Orion Flat Slab Design Training

Orion Training

Flat Slabs

Copyright CSC(UK) Ltd. 2006

Flat Slabs CONTENT Introduction Model Generation Suggested Modelling Sequence Tips for meshing & punching perimeter modelling

Building Analysis FE Analysis Adjusting model properties for deflections

Design and Detailing Comparison with the Code Approach

Flat Slabs - Introduction Why Flat Slab and why FE? Perhaps you can tell us, is it: For flat slab: Reduced Structural Zones? Potential for Fast Formwork Erection and Construction? Un-obstructed service zones?

For FE: A potential to accommodate more irregular column positioning? Only way to deal confidently with more complex isolated load conditions? Only way to deal confidently with significant openings?

Flat Slabs - Introduction

Why Flat Slab and why FE? Whatever the reasons, we are certainly seeing more and more demand for an FE based flat slab solution within the context of a building modelling environment.

Flat Slabs Flowchart 1. Build the Model 2. Run the general building analysis to generate column & wall forces for lateral loads only. *

3a. Use sequential FE floor analyses to chase gravity loads down through the structure & generate slab design forces.

3b. Slab Design and Detailing

4a. Merge FE column results for gravity loads with building analysis results for lateral loads.

4b. Column/Wall Design and Detailing

* If FE Floor Analysis for Beam Loads has been used to decompose slab loads at each floor level, then building analysis generates valid design forces for lateral and gravity load cases in the walls.

3c. Punching Shear Checks

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Orion Training

Flat Slab Model Generation Copyright CSC(UK) Ltd. 2006

Flat Slabs Flowchart 1. Build the Model 2. Run the general building analysis to generate column & wall forces for lateral loads only. *

3a. Use sequential FE floor analyses to chase gravity loads down through the structure & generate slab design forces.

3b. Slab Design and Detailing

4a. Merge FE column results for gravity loads with building analysis results for lateral loads.

4b. Column/Wall Design and Detailing

* If FE Floor Analysis for Beam Loads has been used to decompose slab loads at each floor level, then building analysis generates valid design forces for lateral and gravity load cases in the walls.

3c. Punching Shear Checks

Flat Slab Model Generation We would suggest that by using the following sequence you will ultimately save time.

Flat Slab Model Generation 1. Make slab insertion easy by being organised with grids Avoid multiple closely spaced parallel grids – use one rather than two where possible. If intention is to include column/wall sections, avoid short distances from the slab edge to the column face. (Introduces short length meshing problems). Consider shrinking grids before placing slabs.

Flat Slab Model Generation 2. Create larger regular slab panels, avoid multiple slab panels between columns and especially around columns.

Flat Slab Model Generation 3. As you insert slabs, (and before adding holes and concentrated loads) occasionally check the following: Run Punching Checks and use hatch option to see that punching perimeters can be found. Generate an FE mesh to see that meshing works (using column section modelling if it is your intention to do so).

Flat Slab Model Generation 4. Repeat the previous step after adding holes and concentrated loads.

Flat Slab Model Generation 5. You should now have one floor that you know is going to work in both FE and punching. Other floors may be completely different, in which case the above procedure should be repeated. If other floors are partial duplicates you are now sure that the copied model works before editing starts.

Flat Slab Model Generation 6. Duplicate Floors – It is not essential to model every floor – genuine duplicates can be dealt with as such hence avoiding repetitive meshing etc – take full advantage of his.

Flat Slab Model Generation There are 2 primary difficulties with FE models of flat slabs Meshing fails to work Punching perimeters cannot be found

Flat Slab Model Generation Meshing difficulties can be caused by: Short slab edges Short slab spans between openings/edges Loads within a column boundary (Using the column/wall section modelling option inherently introduces short edges and can cause meshing difficulties)

Flat Slab Model Generation

Example 1: Short slab edge

Enlarged View of Wall Corner

Because walls not meeting at 90 degrees, Short slab edges created at corner of wall.

No problem if column/wall sections not Flat Slab Model Generation included….

But fails to mesh when column/wall sections included.

Solution: Edit grids to ensure walls are orthogonal.

Example 2: Another Short Flat Slab Model Generation slab edge

Flat Slab Model Generation No problem if column/wall sections not included….

Flat Slab Model Generation But problem when column/wall sections included

Flat Slab Model Generation

Solution: Move column down to remove gap

Flat Slab Model Generation Short slab edge problem sometimes indicated in the mesh generator by slabs being incorrectly displayed as triangular.

