## Angle to HSS Moment Connection

## Angle to HSS Moment Connection

(OP)

I'm reviewing the connection for a cantilevered L3x3x0.5" angle welded to the side of an HSS6x4x0.25". There is a load at the tip of the angle resulting in a moment at the interface of the angle and wall of the HSS (see attached sketch).

The angle strength is fine, and the weld is fine, but I'm having trouble trying to check the plastification of the HSS wall.

I tried using the AISC Design Guide 24 assuming just the vertical leg of the angle is effective (ie. acts like a transverse plate), but the plate formulas only cover axial load, not moment. I also tried using the HSS to HSS moment connection formulas (again considering only the vertical leg of the angle), but the Hb/Bb ratio is < 0.5.

Any help would be appreciated.

The angle strength is fine, and the weld is fine, but I'm having trouble trying to check the plastification of the HSS wall.

I tried using the AISC Design Guide 24 assuming just the vertical leg of the angle is effective (ie. acts like a transverse plate), but the plate formulas only cover axial load, not moment. I also tried using the HSS to HSS moment connection formulas (again considering only the vertical leg of the angle), but the Hb/Bb ratio is < 0.5.

Any help would be appreciated.

## RE: Angle to HSS Moment Connection

## RE: Angle to HSS Moment Connection

## RE: Angle to HSS Moment Connection

BA

## RE: Angle to HSS Moment Connection

BA

## RE: Angle to HSS Moment Connection

Watch where you're loading the angle. You could have other local failure mechanisms other than full section bending. Also, make sure you're not torquing the angle.

## RE: Angle to HSS Moment Connection

## RE: Angle to HSS Moment Connection

I should have elaborated a bit more in my original post. This connection is part of a steel frame used to lift equipment (the frame connects to the equipment and a crane lifts the frame). Hundreds of these lifting frames have been manufactured already and have been used across North America for quite some time (without any noted structural issues).

I'm reviewing the lifting frame for the manufacturer to assess the rated load capacity (approximately 8,000 lbs, and there is an angle at each corner of the frame, so 2,000 lbs per angle), in accordance with ASME BTH-1-2008 "Below the Hook Lifting Devices".

I realize this is a bad detail, and I'm going to suggest modifications to make it a more robust connection, but I need to provide justification as to why it doesn't work (in the form of a design calculation package to be submitted to the client).

I've done an FEA and I'm getting very high localized stresses at the interface of the HSS wall and the tips and corner of the angle, but I want to do a hand calculation to compare to the results I'm getting from the FEA.

## RE: Angle to HSS Moment Connection

## RE: Angle to HSS Moment Connection

Assuming only the vertical leg of the angle is effective (a bit conservative but a good first approximation), I don't think the yield lines will be quite as symmetrical as you have shown.

Since y

_{2}> y_{1}, Triangles A and D may be similar but not equal in size.Trapezoids E+B and F+C cannot exist without additional yield lines such that all planes can slope as required to meet the assumed deflections.

I would have to think about the problem a little more, but can't do it right now. Let's see what others come up with.

BA

## RE: Angle to HSS Moment Connection

## RE: Angle to HSS Moment Connection

## RE: Angle to HSS Moment Connection

## RE: Angle to HSS Moment Connection

http://mathcentral.uregina.ca/QQ/database/QQ.09.07...

Note that as BAretired hints the pyramids need not to be of equal sides (yet the method above still will apply), and you will be minimizing the inner work (as a function of the dimensions a,b,h of the pyramid) whilst meeting equilibrium with the applied moment at a concomitant rotation (also a function of a,b,h).

The solution will give the deformation in the hypothesis of plasticity. Examining if plastic behavior at the thickness is reasonable can then be done, as could be through an elastic FEM analysis.

You can also investigate this way the extent of deformation in the hypothesis of plasticity for a range of thicknesses.

## RE: Angle to HSS Moment Connection

Two equal and opposite forces, H are applied to the HSS wall 2" from the top and 2" from the bottom.

External Work = H(1+1) = 2H

Internal Work = 29m where m is the plastic moment of the wall per inch.

m = phi*Z*Fy = 0.9(0.25)2/4*50,000 = 703"#/"

H = 14.5m = 10,195#

M

_{ult}= 2H = 20,390"#The eccentricity of load P was not specified, but P*e = M

_{ult}/SFBA

## RE: Angle to HSS Moment Connection

m = phi*Z*Fy = 0.9(0.25)

^{2}/4*50,000 = 703"#/"In arriving at Internal Work, I assumed yield lines at 45

^{o}from the corners of the plate. The yield lines formed a trapezoid top and bottom and three triangles each side of the plate.BA

## RE: Angle to HSS Moment Connection

## RE: Angle to HSS Moment Connection

Internal Work = 29m where m is the plastic moment of the wall per inch?

Is it that you have some formula for the case? Other than that we need to formulate all the rotations (both at the load applying plane and at each yield line dihedral) as a function of the deformed trial geometry, then whilst meeting equilibriums seeking between the cases we try what is the one of the minimum internal work ...

## RE: Angle to HSS Moment Connection

The attached sketch shows the location of assumed yield lines. Internal Work for each segment is defined as L*m*theta where theta is the angular rotation of the segment.

Dimension 'x' was first assumed to be 2" which led to an Internal Work of 29m.

Differentiating IW with respect to x and setting the result equal to zero indicates that a lesser value of x will be more critical. So Internal Work on this revised basis turned out to be 28.7m, not much different than before.

BA

## RE: Angle to HSS Moment Connection

## RE: Angle to HSS Moment Connection

## RE: Angle to HSS Moment Connection

BA

## RE: Angle to HSS Moment Connection

I did my MS Thesis on HSS connections and used JA Packer's book "Design Guide for Hollow Structural Section Connections", extensively. I remember that there were some examples that pertained to your exact situation and it involves several different equations. I would suggest that you get a hold of this book at your local university library.

## RE: Angle to HSS Moment Connection

BA

## RE: Angle to HSS Moment Connection

Goin4SE: I also have the book you referenced, but like BAretired I couldn't find an applicable example. If you could provide a page reference that would be great.