United States

Department of

Agriculture

Forest Service

Forest

Products

Laboratory

Research

Paper

FPL–RP–568

Jerrold E. Winandy

Patricia K. Lebow

William Nelson

Predicting Bending Strength 

of Fire-Retardant-Treated 

Plywood From ScrewWithdrawal Tests
Abstract

This report describes the development of a test method and

predictive model to estimate the residual bending strength of

fire-retardant-treated plywood roof sheathing from measurement of screw-withdrawal force. The preferred test methodology is described in detail. Models were developed to predict

loss in mean and lower prediction bounds for plywood bending strength as a function of a screw-withdrawal force. Our

analysis of fire-retardant-treated plywood from three different

studies, each with various fire-retardant-treatment, processing, plywood thickness, and exposure temperature groupings, clearly indicated that different fire-retardant-treatments

and plywood thicknesses could not be grouped into a single

“universal” model. Nevertheless, some grouping was possible; parameter estimates for several grouped fire-retardant

formulations and plywood thicknesses are reported for mean

trends and lower prediction boundaries. Although the models

were shown to acceptably predict plywood bending strength,

additional work is needed to expand these models to address

the effects of plywood quality, wood temperature, and moisture content at time of test.

Keywords: Fire-retardant, treatment, plywood, roof

sheathing, models, bending strength, screw-withdrawal force,

field evaluation, in-place evaluation

February 1998

Winandy, Jerrold E.; Lebow, Patricia K.; Nelson, William. 1998. Predicting

bending strength of fire-retardant-treated plywood from screw-withdrawal

tests. Res. Pap. FPL–RP–568. Madison, WI: U.S. Department of Agriculture, Forest Service, Forest Products Laboratory. 20 p.

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Research Highlights

In North America, fire-retardant- (FR-) treated plywood is

sometimes permitted as an alternative to noncombustible

materials in structures that require a high level of fire safety.

In the mid- to late 1980s, some commercial FR treatments

failed to perform adequately when used as roof-sheathing

plywood and roof-truss lumber. This problem was costly

because these roofs needed to be replaced. Since then, extensive research has defined the mechanism of thermal degradation, but field methods are still needed to evaluate the condition of FR-treated plywood in service and to estimate

residual service-life.

Our analysis of FR-treated plywood from three different

studies, each with various FR-treatment, processing, plywood thickness, and exposure temperature groupings, clearly

indicated that various FR treatments and plywood thicknesses could not be grouped into a single “universal” model.

Groups that could be combined were evaluated together.

The ensuing models had the form

 

R SE lower bound = ⋅ p y-t ˆ n- , - 2 1 α

where

 

yˆ = predicted mean plywood strength, 

ˆ ˆ b b 0 1 + (x)

1/2

x mean of multiple screw-withdrawal

measurements, avg xi

 

ˆ ˆ b b 0 1 + fitted parameters (Table 7)

SEp standard error of prediction,

SE · {1 + 1/n + [(x

1/2 − x )2

/SS]}1/2

SE Eq. (3) model estimate of error (Table 8)

 

tn- , - 2 1 α t-test statistic

n number of observations

 x observed mean of square root screw-withdrawal

measurements (Table 8)

SS mean-adjusted sums of squares, ∑(xj

1/2 − x )2

(Table 8)

Parameter estimates are given for several tested FR formulations and plywood thicknesses for the curvilinear lower

prediction boundary (Table 7). Parameter estimates for a less

preferred, but simpler-to-use, linear lower prediction boundary can be calculated using data given in Table 8. Both

lower prediction boundary model forms were found to predict

residual plywood bending strength acceptably for several FR

formulations and plywood thicknesses near the mean. However, the curvilinear form (Eq. (5)) is preferred because of its

more comprehensive nature when predicting values in the

extreme tails of the screw-withdrawal force distribution.

Additional work is needed to expand these models to address

the effects of plywood quality, wood temperature, and moisture content at time of test.
Predicting Bending Strength

of Fire-Retardant-Treated Plywood

From Screw-Withdrawal Tests

Jerrold E. Winandy, Research Wood Scientist

Patricia K. Lebow, Mathematical Statistician

William Nelson, Engineer

Forest Products Laboratory, Madison, Wisconsin

Introduction

Building officials and inspection professionals are frustrated

by the limited nondestructive evaluation (NDE) tools for

assessing the residual strength of thermally degraded

fire-retardant - (FR-) treated plywood. Definitive relationships

between nondestructively measured properties and engineering design properties are needed before NDE techniques can

be completely useful. There are two broad types of NDE

methods, chemical and mechanical.

Chemical-based NDE, such as monitoring relationships

between wood pH and strength (Lebow and Winandy, in

press, b) or changes in carbohydrate chemistry and strength

(LeVan and others 1990, Winandy 1995), is rapidly becoming better understood and more reliable. Nevertheless,

chemical tests are often prohibitively expensive because of

equipment needs, operator time, and lag time between field

inspection–sample collection and test results. Work continues to focus on developing a less expensive chemical NDE

test based on assessing the pH of treated wood.

Mechanical NDE often involves proof-loading-type tests

(APA 1989a) or basic relationships such as those between

stress wave speed and modulus of elasticity or between stress

wave attenuation and strength (Ross and Pellerin 1994). The

use of proof-loading is often complicated by cumbersome

equipment; the use of stress wave analysis is impeded by

inappropriate boundary conditions, which limit field

application by complicating signal processing.

Another variant of mechanical tests is the relationship of

screw withdrawal to strength (ASTM 1996a). Screwwithdrawal tests were initially found to be simple indicators

of biological degradation (Fig. 1) (Talbot 1982; see Ross

and others 1992 for details). Talbot’s work was critical.

Although others had used the relationship between resistance

of a probe (in penetration) to residual strength properties,

Talbot reasoned that a similar relationship existed between

screw-withdrawal resistance and residual wood strength

properties.

Screw-withdrawal tests have recently been used for other

purposes. They have tentatively been shown to be simple

indicators of FR-induced thermal degradation (APA 1989a

(app. H), Cooper 1992, Cooper and Reilly 1991, Ross and

others 1990). Early work at the Forest Products Laboratory

(FPL) evaluated some basic relationships between screwwithdrawal force and bending strength of FR-treated plywood

(Ross and others 1992) (Fig. 2). However, predictive models

with confidence boundaries were not defined. Prior results

had been encouraging, but they were not thorough or robust

enough for developing models. Additional systematic data

were needed. Thus, over the last few years an extensive data

base for matched screw-withdrawal force and destructive

bending strength data has been collected at FPL for various

kinds of FR-treated and exposed plywood. These new and

more comprehensive data are reported here, and the development of predictive relationships between screw-withdrawal

force and residual bending strength for FR-treated plywood is

discussed. When completely developed, such a series of

models can be used to predict lower boundary estimates of

the residual strength of FR-treated plywood roof sheathing

once the user has decided upon an acceptable statistical level

of confidence.

