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Bending fatigue life of two-pin dowel joints in furniture grade pine plywood.



Abstract

The fatigue life of T-shaped, end-to-side, two-pin dowel dowel /dow·el/ (dou´'l) a peg or pin for fastening an artificial crown or core to a natural tooth root, or affixing a die to a working model for construction of a crown, inlay, or partial denture.  joints was investigated by subjecting them to one-sided constant and stepped cyclic cyclic /cyc·lic/ (sik´lik) pertaining to or occurring in a cycle or cycles; applied to chemical compounds containing a ring of atoms in the nucleus.

cy·clic or cy·cli·cal
adj.
1.
 bending loads. Frame-1 furniture grade, 3/4-inch-thick (19.05-mm) 5-ply southern yellow pine plywood plywood, manufactured board composed of an odd number of thin sheets of wood glued together under pressure with grains of the successive layers at right angles. Laminated wood differs from plywood in that the grains of its sheets are parallel.  was tested in the construction of joints with four rail width groups. Dowels were of white birch birch, common name for some members of the Betulaceae, a family of deciduous trees or shrubs bearing male and female flowers on separate plants, widely distributed in the Northern Hemisphere.  wood with spiral grooves Grooves is an American electronic music magazine founded in 1999 by editor Sean Portnoy, initially concentrating on the then-burgeoning IDM music genre and expanding to its more experimental, abstract offshoots, such as microsound, microhouse and glitch, eventually  and a nominal diameter of 3/8 inch (9.53 mm). Results of one-sided constant load tests indicated that the fatigue life of dowel joints averaged 131,253; 78,122; 31,617; 11,023; 4,161; and 329 cycles for load levels of 40; 50; 60; 70; 80; and 90 percent of their mean ultimate bending strengths, respectively. Regression of M-N data (moment versus log number of cycles to failure) indicated a linear relationship existed between the fatigue bending moment A bending moment exists in a structural element when a moment or torque is applied to the element so that the element bends. Moments and torques are measured as a force multiplied by a distance so they have units such as newton.metres (N.m) and foot.pounds (ft.lb).  applied to joints and the log number of cycles to failure. Joints with higher static bending strengths tended to have more resistance to fatigue damage. A simplified method of deriving the fatigue life estimation estimation

In mathematics, use of a function or formula to derive a solution or make a prediction. Unlike approximation, it has precise connotations. In statistics, for example, it connotes the careful selection and testing of a function called an estimator.
 equation based on known information such as the joint static bending strength was proposed. Cyclic stepped load tests verified that the Palmgren-Miner rule was an effective method in estimating fatigue life of two-pin dowel joints subjected to cyclic stepped bending moments based on their M-N curves. Fatigue life comparisons among joint groups with different static bending strengths indicated that a significant increase in static bending strength might not yield a significant fatigue life increase when a joint was subjected to cyclic stepped loads. Joint resistance to fatigue failure should be taken into account in strength design of furniture frames that are subjected to repeated loading.

**********

Strength design of upholstered furniture frames requires information about joint fatigue strength properties since most service failures of the frames appear to be fatigue related (Eckelman and Zhang 1995) and the most common failure to the frames occurs at the joints. Also a quality assurance program requires that upholstered furniture manufacturers conduct furniture performance tests. Performance test standards such as the General Service Administration (GSA (1) (Global mobile Suppliers Association, Sawbridgeworth, U.K., www.gsacom.com) A membership organization of suppliers of GSM products and services. Its goal is to promote GSM as the worldwide mobile communications standard. See GSM Association and GSM. ) performance test regimen regimen /reg·i·men/ (rej´i-men) a strictly regulated scheme of diet, exercise, or other activity designed to achieve certain ends.

reg·i·men
n.
1.
 FNAE-80-214A (GSA 1998) are based on a stepped fatigue load model (Eckelman 1988a and 1988b).

As more plywood and engineered composites, especially plywood, are constructed into upholstered furniture frames, the information related to fatigue strength properties of various types of joints of the composites becomes increasingly essential for furniture manufacturers to re-engineer their products. Currently, the strength properties of furniture frame design have mostly been determined by static tests. Research to determine joint fatigue properties has been minimal. This is especially true for joints constructed of wood composites.

Eckelman (1970) studied the fatigue life of two-dowel joints subjected to constant loading. He tested sugar maple sugar maple: see maple.  joints with an average ultimate static bending strength of 3,180 lb.-in. (359 N.m) under two different cyclic load schedules, alternating fully-reversed loads and one-sided loads. Fatigue loads were applied to joints at a rate of 40 cycles per minute. No failures were found at the 500 lb.-in. (56 N*m) load level in either set of specimens after [10.sup.6] cycles. At the 1,000-1b.-in. (113-N*m) load level, however, the life of the joints dropped to a value of about 200,000 cycles, and at a 1,500-lb.-in. (169-N*m) level, the value was about 12,000 cycles. Results clearly demonstrated that the specimens were subject to fatigue damage, and an endurance Endurance
See also Longevity.

