FEA Discussion DRAFT

8/10/2019 FEA Discussion DRAFT

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T. Messer Beng CPeng RPEQ NPER MIEAust GradIstrutE

[email protected]

Figure 1. A complex finite element model

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Finite element analysis FEA has become a popular method of analysing flat slab concrete structures for practising engineers.There are some interesting issues that surface in the use of Finite element analysis that could catch the uninitiated off-guard.This publication seeks to explain common issue that arise in the modelling of concrete building structures using Finiteelement modelling and processes that can be used to handle these issues.

Keys words: Concrete, Finite element, modelling, design, computers, 3-dimensional, creep, shrinkage, poissons ratio, Mesh,twisting moments.

Advanced Finite element design tools have become the selected big stick of choice for engineers. Inexperiencedengineers are drawn to finite element modelling (FEM) programs as it gives the engineer the feel of freedom to designalmost anything the architect can dream up, from complex floors to unusual loadings without relying on experience orintuition.

Whether it is an approximate calculation to confirm the viability of a concept or the ultimate design analysis, the preferredapproach is to use a computer. This itself this is not necessarily an unscrupulous thing and computers can be valuable inunderstanding behaviour. Nevertheless, if the dependence is such that the engineer loses the confidence to carry outsimpler methods of analysis consequently the ability to carry out a self-regulating check of their model is compromised.Conversely this creates an interesting situation for the checking engineer (senior engineer) as it is almost impossible toensure that a complex FEM model, you have not generated yourself is correct. There are few sources of practical advice onhow to model and analyse using this technology, this guide seeks to highlight some of the topics engineers must be awareof when utilising this software.

The advantages of FEA/FEM is the ability to model complex issues such as transfer slabs, large opening, unusual loadingconditions, easily update calculations and adjustment of structure if changes occur. The other advantages over theequivalent frame method or similar is the ability to account for irregular column layouts. For example circular slabs with

column supports around the outside and one column in the centre, the equivalent slab frame method can be used for thisdesign but unless it is an experienced engineer it will be conservative. FEA models can handle this type of arrangementeffectively without conservative assumptions.

The disadvantage of FEA is the steep learning curve involved and the checking is difficult. Recently graduated engineersare normally not fully educated in the analysis concrete hence errors can occur especially with modelling assumptions.Finite element design requires a feel and experience for the concrete behaviour hence the user should not treat thesoftware as a black box with all the answers and should seek to understand what assumptions are made by the software inboth analysis and post processor.

Most structural problems can be broken down into different classes, these are shown below, this article will discussassuming static analysis.

1.

Static analysis (linear/nonlinear stress analysis);2.

Normal modes (resonant frequencies and mode shapes);3. Buckling behaviour (buckling coefficients and mode shapes);4.

Frequency response;5.

Random response;6. Transient response (linear/non linear stress analysis);


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FEA will return lower bending moments or deflections; this is only true if the previous techniques were

conservative. Studies have shown that the results from FEA compared to traditional techniques gives similarresults, IF an experienced engineer is the analyst.

- Deflections will be more accurate; The best estimate of deflection is in the range +15% to 30% using anytechnique, thus FAE is only as accurate as it assumptions. (However using multipliers (AS3600-09 Kcs) in theFEA instead of modified stiffness methods for long term deflection will cause the FEA to become guess workrather than calculation based)

- Not all structures need FEA, truth is that FEA should only be used for complex/unusual situations as for simpleprojects simple models/calculations will suffice.

- FEM Computer programs save time; this is only true if/when the in-depth checking of the results is omitted.-

Using Software will give accurate results; truth is no software is error free. Most programs have a limitedaccuracy.

- FEA will provide correct design results. On the contrary Elms 1985 All models are wrong, some are useful.FEM should be treated as a calculation with limited accuracy and should only be used for a help but not for the

basis of deign.

FEA/FEM should never be used for preliminary design, this is a waste of time with errors expected to occur during modelling,

for preliminary design stick to rules of thumb and hand calculations. A Good reference is Structural Engineer's Pocket Book

by Fiona.

What type of software does your office have?Taking the time to understand the design software is considered prudent for any professional engineer. This is especially thecase with FEA software. There are many different types of FEM software, 3D whole frame to 2D programs for each floor.The common situation is a 3D analysis is used to do the load take down/lateral analysis with floors exported to a separate2D package for reinforcement and deflection design. We will discuss assuming the later.

Note: there are also programs similar to RAPT which are FEA programs but not complete slab models; they should also beinterrogated to the same extent. However due to simplistic nature of the programs means these are ideal for graduatingengineers to grasp the theories.

Normally this is a linear based analysis package with adjustments in stiffness made to columns and floors to correct model.The concrete is treated as an elastic material and an assumption is made that concrete can transfer the forces as nominatedin the model. This is fine for ultimate limit state if P-Delta effects can be ignored but for service limit state the same does nothold hence the 2D package requirement.


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Figure 2. 3D model of a complex two storey building

Normally a non-linear analysis package; this enables the software to predict cracked concrete properties within a setaccuracy. For this to be accurate the software needs to be able to do this as an interactive process. Generally this will bebased on Brasons formula (hopefullyBischoff (EC2) as this is thought to be more accurate for lightly loaded slabs) orsimilar, as software with the ability to take yielding of the reinforcement into account directly is considered a rarity andgenerally reserved for scholarly type applications.

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A checklist is provided below for evaluation of a companys software

Software Query Discussion Critical for Yes/No

Analyse using the Construction

Sequence load take down?

A FEA analysis reaction load take down is un-

conservative. However an area load take downis conservative. The area method orconstruction sequence is recommended forload take downs.

