Basic Analitical Modelling

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University of StrathclydeDepartment of Civil Engineering

BASIC PRINCIPLES FOR

ANALYTICAL MODELLING

(ANM1)

Produced as

LEARNING INFORMATION

for the BEng/MEng Courses in Civil Engineering

Version 1.2 September 1998

Prepared by: I A MacLeod



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CONTENTS

1 INTRODUCTION..............................................................................................1

1.1 A Modelling Process.......................................................................................1

1.2 Definitions ......................................................................................................2

1.3 Input - Define the Engineering Problem .......................................................2

1.4 The Conceptual Model ....................................................................................2

1.5 Software .........................................................................................................31.6 The Computational Model...............................................................................4

1.7 Results............................................................................................................41.8 Justification.....................................................................................................6

2 EXAMPLES OF MODELLING REVIEWS........................................................7

2.1 STADIUM FRAME........................................................................................7

3 CASE STUDIES ..............................................................................................14

3.1 The Sleipner Platform Collapse .....................................................................14



ANM1 Basic Principles for Analytical Modelling Page 1

1 INTRODUCTION

This document provides guidance on how to carry out structural modelling with emphasis on the use of computer software.

A main issue in the use of computer based models is the need to understand the basis of the behaviour of the system being modelled and how this relates to the behaviour as predicted by the model. Use of the process described in Section 1 of this document helps to develop such understanding.

1.1 A Modelling Process

1.1.1 A Modelling Process MapTable 1.2.1 is a ‘map’ of a process for analytical modelling of engineering systems. There are three

‘Stages’ in the process and seven sub-processes.

Table 1.2.1 Modelling Process Map

A

Model Development

B

Acceptance Criteria

C

Model Assurance

1 Input Define the engineering problem. n1.4

2 Conceptual Model Define the conceptualmodel n1.5.1

Define acceptancecriteria n1.5.2

Validate the conceptualmodel n1.5.3

3 Software Select suitablesoftware

n1.6.1

Define acceptancecriteria n1.6.1

Software validation andverification n1.6.2

4 Computational

Model

Develop thecomputational model

n1.7.1

Define acceptancecriteria

n1.7.2

Verify the computationalmodel

n1.7.3

5 Results Perform Calculations Define acceptancecriteria n1.8.1

Results verification

n1.8.2

6 Justification Define overallacceptance criteria

n1.9.1

Accept or reject theoverall solution

Carry our parameter studies n1.9.2

Produce modellingreview document. n1.9.3

7 Output Pass on results to nextstage of design process

The items in the boxes in the map represent activities and the numbers in the boxes refer to the sections of this document which provide relevant guidance.

Although the map can be interpreted as implying a linear process taking the activities in row order, with atrend from top left to bottom right, the real process may comprise several parallel activities some of whichmay be repeated depending on the outcomes of the previous activities. For example it may not be

possible to complete a model validation exercise until results have been generated.The map can be used as a checklist for modelling.




1.2 Definitions

1.2.1 Validation And VerificationThe words ‘validation’ and ‘verification are not normally clearly differentiated. In this document more

consistent definitions are provided (Knowles and Maguire 1995, MacLeod 1995).In a modelling process, we need to work with the deviations between the target value of a variable and the

value that you have. The target value is the desired value of the variable.• Error - where the target value is true. This corresponds to a situation where it is possible to identify a

unique set of values which will be independent of the method of establishing them. For example a set

of simultaneous equations has a potentially true solution (although real solutions are alwaysapproximations).

• Uncertainty - where the target value is not true. For example Young’s modulus of a material willalways be slightly different each time it is measured.

The word verification represents a process where error is the main consideration.The word validation represents a process where uncertainty is the main consideration.

1.2.2 The Conceptual Model and the Computational Model

The conceptual model is defined in terms of material behaviour, loading, boundary conditions, etc. For example in the analysis of a floor slab, the conceptual model could involve linear elastic material behaviour, thin plate bending theory and point supports. For a geotechnical slope stability problem, the

conceptual model may be a circular slip surface with defined failure criteria.

