Mechanical Grading of

6-Inch-Diameter Lodgepole 

Pine Logs for the Travelers’ 

Rest and Rattlesnake 

Creek Bridges

David W. Green

James W. Evans

Joseph F. Murphy

Cherilyn A. Hatfield

Thomas M. Gorman

United States

Department of

Agriculture

Forest Service

Forest

Products

Laboratory

Research

Note

FPL–RN–0297
Abstract

Forest Products Laboratory (FPL) assistance was requested 

in mechanical grading of logs for two cable suspension 

bridges intended for pedestrian use in parks near Missoula, 

Montana. Two hundred ninety two lodgepole pine logs were 

obtained from a beetle-killed stand near Elk City, Idaho, 

by Porterbuilt, Inc., of Hamilton, Montana, and machined 

(dowelled) to a constant diameter of 6 in. The logs were 

visually graded by Timber Products Inspection, Inc., of 

Longview, Washington, and mechanically graded by FPL 

staff using procedures developed in previous research. Of 

the logs selected, 236 (80.8%) made at least No. 3 visual 

grade and were thus eligible for mechanical grading. Two 

hundred fifteen of the logs (74% of total) made a mechanical grade having an allowable bending strength–MOE assignment of 2150 Fb–1.4E, 21 of the logs (7%) that failed to 

make this mechanical grade could still maintain the assigned 

visual grade, and 56 logs (19%) would have to be used in 

non-structural applications. By comparison, of the 236 logs 

that made at least No. 3 visual grade, 188 (64%) graded as 

TP No.1, which is assigned allowable properties of 1250 

Fb–1.1E. Thus mechanical grading is shown to provide a 

more efficient property assignment than does visual grading.

Keywords: mechanical grading, lodgepole pine, logs, 

timber bridge

June 2005

Green, David W.; Evans, James W.; Murphy, Joseph F.; Hatfield, Cherilyn 

A. 2005. Mechanical grading of 6-inch-diameter lodgepole pine logs for 

the travelers’ rest and rattlesnake creek bridges. Research Note 

FPL-RN-0297. Madison, WI: U.S. Department of Agriculture, Forest 

Service, Forest Products Laboratory. 17 p.

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Acknowledgments

Funding for the mechanical grading of the logs for this 

study was provided by the Forest Products Laboratory. 

Visual grading services were provided by Timber Products 

Inspection, Inc., Western Division, Vancouver, Washington. 

The authors acknowledge the support given by Ron Porter 

and his employees at Porterbuilt, Inc., Hamilton, Montana, 

in providing an excellent location for the grading and material handling equipment for moving the logs. We also 

acknowledge background information and resource discussions provided by Dean Graham, USDA Forest Service, 

State and Private Forestry, Technology Marketing Unit, Missoula, Montana, and Craig Rawlings, Montana Community 

Development Corporation, Missoula, Montana. Finally, we 

acknowledge many productive discussions about this project 

with Tom Beaudette and his staff at Beaudette Consulting 

Engineers, Missoula, Montana.

SI conversion 

Inch–pound unit Multiply by SI unit

inch (in.) 25.4 millimeter (mm)

foot 0.3048 meter

lb/in2 0.45366.894 kilopascal (kPa)

T°C = (T°F – 32)/1.8

Contents

Executive Summary .......................................................... i

Introduction ....................................................................... 1

Background ....................................................................... 3

Methods............................................................................. 9

Results ............................................................................... 10

Recommendations ............................................................. 13

Literature Cited ................................................................. 14 

Appendix A–Mechanical Grading Worksheet .................. 15

Appendix B–Grade Assignments for Individual Logs ...... 16
Executive Summary

Background

Beaudette Consulting Engineers (BCE) of Missoula, 

Montana, requested assistance from the Forest Products 

Laboratory (FPL), Madison, Wisconsin, in mechanically 

grading lodgepole pine logs to use in building two cable 

suspension bridges in western Montana. The grading project 

is a demonstration of a proposed mechanical grading system 

developed by FPL in cooperative research studies with Timber Products Inspection, Inc. (TP), of Conyers, Georgia, and 

the University of Idaho in Moscow, Idaho. Bridge design 

and selection of log design values are the responsibility of 

the engineering consulting firm.

Objectives

The project’s objective is to provide the engineering firm 

with a variety of grade options for using small-diameter 

lodgepole pine logs more efficiently in these two engineered 

roundwood structures.

Procedures

The 292 logs obtained for this demonstration were cut from 

beetle-killed lodgepole pine trees salvaged from a stand 

near Elk City, Idaho. Candidate logs were pre-selected by 

BCE prior to processing. The logs were turned to a uniform 

diameter of 6 in. and cut to lengths specified by BCE at 

Portbuilt, Inc., in Hamilton, Montana. The logs were visually graded by a TP quality supervisor. Forest Products 

Laboratory scientists determined the modulus of elasticity 

(MOE) of all logs in transverse vibration (Etv). Few data 

exist on the properties of small-diameter lodgepole pine logs 

machined to a constant diameter. So using available data on 

3- to 6-in.-diameter Douglas-fir and ponderosa pine logs, 

we developed the property relationships needed to assign 

mechanical grades to the logs in our study. To qualify for 

a mechanical grade, the logs first had to meet at least a TP 

No. 3 visual grade. Assignment of a mechanical grade was 

then based on the measured Etv values, with design values 

in bending (Fb and MOE), tension parallel to the grain (Ft), 

and compression parallel to the grain (Fc||) developed from 

previous studies. Allowable shear strength (Fv) and strength 

in compression perpendicular to the grain (Fc⊥) are the same 

as those assigned by TP to visual grades of lodgepole pine.

Results

The visual grades of the 292 logs selected for this study 

were 188 No. 1 (64.4%), 21 No. 2 (7.2%), 27 No. 3 (9.2%), 

and 56 culls (19.2%). Excessive knot size was the largest 

single defect type in the cull logs. Thus, 236 of the logs 

(80.8%) were eligible for mechanical grading. The average 

moisture content of the logs was 19%. 

A discussion of property relationships from the various 

available data sets and pertinent literature led to the following conclusions concerning assignment of allowable properties. The relationship between static MOE and Etv was 

shown to be independent of species for 3- to 6-in.-diameter 

logs machined to a constant diameter. Equation (1) (page 6) 

for the combined Douglas-fir and ponderosa pine logs is 

MOE = 0.891 × Etv – 0.001 

R2 = 0.97, where MOE and Etv values are given in 

106 lb/in2. 

Two alternatives were developed for estimating the modulus 

of rupture (MOR). The first was based on the MOR–MOE 

relationship for ponderosa pine logs machined to constant 

diameter of 3 to 6 in. 

This alternative generally produces a more conservative estimate and is a result of a statistical comparison of equations 

fit to several alternative data sets. The 90% lower confidence 

interval of this regression is Equation (7) (page 12):

MOR0.901cl = 2.323 × MOE + 1.850 

for MOE in 106 lb/in2 and MOR in 103 lb/in2. Limited data 

on 44 pieces of lodgepole pine machined to a constant diameter of 3.5 in. and technical judgment based on data for 

9-in.-diameter logs suggest that a more representative 

MOE–MOR relationship might be obtained using the 

combined Douglas-fir and ponderosa pine data for logs machined to a uniform diameter of 3 to 6 in. The 90% lower 

confidence interval for the second alternative is Equation (8) 

(page 13): 

MOR0.901cl = 5.125 × MOE – 0.532

Ultimate compression stress parallel to the grain (UCS) was 

estimated from a conservative equation fit to data on the 

bending–compression relationship for 3- to 6-in.-diameter 

Douglas-fir and ponderosa pine logs with taper (Eq. (6), 

page 8). This equation is 

UCS/MOR = 0.00704(MOR)2 – 0.1130(MOR) + 0.750 

for MOR ≤8.018 × 103 lb/in2 or UCS/MOR = 0.30, for 

MOR > 8.081 × 103 lb/in2.

Very limited data on the ultimate tensile stress parallel to 

the grain (UTS) of small-diameter lodgepole pine logs suggested that a more conservative procedure be used than the 

ratio of UTS/MOR = 0.55 (page 8) given in ASTM D 3957. 

The ratio adopted in this study is UTS/MOR = 0.45, which 

is the relationship assumed in ASTM D 6570 for mechanically graded dimension lumber. Allowable properties for 

mechanically graded lodgepole pine logs are developed for 

a variety of grade combinations. These include combinations where two mechanical grades are produced and some 

where all logs are graded into one mechanical grade. Only 

alternatives that involve one mechanical grade are shown in 

this summary. The combinations involving two grades are 
ii

Mechanical 

grade

Number

of logs

Option 1a,b Option 2a,b

Fb

(lb/in2)

Ft

(lb/in2)

Fc||

(lb/in2)

MOE

(×106 lb/in2)

Fb

(lb/in2)

Ft

(lb/in2)

Fc||

(lb/in2)

MOE

(×106 lb/in2)

1.9E 26 2,600 1,150 975 1.9 3,550 1,600 1,150 1.9

 1.8E 49 2,500 1,150 975 1.8 3,350 1,500 1,100 1.8

 1.7E 88 2,450 1,100 950 1.7 3,150 1,400 1,100 1.7

 1.6E 147 2,350 1,050 950 1.6 2,950 1,350 1,050 1.6

 1.5E 196 2,250 1,000 925 1.5 2,750 1,250 1,000 1.5

 1.4E 215 2,150 950 900 1.4 2,550 1,150 1,000 1.4

 1.3E 232 2,050 925 900 1.3 2,350 1,050 950 1.3

 1.2E 233 1,950 875 875 1.2 2,150 975 900 1.2

 1.1E 235 1,900 850 850 1.1 1,950 875 875 1.1

Original visual grades

 No. 1 188 1,250 675 625 1.1 1,250 675 625 1.1

 No. 2 21 1,050 575 525 1.1 1,050 575 525 1.1

 No. 3 27 600 325 300 0.9 600 325 300 0.9

 Cull 56 — — — — — — — —

summarized beginning on page 10 and are shown in Tables 

7 and 8. Design values for visually graded logs are shown 

for comparison.

