United States

Department of

Agriculture

Forest Service

Forest

Products

Laboratory

Research

Paper

FPL-431

Characterization of

Physical and

Mechanical

Properties of 2 by 4

Truss Lumber

C. C. Gerhards
Abstract Nomenclature

This paper summarizes data on dimensional characteristics,

optimum grade, and regressions of strength on modulus of

elasticity and grade class (a function of strength ratio) of

lumber specimens sampled from truss fabricators in Illinois.

Averages of dimensions, area, section modulus, and

moment of inertia of the nominal 2- by 4-inch specimens at

12 percent moisture content were very close to those for

standard dimensions (1.5 by 3.5 in.); distributions of those

properties tended to be skewed toward lower values. Mill

grading of the lumber specimens was generally conservative

compared to optimum grade levels based on the National

Grading Rule. Regressions of strength in compression,

tension, or bending on an edgewise short-span modulus of

elasticity appeared to be adequate for strength prediction or

for machine stress rating. The two or three measures of

bending strength at different positions in a specimen

showed low correlation, suggesting that bending strength at

one position in a specimen can be quite different from that

at another position. This report, along with a previous

report, provides a strength data base for engineering

evaluation of wood truss reliability. The data on species,

grade, and dimensions should be of interest to grading

agencies and code groups.

A,B Regression coefficients

ASTM American Society for Testing and Materials

COV Coefficient of Variation

E Modulus of elasticity

EB Bending E

EC Compressive E

EF Full-Span E

ER E-Ratio

ESP Short-Span E

ESPH Highest ESP per cord

ESPL Minimum ESP per cord

ET Tensile E

GC Grade class

KD Kiln dry

NGR National Grading Rule

S-DRY Surfaced dry

S-GRN Surfaced green
United States

Department of

Agriculture

Forest Service

Forest

Products

Laboratory’

Research

Paper

FPL-431

August 1983

Characterization

of Physical

and Mechanical

Properties of 2 by 4

Truss Lumber

C. C. Gerhards

Introduction

The modern wood truss, with its metal plate connectors,

represents the most highly engineered component in woodThis report deals with physical properties of the lumber

framed houses. Its wide use results from economy and

(cross sectional), mechanical properties based on actual

proven performance. Yet, further improvement of the truss

dimensions at test, correlations of bending strengths within

may be possible with better understanding of the properties

chords, and relationships of strength properties to several

of lumber and of lumber interactions with various

nondestructive variables. Other results of the study were

components of the structure under real loading conditions.

reported at the Metal Plate Wood Truss Conference (4) 2 in

1979. Those findings are briefly summarized below.

In late 1975, the Forest Products Laboratory initiated the

study reported here to learn more about the properties of

lumber used by truss fabricators. The primary purpose of

the study was to characterize the engineering properties of

truss lumber in a format suitable for others to simulate

individual truss strength and variation in strength of

consecutive trusses manufactured by a truss fabricator. For

the study, nominal 2- by 4-inch lumber, representing the top

and bottom chords of 4 consecutive trusses was obtained

in 1977 from each of 44 wood truss fabricators located

throughout Illinois. Trusses had not actually been built, but

the lumber was sampled in a way that the sixteen 2 by 4’s

per fabricator could have been assembled in four

consecutive trusses. Criteria used in obtaining the truss

lumber included: 1) The truss fabricator used metal plate

connectors that were made by a member of the Truss Plate

Institute, 2) lumber had been visually stress graded, and 3)

lumber was of a length typical for a 4 in 12 slope W (or

Fink) house truss to span 26 feet.

Nineteen different species-group-grade combinations were

represented in the 704-piece truss lumber sample. Although

predominantly Southern Pine (85%) Douglas Fir-Larch,

Hem-Fir, and Spruce-Pine-Fir were also represented. The

most common species-grade combination was No. 2

Southern Pine (66% including dense and nondense grades).

The highest grade stamp encountered was No. 1, the

lowest was Standard. The lumber for each truss was tested

for strength in compression, tension, or bending at standard

rates (2) according to the plan shown in Fig. 1 with the

chord orientation chosen by the fabricator. The strength

properties and modulus of elasticity (E) were summarized as

1

The author is a Research General Engineer, Forest Products

Laboratory, U.S. Department of Agriculture. The Laboratory is

maintained at Madison, Wis., in cooperation with the University of

Wisconsin.

2

Underlined numbers in parentheses refer to literature cited at end of

this report.

