United States

Department of
Agriculture
Forest Service
Bolted-Connection
Forest Products
Laboratory
Design
General
Technical
Report Lawrence A. Soltis
FPL-GTR-54 Thomas Lee Wilkinson
Abstract Contents

Recent failures of bolted connections have raised doubts Page

about our knowledge of their design. Some of the design
criteria are based on research conducted more than Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
50 years ago. This paper compares results found in the
literature, using the European Yield Theory as a basis of Review of the Literature . . . . . . . . . . . . . . . . . . . . . . . . . 2
comparison, to summarize what is known about Analytical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
bolted-connection design and what needs further research.
By putting all this information in one place we hope to help Single-Bolt Connections . . . . . . . . . . . . . . . . . . . . . 2
engineers and architects design safer timber buildings and Multiple-Bolt Connections . . . . . . . . . . . . . . . . . . . . 2
structures.
Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
In general, the strength is known for a single bolt in a wood Single- and Multiple-Bolt Connections . . . . . . . . . 5
side member connection loaded parallel to grain in
compression. Less is known for single bolts in tension, Spacing, End, and Edge Distances . . . . . . . . . . . . 5
loaded perpendicular to grain or having steel side members. Other Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
The distribution of strength in a multiple-bolt connection is
Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
known for up to four bolts in a row. In summarizing the
literature we confirm the spacing, end, and edge distance Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
requirements in current multiple-bolt design for Douglas-fir
connections. No information exists for distribution of strength Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
or spacing requirements for multiple rows of bolts. Single-Bolt Connections . . . . . . . . . . . . . . . . . . . . . . . 14

The effects of other factors such as fabrication tolerances, Multiple-Bolt Connections . . . . . . . . . . . . . . . . . . . . . . 16

duration of load, and preservative or fire treatment are not Spacing, End, and Edge Distances . . . . . . . . . . . . . . 17
known. Fabrication tolerances appear to have a large effect
Other Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
on connection strength, but this effect has not been
quantified. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Literature Cited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Keywords: Connections, fasteners, timber, bolts, load
distribution, spacing, end distance, structures

July 1987

Soltis, Lawrence A.; Wilkinson, Thomas Lee. Bolted-connection design.

Gen. Tech. Rep. FPL-GTR-54. Madison, WI: U.S. Department of
Agriculture, Forest Service, Forest Products Laboratory; 1987. 21 p.

A limited number of free copies of this publication are available to the public
from the Forest Products Laboratory, One Gifford Pinchot Drive, Madison, WI
53705-2398. Laboratory publications are sent to over 1,000 libraries in the
United States and elsewhere.

The Laboratory is maintained in cooperation with the University of Wisconsin.

 Errata February 1990

United States
Department of Bolted-Connection
Agriculture
Forest Service
Design
Forest Products Lawrence A. Soltis
Laboratory Thomas Lee Wilkinson
General
Technical
Report
FPL-GTR-54

Page 4, Table 2

The yield theory equations for joints 3 and 3A should be transposed as follows:
Bolted-Connection
Design
Lawrence A. Soltis, Supervisory Research Engineer
Thomas Lee Wilkinson, Research Engineer

Forest Products Laboratory, Madison, WI

Introduction

Current U.S. design for the strength of a single-bolt During the past 60 years, several studies on bolted
connection is based mainly on the research conducted by connections have been conducted. Each study has
Trayer in 1932. The strength of a multiple-bolt connection is investigated one or more of the properties that affect
calculated by summing the single-bolt strength values after connection behavior. Direct comparison is difficult because
multiplying by a modifying factor that depends on how the the studies usually differ in more than one connection
load is distributed to each bolt. The modifying factors derive property. Therefore, in this report we use the European Yield
from research in the 1960’s (Cramer 1966, Lantos 1969). Theory (Johansen 1949) to form a common basis of
Strength in both single- and multiple-bolt connections is comparison.
achieved by having sufficient spacing, end, and edge
distances, as recommended by Trayer. Significant conclusions appear to have been drawn from
various results based on small samples having narrow
Recent failures have raised doubts about our basic ranges of connection properties such as the ratio of main
understanding of bolted connections. The objective of this member thickness to bolt diameter, L2/D. The results
paper is to combine and compare data in the literature on indicate that current design values for the proportional limit
single- and multiple-bolt connections to see what is known of single-bolt connections are generally correct but that
and what needs further research. information on the load-slip behavior and the distribution of
load among bolts is inadequate if the data are to be used for
The strength and stiffness of a single-bolt connection limit-states design or multiple-bolt connections.
depends on the physical and geometrical properties of the
members and the bolt. Member properties include number
and thickness of members, type of side members (steel or
wood), wood species, moisture content, and direction of
loading to the wood grain. Bolt properties include diameter
and yield stress. Geometric properties include bolthole
fabrication tolerances, spacing, and end and edge distances.
In addition, multiple-bolt connection strength depends on the
number of bolts in a row, the spacing and end and edge
distance of bolt rows, the distance between bolt rows, and
whether the rows are staggered or symmetric. Other factors
that affect both single- and multiple-bolt connections are
duration and rate of load and preservative or fire treatment.
Review of the Literature

