United States

Department of

Agriculture

Forest Service

Forest

Products

Laboratory

Research

Paper

FPL 376

December 1980

Assessment of

Modification Factors

for a Row of Bolts

or Timber Connectors
Abstract

When bolts or timber connectors

are used in a row, with load applied

parallel to the row, load will be unequally distributed among the fasteners. This study assessed methods of

predicting this unequal load distribution, looked at how joint variables can

affect the distribution, and compared

the predictions with data existing in

the literature. Presently used design

procedures were also assessed. The

analytical methods were found to

predict proportional limit loads but

not joint strength.

Contents

Page

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

Discussion of Analytical Methods of Analysis ..................................................... . 1

Available Analytical Methods ................................................................. .1

Present Design Procedures .................................................................. . 2

Effect of Variables Upon Analytical Results ..................................................... .

3

Comparison of Analytical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Discussion of Experimental Load-Slip Values for Single Fasteners ................................... . 7

Experimental Results for Rows of Fasteners ...................................................... . 5

Conclusionsand Recommendations ............................................................ . 6

Suggested Additional Work.. .................................................................. . 7

LiteratureCited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
United States

Department of

Agriculture

Forest Service

Forest

Products

Laboratory1

Research

Paper

FPL 376

Assessment of

Modification Factors

for a Row of Bolts

or Timber Connectors

BY

THOMAS LEE WILKINSON, Engineer

Introduction

When bolts or timber connectors

are used in rows parallel to the direction of loading, there is an unequal

distribution of load among the

fasteners in the row. Thus, if the

design load for the row of fasteners

is based on the load for a single

fastener times the number of

fasteners, a modification factor must

be applied for the unequal distribution of load. This modification factor

may be a function of many joint

variables; for purposes of design, it

should be as simple as possible to

apply while being sufficiently accurate and efficient.

Modification factors exist in the

design procedures (1,9)2 for a row of

fasteners. These factors have been

based on analytical methods of

analysis for the distribution of load

among the fasteners. The present

study was initiated to determine the

adequacy of the design procedures

and the underlying assumptions used

to arrive at the presently used

modification factors.

Discussion of Analytical

Methods of Analysis

Available Analytical

Methods

Several investigators have

developed methods of analysis for

the distribution of load among

fasteners in a row. These methods

are based on the extensional stiffnesses of the joint members and the

load-slip characteristics of an individual fastener. Lantos (8) assumed

that the direct stresses in the joint

members are uniformly distributed

across their cross section, and that a

linear relationship exists between

fastener deformation and fastener

load. His work contains no experimental verification.

Cramer (2) developed a similar approach, except he corrected for the

nonuniform direct stress distribution

in the members; Cramer established

the value of the joint slip modulus

with the aid of an analysis of the

bearing stress distribution under the

fasteners. He verified his analysis on

a limited number of perfectly

machined joints.

lsyumov (6) developed a method of

analysis where the timber connectors

and joint members were represented

by a series of either linear or

nonlinear springs. This work contains

numerous test results for multiple

fastener joints.

1

 Maintained at Madison, Wis., in cooperation

with the University of Wisconsin.

2

 Italicized numbers in parentheses refer to

Literature Cited at the end of report.

1
Foschi and Longworth (5) have 

developed a method of determining 

the load distribution (on griplam 

nailed connections) that can predict 

the ultimate load on the joint. 

Present Design Procedures 

Modification factors for application 

to a row of bolts, lag screws, or 

timber connectors are given in CSA 

Standard 086 (1) and in the NDS (9). 

These reduction factors can be defined as: 

(1) 

where α = modification factor for 

the row 

N = number of fasteners in 

the row 

F = total load carried by the 

row 

and P = maximum fastener load. 

The ratio P/F is obtained by use of an 

analytical method of analysis. The 

values of P and F would be design 

loads when designing a joint. The 

presently listed values of α were 

based on the Lantos (8) method (appendix A). The joint variables involved 

in this method of analysis are: 

E1 = elastic modulus of the 

main member, pounds per 

square inch 

E2 = elastic modulus of the 

side members, pounds per 

square inch 

A1 = cross-sectional area of 

the main member, square 

inches 

A2 = cross-sectional area of 

the side members, square 

inches 

= load-slip value for a 

single fastener, pounds per 

inch 

N = number of fasteners in 

the row 

and S = spacing of fasteners in 

the row, inches. 

The present design procedure is: 

First, select the design load for a 

single fastener as listed in either (1) 

or (9) ; second, multiply by the number 

of fasteners in the row; and third, 

multiply by the appropriate modification factor. This gives the design load 

for the row of fasteners. 

The presently used modification 

factors are reproduced in tables 1 

and 2. The only variables listed in 

these tables are number of fasteners, 

N, and the member areas, A, and A,. 

