Utilization Ratio Not Working?

[polskadan]

Hi all, i'm having an issue with using the utilization ratio for a concentrated force on a square HSS section. I am currently analyzing a HSS square spreader beam and am treating the lug plates as concentrated forces on the HSS. I am checking the capacity of the spreader beam and have checked flexural capacity, axial, and interation of the two according to AISC 13th edition. Now I wanted to check for concentrated forces on the HSS flange. To do this I am using AISC equation K1-9 and want to check Rn against the "pull" or axial force on the lug plate. My issue happens to be when trying to calculate 'Qf' which uses the Utilization Ratio found in equation K2-12. My utilization ratio becomes greater than '1' which does not work in the Qf equation under EQ. K1-9 since I will have to be taking the square root of a negative number......I checked all of the limits of applicability and nothing. Also looking at the equation for flexure, since my member is compact, the controlling equation for moment capacity was M=Z*Fy divided by the appropriate Factor of Safety (using ASD). Yet when you look at the utilization ratio you are dividing your required moment by the section modulus and Fc which is .6*Fy. So the result of dividing by these smaller number is what is giving me a Utilization Ratio greater than one. How is this possible as the beam passes all Flexure, Axial, and Interction checks? Has anyone ever run into this issue before? I should be reducing the capacity of Rn as the Flanges of the HSS that is connected to the lug plate is experiencing axial as well as flexural loading...


Thank you in advance for any help!

 

[polskadan]

Come to think of it, tell me if this explains it:

I have analyzed the HSS square spreader beam and let's say it has a flexural capacity of 5 kip-ft. This is simply a global check on the beam, so sure it can handle 5 kip-ft globally, but looking at local checks on the beam if the lug plate is added parallel to the beam direction, I am getting a local effect on the flange so great that I will actually have to reduce the flexural capacity of the beam (this is shown by a utilization ratio that is greater than one that nullifies the equation). One way to fix this is to have the force distributed in a different manner locally on the flange of the HSS so that the beam can finally reach it's global flexural capacity original calculated per AISC.

Am I understanding it correctly? They should could mention something in the code or guides about what happens when your utilization value is greater than one...sheesh

 

[JAE]

U shouldn't be greater than 1 or you have essentially a failed member correct?

 

[dhengr]

Some sketches with dimensions, loads, intended usage, intended connection details, etc. would go a long way toward showing us what you might need help on. I have designed and built dozens of spreader beams over the years and I don’t believe I ever applied a ‘Rn’ or ‘Qf’ to any of them, although I may have applied some of the thinking embedded (hidden) in these symbols and equations. Their Utilization Ratio was very high, being used many times per day, over many years, with some regular inspection, in service. There probably shouldn’t be any “concentrated forces on the HSS flange,” that’s probably not a very clean detail in load transfer or welding. While there may be some advantages to using a HSS for a spreader beam, there may also be as many or more disadvantages on some beams when it comes to connections and welding at lifting and loaded lugs. Sometimes a fabricated section is superior to a rolled section because it cleans up these connections and leads to a more direct load path btwn. the load and the hook.

I don’t have a copy of the AISC 13 Ed., so I can’t be of much help there. It may be a good guide for the general design of your spreader beam, but it was not developed with spreader beam design in mind, and it may not be the last word for loads below a crane hook in many jurisdictions. Good clean detailing of lugs and welds, and direct load paths, almost always trumps general stress and buckling considerations on this type of equipment.

 

[polskadan]

AISC has a guide on how to design and construct lifting beams written by David T. Ricker written in 1991. In it he goes over a very general method for designing spreader beams (one that doesn't even mention axial forces...) for an I-beam section. Using the guide hand in hand with the AISC steel code covers most of the aspects of the design. Also using an HSS section has its benefits as a spreader beam for those unknown torsion forces that it may experience...the downside however is that by putting a lug plate on the beam you are in fact putting a concentrated force on the flange of the HSS rectangle, this is a local effect and must be checked according to AISC 13th ED Chapter K and thus the 'Rn' and 'Qf.' I now think I understand how the utilization ratio, 'U' works and upon reducing the applied load am able to get a working number, what I think this means is that the local effect in fact prevented the beam to achieve the full global flexural capacity calculated earlier. With that in mind I wouldn't mind if someone could confirm the thought process behind this ratio

 

[nutte]

Bending on the HSS is checked using Z, so you might have an allowable moment Mn/Omega that results in a stress (Mn/Omega)/S that is greater than your allowable stress. This is why your utilization ratio is greater than 1. There seems to be a discontinuity in the equations: the HSS is good for bending, but it can't take any concentrated force applied to the face, even at moment less than the full allowable value. I don't know if this was intentional, or the result of a conservative decision to use S instead of Z when calculating U. Either way, I'd use a heavier HSS and avoid this pesky problem completely.

 

[dhengr]

You picked the downside of what you are trying to do correctly, and it won’t become an upside just because you fiddle around with ‘Rn,’ ‘Qf’ and ‘U.’ But, now we have another meaning for HSS, and that is... horse sh- - stress condition. And, the bending in the flange, around the lugs and their welding will need some serious consideration or they could drastically effect the Utilization of your design, Ratio or not. I can’t see from here what you are actually trying to do, but I had guessed that you were talking about lifting lugs parallel to the beam axis. I don’t think you will have much torsional loading on the spreader beam unless your detailing or lifting methods induced it. Also, some types of lifting beams don’t have much of an axial loading component.

Good Luck