Analytical The methods of basic mechanics suggested the use of

modifying factors to account for the distributions of load
Single-Bolt Connections among bolts in a row. lsyumov (1967) modeled connected
The only model describing the strength of a single-bolt members and bolted timber connectors as a series of linear
connection is the European Yield Theory originated by or nonlinear springs and then used a flexibility matrix
Johansen (1949). method of analysis. lsyumov verified his analysis by testing
bolts in combination with connectors and shear plates.
McLain and Thangjitham (1983) examined this theory for Cramer (1968) developed an analysis of mechanics based
bolted wood connections loaded parallel to grain and found on the extensional elastic stiffness of the connected
good agreement between predicted and observed values. members, the nonuniform stress distribution in the members,
Soltis and others (1986) found agreement between predicted and a connection slip modulus. He included deflection
and observed values for both parallel- and caused by bolt bending in his analysis. Cramer’s work was
perpendicular-to-grain loading. based on earlier work for steel construction. He verified his
analysis with perfectly machined connections having small
The yield theory assumes that the bearing capacity of a L2/D ratios. Lantos (1969) developed a similar approach
bolted connection is attained when either (a) the except that he assumed uniform stress distribution in the
compressive strength of the wood beneath the bolt is members. His work does not contain experimental
exceeded (Mode I failure) or (b) one or more plastic hinge verification.
develops in the bolt (Mode II or Ill failure). These
assumptions provide for several modes of failure depending The modifying factors in current design practice (American
on connection member dimensions, member strength, and Institute of Timber Construction (AITC) 1985, National Forest
bolt strength. Failure modes are displayed in table 1 for Products Association (NFPA) 1986) for load distribution
three-member connections and in table 2 for two-member between bolts is based on the Lantos (1969) and Cramer
connections together with the formulas for the yield strength, (1968) analyses. Wilkinson (1980) compared modifying
Fy, corresponding to each failure mode. factors calculated by the Cramer and Lantos methods and
found the resulting values for proportional limit loads varied
A common way of presenting bolted-connection test results by less than 2 percent. He also found the two methods
is to plot the normalized bolt-bearing stress versus the L2/D predicted the experimentally-found proportional limit strength
ratio. The normalized bolt-bearing strength is but overestimated the failure strengths. This was to be
expected because, by either method, the calculation
assumes linear load-slip behavior in single bolts. Wilkinson
(1986) extended Cramer’s work by using a piecewise linear
load-slip curve to predict failure loads. He took account of
where variability in single-bolt load-slip behavior and fabrication
Pn = normalized bolt-bearing strength tolerances to reflect actual connections. He concluded that
Fp = proportional limit strength, lb the load distribution in any row of bolts is unique and
L2 = main member thickness, in depends on the random fabrication effects on single-bolt
D= bolt diameter, in load-slip curves.
fc = main member compressive strength, Ib/in2.
Finite element analyses have been used to find the influence
If the yield strengths, Fy, are normalized, the formulas in of the connection parameters on stresses and strength.
tables 1 and 2 result. Much of the finite element work was developed for
orthotropic composite materials rather than wood.
There is a difference between proportional limit strength and
yield strength (fig. 1). The proportional limit is defined as the Tsiang (1984) reviewed the literature on finite element
point where the load-deformation curve becomes nonlinear. analyses of composite laminates. Most of the studies cited
For this paper, the yield strength is defined as the load at dealt with two-dimensional analyses of a single bolt.
the intersection of the tangents to the linear and nonlinear References to multiple-bolt connections indicated that their
portions of the curve. It has been defined differently by some failure mode was related to the ratio of the bolt load to the
researchers. Thus the yield theory may be expected to give total applied connection load. As this ratio approached unity,
higher normalized bolt-bearing strengths than reported in the the failure mode changed from a tensile or crack failure to a
literature. local bearing failure.

Multiple-Bolt Connections Wong and Matthews (1981) did a two-dimensional analysis

Three types of analysis have been used in research on of a two-hole bolt connection. They ignored the
multiple-bolt connections: basic mechanics, finite element, through-thickness stresses (tacitly assuming small L2/D).
and fracture mechanics analysis. Sometimes finite element Although their analysis showed some correlation with
and fracture mechanics analyses are combined. experimental data, they concluded a three-dimensional finite
element method was needed.
Table 1.–Yield theory equations for three-member joints
Mode of
failure number Normalized yield strength Pn
and failure Yield strength Fy
geometry

Fy = DL2S2

Fy = 2DL1S1

D = bolt diameter.

Sy = bolt yield stress.

S1 = embedment yield stress of side members.

S2 = embedment yield stress of main member.

L1 = side member thickness.

L2 = main member thickness.

fc = main member compressive strength.

β = S2/S1.

α = L2/L1

3
Table 2.–Yield theory equations for two-member joints
Mode of
failure number Yield strength Fy
and failure Normalized yield strength Pn
geometry

Fy = DL2S2

D = bolt diameter.
Sy = bolt yield stress.
S1 = embedment yield stress of member 1.
S2 = embedment yield stress of member 2.
L1 = thickness of member 1.
L2 = thickness of member 2.

