Shear Wall Modelling Presentation

Orion TrainingPresentation

Copyright CSC(UK) Ltd. 2006

Orion Training

Orion Training

Shear Wall Modelling

Copyright CSC(UK) Ltd. 2006

Shear Wall Modelling

CONTENTIntroductionSimple 2D Wall Panel2D Wall Panel With Openings3D Core WallInteraction of Beams & WallsExamples in OrionOverview and Conclusions

Introduction

This presentation expands upon a Technical Note Published in “The Structural Engineer” 1st February 2005, Vol 83 No.3, page 20.It can be downloaded from the CSC website – www.cscworld.comSeveral other articles, papers etc prepared by CSC staff are available from the web site.

Introduction

The Technical Note was titled:NEW MODELLING, SAME ANSWERSIn writing this the objectives were:

To emphasise that FE modelling does not give new answers.

The same answers can be achieved using FE or traditional Beam Element Idealisations.

To raise awareness of issues introduced as you begin to model with FE (Shell) elements.

That in fact more care is needed to get acceptable answers using FE.That there is probably more chance of making serious mistakes using FE.

Introduction

Do we actually know what the “correct”answers are?A quote from another Technical Note:

“Engineering (and some may think FE practice also) is the art of modelling materials we do not wholly understand, into shapes we cannot precisely analyse, so as to withstand forces we cannot properly assess, this in such a way the public and (hopefully) the customer has no reason to suspect the extent of our ignorance.”

Structural Engineering Modelling and Analysis,by Arthur T. MurphyThe Structural Engineer – 3rd Feb 2004

Introduction

What does this mean in the context of concrete shear walls?If deflections and the distribution of forces are important to you then you need to get all aspects of your model right, this means:

Accurate material properties for each member.Short term E for C40 somewhere between 22 and 34kN/mm2, then what about creep allowance?

Accurate section properties for each member.Allowance for flanges and cracking?

A good arrangement of members to idealise the overall physical geometry.

This is what we are concentrating on in this presentation.

Introduction

Remember:We are engineers.Engineers routinely idealise structures in order to make reasonable (safe) estimates of design forces.We should not expect or demand exact correlation between results achieved by using different structural idealisations.

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Simple 2D Wall Panel

Can Wall Panels be idealised with Beam Elements?To be convinced that they can we need to start with something simple - consider the wall shown here.


What Deflection would you expect?

Deflection = F L3 / 3 E I (Ignoring shear deformation)

F = 100kNL = 35mE = 13E6 kN/m2

I = 3.6m4

Deflection= 100 x 353/(3 x 13E6 x 3.6)= 30.5mmSo allowing for shear deformation should expect something a little greater than 30.5mm


5 different models of the same wall.As meshing increases result converges on that given by the simplest beam element idealisation.First hint at importance of meshing and mesh sensitivity.And the beam idealisation has other advantages….

31.231.231.029.731.2Lateral Deflection(mm)

81 Shell36 Shell9 Shell1 ShellBeam


In order to design a wall panel you need to know “Panel Forces”.


For a beam element idealisation Panel Forces drop out naturally:

Panel Forces = Member ForcesFor a meshed wall the panel force is determined by re-integration of shell results along a cut line.

S-frame has tools allowing you to do this interactively.Orion will automatically re-integrate results to generate design forces at each floor level.


A similar model in Orion…..


Conclusions on Simple 2D Wall PanelThe beam element idealisation is excellent.

Results are potentially better than those that would be achieved by using a poorly meshed FE model.Results are more readily usable than those given by an FE model.

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2D Wall Panel With Openings

Some engineers may be surprised at the accuracy of the good old fashioned beam model in the previous example but still feel that the only way to take account of openings in walls is to resort to the use of shells.In this example we will look at the same wall panel, with the same loads applied, but with significant (door) openings cut out of the wall at every floor level.


First we will examine the results obtained from a series of increasingly finely meshed shell models as shown above.