Transfer

slabs/beams,columns,

Ability to reduce torsion stiffness? This is extremely important for beams intorsion. Can the beam generate the nominatedstiffness required to take the torsion loading, ifnot can you reduce the stiffness

Transfer Edgebeams, equilibriumtorsion, servicedeflections

Cracked section propertiescalculated and recalculated forsubsequent iterations for everyelement, in all directions

Reduction in stiffness due to cracking isimportant , Cracked section properties varythroughout the slab and direction both x & ydirections

deflections

What column/wall stiffness does the

program assume?

Column stiffness is hard to calculate due to the

large interaction of P/A and bending. Extremelyimportant for flat slabs

Column to beam

connection andcolumn moments

What does the program take intoaccount when working out bendingmoments and reinforcement

The bending moments in orthogonal directionsMxy need to be taken into for reinforcementand deflection design (e.g. is Wood Armeror Denton and Burgoyne methods used forsteel design?)

Reinforcement

Does the program generate bendingmoments Mx, My and Mxy orconverted moments Mux and Muy

The unconverted moment reported by FEA(Mx, My, Mxy) are not the same as momentreported by simple analysis (Mux, Muy). Themoments reported by FEA need to beconverted to design moments either usingWood Armer orDenton and Burgoyne.

Comparing/checkingmoments

Automatically apply load patterningto determine worst case designforces

Ensures worst credible design forces obtained Moment and shearforces

Does Software analyses in-planeforces ie variations in centroidelevation?

Allows realistic analysis of structure withvarying thicknesses containing beams ect

Beam stiffness andstep in the slabs

Incorporate curvature due to freeshrinkage strain

Required for determining deflections accurately deflections

Partially cracked properties arecalculated

Tensioning stiffening will prevent a fullycracked situation

Deflections for slabs

Separate analysis used for ULS andSLS

Less cracking occurs at the SLS, so the slab ismore stiff

deflections

Software calculates creepcoefficients, tensile strength for eachchange in loading throughout the lifeof the slab.

Important for the long term deflectioncalculations.

Long termdeflections

What creep or shrinkage propertiesis assumed for the vertical elements?

This is especially important if you have adifferent material used for vertical element (ega steel core with concrete column, as thecolumns will creep and shrink and the core willnot, and if not attended to a nice slope betweenthe core and the column will develop).

Columndeflections/slabslopes

Areas of required reinforcement canbe averaged over a specified width

This automation saves time for distributing overthe strips


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Reinforced concrete is a material made up of reinforcing steel, aggregates, water, cementious material (some unhydrated),

admixtures and voids. By varying the constituents of this material you will get highly varied results for the structuralbehaviour of the concrete. For example the young modulus depends highly on the aggregate selected and quantities. Theproperties of concrete can also be externally modified as well, such as weather, age of loadings, workmanship and curingconditions. The main codes allow concrete to be modelled as an elastic isotropic material, but there are a number ofassumption that are made to enable this, these will be discussed further throughout this guide.

The flexural tensile strength of the concrete is important as the concrete will crack once the tensile strength of the concreteis exceeding in the extreme fibre. In AS3600 the tensile strength is taken as 0.6sqr fc or for slab .5squ fc. The tensilestrength has an influence in the deflection of slabs and shallow beams through tension stiffening. The tensile strength ishighly variable as a rule and should be treated this way.

The value of elastic modulus can vary markedly depending on aggregate type, workmanship and curing condition to name afew. AS3600 gives an equation based on the mean compressive strength. It should be noted that the code points out thatthe Ej can vary by 20% under good conditions.

Creep is phenomenon where by the compressive strain in the elements increase over time under constant compressive

stress.All building material experience creep (plastic flow) strains, when added to the elastic strains this can increasedefection for concrete spanning members by a factor of 2-7. The quantity depends on many factors such as age at (durationof) loading, environment, and proportioning of materials are some of the main factors. To accurately predict the creepdeflections would require a large amount of effort with regards to testing ect. There are methods available to include thecreep effect, Kcs, AAEM and eurocode 2. The Kcs multiplier is a best guess design method, with an allowance forcompression steel. This has created confusion as often the steel in the top of slabs was considered compression reinforcing.For compression reinforcing to have an effect on long term creep, The reinforcement must at least be in the top half of thecompression zone gamma kud, Not just at the compression face of the member where it may be in tension or only very lowcompression stress and will have no effect on creep. This issue have been clarified in the latest edition of the code. Thegeneral rule of thumb is for a slab thickness of less than 250mm compression reinforcement will not affect long termdeflection. The AAEM or Eurocode method is far superior methods for estimating the deflection. These methods should beused for long term deflection estimate. The kcs method is not usable for PT slabs or beams.


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Creep shortening is important in vertical members, especially if different materials are used for the vertical elements such asa steel truss core with concrete columns, or if columns have different stress levels, this will results in differential deflections.The other possible problem occur whenthe columns and shear walls are sized for vertical loads only, ignoring creep andshrinkage in the vertical deflection, this causes the shear walls will be relatively lightly stressed under vertical loads as theyhave been dimensioned for earthquake/wind effects. The creep shortening of the columns will be far higher than the creepshortening of the shear walls. This will create extra stresses in the column slab connections and, if the building is not

symmetrical, will cause severe sway deflections (this is under vertical loading only and is a permanent condition).

Creep should also be considered for any other permanent loading conditions, such as water, earth and equipment loads.These loads can be either vertical or horizontal, for the horizontal loading, careful consideration needs to be given to theseeffects to ensure the building doesnt become unstable over time.

Rule of thumb: A good way to account for vertical creep is to ensure the entire vertical concrete elements have sameaverage stress under long term loads with the same concrete properties. For preliminary design the Author has found forservice load keep the total stress about 0.3fc for gravity load keep this about 0.15fc.

The supports restraint effects will be discussed further in the article, however the reinforcement restraint induced curvatureshould be included in the calculations for defection. Shrinkage curvature depends on the water/cement ratio, relativehumidity and the size and shape of the member. The effect of shrinkage in an asymmetrically reinforced section is to inducea curvature that can lead to significant deflection in shallow members. This effect should be considered in the deflectioncalculations. Vertical members also undergo shrinkage and this should be included in your.