Figure 1—Relationship of residual strength

(modulus of rupture) to probe withdrawal

resistance—Talbot 1982.
2

Background

In the United States, replacement costs for thermally degraded FR-treated plywood roof sheathing have been predicted to exceed $2 billion (NAHB 1990). The first stage of

a research program at the FPL involved a systematic series of

studies to identify chemical mechanisms and quantify

strength loss (Winandy and others 1991b). Preliminary

investigations had indicated that field problems resulted from

thermal-induced acid degradation of wood carbohydrates by

the acidic FR chemicals (LeVan and Winandy 1990). More

comprehensive work confirmed the proposed acid-degradation

mechanism and showed that the relative effects of many FR

treatments could be classified by the type of FR chemical

employed and the time–temperature combination required to

convert the FR formulation into its acidic form (LeVan and

others 1990, Winandy 1995). Additional work found that the

rate of strength degradation for untreated and FR-treated

plywood increased as relative humidity increased; consequently, a test method was developed to evaluate commercial

FR treatments (Winandy and others 1991a). This test

method led to consensus standards for plywood (ASTM

1996b) and lumber (ASTM 1996c). To elevate the resulting

test data, several kinetics-based models for thermal degradation of FR-treated material have been presented (APA 1989b,

Pasek and McIntyre 1990, Winandy and others 1991a, Woo

1981). Winandy and Lebow (1996) built on this work to

develop a single-stage time–temperature model based on

first-order kinetic theory for a series of generic FR treatments.

They later verified that this model could accurately predict

strength loss (Lebow and Winandy, in press, a). LeVan and

others (1996) found that strength losses from cyclic thermal

exposure were generally similar to those from steady-state

temperature exposure when compared on a cumulative

time-at-temperature basis.

Objectives

The objectives of the work reported here were

1. to develop a preferred screw-withdrawal test methodology,

2. to define basic relationships between nondestructively

measured screw-withdrawal properties and an engineering

property, such as bending strength, for FR-treated plywood roof sheathing, and

3. to use those models to predict lower boundaries for residual plywood bending strength in service after assuming

various levels of confidence.

Methods and Materials

Based on screw-pull testing procedures developed in earlier

work (appendix H, Rep. SPE–1007, APA 1989a; Ross and

others 1990, 1992; Talbot 1982), we developed a simple

screw-pull testing technique that involved inserting, then

extracting, a No. 10 wood screw from various FR-treated and

untreated plywood specimens that had been exposed for some

time at various elevated temperatures (>54 ̊C (>130 ̊F)).

Material from three FPL studies was used to define the relationship between screw-withdrawal resistance and remaining

plywood bending strength. The data used in this report

involved matched strength–screw pull data from three studies

of larger scopes that individually evaluated the strength–

thermal degrade relationship as their primary objective. The

experimental variables of each study are shown in Table 1.

These three studies involved

1. the effects of FR processing factors, retention, and buffers

on thermal degrade, hereafter called the Factors Study

(Winandy 1997),

2. the interrelationship between steady-state high-temperature

laboratory exposure and variable (daily or seasonally) field

exposure, hereafter called the Lab–Field Study (Winandy,

in progress), and

3. the base data set used to verify the potential of new

ASTM Standard D5516 (ASTM 1996b) to induce thermal degrade, hereafter called the FPL–501 Study

(Winandy and others 1991a).

The experimental designs of the Factors Study (Winandy

1997) are shown in Tables 2 and 3; preliminary results of

screw–pull tests from all laboratory-exposed specimens and

1- and 3-year field-exposed specimens of the on-going 5-year

Lab–Field Study (Winandy, in progress) are shown in

Tables 4 and 5. The primary objective of this Lab-Field

Study was to relate laboratory degrade in strength from

thermal degrade to real-world field degrade in matched

specimens. However, after destructive testing of preliminary

specimens to address the primary objective, these same

Figure 2—Relationship of bending strength

(modulus of rupture) to screw withdrawal

resistance—Ross and others 1992.
3

Table 1—Experimental protocols of studies used to develop predictive models for plywood bending strength

from screw-withdrawal-force measurementsa

Exposure FR composition (%)

Treatmentb

Redryingc

(°C)

Max.

temp

 (°C)

Days

(no.)

Sample

size

Monoammonium

phosphate

Phosphoric

acid

Borate/

boric acid

Factors Study–12 mmd

MAP 49/32 66 290 72 100 0 0

MAP 71/54 66 290 94 100 0 0

MAP/PA 71/54 66 290 92 90 10 0

MAP/TB 71/54 66 290 87 75 0 25

MAP 88/71 66 290 93 100 0 0

Untreated None 66 290 84 None None None

Factors Study–16 mmd

100/0/0 66/60 66 290 40 100 0 0

 80/20/0 66/60 66 290 60 80 20 0

 80/0/20 66/60 66 290 60 80 0 20

 60/20/20 66/60 66 290 60 60 20 20

 80/10/10 66/60 66 290 60 80 10 10

 Water 66/60 66 290 18 None None None

 Untreated None 66 290 20 None None None

Lab–Field Study–16 mme

MAP 71/54 66 160 40 100 0 0

MAP Nonef 66 160 40 100 0 0

MAP/PA 71/54 66 160 40 90 10 0

MAP/PA Nonef 66 160 40 90 10 0

MAP/TB 71/54 66 160 40 75 0 25

MAP/TB Nonef 66 160 40 75 0 25

Water 71/54 66 160 40 0 0 0

Water Nonef 66 160 40 0 0 0

Untreated None 66 160 40 None None None

FPL–501 Study–16 mmg

MAP–77C 77/66 77 63 79 100 0 0

Untreated 77/66 77 63 118 None None None

a

TF = TC (1.8) + 32. b

MAP is monoammonium phosphate; PA, phosphoric acid; TB, Timbor (disodium octaborate tetrahydrate).

c

Dry-bulb/wet-bulb temperature.

d

Winandy 1997.

e

Winandy, in progress.

f

Not redried after treatment and exposed to extended high-temperature while wet.

g

Winandy and others 1991b.

Table 2—Results of individual paired t-tests on data for 12-mm- (1/2-in.-) thick plywood from Factors Studya

t-value for exposure at 66°C (150°F)/ 75% RH

Treatment

Redrying temp

(°C (°F)) Exposure

 0

days

 60

days

160

days

290

days

MAP 54 (120) Dry 0.077 — 0.365 0.529

MAP 71 (160) Dry 0.716 0.865 0.888 0.207

MAP/TB 71 (160) Dry 0.206 0.039 0.925 0.274

MAP/PA 71 (160) Dry 0.974 0.682 0.455 0.932

MAP 88 (190) Dry 0.076 0.168 0.490 0.210

MAP 71 (160) Wet/dry — 0.479 0.140 0.431

MAP 71 (160) Wet/wet — 0.338 0.806 0.066

Untreated None Dry 0.624 — 0.510 0.271

MAP None Wet/dry — 0.828 0.145 0.999

a

Data from Winandy 1997. For t-tests, H0: SWFt − SWFc = 0. Differences are significant for t-values < 0.05.
4

specimens were also evaluated using our screw–pull test and

used in the study reported here. The experimental design of

the FPL–501 Study (Winandy and others 1991a) was a

2 × 2 × 7 fractional factorial with 2 treatments (untreated and

MAP-treated), 2 exposure temperatures (54 ̊C (130 ̊F) and

77 ̊C (170 ̊F)), and 7 durations of exposure (7, 14, 21, 28,

35, 49, and 63 days); not all combinations of treatment,

temperature, and exposure duration were tested.

