Hurd Revised Formwork Formulas

l P f Fwk Dg A viw of th fomlas to tmi th pss of fsh coct

By M.K. Hurd

resh concrete exerts pressure on vertical form surfaces, and an assessment of that pressure is needed for designing forms. In the simplest theory, fresh concrete acts as a fluid exerting pressure equally in all directions at whatever point the measurement is made—essentially assuming a hydrostatic pressure effect. This is reasonable because the fresh concrete behaves much like a fluid at least briefly during vibration, or for a longer time if flowability of the mixture has been enhanced through use of admixtures or special proportioning proportioning and materials selection. But concrete is not a true fluid, and some method of evaluating the concrete’s actual pressure is needed. Evaluating pressure has been a significant part of the work of ACI Committee 347, Formwork for Concrete. As early as 1958, Committee 347 (then Committee 622) studied available field measurements of lateral pressure on formwork and used the data to develop pressure formulas that could be safely used for form design. A report was published in 1958, 1 and the formulas, with some modifications, were included in ACI’s first formwork

F 

standard, ACI 347-63.2 In the days before the advent of the personal computer, the committee considered it important to keep the equations simple, reasoning that this would encourage their use and minimize mathematical errors. These formulas were carried forward through successive ACI standards until 2001, when accumulating data 3 on lateral pressures enabled the committee to introduce new coefficients for unit weight and chemistry of the mixture, expanding coverage of the formulas to mixtures with cement replacements, admixtures, or both. I wrote about those changes for CI  readers in October 2002. 4 Further modifications modifications were issued in ACI 347-04, 5 however, and clarification of the present status may be needed. To avoid possible confusion, the formulas presented here are given the same identifying numbers as in ACI 347-04. BasiC Formula  Although the pressure at any given point within the form varies over time, the designer usually doesn’t need Cc 

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Table 1: Unit  weight  coefficient  C 

w 

Used in form pressUre eqUations

Unit wight (dnsity) of concrt Lss tha 140 lb/ft 3 (2240 kg/m3 )

C w (in.- vrsion) C w

C w (SI vrsion)

= 0.5[1 + ( w/145)] bt ot lss tha 0.80

140 to 150 lb/ft3 (2240 to 2400 kg/m3) Mo tha 150 lb/ft3 (2400 kg/m3 )

C w = 0.5[1 + ( w/2320)] bt ot lss tha 0.80

1.0 C w

1.0

= w/145

C w

= w/2320

Note: w = unit weight (density) of concrete, in lb/ft 3 (kg/m3 )

Table 2: chemistry coefficient  C 

C 

Used in form pressUre eqUations

Cmnt typ or nd

C c

Tps I, II, a III cmts withot tas* Tps I, II, a III cmts with a ta

1.0 1.2

Oth tps o bls cotaiig lss tha 70% slag o 40% fl ash withot tas*

1.2

Oth tps o bls cotaiig lss tha 70% slag o 40% fl ash with a ta*

1.4

Bls cotaiig mo tha 70% slag o 40% fl ash

1.4

*Retarders include any admixture, such as a retarder, retarding water-reducer, retarding mid-range water-reducing admixture, or high-range water-reducing admixture, that delays setting of concrete

Hvy-duty st formwork rsists concrt prssur in  16 ft (5 m) high rtining w. Custom form ssmy prmittd th contrctor to pc th w nd projcting cors monoithicy  (PhotocourtesyofEFCOCorp.)

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to know the variation in detail. Hence, the equations for lateral formwork pressure provide only the maximum to be used for design. The basic formula is: p = wh

(2.1a), in.-lb units

p = ρ gh

(2.1b), SI units

For the equation in in.-lb units,  p is the lateral pressure, in lb/ft2;w is unit weight of the fresh concrete, in lb/ft 3; and his the depth in feet of fluid or plastic concrete from the top of a placement to the point under consideration in the form. For the equation in SI units,  p is the lateral pressure, in kPa; ρ is the concrete density, in kg/m 3;  g  is the gravitational constant of 9.81 N/kg; and his the depth of fluid or plastic concrete in meters from the top of a placement to the point under consideration in the form. If a form is filled rapidly before any stiffening of the concrete takes place, h should be taken as the full height of the freshly placed concrete. If multiple placements are to be made, h should be taken as the distance between construction joints. This formula is applicable for all conditions other than those specifically defined for the use of Eq. (2.2), (2.3), and (2.4). Column Form Pressure For the purpose of pressure determination, Committee 347 defines columns as elements with no plan dimension exceeding 6.5 ft (2 m). For concrete with a slump of 7 in. (175 mm) or less and placed in column forms with normal internal vibration to a depth of 4 ft (1.2 m) or less, ACI 347-04 recommends the following equation for calculating the maximum pressure  pmax  in lb/ft2 (kPa) to be used for column form design:  pmax = C w C c