Figure 1 .—Schematic of test specimen types

for truss chord lumber. Arrows indicate

loading modes. (M152111)
Results

histograms of fabricator averages and coefficients of

variation (COV’s) based on four trusses per fabricator. All

properties were based on standard dimensions assumed for

engineered wood structures using 2 by 4’s. The average E

equaled the weighted average design value (5) for all of the

species-grade combinations of the truss lumber. The COV

of E was 26 percent. Strength properties of the truss

lumber averaged 90 percent higher in compression, 110

percent higher in tension, and 160 percent higher in thirdpoint bending than the weighted average design values (5)

for the species-grade combinations adjusted to a 5-minute

test loading condition. However, a few of the 2 by 4’s,

particularly in tension, had strengths lower than the

adjusted design values. More information on standard

dimension-based data is available in the conference

paper (4).

The data developed in this study differ from that of the “ingrade” testing program (3). The in-grade mechanical

property data are based on tests of lumber at sawmills

(producers) where moisture content is not equilibrated,

whereas the truss lumber data are based on lumber

sampled from fabricators (users) and after equilibration at

75° F and 64 percent relative humidity.

This report, along with the conference report, should

provide a broad data base for engineering evaluation of

truss reliability.

Table 1.—Physical properties of the truss 2 by 4’s

Because of the preponderance of Southern Pine in the

sample truss lumber, results are presented in two

categories: Southern Pine specimens and all specimens.

Physical Properties

Statistics on moisture content, specific gravity, and crosssectional properties (table 1) are dominated by Southern

Pine, as differences in statistics between the Southern Pinespecimen category and the all-specimen category are small.

Rather than four chord members per truss, the data on

moisture content and specific gravity are based on all seven

test specimens per truss (fig. 1)—one compression, one

tension, and five bending specimens. Moisture content

averaged 12 percent and ranged from 9 to 14 percent,

which is common for lumber in equilibrium at 75° F,

64 percent relative humidity. Specific gravity averaged

about 0.5 and ranged from 0.33 to 0.86.

Standard dimensions for 2 by 4 lumber are 3.5 inches wide

by 1.5 inches thick when surfaced dry (S-DRY), which

implies 15 percent average, 19 percent maximum moisture

content, or kiln dry (KD) which, for Southern Pine, implies

12 percent average, 15 percent maximum moisture content.

Lumber surfaced green (S-GRN) is oversized 1/16 inch in

both dimensions to allow for shrinkage. Storage at 75° F,

64 percent RH should have minimal effect on dimensions of

KD lumber, but S-DRY or S-GRN lumber can be expected

to shrink. All of the Southern Pine lumber had been grade

stamped KD. All other lumber had been grade-stamped SDRY except one 16-specimen sample of Douglas-Fir-Larch

which was grade stamped S-GRN.

Lumber width averaged 3.49 inches, very close to standard,

and had very small COV (table 1). Width, however, ranged

from 5 percent below to 3 percent above standard, and its

distribution was skewed to the smaller measurement (fig. 2).

Property

Moisture content (pct)

Specific gravity2

Width (in.)3

Thickness (in.)3

Area (in.2)

Section modulus (in.3

)

Moment of inertia (in.4

)

Southern Pine

Number of Averspecimens age COV

Pct

1,042 12.1 8.8

1,042 .51 13.9

596 3.49 1.1

596 1.50 1.6

596 5.23 2.3

596 3.05 3.3

596 5.33 4.3

MinimumMaximum

9.1 14.4

.35 .86

3.34 3.60

1.42 1.58

4.79 5.56

2.70 3.29

4.56 5.90

Number of

specimens

1,230

1,230

704

704

704

704

704

All

Aver- Mini- Maxiage COV mum mum

Pct

12.2 8.6 9.1 14.4

.50 14.4 .33 .86

3.49 1.1 3.34 3.60

1.50 1.6 1.40 1.58

5.23 2.3 4.79 5.56

3.05 3.2 2.70 3.29

5.32 4.2 4.56 5.90

1

 Ovendry method.

2

 Based on test volume and ovendry weight.

3

 Based on average of measurements at midlength and 2 to 3 feet in from each end of the chord lumber.

2
Lumber thickness had an average of 1.50 inches and a

slightly larger COV than lumber width (table 1), ranging from

7 percent below to 5 percent above standard (fig. 3).

