Stress in fillet weld. Two conflicting sources for calculating shear stress

[FONT=Calibri][SIZE=3][COLOR=#000000]The problem is not complicated but two references provide the same equation but define the type of stress differently.[/COLOR][/SIZE][/FONT] See attached pdf

[FONT=Calibri][SIZE=3][COLOR=#000000]Actual project: A round shaft is fillet welded to a plate forming a cantilever. A tip load perpendicular to the shaft is applied. [/COLOR][/SIZE][/FONT]

[FONT=Calibri][SIZE=3][COLOR=#000000]Conflict: A textbook has an example of the above cantilever BUT with a moment applied at the free end. The provided stress formula = 5.66M/Pi(b)D^2. This stress is identified as the normal stress. The text continues that if the moment was created by an applied force (as is the case for my project) then the direct shear force would also be calculated F/A (A= throat area) and the stresses combined with vector addition to get Max shear. In that approach the normal force is divided by 2 then squared then added to the square of F/A (direct shear) then the square root of the sum taken.[/COLOR][/SIZE][/FONT]

[FONT=Calibri][SIZE=3][COLOR=#000000]In a chart from the American Welding Society (AWS) the same formula (5.66M/Pi(h)D^2) is provided for the applied moment at the free end BUT is identified as the shear stress vs. a normal stress. Since the actual problem is a point load at the free end I believe I must also address the direct shear. All I have is the AWS chart. If AWS suggests how to account for a point load vs. applied moment I don’t have that information[/COLOR][/SIZE][/FONT]

[FONT=Calibri][SIZE=3][COLOR=#000000]If I just accept the AWS as is I get a shear stress twice the text book approach and I have not adjusted for the fact that there is an applied force vs. moment.[/COLOR][/SIZE][/FONT]
[FONT=Calibri][SIZE=3][COLOR=#000000]I understand that with fillet welds the stress of concern is shear and taken through the throat of the weld.[/COLOR][/SIZE][/FONT]
[FONT=Calibri][SIZE=3][COLOR=#000000]Does the AWS bake in factor of safety? [/COLOR][/SIZE][/FONT]

JAG-ENG,

I am entering this post in hopes of getting some additional posts from our other members that might shed some light on this question.

I know you looking for a resolution of the method used by AWS and I can't give that to you; but, with regard to your post I have a couple of questions/comments.

In your description of the text book solution you stated that the "normal force" was divided by 2. I assume you meant the "normal stress". Is that correct?

With regard to the dividing of the normal force/stress by 2, that is not something I can understand. Beyond that the sqrt of the sum of the squares part is simply resolving the perpendicular normal stress and shear stress vectors into their single combined vector.

As to the conflict of the normal stress vs. shear stress terminology between the text and AWS; I think that they may both referring to the same thing but since, as you stated, "for fillet welds all stresses are considered shear stresses" it may be that AWS simply decided to utilize that term for the normal stress on the weld. I can somewhat understand that because if you think about the angular orientation of the weld throat then the moment loading clearly creates a shearing force on that x-section; and the same situation applies to the direct shearing load as well.

As for the combining of the shearing load and tensile load stresses, one thing I noticed in my Machinery Handbook and other texts is for round cantilever beams all display the moment stress solutions but none of them address the point loading; and, during rather rigorous Googling I still could not I find any academic or other sources, that address all types of cantilever beam and welded beam issues, that the address point loading condition.

JAlberts
Yes I meant normal stress not force. The dividing by two of the normal stress is nothing unique. The max shear equation is used when you have combined stresses and the vector addition of the values squared, includes dividing the normal stress by two then squaring. The AWS chart explicitly defines the equation above as shear stress. I have two text books that use the max shear stress approach which the AWS chart appears to ignore. One text example provides the weld size and you are required to find the stress. The other provides a max stress allowed and you need to find the required weld size.