Building and Environment, Vol. 26, No. 2, pp. 223-229, 1991. 0360-1323/91 $3.00+0.00 Printed in Great Britain. © 1991 Pergamon Press plc.

Computer-based Modelling of Concrete Pressures on Complex Shaped Wall Formwork

J. H. M. TAH* A. D. F. PRICE?

The determination o f concrete pressures on formwork is an important aspect of temporary works design. CIRIA provides a data sheet for easy abstraction of maximum concrete pressure values for formwork design. The data sheet cannot be used directly where complex shaped walls are encountered. A data model has been developed to describe the geometry of wall cross-sections so that the concrete pressure envelopes on complex shaped wall formwork can be computed systematically. The procedure described in CIRIA Report 108 for computing maximum pressures on non-parallel sided walls is used to implement the data model in a computer program developed to interface with a computer-aided drafting package. This allows the use of CAD techniques for describing the model geometry and associated attribute information to the computer, thereby providing a good user interface. An example is used to illustrate the application of the model to a complex shaped wall.

Key symbols Pmax

D H h K T Q R

C1

C2

L W

SeC

a

b

Xb, Yb a t

b"

Xa,, Ya, Xb.,Yb,

0

N O T A T I O N

maximum concrete pressure on formwork, kN/m 2 weight density of concrete, kN/m 3 vertical form height, m vertical pour height, m temperature coefficient taken as (36/(T+ 16))2 concrete temperature at placing, °C volume supply rate, m3/h the rate at which concrete rises vertically up the form, m/h coefficient dependent on the size and shape of formwork coefficient dependent on the constituent materials of the concrete length of concrete pour, m width of concrete pour, m wall sub-section designator slope of the left edge line of a subsection slope of the right edge line of a sub-section point on the left edge line of a sub-section point on the right edge line of a sub-section the Cartesian co-ordinates of point a the Cartesian co-ordinates of point b point on the pressure envelope on the left side of a sub-section with pressure corresponding to that at point a point on the pressure envelope on the right side of a sub-section with pressure corresponding to that at point b the Cartesian co-ordinates of point a' the Cartesian co-ordinates of point b' angle the left edge line of a sub-section makes with the horizontal

* Research Fellow, Department of Civil Engineering, Uni- versity of Technology, Loughborough, Leicestershire, LEll 3TU, U.K.

t Lecturer, Department of Civil Engineering, University of Technology, Loughborough, Leicestershire, LE11 3TU, U.K.

223

Ax ~y

F

Subscripts i J

angle the right edge line of a sub-section makes with the horizontal horizontal component of pressure vertical component of pressure scaling down factor for pressure envelope plot

an arbitrary complex shaped wall sub-section an arbitrary level in the wall cross-section

1. I N T R O D U C T I O N

FRESH C O N C R E T E is a fluid and has to be put into a container until it hardens. This container is called form- work and contributes greatly to the shape and surface texture of the finished structure. One of the most impor- tant requirements of formwork is that it should withstand the pressure of fresh concrete during placing. Although formwork is required only temporarily it can be very expensive. Consequently, the pressure exerted by freshly placed concrete is of great concern to temporary works designers. Overestimation of concrete pressures can result in expensive formwork and underestimated values can result in badly formed structural elements or even failure of the formwork.

The method of calculating the concrete pressure on formwork has been the subject of many technical papers. Various theories have been proposed over the years to explain the mechanisms involved. The method currently being used in the U.K. is that of CIRIA Report 108 [1]. Other popular methods are the ACI [2], DIN [3] and that proposed by Gardiner [4]. The method used in this paper is based on CIRIA Report 108. Although CIRIA Report 108 includes a data sheet [5] for easy abstraction of maximum concrete pressures, this cannot be used directly when complex shaped walls are encountered. The re-

224 J. H. M. Tah and A. D. F. Price

quired calculations can become tedious and repetitive, making the problem ideal for computer implementation. Furthermore, some design parameters, such as the tem- perature at placing and the rate of supply of concrete, are least likely to be known with any certainty at the design stage. The computer can allow several simulations to be quickly performed to investigate the magnitude of the maximum concrete pressures resulting from changes in these parameters.