Standard lumber dimensions (1.5 in. by 3.5 in.) result in

area of 5.25 square inches, section modulus (major axis) of

3.06 cubic inches, and moment of inertia (major axis) of

5.36 inches to the fourth power. Average truss lumber

cross-sectional properties (table 1) closely agreed with

those values, but deviated in individual specimens. Area

ranged from 9 percent below to 6 percent above standard,

section modulus from 12 percent below to 7 percent above,

and moment of inertia from 15 percent below to 10 percent

above. All the distributional characteristics were skewed

toward lower measurements (figs. 4, 5, and 6). Variations in

section properties directly affect variations in mechanical

properties based on standard dimensions, area affects load

capacity and stiffness in compression and tension, section

modulus affects load capacity in bending, and moment of

inertia affects bending stiffness.

Grade Class (GC)

All lumber used in this study had been grade stamped at

mills according to visual stress grading rules. Much of it,

however, had been conservatively rated. For example, many

of the Southern Pine pieces grade-stamped No. 2 could

have met all characteristics (warp, knot size, slope of grain,

wane, and manufacturing imperfections) of Select Structural

(6). Consequently, the truss lumber was reevaluated for

grade at Forest Products Laboratory (FPL).

Grade reevaluation followed grading agency rules for warp.

For knots and slope of grain, however, reevaluations were

based on values in American Society for Testing and

Materials Standard ASTM D 245 (7) corresponding to

limiting strength ratios of the National Grading Rule (NGR)

(6) for softwood dimension lumber. While the NGR sets

maximum knot sizes and slope of grain, the values are

generally conservative relative to strength ratio limitations

and ASTM D 245. Also, the 10 grade classes (table 2)

developed, based on ASTM D 245, provide both closer

estimates of strength ratio than could be done by the NGR

and a nearly linear progression of median strength ratios, at

about 10 times the GC number (classes 0 and 1 were

exceptions).

Figure 2.—Distribution of lumber width.

(M152112)

Figure 3.—Distribution of lumber thickness.

(M152113)

3
Figure 4.—Distribution of lumber crosssectional area. (M 152114)

Figure 5.—Distribution of lumber section

modulus (major axis). (M152115)

4

The data on warp and GC were used to reassign the

lumber to NGR grades. Table 3 shows the tally of

specimens as reassigned solely on the basis of either warp

or knots and slopes of grain, with the mill grade stamp tally

for comparison. Of the 704 specimens of truss lumber, 178

had been grade-stamped as No. 1 and 468 as No. 2. Yet,

570 specimens could have rated No. 1 or better due to

knots and slope of grain, 618 could have rated No. 1 or

better based on warp, only 22 would have rated No. 2

based on knots and slope of grain, and 59 would have

rated No. 2 based on warp. Thus, the reader should

recognize that the lumber obtained for this study was of

generally higher quality than might have been obtained at

another time, a different location, or under different

marketing conditions.

Mechanical Properties

Strength tests in compression, tension, and bending (fig. 1)

were conducted at standard rates of loading (2). The

compression test was full length with lateral support. The

tension test was also full length except for the 2-foot

gripped length on each end. Bending tests were either thirdpoint loading on a span of 54 3/8 inches or center-point

loading (opposite direction from third point) on a span of

361⁄4 inches, both edgewise. Four times as many third-point

tests were conducted per truss as for center-point tests.

The types of bending tests and orientations shown in

figure 1 were meant to simulate typical bending loads on

W-truss chords.

Each type of strength test furnished load-deformation data

for a specific type of static E-bending E (EB), tensile E

(ET), and compressive E (EC). Also, before the cords were

cut or strength tested, the full-span E (EF) was determined

on each chord member in a flatwise dynamic bending test

and the short-span E (ESP) was determined in an edgewise

static bending test. ESP was determined with the same

span and loading arrangement used for third-point bending

strength tests. Depending on length, four to seven ESP

tests were made per chord. Starting at one end of a chord,

successive ESP test segments overlapped each other by

361⁄4 inches (two-thirds of the short span), thereby yielding a

good profile of how ESP varied along the chord length.