Normally taken as 0-0.2 this value ensures the compressive stresses with are overestimated, which is ok for concretemodels. Conversely in the primary reinforcement areas a minimum of 20% of primary reinforcement should be provided inthe transfer direction to account for errors relating to the poison ratio and transfers strength requirements.

FE is not the only method for analysing concrete structures. For slabs in addition to the FE methods there are tabularmethod, elastic frame methods and grillage. It is often assumed by some engineers that code requirements are not requiredto be checked if an FEA modelled is unutilised, nevertheless the requirements of the code are still required to be checkedsuch as minimum transfer of moments between columns and slabs for punching shear and detailing requirements for reonear columns. The 25% detailing rule Cl9.2.2 is not often understood, the detailing requirement is required for punchingshear, this reo forms the tie in the crude strut tie, and the author hopes that in the future the % steel over the support will beincluded in the punching shear calculations to ensure this is clear to the design engineer.

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Volume change due to thermal, shrinkage and creep cause forces and strains to build up in restrained concrete membersthese actions should not be ignored in analysis. These strains can cause tensile stress in beams and slabs and shear/

moments in columns. Since the volume changes take place over a period of time, the effect of shortening on shear andmoments is reduced due to creep and micro-cracking effects, this causes the estimation of restraint forces is problematic atbest, with assumptions for connections, footing ect playing a major role. Such as if you assume fixed foundation supportsthe forces will be overestimated conversely if you assume pin foundations the forces will be under estimated. This slabrestraint cracking is the most common cause of deflection estimate being wide of the mark. The question is how youdetermine the amount of restraint. Some programs account for shrinkage restraint caused by the reinforcing, however veryfew account for restraint cracking.


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The only method that the author is aware of that attempt to give a method for calculating the restraint forces is the methodsproposed by PCI. The analysis method involves the use of an equivalent shortening principle. This will allow you to computea tensile force in the slab. This can then be used to adjust the expected tensile strength of the concrete.

Most commercial concrete FEA programs are not going provide any information in regards to these forces. Consequently expansion (or more correctly contraction) jointsmust be placed base on experience. Layout of walls and columns to reducerestraint is also important refer to figure 4.

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( ) 4. A .

Temperature changes in a member will cause thermal expansion, which intern can cause tensile stress which intern cancause deflection. This is very important for roof, wall and any other member exposed to the weather. Temperature should betaken into account in design of these members using a similar approach as to shrinkage. These stress will cause problemswith joints and sealants as the movement will cause tensile stress and fatigue to build up in the sealants, this is importantwhen selecting sealants for multistorey buildings, in situation where sealant replacement is expensive.


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In some situations, particularly in massive structures, such as dams, mat foundations, or any element more than about ameter or yard thick, the heat cannot be readily released. The mass concrete may then attain high internal temperatures,especially during hot weather construction, or if high cement contents are used. This requires thought when dealing withlarge columns with sizes greater than 1m sq. This is not able to be modelled in most softwares; accordingly engineering

judgment is required for cement contents.

Deflection of structure is directly related to the amount of cracking. Cracking should be analysised in all directions and notjust assumed. Tension stiffing plays a major role in determining the amount of deflection for concrete slabs. I t is necessaryto know the time of first cracking; this is of interest if the construction loading will be higher than the service loadings. Asonce the slab has cracked the loss in stiffness is permanent.

Owing to the inherent continuity of reinforced concrete construction, elemental design packages often require restraint

conditions to be specified at the boundary edges. The forces generated then need to be transferred to the restrainingmember. The element design package will not check the validity of these boundary conditions and the engineer must do so.For example, a beam framing into a thin wall may be closer to pinned than fixed. Many frame programs overestimate themoments transferred between flat slabs and boundary columns. Inadequate consideration of these factors could lead tocracking in the wall, under-design of the beam and, in the case of flat slabs, cracking and additional deflection.

Commercial concrete design software will only allow specific types of elements for building design. These are generally plate

and beam elements for reinforced concrete are used, with shell elements use for PT slabs. FEA is a modelling procedureand this must be kept in mind at all times. It should be noted that these types of elements are only particularly of use forflexure design and should not be used for bearing or shear applications (span on depth


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Figure 5; Typical element types

The selection on the size of elements is paramount to the accuracy of the design. Since the only place that forces arecalculated is at the notes these are import as to the accuracy of the models. For example 100m long beam modelled with

three nodes, mistakes are guaranteed and the model is unacceptable. However using the same beam and providing nodesat 1m centres then the model is more likely to be acceptable.

Rule of thumb: size of the elements should be no greater than 1m or span on 10.

Most software programs do this automatically; where the larger plates that have been entered by the engineer get turnedinto smaller matrix. The engineer must assess the finesse of the mesh. When a very course mesh is selected the results willnot give an accurate representation of the structure, particularly near supports, openings and under point loads. Converselyif too fine a mesh is selected excessive time to compute will be problem. The maximum hogging moments that the FEAshows will be affected by the size of the mesh. The finer the mesh generally the more intense the support moment. Howevergiven the software will do this for you it is advisable during the modelling stages to use a course mesh to refine the model to

ensure it is error free and using the finer mesh for design, this reduces the time for modelling and increases the accuracy fordesign.

Figure 6; Typical mesh

It is important to have more nodes accuracy, where the model constraint is changed rapidly. This is because the morenodes the better the distribution of the force the more accurate the analysis. Rombach (1) has shown that deflection

converge faster than bending moments in FE analysis and as shown in figure 7. Thus models should always be reviewed towith a few different meshing combinations to ensure a workable model.


