Computer-aided formwork design: A detailed approach

ELSEVIER

Advances in Engineering Sojiware 28 ( 1997) 437-454 0 1997 Elsevier Science Ltd. All rights reserved

Printed in Great Britain PII:SO965-9978(97)00015-X 096%9978/97 $17.00

Computer-aided formwork design: A detailed approach

J. H. M. Taha9* & A. D. F. Priceb “School of Construction, South Bank University, Wandsworth Road, London SW8 252 UK

bDepartment of Civil Engineering, Loughborough University of Technology, Loughborough, Leicestershire LEI I 3TU. UK

(Received 28 June 1995; accepted 31 December 1996)

A rational approach to formwork design based on simplified assumptions and approximate beam formulas is sufficiently adequate when designing formwork subjected to light loads. A detailed structural design may be required for extremely heavy loadings, or where there is unusual danger to life or property. A detailed mathematical model for the analysis and design of formwork assemblies encountered in practice is developed in this paper. The requirements for the detailed mathematical model are presented. The stiffness method of analysis of structural systems is used for formulating the mathematical model. The use of existing software for solving the stiffness equations is assessed. A conceptual model for implementing the stiffness method in formwork design is proposed. This is used to develop the detailed formwork design program. The program’s capabilities are finally illustrated by means of a case study example. 0 1997 Elsevier Science Ltd.

1BACKGROUND

Formwork is a significant aspect of concrete construction as it usually represents a greater cost than the concrete itself.’ There have been some interesting trends and developments in the concrete construction industry concerning formwork over the last few decades. It has progressed from highly labour intensive traditional timber formwork, to sophisticated machinery and proprietary equipment that allows high output rates to be achieved. This has been achieved through developments in the technical knowledge and machinery that makes, large quantities of concrete readily available at a consistent quality. Consequently, equipment for lifting and handling the rapid placement of concrete was developed. This further led to developments in new forming materials such as aluminium, steel, plywood, plastics, glass- fibre and proprietary systems. This has taken the design of formwork further away from the foreman and carpenter on site, and brought in the temporary works designer and an improved engineering approach to design.*

The recent developments in equipment have been equally matched by developments in formwork design. There have been several innovations in formwork design since the intro- duction of the draft BS code of practice for falsework in

*Corresponding author.

1975.3 The joint efforts of the Concrete Society and the Institution of Structural Engineers to produce guidelines to the practice and design of formwork resulted in the publication of the Concrete Society Technical Report No. 13 in 1977.4 Later in 1982 the British Standard Institution (BSI) published the Code of Practice for Falsework, BS~5975.~ The code only covered the support of soffit formwork and there was a need for an all embracing text on formwork. Conse- quently in 1986, the Concrete society and the Institution of Structural Engineers produced a joint textbook entitled Formwork: A Guide to Good Practice.* It gives guidelines and recommendations to the design and use of formwork with separate sections on materials, loadings and design. It was written as a complementary document to BS5975 and superseded Concrete Society Technical Report No. 13. Another major development was the publication of the Con- crete Pressure on Formwork CIRIA Report 1O86 by CIRIA in 1985, which superseded CIRIA Report 1 of 1965.7 These documents have helped to quantify the design of formwork so that safe and economic formwork can be designed more accurately.

The formwork structure should be strong enough to hold the concrete in the desired size and shape until the concrete hardens and becomes self supporting. The design in the preliminary stages generally involves some guesswork backed by engineering judgement and experience. It is

437

438 J. H. M. Tah, A. D. F. Price

based on the known strength of materials and the estimated loads that may be carried. Formwork is made from a number of simple components or a system of components which may be arranged in many different ways. Plywood sheets, timber or metal soldiers and walings, ties, and tie plates are examples of these components. In a typical design process, a component is chosen and its arrangement within the formwork assembly is assumed. A structural analysis is then performed on the arrangement to verify that the resulting forces and deflections are within the allowable limits of the material. If not, an alternative component material is chosen either based on the type or size of component. This process is repeated until the component satisfies the structural requirements as well as the safety and economic requirements. The design formwork is therefore a highly repetitive process which can become very tedious. The design also involves the use of information from various sources and the abstraction of data from codes of practice. Computers have a good information storage and retrieval ability. Sup- pliers of formwork equipment offer many alternative materials and proprietary formwork systems. The use of computers should allow many alternatives to be considered and the most safe and economic designs to be selected with a minimum of effort. A greater amount of time in the design of formwork is spent on the drafting function. The interactive graphics capability of microcomputers offers a power- ful tool for the production, storage, retrieval and editing of drawings. In addition to the design and drafting function the use of computers should allow for the integration of related functions. These may include the scheduling of quantities, preparation of cost estimates and stock control.

The advent of microprocessor technology has placed a microcomputer within reach of virtually every construction professional. With the recent power boosts, in terms of accessible memory, coupled with the decreasing cost of hardware and software, the microcomputer is fast becoming a practical tool for even the smallest of engineering offices. Software engineering has advanced, with commercially available software such as Computer-Aided Design and Drafting packages, Spreadsheets, and Database Manage- ment Systems with interactive graphics. Civil Engineering and Construction disciplines, such as structural analysis and design, have benefited greatly and are in a more advanced stage in terms of computer implementation. However, formwork and temporary works in general have not received equal attention.

The lack of software in temporary works was first addressed by Neale and Boland’ in 1980. To support their case for the use of computers in temporary works, they developed a small set of computer programs for the design of vertical falsework to support rectangular concrete slabs. The programs produced plans and elevations of vertical or horizontal members in any plane, a schedule of materials required and a cost estimate. It was concluded that the use of computers to design simple temporary works appeared feasible, and could result in savings in design time and hence costs. Further research by Neale et aL9

identified areas of temporary works that were most likely to yield economic benefits and which were technically feasible, practically sensible and humanly desirable. Form- work was one of these areas. It was concluded that computers will be used more in this area. Since Neale and Boland first addressed the use of computers in temporary works, several innovations have occurred in both formwork and computers as previously mentioned. At the start of this work there were very few systems in use and construction firms were reluctant to use computers for the following reasons.