Statistics on averages and COV’s of strength and E, based

on actual lumber dimensions, are given in table 4. Table 4

also includes data based on the minimum bending strength

per chord. Used here, minimum means the lowest modulus

of rupture of the bending strength tests per chord, based

on the two third-point and one center-point tests for the top

chord or the two third-point tests for the bottom chord. The
true minimum per chord cannot be guaranteed with the

testing scheme used in this study, because the third-point

bending test imposes maximum moment on the middle third

length of its test span, and the center-point test only at its

midspan, but the lowest moment capacity can occur at any

point in the chord length. Thus, for a 14- foot top chord

length, the chance of imposing the maximum moment on

the weakest point is about 22 percent. This may partially

explain why the minimum bending strengths averaged

considerably higher than either compressive or tensile

strengths (table 4) which reflect weakest points in chords.

Relation of Strength to Other Properties

As suggested by data plots (figs. 7 - 10, pp. 12 - 20),

regression models may be useful for predicting strength

properties of individual chord members. The data plots

show strength of Southern Pine specimens in relation to

the three types of MOE determined in this study and grade

class. Data plots for all specimens were very similar. In

plots with ESP, the minimum ESP per chord (ESPL) was

used.

Some strength properties were found to be more closely

related to E or grade class than other strength properties.

For compression (fig. 7), the strength distribution showed a

good increasing trend with any of the E, a desirable trait for

machine stress rating, and a moderately good increasing

trend with grade class which had a relatively small range.

The tensile strength distributions (fig. 8) had more scatter,

particularly for higher E, and a less well-defined increasing

trend than those for compression. Although tensile strength

tended to increase with E on average, the lower values of

the tensile strength distribution appeared more or less

constant over a considerable portion of the modulus range,

particularly for EF. Thus, E seems a relatively poor

discriminator of tensile strength unless ESP or ET are

above about 1.2(106) pounds per square inch (psi) and EF is

somewhat greater. Grade class does not appear to be a

discriminator of tensile strength except for the two highest

class numbers (fig. 8). For minimum bending strength per

chord (fig. 9) the strength distribution showed as good a

progression with ESP as did compressive strength, but with

a broader range. Thus, ESP appears to be a good

discriminator of the minimum bending strength per chord

and would be useful for machine stress rating for bending

strength. The minimum bending strength regression

distribution on EF was similar to that on ESP, except the

lower values in the distribution were spread over a broader

range for EF than for ESP. The minimum bending strength

distribution showed some progression with grade class for

classes 5 through 9, similar to that for compressive

strength. The-bending strength distribution of individual

specimens also showed good progression with EB, better

for center point than for third point (fig. 10).

Simple regression equations of the form Y = A + BX were

fitted to the data shown in each plot (figs. 7-10), where

Y = strength in compression, tension, minimum bending

strength per chord, third-point bending strength, or centerpoint bending strength, and X = EF, ESPL, EC, ET, EB, or

Figure 6.—Distribution of lumber moment of

inertia (major axis). (M 152116)

GC. Multiple regressions, Y = A + BX1 + CX2, were also

fitted to the data where X2 = GC. An additional multiple

regression of the same form fitted strength on X, = ESPH

(the highest ESP per chord) and X2 = ER (the ratio of

ESPL to ESPH per chord); this will be referred to as the

E-ratio model. Results of regression calculations are shown

in table 5, which includes data on standard deviation about

the regression, S, and coefficient of determination, (r 2) as

well as the regression coefficients, A, B, and C.

For compressive strength, the three types of MOE were all

about equal in accounting for strength variation, about

60 percent as evident in the r

2

’S of table 5. While grade

class by itself was a poor correlator with compressive

strength (r

2

 = 0.2) it did add significantly in the multiple

regression with any of the three types of E, accounting for

an additional 5 to 8 percent of the variation in strength. The

E-ratio multiple regression accounted for about 63 percent

of the variation in compressive strength, but it did not

appear to be particularly better than the simple regressions

with ESPL or EC.

5
Table 2.—GC limits on knots and slope of grain

Lower limit of Median GC

Maximum knot size1 Worst slope of grain1,2

NGR

GC strength strength Bending Bending grade

ratio ratio

Compres- Compres- Bending

sion and tension and tension

centerline knots edge knots sion and tension equivalent

1

 Based on ASTM D 245 (1).

2

 Strength ratios for slope of grain of 1:3 and worse are estimates.

Table 3.—Tally of lumber, based on American softwood lumber stress grade limitations and mill grading

NGR Grade based solely Grade based solely on

grade on warp1 knots and slope of grain Southern

Pine

Mill-grade stamped

Douglas-Fir- Hem-Fir2

Larch2 Spruce-PineFir3

1

 Data missing on seven specimens.

2

 Includes some Canadian lumber.