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HFigure 7; convergence of bending moments vs deflections in the centre of a circular simply supported slab for differentnumber of elements. Extract from G.A. Rombach;

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Beams, flat plate and shells cannot be used to model discontinuity regions; for commercial FEA programs with only thesefeatures the programs use should be limited to application where the Bernoulli principle would be applicable. Finite-elementmodels are seldom capable of reproducing the complexities of boundary conditions and related stress disturbances in thebeam column joints, thus it is recommended that further analysis is undertaken to ensure adequate reinforcing is provided.

Meshing normally carried out by the computer these days, however the user needs to ensure a well-conditioned model iscreated. To ensure the model is acceptable the ratio of shapes should not exceed 1:2 (the minimum length to maximumlength). It is also important to ensure that the areas in the model where forces change rapidly more nodes are present toensure the accurate results are obtained.

Figure 8; elements shapes


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FEA programs require faithful modelling of the geometry; this must be accompanied by engineering judgement. Mostsoftware package offer a limited number of possible modelling elements, plates (shell for PT) and beams. Plates aregenerally triangular or quadrilateral elements with noted at corner and sometimes include additional nodes on the sides.

Beam element are used to model narrow beams, while plate elements are used to model wider beams, this is due to theaccuracy of the slab bending moment dimensioning when beam width increase when modelled as a beam element. AS3600allows moments to be taken at the face of the supports such as beams for slabs and columns for beams.

Engineers must keep in mind when modelling beams the torsional stiffness is important, while most programs allow thetorsional stiffness to be ignored when modelling beams but is the beams are modelled as plates this normally isnt possible,this must be taken into account of deflections where the reduction in stiffness due to cracking in torsion can be in the vicinityof 90%. When a structure is not dependent on torsional resistance for equilibrium, most codes say that torsion can beignored. However, if torsional stiffness is present in a computer model, the equilibrium found will rely on torsion and thetorsional stresses developed should be designed for. Some packages deal with torsions in the post-processing of results,and some assume that the torsional resistance of all elements is zero. Others will leave it to the engineer to take intoaccount. Again, the engineer must understand the assumption implicit in their design and the computer package being used.

Curves and circles are only able to be modelled by straight edge shapes; this should be kept in mind when modelling, as alarge mesh will give inaccurate answers.

Poor modelling good modelling

Figure 9; circular meshing

It is important to model supports in concrete slabs as accurately as possible, supports modelled correctly will enablebending moments for punching shear calculations to be appropriate (important for edge and corner columns in flat slabs).Ifthe corner and edge columns are modelled as pin-roller supports the bending moments there will be inaccuracies in theforces around the support, this could cause punching shear problems. The way in which the columns are model can varydrastically, the most inaccurate way is at a single node, and the more appropriate ways to model the columns are using ridgoffsets or modelling a thicker area near over the column. Neither of these methods is perfect, but they will provide morecorrect deflection than a single node support. Plastic assumptions are not possible in FEA analysis.


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Corners and connection need to be detailed correctly in any modelling, in FEA there are numinous ways to detail connectionat column to beams ect. The author recommends reading Finite element design of concrete structure ref (1) for thesetypes of models. These are not discussed in this article and require specific modelling assumptions.

St beneera theory for torsion is use for equivalent column stiffness. The equivalent columns theory has been shown to be agood theory for ultimate strength design, however it does have it short coming for deflection design, with care required forlarger spans or significant difference in length. This problem doesnt exist with FEA programs as all parts of the building aremodelled, however the column stiffness still needs to be modelled. Some programs will set the column stiffness to .7Ig fordesign; this is not correct for heavily loaded columns or lightly load columns. Column stiffness can variers from 0.4-1.2, thus

this needs to be taken into account in the model. As explained by:

For example, a low estimate of the effective stiffnesss of columns in a moment-resisting frame usually leads to aconservative (high) estimate of the displacement demands. In contrast, a low estimate of the effective stiffnesss for columnsin a shear-wall building would lead the designer to conservatively underestimate the elastic shear demands on the columns.Kenneth J. Elwood and Marc O. Eberhard ref 2

Edge and corner columns are the mostly likely to suffer from reduction in stiffness due to cracking. However Care should betaken in reducing the column stiffness especially with punching shear, care should also be taken in over estimating thestiffness and attracting more moment to the column than should be, the detailing of the joint should match or exceed thisassumption.

For initial estimates a good rule of thumb for column stiffness is for pin-ended K = 3EIeffI/Land for a fully fixed K = 4EIeff/L,

adjusting Ieff as required. However this only help you check the spring stiffness not the moment.


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Wall elements are normally modelled as vertical plates; however the engineer needs to decide if this is suitable. There aremany possible support conditions, such as Knife edge, with walls free to uplift or not. Rombach ref (1) suggests thatapproximately 20% of an edge of slab will attempt to uplift with a 13% increase in bending moment and an increase insupport reactions in the walls.

How are beams modelled with regards to the slab? All beams in slabs should be modelled as T & L beams for deflectionpurposes, otherwise estimates for deflection will be conservative. Depending on the computer package the beams can bemodelled using different techniques, the most common being with horizontal level of centroids for the beam and slabmatching. When the centroids match the beam effective depth needs to be increased for the eccentricity (For PT slabs thisis not recommended and the model should correctly represent the depth and centroid of the beam). An extract fromRombach is shown below; as you can see the difference in effective stiffness can be important. It is also important to ensureall the moments within the T-beam effective flange width is used to size the reinforcing in the beam.

Figure 12; Depth of equivalent beam hw and relation of moment of inertia. Extract from 1. G.A. Rombach;.


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How does the program model foundations, are these fully fixed, pinned, or neither. Generally foundations are in-betweenfully fixed and pinned and should be modelled as partially fixed or another conservative assume depending on the actionbeing considered. It you are limited to fixed and pinned foundations it is recommend you use model both cases to ensurethe worst case effect is computed.