4
Rowlands and others (1982) looked specifically at wood New Zealand researchers, Harding and Fowkes (1984),
materials and did a finite element analysis of a two-bolt studied the effect of end distance for parallel- and
pin-loaded hole connection based on assumptions of rigid perpendicular-to-grain loading. Their results indicated that
pins and linear elastic material properties. They found the end distance had a marked effect on perpendicular-to-grain
strength of a two-bolt ,connection was constant for bolt strength. As yet, however, New Zealand Standards have no
spacings or end distances more than four times the bolt requirements for perpendicular-to-grain end distance.
diameter.
Other Factors
Fracture mechanics analysis is concerned with determining
the stress intensity factors at a cracked fastener hole. Often Other factors that affect connection strength are moisture
a finite element procedure is used to compute the stress content, tension or compression loading, fabrication
intensity factors. Orringer and Stalk (1975) presented a tolerances, duration of load, and preservative or fire
method for Mode I and Mode II stress intensity factors at a treatment.
cracked fastener hole in a single row or a double staggered
row of fasteners in a panel under tension. Other literature is Several researchers have studied the effect of the moisture
available on orthotropic composites, but little has been content of timber on the strength of bolted connections
applied to lumber. (Doyle and Scholten 1963, Kunesh and Johnson 1968,
Longworth and McMullin 1963). in general, the connections
Experimental were fabricated at high moisture content and either tested at
the high moisture content or seasoned to a lower moisture
content and then tested. They compared results of both
Single- and Multiple-Bolt Connections tests with the strength of connections fabricated and tested
Over the past 60 years, several experimental studies have at the lower moisture content.
been conducted on bolted connections. Some of the more
significant studies for single-bolt connections are in assigning equal parts of a load to the bolts in a row, one
summarized in table 3 and for multiple bolt connections in tacitly assumes all boltholes have identical fabrication
table 4. All the studies listed are for seasoned wood with tolerance. Wilkinson (1980, 1986) identified variability in
moisture content ranging from 9 to 12 percent. fabrication tolerances as having a large effect on how the
load is distributed among bolts in a row. Dannenberg and
Not all geometric and material properties were given in Sexsmith (1976) also observed the significant effect of
these studies. Often the yield stress of the bolt and the hole
fabrication tolerances on load distribution for shear plate
fabrication procedure were not reported. (Goodell and connectors.
Phillips (1944) specifically investigated the effect of hole
roughness on single-bolt connection behavior. They drilled No research has been reported on the effects on the
holes with different drill bits, feed rates, and revolutions per strength of a connection of duration of load or treatment with
minute.) Although the wood species is usually given, the preservative or fire retardant.
specific gravity often is not. This lack of information makes
comparison of results difficult.

Spacing, End, and Edge Distances

Current design criteria for spacing, end, and edge distance
of bolted connections are based on experimental
observation. The 1986 National Design Specifications (NDS)
(National Forest Products Association) for spacing, end, and
edge distance are essentially those recommended by Trayer
in 1932. Trayer had broad experience with bolted
connections for aircraft components during the 1920’s and
based his recommendations on this experience. He also
recommended, for connections with two rows of bolts,
having the bolts opposite each other, not staggered, for
parallel-to-grain loading.

Fahlbusch (1949) made recommendations for spacing, end,

and edge distance based on maintaining critical tensile and
shear cross sections. His recommendations permit closer
spacing and less end distance than Trayer’s. Fahlbusch also
remarked that staggered bolt arrangements are to be
avoided but did not present any experimental results to
support this conclusion. in addition, he developed an
empirical modifying factor to relate the strengths of Figure 1–Schematic load-deformation curve for a bolted
multiple- and single-bolt connections. joint. (ML86 5420)
Table 3.–Geometric and material parameters for various studies of single-bolt connections
Number of Bolt and Load angle Number of
Source reference Main member Side members members in hole L2/D to grain
connection diameters replications

In

Grenoble (1925) White ash, 1/4-in steel plate 2, 3 0.18 to 1/2 1 to 16.5 Parallel 4
Sitka spruce and wood1 0.18 to 1/2

Trayer (1927) Sitka spruce 1/4-in steel plate 2, 3 1/4 to 1/2 2 to 12 30° to 90° 3
1/4 to 1/2

Trayer (1928)2

Trayer (1932) Douglas-fir, 1/4-in steel3 and 3 1/4 to 1 0 to 12 Parallel 4 or 5

yellow pine, wood
Sitka spruce,
oak, and maple

Do. do. do. 3 1/2 0 to 12 Perpendicular 4 or 5

Goodell and Phillips Douglas-fir and Steel 3 1/4, 1/2 3 to 4 Parallel 5, 13
(1944) Sitka spruce 1/4, 1/2
Plywood
Pitz (1952) Douglas-fir Steel 3 1/2 to 1 4 0 to 90 in 3
1/2 to 1 7-1/2° increments

Doyle and Scholten do. 5/1 8-in steel 3 1/2 to 1 2.6 to 5.3 Parallel and 3
(1963) plate or wood (plus 1/16 in) perpendicular
Wilkinson (1978) do. Wood 2, 3, 4 3/8 to 3/4 2 to 6 Parallel 6
(plus 1/32 in)

Smith (1982) Canadian and Wood 3 5/8 (plus 6 Parallel and 50

Polish spruce 1/16 in) perpendicular

Hirai and Sawada Spruce and fir 1/8-in steel plate 3 5/16 to 1/2 2 to 10 Parallel 3
(1982a)
Hirai and Sawada Spruce and fir Wood 3 3/8 2 to 10 Parallel 3
(1982b)
Soltis et al. (1988) Douglas-fir Wood 3 1/2 to 1-1/2 2 to 13.5 Parallel and 15
(plus 1/16 in) perpendicular
1
Wood side members are the same species as the main member.
2
Summarized Trayer (1927) and Grenoble (1925).
3
Except for connections with 1 -in bolts which used 5/8-in steel plate.

Codes The European CIB-Structural Design Code (International

Council for Building Research Studies and Documentation
Current design criteria (AITC 1985, NFPA 1986) for 1983) in contrast, bases the single-bolt design values on
single-bolt connections are based on Trayer’s (1932) equations derived from the European Yield Theory.
research. The codes present single-bolt design values in
tabular form for various species, diameters, and L2/D ratios. Current design criteria for multiple-bolt connections generally
have a load distribution factor and minimum spacing
The National Standard of Canada (Canadian Standards requirements.
Association 1984) has presented single-bolt design values in
a similar tabular form. The British Standard (Booth 1982)
defines single-bolt design values by an empirical formula
fitted to test data based on species and L2/D parameters.

