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# Demand forces from FE plate results - Concrete design7

## Demand forces from FE plate results - Concrete design

(OP)
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!

### RE: Demand forces from FE plate results - Concrete design

Select principal axes that match your typical rebar layout, regardless of element geometry.
You are correct that M_max = Mx + Mxy. Based on your description, not overly conservative.
I am not sure why you mentioned Mohr's circle. Tension and flexure vectors would be additive, no?
Getting meaningful concrete design shears out of FEA is more challenging than flexural design. You may find it easier to start the shear analysis and design from the reaction center, not the plate results.
I always check my FEA results with hand calcs for punching shears.
Keep in mind that we're engineers, not literature majors. Pictures / figures / sketches help.

### RE: Demand forces from FE plate results - Concrete design

(OP)
Thank you for the reply. I certainly agree that pictures help, but man, plate element diagrams and force transformations get messy really quickly.

1) Ideally, I would like to be able to set the local axis of my plate elements to be in the direction of my rebar layout, however, STAAD does not have that functionality. The local x-axis always points in the direction of the vector made from Node 1 to Node 2. (I think SAP might have this functionality, which would be very useful)
2) The reason I mention Mohr's circle is basically for the reason I just stated. STAAD reports local plate element forces which are not aligned with my rebar layout. So, somehow, I need to transform the membrane forces, plate moments to align with my rebar layout. Obviously Mohr's circle takes care of the membrane forces, but I'm not exactly sure if the moment's follow the Mohr's circle transformative laws.
3) Point taken on looking for alternate methods for evaluating the shear. It is a sad reality to face that FE won't solve everything.
4) I will definitely be checking punching shear in my mat at the piles by hand, was mainly wondering if one-way shears could be resolved using FE.

### RE: Demand forces from FE plate results - Concrete design

Are you treating Mxy as analogous to shear stress in Mohr's circle? If so, won't M12 = zero, similar to how shear stress is zero on the principal axes?

Section 5.4.2 of BD44/15 might work better for the results you have available.

### RE: Demand forces from FE plate results - Concrete design

Refer to the following paper: https://www.academia.edu/15396812/Twisting_Moments...
or ACI 447R-18

Couldn't you find required reinforcement for principal directions and then transform it into desired directions (according to my first reference this should work).

If that doesn't work, what would happen if you reduced the twisting stiffness to 0?
That should be safe if plastic redistribution is possible and SLS doesn't govern.

### RE: Demand forces from FE plate results - Concrete design

I'd be sure your Mx, My, etc is local and not global. Some FEA software spits out forces for both local and global (i.e. relative to orthogonal global axis).

Others just kick out either one or the other.

### RE: Demand forces from FE plate results - Concrete design

I agree with WARose. I haven't used STAAD in years but I distinctly remember using GLOBAL force results to design concrete plates. See this link: https://communities.bentley.com/products/ram-staad...

### RE: Demand forces from FE plate results - Concrete design

STAAD.Pro does report Global Moments as you mentioned. You may go to the Postprocessing mode > Plate Results > Go to the Plate Center Stress table and there will be a tab named Global Moments. For meshing where local axes of plates are not oriented the same way and not oriented along the global directions like the meshing you have, you may use the Global Moments to design the reinforcement. As far as shear is concerned, SQX and SQY will give you out of plane shear stress and direction is not of significance as such. You just need to check the values for these stresses at the critical section locations and compare those with the corresponding allowable shear stress. For example if you are checking for column punching then you would be looking at SQX and SQY at d/2 from the face of the column and compare that against the allowable value for punching shear stress. Similarly you would be looking at SQX and SQY at a distance of d from the face of the column and compare those with the allowable shear stress for the one way shear (d = effective depth of slab).

Last but not the least. If you are trying to design a mat foundation with openings and supported on piles, you may consider using STAAD Foundation Advanced (SFA) to design the foundation mat. SFA is fully integrated with STAAD.Pro and so if you have your superstructure built in STAAD.Pro, it can directly read the support reactions from the STAAD.Pro analysis and you can define your mat with piles in SFA and carry out the analysis and design of the mat in SFA. SFA internally converts plate local axes moments to global axes moments and designs reinforcements based on those global moments so lot of this work mentioned above will be automatically taken care of for you.

### RE: Demand forces from FE plate results - Concrete design

I was going to say the same thing about using global moments or preferably global nodal moments for design. If I remember correctly, a prominent program (STAAD or RAM, IIRC) did not properly account for Mxy when coming up with demand moments in the global directions. Though, my memory is from 10 year ago or so... maybe longer.

For what it's worth, for a single plate element with a reported Mx, My, and Mxy local moments the proper way to convert that into design is to use the "wood-armer" method to determine demand moment. I usually simplify it a little to the following:

Moment demand to be resisted by bars parallel to the local x direction = Mx +/- abs(Mxy)
Moment demand to be resisted by bars parallel to the local y direction = My +/- abs(Mxy)

Wood armer is a little more complicated because we could be talking about top bars or bottom bars. But, I prefer the simple method that I know I'm never going to get confused about.

Caveat:
I worked for RISA for 16 years, and I currently work for CSI / SAP. So, I am not a neutral person on these sorts of topics. I try to be reasonably neutral.
But, others would be better judges as to how impartial I really am.

### RE: Demand forces from FE plate results - Concrete design

Josh's method is both practical and conservative.

### RE: Demand forces from FE plate results - Concrete design

Just want to add that the contribution from Mxy is considered in the computation of global moments in STAAD.Pro. If you go to the Bentley Communities forum, you will find a wiki article titled "Global Moments in Plates" which explains this calculation with an example.

