Interactive CAD of prestressed concrete using a mini-computer

Interactive CAD of prestressed concrete using a mini-computer J. H. B U N G E Y Department of Civil Engineerin,q, University of Liverpool, PO Box 147, Liverpool L69 3BX, UK

An interactive approach to the design of prestressed concrete members and structures is described. This has been developed for use on an office-based minicomputer system and programs are suitable for engineers who have little experience of computing. Emphasis is placed on the use of visual display facilities to present the results of calculations necessary for design decisions, and data are stored in disk files which are automatically accessed as required. Individual program modules are produced for each separate stage of the design process, and these can either be used to undertake isolated calculations or can be combined to form suites for designing complete structures. Attention is paid to the simplification of analyses wherever possible both to minimize time delays and to accommodate limits of computer size. It is found that in this way complex designs can be produced with much greater flexibility than is possible with automatic approaches, and much more quickly than by manual methods.

INTRODUCTION There are many well established examples of worthwhile computer usage in the field of structural engineering. The majority of these could be classified as 'Analysis' programs, ranging from sophisticated packages for complex structures which require large computing power, to simple programs for everyday use with desk-top programmable calculators. However, structural 'design' is not a precise mathematical process and places considerable reliance on experience, especially where concrete structures are concerned. Computer application is thus not straightforward, and although it is possible to design simple individual members using automatic programs, this becomes unrealistic for entire structures because of the large number of variables involved. Even with simple members considerable standardization is necessary to produce practical details automatically. The use of interactive operation enables the designer to direct this process using the calculations as a guide, thus permitting far greater flexibility. The main aim of such programs should be to carry out as many routine operations as possible automatically, and to provide convenient, accurate guidance to enable the designer to take decisions and control those parts of the design which require judgement and experience.

CHOICE O F E Q U I P M E N T Many individual design operations do not require large computing power, and could be handled quite adequately on a desk-top machine. However, the quantities of data generated often involve considerable storage capacity and effectively rule out such equipment when more than one operation is involved. Since the designer will wish to proceed at 'thinking speed' the use of a large computer will be totally uneconomic unless on a time-sharing basis, and this may introduce delays which will be disruptive to the thought processes of the designer. Continuity is essential, thus the system must be prepared to accept data, calculate, return results, and be ready to fulfil the next instruction whenever it may come. The use of a dedicated minicomputer satisfies many of these requirements, and would appear to offer the most convenient and economic approach. This may be sited in the design office, thereby providing many psychological advantages for engineers who are not computer experts, and there is also the benefit of fast response to user demands since data transfer problems are minimal. Efficient communication will require a graphical display to present information, and it has been found that storage tubes are generally adequate for structural design purposes. The greater expense of constantly refreshed tubes is difficult to justify since the need for 'moving' pictures is small. Documentation is essential in 'design' situations, and the use of a 'hard copy' unit is likely to prove the cheapest and easiest method of producing records of screen displays, whilst selected numerical information can be recorded by carefully planned teletype printout. L I V E R P O O L SYSTEM The feasibility of using a mini-computer for interactive design has been examined in the system shown in Fig. 1 which was installed in the Civil Engineering Department at Liverpool University some years ago. The Data General Nova 1200 central processor has 28 k of 16 bit storage, whilst a fixed head disk with 256 k word capacity provides secondary storage and working area with an access time of 8.5 msec to a block of data. Cheap interchangeable moving head disks of 1247 k word capacity are used as backing store for systems and user programs, and also provide a store for design results enabling subsequent interrogation and interpretation. Control and communication is via teletype and Tektronix 4014 storage tube display screen with manually operated cross-hairs, although early work used a smaller 4010 model.

Advances in Engineering Software, 1979, Vol. 1, No. 2 61

USE OF SYSTEM FOR DESIGN The design of a prestressed concrete structure can be b r o k e n d o w n into a n u m b e r of distinct, but inter-related stages. By p r o g r a m m i n g each stage s e p a r a t e l y a n d using overlay facilities, the limited core s t o r a g e a v a i l a b l e can be used efficiently to handle even c o m p l e x problems. A u t o m a t i c d a t a transfer between p r o g r a m s can be achieved by means of a c o m m o n d a t a b a n k serving, and a u t o m a t i c a l l y accessed by, all p r o g r a m s . Basic d a t a for each p r o g r a m are read from the a p p r o p r i a t e disk file and e x t r a d a t a p r o v i d e d by the designer m a y be i n c o r p o r a t e d

