Built-up steel beam with different yield strengths 4

[TehMightyEngineer]

Someone double check my logic here:

Reinforcement of a existing steel wide flange beam, yield strength of 50 ksi. Will be done by welding 36 ksi cover plates on the flanges. For the plastic (Zx) allowable moment I should be able to calculate the plastic section modulus for the beam and plates separately and multiply them by their respective yield strengths and then add the two moments together, correct?

For the cases where lateral torsional buckling, compression flange buckling, correct?

For tension flange yielding I can use the Sx of the tension flange multiplied by the yield strength of the flange added to the Sx of the tension plate multiplied by the plate's yield strength, correct?

Any papers or examples that cover this situation that anyone can point me to would be a great help. Couldn't find anything that specifically covered this situation.

Maine EIT, Civil/Structural.

 

[TehMightyEngineer]

Agreed on all points KootK. I should take a look at Muir's references as well. I presume they're more toward columns as he puts them in his column reinforcement section but I'm sure it's worth reading regardless.

Good point on the distinction of floor beams. The Steel Interchange October 2014 article that Hokie mentioned also had a discussion on design of curved lifting beams on the same page. I just happened to read it and it's also applicable. Link is here:

http://msc.aisc.org/globalassets/modern-steel/archives/2014/10/si.pdf

The important point it mentions, similar to your point, is "generally, residual stresses have no effect on the ultimate strength of a member but can affect stability." They point out that typically the built-in stresses in a rolled vs. unrolled beam will be at similar levels. They state that the AISC specification uses 20% to 80% as the assumed compression flange residual stresses and thus rolling a beam doesn't cause stability issues alone.

For beam/column reinforcement it appears prudent that unless you can reduce your beam/column stresses below 80 percent then you may have buckling issues. I gather this is more or less what you were saying above, if you have a beam at 100% flexural stress then there's very little buckling capacity (Iy/Cw) left in the flanges and as such buckling should be considered when reinforcement is applied. Thankfully about 99% of the time we can remove all but dead load from beams being reinforced so I imagine this typically isn't an issue but I will definitely include this check in my spreadsheet.

Maine EIT, Civil/Structural.

 

[TehMightyEngineer]

Agreed Woodman, I've also come to the conclusion from this discussion that it's not worth it to try to refine the calculation that far. I am curious though, what assumptions are being made that you refer to? The minimum yield strengths should be something we can conservatively assume.

Maine EIT, Civil/Structural.

 

[woodman88]

The two big assumptions are
1) What are the existing live/dead loads,
2) That the field conditions will allow the modifications to be done properly.

It may look simple to meet these assumptions. But I have dealt with having to do to many changes to my repair designs, to refine any field repairs so much in the beginning.

Garth Dreger PE - AZ Phoenix area
As EOR's we should take the responsibility to design our structures to support the components we allow in our design per that industry standards.

 

[TehMightyEngineer]

Well, hence the idea of a spreadsheet. I've also run into similar conditions where the reinforcement had to be changed multiple times. Thus, a fast and accurate tool seems appropriate.

In the end for other reasons I'm not going to consider differing yield stresses in the spreadsheet but you're right that often dead and live loads are not well known. I would put forward that as long as it's well below the point where buckling controls that it such variability can probably be ignored. You could also justify that this variability is already accounted for in the safety factors.

Maine EIT, Civil/Structural.