3

 Includes Canadian Spruce-Pine-Fir and similar species grouping

from the United States.

4

 About 53 percent stamped Dense.

5

 About 25 percent stamped Dense.

6

 Not a stress grade.

7

 Includes six specimens due to cracks, heart shake, or end splits.

6
For tensile strength, ET was the best sole correlator (table

5) accounting for 45 percent of the tensile strength

variation for the Southern Pine specimens and 49 percent

for all specimens. As for compression, grade class was not

a particularly good correlator of tensile strength by itself,

but it did contribute significantly to the multiple regressions

with E, accounting for an additional 13 to 20 percent of the

tensile strength variation. The E-ratio model was not

appreciably better as a correlator of tensile strength than

any of the E’s by themselves.

The E-ratio model, EF, and ESPL were about equal in

accounting for variation in minimum bending strength per

chord, about 45 to 49 percent (table 5). Again, grade class

was not particularly good as a correlator of minimum

bending strength but did contribute significantly in the

multiple regressions with E, accounting for an additional

strength variation of 4 to 6 percent.

EB was a reasonably good correlator with bending strength

of individual specimens (table 5) accounting for about

54 percent of third-point bending strength and about

63 percent of center-point bending strength. Grade class

accounted for an additional 6 or 7 percent of the third-point

bending strength variation, but did not contribute any

significance in the multiple regression with EB on centerpoint bending strength. The lack of significance of grade

class for the latter may be due to the low probability that a

grade-controlling characteristic will occur at the highest

stressed portion of a specimen, that is, at the central load

point in the center-point test.

Overall, the strength regressions showed the highest

correlations for compression and the lowest for tension.

This reflects the lower standard deviations about the

regression for compression (table 5) but compressive

strength also had the lowest variation overall (table 4).

Data plots of EC, ET, and EB on EF are given in Figure 11

(pp. 21 - 24) and the supporting regression statistics in

table 6. EC and ET showed high levels of correlation with

EF (r

2

 > 0.90). EB and EF were less well correlated (r

2

 <

0.83), probably because EF reflected properties of wood

over the full chord length of the truss lumber, whereas EB

reflected properties over less than one-half of a chord

length.

Table 4.—Mechanical properties of the truss 2 by 4’s1

Property

Southern Pine

specimens All specimens

Number of Aver- Number of Averspecimens age COV specimens age COV

Compressive

strength 148

Tensile strength 149

Bending strength

Minimum per

chord

Third point

Center point

299

598

147

EC

E T

147

147

E

ESPL

Third point EB

Center point EB

EF

596

592

145

592

Pct

4,400 25 176 4,390 25

3,830 53 176 3,960 52

7,300 38 352

8,480 35 704

10,110 29 175

1.56 28 174

1.59 30 174

1.48 28 704

1.69 26 698

1.56 25 173

1.65 27 699

Pct

7,200 37

8,330 35

9,930 30

1.59 28

1.62 29

1.49 28

1.68 26

1.55 25

1.67 26

1

 Averages based on psi for strength and 106 psi for E.

Correlations of Bending Strengths Within

Chords

Two ways to present correlations of the within-chord

bending strengths are 1) by simple correlation coefficients

for pairs of within-chord bending strengths, and 2) by

frequency classification. The following tabulation shows

correlation coefficients for within-chord pairs of bending

strengths for the 176 upper chords and 176 lower chords.

Strength Comparison Correlation Coefficient, r

UPPER CHORDS

Inner-Middle 0.579

Inner-Outer .600

Middle-Outer .594

LOWER CHORDS

Inner-Outer .551

The inner-outer r’s shown in the tabulation can be

interpreted to mean that 30 to 36 percent of the variation of

within-chord paired strengths can be accounted for by

knowing the strength of one of the pairs, suggesting that

the strength at one position in a chord does not necessarily

define the strength of another position very accurately.

