formula).

 

[GregTirevold]

Travis,

That looks right except you left out the h^3 term (from the MoI of the rectangle about its own centroid) in your first line. I assume you want to show it there because you don't remove the h terms until the next step so it should appear until then.

Also you would be well served by spending the $4 and getting the Solution to Design of Weldments booklet. (

https://ssl.lincolnelectric.com/foundation/item.asp?prodnum=D810.17&PID=16)

It is basically a book of examples of various types of weld problems complete with Mr.Blodgett's explanation of why he approached a problem a certain way. It has 33 weld types, like the one you are trying to derive, already simplified for use to save you the time of doing it yourself. It also has some good excerpted pages on allowable weld strength, tube welding and fatigue.

http://www.linkedin.com/in/gregtirevold

 

[TravisMcC]

Yes, I did intend for that h^3 to be there at that point.
Thanks, i will look into that book. Looks like I would have little trouble finding plenty of use for it.