This paper describes a data model that uniquely ident- ifies the geometry of a complex shaped wall and its algo- rithmic implementation for computing the concrete pres- sure envelopes on complex shaped walls for formwork design. The procedure outlined in CIRIA Report 108 [1] for the calculation of the maximum concrete pressures on non-parallel sided walls is used to implement the data model. This has been transformed into a computer pro- gram developed to interface with a low cost commercial CAD software package. The CAD software provides a graphics database for the complex wall geometry and the computed pressure envelope.

2. THE MAXIMUM PRESSURE THEORY

Consider a vessel containing a liquid such as water. The horizontal pressure on the side of the vessel, at any point, is the same as the vertical pressure resulting from the weight of fluid above that point. This fluid pressure is numerically equal to the weight density multiplied by the depth below the surface. When concrete being placed is mobilized by vibration, the pressure it exerts is equal to the fluid pressure. However, the mobilizing effects of internal vibration are localized and the full head of concrete is not achieved in most placements. When con- crete is not mobilized by vibration it begins to stiffen. The stiffening of concrete is a combination of increasing mechanical interlock between the solid particles, aggre- gate and cement, and the hydration of cement. As the particles begin to settle against each other, friction develops between them and resists the transfer of pressure onto the form. The solid particles are also bound together by the cement paste, which continues to hydrate with time. The most significant factors which affect the pres- sure of concrete are : concrete density, rate of rise, height of section cast, concrete temperature, cement type, admixtures, latent hydraulic binders and shape and plan area of section cast. The influence of each of these factors are examined in greater detail in CIRIA Report 108 [1].

The full description of the theoretical justification of the CIRIA Report 108 [1] method will not be discussed here as it has been covered fully by Harrison [6]. This method and those previously referenced all have a simple common principle. When concrete is placed in formwork the pressure exerted on the form reaches a value where any further increase in the concrete head does not increase the pressure. After this value has been attained the pressure generally decreases slowly with time despite the increase in load from the concrete being placed above.

CIRIA Report 108 [1] presents the following formulae for the analysis of the maximum concrete pressure on formwork :

??i

Actual pr~sstlre

Dtsign p r ~ u r e

2 4- Pmax ~ Pressure (kN/m )

Fig. 1. Design and actual pressures.

o r

Pmax = Dh (kN/m 2)

whichever is smaller,

Butwhen C ~ / R > Hthen Pmax = Dh

(kN/m 2)

(la)

(kN/m~).

(Ib)

Alternatively, pressures may be read directly from the CIRIA data sheet [5] which quantifies these formulae for normal U.K. conditions where the concrete placing temperature is between 5 and 15°C. The reader is referred to CIRIA Report 108 [1] for details on the application of the formulae.

2.1. The design pressure distribution The pressures given by the data sheet and the equations

are the maximum pressures used to obtain a pressure distribution for formwork design. This distribution is developed by assuming that the concrete acts as a fluid down to the point where the fluid pressure equals the maximum. The design pressure distribution is shown in Fig. 1 with a typical distribution as measured on site. The distribution is a smooth curve and shows the gradual stiffening of concrete, which starts as soon as the mobi- lizing effects of vibration and impact becomes small. The design pressure distribution shows the behaviour sim- plified, but on the safer side.

3. LIMITATIONS OF THE CIRIA DATA SHEET

Although CIRIA Report 108 [1] includes a data sheet for the abstraction of the maximum concrete pressure with little effort, there are various limitations that will require the temporary works designer to resort to the use of the maximum concrete pressure formulae. These limitations are as follows.

Temperature The data sheet is applicable to normal U.K. conditions

where the concrete placing temperature is between 5 and 15°C, whereas the maximum pressure expression is valid between 5 and 30°C.

Computer-based Modelling of Concrete Pressures 225

Concrete density The data sheet assumes a weight density of 25 kN/m 3

which is a safe value for normal-weight concretes. The appropriate weight density should be used in the design for light- or heavy-weight concretes.

Sloping forms This is the greatest handicap in the use of the data

sheet and provides significant justification for the devel- opment of a computer model. The data sheet assumes a uniform rate of rise and cannot be used directly with non- parallel sided walls with a non-uniform rate of rise. If the volume supply rate is varied so that the rate of vertical rise is constant, the equation or data sheet can be used directly, However this is not practical. CIRIA Report 108 [1] suggests the following procedure for the calculation of the pressure envelope on sloping forms for a constant volume supply rate of concrete :

1. Split the pour into horizontal levels with the vertical distance between each level 1 m or less.

2. Calculate the plan area at each level. 3. Calculate the instantaneous rate or rise at each level

from

Uniform volume supply rate (m 3/h) R~evot = Plan area at the level considered (m2) '