Flat Slab Model Generation Example 3: Slab load within column perimeter

Flat Slab Model Generation Meshes OK if column/wall sections not included

Flat Slab Model Generation Error if column/wall sections included

Flat Slab Model Generation Solution: Move the load outside the column perimeter

Flat Slab Model Generation Punching Perimeters As geometry becomes more complex, it becomes increasingly difficult to find the punching perimeter. Potentially very frustrating if you have meshed and analysed lots of floors and then cannot do punching checks.

Flat Slab Model Generation However… This frustration is completely avoidable. You can check the perimeters can be found before even attempting meshing.

Flat Slab Model Generation This is done as follows: Display the Punching Shear dialog Click Hatch Floor Area (Initially with Inc. Col, Wall, Beam Edges Unchecked).

Flat Slab Model Generation If entire floor area is hatched then punching perimeters can generally be determined for all columns.

Flat Slab Model Generation If entire floor area is NOT hatched then punching perimeters can not be determined in the un-hatched areas

Flat Slab Model Generation But, there is a tool that may resolve this: Check the box to Inc. Col, Wall, Beam Edges, and then click Hatch Floor Area again. If entire floor area is hatched then perimeters are OK

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Orion Training

Flat Slab Building Analysis Copyright CSC(UK) Ltd. 2006

Flat Slabs Flowchart 1. Build the Model 2. Run the general building analysis to generate column & wall forces for lateral loads only. *

3a. Use sequential FE floor analyses to chase gravity loads down through the structure & generate slab design forces.

3b. Slab Design and Detailing

4a. Merge FE column results for gravity loads with building analysis results for lateral loads.

4b. Column/Wall Design and Detailing

* If FE Floor Analysis for Beam Loads has been used to decompose slab loads at each floor level, then building analysis generates valid design forces for lateral and gravity load cases in the walls.

3c. Punching Shear Checks

Flat Slabs – Building Analysis Building Analysis has to be run in order to generate lateral design forces for columns and walls. After running a building analysis, the gravity design forces will not be correct unless the FE column/wall results are merged.

Flat Slabs – Building Analysis It should be emphasized that FE analysis only deals with gravity loads, and in building analysis sway load will not be resisted by any framing action between slabs and columns. Sway loads should therefore be resisted by walls (ie braced flat slab construction). Unbraced flat slab construction remains beyond the current scope of Orion.

Flat Slabs – Building Analysis The building analysis will only be valid provided steps are taken to ensure the notional load calculation is correct – use the ‘un-decomposed loads’ option for calculation of storey weight.

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Orion Training

Flat Slabs FE Floor Analysis Copyright CSC(UK) Ltd. 2006

Flat Slabs Flowchart 1. Build the Model 2. Run the general building analysis to generate column & wall forces for lateral loads only. *

3a. Use sequential FE floor analyses to chase gravity loads down through the structure & generate slab design forces.

3b. Slab Design and Detailing

4a. Merge FE column results for gravity loads with building analysis results for lateral loads.

4b. Column/Wall Design and Detailing

* If FE Floor Analysis for Beam Loads has been used to decompose slab loads at each floor level, then building analysis generates valid design forces for lateral and gravity load cases in the walls.

3c. Punching Shear Checks

Flat Slabs – FE Analysis

Sequential finite element analysis in general is covered elsewhere in this course. For flat slabs in particular we need to think about:

Flat Slabs – FE Analysis Selecting an appropriate slab thickness for the load to be carried. If the slab is too thin, Orion will be unable to determine the area of steel required. Therefore, always check the FE results for excessive deflection before moving on to the slab design. For appropriate member sizes refer to:

C H Goodchild, Economic Concrete Frame Elements, British Cement Association

Flat Slabs – FE Analysis Checking for Serviceability BS8110 doesn’t set a definitive limit for deflection. However, the span-to-depth checks in the code imply that the following limits are typically satisfied: Total deflection limited to span/250 Deflection occurring after installing non-structural items limited to span/500 For regular geometries, the span-to-depth check will be automatically satisfied by use of the previously mentioned publication. However, it may be impossible to apply this check to irregular geometries or slabs with holes.

Flat Slabs – FE Analysis A prediction of the actual deflection may often be regarded as a key issue, therefore what analysis model should be used? BS8110 – Suggests Consistent properties

It is your decision, we would suggest: If you are concerned about deflection then you should think about that from the outset. Ultimately, one model should suffice – if it is correct for deflection then it ought to be OK for the design moments.

