Analysis of Mechanical Joints in Wood

Paper p resen ts the s t resses a round a bo l t - loaded hole in tens i le S i tka-spruce plates, and d i scusses the resul ts re la t ive to the fo rmu la t i on of rat ional des ign c o n c e p t s for m e c h a n i c a l jo in ts

by T.L. Wilkinson and R.E. Rowlands

ABSTRACT--Stresses and strains associated with single- fastener mechanical joints in wood are determined numerically and experimentally, Effects of friction, and variations in joint geometry and ratio of pin-to-hole diameter are evaluated. The results obtained provide design information for single- and multiple-bolt connectors, indicating that superior designs would use close-fitting pins and suggesting that optimum end distance should be eight times the hole radius.

List of Symbols a = plate-end distance b = one-half the plate width E = elastic modulus G = shear modulus P = plate load per unit of thickness Q = reduced-stiffness coefficient R = loaded-hole radius r = pin radius I = plate thickness

x = rectangular coordinate y -- rectangular coordinate 3, = shear strain e = normal strain 0 = polar coordinate

= coefficient of friction u = Poisson's ratio o = normal stress r = shear stress

Introduction Wood and composite structures often employ bolted

joints. The design and strength of such fasteners involves proper end distances and spacings of the loaded holes. Since there are no available analytical solutions associated with loaded holes in wood, current design procedures for mechanical fasteners are empirical in nature and exist only for the simplest types of joints . Lack of knowledge

T.L. Wilkinson is Research Engineer, l-orest Products Laboratory, Forest Service, USDA, Madison, WI 53706. R.E. Rowlands (SESA Member) is ProJessor, Department o f Engineering Mechanics, University o f HTsconsin-Madt~on, Madison, H'153705,

Paper was presented at 1979 SESA Spring Meeting held in San I-)'aneisco, CA on May 20-25.

Original manuscript submitted: March 10, 1980. Final version received." t'ebruary 23, 1981.

The korest Products Laboratory is maintained in Madison, 14"1, in co- operation with the University oJ Wisconsin.

of the stress distribution in the neighborhood of loaded holes in anisotropic media has previously prevented development of such design criteria.

This paper presents the stresses around a bolt-loaded hole in tensile Sitka spruce plates, and discusses the results relative to the formulat ion of rational design concepts for mechanical joints. Two joint specimens were deliberately loaded to failure. Fini te elements, ',2 strain gages and moir~ ~ were employed. The analysis is plane-stress. The effect on the stress distribution of joint geometry (end and edge distances), friction, and the ratio of pin-to-hole diameter are evaluated. Although a linear constitutive relationship is assumed for the wood, the problem is significantly nonlinear due to the increasing area of contact with load.

This work may represent the first full-field experimental- numerical determination of the stresses associated with the loaded holes of mechanical joints in wood. Experi- mental results of associated problems are extremely limited: Oplinger 4.~ analyzed pin-loaded holes in metal and composite plates; Frocht and HilF presented photo- elastic and strain-gage results of a pin-loaded hole in a loaded aluminum plate; photoelastic studies on inter- ference-fit pins have been conducted by Lambert and Brailey,: and Jessop, Snell, and Holis ter? Nisido and Saito ~ combined photoelasticity and interferometry to separate the stresses in the neighborhood of pin-loaded holes in plates. All investigations but those of Refs. 1 through 5 involved isotropic materials. The only previous photomechanical applications to wood known t o the authors are those of Refs. 3, 10 and 11.

While details of the analysis technique employed here are described in Refs. 2 (finite element) and 3 (molr6 and holography), the present paper extends the concepts to the solution of a class of pressing engineering problems.