7
Table 5.—Regression of strength on E and GC1,2

Southern Pine All

X 1 X 2 Number Standard Standard of A B C deviation r2 Number of A B C deviation r 2

specimens about specimens about regression regression

Y

0.58

.62

.61.21.65.67

.66.63.40.43.49.29.59

.56

.64

.43.47.46.20.52.50.49.55

.61.65

.65

Compressive strength EF

ESPL

EC

GC

EF

ESPL

EC

ESPH

EF

ESPL

E-r

147 1,245148 1,374

148 1,299

148 625147 – 939148 – 515

148 – 696148 – 1,209149 – 717149 – 625147 – 774

149 – 159149 – 3,700149 – 3,064

147 – 3,364

149 – 3,648

1,949

2,113

1,983

486

1,798

1,9431,8311,867

2,823

3,049

2,904

593

2,5492,6062,5812,7024,2764,540

869

3,7223,9064,157

4,872

4,2285,8175,525

—

——

—

313

274

287

2,825

——

—

—

509

459

460

a3,182

——

—

496

470

c4,413

—

575

—

d228

681667

650979615618

593659

1,6221,6111,5161,749

1,3481,400

1,2851,608

2,0102,0492,446

1,8881,946

2,0172,016

1,8571,8201,805

0.61 174

.62 176.64 176

.19 176.68 174.68 176

.70 176.63 176.37 176.38 176.45 174.27 176.57 176

.54 176

.61 174

.39 176

1,2951,334

1,365

652

– 665– 285– 288

– 1,246

– 954– 845– 988

– 39

– 3,662– 2,790

– 3,281– 4,481

180

500

1,856

– 1,877

– 1,333

– 3,789

159

– 2,416

639

– 540

1,8802,1101,900

481

1,6771,9121,7191,867

702

670678

963

644

628

634

664

——

——

295

245250

2,830

———

—

485

408430

b4,002

——

—

—

GCGC

GC

ER

—

—

——

GCGC

GC

ER

—

—

—

GCGCER

3,0183,2343,069

589

2,661

2,681

2,678

2,845

1,5941,5531,4681,7401,321

1,375

1,2431,563

Tensile strength

GC

EF

ESPL

E-r

ESPH

Bending strength,

minimum per chord 296 90

299 453299 1,008296 -2,570

299 -1,996299 -4,070

.47 349.45 352.22 352.53 349

.51 352.47 352

4,1484,429

740

3,6583,8944,104

1,9711,979

2,422

1,8761,9041,940

EF

ESPL

GC

EF

ESPL

ESPH

Bending strength,

individual specimens

Third point

Center point

598 284598 -3,025

147 1,054

147 -273

.54 704

.61 704.61 175

.62 175

4,8674,2366,0145,777

1,964

1,8381,7461,735

EB —

EB GCEB —EB GC

—

—

479

—

e

—

—

400

366

198

4,089

1For E in 106 psi.

2 Each variable significant at the 0.01 percent level or better, except for coefficients with “a” (1.3% level), “b” (0.03% level), “c” (0.02% level), “d” (6.4% level, not significant), and “e”

(7.6% level, not significant).

.

8
Table 6.—Regression of static E on dynamic E1

Standard

Model N A B deviation r

2

about

regression

EC = A + B (EF)

ET = A + B (EF)

EB = A + B (EF)

Third point

Center point

EC = A + B (EF)

ET = A + B (EF)

EB = A + B (EF)

Third point

Center point

SOUTHERN PINE

147 0.006 0.962

147 – .067 1.032

592 .196 .881

145 .237 .777

ALL

174 – .002 .968

174 – .083 1.047

698 .183 .883 .212 .77

173 .230 .772 .163 .82

0.130

.125

.217 .76

.165 .82

.127

.128

0.91

.93

.92

.93

1

 For E in 106 psi.

Table 7.—Frequency of lower chord bending strength (in psi)

for 176 chords-two-way classification

Inner Outer strength class

strength 2,000 4,000 6,000 8,000 10,000 12,000 14,000

class to to to to to to to

3,999 5,999 7,999 9,999 11,999 13,999 15,999

0 to 1,999 — —— 1— — —

2,000 to 3,999 4 3 3 2 —1—

4,000 to 5,999 1 11 14 4 2 — —

6,000 to 7,999 4 9 11 12 7 — —

8,000 to 9,999 — 4 4 15 7 1 1

10,000 to 11,999 — 2 8 10 10 5 3

12,000 to 13,999 — — 1— 372

14,000 to 15,999 — ——— — 2 1

16,000 to 17,999 — 1—— — — —

Table 7 presents withinchord correlations for lower chords

by two-way frequency classification, and table 8 shows

them for upper chords by three-way frequency

classification. The three-way classification of table 8 is

necessary because of the three bending strength tests per

upper chord.