Recommendations

Both alternatives for mechanical grading generally provide grades with design values higher than those assigned 

through visual grading. If the assigned values developed 

using the more conservative option 1 are adequate, this 

would be the preferred alternative. If higher strength values 

are required, then option 2 could be used. A research study 

tentatively planned to begin in 2006 should provide conclusive evidence on the effect of species on the MOE–MOR 

relationship for small-diameter lodgepole pine logs. We do 

not recommend that the equation presented in this paper be 

used to assign strength values to individual logs. These procedures are valid only for logs grouped into grades.

Potential design values for lodgepole pine logs

aOption 1 is based only on data for ponderosa pine, and option 2 is based on the combined ponderosa pine and Douglas-fir data.

bFv = 95 lb/in2 and Fc⊥ = 395 lb/in2 for all grades (Log Home Grading Rules (including supplements 1–5). 1995. Timber 

Products Inspection, Inc., Conyers, Georgia).
Introduction

The critical structural members for two wooden pedestrian 

bridges were visually graded by Timber Products Inspection, 

Inc. (TP), of Conyers, Georgia, and their properties estimated using a proposed mechanical grading system for round 

structural members developed cooperatively by the Forest 

Products Laboratory (FPL) in Madison, Wisconsin, and the 

University of Idaho, Moscow, Idaho. One of these bridges is 

to be a 165-ft span cable suspension bridge over Lolo Creek 

at Travelers’ Rest State Park, Lolo, Montana, and the other a 

120-ft span cable suspension bridge over Rattlesnake Creek 

in Missoula, Montana. Most structural members are lodgepole pine (Pinus contorta) machined to a uniform diameter 

of 6 in. The primary objective of this report is to summarize 

the visual and mechanical grading options for the lodgepole 

pine logs so that the engineering firm can use the logs most 

efficiently in their bridge design. The paper also documents 

the first commercial application of mechanical grading to 

small-diameter logs.

Travelers’ Rest Bridge

From September 9 to 11, 1805, and June 30 to July 3, 1806, 

Lewis and Clark’s Corps of Discovery camped along a creek 

they called Travelers’ Rest. Here they took a needed rest and 

made sure they were adequately equipped for their journey 

ahead. The first time they stopped at this creek was in preparation for racing the winter into the Bitterroot Mountains, 

and the second time was on their return trip prior to splitting the party for exploratory jaunts to the Great Falls of the 

Missouri (Lewis) and the Yellowstone River region (Clark). 

This small cross-roads campsite is of special historical 

importance because it is one of only two places along the 

Lewis and Clark journey where physical evidence verifies 

their presence.

Travelers’ Rest State Park is located about 10 miles south 

of Missoula, Montana, near the intersection of Highways 

93 and 12. It is a relatively new park, with park offices and 

facilities that opened in 2003. Plans for the park include 

the establishment of areas telling the story of the Lewis and 

Clark Expedition, the Native American presence, the experiences of the pioneer homesteads, and the natural history of 

the area (Fig. 1). A parking lot will be established on the 

west side of what we now call Lolo Creek, with the historical areas on the other side. A bridge will be constructed 

across Lolo Creek to minimize environmental damage and 

to connect the parking lot to the historical areas. 

The Travelers’ Rest bridge was designed by the engineering firm. It will be a 165-ft cable suspension bridge with a 

main span of 110 ft and side spans of 27.5 ft (Fig. 2). Forest 

Service experience has shown that the tops and bottoms of 

posts in the towers of suspension bridges are very vulnerable to decay. Sometimes an entire bridge must be taken 

down to repair a tower post. An innovative solution is a 

composite tower composed of four logs for each of the four 

cable support towers. Only two logs per tower will be required to support the bridge; therefore, it will allow an individual log to be removed for repair or replacement. 

Rattlesnake Creek Bridge

The Upper Rattlesnake Creek Bridge will be part of the City 

of Missoula trail system. It will connect the Duncan Drive 

terminus on the west side of Rattlesnake Creek with the 

city’s trail system on the east side of the creek (Fig. 3). The 

east side trail system connects with the Rattlesnake National 

Recreational Area within the Lolo National Forest. The 

bridge is in an area of very high recreational use and will 

have high public visibility.

The Rattlesnake Creek Bridge was also designed by the 

engineering firm. It will be a 120-ft-span cable suspension 

bridge with a main span of 80 ft and back spans of 20 ft 

(Fig. 4). The bridge is designed to support the dead load for 

the main span. Constructed and placed on the abutments, 

Mechanical Grading of 6-Inch-Diameter 

Lodgepole Pine Logs for the Travelers’ Rest 

and Rattlesnake Creek Bridges

David W. Green, Supervisory Research Engineer

James W. Evans, Supervisory Mathematical Statistician

Joseph F. Murphy, Research Engineer

Cherilyn A. Hatfield, Statistician

Forest Products Laboratory, Madison, Wisconsin

Thomas M. Gorman, Professor and Department Head 

Department of Forest Products, University of Idaho, Moscow, Idaho
Research Note FPL-RN-0297

2

Figure 1—Conceptual master plan for Travelers’ Rest State Park, Lolo, Montana.

Figure 2—Cable suspension bridge planned for Travelers’ Rest State Park, Lolo, Montana.
Mechanical Grading of 6-Inch-Diameter Lodgepole Pine Logs for the Travelers’ Rest and Rattlesnake Creek Bridges

3

the cable stays will be attached to support the required live 

loads. All bridge components will be composed of 6-in.- 

diameter lodgepole pine logs machined to a uniform crosssection. Towers for the cable will be 10-in.-diameter 

lodgepole pine.

Background

Visual Grading and Property Assignment of 

Logs by ASTM D 3957

ASTM D 3957, Standard Practices for Establishing Stress 

Grades for Structural Members Used in Log Buildings, was 

first approved in 1980, with the current revision adopted 

in 1993 (ASTM 2004). In addition to wall logs, two types 

of structural round timbers are used in log home construction: unsawn and sawn round timbers (TP 1995). Unsawn 

round timbers are primarily intended for bending or truss 

members. Sawn round timbers may have a flattened surface 

that is sawn or shaved along one side and are also primarily 

intended for use as bending members. The sawn surface is 

limited to a penetration of no more than 0.30 of the radius 

of the round log. This limits the reduction in the cross section to less than 10%. Timber Products Inspection, Inc., has 

developed structural grading rules for No. 1, 2, and 3 grades 

of sawn round timbers (TP 1995). A flattened surface on one 

side is not a grade requirement for “sawn round timber.” 

A round log can be graded as No. 1, 2, or 3, but the allowable properties would be derived assuming that the flattened 

surface was present. Logs of all grades may also be used 

as compression members, but the logs for this usage do not 

usually have a flattened surface. As with visually graded dimension lumber or structural timbers, the grade description 

of structural logs is a combination of limits on characteristics that affect strength and possibly serviceability for the 

intended application. Table 1 summarizes the limits on knot 

size and slope of grain for four TP grades. In addition, there 

are limits on potential decay associated with knots, shake, 

splits, and compression wood. Examples of serviceability 

factors include limits on lack of “roundness” and excessive 

warp and wane. All these visual grades are suitable for use 

in timber bridges if they have allowable properties high 

enough for the intended application. 

Figure 3—Location of Rattlesnake Creek Bridge site 

northeast of Missoula, Montana.

Table 1—Limits on knot size and slope of grain and 

allowable properties for visually graded lodgepole 

pine structural round timbersa

Gradeb

Maximum

knot size

(in. diameter)

Maximum 

slope of

grain

Allowable propertiesc

Fb E Fc

Unsawn 1/2 1:15 1,500 1.1 775

No. 1 1/3 1:14 1,250 1.1 625

No. 2 1/2 1:10 1,050 1.1 525

No. 3 3/4 1:6 600 0.9 300

aTP (1995). Rules apply to all diameters.

bOther limits on grade characteristics are given in TP (1995). 

cFb, fifth percentile MOR/2.1 (lb/in2); E, mean MOE (106 lb/in2).

Figure 4—Schematic drawing of the Rattlesnake Creek Bridge.
4

Allowable properties for sawn round timbers are derived 

from clear wood data, modified by strength ratios set forth 

in ASTM D 3957 and D 2899 (ASTM 2004). This clear 

wood approach is therefore very similar to the ASTM D 

245 (ASTM 2004) procedures once used to derive allowable properties for all dimension lumber in the United States 

and still used for structural timbers. Allowable properties in 

bending (Fb), modulus of elasticity (MOE), and compression parallel to grain (Fc||) for lodgepole pine are also given 

in Table 1. Allowable properties of visually graded lodgepole pine are also established for tensile strength parallel to 

grain, strength in compression perpendicular to grain, and 

shear strength parallel to grain.