Analysis One member of a mechanical joint in wood w a s

modelled physically and mathematically as a plane-stress, tensile orthotropic strip containing a single, bolt-loaded hole of diameter 2R (Fig. 1). The strip (finite width 2b and finite end distance a) was loaded in tension far from the hole (P newtons per centimeter of plate thickness), this load being resisted by the pin of radius r. Using both finite element and experimental techniques (moir~ and strain gages), the stresses and strains in the neighborhood of the loaded hole were determined as a function of geometry and bolt clearance r /R , Results of this paper are

408 �9 November 1981

TABLE 1 --MATERIAL AND GEOMETRIC PROPERTIES OF SITKA-SPRUCE PLATES USED FOR EXPERIMENTAL ANALYSIS

Exx = 14.5GPa # = 0.7 Eyy = 0.57GPa R = 0 . 6 4 c m Gxy = 0.66 GPa t = ,0.64 cm Vxy = 0.53

Tensile strength parallel to the grain = 89.7 MPa Compressive strength parallel to thegrain = 35.6 MPa Tensile strength perpendicu!atr to the grain = 2.6 MPa Compressive proportional limit perpendicular

to the grain = 4 MPa Shear strength parallel to the grain = 7.9 MPa

used to load the holes. Photomechanical details are in Ref. 3; a representative moir&fringe pattern is presented in Fig. 2. Unless otherwise stated, all results are based on the properties of Table i. These orthotropic elastic quantities presented in 1able l are from tested Sitka spruce (7-percent moisture content) specimens of 0.64~cm thickness.

Stresses were evahmted from measured strains by Hooke's Law:

confined to Sitka spruce wood with the grain parallel to the direction of loading.

The finite-element analysis employed quadratic iso- parametric elements. The orthotropic axes of material symmetry of the wood were parallel and perpendicular to the axes of loading and geometric symmetry. Mathematical and geometric symmetry permitted numerical modeling of only a vertical half of the joint of Fig. 1. The bolt was considered rigid. A coefficient of friction of # = 0.7 was used, '2 and the numerical analysis provided for regions of slip and nonslip along the contacting surface. Details of the numerical analysis are contained in Refs. 1 and 2.

The Sitka spruce plates for experimental, analysis were 0.64 cm thick with a 1.27-cm-diam hole. Steel pins were

P ( N / c m ) .,%

a-U2 I,l,t-woo .

C D

A Y

2 b l --

L x

Fig. 1- -Schemat ic diagram of pin-loaded wood plate

Fig. 2 - -Mo i r~ fr inge pattern for a pin- loaded hole in a Sitka-spruce plate (40 ~'pmm; a = 5.08 cm; b = 2.54 cm; r = 0.60 cm; r/R = 0.936; t = 0.64 cm). Pattern is for lines of constant displacement, u, in the di rect ion of the appl ied load

-35 I I I 1

P=1,4OO N/cm - 3 0 F = 0.7

~ f i n i t e a = 5 . 0 8 c m - Q.

' \ e l e m e n t b = 2 . 5 4 cm -25 - ) \ r e s u l t s R = O . 6 3 5 c m -

m O ~ r /R = 0 . 9 7 4

~ ond e l a s t i c p r o p e r t i e s r ~ o f Table I - _o 0

b~' o i r e results ---~

-5

0 J I I I 0 0.5 I.O 1.5 2.O 2.5 (A) x, cm

Fig. 3 - -Compar ison of numerical and moir~ results along the line A-B of Fig. 1

Experimental Mechanics �9 409

-35

-3O o

n

. -25 m

o, -20 c 0 o

b; -15

- I 0 0=

I I I l P= 1,400 N/cm p.= 0.7

_ ~ < ~ f i n i t e a = 5 . 0 8 cm element b= 2 . 5 4 cm

esults R = 0 . 6 3 5 cm r /R = 0 . 9 6 9 and elastic properties

- - . o ~ , 0f - ~ ' ~ . Table I

- strain "X~,~

o I I I I 0 0.5 1.0 1.5 2.0 (A) x, cm

2.5

Fig. 4 - -Compar ison of strain-gage and f inite-element results along the line A-B of Fig. 1

t ~ ~ 1 } ay = Q,2 Q22 o ~y rxy 0 0 Q 6 6 "Yxy

where

and

Q , , _ Ex,~ Q22 - - Eyy (1 - VxyVyx) ' (1 pxyVyx)

PyxExx Q,2 - ( 1 - vxyuy~) ' Q66 = Gxy

( l )

(2)

-16 ~_ | t 1 P=700 Nlcm :~ ~ (:1=5.08 c m b = 2 , 5 4 c m

I ~ R = 0 . 6 3 5 cm r/R=O.988 ,- I ~ and elastic properties == -I 2 ~ l e l -

o 0 _

G)

-8

~ 0 .o_ 0 I0 20 30 40 " 0

o (A) O, Degrees n-

Fig. 6 - -E f fec t of f r ict ion on the radial stress, or, along the hole boundary star t ing at point A

VxyEyy = vyxExx. (3)

The contribution of ey was normally negligible.