Table 7, easier to evaluate than table 8, shows a central

tendency in that the larger cell frequencies tend to lie on or

near the diagonal cells for equal inner and outer strength

classes. Thus, table 7 supports the concept that the two

bending strengths for a lower chord member tend to be

approximately equal, but that the two strengths can be

quite different for some chords. For example, 15 of the

chords had both inner and outer strengths that ranged

between 8,000 and 10,000 psi; however, another chord had

an outer strength in that range but an inner strength

ranging between 0 and 2,000 psi.

Table 8 shows similar trends to those in table 7, except

that cell frequencies for the inner- and outer-strength

classes in table 8 are considerably diluted by the middlechord strength classification. Thus, the central tendency for

all three strength values for an upper chord to be

approximately equal is not very obvious. Also, several cells

in table 8 indicate that the strength of one portion of an

upper chord was less than one-half the strength of another

portion of the chord. The first cell shown (middle-strength

class = 0 to 1,999 psi) is an example of an even wider

discrepancy in strength, but the chord represented by that

cell was not typical because it arrived at the Forest

Products Laboratory broken at midlength. Such a chord

would obviously be discarded during truss manufacture.

9
Table 8.—Frequency of upper chord bending strength (in psi) for 176 chords–three-way classification

Middle

strength

class

Inner

strength

class

0

to

1,999

2,000

to

3,999

4,000

to

5,999

to

9,999

to to to to to

7,999 11,999 13,999 15,999 17,999

Outer strength class

6,000 8,000 10,000 12,000 14,000 16,000

0 to 1,999

2,000 to 3,999

4,000 to 5,999

6,000 to 7,999

8,000 to 9,999

10,000 to 11,999

12,000 to 13,999

14,000 to 15,999

16,000 to 17,999

18,000 to 19,999

8,000 to 9,999

4,000 to 5,999

8,000 to 7,999

2,000 to 3,999

4,000 to 5,999

6,000 to 7,999

8,000 to 9,999

10,000 to 11,999

4,000 to 5,999

6,000 to 7,999

8,000 to 9,999

2,000 to 3,999

4,000 to 5,999

6,000 to 7,999

8,000 to 9,999

10,000 to 11,999

12,000 to 13,999

2,000 to 3,999

4,000 to 5,999

6,000 to 7,999

8,000 to 9,999

10,000 to 11,999

12,000 to 13,999

4,000 to 5,999

6,000 to 7,999

8,000 to 9,999

10,000 to 11,999

12,000 to 13,999

10,000 to 11,999

12,000 to 13,999

14,000 to 15,999

10,000 to 11,999

16,000 to 17,999

—

—

—

1

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

1

1

1

—

—

4

2

1

—

1

1

1

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

1

—

5

3

—

1

2

2

2

1

2

2

3

—

—

1

2

—

—

—

—

—

—

—

2

1

—

—

—

—

—

—

1

—

1

—

—

—

1

4

2

3

—

4

5

2

1

—

—

3

5

2

2

—

1

—

2

2

—

—

1

—

1

—

1

—

—

—

—

—

—

—

2

3

—

—

2

4

1

4

—

—

2

5

3

2

3

—

2

1

1

1

1

1

—

—

—

—

—

—

—

—

—

1

—

—

—

1

—

—

1

4

—

1

1

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3

3

1

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4

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4

2

2

3

—

—

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—

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3

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1

—

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3

3

1

1

1

—

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—

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—

—

—

—

1

—

—

1

—

—

—

—

1

—

1

—

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—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

1

1

—

—

10
Conclusions Literature Cited

Truss lumber sampled from fabricators in Illinois had

dimensional characteristics at 12 percent moisture content

that averaged very close to those for the standard size of

nominal 2 by 4’s. The distributions of those characteristics,

however, tended to be skewed toward lower

measurements, with variations that may affect compressive

and tensile strength up to 9 percent, bending strength up to

12 percent, and E up to 15 percent.

Since mill grading of the lumber specimens was generally

conservative compared to optimum grading based on the

NGR limitations, strength results from this study may be

different from those that might have been obtained under

different lumber marketing conditions.

Relations of strength in compression, tension, or bending

on ESP appeared adequate for strength prediction or

machine stress rating. ESP accounted for 38 to 62 percent

of the strength variation, depending on loading mode. EF

was about equal to ESP in accounting for strength

variation, but the lower values in the strength distributions

were not as well behaved as for ESP. GC, a function of

lumber strength ratio, was inferior to E as a predictor, but it

did contribute significantly in multiple regressions with E,

accounting for an additional 4 to 20 percent of strength

variation.

