Verifying the correctness of structural engineering calculations

Microsoft Word - phd18.docStructural Engineering
Professor H. Nooshin, University of Surrey
© Douglas William Brown July 2006
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Abstract
In 1997, The American Society of Civil Engineers published a report prepared by their Task Committee on Avoiding Failures caused by Computer Misuse, the self- checking procedures developed in this research have been designed to prevent such misuse. In 2002, The Institution of Structural Engineers, published Guidelines for the use of computers for engineering calculations, which commence "These guidelines have been prepared in response to growing concern regarding the appropriate use of computers for structural calculations" and end with "Ten Top Tips to help get things right". The IStructE guidelines give definitive technical management advice which the writer advocates. This research deals with engineering matters not covered by the IStructE guidelines, the target audience is engineers who develop and support software for the production of engineering calculations. Verifying the correctness of structural engineering calculations considers calculations for both the structural analysis of frameworks and the structural design of components such as beams, slabs & columns, and develops a unified approach for the development of Verified Models for both types of calculation. In this thesis, verifying means establishing the truth or correctness of software models by examination or demonstration. Each model to be verified incorporates a self check, verification is the process of generating a thousand or more discrete sets of engineered data providing high coverage for the model, running the model with each set of data, computing the average percentage difference between key results produced by the model and its self check, averaging the key results for each run, averaging for all runs and when the average percentage difference for all runs is within an acceptable value, typically 3% for models for structural analysis, then the model is said to be a verified model. Tools used for assisting verification are discussed including: benchmarking, flow charts, check lists and aids, help, generating sets of test data, self checking software, checking against known solutions, conversion of parametric files to numeric files, cross referencing of variables. Approximately 50% of calculations submitted to building control departments for approval are now produced by computer. Engineers say that due to the pressure of work in the design office, checking is not as thorough as they would like. From the starting position that the data has been checked, this research develops an extensive set of models which are self checking and have each been verified with sets of automatically generated data providing extensive coverage for each model. All systems are described in sufficient detail such that they may be used by others.
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The systems developed for verifying the correctness of structural engineering calculations, based on:
• the inclusion of an automatic self-check in every structural model • the development of a parameter specification table permitting • the automatic generation of engineered sets of test data for each model • the automatic running of the sets of test data for a thousand runs for each
model • the automatic reporting of the results giving a statistical summary are all new
to the field of structural engineering.
Declaration The content of this research is the work of Douglas William Brown and includes nothing which is the outcome of work done in collaboration or work copied from others, except where that work is quoted herein and given proper acknowledgement. This work was carried out in the Engineering School of the University of Surrey. It has not been submitted previously, in part or in whole, to any University or Institution for any degree, diploma, or other qualification. The full length of this thesis is 105,000 words including appendices. Acknowledgements The writer acknowledges the giants of structural engineering theory on whose work this work depends, particularly Castigliano, Timoshenko, Cross & Hrennikoff, the structural equivalents of Bach, Mozart, Beethoven & Holst; or if preferred Armstrong, Ellington, Brubeck & Davis. The writer thanks his supervisors: Professor Gerard Parke & Dr Peter Disney for their abundant encouragement, their interest in the subject, for the provision of papers for review, for reminding the writer to include subjects which he would have omitted otherwise, and for steering this research towards a unified approach covering both the structural analysis of frameworks and the structural design of components. The writer thanks Jennifer, Ian & James, his wife and sons for their help and support.
