Multi-axial loads on fillet and increased capacity for transverse loads

[ReverenceEng]

I have a situation where I need to sharpen my pencil and try to make use of the increase in capacity for loads in the transverse direction to a fillet weld, but with multi-axial loads. Normally, we would stick to the "traditional" shear capacity of the weld for these more complicated situations, but here, I need to see if I can do more since there is an existing condition.

For clarity, I am speaking about using this equation: Fw = 0.6*Fexx*(1+0.5sin(theta)^1.5)

However, generally, when we "see" this equation, we are usually working with a resultant force vector that has a component along the longitudinal direction of the weld and another component transverse to the weld where the transverse component which would "receive" the increased capacity is parallel to one of the legs of the fillet weld (straight up or to the side). I would consider this the "typical" application as I have sketched in the attached.

In my situation, I have a multi-axial resultant force vector, so when we break it down, we have one component longitudinal to the weld and TWO components transverse to the weld, one parallel to each leg. Thus the "transverse resultant" would no longer be parallel to either leg, but depending on the magnitudes of the components would fall somewhere between and extend "through" the throat.

My question(s):

1) Is this equation still applicable even though my transverse load is not parallel to one of the legs of the fillet?

2) If so, which angle is not the "theta". Is it as I have shown in the attached sketch between the resultant force vector and the longitudinal axis, or is it perhaps "Beta" as shown in the attached, which is the angle between the resultant and the plane. I think it should be theta as I have shown it, but I also think I have thought about this too long and have turned myself around.

Help much appreciated!

 

[jdonville]

From the theory, theta is the angle between the load and the long axis of the fillet weld. So I would use the angle on the plane containing both the true 3d resultant angle and the long axis of the weld.

 

[kingnero]

I don't question you are using the correct equation, however in the Eurocodes there is a formula that considers all three major components (except sigma_longitudinal, as that one doesn't carry any (significant) load in reality).
This would be more applicable to your situation. Perhaps you are using a simplified formula ?

See attachment:

 

[DrZoidberWoop]

The strength increase is a product of industry testing and standards. It's not often used in 3D loading cases, but you could if you wanted to. Realistically, it's going to end up being decided by your boss or the approving EOR whether they'd allow a strength increase in 3D. I've invoked it when sizing simple weld groups that are loaded in 3D when the elastic method is giving me an undesirably large fillet weld.