6
Table 4.–Geometric and material parameters for various studies of multiple-bolt connections
Main member Side member
Bolt Number of Bolt Bolt end
Reference Specific Specific bolts L2/D
Species diameter spacing distance
Species gravity gravity
In In In
1
Doyle and Schotten Douglas-fir 0.43 5/16-in 0.43 1/2, 3/4, 1 1,4 2.5 to 5 4 5.25
(1963) steel and
Douglas-fir

Longworth and do. 0.49 to Douglas-fir 0.49 to 3/4 4 3.5 3 3

McMullin (1963) 0.52 0.52
1
Doyle (1964) do. 0.47 to 1/2-in 1/2, 3/4, 1, 8 4.3 to 3; 4.5 5.25
0.52 steel 6.5

Kunesh and Johnson do. 0.42 to Douglas-fir 0.42 to 3/4 1 to 6 2.2 1.5; 3
(1968) 0.54 0.54

Potter (1982) European 0.47 European 0.47 3/8 1 to 40 5.3 1.5 1.5
redwood redwood

Hirai and Sawada spruce 0.42 to steel 1/4 to 5/8 1 1.3 to 2.5 to
(1982b) and Hirai 0.45 6.7 10.5 x
(1983) diameter

Wilkinson (1986) Douglas-fir 0.41 to 3/16-in 3/4 2 to 7 1.5 6

0.55 steel
1
Total number of bolts in two rows.

The load distribution factor, expressed as a modifying factor, The European CIB-Structural Design Code (International
K, modifies the total allowable load on a connection, F. Council for Building Research Studies amd Documentation
1988) presented a modifying factor as an empirical equation
F = nKFb (2) for connections having more than four bolts in a row. The
load-carrying capacity of the connection is reduced by
where n is the number of bolts in the connection and Fb, is one-third for each bolt above the four-bolt threshold.
the allowable strength for a single bolt. Modifying factors for Spacing, end, and edge distance requirements are similar to
steel and wood side plates differ in value. those in the United States.
The modifying factors used in the United States (AITC 1985, The British Standard (Booth 1982) presented a modifying
NFPA 1988) are based on the elastic analyses of Lantos factor as an empirical equation. The spacing, end, and edge
(1989) and Cramer (1988). They are presented in tabular distance requirements are the same as in the United States.
form in terms of cross-sectional areas of the main and side
members. Spacing, end, and edge distance are presented
as multiples of bolt diameter.

The National Standard of Canada (Canadian Standards

Association 1984) similarly has presented modifying factors
and spacing, end, and edge distance requirements.

7
Results

The proportional limit load has been used as the basis of

comparison of the effects of connection variables on
single-bolt connections. Data on maximal loads or loads at a
given deformation, although included by some researchers,
are usually missing from the record. Actual load-deformation
curves have not been published, but example curves are
sometimes given.

In figures 2 to 17 we show the yield theory predictions for

comparison with experimental results. In some cases, the
compressive strength of the wood and/or yield strength of
the bolt had to be assumed.

Figures 2 and 3 show results from Grenoble (1925) as plots

of normalized proportional limit-bearing stress versus L2/D
ratio for two- and three-member connections with steel side
plates and loading parallel-to-grain.

Figures 4 to 8 show results from Trayer (1932).

Three-member connections with steel side plates, with
softwood species (fig. 4) and hardwood species (fig. 5)
were loaded parallel to grain and perpendicular to grain
(fig. 6). Three-member connections with steel and wood side
plates are compared in figures 7 and 8.

Figures 9 to 11 show results from Doyle and Scholten

(1963). Three-member connections with steel side plates
(fig. 9) and wood side plates (fig. 10) were loaded parallel to
grain. Perpendicular-to-grain results are shown in figure 11
along with results from Trayer (1932) on effect of bolt
diameter.

Results from Wilkinson (1978) are presented in figures 12

and 13 for connections loaded parallel to grain with various Figure 2–Results for proportional limit (Grenoble 1925)
ratios of main- to side-member thickness (fig. 12). Two- and and yield load (European Yield Theory) for
three-member connections are compared in figure 13. (a) three-member and (b) two-member connections of ash
with steel side plates. Parallel-to-grain loading
(Sy = 125,000 lb/in2; fc = 7,600 lb/n2; β = 0.16;
Results from Soltis and others (1986) are presented in S2 = 7.220 lb/in2). (ML86 5428)
figures 14 and 15 for three-member wood connections of
Douglas-fir loaded parallel to grain (fig. 14) and
perpendicular to grain (fig. 15).

Geometric and material parameters published with

experimental research on multiple-bolt connections are listed
in table 4.

Experimental results of three research teams are given for a

bolt pattern of 2 rows by 2 columns (table 5). The results are
given as modifying factors at proportional limit and at
ultimate strength. The current NDS design values (NFPA
1986) are given for comparison but recall that the NDS
values are based on the elastic theories of Lantos (1969)
and Cramer (1968) and applicable only below the
proportional limit. The results for a composite product (Pyner
and Matthews 1979) are included because of the orthotropic
nature of the material, the geometry of bolt patterns, and the
observed failure types in which composite resembles wood.
The results are useful for comparing load distribution among The modifying factors used in the United States and
bolts. Longworth and McMullin (1983) also tested the 2 by 2 Canada, Britain, and Europe are compared for connections
bolt pattern to determine the effects of moisture content, but having 1 to 10 bolts in a row with wood side members
we could not determine a modifying factor because they did (fig. 16a) and steel side members (fig. 16b). In all the
not give a value for a single bolt to use as a basis. standards, bolt spacings are four times bolt diameter, while
bolt end distance is four times bolt diameter for compression
Experimental results for load distribution of various bolt and seven times bolt diameter for tension loading. Edge
patterns are compared to the NDS-based analytic results in distance vanes from 1.5 to 2.0 times bolt diameter in the
table 6. Note some modifying factors have experimental various standards.
values greater than unity, which is theoretically impossible.
These results reflect experimental variability.