Technical Basis for Mechanical Grading of 

Small-Diameter Logs

The proposed mechanical grading system for the 6-in.-

diameter lodgepole pine logs requires the following:

1. Establishment of a relationship between modulus of 

 elasticity in transverse vibration (Etv) and static 

 modulus of elasticity (MOE)

2. Establishment of a relationship between modulus of rup- 

 ture (MOR) and MOE

3. Establishment of a relationship between ultimate com- 

 pression stress parallel to the grain (UCS) and MOR

4. Procedures for estimating other allowable properties

The background for establishment of the required relationships will be summarized in this section.

A study was initiated in 2000 to develop the technical basis 

for a mechanical grading system for round timbers, primarily for use by the log home industry (Green and others 2004; 

Green and others, in press). This study involved testing 

233 logs of the Engelmann spruce (Picea engelmannii), 

alpine fir (Abies lasiocarpa), lodgepole pine species group 

(ES–AF–LP) in bending and compression parallel to the 

grain. These logs were machined to a constant diameter of 

9 in. A static test on 170 logs showed that the relationship 

between MOR and MOE on these larger logs could be considered independent of species (Fig. 5, R2 = 0.68). The study 

also found a predictable relationship between UCS and 

MOR (Fig. 6). A prototype machine was built for this project to determine the dynamic modulus of elasticity in Etv of 

a log based on its natural frequency of vibration (Murphy 

2000). Compared with the visual grading, the proposed mechanical grading system gave higher yields for a specified 

set of allowable properties and could produce grades with 

allowable properties higher than could be justified by 

D 3957 procedures.

While the log home study was in progress, interest began 

to develop in using small-diameter logs as truss members 

and columns in engineered roundwood structures (Wolfe 

and Moseley 2000). The success of the proposed mechanical grading system for the 9-in.-diameter logs prompted 

extension of the research to smaller diameter logs. In the 

small-log studies, approximately 300 logs were selected 

for each of two species—suppressed growth Douglas-fir 

(Pseudotsuga menziesii) and plantation grown ponderosa 

pine (Pinus ponderosa). The logs were predominately 3 to 

7 in. in diameter and mechanically debarked. Using Etv in 

the green condition, the logs for each species were separated into three groups that were “matched” in terms of the 

average value and the range of values. The logs were then 

air dried in Hayfork, California, to a moisture content of 

15% to 20%. Two groups of logs were shipped to FPL and 

one to the University of Idaho. One of the two groups of 

tapered logs sent to FPL was tested in 1/3-point bending and 

the other in short-column compression parallel to the grain 

Figure 5—Relationship between modulus of rupture 

(MOR) and modulus of elasticity (MOE) for 9-in.-diameter dry logs of the Englemann spruce–Alpine fir–lodgepole pine species group (Green and others, in preparation). (Solid line is mean trend, and dotted line is 90% 

lower confidence interval.)

Figure 6—Relationship between ultimate compression 

stress parallel to grain (UCS) and modulus of rupture 

(MOR) for 9-in.-diameter logs (Green and others, in 

preparation).

Research Note FPL-RN-0297
Mechanical Grading of 6-Inch-Diameter Lodgepole Pine Logs for the Travelers’ Rest and Rattlesnake Creek Bridges

5

(Green and others, in preparation). The logs sent to the University of Idaho were machined to a constant (here referred 

to as “uniform”) diameter and tested in 1/3-point bending 

(Gorman and others, in preparation). Pertinent results from 

both the small- and large-log studies for the proposed mechanical grading of the logs for two pedestrian bridges are 

summarized in the following section. 

Effect of Mechanical Processing on the 

Flexural Properties of Small-Diameter Logs

In general, machining small-diameter logs to a constant diameter removes much of the mature wood on the outside of 

the beam, thus exposing more of the juvenile wood core. It 

also tends to expose more knots, especially in species that 

readily self-prune limbs on the lower part of the stem as the 

tree grows. The net effect of the machining is to lower both 

MOR and MOE. For 3- to 6-in. suppressed-growth Douglasfir logs, the MOR of logs machined to a uniform diameter 

was reduced by about 8%, whereas the MOE was reduced 

about 15% (Table 2). For 3- to 6-in. ponderosa pine logs, the 

MOR was reduced about 12% and the MOE about 33%. The 

greater effect of processing on the properties of ponderosa 

pine compared with those of Douglas-fir was probably a 

result of the respective ages of the trees, coupled with the 

relatively larger juvenile wood core of the shade-intolerant 

ponderosa pine. The suppressed-growth Douglas-fir trees 

had an average age of 67 years, whereas the average age of 

the ponderosa pine was only 42 years. The effect of processing on flexural properties is graphically shown in Figures 7 

and 8. Note that the 95th percentile of the uniform diameter 

ponderosa pine logs MOE was slightly less than the mean 

value of the MOE of the tapered logs (Fig. 8). 

Both the ponderosa pine and Douglas-fir logs machined to a 

constant diameter made the assigned Fb values for the Unsawn visual grade, and Douglas-fir made the assigned MOE 

value (Gorman and others, in preparation). However, the 

high juvenile wood content of the logs caused logs tested in 

bending to fail suddenly with a brash-looking failure surface. For the Unsawn grade, the MOE of the ponderosa pine 

logs machined to a constant diameter was about 25% lower 

than the average assigned by D 3957 procedures. One advantage of mechanically grading small-diameter logs is that 

the MOE of each log is measured, rather than basing MOE 

on a visual grade.

MOE–Etv

Table 3 summarizes regression relationships between MOE 

and Etv by log size, type of processing (tapered or uniform 

Table 2—Effect of machining to a constant diameter on the flexural properties of 3- to 6-in.-diameter Douglas-fir and 

ponderosa pinea

Property Species

Tapered Uniform U/T

(mean 

Mean value) 5th 95th Mean 5th 95th

MOR

(×103 lb/in2)

Douglas-fir 12.398 8.500 16.104 11.458 8.610 14.230 0.924

Ponderosa pine 5.506 3.478 8.269 4.866 3.600 6.332 0.884

MOE

(×106 lb/in2)

Douglas-fir 2.327 1.720 2.971 1.981 1.474 2.466 0.851

Ponderosa pine 1.128 0.710 1.520 0.756 0.386 1.101 0.670

aGreen and others (in press), Gorman and others (in preparation).

Figure 7—Effect of log processing on the modulus of 

rupture (MOR) of 3- to 6-in.-diameter logs (5th percentile, mean, 95th percentile).

Figure 8—Effect of log processing on the modulus of 

elasticity (MOE) of 3- to 6-in.-diameter logs (5th percen- tile, mean, 95th percentile).
6

cross-section along the length of the log), and species (or 

species group). In all cases, the correlation is good to excellent. For small-diameter logs with taper, the MOE–Etv relationships for the two species are significantly different at the 

0.001 probability level (highly significant). Visual inspection shows that both the slopes and intercepts are different 

(Fig. 9) because of the difference between the two species in 

percentage of juvenile wood in the log cross-section. Smalldiameter logs machined to a uniform cross-section show 

no significant difference at the 0.05 probability level in the 

MOE–Etv relationship between the two species (Fig. 9 solid 

lines). For these machined logs, the percentage juvenile 

wood content is very high for both species. Thus, for smalldiameter logs machined to a uniform diameter, it would be 

more conservative to use the MOE–Etv relationship for the 

combined Douglas-fir–ponderosa pine data (Table 3): 

 MOE = 0.891Etv – 0.001 (1)

Although not plotted in Figure 9, the MOE–Etv relationship for the 9-in.-diameter uniform logs appears to be a 

composite of the results for the Douglas-fir and ponderosa 

pine tapered logs (Table 3). This is probably because these 

logs were initially large enough that even with machining 

to a constant diameter, the juvenile wood had little effect on 

properties. 

Figure 10 compares the results obtained on the 3- to 6-in. 

Douglas-fir and ponderosa pine logs with some limited 

unpublished data from the University of Idaho on tests of 

44 lodgepole pine logs, which likely came from Canada. In 

the Idaho study, the logs were obtained from a pole manufacturer in northern Idaho and were dowelled in the green 

condition to a constant diameter of 3.5 in. The logs were 

then dried and conditioned in a relative humidity of 65% 

and tested in 1/3-point bending following ASTM D 198 procedures. The average moisture content of the logs was about 

12%. Because the tests showed no statistical difference 

between the Douglas-fir and ponderosa pine, there would 

appear to be no difference in the MOE–Etv relationship between these species and the lodgepole pine. Thus we 

Table 3—Relationship between modulus of elasticity by static test (MOE) and modulus of elasticity by transverse 

vibration (Etv) for round timbers

Y X Processing Speciesa

Diameter

(in.) N

Y = A + BX

A B R2 Referenceb

MOE

(×106 lb/in2)

Etv

(×106 lb/in2)

Tapered DF 3 to 6 93 0.7704 0.7218 0.54 1

 PP 97 0.1346 0.8770 0.66 1

 DF+ PP 190 –0.0376 1.0712 0.90 1

Uniform ES–AF–LP 9 169 0.0038 0.9780 0.83 2

 DF 3 to 6 93 0.1636 0.8195 0.79 3

 PP 100 –0.0046 0.8878 0.83 3

 DF+PP 193 –0.0010 0.8908 0.97 3

aDouglas-fir, DF; ponderosa pine, PP; Engelmann spruce, ES; alpine fir, AF; lodgepole pine, LP.

b1, Green and others (in preparation); 2, Green and others (2004); 3, Gorman and others (in preparation).