### RE: Demand forces from FE plate results - Concrete design

Sye123 -

Thank you for the info / correction.

I now regret mentioning the program names. I should merely have pointed out that some years ago I encountered a program that did NOT properly account for Mxy in the design moments for plates. Thereby, highlighting the fact that engineers should take for granted that this is being done properly.

### RE: Demand forces from FE plate results - Concrete design

Hey Josh, No worries. Good to know that you are with CSI. It's a small world. All the best.

### RE: Demand forces from FE plate results - Concrete design

Josh,

All European software that I know of includes it automatically.

STAAD has been including Mxy in design actions for concrete for many years having been convinced by the Europeans in the late 80's/early 90's that it is necessary. Their initial concrete design solution did not include it.

RAM Concepts default setting is to ignore it, for some reason equating it to compatibility torsion as I understand it. They calculate it and report it, but do not include it in design actions unless expressly requested by the designer. Unless they have changed this recently. Maybe My Hershey can explain why.

### RE: Demand forces from FE plate results - Concrete design

I don't believe that that wiki article shows proper combination of Mxy for use in design, and my experience doesn't line up with it either.

For example, with the methodolgy shown, if the global axis lines up with the local axis, the contribution of Mxy to the global moment is zero because sin of zero is zero. The Mxy effects are then neglected.

I believe this example is potentially showing a transform that takes Mxy into account in the determination of the global moment in the x and y directions, but that there's an Mxy component that exists in relation to the global axis as well that isn't reported and needs to be combined for design.

So if you have a case where global axis and local axis coincide and your local moments are:

Mx=50kN*m
My=75kN*m
Mxy=30kN*m

You would have global moment reported for 'design' of

Mx=50kN*m
My=75kN*m

This isn't what you'd expect from how you're describing it. This is reporting the Mx and My on the global axis, but doesn't include the design effects of Mxy.

### RE: Demand forces from FE plate results - Concrete design

The capability of STAAD has changed since my last use. But I reserve my opinion on correctness of the equations used in the wiki.

### RE: Demand forces from FE plate results - Concrete design

(OP)
Very much appreciate the replies. A lot to unpack here but it seems the fundamental issue here is the facilities of STAAD.

If I may go on a bit of a rant about STAAD and Bentley, I would like to preface this by saying that I am in no way affiliated with any FE software company

The first thing I'll address is TLHS's assessment of the global moment equations that Bentley provides. As TLHS points out, the global moment procedure provided by Bentley is incomplete. It is not enough to simply transform the moments onto the global axis. You then must account for Mxy in some way on the global axis by using, for example, Mx +/- abs(Mxy) and My +/- abs(Mxy), as JoshPlumSE suggests.

Another point that annoys me about the implementation in STAAD is that it limits the transformation to global moments to the global axis. Why can't I define a new axis to transform onto? Not every reinforcement layout is going to be orthogonal to the global axes. STAAD will not report global moments for plates that are non-orthogonal to the global axes.

Finally, the equations on Bentley's Wiki (https://communities.bentley.com/products/ram-staad...), they mention that these equations hold "If Sx and Sy are zero" with no further explanation. What changes with these equations if Sx and Sy are zero? They don't site any reference for the development of their approach which makes me very hesitant to rely on it at all for design.

If STAAD would just allow you to re-orient the local axis of the plates (and do the force transformations correctly), this would not be an issue.

Rant over.

What I am trying to do here is come up with a relatively simple postprocessing method that allows me to conservatively overcome all of these issues. The approach that I've come up with is: 1) Take the local moments Mx, My, Mxy and determine the principal moments M1, M2, M12 using Mohr's circle transformation. 2) Size my rebar to resist the principal moments, M1 +/- abs(M12) and M2 +/- abs(M12). My thought is that by using the principal moments and not the local moment, I could essentially orient my rebar in ANY direction and be safe. My concern is that this is too much conservatism?

Side note about the shear demand - I've essentially given up on that, I'm going to go to hand calcs for that.

### RE: Demand forces from FE plate results - Concrete design

Thank you rapt, you're always a wealth of information on these subjects!

### RE: Demand forces from FE plate results - Concrete design

This thesis by one of the GTSTRUDL developers is my go-to reference for FEM concrete stuff And has some good discussion on post processing. https://smartech.gatech.edu/bitstream/handle/1853/...

### RE: Demand forces from FE plate results - Concrete design

My view on finite element analysis is that you should consider whether you want to/can deal with the mass of output it provides before starting. That depends on the quality of the post-processor as you've found.

Is the issue that your reinforcement orientation changes throughout the slab? Most design methods rely on knowing the orientation of the reo to the analysis axes. You mentioned orienting the reinforcement in any direction which may work but be a poor performer. Consider large Mx with small My. Ideally you would have heavy X reo with light Y reo, but it sounds like you want to be free to rotate it even 90 degrees, which will give cracking problems and maybe deflection problem (and doesn't sound great for strength). There are recommended limits on the redistribution, eg the superseded Eurocode said no more than twice/half Wood Armer moments.

### RE: Demand forces from FE plate results - Concrete design

(OP)
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.

### RE: Demand forces from FE plate results - Concrete design

2

#### Quote (pyseng (Civil/Environmental)(OP)16 Oct 20 14:31 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....)

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 ?

#### Quote (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.)

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

#### Quote (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?)

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..

### RE: Demand forces from FE plate results - Concrete design

(OP)
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.

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