4. Calculate the pressure at each level using the full height of the form, H, with either the equation or data sheet.

5. Produce the design pressure envelope acting at right angles to the forms.

It should be noted that the pressure at any level in the pour is the same on both sides or faces, and the direction of action is perpendicular to the form. The procedure described above for inclined formwork has not been quantified experimentally and further site investigations are required [7]. Unless the findings of these inves- tigations prove otherwise, the above procedure will con- tinue to be used. The above procedure for computing pressures on sloping forms is quite straightforward, but the computation can become very repetitive and tedious where complex shaped walls are encountered. The fol- lowing section is concerned with the development o f a geometric data structure for the computer implemen- tation of this process.

4. THE MODEL FUNCTIONAL SPECIFICATION

The previously suggested method for the calculation of the pressure envelope on sloping forms involves a series of repetitive calculations which can easily be han- dled by a computer. Furthermore, the results of the cal- culations including the pressure envelope, can be dis- played on the monitor in a graphical form. This has the advantage of revealing any errors in the preparation and entry of data. As in the development of any computerized system it is necessary first to define the system functional specification. The system requirements are as follows :

1. It should be able to handle the majority of walls en- countered in practice. Wall cross-sections vary from simple parallel sided and non-parallel sided shapes to

complex shapes with sides sloping in various directions [7].

2. The modeller should interface with a commercial draft- ing software package. This will allow digitized entry of co-ordinates by means of a mouse and a graphical display of the final results.

3. The results of the calculations should be stored on disk as text and graphics, and displayed on the monitor in both text and graphical forms for inspection by the user.

5. A DATA MODEL FOR COMPLEX SHAPED WALLS

A representative complex shaped wall is shown in Fig. 2a. In Fig. 2b the wall section has been sub-divided at each change of slope on either the right or the left edge of the wall. It can be seen that a complex wall cross- section consists of a series of quadrilateral sub-sections lying on top of each other. Therefore, each sub-section can be uniquely identified by the co-ordinates of its four vertices. It should be noted that the wall cross-section is sub-divided such that the top and bottom edges of each sub-section are horizontal.

The representation of an isolated arbitrary sub-section i is shown in Fig. 2c. The vertices of each sub-section are numbered from the bottom-left vertex clockwise to the bottom-right vertex, as shown in Fig. 2c. Individual sub- sections are numbered sequentially from the top of the wall to the bottom of the wall. This representation allows for the handling of virtually any shape of wall.

In some cases such as in sloping walls (Fig. 3a) the top and bottom sub-sections may consist of trilaterals as shown in Fig. 3b. The same data representation for a quadrilateral sub-section can be used for a trilateral one. The difference is that either the top vertices numbered 2 and 3 are coincident or the bottom vertices 1 and 4 are coincident. This is shown in Fig. 3c. The use of four

a Complex shaped wall cross-section b Wall sub-~cticets

Top Edge

I..dtEd~ f See i 3 ~ 4

vt, Bect~n Ed~

Paght ~

Vi,4

c Description of an isolated sub-soetion i

Fig. 2. Graphical representation of a wall shaped structure.

226 J. H. M. Tah and A. D. F. Price

a Sloping Wal l b Sloping Wall sub-sections

VI, 2 = VI, 3 V3, 2 V3,3

Vl, l V l , 4 V3,1 = V3, 4

c Descript ion of sub-sections I and 3

Fig. 3. Graphical representation of a sloping wall.

[ WALL ]

r--2 r-2:-i

Fig. 4. A hierarchical tree representation of complex shaped wall model

vertices, with two coincident, in a trilateral sub-section allows the data model for a quadrilateral to be used.

Figure 4 shows a hierarchical tree representation of a wall shaped structure data model. It shows that a wall consists of 1 to N sections, Each sub-section has four vertices numbered 1 to 4 and each vertex is described by its X and Y Cartesian co-ordinates. The actual data representation of the model is shown in Table 1.

In addition to the geometric data for describing the shape of the structure, general data about the concrete pour are required as follows: the concrete temperature at placing, weight density of concrete, rate of concrete placement, the shape and size of form coefficient C~, the constituent materials of concrete coefficient C2, the vertical form height, and the length of pour. These data and the geometric data model presented earlier can be used to produce the pressure envelope, which is discussed in the next section.

