Aug 1, 1995 - width), their lumber species, and their lumber grades. Ties are defined by their .... Figure 4 presents a schematic diagram for the multi- step computational ..... Meril/MacMillan,. Columbus, OH ... McGraw-Hill,. New York, 1989.
Buildmg and Enorronment, CopyrIght % 1996 Elsevier
Pergamon
Vol. 32, No. 1, pp. 57-67, 1997 Science Ltd All nghrs reserved Printed III Great Britam 036&1323/97 $17.00+0.00
PII: SO360-1323(96)00037-6
Material Cost Minimization Wall Forms AWAD S. HANNA* AHMED B. SENOUCI*
of Concrete
(Received 1 August 1995; accepted 17 April 1996)
An automated procedure for minimizing the material cost for all-wood concrete wall forms is presented. This procedure was formulated to provide for a safe wall form design with minimum cost. The performance of the optimum design method is compared to that of the traditional design method, which uses design charts/tables. The automated method was found to have potential cost savings over the traditional design method. A study was conducted to con$rm these cost savings. Copyright 0 1996 Elsevier Science Ltd.
INTRODUCTION
sheathing, a number of studs spaced at a distance Sl, a number of wales spaced at a distance S2, and finally a number of ties spaced at a distance S3. Sheathings are defined by two parameters: thickness and type. The type refers to the design values of the sheathing such as modulus of elasticity and bending and rolling shear strength. Studs and wales are defined by their sizes (thickness and width), their lumber species, and their lumber grades. Ties are defined by their load capacity. The traditional design method refers to the design method used in the development of the design tables [2]. The objective of the traditional design method is to determine the spacings Sl, S2, and S3 so that each wall form component (sheathing, stud, wale, and ties) has adequate strength to resist the applied pressure and sufficient stiffness to maintain an allowable deflection. In the analysis of the wall form components the traditional stress equations are used [4]. Figure 3 summarizes the design process of the traditional method. A FORTRAN program has been written to automate this design process and to compute the total minimum cost of the designed wall forms.
FORMWORK consists of temporary structures whose purpose is to provide support and containment for fresh concrete until it can support itself. Concrete forms are engineered structures that are required to support loads composed of the fresh concrete, construction materials, equipment, workers, impacts of various kinds, and sometimes wind. The forms must support all the applied loads without collapse or excessive deflection. AC1 Committee Report 347 [l] defines those applied loads and gives a number of guidelines for safety and serviceability. Based on these guidelines, a number of design tables have been developed for the design of concrete formwork [2]. These tables are very useful design tools. However, they do not guarantee a design of minimum material cost. Formwork costs are significant, generally amounting to anywhere between 40 and 60% of the cost of a concrete structure [3]. Figure 1 shows a typical cost breakdown for a one foot wide strip of concrete wall. Formwork material cost is an important cost item, representing about 11% of the total formwork cost [3]. A reduction in the cost of the formwork material can produce a real cost saving, thus emphasizing the importance of formwork design optimization. A reduction in the material costs may also lead to a reduction in labor costs, which account for 52% of the total cost. Formwork design optimization produces not only safe and reliable designs but also economical ones. To date, design optimization of concrete forms has not been addressed in the literature. This paper presents a design optimization procedure for all-wood concrete wall forms. This procedure was formulated to provide for a safe and reliable wall form design whose cost is minimum. TRADITIONAL
OPTIMUM Design loads
Formwork must be designed to resist the lateral pressure of concrete. The maximum lateral pressure has been found to be a function of concrete type, rate of vertical placement, form height and temperature. The American Concrete Institute (ACI) suggests the following formulas for the lateral pressure computations on wall formwork
PI. (1) For vertical rate of placement
WALL FORM DESIGN
of 7 ft/hr or less
p = 150+9000R/T
Figure 2 shows a typical structural system for all-wood wall forms. All-wood wall forms are composed of a
*University of Wisconsin, 460 Henry Mall, Madison,
DESIGN METHOD
(1)
with a maximum of 2000 lb/f? or (150*/r), whichever less. (2) For vertical rate of placement of 7-10 ft/hr
is
p = 150+43,400/T+2800R/T
(2)
WI
53706, U.S.A. 57
A. S. Hunna and A. B. Senouci
58
Concrete Material 32%
Formwork Labor 56%
Fig. I. Typical cost breakdown for a I ft wide strip of concrete wall.
