Two Way Shear Stress - ACI Property Polar Moment of Inertia

[callawaygolfer]

thread507-479051
I've read all of the threads related to this topic for the polar moment of inertia for two-way punching shear. All of the text books and examples I've seen only deal with bending about one axis. I find it hard to imagine that for a corner column you don't have bending about the X and Y axis of the column. So do you have to calculate a Jx for bending about the X axis and a Jy for bending about the Y axis and add the stresses together to get the maximum? I'm designing a small reinforced concrete structure with a flat slab (no beams) that is supported on 4 concrete columns in a high wind area and there's a significant amount of moment transfer from slab to column.

Any help would be appreciated.

Can someone repost this blog below that was mentioned in one of the threads? The link doesn't seem to be working correctly.

"For what it's worth for comparison purposes, the author of this blog went through and derived all the common cases. Refer to the linked pdfs near the end of the post."

 

[Agent666]

This was an alternative link to the blog post.

https://dennismercadosstructuralengineersblog.wordpress.com/2018/03/01/punching-shear-with-a-punch/

https://engineervsheep.com

 

[dijonnaise]

Hey Callaway - definitely good to think about moments in both directions, especially at corners!

We use a software, used to be called "DECON" by Jordahl to do the heavy lifting for us. It's a software from a studrail manufacturer to help you design headed stud reinforcement around columns but it also does a nice job of calculating and summarizing max vf. I believe the install file is at this link:

https://www.constud.ca/downloads/software.

Edit: should note that the software is free

 

[Agent666]

If you have access to ACI421 series of codes it is also a good read and they provide guidance on analysing two way actions (don't ignore it as you discuss). You can simply use superposition.

https://engineervsheep.com

 

[1.392DL]

I've had to calc this for property line footings too. Yes the X & Y components of shear stress can be added together; so the typical two term (P/A + M/J) becomes three terms (P/A + Mxx/Jxx + Myy/Jyy). However the polar moment of inertia is different for corner and edge columns since some of the planes are removed at the edges.

The formulas for polar moment of inertia for edge, corner, and interior conditions were derived and are shown in this PDF for spSlab:

https://structurepoint.org/pdfs/Two...or-System-Design-&-Detailing-(ACI-318-14).pdf