The two or three short-span bending strengths measured at

different positions in a specimen showed low correlation,

suggesting that the bending strength at one position in a

specimen can be quite different from that at another

position.

1. American Society for Testing and Materials. Standard

methods for establishing structural grades and

allowable properties for visually graded lumber. ASTM

D 245-74. 1978.

2. American Society for Testing and Materials. Standard

methods of static tests of timbers in structural sizes.

ASTM D 198-76. 1978.

3. Galligan, W. L.; Green, D. W.; Gromala, D. S.; Haskell,

J. H. Evaluation of lumber properties in the United

States and their application to structural research.

Forest Prod. J. 30(10):45-50; 1980.

4. Gerhards, C. C.; Percival, D. H. Species, grades, and

mechanical properties of lumber sampled from truss

fabricators. Proc. Metal Plate Wood Truss Conf.,

Forest Prod. Res. Soc. P-79-28, p. 21-31; 1979.

5. National Forest Products Association. Design values for

wood construction. A supplement to the 1977 edition

of National Design Specification for Wood

Construction. NFPA, Washington, D.C.; 1977.

6. Southern Pine Inspection Bureau. National grading rule

for dimension lumber. In: SPIB Grading Rules, 1977

edition, Pensacola, Fla.; p. 65-90; 1977.
12

Figure 7a.---- Data plots of compressive strength on EF and ESPL A = 1 observation, B = 2 observations, etc.

(M152117, M152118)

Compressive Strength (10

3 psi) Compressive Strength (103 psi)
Figure 7b.—Data plots of compressive strength on EC and GC. A = 1 observation, B = 2 observations, etc. (M152119,

M152120)

Compressive Strength (103 Compressive Strength (10 psi) 3 psi)

13

GC

EC (106 psi)
Figure 8a.—Data plots of tensile strength on EF. A = 1 observation, B = 2 observations, etc. (M152121)

Figure 8b.—Data plots of tensile strength on ESPL. A = 1 observation, B = 2 observations, etc. (M152122)

ESPL(106 psi)

ESPL(106 psi)

Tensile Strength (103 Tensile Strength (10 psi) 3 psi)

14
15

Figure 8c. ----Data plots of tensile strength on ET. A = 1 observations B = 2 observations, etc. (M152123)

ET (106 psi)

Figure 8d.----Data plots of tensile strength on GC. A = 1 observation, B -- 2 observations, etc. (M152124)

GC

 psi)3 Tensile Strength (10 psi)

3 Tensile Strength (10
EF (106 psi)

Figure 9a.—Data plots of minimum bending strength per chord on EF. A = 7 observation, B = 2 observations, etc.

(M152125)

16

 psi)3 Bending Strength, Minimun Per Chord (10
17

ESPL (106 psi)

Figure 9b.---Data plots of minimum bending strength per chord on ESPL A = 1 observation, B = 2 observations, etc.

(M152126)
GC

Figure 9c.—Data plots of minimum bending strength per chord on GC. A = 1 observation, B = 2 observations, etc.(M152127)

18

Bending Strength, Minimum Per Chord (10

3 psi)
EB (106 psi)

Figure 10a.—Data plots of third-point bending strength on EB. A = 1 observation, B = 2 observations, etc. (M152128)

19
EB (106 psi)

Figure 10b.—Data plots of center-point bending strength on EB. A = 1 observation, B = 2 observations, etc. (M152129)
21
22
EF (106 psi)

Figure 11c.—Data plots of EB, third-point, on EF. A = 1 observation, B = 2 observations, etc (M152132)
24 2.5-9/83
Gerhards, C. C.; Characterization of physical and mechanical properties of 2 by 4

truss lumber; USDA Forest Serv. Res. Pap. FPL-431, 24 p., Madison, WI:

Forest Products Laboratory; 1983.

This paper summarizes data on dimensional characteristics, optimum grade, and

regressions of strength on modulus of elasticity and grade class (a function of

strength ratio) of lumber specimens sampled from truss fabricators in Illinois. The

two or three measures of bending strength at different positions in a specimen

showed low correlation, suggesting that bending strength at one position in a

specimen can be quite different from that at another position.

KEYWORDS: Physical properties, Mechanical properties, 2 by 4’s, truss lumber,

bending, tension, compression, strength, modulus of rupture, modulus of

elasticity, moisture content, grade, width, thickness, distributions, regressions