Table 1. Data model implementation for complex shaped walls

Vertices vertex 1 vertex 2 vertex 3 vertex4

Wall Sub-section No. No. X Y X Y X Y X Y

1 1 2

A;-1 N

Levds (i) 0 . . . . . . . . . . .

2 . . . . . . . . .

3 . . . . . . . .

4 . . . . . . .

5 . . . . . .

Fig. 5. Step 1 of the CIR1A Report 108 procedure.

6. I M P L E M E N T A T I O N O F T H E D A T A M O D E L

The CIRIA Report 108 [1] step-by-step procedure for the production of the pressure envelope is presented in Section 3. Each step is now described in detail along with the relevant aspects of the data model.

Step 1: Split the pour into horizontal levels with the vertical distance between each level 1 m or less.

The wall cross-section is drawn and then divided into a series of sub-sections at each change of slope as shown in Fig. 2b. Each sub-section is split into horizontal levels with the vertical distance between each level 1 m or less, as shown in Fig. 5

Step 2 : Calculate the plan area at each level The plan area at any level is computed by multiplying

the cross-sectional width at that level by the length of wall pour. The width at any level is computed by first calculating the slopes of the left and right edges of a wall sub-section. The slopes are then used to compute the co-ordinates of the points of intersection of the level concerned with the left and right edges. The difference between the X co-ordinates of these points give the width at that level. An isolated arbitrary sub-section i with a level j, as shown in Fig. 6, will be used to illustrate the general principles involved in the computations.

The ensuing computations lead to the derivation of the plan area at level j . The co-ordinates of the four vertices Vi.~, V~.2, V~.3 and V~.4 of the arbitrary sub-section i are given by (Xi.t, Y~.0, (Xi.~, Y~,2), (-tl,-.3, Y,.3) and (X~.4, Yi.4). The slope 2~ of the left edge line between vertices V~.t and V~.2 is given by

Yi .z- Yi, I L - (2)

X,.~ -X, . ,

and the slope ~b~ of the right edge line between vertices V~.3 and V~.4 is given by

'T

Levels

j-2 j - I d

j+l j÷2

Vi. l Vi. 4

-'-x

Fig. 6. Details of an isolated sub-section i.

Computer-based Modelling o f Concrete Pressures 227

~1 i = Y i , 3 - Y i , 4 (3) X i , 3 - X i , 4 "

The x co-ordinate X,,.j of point a~,j is therefore given by

d X.,.j = X,.2- ~ (4)

and that of point btj is

d X~,j = X,.~- ~--. (S)

The y co-ordinates of both at,j and bt.j are equal and are given by

Ya,j = Y% = Yt .2-d (6)

where d is the depth from the top of a sub-section to the level considered as shown in Fig. 6. Therefore, the width w,.j can be calculated as

wt,s = abs (X~,j- Xb,,) (7)

and the plan area At.s is given by

Aij = w,,jL. (8)

Hence the plan areas at each level can be calculated in a similar manner.

Step 3: Calculate the instantaneous rate of rise at each level

At levelj in the sub-section i the rate of rise is given by

Q Rtj = ~ (m/h). (9)

Step 4: Calculate the pressure at each level using the full height of the form, H, with either the equation or tables

In a computer implementation the equation is pref- erable. The maximum pressure at level j in sub-section i is therefore given by

P,,,.,,. = D [ C , ~ + C ~ K ~ H - C , ~ ] (kN/m 2)

(10a)

or

Pr.,~,,j = Dhij (kN/m 2)

whichever is the smaller

But if C 1 ~ > Hthen Pr,a~,.j = Dht,j (kN/m 2)

(lOb)

where h~j is the depth from the surface of the pour to level j in sub-section i. The maximum pressures for all levels can therefore be obtained.

Levels

: + 2 . . . . . . . . . . . . . . . . . . . .

Fig. 7. Pressure envelope construction on sub-section i.

The calculations of the points a~j and b~j on the pres- sure envelope (Fig. 7) are as follows : the angles 0, and q~, are calculated by

0, = tan- ~ (2,) and q~t = tan- i (~bt).

Also,

Axa =Pm ..... sin (Ot)F Axb = Pmax,,j sin (c~,)F

Aya = P~ax,j cos (Ot)F Ayb = emax,j COS (t4pt)F.