Interactionfacilities STORAGETUBEt [ HARDCOPIER] VDU -OR CAMERA

TELETYPE

J CORE ] tProgram [ CENT?2LVpARlggg\ S O R ~ I [ F ~ , ~ 1 2 5 6 k , 16bit words ] Execution INTERCHANGEABLE] DISK 1247k,16bit words

PAPERTAPE READER& PUNCH

PROGRAM

Storagefacilities Figure 1. Liverpool mini-computer system

"luhh, 1.

d u r i n g running. Results are a r r a n g e d in a suitable format for access by subsequent p r o g r a m s and stored either by creating a new file or u p d a t i n g an existing one. The design of a structure using this system thus tends to follow t r a d i t i o n a l methods, but uses the calculation and d a t a h a n d l i n g p o w e r of the c o m p u t e r to facilitate the process. C o m m u n i c a t i o n between designer and c o m p u t e r p r o v i d i n g c o n t r o l of the design can be kept as simple as possible by careful p r o g P a m m i n g to restrict numerical transfer to the m i n i m u m that is necessary at each stage, and by sensible use of screen displays. T o be worthwhile, it must be possible for p r o g r a m s to be executed by engineers who, a l t h o u g h experienced in the a p p r o p r i a t e aspects of design, m a y have very limited c o m p u t i n g k n o w l e d g e and experience, or be unfamiliar with a p a r t i c u l a r p r o g r a m . The use of c o m p l i c a t e d m a n u a l s or instruction sheets is b o t h t i m e - w a s t i n g a n d disruptive; thus the engineer must be led t h r o u g h the design by c o m p r e h e n s i v e but simple instructions from the c o m p u t e r which indicate clearly the necessary response to initiate a p a r t i c u l a r course of action. This m a y be achieved either by q u e s t i o n / a n s w e r routines on the teletype, which is preferable where precise numerical input is required, or by using the V D U cursors with menus of alternative o p t i o n s or to indicate areas of a structure for a t t e n t i o n (Table 1). ORGANISATION

AND DETAILS

The basic o p e r a t i o n s involved in the design of a prestressed concrete structure are indicated in T a b l e 2, and

Typical teletype output dm'imt came detailing1

Input teletype or VDU

Teletype printout START(I) OR RESTART(2)'?

W.W. - +

T.T.-* T.T.~ T,T.--, T.T.-* T.T.---*

1

INPUT STRESSING END - LEFT(l), RIGHT(2), BOTH(3) 3 INPUT COEFFTS. FRICTION & WOBBLE 0.4, 0.003 INPUT COVER & CABLE ZONE WIDTH (MM) 50, 100 INPUT MAX/MIN STRESSES TOP & BOTTOM (N/MM2) 14, - 1, 14.0 END LOAD/CABLE (KN) & NO. SIMILAR PROFILE? 1000, 5 11961 KN=MIN. FINAL PRESTRESS FORCE STOP CABLE NO 1

Notes Facility to recall unfinished design

Calc. automatically End of overlay prog. Input cable profile by cursors

VDU-* T.T.--,

T.T.-,

W.W. ---+

T.T.-,

NEXT SPAN(l), CABLE(2), AMEND(3), DELETE(4), FINISH(5)? 2 END LOAD/CABLE (KN) & NO. SIMILAR PROFILE? 1000, 7 11961 KN =MIN. FINAL PRESTRESS FORCE STOP STRESS FIBRE LEVEL (TOP = 2, OTHER = 3)? 3 DEPTH FROM TOP (MM)? 150 ('ABLE NO. 2

Define next operation

Stress calculated and displayed at top or other level due to detailed prestress and other loading

VDU-+ T.T.-+ T.T.--+

62

NEXT SPAN(l), CABLE(2), AMEND(3), DELETE(4), FINISH(5)? 5 PRINT CABLE DETAILS (YES = 1, NO =2)'? 2 STOP

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Results stored and printed on demand

Table 2. Prestressed concrete desion operations Operations

Proorams

Preliminary analysis:

Analysis I

data files Preliminary B.M.

envelopes

Approximate elastic analysis for the serviceability Limit State using assumed member properties and estimated loadings

Member sizino and structure specification:

Calculation ofminimumsection properties based on permissible materials stresses and economic limits to prestress force. Development of crosssections to satisfy these requirements throughout the

Cross-sections

Member structure

Cross-section properties Member details Structure details

and

definition

structure Main analysis:

Elastic analysis of structure for all load cases

Analysis II

Influence coefficients

Serviceability B.M. envelopes Prestress calculation and detailino: Calculation of minimum and maximum prestress force levels throughout the structure, provision and location ofthis in practical terms, and allowance for the influence of this on overall behaviour