Notice convergence as meshing is refinedAlso note reasonably significant variation in section design forces.

5658102354125236.8567 Shell

5758112324125336.6252 Shell

5860122254025636.063 Shell

6669171943526933.67 Shell

Moment (kNm)

Shear (kN)Axial (kN)Moment (kNm)

Shear (kN)Axial (kN)

Section B-BSection A-ASway (mm)Model


In the Technical Note we looked at two styles of model as shown below.We noted the importance of attaching the coupling beam to the mesh but did not demonstrate this issue in detail. Let’s consider that in a little more detail now…


Coupling Beam modelled with beam (not meshed)Analysis Without “DDF”

Deflections Huge (414mm) –nothing like the expected 37mm.No moments develop in coupling beams.

Obviously wrong – there is no moment interaction between the beams and the meshed wall panels.


Analysis With “DDF”Deflections much smallerAs the mesh is refined the peak deflections do not converge.

37.7mm46.8mm60.9mm118.0mm

The moments in the coupling beams also vary – lower moments where mesh is finer.

Obviously wrong ?You might only notice if you undertake a mesh sensitivity assessment.


Connection DetailLeft – the coupling beam induces large local stresses (and distortions) in the fine mesh.Right – by modelling the physical extent of the connection this stress concentration is reduced.


Some initial surprise that the DDF potentially produces such poor results.There are other ways to model the interconnection of the beam and the meshed wall, we will introduce that later.For now we will continue with the models and comparisons made in the technical note…


Mid-Pier ModelWall is not meshed, it is idealised by a single beam element positioned centrally in the panel (hence “mid-pier”)Coupling beams are attached to the face of the wall and designed for moments that occur at this location.So the connection between the coupling beam and the mid-pier (wall) beam has to be made with something else - a rigid beam.Suggested properties of rigid beam elements are given in the technical note – in this example they are taken as 10 to 100 times stiffer than a 3.5m deep beam.


4 models were considered:Models 1 and 3 have meshed wall panels, models 2 and 4 use the mid-pier idealisation.Models 1 and 2 have the coupling beams modelled at mid-height.Models 3 and 4 are essentially the same, but the coupling beams are moved up and modelled at the top level of the beam.

Results can now be compared.


5658102354125236.8567 Shell

5758112324125336.6252 Shell

5860122254025636.063 Shell

6669171943526933.67 Shell

Moment (kNm)




676702495025136.2Model 4

5357112344025536.5Model 3

616102395025636.2Model 2

5557142293725636.4Model 1

Moment (kNm)





Discussion of Results:

MODEL 1 – Meshed wall panels to each side of the opening with a beam element used for the coupling beam positioned on its physical centreline.

The results for this model agree well with the results of the fully meshed versions of the model.

MODEL 2 – Mid-Pier wall model with a beam element used for the coupling beam positioned on its physical centreline

The results in table 3 indicate that this simple model also compares well to the meshed models in table 2.The only exception is that the shell models indicate an axial load within the coupling beam while the beam models do not. This is explicable and relates entirely to the vertical load in each meshed panel – when a meshed panel is compressed vertically the sides of the panel expand laterally (as dictated by Poisson’s ratio) and these opposing lateral expansions are resisted by the coupling beam. This effect is negligible and would normally be ignored therefore this difference is not considered significant.


Discussion of Results (cont’d):

MODELS 3 & 4 – Repeats of models 1 and 2 but with the coupling beams and rigid arms lifted and idealised at the top ofthe coupling beam rather than on its centreline.

Clearly this is a less accurate idealisation but it is often much more convenient to model everything in one floor at a common level and top of structure is often chosen for this purpose.It is interesting to confirm that this common idealisation has very little impact on the results.


A similar model in Orion…..


Modelling NotePreviously showed modelling at beam – wall interface with rigid links extending up/down the wall.In Orion we have taken the links through the wall. There are various reasons for this. The properties of these links have been tuned by testing of numerous cases – more on this later.