Results of elastic theory analyses have been compared by

Wilkinson (1980). The studies of finite element analysis were
undertaken to determine the influence of diverse parameters
on connection strength and thus are not comparable.

Figure 4–Results for proportional limit (Trayer 1932)

(fig. 5) and yield load (European Yield Theory) for
three-member connections of softwood species with steel
side plates. Parallel-to-gain loading (Sy = 45,000 Ib/in2;
fc = 5,250 lb/in2; β = 0.07; S2 = 3,360 lb/in2). (ML55 5421)

Figure 3–Results for proportional limit (Grenoble 1925) Figure 5–Results for proportional limit (Trayer 1932) and
and yield load (European Yield Theory) for yield load (European Yield Theory) for three-member
(a) three-member and (b) two-member connections of Sitka connections of hardwood species with steel side plates.
spruce with steel side plates. Parallel-to-grain loading Parallel-to-grain 2loading (Sy = 45,000 lb/in2; 2
(Sy = 125,000 lb/in2; fc = 5,400 lb/in ; β = 0.10; fc = 5,0245 lb/in ; β = 0.09; S2 = 4,020 Ib/in ; L1/D = 0.5).
2
2
S2 = 4,320 lb/in ). (ML54 5427) (ML86 5422)

9
Figure 6–Results for proportional limit (Trayer 1932) and Figure B-Results for proportional limit (Trayer 1932) and
yield load (European Yield Theory) for three-member yield load (European Yield Theory) for three-member
connections with steel side plates. Perpendicular-to-grain connections of softwoods with steel and wood side plates.
loading (Sy = 45,000 Ib/in2; L1/D = 0.5). (ML86 5412) Parallel-to-grain loading (Sy= 45,000 lb/in2;
fc = 5,130 lb/in2; S2 = 3,283 lb/in2). (ML86 5413)

Figure 7–Results for proportional limit (Trayer 1932) and Figure 9–Results for proportional limit (Doyle and Scholten
yield load (European Yield Theory) for three-member 1963) and yield load (European Yield Theory) for
connections of hardwoods with steel and wood side plates. three-member Douglas-fir connections with steel side
Parallel-to-grain loading (Sy = 45,000 Ib/in2. plates. Parallel-to-grain loading (Sy= 48,000 Ib/in2;
fc = 5,024 Ib/in2; S2 = 4,020 Ib/in2). (ML86 5424) fc = 6,460 lb/in2; β = 0.09; S2 = 4,134 lb/in2). (ML86 5414)

10
Figure 10–Results for proportional limit (Doyle and Figure 12–Results for proportional limit (Wilkinson 1978)
Scholten 1963) and yield load (European Yield Theory) and yield load (European Yield Theory) for three-member
for three-member Douglas-fir connections with wood all-wood connections with various side member
2
side plates. Parallel-to-grain loading (Sy = 48,000 lb/in ; thicknesses. Parallel-to-grain loading (Sy = 45,000 lb/n2;
fc = 6,460 lb/in2; S2 = 4,194 Ib/in2; α = 1.615; β = 1). fc = 7,670 lb/in2; S2 = 4,960 Ib/in2; β = 1). (ML86 5425)
(ML86 5415)

Figure 13–Results for proportional limit (Wilkinson 1978)

and yield load (European Yield Theory) for two- and
three-member all-wood connections. Parallel-to-grain
loading (Sy = 45,000 lb/in2; fc = 7,000 lb/in2; β = 1;
S2 = 4,480 Ib/in2). (ML86 5410)

Figure 11–Effect of bolt diameter on normalized bearing

stress at zero L2/D. Perpendicular-to-grain loading.
(ML86 5416)

11
Figure 14–Results from Soltis, Hubbard, and Wilkinson Figure 15–Results from Soltis, Hubbard, and Wilkinson
(1986) comparing yield theory with experimental results for (1985) comparing yield theory with experimental results for
(a) 1/24-inch-, (b) 1-inch-, and (c) 1-1/2-inch-diameter bolts in (a) 1/2-inch-, (b) 1-inch-, and (c) 1-1/2-inch-diameter bolts in
connections loaded parallel to grain. (ML86 5417) connections loaded perpandicular to grain. (ML86 5409)

12
Table 5.–Values of modifying factor K for a two-row by tow-column bolt pattern.
Reference Proportional Ultimate
limit NDS

Doyle and Scholten (1963) 1 2

Wood side plates, parallel-to-grain 0.65-0.95 0.85-0.98 0.97
1 2
steed side plates, parallel-to-grain .76- .92 .84- 94 .88
1 2
Wood side plates, parpendicular-to-grain .53- .82 .70- .80 .97
1 2
Steel side plates, perpendicular-to-grain .68- .89 .63- .82 .83

Kunesh and Johnson (1988)

Wood side plates, parallel-to-grain 0.91 0.99 .92

Pyner and Matthews (1979)

Laminated glass fiber reinforced plastic .81
1
Based on 0.08-in slip; proportional limit values not given in the original paper.
2
Dependant on bolt diameter.

Table 6.–Values of modifying factor K for various bolt patterns

Bolts Modifying factor, K
Reference Number Pattern Proportional Ultimate
limit NDS

Doyle (1964) 1 1
Steel side plates, parallel-to-grain 8 4 rows × 1.03 to 1.24 0.61 to 0.87 0.87
2 columns

Kunesh and Johnson (1988)

wood side plates, 2 1 row × 1.05 1.08 1.0
parallel-to-grain 2 columns
2 2 rows × .90 .86 1.0
1 column
8 3 rows × .89 .71 .98
2 columns
8 2 rows × 1.10 .79 1.0
3 columns
Potter (1982)
Wood side plates, 2 1 row × .96 1.0
parallel-to-grain 2 columns
2 2 rows × .92 1.0
1 column
6 3 rows × .79 .95
2 columns
1
Dependant on bolt diameter and spacing.