M e m b e r sizing and structure specification Prestress

Detailing

Prestress details

Analysis II1

of structure Ultimate limit state checks:

Elastic analysis for ultimate limit state load combinations and comparison of results with calculated ultimate moment of resistance and

shear

resistance

the major part of the calculations only once 1. The entire matrix is inverted and columns of the inverse are stored for use as influence coefficients to predict the effects of all types of loading, including prestress, and also to take account of subsequent modifications of cross-sections or spans. This is used for the main analysis by a program which extracts the necessary details of the structure from data files and creates a new file containing the appropriate influence coefficients. These are then used to produce serviceability bending moment envelopes based on load cases input interactively by the designer. The analysis program at the prestress detailing stage incorporates the secondary effects due to prestress. These are represented by an equivalent static loading, and the influence coefficients calculated above are then used to update the live and dead load bending moment envelopes. The ultimate limit state analysis similarly uses the influence coefficients in conjunction with the factored load combinations recommended by BS: CP110:1972 2 or BS: 5400:1978 3. Ultimate bending moment and shear force envelopes are thus produced.

Analysis IV

Ultimate and envelopes

B.M. S.F.

Ultimate moment U n t e n s i o n e d Ultimate shear reinforcement

of

members

the individual programs are described below. All calculations are based on equally spaced sections along the length of each member, with variables assumed to change linearly between these stations. Initially, programs were based on 21 stations, but it was subsequently found that 13 were adequate for design purposes, and enabled considerable economy of core store and data file size. Analysis programs

Complex analytical methods can frequently be replaced by quicker approximate methods. Prestressed concrete design is one area where this is particularly convenient, and is indeed almost essential when using a minicomputer with limited storage capacity. The preliminary analysis prior to member sizing is based principally on the live loading for the structure, and requires only a very approximate estimate of the self weight. The use of moment coefficients is considered adequate and these are provided by the designer together with the spans and loading for the anticipated structure. The resulting bending moment envelopes are stored in a data file ready to be used as a guide to member cross-section development. Where more detailed analysis is required, a convenient approach using the stiffness method effectively performs

These two operations can be conveniently handled by separate programs linked by data files. The minimum cross-sectional properties necessary for a given range of values of bending moment can be easily calculated using well established theory 4. The designer must provide details of permissible concrete stresses upon demand, whilst moments are read from data file automatically. This calculation will be performed at each of the stations for each member throughout the structure, and will yield minimum values of each section moduli. This information is most readily understood by the designer if presented in the form of a practical crosssection which satisfies these requirements. Most prestressed members are some form of I-section, thus it is convenient to provide a suitably proportioned crosssection of this type, incorporating approximate limits to span/depth ratio, web thickness and flange breadth. Whilst this may initially bear little resemblance to the final cross-section at any point along the member, it will assist the engineer to develop a suitable longitudinal profile. Aesthetic considerations and practical constraints will be involved also, and individual cross-sections may be subsequently developed to satisfy these. A proposed cross-section is displayed on the screen together with its relevant section properties and the calculated minimum required values [Fig. 2). This is modified graphically by the designer until he is satisfied, and the details are then allocated to the appropriate data file. For constant section members this need only be performed for the critical section, but ira varying section is required then the original section can be easily modified and stored as required. In cases where a complex crosssection is required, as in cellular bridge decks for example, a general purpose cross-section program 5 may be used in a similar manner. Member specification consists simply of allocating defined cross-sections to each of the thirteen individual stations in a member and defining the span. This is performed interactively by the designer, and the approach allows many members to be defined using the stock of cross-sections available. An elevation of each member may be displayed to check general proportioning and to

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B1 =1000

B2 =150

B3 =300

D1 = 250

Centroid D 2 =800 Y1 --839

D3 =300

1

Z1 = 108.1

Z2 = 177.4 E6

Zl (MIN) =100-0

Fiqure 2.

MM4

Z2 (MIN) =100.0

Typical cross-section display

enable gross errors to be identified visually. At this stage, the cross-sections associated with the defined member are stored in a new data file, and the member is assigned an identification number. Structures are then defined numerically by the designer in terms of member numbers, with orientations fixed by the assignment of joint numbers. Details of structures are thus stored in terms of member numbers, joint numbers and co-ordinates.