Figure 9—Relationship between modulus of elasticity by static test (MOE) and modulus of elasticity by 

transverse vibration (Etv) for 3- to 6-in.-diameter logs 

(Green and others, in preparation; Gorman and others, 

in preparation).

Figure 10—Effect of species on the relationship between modulus of elasticity by static test (MOE) and 

modulus of elasticity by transverse vibration (Etv) for 

small-diameter logs machined to a constant cross section (Gorman and others, in preparation).

Research Note FPL-RN-0297
Mechanical Grading of 6-Inch-Diameter Lodgepole Pine Logs for the Travelers’ Rest and Rattlesnake Creek Bridges

7

conclude that Equation (1) should be used to predict the 

static MOE of the lodgepole pine logs for the two bridges.

MOR–MOE

Table 4 summarizes regression relationships between MOR 

and MOE determined by static test, log size, type of processing, and species. With the exception of small-diameter 

ponderosa pine logs that have been machined to a uniform 

diameter, the relationships are generally good to excellent. The relationship for the uniform ponderosa pine logs 

is highly significant, even though the R2 value is low. The 

lower value might be a peculiarity of this data set; however, 

Larson and others (2004) found R2 = 0.22 in a study of 3- to 

13-in. ponderosa pine logs. The MOE–MOR regression for 

the Larson study is reported only for the combination of 

uniform and tapered logs, and the data were adjusted to a 

moisture content of 12% using a procedure previously given 

in ASTM D 2915 for adjusting the MOE of 2- to 4-in.-thick 

dimension lumber. The regression equations between 

tapered and uniform diameter logs for the combined Douglas-fir and ponderosa pine logs show significant statistical 

difference at the 0.05 level of confidence. For Douglas-fir, 

the slopes are relatively the same for tapered and uniform 

logs, but for ponderosa pine they are not (Fig. 11). For 

MOE > 1.252 × 106 lb/in2, the equation for uniform ponderosa pine provides the more conservative estimate of MOR, 

 MOR = 2.323 × MOE + 3.110 (2)

whereas below this value the equation for tapered ponderosa 

pine is more conservative:

 MOR = 4.125 × MOE + 0.853 (3)

Although the MOE–MOR regression equations for the two 

species are statistically different for logs of uniform crosssection, there is room to debate the practical implementation 

of this relationship. Figure 12 shows the actual data plotted 

with both species on the same graph for logs of uniform 

cross section. Here the regression equations for each 

individual species and for the combined species data are 

Figure 11—Relationship between modulus of rupture 

(MOR) and modulus of elasticity (MOE) for small-diameter logs (Green and others, in preparation; Gorman 

and others, in preparation; Larson and others, in preparation). 

Table 4—Relationship between modulus of elasticity by static test (MOE) and modulus of rupture by static test 

(MOR) round timbers

Y X Processing Speciesa

Diameter

(in.) N

Y = A + BX

A B R2 Referenceb

MOE

(×106

lb/in2)

MOR

(×106

lb/in2)

Tapered DF 3 to 6 92 1.961 4.513 0.58 1

PP 97 0.853 4.125 0.54 1

DF + PP 189 –0.559 5.518 0.91 1

Uniform ES–AF–LPa 9 169 –1.340 5.586 0.68 2

DF 3 to 6 102 1.766 4.865 0.71 3

PP 101 3.110 2.323 0.30 3

DF + PP 203 1.122 5.125 0.92 3

aDouglas-fir, DF; ponderosa pine, PP; Engelmann spruce, ES; alpine fir, AF; lodgepole pine, LP.

b1, Green and others (in preparation); 2, Green and others (2004); 3, Gorman and others (in preparation).

Figure 12—Relationship between modulus of rupture 

(MOR) and modulus of elasticity by static test (MOE) 

for 3- to 6-in.-diameter logs machined to a constant 

cross section (Gorman and others, in preparation).
8

shown. The influence of the lowest four pieces of ponderosa 

pine on the MOR–MOE regression is apparent. It would be 

easy to imagine one curve fitting both species. Figure 13 

shows the same plot for tapered logs, in which the slopes of 

the regression equations for the individual species are closer. 

One regression equation could possibly fit both species, but 

again a few pieces of ponderosa pine with low MOE values 

lie above the regression equation and reduce the slope of the 

ponderosa pine equation. Figure 14 compares the limited 

data on the 44 3.5-in. uniform-diameter lodgepole pine logs 

with the 3- to 6-in. uniform-diameter logs. These limited 

data would suggest that an equation fit to both species for 

the 3- to 6-in.-diameter logs might be a better predictor of 

properties than would ponderosa pine data alone: 

 MOR = 5.125 × MOE + 1.122 (4)

UCS–MOR

Green and others (in preparation) investigated the relationship between UCS and bending strength for dry 3- to 6-in. 

Douglas-fir and ponderosa pine logs. The logs all came from 

Shasta–Trinity National Forest in northern California. The 

logs were debarked (therefore tapered) and matched by Etv 

in the green condition to provide data sets of equal estimated quality. Ninety nine logs of each species were tested 

in bending, and 87 Douglas-fir logs and 99 ponderosa pine 

logs were tested in compression following procedures of 

ASTM D 198. A plot of the UCS/MOR relationship by position in the strength distribution (percentile level) shows the 

expected curvilinear relationship between the UCS/MOR 

ratio and MOR (Fig. 15). The average trend in the relationship is given:

 UCS/MOR = 0.00704(MOR)2 – 0.1130(MOR) + 0.853 (5)

for MOR ≤ 8.018 × 103 lb/in2 and UCS/MOR = 0.400 for 

MOR > 8.018 × 103 lb/in2.

Also as expected (Green and others 2004), the relationship 

for the 3- to 6-in.-diameter logs yields a lower UCS/MOR 

ratio for a given MOR value than the relationship previously 

found for 9-in.-diameter logs. When the small-diameter logs 

are classified into diameter groupings based on the average 

diameter at the middle of the log, the ratio is also seen to 

vary somewhat by diameter (Fig. 16). A more conservative 

estimate for the UCS/MOR relationship could be obtained 

by adjusting Equation (5) downward:

 UCS/MOR = 0.00704(MOR)2 – 0.1130(MOR) + 0.750 (6)

for MOR ≤ 8.018 × 103 lb/in2 and UCS/MOR = 0.30 for 

MOR > 8.018 × 103 lb/in2.

Machining small-diameter logs to a constant diameter lowers flexural properties and the MOR–MOE relationship. 

Because no data are available on the UCS/MOR relationship 

for small-diameter lodgepole pine logs machined to a constant diameter, we recommend that the more conservative 

UCS/MOR relationship given in Equation (6) be used to 

estimate Fc|| for the lodgepole pine logs tested in this study.

UTS–MOR

Currently, the allowable tensile strength parallel to the grain 

(Ft) of round timbers is estimated as 0.55Fb (ASTM D 

3957). This is an average value given in ASTM D 245 and 

is based on tests of 2-in.-thick dimension lumber. Direct evidence to support the use of the 0.55 ratio for logs is lacking. 

ASTM D 1990 for visually graded lumber and D 6570 for 

mechanically graded lumber use a more conservative ratio 

of 0.45 if no collaborative data support a higher ratio. Green 

Figure 13—Relationship between modulus of rupture 

(MOR) and modulus of elasticity by static test (MOE) for 

tapered 3- to 6-in.-diameter logs (Green and others, in 

preparation).

Figure 14—Effect of species on the relationship between modulus of rupture (MOR) and modulus of 

elasticity (MOE) by static test for small-diameter logs 

machined to a constant cross-section (Gorman and 

others, in preparation).

Research Note FPL-RN-0297
9

and others (in preparation) reviewed the limited available 

data on the tensile strength of round timbers. The following 

information is summarized from their discussion. 

Pellerin and others (1987) tested 81 lodgepole pine logs in 

tension parallel to the grain following procedures of ASTM 

D 198. The logs were sampled from throughout the growth 

range of interior lodgepole pine. The logs were approximately 3 in. (76 mm) in diameter after debarking and were 

at about 13% moisture content at time of test. To overcome 

the problems of crushing in the special grips developed 

for the study, the center portion of each stem was necked 

down to approximately 2.25 in. prior to loading. Mean tensile strengths for these logs are not reported in Pellerin and 

others (1987); however, the mean value is given in Koch 

(1996). The UTS values range from 4,060 lb/in2 for logs 

sampled at 42.5° latitude to 5,680 lb/in2 for those sampled at 

60° latitude. The overall mean value was 5,158 lb/in2. 

The mean MOR value for the 44 lodgepole pine logs from 

the unpublished University of Idaho data was 10,803 lb/in2. 