Atalanta

feminine name denotes power of endurance. [Gk. Myth.: Jobes, 148]

Boston marathon

famous 26-mile race held annually for long-distance runners. [Am. Pop. Culture: Misc.
 limit existed for the joints. The suggested design strength for two-pin dowel joints should be limited to no more than one-third of joint ultimate static bending strength.

One-sided fatigue tests (Eckelman 1980) on T-shaped, end-to-side-grain, metal-plate-connected joints constructed of red oak, yellow-poplar, soft maple, and Douglas-fir indicated that the fatigue life of joints loaded to three-eighths of their mean ultimate bending strength amounted to an average of 22,000 cycles. Joint fatigue life averaged 100,000 cycles at one-fourth of their mean ultimate bending strength. As the load level was reduced from one-fourth to one-sixth of the mean ultimate bending strength, the fatigue life of the joint increased to a point where it might be regarded as infinite with respect to the life of the furniture.

Few studies were found on the fatigue life of furniture frame joints subjected to cyclic stepped loads. To study fatigue strength properties of furniture frame joints subjected to one-sided constant and stepped cyclic bending loads, Zhang et al. (2001) evaluated T-shaped, two-pin moment-resisting dowel joints constructed of red oak, yellow-poplar, southern yellow pine plywood, aspen engineered strand lumber lumber, term for timber that has been cut into boards for use as a building material. The major steps in producing lumber involve logging (the felling and preparation of timber for shipment to sawmills), sawing the logs into boards, grading the boards according to , and particleboard. Regression of M-N data (moment versus log number of cycles to failure) of each joint material subjected to constant cyclic bending loads resulted in linear equations for M-N curves. Fatigue life of dowel joints subjected to a given stepped cyclic bending schedule could be estimated with the Palmgren-Miner rule (Palmgren 1924, Miner 1945) based on their M-N curves. Since in the study (Zhang et al. 2001) all joint specimens were constructed of 4-inch-wide (101.6-mm) rails with a limited bending strength range from 1,850 lb.-in. (209 N*m) to 2,875 lb.-in. (325 N*m), further verification should be performed at a higher strength range.

To continue this verification process, static bending tests were first performed (Zhang et al 2003) on T-shaped, two-pin dowel joints constructed of 4-(101.6-mm), 5-(127-mm), 6-(152.4-mm), and 7-inch-wide (177.8-mm) furniture grade pine plywood rails with 2-inch (50.8-mm), 3-inch (76.2-mm), 4-inch (101.6-mm), and 5-inch (127-mm) spacing between two dowels, respectively, followed by a joint fatigue study reported in the paper. Static bending tests indicated that joint bending strength increased significantly as rail widths increased from 4 inches (101.6 mm) to 7 inches (177.8 mm) with an increment To add a number to another number. Incrementing a counter means adding 1 to its current value.  of 1 inch. Mean ultimate static bending strengths of joints were 2,471 lb.-in. (279 N*m), 3,093 lb.-in. (349 N-m), 4,399 lb.-in. (497 N*m), and 5,541 lb.-in. (622 N*m) for 4-(101.6-mm), 5-(127-mm), 6-(152.4-mm), and 7-inch-wide (177.8-mm) rail joints, respectively.

Therefore, the objectives of this study were to: 1) study static strength influence on fatigue behavior of joints subjected to one-sided constant and cyclic stepped loads; 2) obtain M-N curves; 3) compare joint fatigue life; 4) verify the Palmgren-Miner rule in predicting the fatigue life of dowel joints subjected to stepped fatigue loads; and 5) derive estimated M-N curves for furniture dowel joints.

Materials and methods

The T-shaped, two-pin, end-to-side dowel joint a joint secured by a dowel or dowels.

See also: Dowel
 specimen for this study is shown in Figure 1. In general, each specimen consisted of two principal structural members, a post and a rail, joined together by two dowels symmetrically sym·met·ri·cal   also sym·met·ric
adj.
Of or exhibiting symmetry.



sym·metri·cal·ly adv.

Adv. 1.
 spaced in the rail with reference to the rail width centerline cen·ter·line  
n.
1. A line that bisects something into equal parts.

2. A painted line running along the center of a road or highway that divides it into two sections for traffic moving in opposite directions, or, in the case of
. Both the rail and the post were constructed of the same plywood with the face ply-grain direction oriented o·ri·ent  
n.
1. Orient The countries of Asia, especially of eastern Asia.

2.
a. The luster characteristic of a pearl of high quality.

b. A pearl having exceptional luster.

3.
 in the same direction as the member length direction. Rails measured 16 inches (406.4 mm) long and 3/4 inch (19.05 mm) thick with four widths of 4 inches (101.6 mm), 5 inches (127 mm), 6 inches (152.4 mm), and 7 (177.8 mm) inches. The distance between the centerlines of the two dowels were controlled at 2 inches (50.8 mm), 3 inches (76.2 mm), 4 inches (101.6 mm), and 5 inches (127 mm) for rail widths of 4 inches (101.6 mm), 5 inches (127 mm), 6 inches (152.4 mm), and 7 inches (177.8 mm), respectively. The post measured 16 inches (406.4 mm) long by 4 inches (101.6 mm) wide by 3/4 inch (19.05 mm) thick.