The computational model incorporates the means of achieving a solution. In the case of the floor slab

model, the computational model could be based on a specific plate bending finite element mesh, a grillagemodel or a lower bound model. In the slip circle situation the computational model would involve analgorithm to find the critical failure surface. In some cases the boundary conditions may be part of the

computational model; for example an elastic half space conceptual model might be reduced in thecomputational model to a finite size by imposing boundary conditions.

1.3 Input - Define the Engineering ProblemItems to be considered may include:1. Portrayal of the engineering system to be modelled. This would be mainly in the form of references

to drawings, sketches and written descriptions.

2. Objectives of the model. It is essential to define what outcomes are required from the modellingactivity. Typical objectives of modelling are to predict:

• Resultant internal forces/stresses.

• Failure conditions

• Local internal forces/stresses

• Short term deformations

• Long term deformations

• Instability conditions

• Dynamic characteristics

1.4 The Conceptual Model

1.4.1 Defining the Conceptual ModelA useful strategy at the early part of modelling is to draw up an Issue List which is used to help inmaking decisions about the model. In this context an ‘issue’ is any feature or factor which may need to beconsidered in relation to the model. The issue list may be used later in the validation process.

For example, consider the support frame for a football stadium shown in Figure 2.1.1. Issues in creatingan analytical model for this include:

1. What support conditions are to be imposed - pinned or fixed?2. Should the joints be treated as pin connected or as moment resisting?




3. How does the frame interact with the other parts of the structure? Is it reasonable to treat it as aseparate plane system?

4. What will be the loading - dead, live, wind, snow, dynamic, etc.5. Will any second order effects be significant (column buckling, lateral torsional buckling, etc.)?

This list may be augmented as the process develops. The model is created taking account of the issues

and objectives.

Principles which may be used in creating conceptual models include:

• Do not us a model that is more complex than is necessary. The simplest modes which satisfy theobjectives of the modelling exercise are normally the most useful

• It is not normally worthwhile to examine local behaviour in a model which deals with resultantactions. The local behaviour is normally treated by extracting it from the overall model

The conceptual model is defined by a portrayal which is in the form of drawings and materialdescriptions of the model plus statements about the assumptions made.

1.4.2 Acceptance Criteria for the Conceptual ModelThe acceptance of a model involves risk and a risk assessment approach may be used for acceptance -

See Section 2.1.2

1.4.3 Validation of the Conceptual ModelThe differences between the system being modelled and the conceptual model are mainly uncertainties

and therefore consideration of this aspect is ‘validation’. The process involves making a list of assumptions for the model and comparing these with the real behaviour of the system.The question to be asked is: “Is the conceptual model capable of satisfying the objectives of the

engineering problem?”

Issues to be considered in the validation may include:

1. The validity of the constitutive relationships used.2. The validity of the restraints/boundary conditions and the constraints applied.3. Assumptions in relation to small deformations.

4. Assumptions in relation to loading

Information about the validity of the model may be gained from records of previous testing.

Alternatively, in innovative situations, new testing work may need to be commissioned.

1.5 Software

1.5.1 Selecting Software, Acceptance CriteriaAll software, no matter how well tested, is likely to contain errors. This is a consequence of the fact thatit is impractical to test completely a non-trivial program; the number of test cases needed is so vast that

they would take forever to run. Since testing can be used to show the presence of errors, but their absence,inevitably bugs are likely to remain. Users of software should be mindful of this and take precautions tominimise the impact of any software error on their engineering designs.

As a minimum, users should check that they can reproduce the results of any test the developer has performed. They therefore need to obtain evidence of such tests from the developer.

Practical advice about how end-users can test engineering software can be found in AGS (1994). Thisdocument has broad application to software beyond geotechnical engineering.