Using the mean values for these logs and the mean UTS 

value from Pellerin and others (1987) gives a UTS–MOR 

ratio of 0.48. Although recognizing the limitations of the 

available data, we recommend using the UTS–MOR ratio 

of 0.45 given in ASTM D 4761 for determining allowable 

properties for a given mechanical grade. This ratio might 

provide safer estimates of Ft than the ratio of 0.55 specified 

in D 3957/D 245 for small-diameter logs, especially those 

machined to a constant cross section.

Allowable Shear Strength (Fv ) and Compression 

Strength Perpendicular to the Grain (Fc┴)

Allowable shear strength (Fv ) and allowable compression 

strength perpendicular to the grain (Fc┴) are determined 

from tests of clear wood and do not vary with visual grade 

(ASTM D 3957). Thus, we recommend that the Fv and Fc⊥

values assigned to visually graded lodgepole pine logs be 

used for mechanically graded round timbers. This recommendation is consistent with the recommended practice for 

mechanically graded dimension lumber (ASTM D 6570).

Methods

Material 

The superstructure of both bridges will be constructed primarily of lodgepole pine salvaged from beetle-killed trees 

cut on private property near Elk City, Idaho. After harvest, 

the logs were transported to Porterbuilt, Inc., near Hamilton, 

Montana. There the logs were machined to a constant diameter of approximately 6 in. and cut to various lengths from 

12 to 20 ft, as specified by Beaudette Engineering. The logs 

were graded as No.1, 2, or 3 by a quality supervisor of Timber Products Inspection, Inc. Because of an oversight, the 

Unsawn grade was not separated from the No. 1 grade logs.

Procedures

Immediately prior to testing, the moisture content of about 

five logs of each of the various log length groupings was obtained using a Delmhorst model J-2000 electrical resistance 

moisture meter (Delmhorst Instrument Company, Towaco, 

New Jersey) using an insulated two-prong probe driven to a 

depth of about 2 in. Air temperature at time of test was generally from 75°F to 90°F.

Figure 15—Relationship between ultimate compression 

stress parallel to the grain (UCS) and modulus of rup- ture (MOR) for 3- to 6-in.-diameter logs (Green and oth- ers, in press) (solid line, mean trend for this study; dot- ted line, mean trend for 9-in.-diameter logs from Green 

and others, in preparation).

Figure 16—Effect of log diameter class on relationship 

between ultimate compression stress parallel to the 

grain (UCS) and modulus of rupture (MOR) for smalldiameter logs at approximately 14% moisture content 

(conservative relationship fit to the data).

Mechanical Grading of 6-Inch-Diameter Lodgepole Pine Logs for the Travelers’ Rest and Rattlesnake Creek Bridges
10

The MOE of the logs in transverse vibration was determined 

on all the candidate logs in the log yard of Porterbuilt, Inc., 

in Hamilton, Montana (Fig. 17) (Murphy 2000; Murphy, in 

press). The logs were supported full length, with the span 

being approximately 4 in. shorter than the log’s length. Log 

lengths, log spans, and log circumferences were determined 

for all logs. The FPL prototype machine determines the 

weight and frequency of vibration from load cells on each 

end of the log. This information is used to determine the 

average Etv of the log.

Mechanical grades for the logs were determined using procedures developed in previous studies on the mechanical 

grading of round timbers (Green and others 2004; Green 

and others, in preparation). The exact procedures are discussed and examples provided in the Results section under 

Mechanical Grading. In general, we followed established 

procedures for Machine Stress Rated (MSR) lumber

(Galligan and McDonald 2000), a specific process, as opposed to “mechanical grading.” In the MSR process, the 

MOE is limited to a coefficient of variation (COV) of 11% 

on the lower tail of the stiffness distribution. Other types of 

mechanically graded lumber are produced commercially, 

some of which allow a user-specified COV. A good discussion of mechanical grading for softwood dimension lumber 

is given in Smulski (1997). The mechanical grading procedure used here has been used successfully in a number of 

FPL studies on softwood and hardwood dimension lumber 

and rectangular timbers. Although it addresses softwood 

dimension lumber, a good discussion of some marketing 

considerations in the production of MSR lumber may be 

found in appendix B of Green and others (2000).

Results

Visual Grading

The average moisture content of the 30 logs sampled was 

19.3%, with a range from 12% to 24%. The diameter of the 

logs was constant at about 6-1/8 in. 

The visual grades of the 292 logs used in this study are given in Table 5. All were lodgepole pine except one (log no. 

594), which was identified by the TP grader as Engelmann 

spruce. This log was retained in the data set and is included 

in all subsequent discussion. Additional information on the 

individual logs is given in Appendixes A and B. About 64% 

of the logs made No. 1 grade, with less than 10% each in 

No. 2 and 3 grades. Probably a high percentage of the 

No. 1 logs would have qualified for the Unsawn grade, but 

as noted previously, this grade was not identified separately. 

More than 19% of the logs failed to make No. 3 grade and 

were considered culls. Of these logs, by far the largest cause 

for downgrade was excessive knot size, which characterized 

64% of the 56 cull logs. As is common industry practice for 

the highest grade, no limiting characteristic was recorded for 

the No.1 grade logs. Slope of grain was the most prevalent 

limiting characteristic for the No. 2 and 3 grade logs. The 

higher occurrence of unsound wood and insect damage in 

the No. 3 and cull logs is a reflection of using logs cut from 

salvaged (dead) trees.

Mechanical Grading

Only the 236 logs that made at least a No. 3 visual grade 

were considered for mechanical grading. All subsequent discussion pertains only to these logs.

Modulus of Elasticity 

The Etv values measured on the logs averaged 1.639 ×

106 lb/in2, with a range from 1.002 to 2.633 × 106 lb/in2

(Table 6). The static MOE values were estimated from the 

combined ponderosa pine–Douglas-fir data sets for logs 

Figure 17—Determination of modulus of elasticity by 

transverse vibration of lodgepole pine logs at Portbuilt, 

Inc., Hamilton, Montana, in July 2004. 

Table 5—Grade yield and grade-controlling 

characteristic for visually graded 6-in.-diameter 

lodgepole pine logs

Log gradea

Characteristic No. 1 No. 2 No. 3 Cull

Number of logs 188 21 27 56

Knots 8 2 36

Slope of grain 12 13 1

Splits 3 2

Unsound wood 3 3

Break 2

Insect damage 3

Saw cut 1

Shake 3 3

Wane 2

Under size 1

Check 1

Not specified, 

or not recorded

188b 1 2 2

aTP (1995).

bNo defect specified, as is typical industry practice

 for the highest grade determined.

Research Note FPL-RN-0297
11

machined to a constant diameter (Eq. (1)). The MOE values 

averaged 1.460 × 106 lb/in2, with a range 0.893 to 2.460 × 

106 lb/in2 (Table 6). 

Assignment of Mechanical Grades 

As discussed previously, mechanical grades were determined from the estimated static MOE values. For the assigned MOE of mechanically graded logs to qualify for a 

grade, two criteria must be met:

1. The minimum MOE accepted into the grade must be 

 0.82 times the target average MOE of the grade.

2. The actual MOE of all pieces that meet the first criteria 

 must be at least as high as the target average MOE of the 

 grade.

Criterion 1 establishes the “5th percentile MOE” and ensures the traditional 11% COV on the lower-tail MOE for 

mechanically graded lumber. As an example, first consider 

that only one MSR grade with an MOE of 1.4 × 106 lb/in2

will be produced. On the basis of the first criterion, 215 of 

236 lodgepole pine logs for the bridge project potentially 

qualified for a mechanical grade (see Table 6 and worksheet 

in Appendix A). The average MOE of these 215 logs is 

1.497 × 106 lb/in2, thus criterion 2 is satisfied, and all the 

215 logs may be assigned a grade of “1.4E.” 

As another example, assume that two MSR grades are desired. First, let’s target an average MOE of 1.9 × 106 lb/in2

for the upper grade. With criterion 1, all logs with an MOE 

at least as high as 0.82 × 1.9 = 1.558 are candidates. Seventy 

one logs meet criterion 1 (Appendix A). However, the average MOE of these logs is only 1.748 × 106 lb/in2. So to raise 

the average MOE to at least 1.9 × 106 lb/in2, it is necessary 

to throw out logs with the lowest MOE values. When sufficient logs are eliminated, 26 logs meet criterion 2 and can 

be assigned a grade of “1.9E.” The remaining 210 logs can 

now be considered for a lower grade. Average MOE of the 

remaining logs is 1.404 × 106 lb/in2, so we first consider 

how many of the logs might qualify for a 1.4E grade. Applying the two criteria to these remaining logs, the minimum 

MOE must be 0.82 × 1.4 = 1.148 × 106 lb/in2. One hundred 

eighty nine of the 292 logs meet criterion 1, and the average 

MOE of these logs is 1.441 × 106 lb/in2. Thus, all 189 logs 

may be assigned 1.4E. The remaining 21 No.1, 2, and 3 logs 

have visual grades with assigned properties below the mechanical grade for which they failed to qualify. Thus, these 

logs can retain their assigned allowable properties for the 

visual grades (Table 6).

The allowable bending strength (Fb) is determined from 

the assumed regression equation between MOR and MOE. 