[FIGURE 1 OMITTED]

The same type of Frame-1 furniture-grade, 3/4-inch-thick (19.05-mm) 5-ply southern yellow pine plywood in the static bending test (Zhang et al. 2003) was included in this study. Joint members were randomly selected from five member sources created in the joint static strength evaluation, one source of post members, and four sources of each of four rail width groups (4 in. [101.6 ram], 5 in. [127 mm], 6 in. [152.4 mm], and 7 in. [177.8 mm]). All joints were constructed with spiral groove white birch dowels with a nominal diameter of 3/8 inch (9.53 mm) and a length of 2 inches (58.8 mm), which were the same type of dowels included in the static bending tests. Penetration depths of the dowels in both the rail and the post were 1 inch.

To obtain joint fatigue M-N curves (moment versus log number of cycles to failure) for each rail width group, the one-sided constant fatigue tests of seven load levels: 90, 80, 70, 60, 50, 40 and 30 percent of the mean ultimate bending strength of tested joints obtained from static bending tests. The tests were performed on the joints at the same loading rate of 20 cycles per minute specified in GSA FNAE-80-214A (GSA 1998). The typical fatigue cycle starts with zero load, then the load reaches its maximum value within .75 second, maintains maximum value for .75 second, drops to zero and retains zero for .75 second until the next load cycle starts. Mean ultimate static bending strengths were 2,471 lb.-in. (279 N*m), 3,093 lb.-in. (349 N*m), 4,399 lb.-in. (497 N*m), and 5,541 lb.-in. (622 N*m) for 4-inch (101.6-mm), 5-inch (127-ram), 6-inch (152.4-mm), and 7-inch-wide (177.8-mm) rail joints, respectively. Ten replications were tested for each of the fatigue load levels so that a total of 70 specimens were tested for each of the four rail width groups. Therefore, a total of 280 specimens were subjected to a constant load fatigue test.

Joints were tested under a stepped load schedule following the same schedule of the GSA outward arm test (GSA 1998) to compare the fatigue life of joints with different rail widths and validate To prove something to be sound or logical. Also to certify conformance to a standard. Contrast with "verify," which means to prove something to be correct.

For example, data entry validity checking determines whether the data make sense (numbers fall within a range, numeric data
 the Palmgren-Miner rule in predicting the fatigue life of dowel joints subjected to cyclic stepped loads. Table 1 shows the detailed cyclic stepped load schedule with specified service acceptance levels. The cyclic stepped fatigue load schedule started at the 600 lb.-in. (68 N*m) level. After 25,000 cycles, the load was increased by an increment of 300 lb.-in (34 N*m). The test was continued for another 25,000 cycles, and then the procedure was repeated until joints failed to resist the applied load. Five specimens were tested for each of the four rail width groups, therefore a total of 20 joints were tested under stepped fatigue loads.

All specimens were assembled with a vinyl-copolymer-resin emulsion emulsion: see colloid.
emulsion

Mixture of two or more liquids in which one is dispersed in the other as microscopic or ultramicroscopic droplets (see colloid). Emulsions are stabilized by agents (emulsifiers) that (e.g.
 adhesive adhesive, substance capable of sticking to surfaces of other substances and bonding them to one another. The term adhesive cement is sometimes used in place of adhesive, especially when referring to a synthetic adhesive.  with 52 percent nonvolatile solids content. Joint assembly began immediately after the drilling operation. Dowel-hole clearances were minimized. The hole diameter on average was 0.003 inch (0.08 mm) larger than the dowel diameter. The walls of the holes and the sides of the dowels were liberally coated with glue prior to the insertion insertion n. the addition of language at a place within an existing typed or written document, which is always suspect unless initialled by all parties.  of dowels. In all samples, a piece of wax paper was included between the two members to prevent the members from adhering. Specimens were conditioned in an equilibrium moisture content The moisture content of wood below the fibre saturation point is a function of both relative humidity and temperature of surrounding air. The equilibrium moisture content is the moisture content at which the wood is neither gaining nor losing moisture; this however, is a dynamic  (MC) chamber at 75 [+ or -] 4[degrees]F and 44 [+ or -] 2 percent relative humidity relative humidity
n.
The ratio of the amount of water vapor in the air at a specific temperature to the maximum amount that the air could hold at that temperature, expressed as a percentage.
. All specimens were allowed to cure for at least 48 hours before testing.