Acceptance criteria could be based on benchmarks published by NAFEMS




1.5.2 Software Validation and VerificationThe validation question for the software is “Is the software capable of solving the conceptual model?”

This question can be answered by comparing the specification for the software with the conceptual model.

The verification question for the software is “Has the software been subject to adequate quality assurance procedures?” For commercial software this question may be difficult to obtain. Much depends on the

reputation of the supplier. For in-house software, information to help answer the question may be morereadily available. The need for users to pose the question to suppliers and the need for suppliers to be able

to answer it needs to be borne in mind by these parties.

1.6 The Computational Model

1.6.1 Develop the Computational ModelIssues in relation to a computational model include:

• The type of element or finite difference scheme to be used

• The degree of mesh refinement

The portrayal of the computational model in terms of mesh /element definition would normally be

included with the portrayal of the conceptual model.

1.6.2 Acceptance Criteria and Verification of the Computational ModelThe computational model will solve the conceptual model with some degree of error. The question to beasked is “Is the level of error in the computational model acceptable?” Two main sources of error incomputational models are discretisation error and truncation error.

Discretisation error is generated by the process of dividing the system into finite elements, finitedifference mesh, etc. Experience, advice and reference to published information (e.g. from NAFEMS)may be needed in assessing discretisation error. The concept of discretisation normally infers that, as the

mesh density is increased, the true solution is approached. Use of trial meshes to investigate suchconvergence may be appropriate for important projects.Truncation error is the error generated in the numerical processing of the simultaneous equations. An

equilibrium check (which is in effect a check on the residuals of the solution) can sometimes identifytruncation error but this is not a foolproof check. Some equation solvers include a report on the ratio of the leading diagonal elements of the original stiffness matrix to that of the ‘decomposed’ form of this

matrix which is created in the solution process. This is again an indication but not a measure of accuracy.Accuracy of solutions can be assessed but this requires a significant amount of computation.

1.7 Results

1.7.1 Acceptance Criteria for ResultsThe acceptance criteria for results can be based on risk principles. The amount of resource to be appliedin the checking process to reduce the likelihood of errors needs to take account of the consequences of

such errors.Thus the complexity of the results verification process will depend on the degree of risk involved in themodelling exercise. For systems in high risk situations it may be necessary to commission a complete re-analysis using different personnel to set up the data and a different software system.

1.7.2 Results VerificationThe question to be asked in a results verification is: “Do the results correspond to that expected from themodel?”

In the results verification process the following checks may be carried out:

• Check the data

• Check overall equilibrium

• Check that the support restraints have been correctly applied by looking at the deformations of therestrained nodes.




• Check for symmetry if present.

• Check the overall form of the results. Look at the deflected shape and the distribution of element

forces/stresses. Do these conform with what is expected?

• Create a Checking Model

Checking Model A checking model is a simplified version of the main model having adequate accuracy

for checking purposes (MacLeod 1990). The results from the checking model should show a correlationwith the main model results which is consistent with degree of approximation made for the checkingmodel. The checking model should be used if practicable to check both deformations and element

forces/stresses.The checking model can be a simplified model of the system suitable for 'back of an envelope'calculations or could require a computer solution. It is most important however that it does adequatelyrepresent the system being modelled.

If the checking model is a simplified version of the main model, the results will not correspond exactly. Itis important to be able to justify the degree of difference between the two. If you cannot do this then thechecking model may have limited value.

Four possibilities when comparing the results from a main model and a checking model are:

1. The two results are satisfactorily close and are both essentially correct. This is the desired situation

but it is not easy to be fully satisfied that it exists,2. The two results are significantly different. In this case work is required to establish the reasons for

the difference. The main model may have errors. The checking model may be conceptually wrongor it may have errors in the calculation.

3. The two results are similar but are both in error by a similar amount, possibly for different reasons.4. The two results are similar, with the main model correct but with the checking model based on false

information due an arithmetic error or to compensating erroneous assumptions.