Lets, consider deflection in more detail…

Flat Slabs – FE Analysis Deflection results for concrete structures should be regarded as estimates no matter what type of analysis is used. Unknowns associated with the accuracy of the material properties dictate this. For example, BS8110 indicates for C40 concrete, E in the range 22 - 34kN/mm2 so Orion defaults to 28kN/mm2.

This stiffness needs to be modified to allow for creep and cracking.

Flat Slabs – FE Analysis Three sources of reference considered here: 1. CIRIA Report 110 (2nd Edition) “Design of Reinforced Concrete Flat Slabs to BS8110” 2. Hossain T.R. and Vollum R.L, “Prediction of Slab Deflections and validation against Cardington Data”, Proceedings of the Institute of Civil Engineers, Structures and Building, paper 12500. 3. Concrete Society Technical Report No. 58, “Deflections in concrete slabs and beams”

Flat Slabs – FE Analysis

CIRIA Report 110 (2nd Edition) gives some guidance on adjustments appropriate to allow for both creep and cracking. In simple terms this suggests: reducing E by half to two thirds to allow for creep reducing I by half to allow for cracking. Hence the stiffness (EI) should be adjusted (reduced) by a factor of between 4 and 6, i.e. a stiffness multiplier of between 0.16 and 0.25 should be applied.

Flat Slabs – FE Analysis

Prediction of Slab Deflections and Validation against Cardington Data These studies indicate the importance of propping and the timing of prop removal on deflections. In the absence of better data, this work appears to conclude that long term deflections can be estimated on the basis of a linear static analysis with an adjusted EI value. Suggested adjustments are towards the bottom end of the 0.16 to 0.25 range. Where the pace of construction is slower or more controlled it is feasible that higher multipliers can be justified.

Flat Slabs – FE Analysis Technical Report 58 - Deflections in concrete slabs and beams This recent report provides the most up to date and comprehensive review of available guidance and methods. Suggested methods of assessing compliance with deflection criteria range from continued use of span/effective depth ratios, to estimation based on linear analysis, through to sophisticated non-linear solutions. A key point that is repeatedly emphasised is that you are always dealing with an estimate, no matter how sophisticated a method you use, “Calculated and measured deflections may differ by up to 30%”

Flat Slabs – FE Analysis Technical Report 58 - (continued) The report makes a distinction between assessing likely compliance with normal deflection limits and actually estimating deflection for consideration against other limits. It notes that where normal limits are considered applicable then use of span/effective depth ratios are perfectly adequate. In fact it even notes that these ratios will often give more economic solutions. It emphasises that the more sophisticated solutions need to be applied with greater caution and a full understanding of all the factors involved which should take account of construction/propping sequence, loading history.

Flat Slabs – FE Analysis

Technical Report 58 - (continued) Orion currently uses linear elastic analysis the simplest analytical method discussed in the report. So it should be the simplest method for you to use.

In terms of estimating deflections based on a linear analysis the report suggests some initial conservative defaults.

Flat Slabs – FE Analysis

Technical Report 58 - (continued) Reduce E by half to conservatively allow for cracking and shrinkage. Reduce E to Ec,eff to allow for creep

Ec,eff = E / (1 + φ ) where φ = creep coefficient (from figure 7.1 of BS 8110 Part 2)

The creep coefficient is dependent on the timing of loading, but the above would probably generally result in a suggested adjustment at or below the bottom end of the 0.16 to 0.25 range

Flat Slabs – FE Analysis

Technical Report 58 - (continued) TR 58 also provides more rigorous formulae for estimating the adjustment factors and deflection (suitable for spreadsheets) NOTE: These adjustment factors are aimed at providing conservative deflection estimations rather than showing likely compliance with serviceability limits. As will be shown in the following example use of these factors on a slab that satisfies span/effective depth limits will tend to predict deflections that a little higher than the suggested limits.

Flat Slabs – FE Analysis Minimising Slab Depths

The potential advantage of a more sophisticated method is that the analysis lets you control deflection by the introduction of more reinforcement. TR58 notes that if you do this rather than use span effective depth ratios you may start adding steel before even starting to reduce the slab depth. Consider a typical 300 thick slab that you want to try and reduce to 275 thick. Based on gross section properties the relative stiffness of these slabs is 3004/2754 = 1.4. This is an over-estimate, but it is easy to see that a small reduction in slab depth potentially leads to a significant reduction in stiffness and hence to a significant addition of reinforcement if this difference is to be catered for by adding reinforcement. Swapping to a post tensioned design would typically allow a depth saving of between 50 and 75mm on a 300mm thick slab. This represents the upper bound of depth saving that could possibly be achieved by adding steel in an RC design.