Results

Experimental-Numerical Correlation Although parametric studies concerning the effect of

geometric variations can be conveniently conducted

-161 I I I I

l P : 7 0 0 N/cm a = 5.08 b= 2.54 c cm

1 2 t - - \ r /R = 0 .988 _ ~ _ I \ R = 0.6:35 cm

I L..._. = r~.-7 and e las t ic proper t ies

"*" - 4

0 0 1.0 2,0 3,0 4.0 5s (A) x, cm

Fig. 5 - -E f fec t of f r ict ion on the stress in the x-direct ion along the line A-B below the hole of Fig. 1

-7O P- = 0"71 I I l

o - 6 0 - R = 0.6:35 cm b = 2 . 5 4 cm

"~ and e las t ic p rope r t i es ~ 6 ~ "~ of Table I ~ o ~ _

o ' ' r / R : 0 . 9 8 8 . ~ f _ / % ~ _ ' ~ - ' - "

- 5 0

~ -20

0 �9 I I I . . . . . " I

0 4 0 0 8 0 0 1200 1600 Pin load, P, N / c m

Fig. 7 - -E f fec t of end distance on the radial stress at A of Fig. 1 for two ratios of pin-to-hole size

410 �9 November 198t

-55 I I I I 1

-50 P= 1,400 N/crn /~ = 0.7 R = 0.635 cm

nO -45 b = 2.54 Cm o~ and elastic properties

~, of Table I ~ - 4 0

g o -35

~ -30

o "6 -25

b: g -20

r / R = 0 . 9 3 6

- - - r / R = 0 . 9 8 8

-'< / / \

i . / \

v% - Io , , ,% ~,

XxO

- 5 ~ / \o \v~

o I __ I I \\ '~ 0 I0 20 30 40 (A) 8, Degrees

, \ a

\,,~,\ -

\,~\x IN x

50 60

Fig. 8 - -Rad ia l stress dist r ibut ion on the hole boundary start ing at point A for di f ferent end distances, a, and pin-to-hole ratios, r/R

numerically, it was desirable to compare experimental and finite-element results for selected cases. Numerically predicted stresses are correlated in Fig. 3 with those from lnoir6 patterns such as that in Fig. 2, and with strain-gage information in Fig. 4. The plots in Figs. 3 and 4, which are for slightly different r / R ratios, are of the normal stress in the x-direction along the axis immediately below the bolt.

Effects of Frict ion

The effect on the stresses o f f r ic t ion between the pin and the hole boundary is illustrated in Figs. 5 and 6. Figure 5 shows the influence on the normal stress ox below the hole, while the effect on the radial stress along the hole boundary is seen in Fig. 6. The absence of friction would allow the wood to wrap further around the pin, distributing the pressure more evenly. At some distance below the hole, the effect of friction disappears (Fig. 5). The presence o f friction was observed to reduce the tangential stress beneath the pin, in some cases causing it to become compressive. Oplinger and Gandhi '3 demon- strated previously that this friction-induced effect on the tangential stress beneath the pin can modify the mode of failure of mechanical joints. This tendency for friction to reduce the tangential stress while increasing the radial stress under the pin has also been noted by Hussain and Pu '~ and Ojalvo. '~ Experimental results confirm that friction is a significant factor and must be included in any numerical analysis of pin-loaded holes in wood.

Effect of End Distance

The effects on the stresses of varying the end distance, a, are illustrated in Figs. 7 through 13. All but the strain-gage results of Fig. 10 were obtained using finite elements. Analyses were based on the measured Sitka- spruce properties of Table 1.

Figure 7 demonstrates the effect of different end distances on the radial stress at point A (immediately under the pin, Fig. 1) for r / R = 0.988 and 0.936. For this plate, the radial stress at A decreases with decreased end distance. For very short end distances, the stress also decreases with increasing load, especially at the higher r / R ralio. A belier understanding of what occurs with reduced end distance is seen by observing the radial stress distribution on the hole boundary in Fig. 8. The wood wraps around the pin more easily with the shorter end distances, and the point of maximum radial stress may

I0

9

8

-6

�9 , 5 I

lid

4 g

m 3

2

I

0 0

I I I P = 1 , 4 0 0 N l c m

/L = 0.7 - r ~ R=0 .6 :55cm

/ ~ b = 2 .54 cm / \ e n d elastic _

/ o \ properties / ~ o f Table I

= . .