An undamaged end-section of a 600-mm- (24-in.-) long by

75-, 100-, or 150-mm- (3-, 4-, or 6-in.-) wide by 12- or

16-mm- (1/2- or 5/8-in.-) thick plywood specimen was used

for the screw-pull testing procedure. This specimen had been

previously tested for maximum load by destructive tests.

The face of the specimen subjected to tension stress in

service was then destructively stressed in tension using

ASTM D5516 (ASTM 1996b) bending test methodology.

In each undamaged end-section from the plywood bendingtest specimen, two or four pilot holes (as appropriate) were

marked and drilled to a set depth (75% of screw depth), No.

10 wood screws were inserted to another set depth (either

half- or full-thickness), and a handheld “load-cell” device was

used to measure maximum screw withdrawal for each inserted screw. Specifically, a template was used to mark the

location of screws. The screw sites were located on opposite

ends and faces of the plywood specimen (Fig. 3A), exactly

25 mm (0.98 in.) from each end and side but on opposite

faces. Pilot holes were drilled using a jig to ensure a perpendicular hole, and a 3.1-mm- (1/8-in.)-diameter drill bit

(Figs. 3B and 4A) was placed in a battery-powered screwdriver (Fig. 3C). This jig was used to determine a precise

hole depth and to ensure that the pilot hole was perpendicular to the specimen surface. A new 22-mm- (7/8-in.-) long

No. 10 wood screw (Fig. 3D) was then inserted and driven

using a different jig (Jig E, Figs. 3E and 4B) and a batterypowered screwdriver. Jig E ensured that the screw was driven

in vertically. The jig was fitted with a clutch that prevented

the screw from being driven completely through the opposite

surface of the plywood, and it left the bottom surface of the

screw head exactly 6.35 mm (1/4 in.) above the plywood

surface. Each screw was extracted using a specially designed

screw-extraction-force tool (Figs. 3F and 4C). The technicians attempted to apply the load at a uniform rate of

Table 3—Results of individual paired t-tests on data for

16-mm- (5/8-in.-) thick plywood from Factors Studya

Redrying

t-value at 66°C (150°F)/

75% RH

Treatment

(MAP/PA/BA)

temp

(°C (°F))

0

days

160

days

290

days

100/00/00 66 (150) 0.735 — 0.698

 80/20/00 66 (150) 0.177 0.625 0.362

 80/00/20 66 (150) 0.661 0.867 0.032

 60/20/20 66 (150) 0.175 0.032 0.552

 80/10/10 66 (150) 0.072 0.014 0.128

Water 66 (150) 0.022 — —

Untreated None 0.912 — —

a

Data from Winandy 1997. For t-tests,

 H0: SWFt − SWFc = 0. Differences are significant

 for t-values < 0.05.

Table 4—Results of individual paired t-tests on data for

16-mm- (5/8-in.-) thick plywood from laboratory part of

Lab–Field Studya

Redrying

t-values for exposure at

66°C (150°F)/75% RH

Treatment

temp

(°C (°F))

0

days

60

days

180

days

Untreated None 0.006 — —

MAP 71 (160) — 0.940 0.019

MAP None — 0.002 0.591

MAP/TB 71 (160) — 0.062 0.125

MAP/TB None — 0.082 0.007

MAP/PA 71 (160) — 0.179 0.889

MAP/PA None — 0.442 0.564

Water 71 (160) — 0.029 0.007

Water None — 0.224 0.431

a

Data from Winandy, in progress. For t-tests,

 H0: SWFt − SWFc = 0.

 Differences are significant for t-values < 0.05.

Table 5—Results of individual paired t-tests on data

for 16-mm- (5/8-in.-) thick plywood from field

exposure of Lab–Field Studya

Redrying

t-values for field

exposure

Treatment

temp

(°C (°F))

Roof

color

 12

months

 36

months

MAP 71 (160) Black 0.520 0.745

MAP 71 (160) White 0.191 0.738

MAP None Black 0.878 0.882

MAP None White 0.789 0.551

MAP/TB 71 (160) Black 0.627 0.400

MAP/TB None Black 0.831 0.149

MAP/PA 71 (160) Black 0.116 0.342

MAP/PA 71 (160) White 0.423 0.787

MAP/PA None Black 0.348 0.603

MAP/PA None White 0.083 0.899

Water 71 (160) Black 0.739 0.003

Water None Black 0.720 0.280

a

Data from Winandy, in progress. Specimens were

 exposed in simulated attic structures near Madison,

 WI, for various durations. For t-tests,

 H0: SWFt − SWFc = 0. Differences are significant

 for t-values < 0.05.
5

increase; total time from load initiation to failure was

approximately 2 to 4 s.

The screw-extraction-force tool was designed and supplied by

Sensor Development, Inc. (Lake Orion, MI), but other comparable devices are available. The load cell in the screwextraction-force tool measured load to the nearest 44.5 N

(10 lb). The load cell was factory calibrated; zero load could

be re-verified by an internal resistor circuit. Factory documentation of the electrical resistance of the load cell at zero

load was also provided. During testing, ongoing calibration

procedures included checking of the digital “read-out zero” of

the load cell prior to each screw-withdrawal test and periodic

re-verification of “electrical zero” via the internal resistor.

Results

Our original plan called for using the basic relationships

between screw-withdrawal force and residual bending strength

in a similar manner as modulus of elasticity is used to predict bending strength in machine-stress-rated grading of

lumber. We had hoped that a single “universal” relationship

between decline in screw-withdrawal force and loss in

strength over time could be identified. A preliminary analysis of the test data indicated that not all study–treatment–

exposure groups could be grouped simultaneously for analysis. This clearly indicated that the test methodology was not

independent across treatments, especially across various

plywood thicknesses, as earlier studies had anticipated

(Cooper 1992, Cooper and Reilly 1991, Ross and others

1990, 1992). Accordingly, the screw-withdrawal data were

separated by plywood thickness and study (Table 1).

These multi-study data were then evaluated across comparable thickness–treatment–exposure groups using graphical and

analytical methods. In the graphical analysis, plots were

reviewed to explore the relationship between screw- withdrawal force and strength. In cases where sets of similarly

treated groups exposed for different periods were available,

Figure 4—Screw-withdrawal test. Battery-powered

screwdriver and jig are used to drill pilot hole (A)

and insert screw (B); screw-extraction-force tool is

used to withdraw screw while peak withdrawal force

is monitored (C).

Figure 3—Specimen and equipment for screwwithdrawal test: (A) plywood specimen, (B) 3.1-mm-

(1/8-in.-) diameter drill bit, (C) battery-powered

screwdriver, (D) 22-mm- (7/8-in.-) long No. 10 wood

screws, (E) jig, and (F) screw-extraction-force tool.
6

the analytical methods showed a general relationship between

decline in screw-withdrawal force and loss in strength over

time. Nevertheless, before comprehensive statistical analysis

and model development could be more fully undertaken,

several preliminary questions had to be answered:

1. What is the effect of specimen width?

2. Is there any underlying relationship between multiple

screw-withdrawal measurements taken from each panel?