Some other variables involved in the 

analytical analysis are listed in table 

3.3 Reviewing the data in these tables, 

it appears the Lantos method of 

analysis was used to calculate 

modification factors for joints with 3 

through 8 fasteners in a row; these 

results were then extrapolated to 

joints with 12 fasteners in a row and 

for joints with 2 fasteners in a 

For a row with two fasteners, it 

was assumed that the load is shared 

equally. This is not borne out by the 

Lantos analytical results. For a row 

with more than eight fasteners, the 

extrapolation resulted in modification 

factors smaller than the analytical 

results in some cases and larger in 

other cases. The factors for the larger 

Based on unpublished information obtained from the Canadian Wood Council. 

Figure 1.-Modification factors based on each of the end fasteners in a 

6-fastener row for two values of the single fastener load-slip constant. 

(M 148 227) 

2 
evident in figures 10 and 11.

Figures 7 through 11 show that,

when there is a large imbalance in

stiffness between the side members

and main member, the load will be

unequally distributed among the

fasteners in the row. In practice,

when there is a large difference in

elastic modulus of the members there

can be a compensating difference in

cross-sectional area of the members.

Comparison of Analytical

Methods

The most applicable methods to

use for calculating modification factors for design procedures are those

by Lantos (8) (appendix A) and by

Cramer (2) (appendix B). The difference in these methods is a correction by Cramer for the nonuniform

direct stress distribution in the

members.

A comparison of the modification

factors calculated with the Lantos

and Cramer methods is given in

figure 12 for a joint with steel side

plates and in figure 13 for a joint with

wood side plates. A 1/2-inch-diameter

bolt was arbitrarily chosen as the

fastener for use with the Cramer

method. (Use of a larger diameter bolt

would result in a smaller modification

factor, assuming that both bolts had

the same load-slip value. For example, the modification factor for a

1-inch bolt is approximately 1 percent

smaller than for the 1/2-inch bolt. The

Schulz multiplying factor which

causes this difference is explained in

appendix B.) This comparison shows

a difference of less than 2 percent in

calculated modification factors by the

two methods. The Cramer method

gives slightly greater reduction.

Because there is such a small difference between the two methods, the

Lantos method would be-more

favorable for use in calculating

design factors because of its simpler

nature.

Discussion of

Experimental Load-Slip

Values for

Single Fasteners

A search of existing U.S. Forest

Products Laboratory data for bolt and

timber connector joints was made to

gain an insight of the single fastener

load-slip characteristics.

4

Some typical load-slip curves are

shown in figures 14, 15, and 16. The

slopes of the assumed linear portions

that would be used in the analytical

methods are indicated on the plots. It

can be seen that a single value for a

load-slip curve does not fully

characterize the behavior of a single

fastener. This is especially true if the

analytical methods are to be used to

predict the maximum load for a row

of fasteners.

Many joint variables may affect the

load-slip value for a single fastener

joint. These variables include such

things as kind and size of fastener,

bearing length of the fastener in the

members, species of wood, type of

side plate (wood or metal), and direction of loading with respect to the

wood grain. These variables also affect the proportional limit and maximum loads.

A comparison of load and load-slip

values for some different kinds of

fasteners is contained in table 4. As

would be expected, the timber connectors have larger values than bolts.

Size and type of connector appears to

have a greater effect on load values

than it does on the load-slip value.

The effect of fastener bearing

Figure 3.–Modification factors based on each of the end fasteners in a

g-fastener row for two different side member areas.

(M 148 229)
length in the member is given in table

5 for a 4-inch shear plate and table 6

for a 1/2-inch bolt. The load-slip value

appears to remain nearly constant

with changes in bearing length for

both fasteners. The greatest effect is

upon the maximum load. Both maximum load and proportional limit load

become fairly constant after a

limiting bearing length is exceeded.

The effect of wood species is

shown in table 7 for a 1/2-inch bolt

and in table 8 for a 4-inch shear plate.

This effect appears to be very slight

except upon maximum load.

Table 7 also shows the effect of

side member material upon load and

load-slip values. All values are considerably larger for metal side

members.

Table 9 shows the effect of grain

direction upon proportional limit load

and load-slip value. Values are considerably higher for parallel-to-grain

loading than for perpendicular-tograin loading.

Another fact observed in looking at

the load-slip values for individual

fasteners was the large range in

values for supposedly matched

specimens. This is illustrated by the

values in table 10 for a 1/2-inch bolt in

southern pine.

From the examined FPL data, the

assumed load-slip values used to arrive at the modification factors in (1)

and (9) are on the conservative side

with the exception of 4-inch shear

plates and 4-inch split rings. These

larger timber connectors have loadFigure 4.–Effect of single fastener load-slip value upon the multiple-fastener

joint modification factor for a joint with wood side plates.

(M 148221)

slip values of about 400,000 pounds

per inch. The assumed values may be

overly conservative for most bolts and

also for perpendicular-to-grain

loading.

From the number of variables that

may affect the load-slip value and its

range, it is apparent that a means of

predicting the load-slip value or distribution of load-slip values is desirable.

It would be desirable to predict the

entire load-slip curve up to maximum

load. This would permit the prediction

of load distribution for a row of

fasteners up to maximum load.