When comparing the equations for ponderosa pine, we noted that the equation based on tapered samples (Eq. (3)) was 

Table 7—Grade yields from mechanically graded 6-in.-diameter lodgepole pine logs as predicted 

using Equation (7), page 12, for ponderosa pine

Option MSRa grade

Pieces

of MSR

Pieces from visual falldowns Total

No. 1 No. 2 No. 3 Cull pieces

1 1.9E-2600Fb 26 — — — — —

1.4E-2150Fb 189 16 2 3 56 292

2 1.8E-2500Fb 49 — — — — —

1.3E-2050Fb 183 1 1 2 56 292

3 1.7E-2450Fb 88 — — — — —

1.3E-2050Fb 144 1 1 2 56 292

4 1.6E-2350Fb 147 — — — — —

1.2E-1950Fb 86 1 1 1 56 292

5 1.5E-2250Fb 196 — — — — —

1.1E-1900Fb 39 — 1 — 56 292

6 1.4E-2150Fb 215 16 2 3 56 292

7 1.3E-2050Fb 232 1 1 2 56 292

8 1.2E-1950Fb 233 1 1 1 56 292

9 1.1E-1900Fb 235 — 1 — 56 292

 aMachine Stress Rated.

Mechanical Grading of 6-Inch-Diameter Lodgepole Pine Logs for the Travelers’ Rest and Rattlesnake Creek Bridges

Table 6—Measured values of modulus of elasticity by transverse vibration (Etv) and estimateda values by static 

test (MOE) for 236 lodgepole pine logs

Property

(106 lb/in2) Mean

Percentile level

5th 10th 25th 50th 75th 90th 95th

Etv 1.638 1.237 1.310 1.446 1.608 1.822 2.008 2.086

MOEa 1.459 1.102 1.167 1.288 1.433 1.623 1.789 1.859

a MOE estimated from combined data on 3- to 6-in. ponderosa pine and Douglas-fir logs machined to a constant diameter 

(Eq. (1), page***).
12

more conservative for MOE values below 1.25 × 106 lb/in2, 

whereas the equation for uniform diameter logs (Eq. (2))

was more conservative for higher MOE values. Because 

most of the predicted MOE values for the lodgepole pine 

logs are above 1.25 × 106 lb/in2 (Table 6), Equation (2) 

seems a better choice. At an MOE of 1.0 × 106 lb/in2, Equation (2) predicts MOR that is about 9% higher than that predicted by Equation (3), and with an MOE of 1.1 × 106 lb/in2, 

the difference is about 5% too high. For all higher MOEs, 

the MOR predicted by Equation (2) would be lower than 

those predicted by Equation (3). Whether to use Equation 

(2), which is just for uniform diameter ponderosa pine, or 

Equation (4), which is based on the combined species with 

uniform cross-section, is more arbitrary. Whereas we tend to 

think Equation (2) is better given the lack of knowledge on 

small-diameter ponderosa pine, both will be used to allow 

comparison of predicted properties. 

First, we use the ponderosa pine data of Equation (2) as a 

basis for predicting MOR. Here we fit a 90% lower 

confidence interval on the regression equation on ponderosa 

pine machined to a constant diameter of 3 to 6 in. This provides an equivalent to the traditional 5th percentile used for 

visually graded lumber because it excludes 5% of the data 

on the lower side of the mean regression line. The equation 

is

 MOR0.05 = 2.323 × MOE + 1.850 (7)

For a 1.4E grade, the required minimum MOE value of 

1.148 is used in Equation (7). Thus the estimated MOR value would be 2.323 × 1.148 + 1.850 = 4.517 × 103 lb/in2, or 

4,517 lb/in2 (App. A). This estimated 5th percentile would 

be divided by 2.1 (the general adjustment factor of ASTM D 

245/D 6570) to give 2,151 lb/in2. When rounded according 

Table 8—Grade yields from mechanically graded 6-in.-diameter lodgepole pine logs as predicted using Equation 

(8), page 12, for the combined Douglas-fir and ponderosa pine data

Option MSRa grade

Pieces

of MSR

Pieces from visual falldowns Total

No. 1 No. 2 No. 3 Cull pieces

1 1.9E-3500Fb 26 — — — — —

1.4E-2250Fb 189 16 2 3 56 292

2 1.8E-3350Fb 49 — — — — —

1.3E-2350Fb 183 1 1 2 56 292

3 1.7E-3150Fb 88 — — — — —

1.3E-2350Fb 144 1 1 2 56 292

4 1.6E-2950Fb 147 — — — — —

1.2E-2150Fb 86 1 1 1 56 292

5 1.5E-2750Fb 196 — — — — —

1.1E-1950Fb 39 — 1 — 56 292

6 1.4E-2550Fb 215 16 2 3 56 292

7 1.3E-2350Fb 232 1 1 2 56 292

8 1.2E-2150Fb 233 1 1 1 56 292

9 1.1E-1950Fb 235 — 1 — 56 292

 aMSR, Machine Stress Rated.

Table 9—Design values for mechanically graded 6-in.-diameter lodgepole pine 

logs developed using Equation (7), page 12, for ponderosa pine

Grade

Design values

Fb

(lb/in2)

Ft

(lb/in2)

Fv

(lb/in2)

Fc┴

(lb/in2)

Fc║

(lb/in2)

MOE

(×106 lb/in2)

1.9E 2,600 1,150 95 395 975 1.9

1.8E 2,500 1,150 95 395 975 1.8

1.7E 2,450 1,100 95 395 950 1.7

1.6E 2,350 1,050 95 395 950 1.6

1.5E 2,250 1,000 95 395 925 1.5

1.4E 2,150 950 95 395 900 1.4

1.3E 2,050 925 95 395 900 1.3

1.2E 1,950 875 95 395 875 1.2

1.1E 1,900 850 95 395 850 1.1

Visual gradesa

No. 1 1,250 675 95 395 625 1.1

No. 2 1,050 575 95 395 525 1.1

No. 3 600 325 95 395 300 0.9

aTP (1995).

Research Note FPL-RN-0297
13

to ASTM procedures, the assigned Fb value would be 2,150. 

Thus, these logs would qualify as a 1.4E-2150Fb grade. 

Table 7 presents the results for nine sorting options for 

producing mechanical grades from the 228 lodgepole pine 

logs using Equation (7) to predict MOR. The option chosen 

in practice depends upon the material requirements of the 

bridges. Grade assignments for individual logs using 

option 1 (two mechanical grades, 1.9E and 1.4E) are shown 

in Appendix B.

If the combined Douglas-fir and ponderosa pine data of 

Equation (4) are used to predict MOR, the 90% lower confidence interval is

 MOR0.05 = 5.125 × MOE – 0.532 (8)

Table 8 gives grades for the same MOE combinations used 

in Table 7. As expected, the Fb value is higher using Equation (8) than if Equation (7) is used.

Assignment of Other Allowable Properties

Other allowable properties may be assigned for each of the 

grade options. As previously discussed, Fc is estimated from 

Equation (6). The recommended Ft value is obtained as 

0.45 × Fb. Allowable shear strength (Fv) and allowable 

strength in compression perpendicular to the grain (Fc⊥) do 

not vary by grade, so these values remain those assigned to 

lodgepole pine by Timber Products (TP 1995). Table 9 gives 

the design values predicted on the basis of Table 6 Fb values 

(Eq. (7)) for MOR–MOE based only on ponderosa pine) and 

Table 10 gives them based on Table 8 Fb values (Eq. (8)) for 

MOR–MOE based on the combined Douglas-fir and ponderosa pine data). The design values for visual grades are given 

in both tables for comparison.

Recommendations

Two options are presented for determination of the allowable bending strength Fb for the lodgepole pine logs that 

were mechanically graded in this study. Option 1 is based 

on the MOR–MOE relationship for 3- to 6-in.-diameter ponderosa pine logs machined to a constant diameter 

(Eq. (7), Tables 6 and 9). Given that there are few data on 

the MOR–MOE relationship for small-diameter lodgepole 

pine logs machined to a constant diameter, option 1 provides 

our preferred set of allowable properties. For a mechanical 

grade assigned an MOE = 1.4 × 106 lb/in2, option 1 provides 

a 27% increase in MOE and a 72% increase in Fb compared 

with a No. 1 visual grade. Property assignments under option 1 are more conservative than under option 2.

Option 2 is based on the MOR–MOE relationship fit to the 

combined ponderosa pine and Douglas-fir data for 3- to 

6-in.-diameter logs machined to a constant diameter 

(Eq. (8), Tables 8 and 10). Statistics show that the MOR–

MOE regression equations fit to the individual species are 

not the same (the difference is highly significant at the 0.001 

probability level). However, limited data on 44 lodgepole 

pine logs machined to a constant diameter of approximately 

3-3/8 in. appear to support the concept that the MOE–MOR 

relationship is virtually independent of species. This observation, plus previous results for logs of three species 

machined to a constant diameter of 9 in., suggests that a regression fit to the combined data set would provide more realistic design values. Therefore, we feel that option 2 is also 

technically valid. A further study on lodgepole pine logs was 

already contemplated prior to the initiation of this project 

and should provide definitive conclusions on the effect of 

species on the MOE–MOR relationship for small-diameter 

logs. For a 1.4 × 106 lb/in2 MOE grade, the increase in Fb is 

80% larger than that assigned to a No. 1 visual grade. 