Formwork design was a practical subject, requiring the use of the designer’s experience and a great deal of engineering judgement. The computer solved the mathematical problem but not the practical one. Computers could impair the designer’s understand- ing of the design, which could lead to failures. Computers could inhibit the development of engineering judgement. There could be problems with the interpretation of the computer output. There were no standard procedures for the design of most temporary works. Computer technology was in a dynamic state in both hardware and software, with a diversity of systems on the market. They were concerned about making faulty choices and had taken a ‘wait and see’ attitude.

The aforementioned reasons for not implementing computers point to the fact that most construction companies were resistant to the use of computers within the temporary works design process, even though research had identified areas within which computers could be beneficial. This resistance is characteristic of that encountered where changes are being introduced into an existing system within an organization. Baldwin” encountered similar resistance in developing a computer aided estimating system for Civil Engineering contractors, which are now widely used in industry.

This background has so far pointed to the fact that there is sufficient cause for research into the investigation of actual software development and implementation of computers in temporary works design. This research work has attempted to redress the use of computers in temporary works from a system development point of view. There are several classes of temporary works, however, formwork design was selected as it provided a greater and self-contained problem area. A Formwork Integrated Computer-Aided Design System” (FICADS) was developed. The emphasis was on the state-of-the-art in both formwork and microcomputer technology.

An integrated program network strategy was used in the development of FICADS. This involved the coupling of packaged Computer-Aided Drafting/Design and Database Management Systems with formwork design applications. Thus, providing a conceptual framework within which

Computed-aided formwork design: A detailed approach 439

temporary works design systems can be developed with confidence, flexibility, and a minimum of programming effort. The functions integrated include the design, drafting, scheduling of quantities, and cost estimating of formwork. Formwork design covers vertical and horizontal construction in both timber and proprietary systems. Formwork members are designed to BS59755 and the recommendations of the Concrete Society’s text Formwork: A Guide to Good Practice.2 Formwork can be designed using a rational approach based on simplified assumptions commonly used in practice and/or a detailed approach based on the stiffness method of structural analysis. The reader is referred to Refs 1 l-14 for the details of FICADS and its individual modules. The paper presents a model and system (DetForm) developed for the detailed analysis and design of formwork.

2 THE REQUIREMENTS OF THE MODEL

The most commonly used formwork components such as walings and soldiers may be considered as beams. In the construction of a panel of formwork, such a member may rest on three or more supports, forming a redundant continuous beam system. In the rational design approach, where a formwork member rests on more than three supports, approximate beam formulas are used to compute safe support spans. Clearly, a continuous beam analysis would be more realistic. Therefore, the detailed analysis model should allow for a continuous beam analysis to be performed.

In addition to the commonly used beam type formwork, there are the lattice or truss type strongbacks often used in dam or mass concrete construction. Where these strongbacks have been pre-fabricated and supplied as proprietary items, the user is not concerned with the design of the individual members in the lattice. The supplier gives the maximum bending moments and forces that must not be exceeded. Formwork including such strongbacks are therefore, designed as beam type walings and soldiers. However, where the strongbacks are to be constructed on site, the individual members making up the lattice have to be checked to ensure structural satisfaction. This may involve truss analysis or a plane frame analysis or a hybrid of both, depending on the method of construction. This implies an analysis of 2-dimensional skeletal structures assembled from different types of members. They may be pin jointed, rigidly jointed or contain both types of joints. The model should, therefore, allow for the analysis of hybrid structures containing rigidly jointed and pinned connections.

The loads encountered in formwork design are usually assumed to be uniformly distributed. In vertical formwork design, the pressure from concrete is hydrostatically distributed. When designing tie sizes and positions, walings produce a series of discrete point loads. Therefore, the model should be able to handle point, distributed and hydrostatic loads.

The effect of shear deformation is usually neglected in most structural analyses, because the major part of

deformation is caused by the bending moments. Where a heavily loaded member has a relatively low ratio of span to depth of beam, shear deformation effects become significant. The significance of shear deformation on the design of metal soldiers was first highlighted by Ash.” He recommended that shear deformation effects should be considered when designing soldiers and that manufacturers of metal soldiers should quote shear stiffness as well as bending stiffnesses. How- ever, only one manufacturer was found to have taken this up and provided shear stiffness values for soldiers. It was decided that the effects of shear deformation should be included in the model and should be made optional.

The design of formwork involves the computation of bending moments, shear forces and deflections. These are checked to be within the allowable limits for the component under consideration. Limits are also placed on the allowable bending moments at the joints where individual formwork beams are jointed to make up a required length of formwork. The model should, therefore, produce deflections, axial forces, shear forces and bending moments at any point of interest in the structure.

3 THE STIFFNESS METHOD OF STRUCTURAL ANALYSIS

The major requirements of the model are that it should perform the analysis of continuous beams and two dimensional skeletal structures. Also the effect of shear deformation must be allowed for, and various load types are involved. These requirements render the model complicated but with some programing effort and using the right tools it can easily be handled by a computer. The stiffness method of structural analysis was considered the most appropriate tool for the implementation of the model. It is used in the analysis of highly redundant structures, for example, frames, gril- lages of beams and trusses. This is a very versatile technique and can include the effects of axial loading on a member’s flexural stiffness, shear stiffness, large changes in geometry, dynamic loads and material non-linearity. Naturally, it is the advent of the computer that makes such methods practically applicable. The details of such methods can be found in the standard text books on the subject. However, a rather short description is given here for the sake of completeness.

3.1 Theoretical background

The stiffness method consists of the following five basic stages.