Experimental Results

for Rows of Fasteners

A limited number of experimental

evaluations of multiple-fastener joints

are listed in the literature (4,6,7,9,10).

A comparison was made of the predicted loss in joint strength as given

by the Lantos method of analysis and

by the present design procedures

with the experimental results in these

studies. Tables 11 through 15 contain

joint variables and modification factors for studies by lsyumov (6), Doyle

(4), Kunesh and Johnson (7),

Dannenberg and Sexsmith (3), and

Stern (10). The information needed to

calculate the modification factors

was not always provided. Where it

was lacking, estimated values (as indicated in the tables) were used.

Some studies gave only maximum

loads and others gave both maximum

loads and proportional limit loads. Experimental modification factors are

given for both loads where available.

In all cases, the Lantos method of

analysis over-estimated the maximum

strength of the joint. This can be seen

by comparing the modification factors based on maximum test loads to

the calculated factors. The present

design factors also over-estimated

the strength. This may be due to unequal contact between each of the

fasteners and the fastener holes at

zero load. This could cause some of

the fasteners to carry more than their

predicted amount of the joint load.

Another possible contributing factor

could be the mode of failure. This

could possibly be different for the

fasteners in a row than for a single

fastener.

The Lantos method of analysis

came closer to predicting the reduction in proportional limit loads. This

is as expected because the single

fastener load-slip value is that up to

5
proportional limit load. In some

studies the modification factors

based on proportional limit test loads

were higher than predicted by the

Lantos method of analysis; in other

studies, they were lower. This may be

due to difficulties in determining what

the proportional limit load is for a row

of fasteners.

Reference (3) also contained information on the distribution of load

among the connectors in a row. From

these data, Dannenberg and Sexsmith

concluded that (1) the connector

loads of a multiconnector joint are

nonuniform, and (2) the permissible

dimensional tolerances in the

manufacture of the specimen have a

significant effect upon the load

distribution and the ultimate load of

the specimen. They suggest that any

analysis of load distribution should

include random errors for dimensional

tolerances in order to accurately

predict the connector loads. Their

data not only showed erratic distribution of load among the fasteners (fig.

17), but it also showed that the

distribution was different for each

side plate (fig. 18).

A comparison of design loads (arrived at by following procedures in

reference (9) and maximum test loads

showed a ratio of test to design load

of 4.5 to 5.8 for the joints in reference

(7) and 4.3 to 6.1 for the joints in

reference (10). Thus, even though the

present recommended modification

factors for multiple-fastener joints do

not accurately predict, the loss in

strength from test, the ratio of test to

design loads appears adequate. It

should be kept in mind that the tests

reported herein do not reflect the entire range of joints listed in the

design procedures.

Conclusions and

Recommendations

The following conclusions apply to

fasteners placed in a row parallel to

the grain and loaded parallel to the

grain:

1. Present methods of analysis appear to predict the proportional limit

load for a row of fasteners. However,

the actual proportional limit load can

be difficult to determine experimentally.

2. Present analytical methods overestimate the strength (failure load) of

a row of fasteners as would be ex6

petted because the methods do not ference in single fastener stiffness,

take into account the nonlinear load- and (b) the different procedures by

slip behavior of a single fastener. which design loads are developed.

3. Assumed values of joint

variables used to arrive at modification factors for use in design procedures are adequate to conservative.

Fewer assumptions would be needed

if tables of modification factors were

based on EA rather than A.

5. It would be desirable to have an

analytical method of predicting single

fastener load-slip relations to failure.

4. It may be desirable to have

separate tables for bolts and timber

connectors due to (a) the large dif6. It would be desirable to have an

analytical method of predicting the

distribution of load among fasteners

in a row; such a method must account for fabrication tolerances and

nonlinear load-slip relations for single

fasteners.

Figure S-Effect of single fastener load-slip value upon the multiple-fastener

joint modification factor for a joint with steel side plates.

(M 148222)
Suggested

Additional Work

From the preceding assessment of

analytical methods of determining

load distribution among fasteners in

a row and of experimental data for

single- and multiple-fastener joints,

several areas for additional experimental and analytical work are

apparent. The following list contains

some of those areas:

1. Modify present methods of

analysis to allow for different

nonlinear load-slip relations for each

fastener. These modifications could

also include fabrication tolerance effects by allowing for slip without

load.

2. Conduct a random simulation of

nonlinear load-slip relations and

fabrication tolerance for fasteners in

a row to obtain statistical distributions of modification factors for

design procedures.

3. Verify modified methods of

analysis with experimental tests in

which (a) the amount of slip before

contact between the fasteners and

members is measured, (b) the

distribution of load among the

fasteners is measured all the way to

failure, (c) the slip of each fastener is

measured, and (d) joints are evaluated

over a range of member stiffnesses,

EA, and number of fasteners per row.

4. Reassess the procedures for arriving at the values of design loads

for single fastener joints.

5. Develop an analytical method of

predicting the single fastener loadslip relation all the way to failure

load.