[150 + 9000 R T ]

(2.2), in.-lb units

 

 p max = C w C c 7.2 +

 T  + 17.8  785 R

(2.2), SI units

with a minimum of 600 C w lb/ft2 (30C w kPa), but in no case greater than Eq. (2.1). C w and C c are the unit weight and chemistry coefficients shown in Tables 1 and 2, respectively;  R is the rate of placement, in ft/h (m/h); and T  is the temperature of the concrete during placement, in °F (°C). With rapid placement and intensive vibration or with self-consolidating concrete, it is possible to have concrete remaining in a fluid condition for the full duration of the placement, in which case the only theoretical pressure limit will be as in Eq. (2.1). Committee 347 didn’t have sufficient test data to develop separate provisions for self-consolidating concrete. A number of studies have been or are being conducted—for example, Reference 6— but definitive results have yet to be found. Wall Form Pressure For purposes of pressure determination, ACI 347-04 defines a wall as a vertical structural element with at least one plan dimension greater than 6.5 ft (2 m). ACI 347-04 gives two equations for wall form pressure. As in the case of the column formula, both are applicable to concrete with a slump of 7 in. (175 mm) or less and vibration to a depth of 4 ft (1.2 m) or less. The first, Eq. (2.3), applies to walls with a rate of placement less than 7 ft/h (2.1 m/h) and a placement height of 14 ft (4.2 m) or less:  p max = C w C c [150 + 9000 R T ]

 

 p max = C w C c 7.2 +

 T  + 17.8  785 R

(2.3), in.-lb units (2.3), SI units

 aDDitional inFormation For examples showing how to apply these formulas, refer to the 7th Edition of ACI SP-4,  FormworkforConcrete.7 Lateral pressure calculations are also presented in the interactive spreadsheet program made available to ACI by William C. Epstein, formerly a Professor of Construction Management at California State Polytechnic University, San Luis Obispo, CA. To use the spreadsheets, visit the Concrete Knowledge Center at www.concrete.org , click on the “Construction” button, and click on the “Form Design Spreadsheet” button. Then go down to the bottom of the page and select “Walls.” rfc 1. ACI Committee 622, “Pressures on Formwork,” ACI J OURNAL,  Proceedings V. 55, Aug. 1958, pp. 173-190. 2. ACI Committee 347, “ACI Standard Recommended Practice for Concrete Formwork (ACI 347-63),” American Concrete Institute, Farmington Hills, MI, 1963, 52 pp. 3. Barnes, J.M., and Johnston, D.W., “Modification Factors for Improved Prediction of Fresh Concrete Lateral Pressures on Formwork,” Institute of Construction, Department of Civil Engineering, North Carolina State University, Raleigh, NC, Oct. 1999, 90 pp. 4. Hurd, M.K., “Putting the Pressure on Formwork,” Concrete  International , V. 24, No. 10, Oct. 2002, pp. 49-55. 5. ACI Committee 347, “Guide to Formwork for Concrete (ACI 347-04),” American Concrete Institute, Farmington Hills, MI, 2004, 32 pp. 6. Billberg, P.; Silfwerbrand, J.; and Österberg, T., “Form Pressures Generated by Self-Consolidating Concrete,” ConcreteInternational , V. 27, No. 10, Oct. 2005, pp. 35-42. 7. Hurd, M.K.,  FormworkforConcrete (SP-4), 7th Edition, American Concrete Institute, Farmington Hills, MI, 2005, 516 pp. Selected for reader interest by the editors.

The second equation, Eq. (2.4), applies to all walls with a placement rate of 7 to 15 ft/h (2.1 to 4.5 m/h), and to walls placed at less than 7 ft/h (2.2 m/h), but having a placement height greater than 14 ft (4.2 m).  p max = C w C c [150 + 43,400 T  + 2800 R T ]

 

 p max = C w C c 7.2 +

1156

T  + 17.8

+

 T  + 17.8  244 R

(2.4), in.-lb units (2.4), SI units

For both Eq. (2.3) and (2.4),  pmax  should be a minimum of 600C w lb/ft2 (30C w kPa), but not greater than Eq. (2.1). Because Committee 347 has insufficient data on observed pressure at higher rates, Eq. (2.4) does not apply for rates of placement greater than 15 ft/h (4.5 m/h).

ACI Hooa Mmb M.K. Hurd is a mmb of ACI Committs 124, Coct Asthtics, a 347, Fomwok fo Coct. Sh has civ mos awas fo h  svic a cotibtios to ACI, iclig th ACI Costctio Awa (1982 a 1988), th dlma L. Blom Awa fo distigish Svic (1990 a 2006), a th H C. T Mal (1995). Th atho of sv itios of ACI SP-4, Formwork for Concrete , H is th fist fmal cipit of th Masto Mal, th highst awa bstow b th Collg of egiig at Iowa Stat uivsit. Cc 

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