Infinite stress both shear and bending are developed at the edge of supports due to numerical modelling. These peaks arenot actual and are created from the modelling process. If the opening is smaller than 15 times the depth Rombach ref (1)suggests that you can ignores these completely in your analysis. However if your opening is greater than15 d it issuggested that engineering judgment be used to decide on the redistribution required using for the theoretical bendingmoment required vs the numerical results.

Support problems can occur for other reasons such as closely spaced walls, in these situations results will show sharppeaks in the bending moments, shear and support reactions. This is due to singularities similar to columns being modelledon a single node. In relatively again these peaks will be disturbed across sections due to cracking and yielding. One methodis to handle this is using spring supports to spread the peak moments to the sounding nodes. Some programs have features

to help with this situation.

How do you handle redistribution of moments with FEA, This is easy for the equivalent frame method, but when you havemoments in contours do you redistribute the maximum moment? The average?. How does your computer package handlethis? Most computer programs recommend redistribution of the moments from the columns due to singularities.Redistribution is not allowed to reduce the moment taken by the columns (when modelled correctly), This is due to punchingshear being a brittle (non-ductile) failure mode and therefore have not allowed for moment redistribution in calculating themoments and reactions that have to be designed for in the punching shear calculation Mv*. Interestingly, it is the authorsexperience that redistribution of moments in beams is not of benefit as because moment redistribution cannot be used forthe service moments. For design it is recommended that all actions be redistributed after the actions have been distributedinto strips. For Non-linear analysis will 'automatically' allow some redistribution, due to cracking. If further hand redistribution

of the moments is undertaken, greater overall redistribution than that assumed by the code will be implied. In any case,suitability of code rules dealing with detailing should be carefully considered when non-linear analysis has been used for theultimate limit state.

Buckling in concrete building can be a governing design consideration for slender elements. Slender columns, Slabs withlarge opening, slender inverted t beams and walls need to be taken into account during anaylsis. Depending on the softwareanalysis method the program can help with this analysis, however care should be taken when using the software as therewill be strict limits to the softwares capabilities. Selecting the correct effective length is the normal problem for programs,with engineering judgment required to ensure realistic response. Generally it is advisable that the engineer check anyslender elements for buckling by hand using the factored up loads as appropriate for sway and non sway condition.

/According to the commentary: When this method is applied to the analysis of columns, allowance should be made for aninitial eccentricity (crookedness). Thus geometric imperfections should be included in your analysis. In the authors opinionthe models should reflect and justify the allowable tolerances. This is partially important for joints, as you can have rotationof the element being supported and the loading can end up cantilevering if the joint is poorly detailed. This eccentricityshould be included in you model, but the detailing should be by another method refer to disturbed areas discussion.

Attached finishing materials when attached so do provide some stiffening to the member. Unfortunately, in most cases thebenefit of this stiffening is unpredictable and cannot be considered in design. Where deflection is of particular importance

decks can be fastened to supporting beams by special methods and the value of the composite action determined.


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Number of load cases are required for finite element modelling, the engineer needs to determine how many load case arerequired. As3600 required pattern loading to be included for live load over 75% of dead load, the author prefers to do patternloading for all slabs because even though we treat the load as uniform for design, loads are never uniform. This canincrease the number of load combinations substantially and a checker pattern doesnt give the correct results. What about

point loads from the slabs above should these be patterned as well for transfer slabs, this requires engineering judgement.

Point loads if modelled as a single point will cause singularises, point loads should be distributed over an area of the actualloading, generally codes have foot prints for consideration of point loads, it is recommend that these be incorporated using ahigh pressure load instead of point loads, if possible.

A 1 A 3

A 2 A 4

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Figure 12; Suggested Loading arrangements for pattern live loading

Commercial pressures often lead to a requirement to strike the formwork as soon as possible and move on to subsequentfloors, with the minimum of propping. Tests on flat slabs have demonstrated that as much as 70%of the loads from a newlycast floor (formwork, wet concrete, construction loads) may be carried by the suspended floor below. It can generally beassumed that early striking of formwork will not greatly affect the deflection after installing the cladding and/or partitions. Thisis because the deflection affecting partitions will be smaller if the slab becomes cracked before, rather than after, theinstallation of the cladding and/or partitions.

It is essential that all members of the project design and construction team understand the implications of this deflection andmake adequate allowances to accommodate it.

Construction loads should not be ignored, writing that the structure should be fully propped by the contactor until thestructure is fully stable is NOT engineering. On most projects the arrangement for back propping is to backprop for threefloors. This can be seen in the loading selected to be taken by the slabs.

Loading sequenceThe loading sequence and timing is critical in determining the deflections, because it will influence the point at which theslab cracks. A loading sequence from the St George Warf study is shown below. Which shows the relative high loadsapplied during casting of the floor above. If an earlier stage proves critical, the crack depth at that stage should be carriedforward to all subsequent stages.

Figure 12; StGeroge study loading of slab during construction extract from the concrete centre study of the StGeorgeproject.


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( )

Points of high amounts of reinforcement with show up on contour plots often, these should be distributed as column andmiddle strips. This is due to the micro cracking reliving the slab at the support locals to the surrounding areas. There is atemptation to provided reinforcement to resist the peak moments, this should be avoided. This means design strips andsections must be defined for the serviceability and strength checks. The advantage of FEA is that design strips can bedefined after the slab has been modelled. Design strips can be defined by code definitions or points of zero shear,engineering judgment should ensure that the deign strip is designed for load acting on it. The points of zero shears isespecially useful for complex geometries, defining the strips based on FEA result should result in more economicalreinforcement for complex support situations referConcrete Society report TR43 (2).