Flat Slabs – FE Analysis

Minimising Slab Depths (Continued) As slab thicknesses are reduced other design issues such as punching shear checks can become more critical. Clearly there are cases where engineers are reducing slab thicknesses at the expense of a significant increases in reinforcement. There is some debate as to whether this is in fact an economic balance that should be pursued in the majority of cases.

Flat Slabs – FE Analysis Overview of Serviceability (Deflection) Guidance. This subject can potentially get very complex, but is there actually a problem to solve? There does not seem to be any reported problems with apparently well designed slabs suffering from excessive deflection. Provided you have not completely ignored traditional limits/guidance you are unlikely to experience problems.

Flat Slabs – FE Analysis Applying Adjustment Factors in Orion

We require total dead and imposed deflection under service load (i.e. unfactored) However, in the Orion FE Post Processor the results are for G+Q*F (i.e. factored). To account for this, the stiffness adjustment factors ought to be increased again by something between 1.4 and 1.6. Hence the range for the overall stiffness adjustment might be 0.22 to 0.40. Noting that 0.22 and 0.4 are each derived by taking the most extreme view of each contributing factor, a range of 0.25 to 0.35 might be regarded as more reasonable.

Flat Slabs – FE Analysis Implications of adjusting slab stiffness Distribution of moments will be affected In general reducing slab stiffness will increase moments thrown into columns Options available 1. All adjustment to slab 2. Some adjustment to columns and bigger adjustment to slab 3. Adjust all equally

Flat Slabs – FE Analysis Option 2. - Some adjustment to cols and bigger adjustment to slab Adjust the basic material properties – 50% reduction applied below (Applied to All Members)

Flat Slabs – FE Analysis Option 2 (continued) A further 50% reduction is applied using the slab stiffness multiplier

Total adjustment = 0.5 x 0.5 = 0.25 – hence in required range.

Flat Slabs – FE Analysis Summary of Options Options available

Adjustment

Slab stiffness

Column stiffness

Effect on Col Moments

Effect on Slab Deflection

All adjustment to slab

SSM 25% E 100%

Reduced to 25%

Not reduced

Attracts more moment into cols

Reduces deflection

Some adjustment to cols and bigger adjustment to slab

SSM 50% E 50%

Reduced to 25%

Reduced to 50%

Adjust all equally

SSM 100% E 25%

Reduced to 25%

Reduced to 25%

Reduces moment in columns

Increases deflection

The highlighted option is probably favoured by most engineers because it complies with code guidance that consistent properties should be used throughout, and it keeps transfer moments to columns to a level that seems to be more in keeping with traditional engineering expectation.

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Orion Training

Flat Slabs Design and Detailing Copyright CSC(UK) Ltd. 2006

Flat Slabs Flowchart 1. Build the Model 2. Run the general building analysis to generate column & wall forces for lateral loads only. *

3a. Use sequential FE floor analyses to chase gravity loads down through the structure & generate slab design forces.

3b. Slab Design and Detailing

4a. Merge FE column results for gravity loads with building analysis results for lateral loads.

4b. Column/Wall Design and Detailing

* If FE Floor Analysis for Beam Loads has been used to decompose slab loads at each floor level, then building analysis generates valid design forces for lateral and gravity load cases in the walls.

3c. Punching Shear Checks

Flat Slab Design - Introduction

Where should we start? We are quite often faced with questions about highly irregular layouts where the engineer is questioning the results – they are not what he expects, but he has no strong basis for suggesting what the “correct” results should be. High Hogging Moments ? Sagging Moments Small (What about Pattern Loading ?)

SO - The place to start has to be with a regular structure where we can compare the expected results based on longstanding and proven code idealisations with the results from FE analysis.

Flat Slab Design - Introduction

The Example Model A regular model. 5 bay by 5 bay. 8m bays throughout. Top Floor – columns below only – 400square section. 300mm thick slab. G = 8.7kN/m2 Q = 5.0kN/m2 Ult Load = 20.18kN/m2

Flat Slab Design Introduction The following accepted techniques can be run on this model to give us some expected results The Yield Line Method The Code Approach (BS8110)

Flat Slab Design Introduction The Yield Line Method The basic expectation is that yield line approach needs less reinforcement than is required using an FE approach. It should be more efficient where structural regularity allows it to be applied. Although FE is conservative in comparison, it can deal with more irregular cases.