Prestress calculations and detailin.q This program handles the most tedious and complex part of the design, and takes the form of a number of overlayed sub-programs. The first stage is to extract all the necessary physical details of the structure, together with moment envelopes, from the appropriate data files. For the given serviceability stress limits, and for the practical constraints such as cover and minimum cable zone width specified by the designer, each section is checked for structural adequacy, and the minimum longterm prestress force is calculated together with the allowable zone for the centroid of this force 4. The value of prestress force required is given numerically by teletype, whilst the allowable zone is displayed on an elevation of the appropriate member. At this stage the routing of the p r o g r a m will depend upon the type of construction involved, i.e., pretensioned with either debonded or deflected tendons, or posttensioned. Programs have been developed to cater for each of these cases. In the case of pretensioning, which will normally be used for precast members, the required number of wires will automatically be provided in standardized locations in the cross-section, and the designer indicates debonding or deflection points by means of the cursors on a displayed elevation of the member. He is guided in this operation by displays of bending moment and resistance diagrams. If a designer wishes to use a beam from a standard range, the program can instead interrogate files containing data for such beams, select the most suitable and

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display for checking before proceeding with the prestress detailing. Selection is based on span, section moduli and the feasibility of providing an adequate prestress force using standard strand arrangements. If the beams are used compositely with an in situ slab, beam spacing and slab depth are allowed to vary over a range specified by the engineer. For in situ members it is necessary to develop profiles for the prestressing cables, and these are detailed by the designer on a displayed elevation of the member which shows the permissible zone for the centroid of the minimum prestress force (as shown in Fig. 3). A profile is developed by indicating points through which the cable is required to pass and by specifying zero slope or zero curvature simply by pressing the appropriate key. Parabolic curves and straights are automatically generated to fit, calculation of wobble and friction effects is automatic, and cables can be stressed from either or both ends of a member. The current centroid of prestress force is displayed and automatically updated as new cables are added or as existing cables are amended or deleted. As an additional design aid, the stress levels at specified positions on the member are plotted relative to the permissible values. When beams are continuous, it is necessary to detail one span at a time because of screen size limitations. Cables are detailed throughout the length of the beam, and when this process is complete, secondary moments due to prestressing are automatically assessed by an analytical module, and the cable zone and stress level displays amended to incorporate these effects. If intelligent use has been made of the design guides, few modifications will be required. Using this method, changing stress levels and centroid of prestress force can be seen at a glance and compared with the appropriate limits. Experiment is therefore possible, and in the author's experience, typical continuous structures can be prestressed with ease in one sitting at the computer.

Ultimate limit state Although prestressed concrete members are designed primarily for the serviceability limit state, checks hmst be

LEVEL 2

1

2

Structure 4

3

4

5

6

7

8

9

10

Member

1

11

13

12

Permissible zone

Cable profile Actual stress LEVEL 1 1

Figure 3.

C~ ntroido f ~ " " - - ~ ~ Permissibj_lestress

I

, I __"~

Typical beam prestressin,q development

DATA FILES

DATA FLOW

CROSS-SECTION]_ DETAILS

PROGRAMS

CONTROL

Cross-section development

SEGMENT DETAILS

Segment development

MAIN STRUCTURE GEOMETRY

Main structure definition

E N

I L.LMOMENT ENVELOPES

G

Live load analysis

i

N E SUBSTRUCTURE GEOMETRY

Substructure definition

D-

E R

D.L.MOMENT ENVELOPES

SEGMENTAL STRESSES

Substructure analysis

Prestress detailing (a) final structure (b) substructure

SEGMENTAL PRESTRESS DETAILS

Figure 4.

Allowable values of concrete shear stress depend upon both concrete strength and percentage of tensile reinforcement z and are programmed as a table from which the appropriate value can be automatically extracted. This enables the ultimate shear resistance to be calculated on the basis of the section being either cracked or uncracked in flexure. The resulting shear resistance diagram, together with a calculated upper limit, can then be superimposed on the shear force diagram for visual comparison. If it is necessary to enhance the shear strength by provision of shear reinforcement, the minimum quantity required can be easily calculated, and presented to the engineer for consideration. Automatic specification of such steel is not necessarily advantageous since a number of factors may influence the detailing, and the programming of this aspect of the design is currently being developed and refined. The various calculations undertaken by these programs will take the same course whether dealing with a simple or complex case of a particular member type. Thus each is programmed separately and may be used independently to fulfill a particular function or may be combined as part of a suite to deal with a complete problem. Since all programs rely on data files for much of their input, they can only function if the appropriate files have been previously established. However, for independent operations this can be achieved by simple programs to input and store the necessary information in the appropriate configuration.

Complex problems Complex design ,suite

made to ensure that the ultimate strength is adequate both in bending and shear.