6. Investigate the load distribution

in rows of fasteners where the

loading is perpendicular to the grain.

This should include how to define

joint area and also the effects of

shrinkage.

Figure 6.–Effect of fastener spacing upon the multiple-fastener joint modification factor for a joint with steel side plates. 

7

(M 148 223)

Figure 9.–Effect of relative member area upon the multiple-fastener joint

modification factor for a joint with wood side plates. Curves for A1/A2 > 1 are

governed by first fastener in the row, while curves for A1/A2 < 1 are

governed by the last fastener.

(M 148 224)

Figure 10.–Effect of relative member elastic modulus upon the multiplefastener joint modification factor for a joint with wood side plates. The

curve for E1/E2 = 1.5 is governed by the first fastener in the row, while

the curve for E1/E2 = 0.75 is governed by the last fastener.

(M 148 219)
Figure 11.–Effect of main member elastic modulus upon the multiple-fastener

joint modification factor for a joint with steel side plates. The curve for

E1 = 0.6 x 106 lb/in2 is governed by the last fastener in the row while the

other curves are governed by the first fastener.

(M 148 228)

10
Figure 12.–Comparison of the Cramer and Lantos methods of calculating

modification factors for rows of fasteners in a joint with steel side plates.

(M 148 218)

Figure 13.–Comparison of the Cramer and Lantos methods of calculating

modification factors for rows of fasteners in a joint with wood side plates.

(M 148 217)

11
Figure 14.– Typical load-slip curve for

a 2-5/8-inch shear plate in white

pine. (3/4-in. bolt; 3/8- by 4-in. steel

side plates, and 3.0- by 3.6-in. main

member).

(M 148 214) Figure 15.–Typical partial load-slip

curve for a 1/2-inch bolt in Sitka

spruce with loading parallel to the

grain. (2- by 3-in. wood side plates;

4-by 3-in. main member; maximum

load = 9,100 lb.; L/D = 8.)

(M 148215)

Figure 16.–Typical partial load-slip

curve for a 1/2-inch bolt in Sitka

spruce with loading perpendicular

to the grain in the main member.

(2-by 3-in. side members; 4- by 3-in.

main member; maximum load =

4,400 lb.; L/D = 8.)

(M 148 216)

12
Figure 17.–Distribution of load among four connectors in a row as measured

by Dannenberg and Sexsmith (3).

(M 148231)

13
Figure 18.–Load in each side plate carried by connector number 3 as determined by Dannenberg and Sexsmith (3).

(M 148 230)

14
Table 1 .–Modification factors for timber connector, bolt, and laterally loaded lag-screw joints with wood side plates as listed

in (1) and (2)

A1/A2

(1) A1

(2) Number of fasteners in a row

2 3 4 5 6 7 8 9 10 11 12

.......................................................................................................................................................................................

In.2

0.5(3,4) <12 1.00 0.92 0.84 0.76 0.68 0.61 0.55 0.49 0.43 0.38 0.34

12-19 1.00 .95 .88 .82 .75 .68 .62 .57 .52 .48 .43

>19-28 1.00 .97 .93 .88 .82 .77 .71 .67 .63 .59 .55

>28-40 1.00 .98 .96 .92 .87 .83 .79 .75 .71 .69 .69

>40-64 1.00 1.00 .97 .94 .90 .86 .83 .79 .76 .74 .72

>64 1.00 1.00 .98 .95 .91 .88 .85 .82 .80 .78 .76

1.0(3,4) <12 1.00 .97 .92

12-19 1.00 .98 .94

.85 .78 .71

.89 .84 .78

.65 .59 .54 .49 .44

.72 .66 .61 .56 .51

>19-28 1.00 1.00 .97 .93 .89 .85 .80 .76 .72 .68 .64

>28-40 1.00 1.00 .99 .96 .92 .89 .86 .83 .80 .78 .75

>40-64 1.00 1.00 1.00 .97 .94 .91 .88 .85 .84 .82 .80

>64 1.00 1.00 1.00 .99 .96 .93 .91 .88 .87 .86 .85

(1)A1 = Cross sectional area of main members before boring or grooving; A2 = sum of the cross-sectional areas of side members before boring

or grooving.

(2)When A1/A2 exceeds 1.0, use A2 instead of A1.

(3)When A1/A2 exceeds 1.0, use A2/A1.

(4)For A1/A2 between 0 and 1.0, interpolate or extrapolate from the tabulated values.

Table 2.–Modification factors for timber connector, bolt, and laterally loaded lag-screw joints with metal side plates as listed

in (7) and (9)

A1/A2

(1) Number of fasteners in a row

A1 2 3 4 5 6 7 8 9 10 11 12

................................................................................................................. .