3. What is the effect of screw-insertion depth and which

depth is best?

4. What is the distributional form of the data and should it

be transformed to facilitate modeling?

Specimen Width

As described in Methods and Materials, a different specimen

width (75, 100, or 150 mm (3, 4, or 6 in.)) had been used in

each study. As expected, specimen width exerted no significant influence on screw withdrawal when other factors (such

as FR treatment and plywood thickness) were held constant.

Thus, specimen width was not further considered, or differentiated, during subsequent development of the models.

Multiple Measurements

Preliminary work (Winandy, in progress) had indicated no

discernible or significant differences between mean estimates

for two or four measurements of screw-withdrawal force per

specimen. However, that same preliminary work had shown

that estimates obtained by using only one test per specimen

were often not as stable as estimates obtained from two

measurements per specimen. Screw-withdrawal force estimates from a single-observation were often more than 25%

greater or less than estimates from the average of two or more

matched measurements. In view of this, we advise that at

least two full-depth measurements should be used to estimate

screw-withdrawal force per specimen.

Two screw-withdrawal force measurements were taken per

specimen, one on the tension face (SWFt) and the other on

the compression face (SWFc) of FR-treated plywood. (Note:

tension and compression faces refer to plywood sides used in

ASTM D5516 destructive bending test.) To examine

whether the two measurements exhibited significant differences, pair-wise t-tests were used to analyze each treatment–

redrying–exposure combination (homogeneous groupings) for

the Factors Study (Winandy 1997) and Lab–Field Study

(Winandy, in progress) (Tables 2 to 5). These two studies

allowed comparison of two complementary scenarios. For the

Factors Study, we expected no difference in screw-withdrawal

force between tension (top) and compression (bottom) plywood faces because the high-temperature exposures on each

face were similar. Likewise for the Lab–Field Study, we

expected no difference between top and bottom plywood faces

of the laboratory-exposed specimens. However, we anticipated a real difference for the matched field-exposed specimens because the cumulative thermal exposures on the top

and bottom faces were not equal in this outdoor exposure

(roof sheathing) (Winandy and Beaumont 1995). Also, when

used as a “field evaluation” technique, screw-withdrawal

measurements are taken from only the tension face

(underside) of roof sheathing plywood.

Few significant (α < 0.05 by Student’s t-test) differences

between top- and bottom-face screw-extraction measurements

were found, especially in the critical field-exposed groups.

Since significant differences were expected in 1 of 20 cases as

a result of naturally occurring variability, those few significant differences that did occur appeared random—they

showed no distinct pattern in any one treatment or exposure

category or in any particular direction. When the tests were

analyzed in respect to duration of exposure, a higher percentage of results were significantly different. But again these

occurrences appeared random in that they were not apparently

systematic across any treatment or exposure type. Thus, we

considered the two observations on matched tension and

compression faces as replicates (subsamples) and used the

mean of the tension- and compression-face measurements as

the “optimum” screw-withdrawal-force measurement for each

specimen.

Screw Depth

We used 16-mm- (5/8-in.-) thick plywood material from the

FPL–501 Study (Winandy and others 1991a) to evaluate the

influence of screw insertion depth on the relationship of screw

withdrawal force to bending strength. We compared the

variability and reproducibility of half-depth (8-mm (5/16-in.))

screw insertion to the results of full-depth (16-mm (5/8-in.))

screw insertion on the same panel. The half-depth measurements appeared to be less stable; they exhibited lower measurements with an increased coefficient of variability. In many

instances, load-cell resolution (±4.5 kg (±10 lb)) exceeded

25% of the measured value. For the full-depth measurements,

load-cell resolution seldom exceeded 10% of the measured

value. Thus, we selected the full-depth screw-withdrawal

measurements as the preferred technique. Since screwwithdrawal load is a function of insertion depth (Forest

Products Laboratory 1987), we did not evaluate the variability of half-depth screw-extraction for 12-mm- (1/2-in.-) thick

plywood because it was reasonable to assume that screwwithdrawal force would be less than that for 16-mm- (5/8-in.)

thick plywood, which had been shown to be unacceptable.

Consequently, all models hereafter were fit using full-depth

screw-withdrawal measurements.
7

Transformations

Initial analysis of the data showed that several of the multistudy groups (Table 1) could be better modeled by transforming the strength and/or the screw-withdrawal measurement. The traditional Box–Cox tests for transforming response and Box–Tidwell tests for transforming predictors did

not consistently select the same transformations for all the

groups or subsets of groups (Weisberg 1985). The Box–Cox

procedure indicated fairly flat likelihood, which prompted us

to compare models based on root mean squared error

(RMSE) and graphical (visual) analysis. This graphical and

RMSE analysis allowed us to narrow the alternative transformations to identity, square root, and logarithmic transformations for both the strength and screw-withdrawal measurements.

That is, we considered writing a model form for each treatment group of the form

 g (MOR) = f (SWF) + error (1)

where either or both g(x) and f(x) are one of the following

transformation functions:

identity h (x) = x

square root h (x) = x

1/2

logarithm h (x) = ln(x)

In another attempt to identify potential common transformations, we used a nonparametric ranking procedure to compare

RMSE of several variously transformed models (Table 6);

RMSE can be defined as

 

RMSE )2 =− − [ ] ∑( yy np ˆ /( ) 1 2 (2)

where

y is observed strength value on original scale (MPa),

 

yˆ estimated strength value (MPa) for a candidate

 model,

n number of observations used in developing the

 model, and

p number of parameters estimated for the model

 (two in all cases considered).

From this ranking procedure and review of the graphs, the

general model form

 MOR = b0 + b1(SWF)1/2 + error (3)

was selected as most appropriate. Two notable exceptions in

the ranking procedure are the 80/0/20 and the 80/10/10

treatment groups of the Factors Study–16 mm, which might

be better modeled by

 MOR1/2 = b0 + b1SWF + error (4)

However, after a thorough comparative examination of the

graphs and residuals from both models (expressed as Eqs. (3)

and (4)), it is our opinion that the previous model (Eq. (3))

can also adequately model these two treatment groups. The

relationship between plywood bending strength and screwwithdrawal force for square-root transformation of the Factors

Study data (Winandy 1997) is shown for 12-mm- (1/2- in.-)

thick plywood in Figure 5 and for 16-mm- (5/8-in.-) thick

plywood in Figures 6 and 7. The relationship between plywood bending strength and screw-withdrawal force for squareroot transformation of the laboratory portion of the Lab–Field

Study (Winandy, in progress) is shown for 16-mm- (5/8-in.-)

thick plywood in Figures 8 and 9.

Modeling

Each treatment group listed in Table 6 was fit by the selected

model (Eq. (3)), obtaining 26 separate regressions. Since the

parameter estimates for several treatment subgroups appeared

similar, the similar-appearing groups were separated out by

thickness and similarly acting treatments; these groups were

then evaluated for common parameter estimates of slope and

y-intercept.