1. Structural idealization and identification. 2. Evaluation of the element matrix equations. 3. Assembling of the total structure stiffness matrix,

taking the boundary conditions into account. 4. Generation of the loading vector and the solution of

the structure equilibrium equations. 5. Evaluation of the element forces.


The fundamental aspects of each of these steps are briefly discussed in the following sub-sections.

3.1.1 Structural idealization and identi#cation This involves making a judgement on the structures geometric characteristics and numbering the nodes for identification purposes. A global reference system is selected to which all the nodal quantities are referred. A local reference system is selected for each element or bar, to which all the bar quantities are referred. Based on the node and element numbers, and taking into account the reference system selected, the structure’s data is prepared. As a minimum the data should include the nodal co-ordinates, element connectivity data, element properties, boundary or support conditions, and a description of the applied loads.

3.1.2 Evaluation of the element matrix equations In this stage equations relating end forces and displacements of a member are set up. The coefficients relating forces and displacements of a member forms its stiffness matrix in terms of it’s geometry and material properties. Their derivation is described in standard texts on structural analysis.‘6-‘9 The matrix used in this paper takes the effects of shear deformations into account and the derivation is found in Ref. 16. For a member ‘ij’ of a rigid-jointed frame, lying in the xy plane such that the member longitu- dinal axis is inclined at an angle cp to the global x-axis (as shown in Fig. l(b)), the stiffness equation linking member end forces in the global system, f, to the corresponding end displacements, d, is as follows:

VI = mm where

(1)

(f] = (Dip Vi, &Ii, Dj’i, Vj, lifj)’

this is a vector of forces applied at the element nodes . . I,

and

- T (2) = {iii, 3i, Bi* Uj, Vj, Oj)

this is a vector of displacements at the element nodes j; and k is the element stiffness matrix in the global

and axis

system including shear deformations effects and is given by

El -- k- L(1 +P)

B -H -M -B H -M

-H P N H -P N

-M N Q M-N Z

-B H M B -H M

H -P -N -H P -N

-M N Z M-N Q

(2)

where [P] = [k]{b) (3)

1 2(s2 + ac2) B= L2

Q=4+/3 using a Gaussian elimination method. The displacements [D] in the local axis system are obtained by transforming

H- 12(1 -o!)sc L2

z=2+p

p _ 12(c2 + crs2 L2

) s=sin(o

M=$ c=cosp

12EIy M=; /3=-

AL?1 + P) (Y=

121

Note: (i) If shear deformations are to be ignored then y = 0. (ii) If the members are assumed to be axially rigid and if A is an unknown then set (Y = 0 for numerical convenience.

3.1.3 Assembling of the total structure stifiess matrix In this stage of the analysis, the stiffness matrix for the whole structure is compiled from the member stiffness matrices. This is accomplished by forming equations of equilibrium at each member connection and by stipulating that the members meeting at a connection, or joint, have the same displacement components as the joint. When the global stiffness matrix has been assembled, displacement boundary conditions are imposed. This is done by setting displacements at rigid supports to zero, or by adding stiffness coefficients to simulate the action of the connecting structural system. The resulting structure stiffness matrix [El is banded.

3.1.4 Generation of the loading vector and solution of the structure equilibrium equations Loading causes a structure to deflect, and an equilibrium position is reached when the internal end forces produced by deflected members balance the external, applied load at each joint. The loading vector is computed in the third stage of analysis. This is a vector of loads applied at each joint in the structure. The equivalent joint forces are computed for loads applied along the member length, and added to the nodal loading vector to generate the structure loading vector (F). The fixed end moments and reactions due to member loads are presented in Section 3.2.3. Once the structure stiffness matrix [El and the structure loading vector (F} are known, the displacements (D), in the global axis system can be computed from the structure equilibrium equation


Fig. 1. (a) Plane frame member (member axis system); (b) plane frame member (global axis system).

[D] into the local axis system using the equation

where

s = sin+9 and c = coscp.

3.1.5 Evaluation of the element forces Lastly, the end forces acting on individual members are determined by multiplying the local stiffness matrices by the determined joint displacements as follows

where

(f) = (ui, Vi, Mi, uj, 59 Mjl'

this is the member load vector in the local axis.

d=(ui, vi,‘0i, uj, vi, 0j}’

this is the displacement vector in local axis, where k is the member local axis stiffness matrix given by

-ax 0 o-ax 0 o-

0 x Y o-x Y

EI 0 Y R O-Y s

k= w+P) --ax 0 0 ax 0 0

0 -x -Y 0 X-Y

0 Y s 0 -Y R

VI = WlI4 (5) (6)

442 J. H. IV. Tah, A. D. F. Price

Table 1. Shape factors for typical shapes

Shape type Description Shape factor

q solid rectangle 1.2

0 solid circle 1.1

0

thin circle tube 2.0

ET I, T and box sections Major axis bending = 1.2 X (total area)/

(web area) Minor axis bending = 1.2 X (total area)/(flange area)

101

where

+ R=4+/3

Y=; s=2-p

and /3 and (Y have the same definitions as in eqn (2).

3.2 Effects of shear deformation

The effects of shear deformations are not usually included in most structural analyses. In this section, the effects of shear deformations and the relative significance of shear deflections to bending deflections are discussed. Shape factors are presented for various shapes of beam cross-sections.

3.2.1 The significance of shear effects Shearing forces usually have only a secondary effect on the behaviour of beams and rigid frame structures, since the major part of the deformation is caused by the bending moments. Consequently, the effects of shear are usually neglected from most analyses. However, occasions some- times arise where a heavily loaded member has a relatively low ratio of span-to-depth of beam, or where the material has a shearing modulus of elasticity which is smaller than the modulus in tension.‘* In ordinary cases where the span- to-depth ratio is 10 or more the shear deflection is insig- nificant in relation to the bending deflection.20

The derivation of the stiffness matrix including shear effects is well covered in the text of Bhatt.16 The derivation of some fixed end moments and shear forces in simple beams including shear effects is well treated in the text of Gere.‘* Therefore, only the data required for use with the formwork model and the derivation of fixed end moments and forces including shear effects, not covered in these texts, are presented in this paper.