2-12

12-18

18-24

24-30

30-35

35-42

In.2

25-39

40-64

65-119

120-199

40-64

65-119

120-199

200

40-64

65-119

120-199

200

40-64

65-119

120-199

200

40-64

65-119

120-199

200

40-64

65-119

120-199

200

1.00 0.94 0.87

1.00 .96 .92

1.00 .98 .95

1.00 .99 .97

1.00 .98 .94

1.00 .99 .96

1.00 1.00 .98

1.00 1.00 1.00

1.00 1.00 .96

1.00 1.00 .97

1.00 1.00 .99

1.00 1.00 1.00

1.00 .98 .94

1.00 .99 .97

1.00 1.00 .98

1.00 1.00 .99

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

.96 .92

.98 .95

.99 .97

1.00 .98

.95 .89

.97 .93 .88

.98 .96 .93

.99 .98 .96

0.80

.87

.91

.95

.90 .85 .80 .75 .70 .67

.93 .90 .86 .82 .79 .75

.96 .94 .92 .89 .86 .83

.98 .97 .95 .93 .91 .90

.93

.94

.98

1.00

.90

.93

.96

.98

.86

.90

.95

.97

.82

0.73 0.67 0.61 0.56 0.51 0.46 0.42

.81 .75 .70 .66 .62 .58 .55

.87 .82 .78 .75 .72 .69 .66

.92 .89 .86 .84 .81 .79 .78

.62 .58

.72 .69

.80 .78

.88 .87

.89

.93

.96

.98

.85

.90

.94

.97

.80 .74 .69 .65

.86 .82 .79 .76

.92 .89 .87

.95 .93 .92

.85

.90

.80 .74

.86 .81

.92 .88

.95 .93

.75 .69

.82 .77

.89 .85

.93 .90

.84

.89

.94

.96

.79 .74 .69

.86 .83 .80

.92 .90 .88

.95 .93 .92

.68 .64

.76 .72

.85 .82

.90 .89

.63 .58

.71 .67

.81 .78

.87 .84

.64 .59

.76 .73

.86 .85

.92 .91

.61 .58

.73 .71

.83 .81

.89 .89

.60 .57 .55

.68 .65 .62

.80 .78 .77

.87 .86 .85

.53 .49 .46

.63 .59 .56

.76 .73 .71

.82 .80 .78

(1)A1 = Cross-sectional area of main member before boring or grooving; A2 = sum of cross-sectional areas of metal side plates before drilling

15
Table 3.–Values of variables used in

Lantos’ method of analysis to

arrive at modification factors for

rows of fasteners(l)

Joints with E, E2

S

.......................................................................

Million Million Million

Ib/in.2lb/in.2lb/in. In.

Wood side

members 1.8 1.8 0.22 6.5

Metal side

members 1.4 30.0 .33 5.75

(1) Moduli and load-slip values are from

unpublished information obtained from the

Canadian Wood Council.

Table 4.–A comparison of load and load-slip values for some different kinds of fasteners

in southern pine with loading parallel to the grain

Fastener

type

Main member

Thick- Width

ness

.................................................................

In. In.

4-inch split ring 3 5-1/2

4-inch shear plate 3 5-1/2

2-5/8-inch shear plate 3-1/2 3-1/2

1/2-inch bolt 3 3

Side

member

material

Load at

Proportional Maximum

limit

Load.

slip

value

wood

metal

metal

wood

Lb Lb

27,000 40,440

17,670 43,050

9,670 25,830

2,100 8,730

Lb/in.

422,660

431,240

390,160

86,840

Table 5.–Effect of fastener bearing length in the main member u on load and load-slip

values for a 4-inch shear plate in southern pine with loading parallel to the grain

Main member (1)

Width Thickness

Load at

Proportional Maximum Load-slip

limit value

........................................................................................................................................

In. In. Lb Lb Lb/in.

5-1/2 1-1/4 14,330 24,860 442,820

5-1/2 2 15,330 36,360 413,290

5-1/2 3 17,670 43,050 431,240

5-1/2 4-1/4 19,330 44,070 409,970

5-1/2 5-1/2 19,330 42,730 382,460

5-1/2 7 20,000 44,310 482,080

(1) Side members were steel

Table 6.–Effect of bolt bearing length upon load and load-slip values for a 1/2-inch bolt in

southern pine with loading parallel to the grain

Main member Side member Load at

Width Thickness Width Thickness Proportional Maximum Load-slip

limit value

.........................................................................................................................................

In. In.

3 2

3 3

3 4

3 5

In. In. Lb

3 1 1,900

3 1-1/2 2,100

3 2 2,180

3 2-1/2 2,000

Lb Lb/in.

5,720 78,400

8,730 86,840

9,240 79,890

9,720 68,560

16
Table 7.–Effect of species and side member material upon load and load-slip values for a

1/2-inch bolt with loading parallel to the grain

Main member Load at

Species Width Thickness Proportional Maximum Load-slip

.......................................................................................................................

limit value

In. In. Lb Lb Lb/in.