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Contents
1. Introduction 1 1.1 History of structural design from 1900 to the present 2 1.2 Longhand and computer produced calculations 3 1.3 Growing concern 5 1.4 Objectives 5 1.5 Outline 7 1.6 Overview 10
2. Literature review 12
2.1 Testing software 12 2.2 Knowledge based expert systems 17 2.3 Artificial neural networks 18 2.4 Checking models 19 2.5 Self checking software 20 2.6 Classical structural theory 22 2.7 Moment distribution 24 2.8 Column analogy 25 2.9 Kleinlogel 25 2.10 Hetényi 26 2.11 Flexibility 26 2.12 Influence lines & Müller-Breslau 26 2.13 Castigliano's first theorem method 27 2.14 Unit load method 27 2.15 Method of joints 27 2.16 Pierced shear walls 28 2.17 Roark's formulas 28 2.18 Reynolds 28 2.19 Arches & bow girders 28 2.20 Cables and suspension bridges 28 2.21 Plates and grillages 29 2.22 Circular tanks 30 2.23 Natural frequency 30 2.24 Stability 31
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3. Tools 32 3.1 Definition of terms used 32 3.2 Software maintenance 35 3.3 Flow charts 37 3.4 Comments in the data 39 3.5 Checking aids 39 3.6 Proactive help versus reactive help 42 3.7 Worked examples 42 3.8 Guidance for modelling 43 3.9 Self checking engineering software 44 3.10 Checking against known solutions 44 3.11 Engineered sets of test data 44 3.12 Symmetry 45 3.13 Avoiding information overload 45 3.14 File conversion 45 3.15 Cross referencing of variables 49
4. The nature of data 52
4.1 Data for structural analysis 53 4.2 Data for structural design 54 4.3 Regular sets of integer data 55 4.4 Irregular sets of integer data 56 4.5 Sets of real values as data 58 4.6 Dependency 59 4.7 Subscripted variables 60 4.8 Compilers vs. interpreters 60
5. Logic to check logic 62
5.1 Special character usage 62 5.2 Expressions 62 5.3 Functions 63 5.4 Storage of data 63 5.5 Control 64 5.6 Devising sets of test data 64 5.7 Example calculation 65 5.8 Patterns of variation 69 5.9 Dependency conditions 71 5.10 Tabular form 75 5.11 Variable ranges and redundant data 76 5.12 Section property dependency 77
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6. Sustainability of systems 82 6.1 Systems which have been abandoned 83 6.2 Large software systems 84 6.3 Genesys & Lucid 85 6.4 Engineering shareware 85 6.5 On a personal level 85 6.6 Education 86 6.7 SOS Save Old Software 86 6.8 Text files and manageable proportions 88
7. Verified models for structural analysis 90
7.1 Data input and checking 90 7.2 Simple structure written in 1963 STRESS 91 7.3 Cantilever beam - data preparation by GUI 91 7.4 Parameters 92 7.5 Words used as tools 92 7.6 Other languages 93 7.7 Aims of verified models 95 7.8 List of verified models 97 7.9 Structure/form of each verified model 106
8. Compatibility, energy & equilibrium 110
8.1 The particular solution 111 8.2 The verified conjecture 113 8.3 The incorrectness conjecture 114 8.4 Verifying the data 114 8.5 Verifying the output 114 8.6 Plane frame verification 115 8.7 Plane grid verification 121 8.8 Space frame verification 127 8.9 Clerk Maxwell, Betti, Southwell 128
9. Benchmarking 130
9.1 The Inexact conjecture 130 9.2 The Checksum conjectures 131 9.3 Benchmark audit trail 132 9.4 Traditional benchmarks 133 9.5 Parametric benchmarks 137 9.6 Verified models as benchmarks 140 9.7 Other checking matters 141
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10. Models for structural design 142 10.1 Engineers' arithmetic 143 10.2 Upheaval caused by changes to codes of practice 144 10.3 Commonality of analysis & design models 145 10.4 Classical and modern structural component design 146 10.5 Differences between analysis & design models 147 10.6 Typical structural steelwork component 148 10.7 Typical reinforced concrete component 156 10.8 Run time reporting 161 10.9 Non intuitive design 162 10.10 Some parametric dependency devices 164
11. Discussion 169
11.1 Models for structural analysis 169 11.2 Models for structural design 206 11.3 Limit state design 207 11.4 Eurocodes 208 11.5 Further models 210
12. Conclusions 219
12.1 Models for structural analysis 219 12.2 Models for structural design 239 12.3 General conclusions 239 12.4 How the objectives have been met 240
13. Recommendations 243
13.1 Robustness of conceptual/computational models 244 13.2 Self checking 244 13.3 Sustainability 244 13.4 Tools 244 13.5 Simple systems 245 13.6 Computer toolkit for small consultancies 245 13.7 The elastic analysis of plates and grillages 245 13.8 Yield line analysis 245 13.9 Calibration of Eurocode 2 246 13.10 Calibration of Eurocode 3 246 13.11 Matters which affect correctness of calculations 246 13.12 Bring back the serviceability limit states 247 13.13 Structural Calculations' Centre 247
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13.14 Neural networks 248 13.15 Mathematical assistants 248
14. References 249 Table 3.1 Occurrences of variables 50 Table 3.2 Collected lines containing variables 50 Table 3.3 Cross referencing of variables 50 Table 5.1 Parameter table with dependencies coded 72 Table 5.2 Sets of test data ignoring dependencies 73 Table 5.3 Sets of test data considering dependencies 74 Table 5.4 Parameter table for the structural analysis of a framework 75 Table 5.5 Parameter table for the structural design of a component 76 Table 9.1 Traditional benchmarks 133 Table 9.2 Parametric benchmarks 137 Table 9.3 Benchmarks for verified models 141 Table 10.1 Nominal effective length for a compression member 147 Table 10.2 Strengths of stainless steel to BS EN 10088-2 150 Table 10.3 Storage of short tables in the parameter table 151 Table 10.4 Stainless steel square hollow section sizes 151 Table 10.5 Parameter table for stainless steel hollow section design 152 Table 10.6 Parameter table for reinforced concrete flanged beam design 159 Table 10.7 Extract from a parameter table for a reinforced concrete slab 165 Table 11.1 Flexural reinforcement: BS 8110 c.f. Eurocode 2 213 Table 11.2 Column reinforcement: BS 8110 c.f. Eurocode 2 215 Table 11.3 Shear reinforcement: BS 8110 c.f. Eurocode 2 217 Figure 1.1 A Unified System 11 Figure 2.1 Four colour theorem 21 Figure 3.1 Design and checking aid for reinforced concrete beams 41 Figure 5.1 Tee beam 72 Figure 7.1 Verified models 100 Figure 7.1 Structure/form of each verified model 106 Figure 7.2 The self check 107 Figure 7.3 The self check by equilibrium, compatibility & energy 107