In this list, Situations 3 and 4 are false correlations. Such situations are remarkably common. InSituation 4 the right conclusions may be drawn for the wrong reasons. This may not result in fault but itis nevertheless unsatisfactory. People tend to take an optimistic view and when they find that results are

close they are quick to accept this as proof of accuracy. A single apparently favourable correlation doesnot provide a full verification. It is necessary to treat all results with suspicion and not jump to

conclusions.

It is very useful to have an idea of the likely sign of the difference between the main model and thechecking model. For example, if the assumptions made for the checking model provide extra stiffness,then one would expect the deflections from it to be basically less than those from the main model. It can

be useful to make assumptions for the checking model which are alternately stiffer and then more flexiblethan the main model. This can then allow a bracketing of the main model results between upper andlower limits.

Equivalent Frames

A common type of equivalent model is to treat the system as an equivalent frame i.e. as a set of bendingor axial force elements. Obviously reduction to one bending element is desirable from the computational point of view and this indeed is sometimes possible, e.g. lateral supports for structures can be treated as

single ‘stick’ model. Typical models are:

• Treat a beam with varying cross-section as one with constant cross section.

• Treat a truss as an equivalent beam using the formulae given in Figure 2.1 taking account of shear

and bending deformation if necessary.

• Assume either simple supports or fully fixed supports for systems which have partial support fixity.

Solutions for checking models may be found in publications such as Young (1989)

Checking Load Case A useful concept is a checking load case where a simplified load (possibly asingle point load which tend to affect the whole structure) is applied for checking purposes only. Analysis

of the results of such a load case would be carried out before production load cases are run and a checking

model applied to it. However, despite early favourable indications of accuracy a constant watch for errors must be maintained. Results should always be suspected of being in error. Changes made to data

(change of member properties, additional load cases, etc.) have potential for introducing of fresh errors.




1.8 Justification

1.8.1 Overall Acceptance CriteriaThe acceptance of the modelling work needs to take account of all the validation and verification

outcomes. An overview of this information needs to be taken before an acceptance decision is made.

1.8.2 Parameter StudiesParameter studies can prove useful in promoting better understand of the behaviour of systems beingmodelled. In a parameter study (also called a sensitivity analysis) variables in the model are changed soas to investigate their effect on behaviour. For example, if the results of the analysis are not sensitive to

the value of a particular parameter this can help to validate the model and provides information which canhelp in the design.It is best to base comparisons as part of a parameter study on the results of a reference model. This may

be the version of the model which is expected to be used for design. Each parameter to be studied isvaried one at a time, reversing each change before proceeding to the next parameter. The reference modelmay be modified as the study proceeds but it is important not to accumulate changes.

When comparing trends in behaviour it is best to make parameters non-dimensional. Quote, for example, percentage changes rather than absolute values.

1.8.3 The Modelling ReviewA modelling review is a collection of information about the modelling activity. The extent of theinformation to be recorded will depend on the degree to which the analysis is non-standard and the

importance of the model. The modelling review document for a non-standard analysis of a nuclear facility is likely to be extensive whereas that for a frame in a conventional building would be quite short.Reviews should not contain more information than is necessary.

Re-use of information from previous modelling reviews is a good way of minimising the resource neededfor this activity.All of the activities set out in Table 1.2.1 may have corresponding items in the review.




2 EXAMPLES OF MODELLING REVIEWS

2.1 STADIUM FRAME

2.1.1 The Engineering Problem(a) Geometry, etc. - see Figure 2.1.1

(b) Objectives:1. Estimate internal forces due to dead and live loading2. Estimate internal forces due to wind loading

3. Estimate deflections due to crowd loading.4. Estimate roof deflections due to wind loading5. Estimate natural frequencies of the system.

2.1.2 The Conceptual Model

Portrayal

See Figure 2.1.2.