with a maximum of 2000 lb/f? or (150*/z), whichever is less. (3) For vertical rate of placement greater than 10 ft/hr p = 150*h,
(3)
with p = lateral pressure in lb/f? R = rate of vertical placement of concrete T = temperature (“F) 11 = height of the form. When the forms are vibrated from the outside, these loads must be doubled, and when concrete is pumped from the bottom of the form, equation (3) must be used. Straining
uctions
After design loads are selected, straining actions are calculated using the conventional equations of structural mechanics for three or more equally spaced spans carrying equal uniformly distributed load [2]. (4) with IV = M = V = A = I =
uniform load of foot per span (lb/ft) maximum bending moment (lb-ft) shearing force (lb) deflection (in.) length of span (ft) E = modulus of elasticity (psi) I = moment of inertia (in”). Optimum
design method
The optimum ditional method.
design method, as opposed to the traconsiders the form component costs as
variables in the design process, Assume that Ml sheathings (different in type and/or thickness), M2 studs (different in size, lumber species, and/or lumber grade), M3 wales, and M4 ties are available to the designer to choose from to design a specific concrete wall form. The objective of the design optimization procedure is to choose a specific sheathing SHi (SHi = l,...,MI), a specific stud STi (STi = l,...,M2) with its spacing Sl, a specific wale WLi ( WLi = l,....M2) with its spacing S2, and a specific tie TEI‘ (TEI’= l,...,M4) and use them as the program input so as to minimize the following wall form cost function: Cost = C(SHi) + C(STi) + C( WLi) + C( TEi),
(5)
where Cost is the total material cost, C(SHi) is cost of the total area of sheathing, C(STz’)is cost of all the studs, C( WLi) is cost of all the wales, and C( TEi) is cost of all the ties. In the minimization of the cost function [equation (5)], each selected form component (sheathing SHi, stud STi, wale WLi, and tie TEi) must have adequate strength to resist failure in bending, compression. tension, or shear due to the loads applied to it and must have sufficient stiffness so that its deflection does not exceed the allowable. Figure 4 presents a schematic diagram for the multistep computational algorithm. The computational steps can be summarized as follows. The input data is read in first. The input data consists of information about wall dimensions, concrete lateral pressure, allowable deflection limits, sheathings, studs, wales, and ties, Wall dimensions represent the length, width, and height ofthe wall form. The lateral pressure exerted on wall forms depends upon the weight of the
Material Cost Minimization of Concrete Wall Forms
59
Shrthina Tic
Settion A-A lb)
Fig. 2. Typical structure for all-wood wall forms [3].
concrete, temperature of the concrete, vertical rate of placement, height of the form, and method of consolidation (hand spaded or mechanically vibrated). AC1 347-88 [l] establishes the lateral pressure exerted on walls forms by fresh concrete. Two deflection parameters are used to control the deflection of sheathings, studs, and wales. The first parameter is expressed as a fraction of the span length (e.g. I /360). The second parameter is independent of the span length and represents the maximum allowable deflection (e.g.
0.25 in.). Sheathing
input data consists of: (1) the number of different sheathings (different in thickness or type); (2) the cost per square foot of each sheathing; and (3) the dimensions, the unit weight, the allowable bending stress, the allowable shear stress, and the modulus of elasticity of each sheathing. Stud/wale input data consists of: (1) the number of different studs/wales available; (2) the cost per linear foot of each stud/wale; and (3) the dimensions, the unit weight, the allowable bending stress, the allowable
60
A. S. Hanna and A. B. Senouci PROGRAM
I 1Read inuut data
1
t Compute
allowable
span Sl
Compute
+ allowable
span S2
#
Check bearing of stud STi on Wale WLi +j
S2=S2-DS
N
1
Compute allowable span S3 1 Check bearing of tie TEi on Wale WLi t+
1
Print Sl. S2. and S3
ri
S3 = S3 - DS
1
End
Fig. 3. Algorithm
2.
3.
4.
5.
6.
of traditional
design method.