Flat Slab Design Introduction Both the Yield Line and the Code Approach check deflections by means of span to depth ratios. Because they determine the As required by different methods, the resulting allowable span to depth ratios will vary. Both techniques would indicate the span to depth ratio is OK. Lets examine the Code Approach in more detail…

The Code Approach (BS8110) The code actually provides alternative simplified methods of dealing with something as regular as this. The very simplest method is outlined in cl 3.7.2.7 and allows strip design moments to be determined using the coefficients in table 3.12. The more complex option requires an idealised frame analysis that is more tailored to the geometry of each specific building - we will only look at this option in this example.

The Code Approach (BS8110) This method requires you to idealise and analyse a flat slab structure: The idealisation depends on you being able to identify column strips and middle strips. You analyse the sub-frame as you would any other beam and column sub-frame model. You need to cater for pattern loads or apply moment re-distribution to the results based on the case with all spans fully loaded. You proportion the resulting forces between “column strips” and “middle strips” in an empirical fashion.

The Code Approach (BS8110) The Analysis Model Clause 3.7.2.2 indicates that the idealised 2D frame analysis should be based on the gross section properties of the columns and the slab strips (where the strip width is equal to the full panel width 8m in this case). The strips are loaded with the full slab load. We can analyse this simple frame in any general analysis package, e.g. S-Frame.

The Code Approach (BS8110)

The Basic Analysis Results The results for the case with all spans fully loaded are shown above. Since these are the results of a linear elastic analysis clause 3.7.2.1 (refers you to 3.5.2.3) applies and a 20% redistribution of moments from the supports to the spans is required.

The Code Approach (BS8110) Results after Redistribution Supp’t 1

Supp’t 2 Span 1

Mmt’s before Redistribution

91

Mmt’s after redistribution

73

Percentage change

-20%

Supp’t 3 Span 2

1057 763

830 363

846 877

461 664

550 -20%

+15%

Span 3

627 -20%

+52%

+36%

The Code Approach (BS8110) Proportioning of Design Moments in Strips. BS8110 Table 3.18 indicates how the design moments should be proportioned between Column Strips and Middle Strips. Note that clause 3.7.3.1 also requires that the central half of the column strip be designed for 2/3 of the hogging moment. The distribution of design forces in each of the 4m wide strips is therefore as follows:

Distribution of Moments Explained

The Code Approach (BS8110) Distribution of Re-distributed Design Moments in Strips. Column Strip Max Hogging (-ve) strip Red’d Hogging strip Max Sagging (+ve)

50% in 2m wide central section of 12.5% in 1m wide edge sections of 55% over full 4m width of strip

Middle Strip Max Hogging (-ve) Max Sagging (+ve)

25% over full 4m width of strip. 45% over full 4m width of strip

The Code Approach (BS8110) Distribution of Design Moments Supp’t 1

Supp’t 2 Span 1

Design Mmt’s after red’n

73kNm

Column Strip Central 2m

Special provisions apply

Column Strip 2 Edges (2m)

0

Middle Strip 4m wide

0

Supp’t 3 Span 2

846kNm 877kNm 55% 120kNm/m Ditto 45% 99kNm/m

Span 3 664kNm

550kNm 50% 212kNm/m 25% 106kNm/m 25% 53kNm/m

55% 76kNm/m Ditto 45% 62kNm/m

627kNm 50% 166kNm/m 25% 83kNm/m 25% 42kNm/m

55% 86kNm/m Ditto 45% 71kNm/m

The Code Approach (BS8110) Consider the relative magnitudes of design moments (after moment redistribution and proportioning). Sagging Moments Clearly the moments vary from span to span – highest moments in the end spans. For a regular layout like this internal span moments are restricted to around 70% of the end span moments.

Hogging Moments Clearly the hogging moments intensify rapidly as you approach the support (4 times higher than in middle strips)

We can utilise these expectations when we come to determining reinforcing requirements in FE.

The Yield Line Method There is a Yield Line Calc in the TEDDS software which can be run for this simple example

The Yield Line Method This does the deflection check on a span/eff depth basis And for the 300 deep slab this is shown to be OK

Comparisons with FE We have established some “expected” results using the code’s idealised approach. We can now create FE models and make comparisons…

The FE Approach Creating the FE Model Creep and cracking is allowed for by making some adjustment to cols and bigger adjustment to slab Adjust the basic material properties – 50% reduction applied to Modulus of Elasticity, E A further 50% reduction is applied using the slab stiffness multiplier Total adjustment = 0.5 x 0.5 = 0.25 – hence in required range. This is equivalent to using a deflection multiplier of 6 with unadjusted properties. (Ref TR 58)

Creating the FE Model Include Column and Wall Sections : If not included, the slab is meshed up to the column centreline. If included, the slab is meshed up to the physical perimeter of the column and a frame of rigid elements is created within this boundary.