Validation of the Conceptual Model

AssumptionsA Linear elastic behaviour - OK for stresses below yield and for lower bound solutions

Use of beam elements:B Bending with no shear deformation - maximum span to depth ratio 12:1 OK C Axial force does not cause bending (first order theory) No sway - check element critical load

ratios from output. Design criteria likely to result in this assumption being valid.D Assume full moment connections at joints. This will tend to overestimate axial forces andunderestimate deflection. Since it is a triangulated system with relatively slender members, this

assumption will not be of major importance.

E Pin supports. This will tend to underestimate bending moments (locally) and overestimate deflection.Since it is a triangulated system this assumption will not be of major importance.

F Small deformations. Sway critical load ratio to be checked for relevant loadcasesG Neglect the finite sizes of the members. This is not an important issue in this situation.Loading:

H Dead loading - quite accurate.I Crowd loading - quite accurateJ Wind loading - low accuracy

K Dynamic Loading - medium to low accuracy.

Assessment Matrix

Table 2.1.1 shows an assessment matrix for the frame. The rows in the table represent the degree of uncertainty (probability in relation to uncertainty) in the assumption and the columns represent the

importance of the assumption (consequence of getting it wrong). A scale of 1 to 5 with 5 high is used for both factors. In this table entries in the bottom right corner indicate the assumptions which represent thegreatest risk. There is a high degree of uncertainty about the intensity of the wind loading on the

cantilever roof and if this collapsed the consequences could be disastrous. Whereas the uncertainty on theestimate of dead load is low and it is less important than the crowd loading.




Table 2.1.1 Stadium Frame Risk Assessment

Importance of Assumption (5 high)

1 2 3 4 5

Degree 1 H C

of 2 G A,B,F I

Uncertainty 3D,E

(5 high) 4 K J

5

It can be seen from Table 2.1.1 that the most critical feature in the analysis is the wind loading on the roof structure. There is a high degree of uncertainty in the loading and collapse of the roof would be

catastrophic. The dynamic loading uncertainty is also high but it is unlikely that dynamic loading wouldcause collapse in stadium of this type if it is well braced.

Validity conclusion. Box 3-5, 3-5 is the critical area. The model is therefore satisfactory apart from thewind loading issues which need special attention.

2.1.3 Software

SofwareThe Lusas system was used for the analysis. BEAM (plane beam) elements were used.

Verification of SoftwareLusas is a standard software package subject to quality control procedures by the suppliers.

2.1.4 Computational ModelWith the beam elements used, the model is solved without discretisation error.

2.1.5 Results

Verification of Results

Use checking loadcase of 6.5 kN vertically down at nodes 18 to 24.Total load = 45.5 kN (approximately uniformly distributed).

Check Data: check is positiveOverall equilibrium: - check is positiveLocal equilibrium: Check moments at node 19

M6 = 9021.81, M19 = 591.78, M5 = -9612.99SUM = 0.0 - check is positive

Restraints: ∆x = ∆y = 0.0 at nodes 1, 27, 29 - check is positiveOverall form of results: see plotter output of frame deflection, Figure 2.1.3. This shows a typical bending type deformation of the boom members. The internal forces show tension in the top chord

members and compression in the lower chord members - check is positive.

Checking model: Assume that the cantilever part of the frame has pin connected supports at nodes 7 and

8. Treat this boom truss as a cantilever beam with uniform properties in its length as shown in Figure

2.1.4. Use the model of Figure 2.1.5 to check the tip deflection ∆tipdue to axial deformation of the chordmembers of the truss:

The axial deformation of the chord members causes a bending type deformation for the truss as awhole. The chord members act as the ‘flanges’ of a beam.

∆ bending = WL3/(8EIe) Ie = Ac b

2/2 Ac is the area of a chord member. Take b (distance

between chord members) as constant 2.85 m (i.e. use a uniform depth of truss corresponding to a

section slightly closer to the support than mid span).