0.2 0.4 0.6 0.8

y , c m

I I I P = 1 , 4 0 0 N / c m y.= 0.7

-- R= 0.635 cm b = 2.54 crn and elastic pi'operties

of Table I r/R = 0.988

S , 0 0.2 0.4

%

0 V'

t

I 0.6 0 . 8

y , c m

Fig. 9 - -E f fec t of end distance, a, on the shear-stress d is t r ibut ion along a line parallel to the end of the plate and located 0.159 cm below the bot tom of the hole

Experimental Mechanics �9 411

P = 1,400 N/cm -so ='o.r

o R = 0.6:35 cm I~\ b = 2 . 5 4 cm

~ ' - 2 5 [--\ r /R = 0 . 9 6 9 _ \ and elastic properties

< I k ~L of Table I

~ , - 2 0 t--~. . ,_~-f inite element

: t 't+X' ~ - I 0 rain gage data

u3

o 0 1.0 2.0 3.0 4.0 ( A ) x , c m

Fig. lO--Effect of end distance, a, on the stress in the x-direction along A-B of Fig. 1 and comparison of strain-gage and finite-element results

80 I I I 0.7

70 -- I~ 0.635 crn b : 2.54 cm r/R = 0.9:36

60 - end elastic properties r~ o of Table I ~o~

0 .

"~4o - ~ ~% -

t5 z 20 0

I 0

0 I 0 4 0 0 8 0 0 1200 1600

Pin load, P, N/cm

Fig: 12--Effect of end distance, a, on the stress in the x-direction at point C of Fig. 2

16

/~= 0.7 / R = 0 .635 cm b = 2.54 cm

_ r /R = 0.9136 ro~,/" _ o 12 and elastic ~ / /

properties \ ~ / ~- of Table I O / ~ 0 ~ m" b-,, a -

~4

/ / /

0 4 0 0 8 0 0 1200 1600 Pin load, P, N/cm

Fig. 11--Effect of end distance on the stress in the y-direction, olv , at point B of Fig. 2

shift away from directly underneath the pin. For r / R =

0.988 there appears to be an end distance for which the radial stress remains fairly uniform over the contact area. In this case, higher maximum radial stresses occur for longer and shorter end distances. In the case of the smaller pin, the radial-stress distribution is much steeper and extends over a much smaller portion of the hole.

The effect of changes in end distance, a, upon the shear stress rxv distribution along a horizontal line 1.59 m m below the hole is shown in Fig. 9. The maximum shear stress increases as the end distance is reduced. Moreover

the location of maximum stress moves further from the axis of symmetry of the plate with decreasing end distance. This is compatible with the radial contact stress (Fig. 8) extending further around the hole for shorter plates. Figure 9 also demonstrates that higher stresses occur with more loosely fitting pins.

Figure 10 illustrates that, at least for narrower plates having relatively close-fitting pins, the increased com- pliance of the structure beneath the pin due to reduced end distance, a, results in a decreased o, stress distribution along the x-axis under the pin. This decrease agrees with the information of Figs. 7 and 8.

Figure 11 shows the Oy stress at point B. The increased stress perpendicular to the wood grain at point B with reduced end distance may precipitate fracture for suf- ficiently small values of a.

The dependence on end distance, a, of the tangential stress ax at point C at the horizontal edge of the hole is illustrated in Fig. 12, while Fig. 13 demonstrates the influence of end distance on the o~ stress distribution across C-D for both r / R = 0.936 and 0.988. Although the response beneath the pin (Figs. 7 and 11) is extremely nonlinear with load, the response away from the region of loading (Fig. 12) is linear with load.