Conclusions on 2D Wall Panel with OpeningsOnce again the beam element idealisation is very good.The results where meshed panels interact with beam elements can be good provided attention is given to the way the connections of beam and shell elements are modelled.IMPORTANT

Issues where beam elements interconnect with shell elements are not restricted to this modelling problem, they apply every time you try to mix beam and shell elements.Enhanced Shell elements that support the “DDF” should be used cautiously, they do not necessarily provide a solution.

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3D Core Wall

Once again, some engineers may be surprised at the accuracy of the mid-pier (beam) model in the previous example but still feel that the only way to deal with core walls is to resort to the use of shells.In this example the mid-pier model will be shown to extend very successfully to the analysis of 3-dimensional core walls .

3D Core WallWe will consider here a simple C-shaped core slightly offset from the centre of a simple 10 storey buildingThe columns around the core are held in position by floor diaphragm action.In this model two load cases are considered.

Sway in X – loads are applied in the X direction (as shown - parallel to the flanges of the core).Sway in Y – similar loads are applied in the Y direction – since the effective line of action of this load is eccentric to the centre of resistance provided by the core we expect this case to result in twisting at each floor level.

3D Core WallAs before we can look at the model using a series of increasingly finely meshed versions of the core and compare these results with those given by a beam idealisation.

848489233+/- 381.95253763-2963132.6Beam Model

8104743-74+/- 383.55083609-3061131.4Meshed model – 99 shells over floorto-floor height.

8434803-49+/- 381.65203659-3030130.7Meshed model – 33 shells over floorto-floor height.

890504039+/- 373.75273886-2883127.2

Meshed model – 11 shell over floorto-floor height.

ShearkN

MomentkNm

AxialkN

ShearkN

MomentkNm

AxialkN

End Panel ForcesMax Swayin X (mm)

End Panel ForcesMax Swayin X (mm)

Loads applied in YLoads applied in XModel

3D Core WallDiscussion of Results:

Once again the beam model is in excellent agreement.With loads applied in the X direction all the models sway without twisting.When an eccentric load is applied in the Y direction all the models sway and twist. As expected the twist is symmetrical as is indicated by the +/- values of sway in X.

In the mid-pier model tensions and compressions are developed in the component panels of the core, this can only happen if therigid arms that link the mid-pier elements are effective.

3D Core WallA similar model in Orion…..

3D Core Wall

Load in X direction gives symmetrical sway as expected.

3D Core Wall

Same Load Case Meshed walls give very similar results.

3D Core Wall

Load in Y direction causing sway and twist.

3D Core WallNEED CORRECT VIEW OF MESHED MODEL

Same Load Case and again the result is very similar.

3D Core WallWall Panel Forces

For design purposes you ideally need to know Panel Design Forces.Contouring looks good, but does not yield this information easily – re-integration of results is required.The Forces in the members of the mid-pier model give what you want with no further processing.

3D Core WallWall Panel Forces

Some general analysis software such as S-Frame provides tools to allow you to define integration lines.In Orion Integration Lines are automatically inserted at the top and bottom of every wall panel.The results shown here are for the same wall panel as noted earlier, meshed model results at top, mid-pier at bottom.There is a 5 to 10 % variation.

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Interaction of Beams & Walls

2D Wall Panel with OpeningsWe showed that the rigidity of the connection between the beam and the mesh needed to be modelled with care.We noted that the use of shells supporting the “DDF” is not in itself a robust solution.

3D Wall and Beam modelsThe above is not a 2D phenomenon, it can be demonstrated in simple 3D models….


Consider a model as simple as this.We will apply a horizontal and a vertical loadcase.


Meshed Models (“Correct Answers?)Lateral Load Case

Increased refinement – stable resultsDeflection approx 5.0mmBeam Moments can be determined by re-integration

End Moments = +/- 29kNm


Meshed Models (“Correct Answers?)Vertical Loadcase

Increased refinement – stable resultDeflection approx 4.0mmBeam Moments can be determined by re-integration

End Moments = 16kNm (hogging)Mid Span moment = -59kNm (sagging)


Meshed Wall + Beam ModelNo rigid links at connection.