Most computer programs will report moment and reinforcement in contours, the reinforcement and moments should bedistributed across the column and middle strips as appropriate keeping in mine all detailing requirements of the code. ForFEM it is recommended that bending moment be taken at the centre of the column. This is because of the uncertainties in

the modelling with regards the column. A useful rule of thumb for verifying the results is that top reinforcement in the columnstrip will be in the order of twice the area of the bottom reinforcement (i.e. not the same as, or 4 times as much as, thebottom reinforcement).

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Figure 13; Column/middle strip distribution


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14;

Modelling slabs as plate elements can lead to interpretation problems for bending moments. FEA will give bending momentsin the Mx and My directions, but due to the modelling used it will also give Mxy moments. This moment should be includedin the design of reinforcement as it can be significant. The most common method for including this in the reinforcement

design is proposed by Wood Armer Denton and Burgoyne. This method is slightly conservative and some software may

use more complex methods. Most computer programs will allow you to include Mxy in the outputs for Mx and My, thisshouldbe selected by the user. The standards Australia committee has recently reinforced this with a technical note.Please refer to Appendix A for the theory of twisting.

Figure 15; FE bending moment output

Programs will give you different opinions in the amount of torsions steel provided compared to the amounts required byAs3600. This is due to research by Warner & Ragan whom found during tests on beams integral with slabs torsion have anincreased the shear/torsion capacity of 4-6. These tests were however carried out on torsion beams with same depth as theslab. Yew-Chaye Loo et al showed that the increases resistance is also depended on the depth of the beam relative to theslab. Engineering judgement should always be used when selecting the opinion for design with or without torsion and whenthe compatibility torsion design is selected.


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P-Delta is a non-linear action occurring in all structures with axial loads both vertical and horizontal. The effect is a change isstructure thus possible changes in deflection and moments. The effect of these second order effects are relative to themagnitude of the applied axial force, displacement and slenderness of the elements making up the structure.

These can generally be classified as:

P-BIG delta (P-) - a structure effect P-little delta (P-) - a member effect

It should be ensured that if required p-delta effects are taken into account in the analysis, the software will makesassumptions or requires additional data input, care should be taken to understand and work within the limitations of thesoftware.

Figure 15; P-delta effects

FEA models will produce shear stress results; however these results generally are unable to help in punching shear checks.This is due to columns being modelled at single node points. It is recommended that punching shear be check using therequirements of AS3600, and that column stiffness modelling be included in the model as discussed earlier. However if youprefer to use the software to carry out these checks, all opening (even small) must be modelled correctly especially if nearthe shear permitter. Note also that punching shear is required to be calculated at the edges of drop panels and similar, mostsoftware will not carry out this check and if required the designer should do by hand.

A FEA analysis reaction load take down is un-conservative. However a manual load takes down is conservative. Theconstruction sequence is recommended for load take downs. The reason for this is in straight analysis will take into accountthe strength of element above for contributing to the load resisting behaviour. However this is not how the loading paths willoccurs in the real world. Generally the structures constructed first will take the loadings above.

In the design of the reinforcement in the 2D package stability is assumed to be provided by the cores or alternative system.

If additional moments are imposed on the column/slab/beam interfaces due to frame action these will need to be considered.


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In particular, where the horizontal forces are due to geometric imperfections (notional horizontal loads), the long-term elastic

modulus should be used.

Before the invention of complete building modelling software the engineer had to analysis each design strip for moment

compression/tension, shear and torsion, combined. This gave the engineer a good understanding fo the building andresponse to loadings. Engineers are encouraged to carrying out this in-depth analysis of critical points using engineeringjudgement, and if you dont have the experience carry out the analysis at every point. The limitation is because of the hugevolume of results produced by the models that a single engineer will find had to review all results, This is why it isrecommended that the model be reduced into more simple strips for analysis purpose, with results and calculations beingrecorded.

While the analysis provides the majority of reinforcing for the building, there is additional reinforcement required forserviceability and detailing. While serviceability consideration will be discussed later in the article, this section concentrationson reinforcement due to sound engineering judgement. Additional steel required around opening (possible recesses) to

prevent shrinkage cracking or similar. The end detailing affects the way in which the slabs and beam behaves andengineering judgment should be used to decide if the additional reinforcement needs to be reflected in your modelling.

Hardy Cross once wrote: Strength is essential but otherwise not important

Modelling of the structure must reflect the serviceability performance of the building with regards to cracking, deflection,cracking and stress limitation. Serviceability dominates the design of most structures, with deflection being influenced by,concrete strength (both compression and tension), creep, shrinkage, elastic modulus, restraint, loading/time ofloading/duration of loading, ambient conditions and durability.

Deflection design has many influences none of which can be predicted accurately, thus deflection predictions are bestestimate, and the estimate you make should be the upper bound for deflection, Not lower bound.

While there are minimum deflections quoted in the code, there are lot of instances where deflection is critically important. The designer will have to decide which of these apply to an individual project. Often the load which affects the criticaldeflection (e.g. deflection affecting cladding) is not applied at the same time as the initial loading;

Some critical situations for deflections:

Cladding walls can only handle finite amount of deflection, ranging from 1/250 to 1/2000, and some claddingmanufactures will say there systems can only handle 5mm of deflection.

Ceiling and light weight partition walls need to be considered for visual deflations, and if the edge of the slab isvisible, this should be considered.

In light weight slabs vibration consideration need to be check as well, this is extremely important in mix used areassuch as a gm in a office building.

Glass walls are very sensitive to deflections

Operable walls have very stringent requirements for defection and manufactures input should sort early for eachproject.

The design is best if coordinated with the design of the walls, Edge beams can be used to control of deflections of theexternal facade. Failure to account for deflection under walls will reduce the expect life of seals and joints. Other placesdeflection requirements need to be reviewed are Roof structures with membrane need extra care to ensure that accelerateddetermination of the slab is not a problem, such problems experience in the past have been deflection reducing the drainageof the roof or cracking this accelerates the membrane determination.