Example – Comparing FE Modelling Options

Meshing Try to aim for 6-8 segments between column/support positions. For a simple model like this the suggested default of 2500 plates produces 8 segments.

The FE Approach

AnalysisExample Results – Contouring Options – Comparing FE Modelling Options There are numerous contouring options. In this example we will focus on results including Wood & Armer adjustments. Firstly, we shall use Mdtop contours to investigate the design hogging moments. Contours can be created for both the simpler and the more sophisticated FE models. Shown here are the Md1top moments with column and wall sections not included.

The FE Approach Design Hogging Moments Using the simpler FE model where column and wall sections are not included we expose peak centroidal results at the column heads of 483kNm/m. The more sophisticated FE model inherently allows us to deal with moments at the column face, and the design values reduce to 294kNm/m. The latter model is considered to be more realistic.

The FE Approach Design Hogging Moments A problem we are still faced with is that the contour diagrams display nodal values. These are very localised. They suffer from being mesh sensitive increasing the mesh density will not achieve convergence. They take no account of yielding that would occur in the real model.

The FE Approach Design Hogging Moments However, these peaks can be reduced by averaging the moment across the width of the design strip. Centre of Column Strip Column Strip Middle Strip

Example – Comparing FE Modelling Options

Design Hogging Moments Strips can be cut on the fly in the FE Post-Processor In this view you can see a 2m wide strip cut right across the column heads. Within this strip the peak hogging moments are still 294kNm/m (Note how results are not created within the column boundaries).

Example – Comparing FE Modelling Options

Design Hogging Moments Changing to an “Integral” strip these reduce to 224kNm/m You have the option to convert this into a required area of steel.

Comparing FE with the Code Approach Design Hogging Moments – Comparison

The code approach for this model suggests peak design moments of 212 kNm/m (265 before required 20% redistribution) The simpler FE model gives results of 426 peak, but 364 kNm/m using “integral” strip option. Using this simpler FE model we expose peak centroidal results at the column heads and even when these are averaged out, the design moments are still high. The more sophisticated FE model gives results of 294 peak, but 224 kNm/m using “integral” strip option. This more sophisticated FE model inherently allows us to deal with moments at the column face. The extreme peaks are not generated, and when the moments are averaged out the design values compare well with the tried and tested values established by the idealised code method.

The FE Approach Sagging Moments

Example – Comparing FE Modelling Options

Again contours can be created for both the simpler and the more sophisticated FE models.

Shown here are the Md1-bot moments for the simpler model (column and wall sections not included). Max. 102kNm/m

The FE Approach Sagging Moments

Example – Comparing FE Modelling Options

The contours for the more sophisticated FE model hardly change, giving a max. of 101kNm/m

Note: Cutting strips is not necessary to identify maximum sagging moments as localised peaks do not occur.

Comparing FE with the Code Approach

Design Sagging Moments – Comparison The code approach for this model suggests a design sagging moment of 120 kNm/m (Before redistribution this would have been 763/877 * 120 = 104 kNm/m)

Both the simpler and the more sophisticated FE models give a result of about 102 kNm/m. The above is of concern. Whichever FE model is used the result is a good deal smaller than the code value. But we can make another adjustment to account for this….

Example Sagging Moment Comparison

The positive moment factor is set to 1.2. This will increase all sagging moments by 20% it is not the same as moment re-distribution, but it is an option that provides some allowance for pattern loading. The maximum sagging moment is now reported as 121 kNm/m. In this example this happens to be in very close agreement with the 120 kNm/m derived by the code approach.

- Using FE Analysis

Deflections Example – Comparing FE Modelling Options

Again contours can be created for both the simpler and the more sophisticated FE models. The estimate total long term deflection for the simpler model is 52mm But an important advantage of the more sophisticated model is that it should reduce this deflection

Deflections - Comparison Example – Comparing FE Modelling Options

In the more sophisticated FE model the deflection estimate drops to 45mm We need to limit deflection to span/250 Taking the span as the diagonal across a slab panel, we conveniently arrive at: 11.3m/250 = 45mm Checks should also be made between the horizontal and vertical spans More generally, check max deflection occurring along a straight line between any 2 columns

Comparing FE with the Code Approach

Deflections - Comparison Bear in mind that multipliers are probably conservative and that all deflection estimates are approximate Having used a multiplier of 0.25, most engineers would be happy if deflection is close to or does not exceed span/250. Some engineers might use a larger multiplier (say 0.3) Note that in more complex layouts FE analysis graphically identifies critical locations so that consideration of deflection and perhaps cross checks using span/effective depth can be more focused.