13
 Single-Bolt Connections
The yield theory, giving the equations of tables 1 and 2,
appears to predict the trend seen in the results of all
researchers. In general, experimental values fall below the
yield theory curves, as expected, because the proportional
limit load is smaller than the yield load (fig. 1). Soltis and
others (1988) give yield loads that agree closely with the
yield theory curves (fig. 14).

Results for parallel-to-grain loading appear to agree more

closely with the yield theory than results for
perpendicular-to-grain loading (fig. 6). The ratio between
proportional limit load and yield load is not known but is
suspected to be larger for perpendicular-to-grain loading.

Hardwood species have a higher normalized bearing stress

than softwoods at zero L2/D Grenoble (1925) had Pn = 0.8
for Sitka spruce (fig. 3) and Pn = 0.95 for ash (fig. 2).
Trayer (1932) had Pn = 0.65 for softwoods (fig. 4), and
Pn = 0.80 for hardwoods (fig. 5). Differences in bolthole
diameter are suspected of causing the differences between
researchers.

Trayer (1932) concluded that three-member connections

with steel side plates carried 20 percent more load at
proportional limit than connections with wood side members
when loaded parallel to grain. The yield theory indicates a
difference over only a limited range of L2/D values (figs. 7
and 8). Trayer did not compare connections that had small
L2/D values. The scatter in his data is greatest where the
yield theory predicts the greatest difference between steel
and wood side plates.

Trayer (1932) concluded there was no difference between

steel and wood side plates in connections when the loading
was perpendicular to grain. He gave no results for
connections with wood side plates. The yield theory
indicates no difference over a wide range of L2/D values and
a slight difference at L2/D values greater than 9 (fig. 17).
Figure 16–Load-distribution modifying factors defined by
U.S. and Canadian, British, and European standards for Grenoble (1925) concluded that two-member connections
(a) wood side members and (b) steel side members. carried half the load of three-member connections having
(ML86 5426) the same L2/D value. His data and the yield theory appear
to support his conclusion over the range of L2/D values
evaluated (figs. 2 and 3). His conclusion does not appear
valid for L2/D values less than 2. Wilkinson (1978) obtained
similar results for two- and three-member connections with
wood side plates (fig. 13).

Most tests of three-member wood connections have been

with a main member twice the thickness of the side member.
Doyle and Scholten (1963) used a main-member thickness
1.6 times that of the side member (fig. 10). Wilkinson (1978)
examined several ratios of main- to side-member thickness
(fig. 12). Again, the yield theory predicts the general effect of
various member thicknesses.

14
Tests of connections with steel side plates have generally Trayer (1927) and Pitz (1952) investigated directions of
been made with a constant steel thickness for all bolt loading between 0 and 90° to the grain. In both studies,
diameters and lengths. The yield theory predicts differing boltholes were equal to the bolt diameter, and steel side
results for various ratios of side-plate thickness to bolt plates were used. The Hankinson formula is
diameter (figs. 2-4 and 9). This effect could account for
some of the scatter in experimental results.
(3)
For connections loaded parallel to grain the NDS allows
75 percent more strength with steel than with wood side where
members for bolts of 1/2-inch diameter or less, 25 percent
more for 1-1/2-inch-diameter bolts, and proportional values N = bearing stress at angle θ
for intermediate diameters. The NDS recommendation is P = bearing stress parallel-to-grain
based in part on having equal connection deformation for Q = bearing stress perpendicular-to-grain
wood and steel side members. The yield theory indicates
that the increased strength for steel side members should be Both Trayer and Pitz found that this formula could be used
related to the L2/D ratio and to the ratio of steel thickness to to calculate the bearing stress at various angles to the grain.
bolt diameter, L1/D. Pitz found that the Osgood formula fitted his data slightly
better than the Hankinson formula.
Researchers have used a variety of bolt yield stresses. Steel
aircraft bolts with a yield stress of 125,000 lb/in2 and The Osgood formula is
low-carbon steel bolts with a yield stress of 45,000 lb/in2
have both been used. Trayer (1932) indicated that different
results might be expected for high-strength bolts, and this is
borne out by the yield theory. Soltis and others (1986) found
that the yield stress varied with the bolt diameter:

Bolt diameter Yield stress

In Lb/in2
1/2 44,600
1 87,100
1-1/2 90,500

The size of boltholes has ranged from being equal to the

bolt diameter to being 1/16 inch larger. It has already been
pointed out that bolthole size probably affects the normalized
bearing stress at zero L2/D, and thus the embedment yield
stresses S1 and S2. Hirai and Sawada (1982b, c) had a
Pn = 0.47 for zero L2/D, much lower than the values
obtained by other researchers. Their hole diameter is
unknown.

The smoothness of the bolthole can also affect the value of Figure 17–Comparison of three-member connections of
the proportional limit load, as indicated from results of Sitka spruce and steel side plates when loaded
Goodell and Phillips (1944) (fig. 18). perpendicular to grain.
Trayer (1932) indicated an effect of bolt diameter on the Wood side plates Steel side member
normalized bearing stress at zero L2/D when loading is
perpendicular to grain (fig. 11). Results from Doyle and
Scholten (1968) indicate the possibility of a similar effect
although obscured by the scatter in their data.