Effect of Edge Distance

The effects of relative edge distance, b, on the o, stresses at A and C are shown in Fig. 14. The radial stress at point A (below the pin) of the plate in Fig. 14 is not influenced by the indicated changes in edge distance. The tangential stress at point C also remains unchanged for edge distances greater than 2.54 cm, b u t increases at smaller edge distancesl

Effect of Bolt-to-Hole Ratio

Small changes in the ratio of pin-to-hole size r / R can have a very significant effect on the stresses in the neighborhood of the hole (Fig. t5). The region of boun-

412 �9 November 1981

Fig. 13- -Ef fec t of e n d d i s t a n c e , a, on the s t r e s s in the x-direct on along C-D of Fig. 1 f o r d i f f e r e n t p i n - t o : h o l e r a t i o s

70

60

~. 5O ~E

d 4 0

=~ 3o o

z o

0

~10 0 (c)

P= 1,400 N/crn F=0.7 b = 2 . 5 4 cm R = 0 . 6 3 5 cm and e last ic p r o p e r t i e s

of Table I,

r /R = 0 . 9 8 8

_ 0 = 5 . 0 8 cm

I I I 0.5 1.0 1.5 2.0

I I I

P: 1,400 N/cm F : 0.7 b= 2 . 5 4 cm R= 0 . 6 3 5 cm and e l a s t i c proper t ies

of Table I

r / R = 0 . 9 3 6

- - ~ a = 7 . 6 2 cm

o = 1 . 5 9 cm

I I I 0 0.5 1.0 1.5 (C)

Distance from hope edge, cm

2.0

dary contact decreases appreciably, and the maximum stress and the radial-stress concentrat ion at A increase rapidly for slightly increased pin tolerances. This large influence of pin-to-hole size on the radial stress is probably a large contr ibutor to the variability in results observed when testing bolted joints. If the ratio of pin-to- hole size is decreased, stress beneath the hole is increased (Figs. 7-9 and 13). At least in the presence of high friction, results' predict small compressive tangential stresses at point A throughout the range of r /R covered in Figs. 15.

D e s i g n C o n s i d e r a t i o n s

At least under some conditions, stresses are greatly influenced by the size of" the end distance, a. However, the experimental and numerical results (Figs. 7 and 11) indicate that stresses beneath the pin (along A-B) are little affected by changes in end distance for a > 8 R . Reducing the end distance below 8R does influence the shape and magnitude of the stress distributions (Figs. 7 through 13). Shorter end lengths permit the wood to more easily deform around the pin. Such easier deformation has several effects: it reduces the radial compressive stress immediately under the pin (Figs. 7, 8 and 10); it may relocate the maximum radial stress away from the axis of plate symmetry (Fig. 8); it increases the longitudinal tensile stresses at the edges of the hole (Fig. 13); it in- creases the tensile stress parallel lo the bot tom of the plate (Fig. l l ) ; it increases and relocates the maximuln shear stress below the hole (Fig. 9).

Reference 4 suggests that, at least for anisotropic com- posites, opt imum boll strength is achieved at a = 4R. Results of this study imply this ratio to be closer to a = 8R, at least concerning the stress at point A and point C in Sitka spruce. The increase in shear stress below the hole (Fig. 9) and the increase in tensile stress at the end of the plate (Fig. 1 l) with smaller end distances would also sug.eest the need for longer end distances. Reference 4 also shows that, at least for a/b _< 2 (cases considered here), the maximum shear stress on planes parallel to the wood grain underneath the pin increases rapidly with decreasing end distance. This is substantiated by Fig. 9.

Reference 16 provides the following design requirement

- 2 5

n ~ " 2 0

~-15

bC -I0

~ - 5 m

(a)

I I p.= 0.7 R = 0.635 cm r/R : 0 . 9 8 8 o = 2 . 5 4 cm end elastic properties_

of Table I P= 5 2 5 N/crn

P = 3 5 0 N / c m

P = 1 7 5 N/crn

I I 2 4

Edge distance, b /R

2:5

~ 2o

15

o

m

0 6 0

(b)

I I

_ ~ 5 2 5 N / c m

-- ~ 3 5 0 N/c11~

N / c m

I I 2 4 ~ - 6

Edge distance, b l R

Fig. 14--Ef fect of edge distance, b, on (a) the radial stress, o~, at A of Fig. 2 and (b) the tangential stress, de, at C of Fig. 2

r /R=.S24 r/R=.876 r /R=.924 r /R=.974 - 5 0 -- #

- 4 0 -~

- ~ -3o

_~ - 2 0 - - I ~o a: ~ - IO

o

r /R =.988

-P= 350 N/cm F =0.7

-R : 0 .635 cm a = 5 .08 cm b = 2 .54 crn

-and elastic properties of Table I

L 0 5 0 5 0 5 IO 0 5 I0 15 0 5 I0 15 20 25 (A) (A) (A) (A) (A)