Comparing FE with the Code Approach

Deflections - Comparison TR58 suggests using a 6 multiplier for a 300mm thick slab is on the low side and possibly a multiplier above 7 may be necessary. This might suggest the slab fails? However, traditional techniques using strip methods and span/depth ratios have indicated this model is acceptable.

Comparing FE with the Code Approach

Conclusion For this regular model, by using the option to “include column and wall sections” combined with the “integral” strip feature we have generated very comparable design information in FE when compared with traditional code idealisation. If we were to accept this conclusion from the outset it is possible to show that analysis and design of complex slabs can be carried out in Orion with greater speed, accuracy and productivity than ever before. Lets start again…

Example - Using FE Analysis

The FE Approach Same Model, Same Mesh: With the theory under our belts we do not have to work out what factors / choices to make – the model is created in seconds. During Model Generation the option to Include Column and Wall Sections is checked Prior to reviewing results the positive moment factor is set to 1.2.

Example - Using FE Analysis

Threshold Contours Detailing information can be obtained by selecting an area of steel effect, and switching on the Threshold Contours. For them to be drawn correctly you should first right click to setup the Concrete Cover.

Bottom Steel

Example - Using FE Analysis

The As(d)1-bot effect is selected Right click to display the Contour Setup The maximum As-req’d for sagging moments is 1150mm2/m We noted earlier that we expect reinforcement which provides 70-80% of this peak to be adequate over most of the slab. The threshold can be set by selecting bars and spacings. In this case T16 @ 250 provides 804mm2/m. (69%) The areas where additional steel is required are graphically highlighted.

Bottom Steel

Example - Using FE Analysis

Detailing Information The threshold diagram can be printed out. The additional steel required in the highlighted zones is always less than 1150 – 804 = 346mm2/m. In this case T12 @ 250 provides 452mm2/m. i.e. – lay in extra bars to create T16 and T12 alternate bars at 125crs in the highlighted zones. With closer examination you could reduce the extra bars to T10s in patches – is it worth it?

Example - Using FE Analysis

Bottom Steel Detailing Information User Defined Area of Steel contours can be generated by right clicking. These can then be printed and passed to the detailer.

As (required) Contours for As(d)1-bot

Top Steel

Example - Using FE Analysis

Threshold Contours By setting a threshold level of 0 we can see the areas in which at least some top steel is required. Note that with pattern loading these areas would increase slightly. However, many would regard it as normal/good practice to provide some level of reinforcement throughout the top of the slab.

Top Steel Threshold Contours The maximum As-req’d for hogging moments is reported as 2998mm2/m We noted earlier that hogging moments build rapidly and that a much lower general steel provision will be adequate over much of the slab. In this case T12 @ 250 provides 452mm2/m. This is little more than nominal reinforcement in a 300 thick slab. The areas where additional steel is required are graphically highlighted.

Example - Using FE Analysis

We are only left with deciding what to do about the reinforcement “patches” required over the column heads. This is where the “integral” strip feature really comes into it’s own. Bear in mind that the code approach expects this patch to be twice as heavily reinforced in the middle half as in the outer edges. There are a number of ways you could tackle this, but a good start is to look at the effect of doubling up the nominal steel provision and then cut strips over the top of that….

Top Steel Threshold Contours In this case T12 @ 125 provides 904mm2/m. The areas where additional steel is required are graphically highlighted. The zones are now quite concentrated at the column heads.

Example - Using FE Analysis

Top Steel Strip Results A 2m wide strip is cut over the column heads. Using the integral option the peak As-req’d is determined as 2091mm2/m. The additional steel required is therefore 2091 – 452 = 1639mm2/m. Adding T25 @ 250 provides an additional 1960mm2/m. NOTE - the 2m wide strip is narrower than the red zone – it is conservative to cut this narrower strip and then provide the additional reinforcement in a wider zone.