Joint fatigue tests were conducted with a specially designed air cylinder air cylinder can mean:-
  • a gas cylinder used to store compressed air.
  • pneumatic cylinder, a mechanical device used to impart a force from a fluid.
 and pipe rack Noun 1. pipe rack - a rack for holding a smoker's pipes
rack - framework for holding objects
 system as shown in Figure 2. The load was applied to the rail 12 inches (304.8 mm) in front of the post, i.e., the moment arm was 12 inches (304.8 mm). The bending moment applied to the joint, expressed in lb.-in., was equal to 12 times the applied load. In all tests, a one-sided fatigue load was applied to the joint by an air cylinder at a rate of 20 cycles per minute. A Programmable Logic Controller See PLC.

(hardware) Programmable Logic Controller - (PLC) A device used to automate monitoring and control of industrial plant. Can be used stand-alone or in conjunction with a SCADA or other system.
 and electrical re-settable counter system recorded the number of cycles completed. Limit switches stopped the test when a joint suffered disabling dis·a·ble  
tr.v. dis·a·bled, dis·a·bling, dis·a·bles
1. To deprive of capability or effectiveness, especially to impair the physical abilities of.

2. Law To render legally disqualified.
 damage. For constant load tests, all tests were run until the joints failed or 1 million cycles were reached. Seven load levels were tested for each specimen group. Stepped load tests continued until the joints failed.

[FIGURE 2 OMITTED]

Results and discussion

The MC of the plywood averaged 8.7 percent with a coefficient of variation Coefficient of Variation

A measure of investment risk that defines risk as the standard deviation per unit of expected return.
 of 4 percent. Density averaged 42 pcf (673 kg/[m.sup.3]) with a coefficient of variation of 3 percent. Internal bond strength averaged 126 psi PSI - Portable Scheme Interpreter  (869 kPa) with a coefficient of variation of 16 percent. Modulus of rupture the measure of the force necessary to break a given substance across, as a beam, expressed by eighteen times the load which is required to break a bar of one inch square, supported flatwise at two points one foot apart, and loaded in the middle between the points of support.
- Rankine.
 edge-wise averaged 6,600 psi (45.5 MPa) with a coefficient coefficient /co·ef·fi·cient/ (ko?ah-fish´int)
1. an expression of the change or effect produced by variation in certain factors, or of the ratio between two different quantities.

2.
 of 15 percent. Modulus of elasticity modulus of elasticity

The ratio of the stress applied to a body to the strain that results in the body in response to it. The modulus of elasticity of a material is a measure of its stiffness and for most materials remains constant over a range of stress.
 edge-wise averaged 989,000 psi (6.8 GPa) with a coefficient of variation of 17 percent. MC of white birch dowels averaged 8.8 percent with a coefficient of variation of 5 percent. Mechanical properties were evaluated in accordance Accordance is Bible Study Software for Macintosh developed by OakTree Software, Inc.[]

As well as a standalone program, it is the base software packaged by Zondervan in their Bible Study suites for Macintosh.
 with the procedures (ASTM ASTM
abbr.
American Society for Testing and Materials
 D 4761 1998b) for plywood static-bending tests. A span-to-depth ratio of 18 was selected to test the bending specimens measuring 2 inches (50.8-mm) wide by 40 inches (1016-mm).

Mode of failure

Joint failures always occurred first at the dowel in the tension side. The failure modes of dowels in the tension side were recorded. In general, three clearly definable types of failure modes occurred in the one-sided constant cyclic load tests. In the first type (Type I), the dowels withdrew from the joint members; some plywood material was attached to the dowels. In the second type (Type II), the dowels sheared sheared  
adj.
Shaped or finished by shearing, especially cut or trimmed to a uniform length: a sheared fur coat.

Adj. 1.
 parallel to grain; some plywood material was attached to the dowels. In the third type (Type III Type III may stand for:
  • Glycogen storage disease type III, a genetic disorder
  • Hyperlipproteinemia type III, a risk factor for cardiovascular disease
  • The IBM Type-III Library, a distribution mechanism for unsupported IBM mainframe software such as CP/CMS
), the dowel itself fractured. Among the 240 specimens tested and failed (six load levels of 40%, 50%, 60%, 70%, 80%, and 90% for each rail width), 22 percent of the specimens failed due to Type I failure, whereas 77 percent of the specimens had Type II failure. Only 1 percent of the specimens failed with Type III failure. This percentage distribution of joint failure types was very similar to the distribution result from single-dowel withdrawal tests (Zhang et al. 2003a), which yielded 19 percent of Type I failure, 79 percent of Type II failure, and only 2 percent of Type III failure. The joint failure distribution was also similar to the joint static bending test failure mode distribution, which yielded 22 percent of Type I failure, 75 percent of Type II failure, and only 3 percent of Type III failure. This failure mode similarity confirmed that the upper dowel endured the tensile tensile,
adj having a degree of elasticity; having the ability to be extended or stretched.
 load when the joint was subjected to a cyclic bending moment.