O, Degrees

Fig. 15--Ef fect of pin size on the radial stress, e~, along the hole boundary

for end distances in wood joints: " f o r parallel-to-grain loading, the minimum end distance for full design loads shall be: (a) in tension, 7 times the bolt diameter for soft- . . . . . . . . . . . . . . . . . o , v , , , ~ , u v v u u u 3 ~ t u ) i n c o i ] ] p i - e s s J O i ] ,

4 times the bolt d iameter . " For a 1.27-cm-diam boll in Sitka spruce, the minhnum end distance would then be a = 8.9 cm. Reference 16 gives no rules for designing joints with end distances less than the recommended n]inimum. As suggested by results obtained in this work, changes of end distance could very well shift /he mode of

Exper imenta l Mechanics �9 413

joint failure away from the usually desired crushing under the pin.

Reference 16 states that "bolt holes sl~all be 1/32-inch to 1/16-inch larger than the bolt, depending on the size of the bolt." This is a range of r/R = 0.889 to 0.941 for the 1.27-cm-diam pin of this study. Figure 15 demon- strates that such variations in bolt clearance produce significant changes in the stress under the bolt. These results indicate that perhaps hole-size design tolerances should be more tightly specified relative to the bolt diameter, keeping in mind the need for easy assembly. This large influence on stress of variations in r/R probably accounts for much of the scatter in results observed when testing bolted joints to failure.

Regarding relative edge distance or plate width, Ref. 16 states that "for parallel-to-grain loading in tension or compression, the edge distance should be at least 1-1/2 times the bolt d i a m e t e r , . . . " For the R = 0.635 cm considered here, b should then be _1.9 cm. Results of Fig. 14 demonstrate that, for the case considered here, o~ at point A is independent of b for at least 1.6_<b/R_<.6, while o, at point C is independent of b for b/R>_4. Note that while o~ at A is highly nonlinear with applied load, P, the response at point C, is essentially linear with load. At least for the case considered, Fig. 13 plus other in- formation demonstrates that o~ becomes relatively in- significant for y>_2R. These data, together with the shear stress information of Fig. 9, suggest that b = 4R would provide a reasonable design in Sitka spruce, where 2b equals either the total plate width for single-fastener joints, or the fastener spacing perpendicular to the applied load for periodic fasteners. Reference 4 indicates that b = 2R and a = 4R provide an optimum joint design.

Upon satisfying the conditions that b>_3R, 0.889_<. r/R_<0.941 and a > 14R for a 1.27-cm-diam bolt in Sitka spruce, Ref. 16 lists a design load for this situation of 788 newtons per cm of plate thickness. Two specimens ( b = 4 R , r/R=0.969, a=4.88R and b=6R, r/R=0.969, a=4R, respectively) tested to fracture in this study failed at P = 2,800 N/cm. While each of the cases tested com- plied with the above-stated edge condition of Ref. 16, neither satisfied the end requirement or the pin-to-hole size. The observed strengths were 3,56 times the design load for this case.

Summary and Conclusions The stresses in the vicinity of a pin-loaded hole in a

Sitka-spruce plate were investigated experimentally and numerically. The effects on the stress distribution of variations in joint geometry (edge and end distances), friction, and the ratio of pin-to-hole diameter were evaluated. Results are discussed relative to the design of bolted joints.

Results obtained by the various techniques correlated very well. Small variations in pin-to-hole diameter ratio were found to produce very significant changes in the stresses. Superior designs would use close-fitting pins. Moreover, current hole-size design tolerance for bolted wood joints should perhaps be more tightly specified relative to the bolt diameter. Significant changes were found in the shape, as well as tire magnitude, of the stress field below the pin for short end distances. Results suggest that optimum end distance should be eight times the hole radius. Optimum plate width (for single fasteners), or the horizontal fastener spacing (for multiple fasteners), should be at least eight times the hole radius for Sitka- spruce joints. These are more conservative than the

criteria of Ref. 4 or 16. The presence of friction greatly influences the stresses

and must be accounted for in any analysis. The cosine pressure distribution on the hole, as assumed by some researchers, is unreliable and its use is not recommended.