compressive stress perpendicular to grain, the allowable shear stress, and the modulus of elasticity of each stud/wale. Tie input data consists of: (1) the number of different ties available; (2) the cost of each tie; and (3) the dimension and the load capacity of each tie. The first sheathing (SH1’ = 1) is selected and its allowable span Sl is determined. The first stud (STi = 1) is selected and its allowable span S2 is determined. The first stud (STi = 1) is selected by the user as input, and its allowable span S2 is determined as an output from the program. The first wale (WLI = 1) is selected. The bearing at the point where each stud rests on the wales is first checked. Then, the wale allowable span S3 is determined. The first tie (TEi = 1) is selected. The bearing at the point where each tie end bears on the wales is first checked. Then, the capacity of the tie is checked. If all of the constraints are satisfied, the total cost of the wall form is computed. To compute the total cost, the total costs of sheathing, studs, wales, and ties are added together. If the total cost is less than previously computed costs, this computed cost as well as the combination SHi, STi, WLi, and TEi with their respective spacings Sl, S2, and S3 are stored in the computer’s memory. Steps 2 through 6 are repeated for each available tie TEi, for each span S3, for each available wale WLi, for each span S2, for each available stud STi, for each span Sl, and for each available sheathing. At the end of the computation process, the minimum total cost, SHi, STi, WLi, TEi, Sl, S2, and S3 are printed.
DESCRIPTION
The program OPTWALL has been developed for the design optimization of wall forms. OPTWALL is a userfriendly system which allows the user to enter the required input data, perform the design optimization, and view the optimum design. Figure 5 shows the main menu screen of OPTWALL. The first option in the main menu screen allows the user to select the input data file. The second option allows the user to access the input data menu (Fig. 6). Several pop-up input screens, which are accessed through the input data menu, are used for inputting the general data as well as the data for the studs, wales, and shores. Figure 7 shows the general data input screen. The screen is self-explanatory; the user does not have to refer to a user’s manual to enter the required data. Figure 8 shows the spreadsheet-like input screen for the sheathing data. Figures 9-11 show the spreadsheet-like input screens for the stud, wale, and shore data, respectively. The top input screen is for inputting the section properties while the bottom one is for the mechanical properties. The home key is used to toggle between the two input screens. Besides the regular keyboard key functions (up, down, left, right, and return function keys), three additional key functions are also available: delete a line, duplicate a line, and insert a line. A database for section properties and a database for mechanical properties of standard lumber were created so that the user does not have to enter the section and mechanical properties of the studs, wales, and shores. Using the standard dimension and lumber grade and specie input by the user, the program will search the two databases for the section and mechanical properties of the specific stud, wale, or shore and display them The third option in the main menu screen allows the user to perform the wall design optimization. The fourth option allows the user to look at the output of the design optimization without leaving the system. This option is convenient for the user since it allows himiher to check for possible errors in the input data without leaving the system.
OPTIMUM
DESIGN
METHOD
COST SAVINGS
The traditional design method produces safe, reliable and occasionally optimum wail formwork designs. However, the optimum design method guarantees a minimum wall formwork material cost while the traditional design method does not. Thus, the optimum design method offers a potential cost saving over the traditional design method. The potential cost savings are due to the fact that the optimum design method includes the cost of the different wall formwork components whereas the traditional method does not. The total cost of the wall formwork material depends on the unit cost of its components (sheathing, studs, wales, ties) as well as their spacings. All of these variables (unit costs and spacings of wall form components) are considered together in order to obtain the minimum wall form material cost. The use of the maximum allowable spacings, which are based on strength and deflection limits, might not yield a minimum total cost. For example, it might happen that because of the unit costs of the wall formwork components, increasing the number of studs (spacings
Material
Cost Minimization
of Concrete
61
Wall Forms
I
select fust stud (STkl)
I
C
I
I checkbeaingofshxiSTionWdeWLi
I
compute allowable span S3 I
r
check strength of tie TEi
I N
corncute wall form cost
StoreCost, SHi, STi, Wi, TEi. Sl, S2, and S3
I
Fig. 4. Algorithm
of optimum
design method
62
A. S. Hunna und A. B. Smoucz
Fig. 5. Main menu screen
Fig. 6. Input data menu screen
between studs smaller than the maximum allowable) and decreasing the number of wales (spacing between wales equal to the maximum allowable) might yield a smaller wall form cost than if the allowable spacings were used. A study was conducted to confirm the savings potential of the minimum design method over the traditional design method and to give an order of magnitude of these cost savings. The study was divided into four steps. In the first step, two sheathings, five studs, five wales, and two ties were selected. The input data of sheathings, studs, wales, and ties is summarized, respectively, in Tables 14. The unit costs of the different sheathings, studs, and wales were taken from [5]. The unit costs of the ties were provided by a local supplier. It should be noted that costs data are user input because they are a
function of geographic location and time. The information about the deflection limits of the wall form components is summarized in Table 5. In the second step, a number of concrete walls (different wall height and/or length) were selected. Wall heights considered in this study were: 8, 12. 16. and 20 ft. Wall lengths considered were: 300. 400, 500, and 600ft. The thickness of the concrete wall was taken equal to gin. The number of potential reuses of the formwork was taken equal to 10. The expected formwork material wastage for each reuse was taken equal to 10%. The concrete vertical rate of placement was taken equal to 6ft!hr and the concrete temperature was taken equal to 90 F. The unit weight of concrete was estimated at 150 pcf with a 3-m. slump value.