Lateral Load CaseIncreased refinement – deflections keep increasing.Deflection approx 5.4mm for coarsest mesh and 7.5mm for finest.Diverging away from target of approx 5.0mm



Lateral Load CaseBeam Moments reduce as meshing is refined:

End Moments vary from 21kNm to 13.7kNmDiverging away from target of approx 29kNm



Vertical LoadcaseSame issues exist.Results diverging away from target deflections and moments.


Meshed Wall + Beam ModelWith rigid links at finer mesh connections.

Lateral Load CaseDeflections results are stable at 5.1mm. Good agreement with 5.0mm given by fully meshed model.



Lateral Load CaseBeam Moments are also stable at 26kNm.Reasonable agreement with 29kNm given by fully meshed model.



Vertical LoadcaseBeam Moments are again stable and in reasonable agreement with values taken from the fully meshed model.

End Moments = 19.5 (compared to 16kNm)Mid Span moment = -56 kNm (compared to -59kNm)


Automated Modelling in OrionProblem

If we start adding vertical rigid arms everywhere that a beam meets a wall we will create a meshing nightmare!We needed another solution.Rather than extending down the wall we have taken the rigid arms along the wall.

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Examples in Orion

If time permits these examples will be demonstrated live.The following screenshots summarise the points being made.

Examples in Orion

Symmetrical Model with unsymmetrical modelling assumptions.

Examples in Orion

Examples in Orion

Model With Angled Line of Symmetry.Loading applied along angled line.

Examples in Orion

Examples in Orion

Core Wall With Multiple Offset Openings.

Examples in OrionMeshed Model(course mesh?)Loading applied in Y direction causing sway and twist – resultant deflections shown in mm.

Examples in OrionA more finely meshed model shows that previous deflections were reasonable.In this view the moments developed in the coupling beams are shown.

Examples in OrionMid-Pier model results for the same load case cause very similar sway and twist –resultant deflections are 4% greater.

Examples in OrionThe design moment view is dominated by the moments developing in the mid-pier elements. However, the values indicated in the coupling beams are very similar to those seen in the meshed model.For example, at first floor 97.36 shown here compares with 91.73 in the meshed model – a 6% variation.

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Overview & Conclusions

Shear Walls and Core Wall Systems can be modelled with relatively equal accuracy with beam or shell idealisations.Modelling with FE shell elements:

Is not inherently free from modelling issues / difficulties.Does not inherently produce better results.

Modelling with beam elements:Probably requires more care.And, the very fact that you have considered and decided on idealisations tends to develop a feel for the model and an expectation of the results. It is more likely that unexpected results will be spotted and investigated.


These sorts of conclusions are not unique to shear and core walls.

Whenever you mix beam and shell elements in any model there are potential issues.Whenever you use shells at all you need to assess sensitivity to mesh refinement.

In simplest terms, the old analysis adage “RUBBISH IN = RUBBISH OUT”

is as likely to be applicable to shell models as beam models.


Observation of General FE Software in Use:

We have certainly seen a continuing increase in the use of FE.We have the feeling that once complex looking models are developed using shells the results are trusted a little too readily.There are engineers using (or being asked to use) FE with little previous training or understanding and no time allocated to investigate and develop that knowledge.


General analysis software allows you to build your own models and take full responsibility for your own modelling. Building Modelling Products such as Orion are beginning to automate the generation of the underlying analysis models.

However, you still have a responsibility to understand the modelling and check the results.For Shear and Core Walls in Orion:

By supporting alternative methods we are providing a logical way to help cross check results.And importantly, the mid-pier modelling option is often much quicker. On larger projects you might use it for preliminary design and then cross check using the FE option later.

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Thank You

We hope you have found this interesting and informative.

Shear Wall Modelling Presentation

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