The increase in contact area between fastener and plate with load renders the problem highly nonlinear. While not affecting the experimental techniques, this condition does complicate significantly the finite-element analysis.

Although the present study was conducted on wood, the approaches employed are equally effective for analyzing mechanical joints involving other orthotropic composite materials.

Acknowledgments The technical assistance of R.D. Cook, J. Dreger, P.

Lemens, J. Ottelien, N. Severson (University of Wisconsin) and D. Kinney (U.S. Forest Products Laboratory) is greatly appreciated. The research was funded by the Forest Products Laboratory, Forest Service, U.S. Depart- ment of Agriculture. Most of the cited results are from the PhD thesis of the first author (TLW).

References 1, Wilkinson, T.L., "'Stresses in the Neighborhood o f Loaded Holes

in Wood with Applications to Bolted Joints, '" PhD Thesis, Dep. o f Eng. Mech., Univ. o f Wis.-Madison, Madison, ~4'1 (1978).

2. Wilkinson, T.L., Rowlands, R.E. and Cook, R.D., "An lncre- menial Finite-elenlent Deternmlation o f Stresses around Loaded Holes in Finite Hood Plates, " Accepted ja r publication in Computers and Structures.

3. Wilkinson, T.L., I:uehs, E.A. and Rowlands, R.E., "'Photo- nwchanical Determination of Stre.s~es ill /he Neighborhood oj Loaded Holes in Anisotropic Media, " Proc. 6th Int. Conf. on Stress Analysis, Munich, 121-126 (1978).

4. Oplinget, D. 14"., "Stress Analysis o f Composite Joints, " Advances in Joining Technology, ed. by J.J. Burke and A.F. Gorum. Amo ' Mater. Tech. Conj,, Set'. No. 4, 405-452 (1976).

5. Oplingetl D.W. , Parker, B.S. and Kalz, A. , "Moir~ Measurement oj Strains and DeJormations in Pro-loaded Composite Plates, " presented at the 1979 SESA Spring Meeting, San l-?ancisco, CA.

6. I-~'oc.ht, M.M. and Hill, H.N. , "Stres~ Concentration Factors around a Circular ttole in a Plate Loaded through u Pin in the Hole, " J. Appl. Mech., 7, 5-9 (1940).

7. Lambert, T.H. and BIviley, R.J., "The Influence oJ CoeJ]icient o f Friction on the Elastic Stress Concentration Factor Jbr a Pin-jointed Connection, "Aeronaut . Q., 13, 17-29 (1962).

8. Jessop, H.T. , Snell, C. and Holister, G.S., "Photoelastic hl- vesligation on Plates with Single Inteljorenceq~t Pins with Load Applied (a) to Pin Only and (b) to tfin and P/ate Simultaneously, " Aeronaut. Q., 9, 147-163 (1958).

9. Nisida, M. and Saoo, H., "Stress Distribution in a Semi-mJini/e Plate due to a Pin Determined by lnterjerontelric Method, " Proc. Sac'. j a r Exp. Stress Anal., 23 (I), 273-279 (1966).

10. Hill, J.L., Sewell, J.H. and Azzi, V.D., "Continutms Observation o f Drying Strain Development using Bonded Strain Sensing Material, " presented at the 1977 Annual Meet., For. Prod. Res. Sac., Denver, CO (1977).

II. Hoadley, R.B., "Analysis ill Wood by Mewts oj Moir~ Patterns, " For. Prod. J., 18 (5), 48-50 (1968).

12. U.S. Forest Products Lahore/arT, "H'ood handbook." H'ood as an Engineering Material, " USDA, Agric. Handb., 72 (1974).

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14. Hassain, M.A. and Pu, S.L., "Slip Phetlomenon .10t a Circulal Inclusion," J. oJ App/. Mech. Tl~ms. ASME, Serie& E, 38, 627-633 (1971).

15. Ojalvo, 1., -Survey o f Mechanically Pus/erred Splice-joint Analyses, "' Advances ill Joining Tech., ed. by J.J. Burke and A.E. Gorum, Brook Hill Publ. Co., Chesmul Hill, /VIA, 379-403 (1976).

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414 * November 1981