Table 10—Design values for mechanically graded 6-in.-diameter lodgepole pine logs 

developed using Equation (8), page 12, for the combined Douglas-fir and ponderosa 

pine data

Grade

Design values

Fb

(lb/in2)

Ft

(lb/in2)

Fv

(lb/in2)

Fc┴

(lb/in2)

Fc║

(lb/in2)

MOE

(×106 lb/in2)

1.9E 3,550 1,600 95 395 1,150 1.9

1.8E 3,350 1,500 95 395 1,100 1.8

1.7E 3,150 1,400 95 395 1,100 1.7

1.6E 2,950 1,350 95 395 1,050 1.6

1.5E 2,750 1,250 95 395 1,000 1.5

1.4E 2,550 1,150 95 395 1,000 1.4

1.3E 2,350 1,050 95 395 950 1.3

1.2E 2,150 975 95 395 900 1.2

1.1E 1,950 875 95 395 875 1.1

Visual gradesa

No. 1 1,250 675 95 395 625 1.1

No. 2 1,050 575 95 395 525 1.1

No. 3 600 325 95 395 300 0.9

a TP (1995).

Mechanical Grading of 6-Inch-Diameter Lodgepole Pine Logs for the Travelers’ Rest and Rattlesnake Creek Bridges
14

The approach taken in this paper is to recommend property 

assignment procedures consistent with historical practices 

for assigning allowable properties to groups of logs sorted 

into visual or mechanical grades. We do not recommend 

that the equations presented in this paper be used to assign 

separate strength values to individual logs. Such a practice 

would not be consistent with historical assumptions about 

factors of safety for structural lumber products. 

Literature Cited

ASTM. 2004. Annual Book of Standards, Volume 04.10. 

Wood. American Society for Testing and Materials, West 

Conshohoken, Pennsylvania.

D 198-02. Standard methods of static tests of 

 lumber in structural sizes.

D 245-00. Standard practices for establishing structural 

 grades and related allowable properties 

 for visually graded lumber.

D1990-00. Standard practice for establishing allowable 

 properties for visually graded dimension lum- 

 ber from in-grade tests of full-size specimens.

D 2899-03. Standard practice for establishing design 

 stresses for round timber piles.

D 2915-03. Standard practice for evaluating allowable 

 properties for grades of structural lumber.

D 3957-03. Standard practice for establishing stress grades 

 for structural members used in log homes.

D 6570-00. Standard practice for assigning allowable 

 properties for mechanically graded lumber.

Galligan, W.L.; McDonald, K.A. 2000. Machine grading: 

practical concerns for lumber producers. General Technical 

Report FPL-GTR-7, USDA Forest Service, Forest Products 

Laboratory, Madison, WI.

Gorman, T.; Green, D.; Wheeler, M.; Evans, J.W.; Murphy, J.; Hatfield, C. In preparation. Grading and properties 

of small-diameter Douglas-fir and ponderosa pine round 

timbers machined to a constant diameter. Forest Products 

Journal.

Green, D.W.; McDonald, K.A.; Dramm, J.; Kilborn, K. 

2000. Grading options for western hemlock “pulpwood” 

logs from southeastern Alaska. Research Paper, FPL-RP583. USDA Forest Service, Forest Products Laboratory, 

Madison, WI.

Green, D.W.; Gorman, T.M.; Evans, J.W.; Murphy, J.F. 

2004. Improved grading system for structural logs for log 

homes. Forest Products Journal. 54(9): 52–62.

Green, D.W.; Gorman, T.M.; Evans, J.W.; Murphy, J.F. 

In press. Mechanical grading of round timber beams. Journal of Materials in Civil Engineering. 

Green, D.W.; Gorman, T.M., Evans, J.W.; Murphy, J.F. 

In preparation. Grading and properties of small-diameter 

Douglas-fir and ponderosa pine round timbers with taper. 

Wood and Fiber Science.

Koch, P. 1996. Lodgepole pine in North America. Volume 2, 

Part III: Characterization of tree parts. Forest Products Society. Madison, WI. 

Larson, D.; R. Mirth; R. Wolfe. 2004. The evaluation of 

small-diameter ponderosa pine logs in bending. Forest Products Journal. 54(12): 52–58.

Murphy, J.F. 2000. Transverse vibration of a simply supported frustum of a right circular cone. Journal of Testing 

and Evaluation. 28(5): 415–419.

Murphy. J.F. In preparation. Transverse vibrations of woodbased products: equations and considerations. Research 

Note. USDA Forest Service, Forest Products Laboratory, 

Madison, WI.

Pellerin, R.F.; P. Koch; J.J. Vogt. 1989. Mechanical properties of lodgepole pine: 3-in.-diameter stems. Forest Products 

Journal. 39(4): 62–66

Smulski, S. 1997. Machine-graded lumber. Wood Design 

Focus. 8(2): 3–24. Forest Products Society. Madison, WI.

TP. 1995. Log Home Grading Rules (including supplements 

1–5). Timber Products Inspection, Inc. Conyers, GA.

Wolfe, R.; C. Moseley. 2000. Small-diameter log evaluation for value-added structural applications. Forest Products 

Journal. 50(10): 48–58.

Research Note FPL-RN-0297
15

Appendix A—Mechanical Grading Worksheet

Mechanical grading worksheet using Equation (7) for MOR–MOE relationship for only ponderosa pine machined to 

a constant diameter. MOR0.90lcl = 2.323(0.902) + 1.850 = 3.945 × 103 lb/in2 (Eq. (7), page 12)

Mechanical Grade

1.1E 1.2E 1.3E 1.4E 1.5E 1.6E 1.7E 1.8E 1.9E

Mean modulus of elasticity of 1st mechanical gradea

Min E=0.82E1 0.902 0.984 1.066 1.148 1.230 1.312 1.394 1.476 1.558

N>0.82E1 235/292 233/292 232/292 215/292 196/292 168/292 136/292 101/292 71/292

% Yield 80.5 79.8 79.5 74.6 67.1 57.5 46.6 34.6 24.3

Mean E1 1.462 1.466 1.468 1.497 1.525 1.567e 1.618e 1.680e 1.748e

New min E 1.370f 1.510 1.650 1.780

N @ Adj E1 147/292 88/292 49/292 26/292

New min E1 1.600 1.707 1.810 1.903

Adjusted 

percentage yield

50.3 30.1 16.8 8.9

Mean modulus of elasticity of 2nd mechanical grade if target E >1.1Eb

Mean E of E1 

rejects 

0.893 0.918 0.946 1.076 1.135 1.227 1.312 1.367 1.404

Target MOE of 2nd

Grade

1.1 1.2 1.3 1.3 1.4

Min E=0.82E2 0.902 0.984 1.066 1.066 1.148

N>0.82E2 39/292 86/292 144/292 183/292 189/292

Mean E2 1.141 1.237 1.322 1.376 1.439

% yield E2 13.4 29.5 49.3 62.7 64.7

% yield of visual 

gradesd

0 0 0 0 0.3

(1/292)

1.0

(3/292)

1.4

(4/292)

1.4

(4/292)

7.2

(21/292)

% yield of < No. 3 

visual

19.2 19.2 19.2 19.2 19.2 19.2 19.2 19.2 19.2

Estimated Fb of mechanical grade E1

c

MOR 3,9454 4,136 4,326 4,517 4,707 4,898 5,088 5,279 5,469

MOR/2.1 1,879 1,969 2,060 2,151 2,241 2,332 2,423 2,514 2,604

Fb 1,900 1,950 2,050 2,150 2,250 2,350 2,450 2,500 2,600

aSample size of 292 includes 56 pieces that did not make No. 3 visual grade. 

bSecond, lower, grade not considered unless mean E at least 1.1 x 103 lb/in2. cFb estimated from Equation (7) for uniform diameter ponderosa pine logs/2.1. 

dPieces not making mechanical grade, but with visual grade of No. 1, 2, or 3.

eMean E value of sorted logs is less than target average grade E. Must raise minimum value of 0.82E and recalculate.

f

Obtained by dropping off remaining pieces with lowest MOE values until required average MOE is achieved.

Mechanical Grading of 6-Inch-Diameter Lodgepole Pine Logs for the Travelers’ Rest and Rattlesnake Creek Bridges
16