Material
Cost Minimization
Fig. 7. General
Fig. 8. Sheathing
In the third step, the forms of each concrete wall (different height/length) were designed and their total cost was computed using the two FORTRAN programs (traditional and optimum design programs). Tables 6 and 7 summarize, for each concrete wall, the optimum and traditional wall form designs, respectively. Figure 12 summarizes the cost savings, as a percentage of the traditional design cost, for each concrete wall. The percentage of the cost savings varies from 0.8 to 3.5%. Based on 10 potential reuses and 10% material waste in each reuse, the formwork material cost saving varies between $181 and $974. In the last step, another source of cost savings was investigated. The cost savings of the optimum design method may be higher when the traditional design of the wall form is performed using the design tables instead of
of Concrete
Wall Forms
63
data input screen.
input data screens.
a computer program. When a design aid is used, a limited number of wall form combinations are considered; performing the design using all available combinations of wall form components would require substantial time and effort. Usually, a few combinations are selected with the intention that at least one of them would yield the minimum design cost. Because of the large number of variables influencing the total cost, it is seldom easy to immediately choose the optimum combination of wall formwork components. In this study, an experiment was conducted to confirm these suppositions. Three combinations were selected in this experiment (Table 8). Figure 13 summarizes the cost savings of the optimum design method as a percentage of the cost of the traditional wall form design when only the first combination is considered. The cost saving percentages vary from 27 to
64
A. S. Hunna and A. B. Senouci
Fig. 9. Stud input data screens
Fig. 10. Wale input data screens.
33%. Based on 10 potential reuses and 10% material waste in each reuse, the formwork cost savings for the selected walls (different height and/or length) vary from $3272 to $12 406. Figure 14 summarizes the cost savings as a percentage of the cost of the traditional wall form design when only the second combination is considered. The cost saving percentages vary from 10 to 14%, and the formwork cost savings for the selected walls (different height and/or length) vary from $1420 to $6307. Finally, Fig. 15 summarizes the cost savings as a percentage of the cost of the traditional wall form design when only the third combination is considered. The cost saving percentages vary from 38 to 43%. and the formwork cost
savings for the selected walls (different length) vary from $4191 to $17462.
height
and/or
CONCLUSION A computerized method for the optimum design of concrete wall formwork was developed and its performance compared to that of the traditional design method. From the numerical experiments performed, it can be concluded that substantial cost savings in wall formwork material can be achieved by using the optimum
Material Cost Minimization of Concrete Wall Forms
11.Tie input data menu.
Fig.
Table
1. Sheathing
No.
Thickness (in.)
Moment of inertia (in4/ft)
Rolling shear constant (in*/ft)
1 2
0.625 0.750
0.131 0.199
6.526 8.299
Values are adapted
65
input data
Modulus
of elasticity (psi)
Allowable bending stress (psi)
Allowable shear stress (psi)
Unit cost (%iftz)
102 72
0.450 0.850
Allowable shear stress (psi)
Unit cost (Sift)
1400 1450 1150 1930
90 95 75 72
0.327 0.347 0.327 0.850
Allowable bending stress (psi)
Allowable shear stress (psi)
Unit cost (Sift)
75 75
0.653 0.773
1650 000 1500 000
1930 1930
from [6].
Table 2. Stud input data No. Dimensions (in.*in.) 1 2 3 4
Moment
2*4 2*4 2*4 2*6
of inertia (in”)
Section area (in’)
Section modulus (in’)
5.25 5.25 5.25 8.25
3.06 3.06 3.06 7.56
5.36 5.36 5.36 20.80
Values are adapted
Modulus of elasticity (psi) 1600 1700 1400 1500
Allowable bending stress (psi)
000 000 000 000
from [6].
Table 3. Wale input data No. Dimensions (in.*in.) I
2
Moment
2*8 2*10
of inertia (in”)
Section area (in*)
Section modulus (in’)
Modulus of elasticity (psi)
10.88 13.88
13.14 21.93
1400 000 1400000
47.63 98.93
Values are adapted
from [6]
Table 4. Tie input data
No. 1 2
Wedge dimensions (in.*in.) 1.5*1.5 1.5*1.5
Values are adapted
1150 1150
Load capacity
2250 3350 from [6].