Example - Using FE Analysis

Top Steel – Detailing Information In this slab we have provided T12s at 250 throughout. The threshold contours show where additional “patches” are required. In more complex jobs you might define a number of standard patch details (although you may find that the incremental areas provided by standard bar diameters at set spacing mean that this is not practical). In this example we have 1 standard patch over internal columns, we are going to make it 5m square centred on the columns In the middle 2.5m the added bars are T25 @ 250 In the 1.25m strips to each side the added bars are T12 @ 250

Example - Using FE Analysis

Top Steel Detailing Information User Defined Area of Steel contours can be generated by right clicking. These can then be printed to indicate the “patches” to the detailer.

As (required) Contours for As(d)1-top

Example - Using FE Analysis Export of User defined As (required) Contours The contours can be exported as a layer to be displayed in the Graphic Editor Drawings containing the contours can then be exported to dxf for loading into a CAD program.

Example - Using FE Analysis

Top Steel Notes on Edge Patches Moment Transfer requirements at edge columns is well covered within BS8110 and expanded upon in Ciria Report 110. The guidance need not be repeated within the context of this presentation. Various checks/limits and alternatives may be applied/employed – it is all logical but quite idealised/empirical in nature. One way of checking the moment transfer requirement is to use the design moment developed in the column (above and below) and design the strip for that. We will look at what you can do within the FE post-processor in a moment. However, it is worth emphasising that this is a potentially severe limit that ought to be considered early in the design process – careful rearrangement of the slab/column intersection might prove to be important and/or simply more economic.

Example - Using FE Analysis

Top Steel Other Patches For this simple model we would then need to look at additional patches: One for the corners. One for the edges.

In each case the code needs to be referred to for guidance on a suitable strip width (Cl. 3.7.4.2) In this example a 600mm wide strip is appropriate. Cutting a 600mm wide strip as shown here a steel area is determined (1177mm2/m) However, note that the strip is not covering the entire red zone (the threshold based on the general reinforcement provision)

Example - Using FE Analysis

Top Steel Edge Patches The objective here is to ensure that all of the hogging moment in the slab is transferred to the column. By cutting a wider strip (1.8m) we can capture the total steel requirement - 958mm2/m over 1.8m = 1724mm2. If we choose to concentrate this in a 600mm wide strip we need to provide 2874mm2/m within that strip. Therefore the additional steel required within this strip is 2874 – 452 = 2422mm2/m Hence, in this very narrow strip the additional steel requirement might involve (4 No) T32 bars at 250.

Example - Using FE Analysis

Punching Shear Checks are required and can be carried out within the program. For technical information on these refer to the Punching Shear Checks Chapter of the Engineer’s Handbook.

Example - Using FE Analysis

Finished For this Simple Model We are finished in terms of analysis and design and have shown how information can be rapidly produced for detailing and also for estimating.

Flat Slabs - Conclusion

Summary For this Simple Model We have generated design information based on the code’s idealised approach. We have looked at two alternative FE models and shown that very similar design information can be generated with appropriate averaging and adjustment of the FE results.

What about more complex models? It is very difficult to make any comparison simply because you cannot create the idealised code model with sufficient certainty….

Flat Slabs - Conclusion

Idealisation for a Regular Structure An orthogonal system of “column strips” and “middle strips” is easy to visualise.

Flat Slabs - Conclusion

But for an Irregular Structure? No obvious orthogonal system of strips. A system of triangular zones radiating from a core zone that combines the walls and the column would be more rational. Codes give no way to deal with this in a simplified fashion. And we have still not added holes or concentrated loads.

Flat Slabs - Conclusion Orion will automatically generate FE models for this and much larger more complex models

Flat Slabs - Conclusion

Summary For the Simple Model We can make the comparisons and validate the methods. That should give us confidence

For more Complex Models We cannot make the comparisons because the code will not extend to this. But there is no reason why the same principles do not apply.

Flat Slabs - Conclusion The Buildings we are asked about:

Nobody shows us a nice regular layout. In the layouts we see the engineer has usually tried and failed to apply the code’s strip idealisation in a way that he is comfortable with. The engineer is turning to FE as a more sophisticated analysis. And IT IS a more sophisticated analysis, BUT it is not a design methodology. Any FE analysis will yield results that need to be used carefully. The recently published TR58 starts to offer good guidance on deflection, there appears to be less authoritative guidance on issues such as the determination of design moments across column heads. Engineers we speak to are often hoping that we/software can fill such voids. In practice the design methods ought to be established by the profession. We can only offer guidance and this presentation has summarised the most important aspects of this.

Thank You We hope you have found this interesting and informative.