Steel Beam Reinforced wtih Angles Limiting Width-Thickness Ratios 2

[waytsh]

Say you have a rolled or built-up I shaped member that is reinforced with hot rolled angles as shown in this sketch...

[URL unfurl="true"]https://res.cloudinary.com/engineering-com/image/upload/v1578458131/tips/Reinforcing_3-Plate_Member_vfvuok.pdf[/url]

Referencing Table B4.1 - Limiting Width-Thickness Ratios for Compression Elements in AISC there are some items I would be interested to hear your opinions on to see if I am interpreting correctly.

1) Would the member still be considered an I-shaped member with the reinforcing in place?

2) Would b and t still be based on the original flange or some type of equivalent section?

3) Would the new h/t be calculated off the clear distance between the horizontal legs of the reinforcing angles?

4) Not really applying to Table B4.1 but would "ho" also be based on the centroid of the new built-up flange?

Look forward to hearing from you.

Thanks!

 

[KootK]

My take:

1) Would the member still be considered an I-shaped member with the reinforcing in place?

a) Mostly. Still a dual symmetry open section for the most part. In a pinch you could use the saint venant torsional stiffness of little box sections that you'll be creating to improve lateral torsional buckling.

b) You'd do separate b/t ratios for the angle legs assuming them to be supported on two edges.

2) Would b and t still be based on the original flange or some type of equivalent section?

c) The flanges would switch to compression elements supported on two sides instead of one side.


d) I think that wold be a defensible approach.

4) Not really applying to Table B4.1 but would "ho" also be based on the centroid of the new built-up flange?

e) technically, I think that you'd want the distance between the shear centers off the the two, boxed flange assemblies. For practical purposes, the centroid is surely close enough. It's kind of hard to find the shear center of asymmetric celluar things.

 

[waytsh]

Thank you for the reply KootK. What would we do without you!

Regarding your reply b and c. Are you suggesting checking the b/t ratios of the horizontal leg of the angles and the existing flange independently and then use whichever controls? For instance, if we are looking at Table B4.1b in AISC 360-10, the flange and the horizontal leg of the angle would be checked to Case 17 or 18 since in the new configuration they are stiffened elements and the controlling element used for the design of the shape. If so, I think this is a reasonable interpretation, and one I have made in the past as long as the flange does not extend too far beyond the vertical leg of the angle. If it would then that flange tip would have to be evaluated as well to Case 10 or 11 to determine if it controls over the others.

In this same situation then the web of the existing beam would be evaluated per Case 15 and the vertical leg of the angle evaluated against Case 19?

Thanks again for your thoughts.

 

[KootK]

Thank you for the reply KootK.

You're most welcome waytsh.

What would we do without you!

Live in blissful, if slightly less informed, harmony.

Regarding your reply b and c. Are you suggesting...

I agree with all of that. Every plate element seeing compression needs a rational b/t investigation. You got this.

 

[Agent666]

In a pinch you could use the saint venant torsional stiffness of little box sections that you'll be creating to improve lateral torsional buckling

I'd definitely use the increase in torsional properties, you're using the increase in plastic modulus for flexural strength after all, so why ignore the increased torsional and warping section properties if they are relevant to the design situation.

They (and the shear center) are fairly easy to calculate these days with the right software, a free example is this python package if the OP knows a little python, or if a commercial product is your thing IES shapebuilder will do the same thing.

 

[KootK]

Neat. I sure hope that they're teaching lots of programming in university these days. It's pretty clear which way the wind is blowing.

 

[waytsh]

No doubt about it. Although I must admit for the sake of time I have been using RISA Section for my reinforced sections. I think the important thing is to know how it's done before relying on the software. the plan will be to incorporate these calculations into my spreadsheet so I don't have to jump back and forth between the two.