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Expression for the deflection at any point on a rectangular plate 29 Start of a flow chart for a proforma calculation with a bug 38 Comments in the data 39 Example of proactive help 42 NL-STRESS data file before conversion 47 NL-STRESS data file after conversion 48 Masonry wall calculation with a bug 49 Data required for a partial UDL 59
Appendix A The verified models - developed in this research Appendix B Summary of NL-STRESS language followed by a full listing of a verified model for running by NL-STRESS Appendix C Summary of Praxis followed by full listings of a typical model for the design of a structural steelwork component and a reinforced concrete component
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Chapter
1 Introduction
Verifying the correctness of structural engineering calculations is to help engineers who spend a significant proportion of their professional time in the preparation of calculations for the structural analysis of frameworks and for structural component design. Although the examples given herein are structural, they have been kept simple so that civil, mechanical, electrical, refrigeration, heating & ventilation engineers may follow them and thereby see if their discipline can make use of the same principles for verifying the correctness of their computer produced calculations. Proforma calculations written in Praxis (1990), parametric models for structural analysis written in the NL-STRESS language, and tables are shown throughout this document in the Courier font which has a fixed spacing, enabling the text to be lined up. In 1994, the tenth report of the Standing Committee on Structural Safety, (SCOSS, 1994), highlighted the need for guidance in the use of computers in the construction industry, this thesis provides such guidance by developing a system to ensure the correctness of structural engineering calculations produced by computer. In 1997, The American Society of Civil Engineers published an Interim report (ASCE, 1997) prepared by their Task Committee on Avoiding Failures caused by Computer Misuse, the self-checking procedures developed in this research have been designed to prevent such misuse. In 2002, The Institution of Structural Engineers, published Guidelines for the use of computers for engineering calculations (Harris et al. 2002), which commence "These guidelines have been prepared in response to growing concern regarding the appropriate use of computers for structural calculations" and end with "Ten Top Tips to help get things right". The IStructE guidelines give definitive technical management advice which the writer advocates. This research deals with engineering matters not covered by the IStructE guidelines, the target audience is engineers who develop and support engineering software. Verifying the correctness of structural engineering calculations considers calculations for the structural analysis of frameworks and for the structural design of components such as beams, slabs, columns, walls & foundations, and develops a unified approach
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for the development of Verified Models for both types of calculation. Tools used for assisting verification are discussed including: benchmarking, flow charts, check lists and aids, help, sets of test data, self checking software and checking against known solutions. Approximately 50% of calculations submitted to building control departments for approval are now produced by computer. Engineers say that due to the pressure of work in the design office, checking is not as thorough as they would like. From the starting position that the data has been checked, this research develops an extensive set of models which are self checking and have each been verified with sets of automatically generated data providing extensive coverage (Marick, 1995) for the model. Both types of calculation are parametrically written, the engineer need only change typically 10-20 parameters to obtain a set of self checked results; thereby avoiding the mistakes associated with starting with a blank sheet of paper. The systems for verification which have been developed in this research, are described in detail so that they may be used by others. One key component of the verification process is the classification of structural engineering data and engineering that data into a table from which discrete sets of data are automatically generated and run to ensure that the model is tested over its design range. A second key component of the verification process is self-checking. For the structural analysis of a framework self-checking is provided by an appropriate classical method for the model being tested, or by equilibrium, compatibility and energy checks developed as part of this research. For the structural design of components, it is recommended that the self-check be provided by: • checking that a structural framework or component will safely carry the design
loading • checking against an alternative method e.g. classical elastic, Eurocode etc. • providing an alternative model e.g. treating a beam as a structural analysis problem
and comparing the stresses with the empirical results produced by the model which has been written in accordance with a code of practice e.g. BS 5950-1:2000, which is being checked.