∆ bending = 45.5 x 233 x 109 /(8 x 210 x 5880 x 2.852 x 106/2) = 13.80 mm

∆tip(computer),1 = 44.33 mm




For ∆ bending , axial deformation of diagonal members of the truss is neglected. This causes a shear

type deformation of the truss as a whole. The shear deformation of the equivalent beam is - ∆shear =

EΣAd cosθ sin2θ.

θaverage = 45 degrees (say).

(ΑG)e = 210 x 2640 x (1/√2)3 = 210 x 2640 x 1/(√2) = 1.96 x 10

5

∆shear = 45.5 x 23 x 103/(2 x 1.96 x 105) = 2.67 mm New estimate of tip deflection ∆tip(checking model) = ∆ bending + ∆shear

= 13.80 + 2.67 = 16.47 mmThis indicates that shear deformation is not of great significance in this case.The main model was re-run but with pin supports at nodes 7 and 8. This gave

∆tip(computer),2 = 13.83The checking model is based on uniform properties and the ‘average’ values of the parameters used

seem to make it stiffer than that used in the computer analysis. The comparison between ∆tip(computer),2

and ∆tip(checking model) tends to indicate that the model is acceptable as far as the boom part is concerned.These results indicate that the tip deflection of the boom part is not dominated by the deformations of the

boom members themselves. The rotation at the root of the boom due to axial deformation in the rest of the structure is the dominant feature in relation to tip deflection.

Check axial force in member 26. Apply equilibrium to the part to the right of a line joining nodes 7 and8. Take moments about node 7:

N26 x 4.0 cosθ = Moment of loading about node 7N26 = 614.25/(4.0 x 0.993) = 154.64

Computer value = 153.1Difference is likely to be due to bending in the elements of the trussSummary No negative aspects observed in results. Accept at initial checking stage.

2.1.6 Justification

Parameter Study

For the Stadium Frame Model of Figure 2.1.2 the following variations were investigated based on areference model with pin supports, member properties as previously noted and with full momentconnections at all joints.1. Foundation Fixity. The effect of having fully fixity at the supports (as compared with pin connections

in the checking model) on the tip deflection is shown in Table 2.1.2. The effect on tip deflection isnegligible.2. Joint Fixity. Table 2.1.2 shows the effect of having pin connections at all member ends. The effect of

joint rigidity on tip deflection is not significant for design although the stresses due to bending are likelyto be more important.3. Pin supports at nodes 7 and 8. The effect of supporting nodes 7 and 8 shown in Table 2.12 is to

simulate the situation of the checking model used previously and shows the highly significant effect of therest of the structure on the boom deflection.4. Node 9 restrained laterally. The result for this shown in Table 2.1.2 demonstrates the significant

effect of deformation of the seating structure on tip deflection of the boom.

Table 2.1.2 Effect of Various Parameter Changes on Tip Deflection of Boom

MODEL Tip Deflection at end of

boom (mm)

%Difference. from

Reference

Reference (pin supports, member properties asnoted, rigid joints)

44.33 -

Rotational fixity at support nodes 43.77 -1.3%

All nodes pin connected 47.23 +6.5%

Pin supports at nodes 7 and 8 13.82 -69%

Node 9 restrained laterally 31.85 -28%

Design Changes A useful exercise is to assess the effect of design changes on performance of thestructure. For example, for the stadium frame model of Figure 2 the area of the top and bottom chordmembers of the cantilever part was increased by 10%. This produced an increase in the steel mass of 212




kg. The effect on stiffness of adding this mass in other members of the frame is shown in Table 2.1.3From this, it is clear that changing the chord areas is not the best strategy for improving stiffness. It is

clear that the tip deflection is much more sensitive to the size of member 19 and the sizes of the mainsupport columns than the sizes of the members of the boom itself.

Table 2.1.3 Effect of Increasing Stiffness of Various Members

MODEL Tip Deflection at end of boom (mm)

%Difference fromReference

Reference (pin supports, member properties asnoted, rigid joints)

44.33 -

Increase area of top and bottom chords of boom by 10% (212 kg added mass)

42.97 -3.1%

Increase areas web members of boom to add212 kg of mass.

