Torsional Constant "J" Composite Section

[engjg]

I am analyzing lateral torsional buckling per AISC of a WF shape reinforced with angles. Would the Torsional Constant "J" of a composite section simply be the sum of J of the individual members?

In review of AISC DG9 it appears J for an open section can be calculated as the sum of bt^3/3 which would make me believe the torsional constant would be additive and the composite "J" is not dependent on the spatial relationship of the members in the composite shape?

 

[KootK]

The composite J would only be the sum of the individual J's if no parts of the angles overlap with parts of the wide flange, which is unlikely. With overlap, you'll be modifying some rectangles a well as adding some new oness.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[Hokie93]

I would take one-third the sum of bt³ for each individual rectangle or sum the torsional constants ("J") for each part if the torsional constants are known. That assumes you have not created a closed shape by adding the angles and that the angles are adequately attached to the wide-flange shape so as to create a composite section.

 

[engjg]

Hokie93 - I am creating four closed square shapes within the composite section by adding four angles attached to the WF web and flange. I would think these closed sections with be more torsion-ally friendly (but more complicated to analyze) and by simply summing bt^3/3 or known J as you suggest would be conservative to represent the torsional properties of the composite section; do you agree?

 

[KootK]

I agree with that engig. Especially since I expect your LTB resistance to be dominated by warping (Cb).

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[Hokie93]

engjg - I agree with that approach. It might be a little conservative but since you still have an open shape in terms of overall member behavior, I believe it is the correct approach.

 

[KootK]

Another way that you could go is to use four times the J value of the individual closed shapes that you're creating. That would still be conservative but, depending on your particulars, perhaps much less so.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[KootK]

Revision: your four angles are really going to create two larger closed sections rather than four smaller ones. One at the top flange and one at the bottom flange. These two closed sections should provide substantial Saint Venant torsional stiffness.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[KootK]

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[JoshPlumSE]

Just for kicks, I ran a shape like this in RISASection with and without merging the sections together (where merging turns them into closed sections). And, the difference in the J calculation is significant. 23.0 in^4 versus 868.4 in^4. That's an increase by a factor of almost 40 for the J value!!

I used a W30x191 as my wide flange with L6x6x1/2 angles connected in the same manner shown in KootK's picture.

 

[KootK]

@Josh: any chance you'd want to run one of the tubes shown in my sketch above? The two angles and a plate representing the bottom flange? I'd be curious to see how close 2X that number would get us.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[JoshPlumSE]

I think your estimate would be pretty close, but don't think I'll get a chance to check it. At least not today. If I had only saved that original model before I exited.

 

[KootK]

No sweat. Homework assignments are always optional. There's some irony in the fact that I could do this in a heartbeat if I had RISA.

I ran it by hand as a pair of HSS 6x12x1/2, ignoring the thickness difference in the flange. Came to 820 in^4 which is within about 5%.





I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[engjg]

Thanks all for the input. I too was impressed with how significantly the J was increased when calculated for the closed shapes created. I would like to take advantage of this improved torsional stiffness for this reinforced shape with respect to the AISC chapter F-4 flexural lateral torsional buckling provisions but am hesitant if this is appropriate? In looking at KootK's sketch the shear flow circuit would really need to travel up and down the web of the WF right? Can anyone comment on the role of "pure torsion" (St. Venant Torsional Stiffness "J", warping stiffness Cw, radius of gyration of compression zone, and their influence on the derivation of AISC LTB equations? Also, what torsional resistance is required at brace points to engage these stiffness components of the member?

 

[KootK]

Can you give us beam and angle sizes so that we can get a sense of the proportions? Top loaded? Uniform load?

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[engjg]

W24x84 with L3x3x3/8 reinforcement. Member is column of rigid frame pinned base subjected to bending from lateral loads.

 

[KootK]

Given your proportions, I'd expect the LTB benefit to be fairly modest.

I would like to take advantage of this improved torsional stiffness for this reinforced shape with respect to the AISC chapter F-4 flexural lateral torsional buckling provisions but am hesitant if this is appropriate?

The judicious application of code LTB provisions is appropriate in my opinion.

In looking at KootK's sketch the shear flow circuit would really need to travel up and down the web of the WF right?

This is true for shear but less so for torsion (and therefore LTB).

Can anyone comment on the role of "pure torsion" (St. Venant Torsional Stiffness "J", warping stiffness Cw, radius of gyration of compression zone, and their influence on the derivation of AISC LTB equations?

J we've discussed. Iy should be pretty easy. Radius of gyration is manageable as SQRT(I/A) of the compression zone. Cw is a bit trickier. One approximate approach would be to calculate Cw assuming fictional beam flanges having the same Iy as the composite flange/reinforcing angle assembly. Lastly, be conservative with your residual stress assumptions and remember to account for loads locked into the system prior to reinforcement.

Also, what torsional resistance is required at brace points to engage these stiffness components of the member?

Not sure what you're asking here. LTB bracing would need to satisfy the usual AISC provisions. Given that you're looking at a column, however, I would expect that you only have LTB bracing at the top and bottom of the column.


I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.