391 No. 1 No. 1 0.947 16.71

392 No. 1 No. 1 1.114 16.63

393 Cull Cull — 16.81

394 1.4E No. 2 1.169 16.58

395 1.4E No. 1 1.426 16.73

396 No. 1 No. 1 1.093 16.69

397 1.4E No. 1 1.225 16.67

398 1.4E No. 1 1.553 16.71

399 1.4E No. 1 1.351 16.67

400 1.4E No. 1 1.585 18.73

401 1.4E No. 1 1.640 19.00

402 1.4E No. 3 1.476 18.83

403 1.4E No. 1 1.633 18.29

404 1.4E No. 1 1.308 19.23

405 1.4E No. 1 1.627 18.69

406 1.4E No. 3 1.375 18.42

407 1.4E No. 3 1.632 18.90

408 1.4E No. 1 1.769 18.48

409 1.4E No. 1 1.647 19.04

410 1.4E No. 1 1.662 18.77

411 1.4E No. 1 1.564 18.04

412 1.9E No. 1 1.897 17.81

413 Cull Cull — 18.40

414 1.4E No. 1 1.772 18.79

415 No. 1 No. 1 1.101 17.60

416 Cull Cull — 18.06

417 1.4E No. 1 1.630 18.71

418 1.4E No. 3 1.457 18.46

419 1.4E No. 1 1.474 19.02

420 1.4E No. 1 1.719 18.79

421 1.4E No. 1 1.507 18.63

422 1.4E No. 1 1.245 12.75

423 1.4E No. 1 1.502 12.67

424 1.4E No. 1 1.473 12.67

425 No. 1 No. 1 1.103 13.65

426 1.4E No. 1 1.198 12.63

427 Cull Cull — 12.69

428 1.4E No. 1 1.423 12.69

429 1.4E No. 1 1.696 12.25

430 1.4E No. 1 1.329 13.00

431 1.4E No. 1 1.552 12.75

432 1.4E No. 1 1.196 12.50

433 1.4E No. 1 1.379 12.69

434 1.4E No. 1 1.281 12.75

435 1.4E No. 1 1.209 12.44

436 1.4E No. 1 1.489 12.13

437 1.4E No. 1 1.553 12.75

438 1.4E No. 1 1.458 12.81

439 1.4E No. 1 1.433 12.69

440 1.4E No. 1 1.515 12.58

441 1.4E No. 2 1.491 13.10

442 1.4E No. 1 1.295 13.81

443 Cull Cull — 13.21

444 No. 1 No. 1 1.127 13.17

445 Cull Cull — 12.83

446 1.4E No. 1 1.335 12.73

447 1.4E No. 1 1.225 12.85

448 1.4E No. 1 1.180 11.94

449 1.4E No. 1 1.175 12.81

450 1.4E No. 1 1.226 12.83

452 1.4E No. 3 1.406 12.33

453 Cull Cull — 12.75

454 1.9E No. 1 1.826 12.79

455 1.4E No. 1 1.666 13.38

457 1.4E No. 2 1.461 12.54

Log 

number

MSR 

grade

Visual 

grade

MOE

(x106 lb/in2)

Length

(ft)

458 1.4E No. 1 1.328 12.44

459 1.4E No. 2 1.703 12.67

460 1.4E No. 1 1.719 12.73

461 Cull Cull — 12.69

462 1.4E No. 1 1.707 12.73

463 Cull Cull — 13.21

464 1.4E No. 1 1.592 12.71

465 1.4E No. 1 1.427 12.75

466 No. 1 No. 1 1.123 12.88

467 1.4E No. 3 1.304 12.46

469 1.4E No. 1 1.363 14.85

470 No. 1 No. 1 1.133 14.54

471 1.4E No. 1 1.478 14.60

472 1.4E No. 1 1.292 14.31

473 1.4E No. 1 1.219 14.60

474 1.4E No. 1 1.470 14.71

475 1.4E No. 2 1.588 14.75

476 1.4E No. 1 1.249 14.67

477 1.4E No. 1 1.243 14.60

478 Cull Cull — 14.79

479 Cull Cull — 15.40

480 1.4E No. 1 1.371 14.81

481 1.4E No. 3 1.209 15.88

482 1.4E No. 1 1.537 14.29

483 Cull Cull — 14.52

484 Cull Cull — 15.10

485 1.4E No. 1 1.284 14.73

486 1.4E No. 1 1.254 15.00

487 1.4E No. 1 1.245 15.10

488 No.1 No. 1 1.081 15.19

489 1.4E No. 1 1.162 14.29

490 1.4E No. 1 1.275 15.06

491 1.4E No. 1 1.478 14.81

492 1.4E No. 3 1.324 14.83

493 1.4E No. 1 1.454 14.81

494 Cull Cull — 15.02

495 1.4E No. 1 1.414 14.46

496 1.4E No. 1 1.539 12.38

497 1.4E No. 1 1.255 12.67

500 1.4E No. 3 1.512 20.73

501 1.4E No. 1 1.423 18.73

502 1.9E No. 1 1.817 20.69

503 1.9E No. 1 2.112 20.88

504 1.4E No. 1 1.593 20.71

505 1.9E No. 3 1.856 20.77

506 1.4E No. 1 1.702 20.73

507 1.4E No. 1 1.719 20.96

508 1.4E No. 2 1.580 20.75

509 1.9E No. 1 1.813 19.92

510 1.9E No. 2 1.996 20.69

511 1.9E No. 1 1.790 20.79

512 Cull Cull — 18.98

513 1.9E No. 1 1.978 21.15

514 1.4E No. 2 1.417 19.50

515 1.4E No. 1 1.550 20.71

516 1.4E No. 1 1.695 20.75

517 1.9E No. 1 1.787 20.79

518 1.4E No. 1 1.510 18.83

519 1.4E No. 2 1.619 20.71

520 Cull Cull — 18.73

521 1.4E No. 1 1.624 20.58

522 1.9E No. 3 1.949 20.69

523 1.9E No. 2 1.790 20.75

524 1.4E No. 2 1.493 20.63

Log 

number

MSR 

grade

Visual 

grade

MOE

(x106 lb/in2)

Length

(ft)

Research Note FPL-RN-0297

Appendix B–Grade Assignments for Individual Logs 

 Grade assignments for individual logs using option 1 (two mechanical grades, 1.9E and 1.4E)
17

525 1.4E No. 3 1.372 20.79

526 1.4E No. 1 1.385 22.85

527 Cull Cull — 18.52

528 1.4E No. 1 1.744 18.67

529 1.4E No. 1 1.434 18.73

530 1.4E No. 1 1.321 18.54

531 1.4E No. 3 1.356 18.71

532 1.4E No. 1 1.289 18.48

534 1.4E No. 2 1.560 16.67

535 Cull Cull — 18.96

536 Cull Cull — 19.08

537 1.9E No. 3 1.805 18.50

539 1.9E No. 1 1.835 18.60

540 1.4E No. 1 1.734 15.10

541 1.4E No. 3 1.687 16.44

542 1.4E No. 1 1.563 16.54

543 1.4E No. 1 1.425 17.38

544 1.4E No. 1 1.393 19.13

545 1.9E No. 1 1.872 14.44

546 1.4E No. 1 1.293 18.75

547 1.4E No. 1 1.467 19.33

548 Cull Cull — 16.96

549 1.9E No. 1 1.849 18.73

550 1.4E No. 3 1.517 14.88

551 Cull Cull — 14.83

552 1.4E No. 1 1.697 18.67

553 1.4E No. 1 1.678 16.63

556 1.4E No. 3 1.378 16.96

557 Cull Cull — 16.58

558 1.4E No. 1 1.425 14.69

559 No. 1 No. 1 1.075 18.48

560 1.4E No. 1 1.556 16.77

561 1.4E No. 1 1.497 14.52

562 Cull Cull — 14.88

563 Cull Cull — 14.25

564 Cull Cull — 15.75

565 1.4E No. 1 1.201 16.81

566 Cull Cull — 13.27

567 Cull Cull — 16.50

568 1.4E No. 1 1.252 16.94

569 1.4E No. 1 1.219 17.75

570 1.4E No. 1 1.353 17.17

571 1.4E No. 1 1.234 16.67

572 1.4E No. 1 1.425 16.54

Log 

number

MSR 

grade

Visual 

grade

MOE

(x106 lb/in2)

Length

(ft)

Log 

number

MSR 

grade

Visual 

grade

MOE

(x106 lb/in2)

Length

(ft)

Mechanical Grading of 6-Inch-Diameter Lodgepole Pine Logs for the Travelers’ Rest and Rattlesnake Creek Bridges

 Grade assignments for individual logs using option 1 (two mechanical grades, 1.9E and 1.4E) (continued)

597 1.4E No. 1 1.240 15.02

598 Cull Cull — 14.63

599 1.4E No. 1 1.535 14.42

600 1.4E No. 1 1.430 14.75

601 Cull Cull — 14.75

602 Cull Cull — 14.54

603 1.4E No. 1 1.283 14.73

605 Cull Cull — 15.04

606 Cull Cull — 14.73

607 Cull Cull — 14.75

608 Cull Cull — 14.25

609 1.4E No. 1 1.286 14.52

610 1.4E No. 1 1.642 14.88

611 1.4E No. 1 1.659 20.52

612 Cull Cull — 19.00

613 1.4E No. 1 1.689 18.75

614 Cull Cull — 19.15

615 1.4E No. 1 1.394 18.98

616 1.4E No. 1 1.453 18.75

617 1.4E No. 1 1.678 18.83

618 1.4E No. 1 1.299 18.60

619 1.4E No. 3 1.511 20.71

620 Cull Cull — 18.42

621 1.4E No. 1 1.286 18.54

622 1.4E No. 1 1.419 20.73

577 1.4E No. 1 1.646 15.02

578 1.4E No. 1 1.543 14.77

579 Cull Cull — 14.13

580 1.4E No. 2 1.276 15.23

581 1.4E No. 1 1.494 16.27

582 1.9E No. 3 1.789 14.50

583 1.4E No. 1 1.391 14.73

584 Cull Cull .— 16.71

585 1.4E No. 1 1.684 14.44

586 Cull Cull — 14.63

587 Cull Cull — 14.83

588 Cull Cull — 14.44

589 1.4E No. 1 1.471 14.69

590 Cull Cull — 14.58

591 1.4E No. 1 1.613 14.81

592 1.4E No. 1 1.208 14.46

573 1.4E No. 1 1.554 15.02

574 Cull Cull — 14.92

575 Cull Cull — 14.71

576 1.4E No. 1 1.730 14.60