(ML86 5423)

15
 Multiple-Bolt Connections
In general, modifying factors determining the load
distribution among bolts in a row are determined by methods
of basic mechanics analysis that assume fairly widely
spaced bolts and elastic material properties. The
calculations use values of single-bolt elastic load-slip
modulus and areas and moduli of elasticity for the main and
side members. The theory derivation assumes bolt elastic
bending is included in the deformation. The experimental
verification of the theory was based on small values of L2/D,
implying Mode I failure.

Experimental results are the basis for spacing, end, and

edge distances. All experimental studies were three-member
connections with a wood main member and either wood or
steel side members (table 4). Most studies had small L2/D
ratios corresponding to Mode I failures; some studies had
L2/D ratios corresponding to Mode II failures, but no studies
had large L2/D ratios corresponding to Mode Ill failures.
Most studies had connections fabricated with carefully
aligned holes 1/16 inch larger than the bolt diameter,
washers, and nuts tightened finger tight. Usually the yield
strength of the bolts was not determined. Tests were
conducted at slow rates of loading, and loads were
Figure 18–Load-deformation curves for 1/2-inch aircraft bolts considered static.
in 2-inch Sitka spruce showing effect of rate of feed (Goodell
and Phillips 1944). (ML86 5411) The analyses done by finite element and fracture mechanics
usually determined the influence of some connection
variable on its strength properties. All finite element analyses
Most researchers have used sample sizes of three to five were two-dimensional analyses; by implication, they are
specimens. Soltis and others (1986) used 16 replications. valid only for small L2/D ratios and Mode I failures. Most
Smith (1982) concluded that sample size should be 20 or analyzed two bolts in a row at most, using elastic properties.
more for parallel-to-grain loading and 30 or more for Most assumed a load imparted by the bolt to the main
perpendicular-to-grain loading in order to describe the member and thus cannot be used for determining modifying
population of connection behaviors adequately. Smith found factors.
that the three-parameter Weibull distribution best described
the results, while the normal distribution gave good It has been known for many years that the load is distributed
representation in most cases. unequally among bolts in a row. In a butt-type joint, the
outermost and innermost bolts in the row transmit a greater
Trayer (1932) gave some data for bearing stress at a proportion of the load than intermediate bolts.
deformation of 0.1 inch that indicate that the ratio of bearing
stress at 0.1 inch to bearing stress at proportional limit Comparing theoretical (NDS) modifying factors with
decreases with increased L2/D ratio. Doyle and Scholten experimental results for a bolt pattern consisting of two rows
(1963) gave loads at several levels of deformation as well as by two columns (table 5), we find relatively good agreement
at maximal loads. Their range of L2/D values was too narrow for wood side members parallel-to-grain and steel side
to indicate any effect of the L2/D ratio as compared to members parallel- and perpendicular-to-grain. The NDS
deformation results at proportional limit. modifying factor for wood side members
perpendicular-to-grain, however, is larger than that from
None of the researchers presented load-deformation curves experimental results. It appears that, when NDS values were
nor any model for describing the load-deformation derived, the same modulus of elasticity was used for both
relationship. grain directions. Because the longitudinal modulus is much
greater than the radial or tangential modulus of elasticity for
wood, the resulting NDS values are too high. The same
observation applies to values both at the proportional limit
and at ultimate strength, even though the NDS values are
theoretically correct only to the proportional limit. This
problem does not occur in regard to steel side plates which
are isotropic.

16
Comparing NDS modifying factors with experimental results The standard test procedure (ASTM D 1761) requires either
for other bolt patterns (table 5) we see that four is the compression or tension loading. However, to simplify testing
maximum number of bolts in a row considered. The most researchers have used compressive loading. The
modifying factor for four bolts in a row is nearly unity effects of tension loads on spacing, end, and edge distances
(figs. 16a, b). The modifying factor decreases between 4 are not known.
and 10 bolts in a row. Except for Cramer’s work (based on
perfectly machined holes and small L2/D ratios), there is little Most of the research results mentioned above were based
experimental verification of the distribution of a load among on loading parallel-to-grain. Fewer perpendicular-to-grain
more than four bolts in a row. results are available, but these limited data suggest that
current design is adequate. In most of the research
Comparing United States, Canadian, and European Douglas-fir species were used for the main member. For
recommendations (figs. 16a, b), we encountered the other species data are very limited.
prevailing uncertainty regarding more than four bolts in a
row. All recommend modifying factors of 0.9 to 1.0 for a row No research is available to determine the spacing
of less than four bolts, but their values for K diverge for a requirements between rows of bolts for either staggered or
row of more than four bolts. symmetric configurations.