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How to check the deflations in complex slabs systems, the author recommend the procedure shown in the following figure

:

2/

=

A3600 250

Figure 16; interpreting deflections

Actual concrete deflections are influenced by many factors which cannot be fully taken into account.

Tensile strength of concrete a change in strength from 2.7 to 2.1 can increase deflections by 50%

Modulus of concrete +/- 20% Early construction loading

Shrinkage wrapping

Always remember load can only be estimated and even dead loads cannot usually be calculated to with 5% accuracy.Careful checking of the assumed moment transfer between the floor systems and vertical elements is recommended. This isimportant for the beam and slab connection to walls (including the core) as generally these cannot be detailed to take thenominated moments.

Possible methods for calculation of deflections using FEA

deemed to comply span on depth ratio as per cl 9.6.3

linear analysis with section properties adjusted for cracking factored up deflations using Kcs

non-linear analysis with adjusted elastic modulus

This type of analysis is not reflective of the slab deflations and should only be used in the case where slab deflations are notrequired to be the best estimate and a guess will do. This method involves calculating the cracked section by handapplying it to the model in average proportions. The change in stiffness should be accounted for by changing the E value.This e value should also be adjusted for long term creep and shrinkage as well. Again it should be stress that this method isa guess and should not be relied upon for deflection critical situations.

Using nonlinear software for deflection analysis will ensure an iterative analysis is performed. The software will carry outseveral analyses to find a final results using brason equation or similar with an initial assumption for area of reinforcement.An accurate assessment of deflection can only be made where the appropriate section properties are calculated for eachelement in the slab. Software giving the most accurate deflection calculations will consider the shrinkage effects. The effectof shrinkage in reinforced section is to induce a curvature that can lead to significant deflection in shallow members.

Once the initial deflection has been determined, It will be necessary to run the ULS model again with the correctreinforcement, because varying the area of reinforcement will alter the slab stiffness and hence the distribution of themoments (i.e. the stiffness at the supports will be reduced because of cracking and hence moment will be shed to otherareas). There will be different assumptions built into each piece of software and so it is very important that the engineer isfully aware of the assumptions and the effects they will have on the design.


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While AS3600 dose not have limiting cracks widths such as the Eurocode codes, there is in inbuilt requirements within thecode that will ensure the cracking is limited to an acceptable amount.

However there are some cracks that the code does not cover and should be included in your deflection analysis if applicable:

Plastic settlement cracks Plastic shrinkage cracks

Thermally induced cracks

Drying shrinkage cracks

Corrosion spalling

Alkali aggregate cracks and cracks due to other chemical effects

Many FEA programs handle the reinforcement and bending moment calculations for the design of the structure. Thus theengineer needs to have a good method for checking.

Hand calculations are very important for this, some possible checks are:1.

Calculate wl2/8 for a span and check the FEA model give the same value between the positive and negativemoments (10% difference could be considered a pass, anything greater would need further investigation)

2. Compare the total slab weight against the total reactions under dead load.3.

Span on depth rations again if you are well above normal limits then it would be worth checking again.4. Use alterative analysis program (like RAPT) to do a few lines up and down the building and compare.5. Is the span/depth or height to depth ratio in line with standard practice, if not why?6.

Simple Hand bending and shear diagrams7. Using the direct methods from the code and compare, if these vary why?8. Are supports modelled how they are going to really behave? Check walls to slab connections as these are difficult

to reinforce for full moment transfer.9.

Do the contour plots look similar to the pucher charts10.

Static equilibrium; compare total loads to total reactions.11.

checking the load increase (and face shear) in a column at any given floor is approximately equal to the load onthe floor area notionally supported by the column

Items to be considered in design but not discussed in this manual are:

How much the slab contributes to the beam load

Properties of concrete flat slabs, one-way slabs, waffle slabs, and slabs acting as diaphragms supported onsteel joists

Torsional and flexural effects of such systems on the actual stiffnesss of beams

Interaction of shear walls and beams;

Shear lag effects on interconnecting concrete walls (in elevator and stair shafts) Skewed slabs- in skew slabs infinite stress will be caused in the corners and special consideration is required.

Refer to ref 1 for further information on modelling possibilities.

Most software will assume the centre of elements with different thickness will be aligned in the vertical plane, sothe offset of the drop or beam should be defined in the model.

The output is usually in the form of contour plots, and there will be some interpretation required at the interfaceof elements with different thicknesses.

The discussions in this document are not for the design of post-tensioned/prestressed flat slabs

The discussions in this document are not intended to be a substitute for engineering judgement.

The output is usually in the form of contour plots, and there will be some interpretation required at the interface of

elements with different thicknesses.


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New program are being created all the time, these can increase design speed, with some programs developed to analysisdesign detailing and drawing from one package. However the engineer driving this software must understand the software,understand the limitations and things it doesnt do. These can be some of the items discussed above, or the problems notdiscussed above. The possible time saving used with this analysis should be spent on checking, as for these programs in-

depth checking should be completed, to ensure a safe and durable structure.

This discussion paper has only touched on the surface of finite element modelling for reinforced concrete structures, it is

recommended further reading is undertaken to fully understand the more complex issues of finite element modelling. The

Author recommends:

1. G.A. Rombach; Finite element design of concrete structures

2.

Jakobsen and Rosendahl; The Sleiphner Accident

The ultimate end game of any design/analysis should be proportionate to the design requires. This article explores the worldof modelling in Finite element programs; however simple models should still be used to verify the model produced. As youcan see the world of FEA doesnt offer an increased accuracy expect for the ability to model complex layouts, however themore worrying side effects could be a new way to make mistakes.

Most programs have a good solver thus the results for bending moments ect are depended on inputs by the user, howeverthe same cannot be said for the post processor for designing reinforcement. These are less tried and tested, the engineerneeds to know how to treat these results.