Factors Study

For the 12-mm- (1/2-in.-) thick material used in the study by

Winandy (1997), we tested whether the regressions for each

of the five treated groups were coincident; that is, whether

they had the same y-intercept and slope. From the results of

this test, the hypothesis of both common y-intercept and

slope was rejected at p = 0.0443. However, the five treated

groups did appear to have a common slope, which was tested

and accepted at p = 0.2182. Visual analysis suggested that

only the MAP/TB group had a different y-intercept; this

group was consequently removed. The remaining four treated

groups were tested for coincidence, accepted at p = 0.7130.

Thus, for this 12-mm- (1/2-in.-) thick FR-treated material,

three models were estimated: an untreated group, the MAPtreated group buffered with borate (MAP/TB), and the remaining treated groups (MAP alone, MAP/PA without TB).

Model parameter estimates, standard errors, and coefficients

of determination (r

2

) are listed in Table 7.

Combined Factors and Lab–Field Studies

As would be expected from results of tests on the 12-mm-

(1/2-in.-) thick Factor Study material, we found that the

influence of buffering MAP-treated plywood with borate was

significant for the 16-mm- (5/8-in.-) thick material.
8

Table 6—Root mean square error of various potential model forms of transformed y (MOR) to transformed x (mean

screw-withdrawal force)

y y1/2 log y

Treatment, redrying, thicknessa x x1/2 log x x x1/2 log x x x1/2 log x

Factors Study

MAP, KD 49°C, 12 mm 10.98 10.83 11.18 11.43 10.95 10.87 12.37 11.47 11.01

MAP, KD 71°C, 12 mm 10.91 10.70 10.84 11.43 10.89 10.71 12.87 11.61 10.93

MAP/TB, KD 71°C, 12 mm 10.56 10.55 10.74 10.68 10.56 10.65 10.95 10.69 10.67

MAP/PA, KD 71°C, 12 mm 9.10 8.88 9.10 9.58 9.05 8.91 10.82 9.71 9.05

MAP, KD 71°C, 12 mm 10.59 10.42 10.52 10.89 10.55 10.45 11.49 10.90 10.60

Untreated, 12 mm 11.79 11.80 11.80 11.81 11.81 11.82 11.85 11.85 11.85

MAP/PA/BA

100/0/0, 16 mm 10.59 10.63 11.24 11.22 10.63 10.53 12.83 11.53 10.92

80/20/0, 16 mm 8.92 8.81 8.99 9.39 8.96 8.78 10.40 9.61 9.05

80/0/20, 16 mm 8.11 8.65 9.43 7.92 8.25 8.91 8.00 8.06 8.61

60/20/20, 16 mm 9.53 9.47 9.62 9.82 9.54 9.47 10.52 9.94 9.62

80/10/10, 16 mm 7.79 8.42 9.45 7.65 8.66 7.93 7.80 8.35 1211

Water, 16 mm 8.21 8.20 8.19 8.21 8.21 8.20 8.23 8.23 8.22

None, 16 mm 12.19 12.20 12.20 12.20 12.21 12.21 12.24 12.24 12.25

Lab–Field Study

MAP, KD, 16 mm 11.55 11.55 11.55 11.58 11.58 11.58 11.67 11.66 11.66

MAP, no KD, 16 mm 10.04 9.98 9.93 10.13 10.05 9.99 10.28 10.19 10.11

MAP/TB, KD, 16 mm 10.09 10.07 10.05 10.13 10.10 10.08 10.22 10.18 10.15

MAP/TB, no KD, 16 mm 10.39 10.43 10.47 10.39 10.43 10.47 10.45 10.48 10.52

MAP/PA, KD, 16 mm 8.99 8.96 8.94 9.03 9.00 8.98 9.11 9.08 9.05

MAP/PA, no KD, 16 mm 8.01 7.97 7.94 8.05 8.01 7.97 8.13 8.08 8.04

Water, KD, 16 mm 13.07 13.01 12.94 13.14 13.07 13.01 13.26 13.19 13.13

Water, no KD, 16 mm 10.28 10.28 10.29 10.29 10.29 10.30 10.31 10.31 10.32

Untreated, 16 mm 8.56 8.60 8.63 8.54 8.58 8.62 8.54 8.57 8.61

FPL–501 Study (half-depth

 penetration)

Untreated, 77°C, 16 mm 10.92 10.91 10.90 10.93 10.92 10.91 10.97 10.96 10.95

MAP, 77°C, 16 mm 9.43 9.42 9.44 9.47 9.44 9.45 9.55 9.51 9.50

FPL–501 Study (full-depth

 penetration)

Untreated, 77°C, 16 mm 10.92 10.92 10.92 10.94 10.93 10.93 10.98 10.97 10.97

MAP, 77°C, 16 mm 9.76 9.73 9.72 9.80 9.76 9.75 9.89 9.85 9.82

a

KD is kiln drying.
9

Figure 5—Relationship of screw-withdrawal force to bending strength for 12-mm- (1/2-in.-) thick plywood from

Factors Study (Winandy 1997). MAP is monoammonium phosphate; PA, phosphoric acid; TB, Timbor; UNT, untreated.

KD is dry-bulb kiln-drying temperature. Temperature: TF = TC • 1.8 + 32; Force: 1 N = 0.225 lb.
10

Figure 6—Relationship of screw-withdrawal force to bending strength for treated 16-mm- (5/8-in.-) thick plywood

from Factors Study (Winandy 1997). Treatment is MAP/PA/BA.
11

Figure 7—Relationship of screw-withdrawal force to

bending strength for untreated 16-mm- (5/8-in.-) thick

plywood from Factors Study (Winandy 1997).

For the Factors Study material, we found that all the chemically treated groups were not coincident (p = 0.0268) and did

not have common slopes (p = 0.1266). On closer inspection,

we found that the MAP- and MAP/PA-treated groups with

less than 20% borate (all groups except the 80/0/20 group)

were coincident (that is, common y-intercept and slope) at

p = 0.0609. Further, if the 80/10/10 group were not considered, the remaining three groups (100/0/0, 80/20/0, and

60/20/20 groups) were coincident at p = 0.6468. Accordingly, the MAP-treated groups with less than 20% borate

and those with any additional PA were modeled as a single

group. The untreated, water treated, and combined boratebuffered (at least 20% borate) MAP-treated groups (including

the 80/10/10 group, which could only be grouped with

the 80/0/20 group (p = 0.3789)) were then modeled

individually.

For material from the laboratory portion of the Lab–Field

Study, we found that all the treatment groups were not

coincident (p < 0.0001) but did have common slopes

(p = 0.9531). This testing indicated that the chemically

treated model parameter estimates were similar but not identical to those of the Factors Study. The water-treated groups

and the untreated group were distinctly different from the

chemically treated groups and so were modeled separately.

The test of coincidence of the chemically treated Lab–Field

groups was accepted with p = 0.5350 and the test of coincidence of the two Lab–Field water-treated groups was accepted

with p = 0.4838.

For practical reasons, the 16-mm- (5/8-in.-) thick specimens

of the Factors and Lab–Field studies were combined into

similarly treated groups based on (1) similar performance and

(2) presence or absence of supplemental borate in the FR

formulation.