METAL SIDE MEMBERS

Oak

Maple

Southern pine

3 3

3 3

2,440 — 136,890

3,280 — 121,730

3 3 2,880 — 121,810

WOOD SIDE MEMBERS (1- BY 3-INCH)

Oak

Sitka spruce

Southern pine

Maple

2 3

2 3

2,120 6,980 98,860

1,820 5,010 76,200

2 3

2 3

1,900 5,720 78,400

2,150 9,620 83,500

Table 8.–Effect of species upon load and

load slip values for a 4-inch shear

plate with loading parallel to the

grain (3.1/2. by 5-1/2-inch main

member, steel side members)

Load at

Species Proportional Maximum Load-slip

............................................................................

limit value

Lb Lb Lb/in.

Oak

White

pine

20,670 50,280 369,650

16,830 35,870 425,680

Table 9.–Effect of grain direction upon load and load-slip values for a 1/2-inch bolt with

metal side members (3- by 3-inch main members)

Proportional limit with Load-slip value with

loading with respect to

Species

loading with respect

the grain to the grain

Parallel Perpendicular Parallel Perpendicular(1)

....................................................................................................................................................

Maple

Southern pine

Lb Lb Lb/in. Lb/in.

3,280 1,950 143,870 80,940

2,880 2,280 121,810 108,790

(1) Main member only.

Table 10.–Variation in load and load-slip values for matched specimens of southern pine

with a 1/2-inch bolt and metal side members

Main member Load at

Thickness Width Proportional Maximum

limit

Load-slip

.....................................................................................................................................

value

In. In. Lb Lb Lb/in.

1 3 2,100 3,360 150,000

1,900 3,290 126,670

2,300 3,450 109,520

2,500 3,240

2,100

104,170

3,380 123,530

Average 2,200 3,340 122,780

2 3 2,600 7,080 144,440

2,400 6,830 133,330

2,600 6,680 216,670

2,800 6,640 140,000

Average 2,600 6,810 158,610

17
Table 11.–Experimental results by lsyumov (6) for a row of timber connectors in Douglas-fir with steel side members and

loading parallel to the gram

Single fastener Elastic Ratio of Area of Ratio of Maximum Modification factor, a

Shear Number of Spacing Load-slip Maximum modulus elastic main member load for Based on From Present

plate fasteners S value load of main moduli of member areas row of maximum Lantos’

size N

design

member members A1

E1

(1) E1/2

(1) A1/A2

fasteners test loads analysis factor(2)

..........................................................................................................................................................................................................

In.

4

2-5/8

4

2-5/8

2-5/8

Million

In. Lb/in. Lb lb/in.2

In.2 Lb

7 9.00 344,830 29,250 2 0.067 48.56 9.71 160,300 0.78 0.82 0.75

6 6.75 185,190 22,500 2 .067 24.28 8.09 — — .88 (3)—

7 9.00 357,140 30,840 2 .067 45.09 9.02 — — .80 .75

6 6.75 138,890 19,080 2 .067 22.55 7.52 50,800 .44 .89 (4) —

4 6.75 (1)138,890 (1)19,080 2 .067 22.55 7.52 43,500 .57 .96 (4)—

(1) No values were given for the modulus of elasticity, therefore a value of 2 million lb/in.2

 was assumed for dry Douglas-fir and 30 million lb/in.2

for steel.

(2) Values taken from table 2.

(3) The main member area for these joints is smaller than any listed in table 2.

(4) No test of single fastener joints was made with this size member. Single fastener values from previous joint listed in the table were used.

Table 12.–Experimental results by Doyle (4) for a row of bolts in laminated Douglas-fir with steel side members and loading parallel to the

grain

Single fastener(1)

Elastic Ratio of Propor- Modification factor ?

( 2 )

Load- Propor- modulus elastic Area of Ratio of tional Maximum Based on Based on

Number slip tional Maximum of main moduli of main member limit load for propor- maximum From

Bolt

bolts

Spacing value limit load member member member areas load for row of tional test Lantos’

diameter S load E1 E1/E2 A1 A1/A2

row of fasteners limit load analysis

N fasteners test

load

....................................................................................................................................................................................................

Million

In. In. Lb/in. Lb Lb lb/in.2

In.2 Lb Lb

3/4 4 3.0 348,750 5,58 0 13,350 1.93 0.064 12.19 4.06 23,000 32,44 0 1.03 0.61 0.89

3/4 4 4.5 368,820 6,27 0 14,480 2.46 .082 12.19 4.06 26,000 35,96 0 1.04 .62 .88

3/4 4 3.0 360,590 6,13 0 13,930 2.16 .072 12.19 4.06 24,320 38,56 0 .99 .69 .90

3/4 4 3.0 360,590 6,13 0 13,320 1.89 .063 12.19 4.06 26,200 41,40 0 1.07 .78 .89

3/4 4 3.0 300,370 6,60 0 13,180 2.13 .071 12.19 4.06 24,840 33,16 0 .94 .63 .91

1/2 4 3.0 202,140 2,83 0 9,800 2.01 .067 12.19 4.06 14,000 30,92 0 1.24 .79 .94

1/2 4 4.5 176,110 3,17 0 12,130 2.62 .087 12.19 4.06 14,520 42,08 0 1.15 .87 .94

1/2 4 3.0 111,030 3,22 0 9,330 2.02 .067 12.19 4.06 13,320 34,52 0 1.03 .92 .96

(1) Member dimensions for the single fastener test were 3-1/4 by 3-1/4 in. as compared to 3-1/4 by 3-3/4 for the multiple fastener test.