Table 2 summarizes the mean values of Fatigue life (number of cycles to failure) of each joint rail width group subjected to each of the one-side, constant-fatigue bending moment levels. Ultimate static strength values were also included in the table (Zhang et al. 2003). The coefficients of variation of fatigue life ranged from 53 to 169 percent. The fatigue life averaged 131,253; 78,122; 31,617; 11,023; 4,161; and 329 cycles for load levels 40; 50; 60; 70; 80; and 90 percent of the ultimate strength of tested joints, respectively. The mean cycles increased at an average rate of 142 percent for every 10 percent applied moment decrease for joints tested at the 80, 70, 60, 50 and 40 percent levels. This may explain why the fatigue tests had relatively large coefficients of variation, since fatigue loads were based on average ultimate bending strength of the joints. At the 30 percent fatigue load level, joints of each rail width group finished 1 million cycles without failure. The mean fatigue life was 1.26 times 25,000 cycles, 1.04 times 75,000 cycles, and 1.05 times 125,000 cycles for load levels of 60, 50, and 40 percent, respectively. This indicated that under one-sided constant fatigue loads the joints would have an average fatigue life over 75,000 cycles if the joints had a mean bending strength value twice the applied load, and an average fatigue life over 125,000 cycles if the joints had a mean bending strength value 2.5 times the applied load.

The results of constant load fatigue testing of each rail width group were plotted on a log-linear plot (Fig. 3). Since M-N data were found to approximate a straight line, the following equation was employed to fit individual data points to obtain a mathematical representation of the M-N curve:

[1] M = C + D x [log.sub.10] [N.sub.f]

where:

M = applied bending moment (lb.-in.)

[N.sub.f] = number of cycles to failure

C, D = fitting constants

Linear least-squares fit of the individual data points resulted in four regression equations for 4-inch (101.6-mm), 5-inch (127-mm), 6-inch (152.4-mm), and 7-inch-wide (177.8-mm) rail joint groups with coefficient of determination Coefficient of determination

A measure of the goodness of fit of the relationship between the dependent and independent variables in a regression analysis; for instance, the percentage of variation in the return of an asset explained by the market portfolio return. Also known as R-square.
 [r.sup.2] values of 0.87, 0.68, 0.89, and 0.82, respectively. Table 3 gives the regression fitting constant values of C and D for each rail width group. These values indicated that the number of cycles to failure at a given fatigue bending moment could be estimated with the equations for each rail width group. To estimate the fatigue life of a joint between the curves, linear interpolation Linear interpolation is a method of curve fitting using linear polynomials. It is heavily employed in mathematics (particularly numerical analysis), and numerous applications including computer graphics. It is a simple form of interpolation.  could be applied to determine the constants C and D for the estimation equation.

The absolute value of the constant D increased as the rail width increased. This trend seems to indicate that a joint tends to have more resistance to fatigue damage as its static strength increases, since a higher load is needed on the stronger joint to cause joints to have the same fatigue life as the weaker joint. But the curve slope increase rate decreased as rail width increased at an average rate of 171 lb.-in./in. (0.76 N*m/mm) for a joint rail width increasing from 4 inches (101.6 mm) to 5 inches (127 mm); 104 lb.-in./in. (0.46 N*m/mm) for a joint rail width increasing from 5 inches (127 mm) to 6 inches (152.4 mm); and 66 lb.-in./in. (0.29 N*m/mm) for a joint rail width increasing from 6 inches (152.4 mm) to 7 inches (177.8 mm). The intercept of each M-N curve equation, the constant C value (Table 3, Regression column), was close to the mean ultimate bending strength of its joint group (Table 2). This indicated that the fatigue life of a dowel joint could be related to its static strength in terms of the constant C.

To estimate the fatigue life of a joint subjected to cyclic stepped fatigue bending moments based on its M-N curve, the Palmgren-Miner rule may be employed with the following unity summation summation n. the final argument of an attorney at the close of a trial in which he/she attempts to convince the judge and/or jury of the virtues of the client's case. (See: closing argument)  of life fractions:

[2] [N.sub.1]/[N.sub.f1] + [N.sub.2]/[N.sub.f2] + [N.sub.3]/[N.sub.f3] + ...... = [summation of [N.sub.j]/[N.sub.fj]] = 1

where:

[N.sub.j] = number of cycles applied to a joint at the bending moment Mj

[N.sub.fj] = number of cycles to failure from the joint M-N curve for the bending moment Mj

The estimation equation indicates that for a given stepped-load regimen and a known M-N curve, joint fatigue failure is expected when the life fractions sum to unity, that is, when 100 percent of the life is exhausted. The fatigue life of a joint under a given stepped bending load regimen could be estimated based on its M-N curve.

The protected Least Significant Difference (LSD LSD or lysergic acid diethylamide (lī'sûr`jĭk, dī'ĕth`ələmĭd, dī'ĕthəlăm`ĭd), alkaloid synthesized from lysergic acid, which is found in the fungus ergot ( ) multiple comparison procedure (Freund and Wilson 1997) at a 5 percent significance level was performed to separate means for the fatigue life.