Table 5. Wall form deflection (psi)
Unit cost (S/R) 0.47 0.61
Wall form components Sheathings Studs Wales Values are adapted
from [6].
limits
First limit
Second limit
L/360 L/360 L/360
Not used Not used Not used
66
A. S. Hanna and A. B. Senouci
Table 6. Optimum Wall length (ft)
Wall height (ft)
300 300 300 300 400 400 400 400 500 500 500 500 600 600 600 600
8
1
12 16 20 8 12 16 20 8 12 16 20 8 12 16 20
I
Sheathing number
1 1 1 1 1
I 1 1 1 1
I I I 1
Stud number
Wale number
4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
1
1 1
I I 1 1
I 1
I I 1 1 I 1 1
Table 7. Traditional Wall length (ft)
Wall height (ft)
300 300 300 300 400 400 400 400 500 500 500 500 600 600 600 600
12 16 20 8 12 16 20 8 12 16 20 8 12 16 20
8
Sheathing number 1 1 1 I 1 1 1 1 1
I 1 1 I I 1 1
Stud number 1 4 4 4 I 4 4 4 1 4 4 4 1 4 4 4
design of each wall form
Tie number
1 1 1 1 1 1 1
I I 1 1 I I
I 1 1
Stud spacing (in.)
Wale spacing (in.)
9.7 9.7 9.7 9.7 9.7 9.7 9.7 9.7 9.7 9.7 9.7 9.7 9.7 9.7 9.7 9.7
24.6 24.6 24.6 24.6 24.6 24.6 24.6 24.6 24.6 24.6 24.6 24.6 24.6 24.6 24.6 24.6
Stud spacing (in.)
Wale spacing (in.)
Tie spacing (in.) 13.6 13.6 13.6 13.6 13.6 13.6 13.6 13.6 13.6 13.6 13.6 13.6 13.6 13.6 13.6 13.6
design of each wall form
Wale number I 1 1 1 1 1 I
I 1 1 1 1
I 1 1 1
Tie number 1 I I
I 1 1 1 1 1
I I 1 1 1 1
I
10.7 10.7 10.7 10.7 10.7 10.7 10.7 10.7 10.7 10.7 10.7 10.7 10.7 10.7 10.7 10.7
16.4 23.3 23.3 23.3 16.4 23.3 23.3 23.3 16.4 16.4 23.3 23.3 16.4 23.3 23.3 23.3
Tie spacing (in.) 20.6 14.4 14.4 14.4 20.6 14.4 14.4 14.4 20.6 20.6 14.4 14.4 20.6 14.4 14.4 14.4
Material
Cost Minimization
of Concrete
Wall Forms
67
Table 8. Selected wall form combinations Combination
number
Sheathing
1 2 3
number
Stud number
2 1 2
Wale number
Tie number
2 1 2
4 3 1
2 2 2
..”
0.5 I 12
0 8
I 16
I 12
20
Wall height (ft) Fig. 12. Average
Wall height (ft)
cost savings of concrete wall forms binations are considered).
I 12
10.01 8
(all com-
I 16
Fig. 13. Average
wall form design cost savings combination is considered).
Fig. 15. Average
wall form design cost savings combination is considered).
design
method,
the cost stud,
of each
wale,
and
wall formwork
Wall height (ft)
wall form design cost savings (only the second combination is considered).
which
considers
in its design
wall
formwork
component
tie) and
(2)all available
components.
Given
(only the first
20
Wall height (ft) Fig. 14. Average
I 16
process:
combinations
the current
(1)
(sheathing, high
of formwork a few percent
of
method
material, more
in the design
a potential than
justifies
(only the third
cost saving
as small
the use of the proposed
of wall forms.
cost
REFERENCES 1. ACI, Committee 347, Guide to formwork for concrete. American Concrete Institute, P.O. Box 1950, Redford Station, Detroit, MI 48219, 1988. 2. Hurd, M. K., Formwork for Concrete, SP-4,4th edn. American Concrete Institute, Detroit, MI, 1987. 3. PERI Handbook. PERI Formwork Systems, Baltimore, MD, 1993. G. F., Applied Statics and Strength of Materials. Meril/MacMillan, 4. Spiegel, L. and Limbrunner, Columbus, OH, 1991. Construction Weekly, 19 July 5. ENR, Quarterly cost report. Engineering News Record, The McGraw-Hill 1993. New York, 1989. 6. Peurifoy, R. L. and Oberlender, G. D., Estimating Construction Costs. McGraw-Hill,
as