43.83 -1.1%

Increase area of member 19 to add 212 kg of mass

39.72 -10.3%

Increase areas of members 1 to 11 (maincolumn supports) to add 212 kg of mass.

39.21 -11.5%

Acceptance of Overall SolutionUp to this point in the process all indications are positive but the assessment of wind loading anddynamic loading cases will need further consideration.




Ie = Ac b2/2 - Equivalent second

moment of area

Ac = area of chord/column

b = distance between chords/columns

With more than one column:

Ie = second moment of area of chord

members in relation to the depth of the

truss

(AG)e = E ΣAd cos(θ) sin2(θ)

ΣAd = sum of areas of all diagonal members which provide bracing within the

depth of the truss

θ = angle between diagonal and chord/column

(a) Braced Truss

Ie = as for braced truss

(AG)e = E ΣIc / ( [1 + 2λ]h2)

Ic = second moment of area of

column/chord

h = panel width/ storey height

λ = Ιc /h/(I b/b)

I b = I for beam/post

(a) Vierendeel Truss

Figure 2.1.5 Equivalent Beam Models for Trusses

Ad

Ac

θ

b

(a) Truss

(b) Equivalent beam

E, A , I , (AG)ee e

b

h

Ic

Ib

Ac

Ie

(AG)e

(a) Vierendeel Frame (b) Equivalent Bea




3 CASE STUDIES

3.1 The Sleipner Platform Collapse

The Sleipner Offshore Platform was under construction in a fjord in Norway in 1990. A tricell - see

Figure 3.1.1(a) was filled with water while the adjacent compartments were not. The maximum pressurehead in the tricell was approximately 67 metres of water. The platform broke up and sank to the bottom

of the fjord.Two main faults in the design have been identified (Foeroyvik 1991) :1. 3D (brick) elements were used to model the complete structure. Figure 3.1.1(b) shows the mesh for a

tricell section. There was no refinement of mesh within the depth of the tricell wall and therefore thesimulation of bending was probably rather crude. At the junction of the tricell walls, the elementswere distorted (i.e. the angle between the sides was not close to 90o as shown in Figure 3.1.1(b) This

resulted in a 45% (low) error in the predicted shear force in the wall. A simple statical check will givemuch better accuracy than this.

2. The reinforcement was detailed by computer software. This resulted in the use of a T-headed bar asshown in Figure 3.1.1(c) This is clearly unsatisfactory for an opening joint situation. No competentdesigner would specify that detail knowing the circumstances. It is likely that shear reinforcement

was needed in the tricell walls but the system might not have failed if the T-headed bar had been better detailed.

Good quality control on the analysis would almost certainly have identified these problems. Fortunately

there was no loss of life although the financial loss was in the multi-millions.

ReferencesAGS (1994), Guide to the Validation and use of geotechnical software, Association of GeotechnicalSpecialists, Camberley, Surrey, 114 pp.

Foeroyvik F (1991) The Sleipner Accident - Tricell Calculation and Reinforcement Error, Finite Element News, No 6, pp 27-29.Knowles N C and Maguire J R (1995) “On the Qualification of Safety-Critical Structures - the

SAFESA Approach” Proceedings, Symposium on Safety Critical Systems, Brighton UK, 7-9 Feb.MacLeod I A (1990) Analytical Modelling of Structural Systems, Ellis Horwood .MacLeod I A, (1995) A strategy for the use of computers in structural engineering, The Structural

Engineer , Vol 73, No 21, pp 366-370, 7 November. NAFEMS, Finite Element Methods and Standards, Whitworth Building, Scottish Enterprise TechnologyPark, East Kilbride, Glasgow G75 0QD

Young W C (1989) , Roark’s Formulas for Stress and Strain, 6th Edition, McGraw-Hill

Basic Analitical Modelling

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