Therefore the co-ordinates of the point a~.j are given by

X~;., = Xa,.j-abs (AXa) (1 la)

Ya;.j = Y,,.j + abs (Aya) for 2, > 0

= Y,,., for At = 0

= Ya~.j-abs(Aya) for At < 0 (l ib)

and the co-ordinates of point b~,j are given by

Xb;j = Xb,.j + abs (AXb) (12a)

Yb;j = Yb,j-- abs (Ayb) for ~k, > 0

~- gb i J for I/] i ~---- 0

= Yb,j+abs (Ayb) for •t < 0. (12b)

All the points on the pressure envelope at each level can be calculated in the same manner and then plotted.

7. THE COMPUTER IMPLEMENTATION

The implementation of the data model described above has been coded into a computer program called Wal- Press. It runs alongside the ProCAD drafting package on a microcomputer. The ProCAD drafting package has a toolkit consisting of several routines that provide access to information in the drafting software database. These routines are programmed via the PASCAL programming language and interfaced with the drafting software. This method allows digitized entry of the co-ordinates of the wall cross-section and graphical display of the pressure envelope. The architecture of WalPress and a case study for a wall are presented in this section.

Step 5: Produce the design pressure envelope acting at right angles to the form

Having obtained the maximum pressures at each level as Pmax,., to Pmax~.~, these can be scaled down by a con- venient scaling factor F, and the pressure envelope plotted. The pressure at any level acts perpendicular to the sides of the wall pour. Consider the diagram of a

typical sub-section i shown in Fig. 7.

7.1 The architecture of WalPress The architecture of WalPress is shown in Fig. 8. To

run the program, the drafting software is used to create a geometric model of the wall cross-section. Then the design module facility on the drafting package is used to activate the pressure modelling program. It allows interactive entry of data about the concrete pour, and the form height. The co-ordinates of vertices of the wall

228 J. H. M. Tah and A. D. F. Price

Q ~ ~ e wall

Geomela'ic model

Design module interface )

I I +

Q

Fig. 8. The architecture of WalPress.

or column sub-sections are then digitized by means of a mouse. The user then enters the vertical distance, 1 m or less, required between each level. The creation of levels is done automatically and the concrete pressure at each level is then calculated. Values of pressures for the pres- sure envelope are processed automatically by a post- processor routine based on equations (11) and (12). The pressure envelope is also plotted automatically on the monitor. The results of the calculations can be obtained via various options. The results can be displayed on the monitor in tabular text form, saved to a disc file, printed or plotted. The pressure envelope plot-can be saved in the drafting software database for later retrieval.

7.2 A case study Consider the wall cross-section shown in Fig. 9a. The

specified design criteria are as follows :

the concrete is OPC normal-weight concrete with a retarder ;

the concrete temperature at placing is 10°C ; the volume supply rate is 22 m3/h ; the length of wall pour is 6 m.

The wall cross-section in Fig. 9 was drawn and sub- divided into sub-sections using the CAD software pack- age. Poinls consisting of very small circles were placed at the four vertices of each sub-section as shown in Fig. 9a. The pressure modelling program, WalPress, was then started. The specified design criteria data were entered. Then the co,ordinates of the four vertices of each sub- section were retrieved from the CAD software database by pointing to each vertex with a mouse. The calculations and the pressure ettvelope plot were then performed auto- matically. The output from the computer system is shown

in Figs 9b and 9c. The drawing of the section, the data entry, the analysis and presentations of results was done in a matter of a few minutes not hours.

All dimensions in metres.

o

1.0 0.5 1

2.0 I

Fig. 9a. Wall cross-section.

0.000 ~ 12.500 ,,. ...., 25. 000

37.500

62. 500 73. 445 72.843 72. 269 72. 269

........ 70.214 68.474

~ec2 V ' J~ 56.975 65.566

~ e s s u r e in kN/fl~.

Fig. 9b. The pressure envelope.