The following rationale was used for combining the individual Factors and Lab–Field groups by similar treatments:

1. Plywood for both studies was obtained from the same

original batch of material, treated with similar FR treatments, and exposed in the same laboratory chamber.

2. Although there were a few statistically significant differences between some groups, we felt that it was not reasonable that similar material would react in a significantly

different way. Some groups had few different thermal exposures, which resulted in different ranges of response (that

is, strength loss) from thermal degrade. Thus, we compared different subsets of the population or populations.

For an example, see Figure 10.

3. Graphical analysis of the data did not support exclusion;

in fact, it seemed to indicate that data from the two studies

were mutually inclusive when viewed as a whole. In Figure 10, note that although the tested mean trends are different, grouping of the two sets of material tends to fill in

gaps resulting from differing thermal exposures.

Parameter estimates for mean trend models, standard errors,

and r

2

 values for the 16-mm- (5/8-in.) thick material from the

combined Factors and Lab–Field studies are listed in

Table 7.

Finally, material in the field portion of the Lab–Field Study

was not modeled because it did not experience sufficient

degrade after only 3 years of exposure; we hope to revisit

this. These field data were retained to check their predictive

ability using the models developed with the laboratory data.

FPL–501 Study

Untreated 16-mm- (5/8-in.-) thick plywood exposed at either

54 ̊C (130 ̊F) for 14 or 28 days or 77 ̊C (170 ̊F) for 7, 14,

21, 28, 35, 49, or 63 days (Winandy and others 1991a) did

not show any distinct relationship between screw-withdrawal

force and residual bending strength. However, the MAPtreated group exposed at the higher temperature (77 ̊C

(170 ̊F)) exhibited a strong direct relationship between screwwithdrawal force and residual bending strength, while the

MAP-treated group exposed at the lower temperature (54 ̊C

(130 ̊F)) exhibited similar, but nonsignificant, behavior. The

test of coincidence between the two MAP-treated groups

exposed at two temperatures was rejected (p < 0.0001), yet

the test of common slopes was not rejected (p = 0.8440).

Parameter estimates for mean trend models, standard errors,

and r

2

 values of the MAP-treated groups exposed at 77 ̊C

(170 ̊F) are listed in Table 7. Because these groups were

significantly different and the original plywood materials of

the FPL–501 Study were not matched to the Factors or Lab–

Field Study materials, the MAP-treated material was not

combined with materials from the other studies.
12

Figure 8—Strength of 16-mm- (5/8-in.-) thick treated plywood from Lab–Field Study (Winandy, in progress).

Treatments were various combinations of MAP, TB, and PA, with or without kiln drying.
13

Figure 9—Strength of 16-mm- (5/8-in.-) thick watertreated or untreated plywood from Lab–Field Study

(Winandy, in progress).

Prediction Boundaries

Recall that our objective was to develop a method for predicting plywood bending strength (y*) from a set of screwwithdrawal measurements so that the model could be used to

estimate mean trends and construct appropriate prediction

intervals based on model error. The mean trend models and

their resulting prediction intervals (Table 7) could be used to

establish a lower prediction boundary given the appropriate

level of confidence in the lower prediction boundary. Table 8

contains the additional data necessary to construct lower

prediction boundaries from the mean trend models described

in Table 7.

Table 7—Model parameter estimates, standard errors,

and r

2

 values

MOR = 

ˆ

b 0 +

 

ˆ

b 1 (SWF)1/2 Standard error

Treatmenta

 

ˆ

b 0 

ˆ

b 1 

ˆ

b 0 

ˆ

b 1 r

2

Factors Study, 12 mm

Untreated 40.15 0.70 9.0195 0.2842 0.07

FRT <20%

borate −13.59 2.09 1.9988 0.0856 0.63

FRT >20%

borate −2.53 1.78 4.7539 0.1978 0.49

Factors and Lab–Field Studies, 16 mm

Untreated 11.86 1.41 24.3669 0.5503 0.10

Water 1.57 1.50 15.3992 0.3830 0.14

FRT <20%

borate −31.87 2.09 3.3126 0.0993 0.58

FRT >20%

borate −21.62 1.85 3.1636 0.0955 0.66

FPL–501, 16 mm

MAP, 71°C 10.63 0.78 8.5626 0.2432 0.12

a

FRT <20% borate refers to phosphate-based FR

 formulations with <20% borate (by weight relative to

 phosphate). This combined group includes 100/0/0,

 80/20/0, and 60/20/20 groups from Factors Study;

 and MAP with and without KD, and 90% MAP/10%

 PA with and without KD from Lab–Field Study.

 FRT >20% borate refers to phosphate-based FR

 formulations with >20% borate(by weight relative to

 phosphate). This combined group includes 80/0/20

 and 80/10/10 groups from Factors Study, and 75%

 MAP/25% TB with and without KD from Lab–Field

 Study.
14

Figure 10—Example of how combined groups could have

significantly different regressions but support the same

general effect on bending strength of 16-mm- (5/8-in.-)

thick plywood (Winandy , in progress; 1997).

Data from Lab–Field Study material treated with MAP/TB

(<20% or >20% borate). Following the methods outlined by

Weisberg (1985), the typical curvilinear form of a 100(1 − α)

one-sided prediction interval for a single future observation of

bending strength, based on the mean of at least two

screw-withdrawal measurements (x* = avg(xi)), from some

randomly selected single plywood specimen is

 

R SE lower bound = ⋅ p y-t ˆ n- , - 2 1 α (5)

where

 

yˆ = is predicted mean plywood strength,

 

ˆ ˆ b b 0 1 + (x)

1/2, (6)

x mean of multiple screw-withdrawal

measurements, avg (xi),

 

ˆ ˆ b b 0 1 + fitted parameters (Table 7),

SEp standard error of prediction,

SE · {1 + 1/n + [(x

1/2 − x )2

/SS]}1/2, (7)

SE Eq. (3) model estimate of error (Table 8),

 

tn- , - 2 1 α t- statistic,

n number of observations,

 x observed mean of square root screw-withdrawal

measurements (Table 8), and

SS mean-adjusted sums of squares, ∑(xj

1/2 − x )2

(Table 8).

Table 8—Prediction estimates for models described

in Table 7a

Treatmentb n SE x SS SEpress

Factors Study, 12 mm

Untreated 84 11.78 31.41 1722.35 11.96

FRT <20% borate 351 10.18 22.46 14132.05 10.21

FRT >20% borate 87 10.55 23.34 2846.22 10.66

Factors and Lab–Field Studies, 16 mm

Untreated 60 10.86 44.21 389.52 11.08

Water 98 11.09 40.10 839.04 11.23

FRT <20% borate 320 9.83 32.89 9790.52 9.86

FRT >20% borate 200 9.42 32.38 9723.96 9.44

FPL–501 Study, 16 mm

MAP, 71°C 79 9.73 4.92 1601.95 9.83

a

 x is observed mean of square root screw-withdrawal

 force; SS, mean-adjusted sums of squares Σ [xj

1/2 − x ]2

;

 SEpress, estimated prediction error.

 bFRT <20% borate refers to phosphate-based FR

 formulations having less than 20% borate (by weight

 relative to phosphate). This combined grouping

 includes 100/0/0, 80/20/0, and 60/20/20 groups from

 Factors Study; and MAP with and without KD, and 90%

 MAP/10% PA with and without KD from Lab–Field Study.