3.2.2 Shape factors The global stiffness matrix for a 2-dimensional rigid-jointed

frame member is presented in Section 3.1.2. The stiffness coefficients included a factor, y, known as the shape factor. It is a dimensionless property of the cross-sectional area of a beam element. Table 1 shows some values for typical shapes. Details of the derivation of shape factors can be found in Gere.”

3.2.3 Fixed end moments including shear deformation effects When using the stiffness method, member loads are con- verted to equivalent joint forces (or fixed end moments and forces). These are added to the nodal loading vector as discussed in Section 3.1.4. The fixed end moments and forces excluding shear effects are given in most texts on structural analysis. When shear effects are considered, obtaining the fixed end forces become tedious. Fixed end moments and forces for various types of loadings encountered in formwork are presented in this section. The derivation of these values is presented in Ref. 12. The formulas have been presented in a form, such that, the fixed end moments neglecting shear effects can be obtained by setting the shape factor, y, to zero. Where loading is symmetrical over a member’s span shear has no effect on the fixed end moments and forces. The fixed end forces are presented in Table 2.

3.3 Member with pin connections

The stiffness matrix presented in Section 3.1.2 is for 2- dimensional structures consisting entirely of rigidly con- nected members. Most structures usually are either entirely pin jointed or rigid jointed. However, one of the requirements in the formulation of the formwork model was to allow for hybrid structures containing rigidly jointed and pinned connections. This affects the stiffness matrix, and the effect of including pins can be accounted for by the application of suitable factors to the elements of the matrix. The derivation of these factors are well covered in the text of Balfour.” Four types of members with or without pins have been considered as shown in Table 3.

Computed-aided formwork design: A detailed approach

Table 2. Fixed end moments and forces for member loads including shear effects

443

Code Load type Fixed end moments and forces

(0 . 3

!!iz!P a E

b

5 .- ‘y., w a E b

MA = , 2( 1 +w2R)L2 (6L+? - 0’) - 8L(h” - a’) + 3(b” - aJ) R,=F(+,)+ c”,tMB)

+ 2g(3L2(bZ - rr?) - 2L(b3 -a?)))

MB=- w ,(4L?(h7-a’)-3(b4-[II) 12( I + 2g)L-

+ 2~(3L’(h’ - u2) - 2L(h - u3))]

M,, = 60(, + 2;;(b _ a)L2 (30bL?b? - 02) - 40bL(b3 - tr?) RA=!@+L&~)+%$?!$

- 20L2(b’ - a’) + 30L(b’ - rrJ)

+156(b4-a4)-12(b’-a5)

+ 5g(6bL’(b’ -0’) - 4bL(b’ -a’)

- 4LZ(b’ -cl) + 3L(bJ - (14)))

- 15b(b” - <I’) - I 5L(b4 - d) + I2(hS - u5)

+ 5g(6bL2(b2 - a’) - 4bL(b’ - a”)

-4L?(b?-tr?)$-3L(bJ-ul))]

M,, = 60(, +2;;(b-a)L!120w --LI)

,+$f(;+,)-?!$!?!d

- 30L(b4 - ~1’) - 30aL’(b2 - u2) + 40aL(b3 - ~1~)

+ I 2(b4 - a4) - I Sa(bj - u4)

+ 5g(4L2(b3 - u3) - 3L(bJ - a4)

- 6aL’(b’ -a’) + 4aL(h3 - <?))I

J. H. M. Tah, A. D. F. Price

Table 3. Member types coding

Code End ‘i End ‘j Member type

1 Fixed Fixed i a O/j / , B j 0 2 Fixed Pinned 4 0

3 Pinned Fixed 0

4 Pinned Pinned 0 0

3.4 Software for the solution of equations

Many software packages have been developed for the solution of the system of equations involved in the stiffness method of structural analysis. They differ in their complex- ity, capabilities, cost, and availability. Two main types of such systems are available. The first type are packages which comprise of stand-alone programs that can be used directly by the user. All that is required from the user is the input data. The second type are libraries which contain sub- routines that can be called from a program. The advantage of using a package over libraries is that, the latter require programing knowledge, whereas a package user need not perform any programing. The advantage of using libraries is that they are more flexible. They can be modified by the users or used to build more sophisticated software. In other words they can be customized by the user. This is not the case with packages.

The use of existing libraries was considered appropriate for the implementation of the detailed analysis model discussed in this chapter. Existing libraries were developed mainly for the main-frame computers, whereas the system was developed for the microcomputer. Furthermore, these libraries were developed in the FORTRAN programing language, while the PASCAL programing language was to be used in developing the system. However, most structural computation text books, include proven program codings of algorithms for the solution of problems involving the stiffness method. All the algorithms found were coded in either FORTRAN or BASIC. Also, none of them included shear deformation effects which was one of the requirements of the system to be developed. The excellent text book by Balfour17 proved to be the most useful. Although it provided algorithms developed in BASIC it also provided detailed explanations on their implementation. A greatly enhanced version of the coding was developed in the PASCAL programing language. Enhancements included the use of a stiffness matrix including the effects of shear deformation and the inclusion of hydrostatically distributed loads as discussed previously. Once the algorithms for handing the

stiffness computations were developed they were tested on example problems found in various text books. These algorithms tested positively as the solutions were reproduced as in the texts. They were then ready for implementation in the detailed formwork design program, which is the subject of the following section.