However now that you have read this article you should be able to evaluate your program and understand the fullimplications of the models you create, validating and interpreting the results give by your FEA software. Understanding thatsoftware is a utensil to do this in a faster manner not a substitute for engineering knowledge or experience.

As a rule, a program should be used only if engineers can predict the general deflection and distribution of moments in thestructure prior to obtaining a solution. The computed solution is used to verify the results previously predicted by theengineers. If the solution is significantly different from the prediction, engineers should use the results only if they cansatisfactorily explain the reason for the discrepancy and find it acceptable. ACI President's Memo Jos M. Izquierdo-Encarnacin 2003.

With any analysis it is important to validate the software, you should request from the software companydesigns/tests/comparisons that have been used to validate the software. Often the company will have comparisons that

have been published.A further plea is for software houses to produce detailed documentation on the technical assumptionsmade.

References1.

G.A. Rombach; Finite element design of concrete structures2.

THE CONCRETE SOCIETY. TR43; Post-tensioned concrete floors design handbook (Second edition).3. Australian standards AS3600 Design of concrete structures4.

Kenneth J. Elwood and Marc O. Eberhard: Effective Stiffness of Reinforced Concrete Columns5.

Fiona Cobb; Structural engineer's pocket book6. Morrison, John, Jones, Tony; use of computers in the design of concrete structures7.

The concrete Centre 2004 - St Geroge Warf Study8.

THE INSTITUTION OF STRUCTURAL ENGINEERS. Guidelines for the use of computers for engineeringcalculations, 2002. 2 .STANDING COMMITTEE ON STRUCTURAL SAFETY. Structural safety 1997-99: Review

recommendations: 12th Report of


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9.

SCOSS, The Institution of Structural Engineers, London. 2001.10. How to design reinforced concrete flat slabs using Finite Element Analysis - O Brooker BEng, CEng, MICE,

MIStructE

Acknowledgements

Gil Brock - Australia's Concrete Structures Code Committee BD2 and owner/developer of RAPT Software


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Lagranges 4th order partial differentiation equation is applicable to plate elements. The many classical approaches that arestill popular today mainly focus on deriving alternative moment fields for reinforcement design by eliminating the mxy twistingmoment.

All structural mechanics theories, including the beam and plate theories, must satisfy the following three conditions:1. Stress-strain relation material.2. Equilibrium force.3. Compatibility geometry.The stress-strain relation can usually be satisfied using design equations.However, an exact solution to satisfy both equilibrium and compatibility may be difficult and sometimes unnecessary. Whengiven a choice/decision between them, satisfying equilibrium is essential to prevent collapse.

For plates, with the assumptions straight-line-remains-straight and shear deformation excluded, the Lagranges plateequation applies:

The term mxy, the twisting moment, represents the twist, that is, the rate of change of slope in the x-direction as one movesin the y-direction or vise versa. The twisting moment results in shear stress parallel to the plate surface except near theends. Because of this shear flow difference, the reinforcement to prevent torsional beam failure should not be confused withthe reinforcement to prevent twisting plate failure.

This equation provides conception of the problem for reinforced plate design. It reveals that the load q can be subjectively

allocated between mx, my and mxy for reinforcement design as long as the LHS of the equation is larger than the RHS at allpoints of the plate system.

It is extremely important to note if the design moment fields are such that part of the load is carried by the mxy term, thedesign cannot just ignore mxy as that would make the addition of the mx and my terms smaller than the loads. This is theMain difference between the simpler models and the FEMs, Note here that torsion has not been ignored, rather aconcisions decision has been taken by the designer to take mxy as zero and, thus, increase one or both the othercomponents. However to ensure that the system has sufficient ductility additional compatibility reinforcement (as perAS3600-2009 clause 9.1.3.3(e)) must be placed in the high twisting regions to alleviate any adverse twisting effects and seethat the loads can be redistributed to the designers selected load path.as the simpler models do not ignore the Mxy buteliminate by apportioning the loads to Mx and My only. The lower bound theory assumes a moment fields at ultimate load such that:1. The equilibrium condition is satisfied at all points in the plate system.

2. The plate is reinforced according to the assumed moment fields.


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3. Satisfy boundary conditions.

Provided that the stress resultants sum to the total load on the slab, equilibrium is satisfied. 1-way slab design apportionloads only to mx.

1. 2-way moment coefficient chart method apportion loads to mx and my.2.

Equivalent frame method apportion loads to mx and my.

3.

Strip methods including the Hillerborgs strip method apportion loads to mx and my.

In linear-elastic FE package to obtain the design moments, three bending components (mx, my and mxy) must be reportedand two shear components (vx and vy) will be output. In this case, the torsional component is not likey to be zero and mostcertainly cannot be ignored. This is fundamental mechanics. To ignore the torsional moments in such circumstancesviolates equilibrium and is dangerous!

Many people think the plate finite element is just a smaller plate and that the nodal reactive moments mx and my are thesame as my and my in classical plate theory. Well, they are not!Lets take a look at the Lagranges equation:

The Lagranges equation for plate shows that mx, my and mxy are coupled and therefore, according to the Lower BoundTheory, allows the apportioning of loads carry by the mxy term to the mx and mx terms. For slab, this is very natural andcan be easily achieved by increasing the orthogonal mx and my reinforcement.Many conventional reinforced plate design methods, based on the Lower Bound Theory, had been formulated to findalternative mx and my moment design fields that satisfy the following equations:

However, these conventional methods are limited to simple structural forms and loads.

With the plane-remains-plane assumption and shear deformation excluded, the beam theory equations are simple and willnot be repeated, however the torsion equation will be discussed:

The torsion in beam is not related directly to the Mxy, these are two different actions and should be treated as such. Ifanything torsion from beams should be related to My & Mx.

It is important to realize the followings:1. The placements of longitudinal reinforcement and torsional stirrup are coupled.

2. Beam torsion results in circular shear stress.


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Documents

FEA Discussion DRAFT