(2) All main member areas are smaller than listed in table 2, table of modification factors used in design.

18
Table 13.–Experimental results by Kunesh and Johnson (7) for a row of 3/4-inch bolts in 1-5/8-inch thick Douglas-fir members with loading

parallel to the grain

Single fastener Elastic Ratio of Propor- Modification factor ?

Number Load- Propor- modulus elastic Area of Ratio of tional Maximum Based on Based From Present

of Spacing slip tional Maximum of main moduli of main member limit load for propor- on Lantos’ design

bolts S

(1) value limit load(3) member members member areas load for row of tional test analysis factor(5)

N load(s) E

(4)

E1/E2 A1 A1/A2

row of fasteners limit load loads

fastenners test loads

..............................................................................................................................................................................................................

In. Lb/in.

2 3.0 150,000

3 3.0 150,000

2 3.0 150,000

2 3.0 150,000

2 3.0 150,000

Lb Lb

4,680 8,580

4,680 8,580

4,680 8,580

4,680 8,580

4,680 8,580

Million

lb/in.2

2

2

2

2

2

ln.2

1 5.21

1 6.20

1

5.89

1 5.89

1 5.89

0.5

.5

.5

.5

.5

Lb Lb

7,840 13,170 0.84 0.77 0.99 1.00

12,910 18,160 .92 .71 .97 .92

8,340 14,840 .89 .86 .99 1.00

5,000 8,920 .53 .52 1.00 1.00

6,400 16,380 .68 .95 .99 1.00

(1) This spacing is less than the minimum permitted in design and may cause a different mode of failure than occurred in the single fastener test.

(2) No slip values were given, therefore an assumed value of 150,000 Ib/in.2

 was assumed.

(3) These values are from a specimen which was 1-5/8 by 3-13/16 in.

(4) No values were given for the modulus of elasticity, therefore a value of 2 million lb/in2

 was assumed for dry Douglas-fir.

(5) Values taken from table 1.

Table 14.–Experimental results by Dannenberg and Sexsmith (3) for a row of special pressed shear plates in laminated southern pine with

steel side members and loading parallel to the grain

Single fastener Elastic Ratio of Area of Ratio of Maximum Modification factor ?

Number Spacing Load-slip Maximum modulus elastic main member load for Based on From Present

of S value load(1) of main moduli of member areas row of maximum Lantos’ design

connectors member members A1 A1/A2

connectors test loads analysis factor(3)

E1

(2) E1/E2(2)

..............................................................................................................................................................................................

Million

In. Lb/in. Lb lb/in.2

In.2Lb

2 9 152,000 33,820 2 0.067 56.25 8.65 48,700 0.72 1.00 1.00

4 9 152,000 33,820 2 ,067 105.62 10.83 81,600 .60 .99 .95

(1) Single fastener values were obtained on a joint with main member of 6-1/4 by 5 inches.

(2) No values were given for the modulus of elasticity, therefore a value of 2 million lb/in2

 was assumed for dry southern pine and 30 million Ib/in.2 for steel.

(3) Values taken from table 2.

19
Table 15.–Experimental results by Stern (10) for a row of 2-1/2-inch split rings in Douglas-fir with loading parallel to the grain

Single fastener(1)

Elastic Ratio of Modification factor a

Number Loadof

Propor- modulus

Proporelastic Area of Ratio of tional

Spacing slip

Maximum Based on Based on From Present

main member limit

connec- S

load for

value

tional Maximum of main moduli of

limit load(3) member members member

propor- maximum Lantos’

tors E

(2) A1/A2

load for

design

row of tional test

load E1/E2 A1

analysis factor(3)

row of connec- limit load

connec- tors test load

tors

......................................................................................................................................................................................

In Lb/in.