4 THE COMPUTER IMPLEMENTATION OF THE DETAILED FORMWORK DESIGN MODEL

There are various methods of implementing the stiffness method of structural analysis in a computer program. The differences in methods are mainly due to the nature of interaction with the program during data entry and presentation of the final design results. However different the method of interaction used, the five basic stages of the stiffness method presented previously will almost certainly be used. All five stages constitute separate procedures in a computer program. The conceptual model considered for the implementation of the stiffness method of analysis in this paper, is shown in Fig. 2. It consists of three main phases. These are the pre-processing phase, the analysis core, and the post- processing phase.

The pre-processing phase represents stage one of the stiffness method. The result of stage one, i.e. the structural idealization and identification, is a datafile composed of data about a structures nodal co-ordinates, connectivity, boundary or support conditions and a description of applied loads. This datafile can be created in a number of ways. It can be created by a text editor, a database management system or pre-processors which are specialized programs developed to ease the creation of the datafile for particular structural configurations.

The second phase of the conceptual model has been termed the analysis core, as shown in Fig. 2. The analysis core represents stages two to five of the stiffness method. They are the analysis routines that utilize the data obtained from the pre-processing phase. These stages, therefore, form the heart of the detailed formwork design model. The results produced by the analysis core include nodal displacements, bending moments, shear forces and reactions. These can be presented in various ways.

The third phase of the conceptual model is the post-processing phase. This phase is concerned with the presentation of the results of analysis produced in phase two. The results can be presented in tabular text formats and graphically as deflection, bending moment, and shear force diagrams. This is achieved by the use of special purpose programs called post-processors.

The conceptual model shown in Fig. 2 depicts three possible methods of creating a data file in the pre-processing phase. These include the use of text editors, pre-processor programs, and through graphical interfaces provided by general purpose CAD packages. The use of text editors is the most flexible method of creating the datafile. This is


E @

ost-processor

s ro ams

z

Fig. 2. The conceptual view of the detailed formwork design model.

because the user is not constrained to a specific structural configuration by the specification of a pre-processor program. The disadvantage is that it can be very tedious and error prone. In some structures, e.g. formwork beams such as walings and soldiers, the stiffness of the beam is constant throughout its length. The element properties are, therefore, the same for all elements. This implies typing the same information for a number of records where a text editor is used, and can be very tedious. Pre-processor programs are, therefore, developed to speed up the creation of the data file. In this paper, the detailed analysis model which forms the analysis core, was formulated to handle both beam and 2-dimensional frame type structures. However, beam

type formwork is frequently encountered in practice. Con- sequently, the pre-processors and post-processors developed for the detailed formwork designed program were designed to handle beam type formwork. A text editor can, however, be used for creating the datafile for the design of frame type formwork. The following sections describe DetForm, the detailed formwork design program developed.

4.1 The program specification

Based on discussions with expert temporary works designers on the weakness of current formwork design programs and the shortcomings of the rational formwork design


+ I Da3

interface

t

3 FICADS -@

DCtFOIlll

local (analysis core)

Fig. 3. The architecture of the detailed formwork design sub-system.

approach; the following features were seen to be necessary in a detailed formwork design program:

1. The program should be able to design both horizontal and vertical formwork.

2. It should allow the use of traditional and proprietary formwork components.

3. Graphics should be used to generate the geometric model of the formwork structure to be analysed. This should provide a visual check on the correctness of the model to be analysed.

4. The results of analysis should be presented in both tabular text format and graphically as bending moments, shear force, and deflection diagrams.

5. The program should be easy to use.

These requirements require a lot of imagination on the part of the programmer, particularly providision of a graphical interface for the generation of the formwork model. It was a major requirement of FICADS that the system should allow the formwork designer to use his/her engineering judgement. In the case of the detailed formwork analysis, engineering judgement is required mainly in the structural idealization of the formwork arrangement (or generation of a geometric model). Therefore, it implies that the pre- processor should be flexible enough to allow the designer to define the structural model as desired within the capabilities of the analysis core. Another important consideration was the fact that most formwork designers have been using simple analytical methods for designing formwork. There- fore, for the detailed analysis approach to be accepted, it

must be easy to use. The programmer is, therefore, faced with the dilemma of not only providing a flexible tool for formwork design, but also making it easy to use at the same time. The detailed formwork design program developed in this thesis provided a solution to these problems. Its architecture is discussed in the following section.

4.2 The architecture of DetForm

The design of the detailed formwork analysis program was based on the conceptual model presented earlier. The architecture of DetForm is shown in Fig. 3. The program consists of three individual modules representing the three phases described in the conceptual model. These modules constitute a pre-processor program, an analysis program, and a post-processor program. Each program was developed to run independently. The link between individual programs was provided by the ProCad*’ package, a general purpose CAD package. A program was developed to represent each phase for the following reasons:

l The nature of each phase was such that specific software tools were suitable for use. The pre-processing and post-processing phases require a graphics interface, whereas the analysis phase is concerned with a considerable amount of number crunching. There- fore, taking advantage of special state-of-the-art software tools that were suitable for handling the requirements of each phase, should allow the program specification to be achieved. This resulted in a reduction of the program development time.


15-y -4

Pressure envelope

20 61 5 kNh2

r KQ

I Soldier

0 arbitrary nodes

X nodes at supports

- pressure envelope. control poinl

-+ Tie positions

Fig. 4. The geometric model.

options

tS

1

Select component from menu

c

Enter and validate control data

to retreive co-ordinates from ProcAD’s database

1 Enter and vabdate boundary condmons

. Enter nodal loads if any

I c c c + A

Set max. pressure for all Compute pressure values Enter individual

loaded elements automatically at node points automatically loads and positions

I I +

I

Save ail data to the input data file

Fig. 5. Flow chart of FormPrep.

