Demand forces from FE plate results - Concrete design 7

[pyseng]

I'm working through a design for a partially underground concrete tank. The structure is modelled using plate elements in STAAD. I am having difficulty rationalizing the proper way to transform the plate element forces (Sx, Sy, Sxy, Mx, My, Mxy, SQx, SQy) into proper design forces. My problem is that my mesh is non-orthogonal. If the mesh were orthogonal, I understand that I could use Wood-Armor theory to design the reinforcement in the orthogonal axes (Mx + Mxy and My + Mxy). Additionally, if the mesh were orthogonal, my SQx and SQy would line up with the "typical" section cuts that would be appropriate for checking one-way shear.

However, as stated, I have a non-orthogonal grid due to some openings and irregular pile layouts. My current approach for flexural design is to determine the principal membrane stresses (S1, S2) and the principal moments (M1, M2, M12) using Mohr's circle and take the design moment as M1 + M12 or M2 + M12 and design for the interaction of that moment with the membrane forces. I am relatively comfortable that this will produce a very conservative design for my flexural reinforcement and, honestly, is more than most people would likely do. However, this hinges on the idea that the moments can be transformed similarly to in-plane stress. Does anyone have a resource that might confirm this?

Second, is the issue of the transverse shears (SQx and SQy) on the non-orthogonal mesh. I have looked everywhere for a resource that might help explain how to get a "design shear value" however, most, if not all, resources assume a regular grid. My inclination is to assume that SQx and SQy are always "principal" forces, regardless of the orientation of the plate local axes. When I do so, I get reasonable results, but I just can't justify the reasoning. Does anyone have any thoughts on this approach?

I know this is quite a bit to take in, but thank you for taking the time to read and possibly help out!

 

[pyseng]

Definitely agree on your first point, steveh49. My issue isn't that my reinforcement changes orientation, the issue is that, due to geometric constraints, the local axes of my FE plates are not all aligned with my reinforcement orientation. And, my software does not allow one to reorient plate local axes. So, I have to manually go in and transform the local plate moments into "global" plate moments on the axis of my reinforcement. What I was hoping to accomplish was to come up with a sort of "upper bound" approach, but I've decided to work through the transformation in the API.

 

[HTURKAK]

Honestly, i did not read the previous responds , I do not know whether my respond will be duplicate of previous responds...Is this partially underground concrete tank is circular tank? . What is the reason for your mesh is non-orthogonal ?


This approach will be too conservative in some cases .If Mx ≥–|Mxy| and My ≤|Mxy| your approach could be acceptable.


The following snap from (Practitioners’ guide to finite element modelling of reinforced concrete structures ; FIB Bulletin 45);

Vn= Vx COS φ + Vy SIN φ and Vt= - Vx SINφ + Vy COS φ

Just for curious; you define ( irregular pile layouts ). If the slab supported on piles, you need to check two way shear and could be obtained from pile reactions.

I will suggest you to look;
-Finite-element Design of Concrete Structures (G.A. Rombach ),
- FIB-CEB Bulletin no 45,
- The Finite Element Method: Its Basis and Fundamentals (O.C. Zienkiewicz... )

I hope my respond makes sense and will answer to your questions..

 

[pyseng]

Thank you, HTURKAK. I will certainly take a look at some of those resources. I have an irregular mesh because the tank is actually a 6-sided diamond shape, with an irregular pile layout, so it just lends itself nicely to parametric mesh generation (which, I have to give credit where credit is due, STAAD does have a very nice mesh generator). Additionally, the walls of my tank have large pipe openings. So, not just your standard box or circular tank.