Table 4 summarizes the mean fatigue life of the observed and estimated results of each joint width group subjected to cyclic stepped loads, means separation results among tested joint groups, and mean differences in percentage between predicted and observed values. The mean fatigue life of each joint rail width group was based on five specimens.

Mean comparisons indicated that no significant difference existed in fatigue life between 4-inch (101.6-mm) and 5-inch-wide (127-mm) rail joints, and also between 6-inch (152.4-mm) and 7-inch-wide (177.8-mm) rail joints, based on the LSD value of 25,080 cycles. Joints with 6-inch (152.4-mm) and 7-inch-wide (177.8-mm) rails had significantly longer fatigue life compared to joints with 4-inch (101.6-mm) and 5-inch-wide (127-mm) rails. Means separation results supported the 25,000 testing cycle increment and the acceptance levels specified in the GSA FNAE-80-214A testing standard (GSA 1998) since the observed acceptance level indicated that both joints with 4-inch (101.6-mm) and 5-inch-wide (127-mm) rails passed the light-service acceptance level (50,000 cycles), but failed to pass the medium-service acceptance level (125,000 cycles). Joints with 6-inch (152.4-mm) and 7-inch-wide (177.8-mm) rails passed the medium-service acceptance level (125,000 cycles), but failed to pass the heavy-service acceptance level (175,000 cycles). These indicated that both joints with 6-inch (152.4-mm) and 7-inch-wide (177.8-mm) rails had a longer fatigue life than joints with 4-inch (101.6-mm) and 5-inch-wide (127-mm) rails. Also, the results implied that a significant increase in joint static bending strength might not yield a significant increase in joint fatigue life when joints were subjected to cyclic stepped loads and GSA testing criteria. Since the average fatigue life of 4-inch (101.6-mm), 5-inch (127-mm), 6-inch (152.4-mm), and 7-inch-wide (177.8-mm) rail joints subjected to cyclic stepped loads passed 75,000, 100,000, 150,000, and 150,000 cycles, respectively, the ratios of each joint group's static strength value (Table 2) to its passing fatigue load (Table 1) were calculated. The ratios were 2.06, 2.06, 2.09, and 2.64 for 4-inch (101.6-mm), 5-inch (127-mm), 6-inch (152.4-mm), and 7-inch-wide (177.8-mm) rail joints, respectively. This appears to indicate that a joint could pass a stepped load level if its static strength is 2.06 times that of its fatigue load. In the case of the 7-inch-wide (177.8-mm) rail joints, however, even though the ratio of static strength to the load (5,541/2,400 = 2.31) was greater than 2.06, the joints still failed to pass the fatigue load level of 2,400 lb.-in. (271 N-m), having an average fatigue life of less than 175,000 cycles.

To evaluate how well the fatigue life estimation equation (Eq. [2]) agreed with observed results based on M-N curves, mean differences between the estimated and observed fatigue life values were determined and expressed as a percentage of estimated values shown in Table 4, Regression section. Mean differences indicated that the Palmgren-Miner rule underestimated plywood joint fatigue life by 3.7 percent when the rail width was 4 inches (101.6 ram), and tended to overestimate o·ver·es·ti·mate  
tr.v. o·ver·es·ti·mat·ed, o·ver·es·ti·mat·ing, o·ver·es·ti·mates
1. To estimate too highly.

2. To esteem too greatly.
 when the rail width is over 4 inches (101.6 mm) by a maximum of 20.1 percent for 5-inch (127-mm) wide rail joints. The overestimation o·ver·es·ti·mate  
tr.v. o·ver·es·ti·mat·ed, o·ver·es·ti·mat·ing, o·ver·es·ti·mates
1. To estimate too highly.

2. To esteem too greatly.
 is because no account is taken of the time under "creep," i.e., only the cycling load component is considered.

The estimated acceptance levels indicated that 4-inch-wide (101.6-mm) rail joints would pass the light-duty acceptance level, and 6-inch-wide (152.4-mm) rail joints would pass the medium-service acceptance level. Joints of 5-inch-wide (127-mm) rails would also pass the medium-service acceptance level and joints with 7-inch-wide (177.8-mm) rails would pass the heavy-service acceptance level. The estimated acceptance level also showed that the equation tended to overestimate fatigue life for joints with 5-inch (127-mm) and 7-inch-wide (177.8-mm) rails.

An attempt was made to derive the estimation equation with a mathematical representation form (Eq. [1]) based on joint static strength data and minimum fatigue testing results. The intercept of each M-N curve equation derived from the experimental data, the constant C value (Table 3), was close to the mean ultimate bending strength of its joint group (Table 2), which showed that the fatigue life of a dowel joint was related to its static strength in terms of the constant C. Also, the one-sided constant fatigue tests indicated that the fatigue life of tested joints in this study could reach 1 million cycles when joints were loaded with 30 percent of their mean ultimate bending strengths. Therefore, for each joint group, the regression constant C was first replaced with its mean ultimate bending strength as indicated in Table 3, in the newly derived column. To obtain the curve slope value D, the applied moment level (M) and the number of cycles to failure ([N.sub.f]) were substituted with 30 percent of its joint group ultimate bending strength and 1 million cycles, respectively. Table 3 lists the newly derived constant D value for each joint group estimation equation under the newly derived column. A new set of estimation equations was derived. The last two columns of Table 3 show the differences for the constants between the regression and newly derived equations. A paired t-test indicated that no significant differences existed between the two values for constants C or D at the 5 percent significance level.