448 J. H. M. Tah. A. D. F. Price

Datafile for detailed analysis of formwork beams {no.ofncdesl (no.ofmembers) (no.ofrestrainedncules) (no.ofnodal1oad.s) (no.ofmembfzloads)

{NOdE!O.I

1

2 3 4 5

6 7 8 9

10 11 12 13 14 15 16 17 18 19 20

{Node no. ) 2 6

10 14 18

19 5 0 16 {x - co-ordinate) { y - co-ordinate)

4.99655EMO 8.17759E+W 4.9%55E+OO 7.47759E+OO 4.9%55E+OO 7.32759E+OO 4.99655E-t-00 6.77759E+OO 4.99655E+OO 6.22759E+OO 4.99655E+OO 5.67759E+OO 4.9%55E+OO 5.20259E+OO 499655E+OO 4.72759E+OO 4.99655EtOO 4.40259E+OO 4.99655E+OO 4.07759EM.l 4.96655E+OO 3.72759E+OO 4.96655E+oo 3.37759E+OO 4.96655E+OO 3.02759E+OO 4.96655E+oo 2.67759E+OO 4.96655E+Oo 2.32759E+OO 4.96655E+OO 1.97759E+OO 4.96655E+OO 1.62759E+OO 4.96655E+oo 1.27759E+OO 4.96655E+OO l.l2759E+OO 4.96655E+OO 9.77586E01

{Restraint code) 12 12 12 12 12

(Node”?‘) (Ncde”j”) (Loadtype) (L.oad”Y) 3 4 7 O.OOOOOE& 4

: 7 8 9

10 11 12 13 14 15 16 17 18

7

ii 10 11 12 13 14 15 16 17 18 19

7 -1.375OOE+Ol 7 -2.75OOOE+Ol 7 -4.125OOE+Ol 7 -5.3125OE+Ol 7 -6.5OOOOEtO1 1 -6.5OOOOE+Ol 1 -6.5OOOOEtOl 1 -6.5OOOOE+O1 1 -6.5OOOOE+O1 1 -6.5OtXME+Ol 1 -6.5OOOOE+Ol 1 -6.5OOOOE+Ol 1 -6.5OOOOE+Ol 1 -6.5OOOOE+O1 1 -6.5OOOOE+Ol

(Load “j”) {Distance “i”) (Distance ‘3”) -1.375OOE+Ol O.ooOE+OO 5.5OOE-01 -2.75WOE+Ol O.OCKlE+OO 5.5OOE-01 -4.125OOE+Ol O.OOOE+OO 5.5OOE-01 -5.3125OE+Ol O.OOOE+OO 4.75OE01 -6.5OOOOE+Ol O.OOOE+OO 4.75OE-01 -6.5OOOOEtOl O.OOOE+OO 3.25OE-01 -6.5OOtME+Ol O.OOOE+OO 3.25OE-01 -6.5OOOOE+Ol O.OOOE+OO 3.25OE-01 -6.5oooOE+Ol O.OOOE+OO 3.25OE-01 -6.5OOOOE+Ol O.OOOE+OO 3.25OE-01 -6.5OOOOE+Ol O.OOOE+OO 3.25OE-01 -6.5OOOOE+Ol O.OOOE+OO 3.25OE-01 -6.5OWOE+Ol O.OOOE+OO 3.25OE-01 -6.5OfMOE+Ol O.OOOE+OO 3.25OE-01 -6.5oooOE+O1 O.OOOE+OO 3.25OE-01 -6.5OOOOE+Ol O.OOOE+Otl 1.5OOE-01

Fig. 6. The input datafile created by the preprocessor program.

l This approach was considered flexible enough to adapt to future changes. Further pre-processors and post-processors could be developed with time to replace existing ones as the need arose without any major changes to the complete system. The pre- processors and post-processors need not be developed to run within the ProCAD package. Any other package, for example the now popular AutoCAD package, may be used without affecting the analysis program.

The program architecture shown in Fig. 3, shows the links

and the inter-communications between individual program modules. A case study is used to demonstrate the detailed functions of the three sub-systems.

4.3 A case study

A contractor requires formwork for the construction of walls to a reservoir. The height of the wall pour is 6200 mm and the length of pour is 6500 mm. The wall thickness is 450 mm and the height of the kicker is 150 mm. The contractor has computed the design concrete pressure to be 65 kN/m’. It has been described that the facing is to be in


Search and display max. displacement, forces. and moment

Fig. 7. Flow chart of DetForm.

plywood and the walings in timber as these are available in stock. The contractor requires a detailed design solution from a supplier on proprietary formwork.

4.4 Creating the geometric model

Prior to the use of the pre-processor program, the ProCAD drafting package is used to create a geometric model of the anticipated soldier system for the wall, as shown in Fig. 4. The geometric model shows the topology and characteristics of the arrangement of the soldier system. The loading is indicated by the pressure envelope. The thick vertical line depicts the solider as a beam. The triangular supports indi- cate the positions of the ties. The designer has used his engineering judgement and experience to make an initial guess of the tie spacings indicated. Notice how the designer has taken advantage of the reduction of concrete pressure at the upper section of the wall to increase the tie spacing in that region. The length of the soldier must be greater than 6350 mm, that is, the combined length of soldier and kicker. There are no soldiers of this height and the designer decided to use two 3600 mm soldiers to make up the soldier. The designer wishes to perform an analysis to check that this system of arrangement is structurally safe and economic.

This implies checking that the resulting bending moments, deflections, and tie loads are within the allowable limits for the components. These values are required at critical positions along the entire length of the beam arrangement. Nodes (represented by points) are placed at several positions (e.g. at the quarter points within each span) and at the joint between the two soldiers. Nodes at points of support (e.g. tie positions) are represented by crosses, as shown in Fig. 4. Nodes are also placed at three other positions representing control points on the pressure envelope. These are at the top of the wall, at the point where maximum pressure begins, and at the top of the kicker. These points are to be used by the pre-processor to automatically compute the loading within each element of the beam. All node points are then numbered sequentially from the top to the bottom. The creation of the geometric model has been completed and pre-processing can therefore commence.