 FRT >20% borate refers to phosphate-based FR formu-

 lations having more than 20% borate (by weight relative

 to phosphate). This combined grouping includes 80/0/20

 and 80/10/10 groups from Factors Study, and 75%

 MAP/25% TB with and without KD from Lab–Field Study.
15

The lower prediction bounds for the models described in

Tables 7 and 8 and defined in Equation (5) are shown in

Figures 11 to 18. Figures 11 and 12 show lower prediction

bounds for treated (MAP plus <20% or >20% borate) 12-

mm- (1/2-in.-) thick plywood from the Factors Study. Lower

prediction bounds for combined data from the Factors and

Lab–Field Studies for 16-mm- (5/8-in.-) thick plywood that

had been treated predominantly with MAP plus <20% or

>20% borate are shown in Figures 13 and 14, respectively.

Figure 15 shows lower prediction bounds for untreated plywood in the Factors Study, and Figures 16 and 17 show

lower prediction bounds for combined data for untreated and

water-treated materials, respectively. Finally, Figure 18

shows lower prediction bounds for data from Winandy and

others (1991a) for 16-mm- (5/8-in.-) thick MAP-treated

plywood exposed for 7, 14, 21, 28, 35, 49, or 63 days at

77 ̊C (170 ̊F).

Note that when the curvilinear form (Eq. (5)) was used, the

predicted lower bound appears curvilinear rather than simply

parallel with the mean y trend because the variability in the

slope of the predicted lower bound is magnified as the data

move from the center of the curve towards its outer ranges.

The additional variability reflected in Equation (7) results

from the fact that the future observation will be different than

its expected value.

Figure 11—Mean trends and lower prediction bounds

for relationship of screw-withdrawal force to bending

strength for 12-mm- (1/2-in.-) thick plywood treated

with MAP/<20% borate (Winandy 1997).

Figure 12—Mean trends and lower prediction bounds

for relationship of screw-withdrawal force to bending

strength for 12-mm- (1/2-in.-) thick plywood treated

with MAP/>20% borate (Winandy 1997).

Figure 13—Mean trends and lower prediction bounds

for relationship of screw-withdrawal force to bending

strength for 16-mm- (5/8-in.-) thick plywood treated

with MAP/<20% borate (Winandy, in progress;

Winandy 1997).

Figure 14—Mean trends and lower prediction bounds

for relationship of screw-withdrawal force to bending

strength for 16-mm- (5/8-in.-) thick plywood treated

with MAP/>20% borate (Lab–Field Study) and 80/10/10

and 80/0/20 groups of Factors Study (Winandy ,

in progress; Winandy 1997).
16

A linear form of a 100(1 − α) one-sided prediction boundary

for a future strength observation based on the mean of at least

two screw-withdrawal measurements (x* = avg(xi)) from

some randomly selected single plywood specimen is

Rlower bound = yˆ− t n- , - 2 1 α · SEpress (8)

where SEpress is estimated prediction error (from Table 8).

The predicted residual sum of squares estimate of prediction

error (SEpress) is the square root of the average predicted

squared error, where the predicted squared error for each

observed strength value is the difference between itself and

the value predicted from a model fit without it squared

(Weisberg 1985).

As with any empirically fit model, a word of warning is

required since the model parameters are a function of the data

and the inherent characteristics of that data. Thus, the user

should be warned that the ensuing prediction boundaries

from either the curvilinear or linear models (Eq. (5) or (8),

respectively) are based on a future observation from the

population on which the model was originally based.

Furthermore, the user needs to keep in mind that the data

governed which form of model we used. Accordingly, unanticipated departures in the physical characteristics of future

materials from this base population may mean that the resultant statistics are not the same as those given here. Therefore,

the utility of these models may be decreased.

Figure 15—Mean trends and lower prediction bounds

for relationship of screw-withdrawal force to bending

strength for untreated 12-mm- (1/2-in.-) thick plywood

(Winandy 1997).

Figure 16—Mean trends and lower prediction bounds

for relationship of screw-withdrawal force to bending

strength for untreated 16-mm- (5/8-in.-) thick plywood

in both Lab–Field and Factors studies (Winandy,

in progress; Winandy 1997).

Figure 17—Mean trends and lower prediction bounds

for relationship of screw-withdrawal force to bending

strength for water-treated 16-mm- (5/8-in.-) thick

plywood in both Lab–Field and Factors studies

(Winandy, in progress; Winandy 1997).

Figure 18—Mean trends and lower prediction bounds

for relationship of screw-withdrawal force to bending

strength for MAP-treated plywood exposed at

77 ̊C (170 ̊F) in FPL–501 Study (Winandy 1991a).
17

Discussion

A thorough review of the models and their predicted mean

trends and lower predicted boundaries (Table 7, Figs. 11

to 18) revealed three important results:

1. Screw-withdrawal force was directly related to bending

strength of FR-treated plywood.

2. For a given screw-withdrawal measurement, expected

MOR was systematically shifted higher or lower based on

FR treatment.

3. Addition of borate buffered the rate of thermal degrade

when borate concentrations were generally more than

20% of the total salts concentration in inorganicphosphate-based FR formulations.

Screw-withdrawal force clearly has a direct relationship to the

bending strength of FR-treated plywood. Although at first

glance this relationship appears to be consistent and uniform,

such a universal relationship was not always found in comparisons across different FR-treatments or plywood thickness

levels. Instead, we found that these relationships were uniform and systematic only when analyzed within similarly

buffered FR treatments and plywood thickness groupings.

Two primary grouping criteria were thus developed and are

used for the remainder of this discussion:

1. Grouping of phosphate-based FR formulations with less

than 20% borate (by weight relative to total salts concentration). For 16-mm- (5/8-in.-) thick plywood, this combined grouping included the 100/0/0, 80/20/0, and

60/20/20 groups from the Factors Study and the MAP and

MAP/PA (with and without kiln drying) groups from the

Lab–Field Study.

2. Grouping of phosphate-based FR formulations with generally more than 20% borate (by weight relative total salts

concentration). For 16-mm- (5/8-in.-) thick plywood, this

combined grouping included the 80/0/20 and 80/10/10

groups from the Factors Study and the MAP/TB (with

and without KD) groups from the Lab–Field Study.

In the Factors and Lab–Field studies, the intercept parameters between subsets of some FR-treated groups were found

to be different and the slope parameters were more similar.

This infers that for a given screw-withdrawal measurement,

the expected MOR will be systematically shifted higher or

lower based on the FR treatment. Similarity in slopes can

be seen by comparing the slopes (b1) of comparable treatments for each thickness of plywood. Compare slopes for FR

treatment with <20% borate (b1 in Figs. 11 and 13) and with

>20% borate (b1 in Figs. 12 and 14). This similarity is also

apparent in a comparison of the predicted slope parameters

of the grouped Factors and Lab–Field data in Table 7.