Bending. It will not be necessary to check the ultimate bending strength at every station in a member. Critical sections will normally be indicated by the designer, guided by a display of the bending moment envelope generated by Analysis IV, together with his knowledge of the member cross-sections. Details of these, together with cross-sections, including quantities and location of prestressing steel, are obtained from the appropriate data files. Calculations will be based on idealized stress-strain characteristics for the prestressing steel and the 'equivalent rectangular' concrete compressive stress block 6, both of which are incorporated in the program, An iterative procedure evaluates internal compression and tension forces for varying neutral axis locations, using materials' strengths specified by the designer, until a balance is obtained. In this calculation, the initial concrete strain due to prestress is ignored since this has little practical effect on the resulting estimated value of ultimate moment of resistance 4. Shear. In this assessment it is necessary to calculate ultimate shear resistance throughout a member, This is particularly tedious by hand since at every section two values must be evaluated and compared, both of which involve fairly complex expressions 4. A considerable amount of information is required from data files, concerning the properties of the structure including crosssections, prestress details, bending moments and shear forces.

When the programs are combined into a suite, the necessary data files will be generated as the design proceeds and the programs are in this case linked by facilities for program selection coupled with relevant data display. Additional modules can then easily be added to perform tasks not incorporated in the basic system, and program updating is relatively simple. In this way, specific variations of the basic problem type can be handled. Figure 4 shows how some of the programs described above can be combined and augmented to handle the complex problem of a multi-span segmental bridge deck. This suite is capable of examining a whole series of structures which will be generated by the various construction stages of the bridge 7. Members are in this case defined in terms of segments, and interpolation routines convert all results based on 13 stations per member into values associated with individual segments for storage. Thus a complete record of the properties and stress history of each segment may be compiled which covers both the final structure and all intermediate construction stages. VIABILITY O F M E T H O D It must be emphasized that these programs are not intended to be commercially available or comprehensive solutions. They represent feasibility studies to examine alternative approaches to the problems of design, and indicate the basis of a method which could be developed for practical use. The addition of other modules to handle aspects such as losses and temperature effects would be necessary to provide a complete design package, but it is not anticipated that these would present major difficulties.

Advances in Engineering Software, 1979, Vol. 1, No. 2 65

Whilst this approach achieves the objective of providing computer assistance with the tedious calculations and data handling associated with the design of prestressed concrete in a direct and simple manner, the programming effort is considerable. Thus it will only be worthwhile to program commonly occurring problem types, even with this method, which is considerably more flexible than a fully automatic approach. Programs are written in Fortran IV with which many engineers are familiar, but in a design office environment it is also essential that the programs are well documented to permit updating. It has been found that even the programming engineer may soon forget the intricacies of his program, and staffing changes could aggravate this problem, if care is not taken. CONCLUSIONS The approach described has been steadily developed over a period of years in which this mini-computer system has been used to solve a variety of types of problem. It is felt that it offers the most realistic method of computer involvement in the design of concrete structures, and enables considerable time-saving when designing prestressed concrete. As with traditional design, it proceeds in stages, and this helps the designer to concentrate upon one aspect at a time, and prevents him being overwhelmed

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A d v a n c e s in Enqineerinq Software, 1979, Vol. l, No. 2

by data. file limits of processor size prccl.udc the mcorporation of automatic optimization programs, although the reduced time scale may lead to cconomies of design, The most important feature of the approach, however, is the facility for direct engineer control and involvement. These programs demonstrate that office based, and relatively inexpensive, computing equipment can effectively handle the design of prestressed concrete members and structures in this way.

REFERENCES 1 Cope,R, J. and Sinkinson, A. Repeated stiffnessanalysis on a minicomputer, CAD 74, IPC Science and Technology Press, Guildford, 1974 2 BS CP110 Pt. 1, The Structural Use q]'Concrete, B.S.I., London, 1972 3 BS 5400: Pt 2: 1978, Steel, Concrete and Composite Bridqes, B.S.[., London, 1978 4 Sawko,F. (Ed.) Prestressed Concrete Developments, Vol. 2, Applied Science Publishers, London, 1978, Chapter 5 5 Cope, R, J. and Williams,J. R. Interactive design of cellular bridges for longitudinal bending, Proc. Int. Con[i on Computer Oriented Desiqn in Civil En.qineerin9, Aston 1973 6 Mosley, W. H. and Bungey, J. H. ReinJorced Concrete Desiqn, Macmillan, London, 1976 7 Cope, R. J. and Bungey, J. H. An examination of interactive computer usage in structural design, with special reference to bridges, Proc. ICE 1976, 61,525