4.5 The pre-processor program

The term pre-processor has no definite definition as it is used in computing and other fields of study. the term pm-processor in the context of this paper means a subprogram that is used to aid in preparing data required by the analysis program. The

450 J. l?. M. Tah, A. D. F. Price

RESULTS OF FORMWORK ANALYSIS : THE DETAILED APPROACH ***************************************************************

SOLDIER ANALYSIS *******************

Member type

Member code = S3lll36OO Trade name = MK3 3600mm soldier

Proprietary member properties

Length = 3600 mm Weight = 82.00 kg Depth = 230 mm Breadth = 170 mm Cross-sectional area Second moment of area Section modulus Modulus of elasticity Max. bending moment Max. bending moment at joint Max. tie load (reaction) Max. shear capacity Modulus of elasticity (E) Shear modulus (G) Shape factor Bearing stress

= 21.000 = 1940.000 = 168.000 = 208.000 = 30.000 = 25.000 = 160.000 = 120.000 = 208.000 = 83.000 = 1.800 = 190.000

Cm2

cm4 cm3 GN/m2 kNm kNm kN kN GN/m2 GNm2

MN/m2

*********************************

Checks !!!

Constraint Permissible Comment

Deflection (mm) 0.396 3.000 O.K. Bending moment (kNm) -12.766 30.000 O.K. Shear force WI 54.096 120.000 O.K.

Fig. 8. Results of the analysis produced by DetForm.

pre-processor program, FormPrep, was developed to handle this task. FormPrep is a highly-interactive menu driven program developed as a ProCAD design module. It allows the user to enter information about the geometric model by means of the keyboard and the mouse. The program’s logic is shown in Fig. 5 and the resulting data file for the case study is shown in Fig. 6. In running the program, the user starts by selecting the component under consideration from a menu. The menu options are the facing, studs, walings, soldiers, secondaries and primaries. This is used for naming the data file to be created. The control data is then entered. This consists of the number of nodes, the number of restrained nodes, the number of nodal loads, and the

number of member loads. The next data of interest is the nodal co-ordinates. These are entered by digitizing the node points with the mouse. The restrained node numbers and their corresponding restrained codes are also entered. If there are loads at any nodes, the node numbers and the corresponding load values are entered. The pre-processor allows the member or element loads to be considered in three options. In the first option, the loading on the whole arrangement may be considered to be uniformly distributed. In this case, the user is required to enter the load value and the pre-processor then sets the loadings on all elements to be of the entered value. In the second option, the loading on the whole arrangement may be considered as consisting of the

Computed-aided formwork design: A detailed approach

TIE LOADS FROM SOLDIERS ANALYSIS

451

Tie Height No. m --- -----

Top of soldier

***********************I**************

Tie Hogging spacing reactions moments

mm w kNm ------ _-__-- -- --_-----

Shear forces (above) (below)

kN kN ----_-- -_______ -

1 6.500

2 4.700

3 3.100

4 1.700

5 0.300

Bottom of soldier

700 5.028 0.000 0.000 5.028

800 71.113 -10.290 29.003 42.110

1600 95.492 -11.904 50.508 44.884

1400 100.212 -12.766 46.116 54.096

1400 46.654

300

-0.731 36.904 9.750

RESULTS OF SOLDIER ANALYSIS *******************************

Height m

___--- Top of soldier

7.200 6.500

Deflection mm

____-- ---

Moment Shear force kNm kN

------_-- ---------

0.198 0.000 0.000 0.000 0.000 0.000

6.500 O.OOb 0.000 5.028

6.350 0.042 0.754 5.028

5.800 0.132 2.618 1.247

5.250 0.052 0.323 -10.097

4.700 0.000 -10.290 29.003

4.700 0.000 -10.290 42.110

4.225 0.270 4.478 19.696

3.750 0.346 7.260 -8.358

3.425 0.180 1.111 -29.483

3.100 0.000 -11.904 50.608

3.100 0.000 -11.904 44.884

2.750 0.016 -0.176 22.134

2.400 0.057 3.590 -0.616 2.050 0.009 -0.607 -23.366 1.700 0.000 -12.766 46.116

1.700 0.000 -12.766 54.096

1.350 0.221 2.186 31.346

1.000 0.396 9.176 8.596 0.650 0.312 8.204 -14.154

0.300 0.000 -0.731 36.904

0.300

0.150 0.000

0.000 0.152 0.303

-0.731 0.000 0.000

9.750 0.000 0.000

Bottom of soldier

Fig. 8. Continued

concrete pressure envelope only. In this case, the user is required to enter the maximum design and concrete pressure

In this figure any text enclosed in curly brackets are not part of the data but are headings for a block of data. A detailed

value and the pre-processor computes the individual member loads based on the pressure envelope distribution. In the third option, if the loading is none of the previous two options, then all loads are entered individually. A data file is then created automatically. The datafile for the case study is shown in Fig. 6.

description of the use of FormPrep is presented in Ref. 11.

4.6 The analysis program

The input datafile created by the pre-processor program is


Y-uh spec FY Ents Y-axis

spccifutim

Fig. 9. Flow chart of FormPost.

used by the formwork detailed analysis program, DetForm, to compute the displacements and forces resulting from the formwork arrangement. The program is highly interactive and uses the standard window and menu interface developed for FICADS. The program’s flow chart is shown in Fig. 7. The program begins by allowing the user to select the formwork component for analysis from the main menu options. The material to be used is then selected from the database. This could be plywood in the case of the facing, and timber or a proprietary beam in the case of the supporting members. The material and sectional properties of the selected item are retrieved from the database. The program then reads the data file created by the pre- processor and creates the element properties records for all elements. The stiffness analysis is then performed and the resulting displacements and forces are then saved to an output file for use by the post-processor program. The program then searches and displays the maximum displacement and forces for visual inspection. It then checks the maximum computed deflection, bending moment, and’ shear fprce against the allowable values for the selected material. If any check fails, a stronger material may be selected or t

” spacings of the supports may be

reduced by altering th ,,geometric model. The results of analysis are obtained in the first instance as shown in Fig. 8. The bending moment, shear force, and deflection diagrams may be obtained by running the post-processor program.