Note that the data are ranked in a logical manner consistent

with the ranks of thermal degrade data reported in previous

studies (LeVan and others 1990, Winandy 1995, 1997).

Also note how untreated plywood had the smallest response

for the relationship between screw-withdrawal force and

strength, and water-treated material had a slightly stronger

response. Phosphate-treated material buffered with sufficient

borate exhibited a still stronger response and that without

sufficient borate buffers exhibited the strongest response.

Finally, note the similarity in slopes between the 12-mm-

(1/2-in.-) and 16-mm- (5/8-in.-) thick plywood. Although

the intercepts are distinctly different, the slopes are remarkably similar for phosphate-treated material with or without

borate buffers (Table 7).

The addition of borate buffered (lessened) the rate of thermal

degrade when borate concentration was more than 20% of

phosphate concentration in inorganic-phosphate-based FR

formulations. This result can be seen in a comparison of the

slopes (b1) in Figures 11 and 12 to those in Figures 13 and

14. Although the b1 of FR formulations amended with >20%

borate (Table 7) were not “significantly” different from that of

phosphate-only formulations or formulations with <20%

borate for any thickness group, the consistency in the magnitude of these b1 differences suggests a level of practical significance. This result of borate buffering agrees with recent

findings that borate buffers the magnitude of thermal degrade

of phosphorus-based FR-treated wood (Winandy 1997,

Winandy and Schmidt 1995).

When FR-treated plywood is evaluated in the field, the

presence of borate may be quickly established using spray-on

colorimetric methods such as Method 1 of AWPA Standard

A–3 (AWPA 1997), and the presence of phosphorus can be

identified using Method 9 of that standard. Although there

are quantitative laboratory methods for estimating borate and

phosphorus levels, the field methods are merely qualitative.

If the user of the models presented here is unable to ascertain

whether borate is a significant portion of the original FR

formulation, he or she is advised to use the model parameters

for FR formulations that consist predominantly of inorganic

phosphate and are amended with <20% borate.

Model Validation

To test the applicability of the predictive models and

boundaries to other populations, we used the field portion of

the Lab–Field Study that was not used in the development of

model parameters. Examples of the application of the developed models (Eqs. (5) to (7), Tables 7 and 8) for this field

sample can be seen by comparing the predicted mean trends

and lower prediction bounds for a single future observation to

data from the 1-year field exposure of 16-mm- (5/8-in.-) thick

material treated with MAP and <20% borate (Fig. 19) or

>20% borate (Fig. 20) (Winandy, in progress). While the
18

predicted mean trends and lower prediction bounds are in fact

reliable, note that the mean trend is especially conservative.

We believe that because the field exposure was limited to

only one particularly cool year in Madison, Wisconsin,

thermal loading (that is, exposure) was insufficient to produce a measurable response between strength and screwwithdrawal force. This lower-than-expected thermal loading

during the summers of 1992 and 1993 was thoroughly discussed in a previous report (Winandy and Beaumont 1995).

Other Considerations

In accordance with our objectives, the prediction bounds

constructed and reported in this paper were based on the

prediction of a single future value. Similar prediction intervals could also be constructed on the basis of the prediction

of a finite number of future values. Prediction intervals can be

constructed from the information given in Tables 7 and 8.

However, if the number of future predictions is large or unknown, then the use of tolerance intervals is the preferred

methodology. The basic difference between prediction intervals and tolerance intervals is the mechanism by which they

account for variability. As the number of future predictions

increases, the usefulness of prediction boundaries becomes

unacceptable (Miller 1981, Neter and others 1990).

It is important to select an appropriate confidence level.

Selection of a high confidence level may tend to underestimate residual bending strength and thereby reject a higher

number of test specimens than may be considered appropriate. Conversely, selection of too low a confidence level may

tend to overestimate residual bending strength and thereby

increase the chance of accepting a higher number of test

specimens than may be considered appropriate. Users are

advised to thoroughly consider the full implication of these

decisions.

The models developed in this work can accurately predict

residual plywood bending strength within user-specified

levels of confidence from a measurement of screw-withdrawal

force. Two problems still exist. First, while these models

have been shown to work acceptably for special laboratory

plywood constructed from all N-grade veneers, additional

work is needed. Specifically, work is needed on the effects of

plywood quality (such as manufacturing/processing methods,

drying, species, veneer quality, voids), plywood temperature

when it differs from room temperature at time of test, and

deviation in plywood moisture content away from 10%–12%

at time of test. Finally, using the concepts provided in this

and earlier reports, researchers, engineering communities, and

code authorities must work together to develop by consensus

precision estimates and confidence levels that will enable

third-party interpretation of these basic relationships in a

manner similar to the methods used for machine-stress rating

of lumber.

Examples

Using the screw-extraction-force instrument, suppose a user

obtains a reading of 900 N (202 lbf) from a 12-mm- (1/2-in.-)

thick, FR-treated (<20% borate) plywood specimen. The

predicted bending strength would be obtained by substituting the regression estimates from Table 7 into Equation (3),

yielding

Figure 19—Example of applicability of models as shown

by predicted mean trends and lower prediction bounds

compared to real data from material treated with MAP

and <20% borate. Real data was obtained from treated

16-mm- (5/8-in.-) thick material exposed in the field

for 1 year; these data were not used to develop the

model parameters (Winandy in progress).

Figure 20—Example of applicability of models as shown

by predicted mean trends and lower prediction bounds

compared to real data from material treated with MAP

and >20% borate. Real data were obtained from treated

16-mm- (5/8-in.-) thick material exposed in the field

for 1 year; these data were not used to develop the

model parameters (Winandy, in progress).
19

 MOR = −13.59 + 2.09(900)1/2

= 49.1 MPa (7,123 lbf/in2) (3)

The predicted lower bound on that unknown strength, with a

degree of confidence specified by 1 − α (where α = 0.05), as

given by Equation (5) with estimates for Table 8, yields

Rlower bound = 49.1 − 1.6492(10.25)

 = 32.2 MPa (4,671 lbf/in2) (5)

Conclusions

Individual models were developed for similarly performing

groups of fire-retardant (FR) treatments and plywood thicknesses to predict average loss in strength and lower prediction bounds for plywood bending strength as a function of a

screw-withdrawal measurement. Our analysis of FR-treated

plywood from three different studies, each with various FRtreatment, processing, plywood thickness, and exposure

temperature groupings, clearly indicated that various FR

treatments and thicknesses of plywood could not all be

grouped into a single “universal” model. The groups that

could be combined were studied. The ensuing models had

the general form

Rlower bound = yˆ − tn- , - 2 1 α · SEp

The parameter estimates for several grouped FR formulations

and plywood thicknesses are reported for a curvilinear lower

prediction bound. Data are also provided for calculating the

parameter estimates for a less preferable, but simpler-to-use,

linear lower prediction bound. Both lower prediction boundary model forms were found to acceptably predict residual

plywood bending strength for several FR formulations and

plywood thicknesses near the mean. The curvilinear form

(Eq. (5)) is preferred because of its more comprehensive

nature when predicting values in the extreme tails of the

screw-withdrawal-force distribution.

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