The third section of Table 4 gives the predicted fatigue life of each joint group based on the newly derived equations. Mean differences between estimated and observed values were less than 9 percent. The new derived equations estimated 4-inch (101.6-mm) and 5-inch-wide (127-mm) rail joints would pass the light-service acceptance level, 6-inch-wide (152.4-mm) rail joints would pass the medium-service acceptance level, and 7-inch-wide (177.8-mm) rail joints would pass the heavy-service acceptance level. This indicated that the proposed method could be employed to derive the M-N estimation equation, i.e., constants C and D, based on the joint mean ultimate strength and the number of cycles to failure of 1 million cycles at a fatigue load level of 30 percent of the ultimate bending strength.

Conclusions

Bending fatigue behavior of T-shaped, end-to-side, two-pin dowel joints constructed of furniture-grade, 3/4-inch-thick (19.05-mm) 5-ply southern yellow pine plywood were investigated under one-sided constant and stepped fatigue load conditions.

Results of one-sided constant load tests indicated that the fatigue life of dowel joints averaged 131,253; 78,122; 31,617; 11,023; 4,161; and 329 cycles for load levels of 40; 50; 60; 70; 80; and 90 percent of their ultimate static bending strengths, respectively. Regression analysis In statistics, a mathematical method of modeling the relationships among three or more variables. It is used to predict the value of one variable given the values of the others. For example, a model might estimate sales based on age and gender.  of M-N data concluded that the functional relationship between the fatigue bending moment and the log number of cycles to failure could be expressed with the linear equation M = C + D x [log.sub.10] [N.sub.f]. The absolute value of the constant D increased as rail widths increased from 4 inches (101.6 mm) to 7 inches (177.8 mm) with an increment of 1 inch (25.4 mm). This indicated that joints with higher static bending strengths tended to have more resistance to fatigue damage.

A simplified method of deriving the linear equation constants C and D for a joint fatigue life prediction was proposed, i.e., defining the relationship between fatigue bending moment and the log number of cycles to failure, based on known information such as the joint static bending strength and the number of cycles to failure of 1 million cycles at the fatigue load of 30 percent of its static bending strength.

Cyclic stepped load tests verified that the Palmgren-Miner rule was an effective method to estimate the fatigue life of two-pin dowel joints subjected to cyclic stepped bending moments based on their M-N curves. Fatigue life comparisons among joint groups with different static bending strengths indicated that a significant increase in ultimate static bending strength might not yield a significant fatigue life increase when joints were subjected to cyclic stepped loads and GSA testing criteria. Joint resistance to fatigue failure should be taken into account in strength design of furniture frames that are subjected to repeated loading
Table 1.--Cyclic stepped load schedule. (a)

Service acceptance level    Loads     No. of cycles
                           (lb.-in)

                              600         25,000
Light                         900         50,000
                            1,200         75,000
                            1,500        100,000
Medium                      1,800        125,000
                            2,100        150,000
Heavy                       2,400        175,000

(a) 1 lb.-in. = 0.113 N.m.

Table 2.--Mean values of ultimate static bending strengths
of each joint rail width group, and fatigue life (number of
cycles to failure) for each joint rail width group at each
bending moment level. (a)

                            Rail width

               4 in.          5 in.          6 in.

Ultimate
strength
(lb.-in.)    2,471 (11)     3,093 (20)     4,399 (12)

 Bending
 moment
  level                    No. of cycles to failure

   (%)

   90         32 (124)     1,147 (104)      82 (105)
   80         203 (99)     14,171 (138)    762 (161)
   70        665 (120)     34,994 (73)     3,178 (65)
   60       13,814 (126)   63,592 (86)    10,035 (62)
   50       70,137 (103)   86,251 (53)    71,859 (53)
   40       129,974 (53)   111,956 (86)   133,966 (55)
   30        1,000,000      1,000,000      1,000,000

              Rail width

                7 in.

Ultimate
strength
(lb.-in.)     5,541 (9)

 Bending                     Mean
 moment                     cycles
  level

   (%)

   90         56 (142)        329
   80        1,508 (85)      4,161
   70        5,257 (168)    11,023
   60       39,030 (169)    31,617
   50        84,241 (81)    78,122
   40       150,118 (107)   131,253
   30         1,000,000

(a) 1 lb.-in = 0.113 N.m.; values in
parentheses are coefficients of variation
in percent.