WALL POUR DETAI~ ********************

1. C, on~etetempefatmeatplacing : 10.00 Deg:C. 2. Weightden#ityofcon~ = 25,00 kN/m3 3. Rate~f~plyotcon~,ete = 22.00 m3,%" . Formworkfize&shapec~ff,,Ci = 1.00 . Concr~.te mn:fi~ coeff.. ~ 0.30

6. Vefdcal foam height = 6.250 m 7. Veftk:al pour height = 6.000 m 8. I..engthofwallpour : 6.000 m

PRESSURE DISTRIBUTION ON WALL *********************************

Fluid Max. Actual Depth pres,sure Width An:a Ra~ pressure pressure (m) (kN/m2) (m) (m2) (m/kr) (kNhn2) (kN/m2)

0.00 0.00 1.00 6.00 3.67 77,81 0.00 0.50 12.50 1.04 6.25 3.52 76.98 12.50 1.(30 25.00 1.08 6.50 3.38 76.19 25.00 1.50 37.50 1.13 6.75 3.26 75,45 37.50 2.00 50.00 1.17 7.00 3.14 74.75 50.00 2.50 62.50 1.21 7.25 3.03 74.08 62.50 3.00 75.00 1.25 7.50 2,93 73.45 73.45 3.50 87,50 1.29 7.75 2.84 72.84 72.84 4.00 100.00 1.33 8.00 2.75 72.27 72.27 4.00 I00,00 1.33 8.00 2.75 72.27 72.27 4.50 112,50 1.50 9.00 2.44 70.21 70,21 5.00 125.00 1,67 10.00 2.20 68.47 68.47 5.50 137.50 1.83 11.00 2.00 66,97 66.97 6.00 150.00 2.00 12.00 1.83 65.67 65.67

Max. pressure = 73.45 kN/m 2 at 3.00 rn depth

Fig. 9c. The tabulated output of the wall concrete pressure analysis.

Computer-based Modelling of Concrete Pressures 229

8. CONCLUSIONS

There are several methods used for determining the concrete pressures against vertical formwork. The method published in CIRIA Report 108 [1] is currently being used in the U.K. Site investigations are required to quantify the concrete pressures on inclined formwork [7]. Unless the findings of these investigations prove other- wise, the procedure given in CIRIA Report 108 will con- tinue to be used for computing pressures on inclined formwork. Where complex shaped walls and columns are encountered, the computation becomes very repetitive and tedious and is therefore suitable for computer implementation.

In this paper a complex shaped wall cross-section has been represented geometrically by a series of quadri- lateral sub-sections or elements, lying on top of each other. Therefore, each sub-section can be uniquely ident- ified by the co-ordinates of its four vertices. Sub-sections are defined such that the top and bottom edges are hori- zontal. This data model covers a wide range of walls encountered in practice. It is applicable to simple parallel sided walls and complex shaped walls. For walls with curved edges, the curve can be approximated by a series of straight lines and the same data model applied.

The computer implementations should result in con- siderable savings in design time and improve accuracy hence costs. Also, the effects of changes in design or changes in specified design criteria could easily be inves- tigated. The advantages of interfacing the modelling pro- gram to a CAD software package include a good user interface by eliminating the need for pre-calculation of co-ordinate information for alternative input modes, improved productivity, good presentation and storage of the final results. The data model and its algorithmic implementation should prove to be a useful design tool, particularly for the temporary works designer interested in the use of computers for formwork design. Dem- onstrations given to expert temporary works designers were in favour of the system and confirmed the need for such a tool. WalPress is part of FICADS [8], a comprehensive Formwork Integrated Computer-Aided Design System, developed by the authors.

Acknowledgements---The authors express their thanks to Mabey Hire Company Ltd. and Rapid Metal Developments Ltd. for their most useful comments and constructive criticisms during the development of WalPress. This research was supported by a Cameroon Government BS grant.

REFERENCES

1. CIRIA, Concrete pressure on formwork. CIRIA Report 108, Construction Industry Research and Information Association, London (1985).

2. ACI Committee 347 (formerly ACI Committee 622), Pressure on formwork. J. Am. Concrete Ins. 55, 173-190 (1958).

3. DIN 18218, Frischbeton auf Lotrechie (Pressure of concrete on vertical formwork). Berlin, 1980. 4. N.J. Gardiner, Concrete pressure on formwork. Proc. Inst. Civil Engineers Part 1, 80, 145-159 (1986). 5. CIRIA. Concrete pressure : data sheet. Construction Industry Research and Information Association,

London (1985). 6. T.A. Harrison, Pressure on vertical formwork when concrete is placed in wide sections. Research

Report No. 22, 1-30. Cement and Concrete Association, London (1983). 7. Concrete Society, Formwork : a guide to good practice. Joint Committee of the Concrete Society and

the Institution of Structural Engineers, Concrete Society, London (1986), 84-85. 8. J . H . M . Tah, Integrated microcomputer applications in formwork design. Ph.D. Thesis, Lough-

borough University of Technology (1989).