1.1 History of structural design from 1900 to the present In the first three decades of the twentieth century, structural engineering was the domain of Universities and steel manufacturers such as Dorman, Long & Co. (1924), and Redpath, Brown & Co. (1924). Both companies provided a wealth of structural engineering information in their handbooks, which were given freely to engineers and architects. During this period, concrete was reinforced with a variety of steel sections including angles, channels and rolled steel joists, the concrete being provided for fire
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protection and to give a flat surface, the steel sections being designed to carry the loading. Theory of Structures (Morley, 1912) and Elementary Applied Mechanics (Morley & Inchley, 1915) supplemented the structural information available from the steel manufacturers. Heyman (1983) provides Some notes for a historical sketch of the development of the plastic theory 1936-48. The Reinforced Concrete Designer's Handbook (Reynolds) first published in 1932, was a major step forward for the design of reinforced concrete, providing charts and tables and other design information for reinforced concrete design just as Dorman, Long & Co. and Redpath, Brown & Co. had provided for structural steel design a decade before. BS 449 (BS 449, 1969) for the structural design of steelwork was first introduced in 1932 and CP 114 (CP 114, 1969) for the structural design of reinforced concrete was introduced under another name in 1934. Both these codes continued in use until well beyond the introduction of limit state design for reinforced concrete, codified as CP 110 (CP 110 1972). The ultimate load design of steelwork had been in use since the London blitz when steel shelters over beds became the first example of the plastic design of structural steelwork; plastic design was later popularised by the BCSA Black Books (BCSA, 1965-1975). Livesley (1983) discusses early uses of computers for carrying out structural analysis in Some aspects of structural computing: 1943-1983. Structural calculations for the four decades prior to the introduction of limit state design were characterised by simple design principles and formulae, but included many arithmetic mistakes due to the misuse of slide-rules. Structural calculations since the introduction of limit state design are characterised by increasing complexity and consequent reliance on computers. Since the introduction of BS 449 & CP 114, engineering calculations have always been brief and to the point. Older structural engineers will remember their concerns when CP 3 Chapter 5 (CP 3, 1952) was revised nearly doubling wind pressures for Exposures A to D, apparently making all our previous designs unsafe; the considerable number of changes to BS 6399 (BS 6399, 1997) over recent years proves that there is still uncertainty concerning the magnitude of the forces we should be considering in our designs. Today, engineers assume that the results produced by computer will be arithmetically correct and that the complicated semi-empirical formulae given in the codes are being applied correctly from an engineering standpoint; perhaps engineers are too trusting on both counts. With more and more firms registering to ISO 9001:2000 for quality management systems and the advent of the Eurocodes, the subject of verification is of considerable interest.
1.2 Longhand and computer produced calculations From the nineteen fifties to the seventies nearly all calculations were produced longhand, the moment distribution method devised by Professor Hardy Cross was undoubtedly the most widely used pre-computer method for the analysis of indeterminate structures. Known in the US as Hardy Cross and in the UK as moment distribution, the method was intuitive and easy to apply. In the early 1960's, structural design offices were referred to as drawing offices, a misnomer as twice as many
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engineers were employed in structural analysis and structural component design than in drawing. Although continuous beams were by far the biggest workload for engineers with the ambiguous title of reinforced concrete engineers, each year one or two statically indeterminate frames - with the complication of sway - would be tackled.
Prior to the advent of the IBM PC in 1981, calculations were generally produced without computer assistance, for the cost of so called mini-computers was of the order of 5 man-years' salary cf. today's 2 man-days. A further hindrance to the widespread use of computers for the production of structural engineering calculations before 1981, was that each computer manufacturer had their own operating system/s; thus programs designed to run on a DEC Vax, would not run on a Data General, Texas Instrument or a Prime…