Table 3.--Values of estimation equation constants C and D
(lb.-in.) for both regression equations and newly derived
equations of each rail width joint group. (a)

Rail     Regression       Newly         Difference
width                    Derived
(in.)
          C      D       C      D       C       D

                                           (%)

  4     2,396   -261   2,471   -288     3.1    10.8
  5     3,766   -432   3,093   -361   -17.9   -16.4
  6     4,699   -536   4,399   -513    -6.4    -4.3
  7     5,588   -602   5,541   -646    -0.8     7.3

(a) 1 lb.-in. = 0.113 N.m; 1 in. = 25.4 mm.

Table 4.--Comparisons among observed mean fatigue life of joints,
and between estimated and observed fatigue life of each joint rail
width group subjected to stepped loads. Different letters for
observed values indicate that values differed significantly at the
0.05 level. (a)
                                  Rail width

                            4 in.           5 in.

Observed
  Mean no. of cycles    78,681 (8) (a)   100,666 (7)
  to failure                  B               B

  Acceptance level          Light           Light

Regression
  Predicted no. of
  cycles to failure         75,849         125,925

  Mean difference (%)        -3.7           20.1

Newly derived
  Predicted no. of
  cycles to failure         73,155         96,666

  Mean difference (%)        -7.6           -4.1

                                Rail width

                           6 in.          7 in.

Observed
  Mean no. of cycles    157,230 (15)   169,963 (16)
  to failure                 A              A

  Acceptance level         Medium         Medium

Regression
  Predicted no. of
  cycles to failure       159,850        208,372

  Mean difference (%)       1.6            18.4

Newly derived
  Predicted no. of
  cycles to failure       146,383        186,744

  Mean difference (%)       -7.4           9.0

(a) 1 in. = 25.4 mm; values in parentheses are coefficients
of variation in percentage.


Literature cited

American Society for Testing and Materials (ASTM). 1998. Standard test methods for mechanical properties of lumber and wood-based structural material. ASTM D 4761-96. ASTM, West Conshohocken, PA.

Eckelman, C.A. 1970. The fatigue strength of two-pin moment-resisting dowel joints. Forest Prod. J. 20(5):42-45.

-- 1980. The bending strength of furniture joints constructed with metal tooth connector plates. Inter. J. of Furniture Research 2(1):12-14 and 2(2):40-42.

-- 1988a. Performance testing Performance Testing covers a broad range of engineering or functional evaluations where a material, product, or system is not specified by detailed material or component specifications: Rather, emphasis is on the final measurable performance characteristics.  of furniture. Part I. Underlying concepts. Forest Prod. J. 38(3):44-48.

--1988b. Performance testing of furniture. Part II. A multipurpose universal structural performance test method. Forest Prod. J. 38(4):13-18.

-- and J. Zhang. 1995. Uses of the general services administration The General Services Administration (GSA) was established by section 101 of the Federal Property and Administrative Services Act of 1949 (40 U.S.C.A. § 751). The GSA sets policy for and manages government property and records.  performance test method for upholstered furniture in the engineering of upholstered furniture frames. Hols als Roh-und Werstoff 53:261-267.

Freund, R.J. and W.J. Wilson. 1997. Statistical Methods. Academic Press, Inc., San Diego San Diego (săn dēā`gō), city (1990 pop. 1,110,549), seat of San Diego co., S Calif., on San Diego Bay; inc. 1850. San Diego includes the unincorporated communities of La Jolla and Spring Valley. Coronado is across the bay. , CA.

General Service Administration (GSA). 1998. Upholstered furniture test method. FNAE-80-214A. Furniture Commodity Center, Federal Supply Serv., Washington, DC.

Miner, M.A. 1945. Cumulative damage in fatigue. J. of Applied Mechanics the principles of abstract mechanics applied to human art; also, the practical application of the laws of matter and motion to the construction of machines and structures of all kinds.

See also: Mechanics
 12(3):A159-164.

Palmgren, A. 1924. Die lebensdauer von kugallagern. Ver. Deut Ingr. 68:339-341.

Zhang, J., G. Li, and T. Sellers, Jr. 2003. Withdrawal and bending performance of dowel joints in furniture grade pine plywood. Accepted for publication in Forest Prod. J. 53(7/8):41-49.

-- F. Quin, and B. Tackett. 2001. Bending fatigue life of two-pin dowel joints constructed of wood and wood composites. Forest Prod. J. 51(10):73-78.

Jilei Zhang * Gan Li Terry Sellers, Jr. *

The authors are, respectively, Assistant Professor, Graduate Student, and Professor, Forest Products Laboratory, Mississippi State Univ., Mississippi State, MS 39762-9820. Approved for publication as Journal Article No. FP 238 of the Forest and Wildlife Research Center, Mississippi State Univ. This paper was received for publication in March 2002. Article No. 9453.

* Forest Products Society Member.
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Author:Zhang, Jilei; Li, Gan; Sellers, Terry, Jr.
Publication:Forest Products Journal
Geographic Code:1USA
Date:Sep 1, 2003
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