Few research results exist for less than four bolts in a row Other Factors
(tables 5 and 6). Comparisons for one, two, or three bolts in
a row show modifying factors near unity at the proportional Other factors that influence connection strength are moisture
limit and slightly less at ultimate load. content, fabrication tolerances, duration of load, and
preservative or fire treatment.
No theory or experimental results are available to determine
how load is distributed when there are multiple columns of The limited research (Doyle and Scholten 1963, Kunesh and
bolts with either staggered or symmetric rows. Johnson 1968, Longworth and McMullen 1963) on the effect
of moisture content on the strength of multiple-bolt
Spacing, End, and Edge Distances connections yields consistent results. A connection at
30 percent moisture content has about 60 percent of the
Current spacing, end, and edge distance design proportional limit strength of a connection at 12 percent
requirements for bolts in a row are those recommended by moisture content. The three studies were for relatively small
Trayer (1932). Trayer recognized that the stress distribution L2/D ratios (table 4). No results are available for larger L2/D
beneath the bolt for various L2/D ratios affects the spacing ratios. The yield theory suggests effects of moisture content
and end distance required if maximal capacity of the may not be as large at the larger L2/D ratios where
connection is to be developed. He concluded, however, that bolt-bending Mode II and III failures occur.
using spacing and end distance requirements based on
small L2/D ratios would be conservative for larger L2/D Fabrication tolerances have been identified as the variable
ratios. having perhaps the largest effect on connection strength
(Wilkinson 1980, 1986). Earlier experimental research
The effect of L2/D on end distance has only recently been usually followed current design practice of making the bolt
quantified by Hirai and Sawada (1982a) for spruce hole 1/16-inch oversize. This assumes 1/16 inch is an
specimens. Their results are reproduced in figure 19. attainable fabrication tolerance. To approximate actual
fabrication practices more closely, current research at the
Other researchers, referred to in the review of literature Forest Products Laboratory is considering the effects on
above, have studied spacing and end distances connection strength of other oversize hole sizes as well as
experimentally or analytically. Almost al&have confirmed that improper hole alignments.
the current recommendation of an end distance four times
the bolt diameter is satisfactory in parallel-to-grain The effect of the duration of load on the strength properties
compression loading. The experimental studies have noted a of wood has long been recognized. Current design assumes
change in failure mechanism at this end distance. For end the duration-of-load factor applies to the stressed wood
distances less than four diameters, a shear plug or tensile beneath a bolt regardless of L2/D ratio. Intuitively, one
crack failure indicates insufficient end distance. For end expects the effect to be greater for Mode I failures
distances greater than four diameters, there is a bolt-bearing (wood-crushing) than for Mode Ill failures (bolt-bending), but
failure. Figure 19 also confirms this; for end distances no research has been done to verify this.
greater than 4.5 times bolt diameter, the bolt-bearing
strength is relatively constant for all L2/D ratios. For an end The effect of preservative or fire treatment on single-bolt
distance of 2.5 times bolt diameter, the bolt-bearing strength strength or on the distribution of load or spacing, end, or
is notably less than for larger end distances whatever the edge distances has not been researched.
L2/D ratio.

17
Figure 19–Connection bearing strength dependent on ratios
of length in main member to bolt diameter, L2/D, and end
distance to bolt diameter, e/D. (ML86 5419)

Some other observations relate to method of loading, factors are based on strength; connection stiffness is not
proportional limit versus ultimate strength comparisons, and considered.
strength of bolt. Most early research was based on the
ASTM standard test of subjecting a three-member Most of the early work was done before the research related
connection to parallel-to-grain compressive loads. Few data to the yield theory. Thus bolt yield strength was not deemed
exist for tension, moment, or combined axial/moment loading an important parameter. It is difficult to predict how research
or for other angle-to-grain loading. Also, no data exist for results would be affected by a consideration of higher
dynamic or cyclic loading of multiple-bolt connections. strength bolts and larger L2/D ratios.

The analytical methods are based on elastic theory, the

results being valid only to the proportional limit. Experimental
results seem to give more repeatable results at ultimate
load, but proportional limit loads are used to compare to
theoretical results. Modifying factors might be changed if
ultimate strength were used as a basis. Additionally, all

18
Summary

The yield theory presents a means of looking at the results Spacing and end distance requirements of four times the
for single-bolt connections of a number of researchers bolt diameter have been theoretically and experimentally
together. It expresses the general trend of existent data. As verified for Douglas-fir main members with parallel-to-grain
expected, experimental results at the proportional limit compressive loading. Limited information is available for
usually fall below the yield theory curves. The ratio to be other species, loading, or angle to grain. No information is
expected between yield and proportional limit load is available for spacing between staggered or symmetric bolt
unknown. However, the trend of the results indicates current rows.
design values based on the proportional limit are generally
correct. United States, Canada, and Europe have similar code
requirements for modifying factors and spacing
The yield theory indicates that the greater strength of a requirements.
connection with steel rather than wood side plates should be
related to the L2/D ratio and to the ratio of steel thickness to Moisture content affects connection strength at small L2/D
bolt diameter, L1/D. ratios. Its effect at larger L2/D ratios is not known. The
effects of other factors such as fabrication tolerances,
Most research has been done with parallel-to-grain loading. duration of load, and preservative or fire treatments are not
The yield theory agrees more closely with the results of known. Fabrication tolerances are known to have a large
parallel-to-grain loading than of perpendicular-to-grain impact on connection strength, but this impact has not been
loading, for which fewer data exist. quantified.
Significant conclusions appear to have been drawn from
results based on a small sample size and narrow range of
connection properties such as the L2/D ratio. Information on
the load-slip behavior and on the distribution of properties is
inadequate if bolt data are to be used for limit-states design
or multiple-bolt connections.

The strength of a multiple-bolt connection is the sum of the

single-bolt values, multiplied by a modifying factor. The
modifying factor is based on an elastic theory of load
distribution; it is valid only to the proportional limit. The
theory is well verified by a number of experimental studies
for two bolts in a row where the modifying factor is unity.
Less experimental verification exists for two to four bolts in a
row, but the results do indicate a factor near unity (although
the NDS has substantially lower values for steel side plates
and small main member). For more than four bolts in a row,
data to substantiate the theory are very limited.
The NDS modifying factors for connections with wood side
members loaded perpendicular to grain are higher than test
results. This may result from using the longitudinal modulus
of elasticity in the Cramer (1968) theory rather than the
radial or tangential modulus.

The elastic theory does take elastic bending of bolts into

account. Most of the experimental verification is for small
L2/D ratios corresponding to Mode I failures. Some
verification exists for L2/D ratios corresponding to Mode II
failures. No verification exists for a row of bolts with larger
L2/D ratios.

Neither theory nor experimental data exist to determine load

distribution to more than one row of bolts. No theory or data
exist to recommend staggered or symmetric bolt patterns for
multiple rows of bolts.

19
Literature cited

20
 2.2-6/ 87

21
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