4.7 The post-processor program

The term post-processor is used here to represent a subprogram that is used for presenting the results of analysis in a graphical form. The post-processor program FormPost, was developed to handle this task. The flow chart of this program is shown in Fig. 9. FormPost is a highly-interactive menu driven program developed as a ProCAD design module. It

reads the output datafile created by the analysis program and allows the user to plot bending moment, shear forces, and displacement diagrams in the form of graphs within the ProCAD database. The program is very flexible. It allows the user to select the origin of each graph at any point on the screen by indicating with a mouse. The user has control over the size of the graph, the axis labeling, and the scaling. The graphs for the case study example are shown in Fig. 10.

5 CONCLUSIONS

A rational approach to formwork design is adequate when designing formwork which involves light loads. Where extremely heavy loadings are involved, or where there is an unusual danger to life or property a detailed structural design of formwork may be necessary. The requirements of the model for detailed analysis of formwork, as presented in this paper, are that it must: perform a continuous beam analysis; perform the analysis of 2-dimensional skeletal structures containing both rigid and pin joints; include the effect of shear deformation; produce deflections, axial forces, shear forces and bending moments at any point of interest in the structure.

The stiffness method of structural analysis was considered as the most appropriate tool for implementing the detailed analysis model, if all the requirements were to be satisfied. The stages involved in the stiffness method are briefly discussed in this paper. The effects of shear deformations can be significant where deep proprietary beams are used and should not be neglected. Expressions have been derived for the fixed end moments and forces including shear deformation effects, for various loading cases com- mon in formwork design.

Many software packages and libraries have been developed for the solution of equations involving the stiffness



method of structural analysis. None of these were found to be suitable for use in the work undertaken. Algorithms were developed for the implementation of the stiffness method to satisfy the requirements of the detailed design model.

A program has been developed for the detailed design of formwork. The program requires detailed information on the formwork member under analysis including the positions of nodes, nature of applied restraints, and positions and magnitudes of loads. A pre-processor subprogram was developed to ease the entry of this information. A post- processor subprogram was also developed for the graphical display of the results of analysis including bending moments, shear forces and deflections.

The pre-processor and post-processor programs were developed to interface with the ProCAD package. This allowed a geometric model of the formwork assembly to be created within the drafting package. The pre-processor program was then used to retrieve co-ordinate data from ProCAD’s database. Thus, providing a highly interactive environment that allows the designers to use their intuition and engineering judgement to create different geometric models of the formwork assembly for analysis.

The detailed approach is much more involved, thus is slower than the rational approach, but it provides more accurate results. Optimized solutions can be obtained by increasing waling or tie positions towards the top of a wall, where the concrete pressure is less. This is not possible with the rational approach which assumes equal spacings and uniform loadings.

ACKNOWLEDGEMENTS

The authors express their thanks to Mr Peter F. Pallet for- merly of Rapid Metal Developments Ltd for his most useful comments, constructive criticisms, generosity in supplying information and attending a lengthy demonstration session during the development and testing of DetForm. This research was supported by a Cameroun Government BS grant.

REFERENCES

I. Bennet, D. F. H., Chicago-based construction technology.

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Building Technology and Management, June/July 1988, 5- 10. The Concrete Society, Formwork: A Guide to Good Practice. The Concrete Society and The Institution of Structural Engi- neers, London, August 1986. British Standards Institution, Draft Code of Practice for

Falsework. BSI, London, 1975. The Concrete Society, Formwork, Report of the Joint Com- mittee. Technical Report No. 13, The Concrete Society and Institution of Structural Engineers, London, March 1977. British Standards Institution, Code ofpracticefor Falsework,

BS5975. BSI, London, 1982. CIRIA, Concrete pressure on formwork. CIRIA Report 108, Construction Industry Research and Information Association, London, 1985. CIRIA, The pressure of concrete on formwork. CIRIA Report I, Construction Industry Research and Information Associa- tion, London, 1965. Neale, R. H. and Boland, J. N., Research into the application of small computers to the design of scaffold falsework. Pro- ceedings of the Institution of Civil Engineers, 1980,68,463- 476. The University of Technology Loughborough and CICA, Computers in Temporary Works, reported by R. H. Neale, I. Hamilton and K. A. Sane. Construction Industry Comput- ing Association (CICA), Cambridge, August 1986. Baldwin, A. N., Computer aided estimating for civil engineering contractors. Ph.D. Thesis, Loughborough University of Technology, UK, 1982. Tah, J. H. M., Integrated microcomputer applications in formwork design. Ph.D. Thesis, Loughborough University of Technology, UK, 1989. Tah, J. H. M. and Price, A. D. F., Interactive computer-aided formwork design. Computers and Structures, 1991, 41, 1157-l 167. Tah, J. H. M. and Price, A. D. F., A database management system for formwork design. Microcomputers in Civil

Engineering, 199 I, 5. Tah, J. H. M. and Price, A. D. F., Computer-based modelling of concrete pressures on complex shaped wall formwork. Building and Environment, I99 I, 26, 223-229. Ash, J. E., Design, testing and performance of metal soldiers. Concrete, 1978, 12. Bhatt, P., Problems in Structural Analysis by Matrix Methods. The Construction Press, London, I98 I. Balfour, J. A. D., Computer Analysis of Structural Frame-

works. Collins, London, 1986. Gere, J. M., Moment Distribution. Van Nostrand, New Jersey, 1963. Wang, C. K., Intermediate Structural Analysis. McGraw- Hill, New York, 1983. ProCAD Systems, BillMat: Training and Reference Manual.

ProCAD Systems Inc., 1985.

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Computer-aided formwork design: A detailed approach