2 5.5 182,000

2 5.5 182,000

3 5.5 182,000

3 5.5 182,000

3 5.5 182,000

4 5.5 182,000

4 5.5 182,000

2 5.5 182,000

2 5.5 182,000

3 5.5 182,000

3 5.5 182,000

3 5.5 182,000

Lb Lb

9,700 18,400

9,700 18,400

9,700 18,400

9,700 18,400

9,700 18,400

9,700 18,400

9,700 18,400

9,700 18,400

9,700 18,400

9,700 18,400

9,700 18,400

9,700 18,400

Million

lb/in.2

2 1

2 1

2 1

2 1

2 1

2 1

2 1

2 1

2 1

2 1

2 1

2 1

In.2

5.89 0.50

14.95 .50

14.95 .50

5.89 .50

14.95 .79

9.52 1.24

14.95 .79

9.66 .83

10.75 .50

10.75 1.21

10.75 .50

10.25 .50

Lb Lb

16,800 27,70 0

18,200 33,50 0

27,400 41,50 0

28,300 36,20 0

28,000 51,30 0

40,300 53,00 0

39,206 51,80 0

19,400 23,75 9

18,300 31,300

27,200 39,25 0

27,250 40,65 0

29,200 46,00 0

0.87 0.75 0.98 1.00

.94 .91 .99 1.00

.94 .75 .97 .95

.97 .66 .93 .92

.96 .93 .98 .96

1.04 .72 .92 .89

1.01 .70 .95 .92

1.00 .66 1.00 1.00

.94 .85 .99 1.00

.93 .71 .97 .95

.94 .74 .96 .92

1.00 .83 .96 .92

(1) Single fastener values are the average of three specimens, two of which had main and side members of 2-9/16 by 4-15/16 in and one which had a main member

of 1-5/8 by 5-9/16 in. and side members of 2-11/16 by 5-9/16 in.

(2) No modulus of elasticity value was given, therefore a value of 2 million Ib/in.2

 was assumed for dry Douglas-fir.

(3) Values taken from table 1.

20
Literature Cited

1. Canadian Standards Association.

Code of recommended practice for engineering design in timber. CSA

Stand. 086.

2. Cramer, C. O.

1968. Load distribution in multiple-bolt tension joints. J. Struct. Div., Amer.

Sot. Civil Eng. 94(ST5):1101-1117. Proc. Pap. 5939. (May)

3. Dannenberg, L. J., and R. G. Sexsmith.

1976. Shear-plate load distribution in laminated timber joints. Rep No. 361,

Dep. Struct. Engr., School of Civil and Environ. Engr., Cornell Univ. (July)

4. Doyle, D. V.

1964. Performance of joints with eight bolts in laminated Douglas-fir. U.S.

Dep. Agric., For. Serv., Res. Pap. FPL 10. For. Prod. Lab., Madison, Wis.

5. Foschi, R. O., and J. Longworth.

1975. Analysis and design of griplam nailed connections. J. Struct. Div.,

Amer. Sot. Civil Eng. 101(ST12):2537-2555. Proc. Pap. 11766. (Dec.)

6. Isyumov, N.

1967. Load distribution in multiple shear plate joints in timber. Dep. of

For., Pub. No. 1203, Ottawa, Ontario, Canada.

7. Kunesh, R. H., and J. W. Johnson.

1968. Strength of multiple-bolt joints: influence of spacing and other

variables. Report T-24, For. Res. Lab., School of For., Oregon State Univ.,

Corvallis. (Mar.)

8. Lantos, G.

1969. Load distribution in a row of fasteners subjected to lateral load.

Wood Sci. 1(3):129-136. (Jan.)

9. National Forest Products Association.

1977. National design specification for wood construction. Wash., D.C.

10. Stern, E. G.

1940. A study of lumber and plywood joints with metal split-ring connectors. Bull. No. 53, The Pennsylvania State College, Engr. Exp. Stn. (July)

21
APPENDIX A 

Lantos’ Method of Analysis (8) 

The modification factor for a row of fasteners as given by Lantos’ method is the smaller value of 

or 

where 

n = the number of fasteners 

and 

and 

where 

and 

Ei, Eo = modulus of elasticity of the main and side members, respectively. 

Ai, A, = cross sectional area of the main and side members, respectively. 

and 

where 

In equation A8, 

y = the single fastener load-slip value 

and 

S = the fastener spacing. 

22 

The quantities in equations A3 and A4 are defined as 
APPENDIX B 

Cramer’s Method of Analysis (2) 

The modification factor for a row of fasteners as given by Cramer’s method is the smaller of 

or 

Where 

n = the number of fasteners, 

F = total load on the row of fasteners, 

P1 = load carried by first fastener in the row, and 

Pn = load carried by nth fastener. 

P1 and Pn are obtained by solving the following set of simultaneous equations for the individual fastener 

loads, Pi. 

(B3) 

(B4) 

and 

The quantities in equations B3 through B5 are given by 

and 

where 

r = fastener spacing, 

Y = slip-load value (i.e. /P) for a single fastener, 

bp = width of side plate, 

bw = width of main member, 

tp = thickness of one side plate, 

tw = thickness of main member, 

Ep = modulus of elasticity of the side plates, 

Ew = modulus of elasticity of the main member, 

= Schulz multiplying factor for the side plates, and 

= Schulz multiplying factor for the main member. 

The Schulz multiplying factor is shown in figure B1 and is a function of bolt diameter, d. 23 

(B5) 

(B6) 

(B7) 

(B8) 

(B1) 

(B2) 
Figure B1.–Schulz multiplying factor.

(M 148 237)

24

U.S. GOVERNMENT PRINTING OFFICE: 1980-750-027125

2.5-25-12/8 0
Metric Conversion

Factors

1 in. = 25.4 mm

1 in.2 = 645.16 mm2

1 lb = 4.4482 N

1 lb/in. = 0.175 N/mm

1 lb/in.2 = 6894.7 Pa