Exploratory study of the moment capacity and semirigid moment-rotation behavior of round mortise and tenon joints.
Tests were conducted to determine the moment capacity and semirigid joint behavior of round mortise and tenon joints with 2-, 3-, and 4-inch-diameter tenons. Purpose of the tests was to obtain information concerning ultimate moment capacity, capacity at a "5%" yield point, and semirigid behavior of the joints. Tenons containing juvenile wood had substantially reduced bending moment capacity compared to computed capacities based on Wood Handbook MOR values. Cross pins substantially reduced moment capacity, whereas tenon shoulders substantially increased moment capacity. Moment capacity of the joints at a specified "5% yield point" averaged 55 percent as great as ultimate capacity. Semirigid connection factors, Z, averaged 7 x [10.sup.-5] rad/ft-lb for 2-inch tenons; 2 x [10.sup.-5] rad/ft-lb for 3-inch tenons, and 1.2 x [10.sup.-5] rad/ft-lb for 4-inch tenons. For tenons with shoulders, joint stiffness was found to be related to the side hardness of the mortised member.
The deflection characteristics of frames constructed with semirigid joints along with corresponding force distributions may differ substantially from estimates based on rigid joint analyses (Lothers 1960). Bulleit et al. (1999) treated the semirigid behavior of rectangular mortise and tenon joints used in heavy timber flame construction and concluded that the joints should be assumed to carry no moment and that the stiffness of pinned axial connections should be based on pin behavior alone. Eckelman, Akcay, and Haviarova (2006) investigated the deflection characteristics of a small barn flame constructed with round mortise and tenon joints and found that although the connection itself is mechanically rigid and can carry substantial moment, the joints, nonetheless, must be treated as semirigid.
Information concerning the structural characteristics of light timber frames constructed with round mortise and tenon joints along with information concerning semirigid connection factors for round mortise and tenon joints is essentially limited to the above study. Likewise, information concerning bending moment capacity of these joints is limited to a study conducted by Akcay (2006). Because such information is needed for the rational analysis and design of light timber frames constructed with these joints, a study was undertaken to obtain insight into the semirigid behavior of the joints and to obtain background data that would provide initial estimates of the magnitudes of semirigid connection factors for such joints--in particular, semirigid connection factors for selected joint configurations constructed with 2-, 3-, and 4-inch-diameter tenons. An additional objective was to expand the database of information concerning the moment capacities of joints constructed with 2-, 3-, and 4-inch tenons and, additionally, to determine if initial "yielding" of the joints occurs at regular percentages of ultimate moment levels. Test results obtained by Akcay (2006) were incorporated into these results.
Typical configurations of the bending moment specimens are shown in Figure 1. Dimensional data for all specimens--those of Akcay (2006) are shown in bold type--along with moisture contents (MC) at time of test are given in Table 1. In general, each specimen consisted of a vertical post containing the mortise and a horizontal rail or beam with a corresponding tenon machined on one or both ends. Each specimen set consisted of 3 replications. MCs were determined by the ovendry method immediately after testing.
[FIGURE 1 OMITTED]
The materials used in this study, particularly the yellow-poplar, varied substantially in quality. Specimens with 2-inch diameter tenons were constructed of Douglas-fir (Pseudotsuga menziesii), southern yellow pine (P. echinata, P. elliotti, P. palustris, P. taeda), eastem white pine (Pinus strobus), and yellow-poplar (Liriodendron tulipifera); specimens with 3-inch diameter tenons were constructed of southern yellow pine, yellow-poplar, and white ash (Fraxinus americana); and specimens with 4-inch tenons were constructed of southern yellow pine and yellow-poplar. As indicated in Table 1, specimens were constructed both with and without cross pins to investigate constructions in which both pinned and unpinned joints are used. Both red oak and steel cross pins were used in construction of the specimens as indicated in Table 1. Finally, two sets of specimens were constructed with a notch cut on the underside of the rail in order to minimize shoulder effects.
Method of test
Specimens were supported for testing in a universal testing machine by means of the jig shown in Figure 2. This is a nonstandard procedure that initially had been developed and used to evaluate the semirigid behavior of furniture joints (Eckelman 1968). Dial gages were supported by a half-inch diameter threaded rod that was inserted through a hole drilled through the rail of each specimen at a point 4-inches away from the post. Distance between dial gage stems was either 10 or 12 inches (x, Fig. 2). Loads were applied to the rails of the specimens 18 inches (L, Fig. 2) away from the faces of the posts. Rate of loading was 0.125 inches/minute. Testing was continued until the applied load ceased to increase or an obvious joint failure with sudden fall off in load occurred. Dial readings were taken at intervals such that at least 10 readings were taken per test.
Bending moment capacity
Results of the bending moment tests are given in Table 1. Two factors are of particular concern with respect to these results. Firstly, what are the ultimate moment capacities of the joints and what are the ratios of these values relative to computed bending moment capacities of comparable dowels based on Wood Handbook (USDA Forest Serv. 1999) modulus of rupture values. Secondly, are there reasonably well-defined points--expressed as a percentage of the ultimate strength of each of the tenon diameters--where initial "yielding" of the tenon occurs.
Analysis of data
To better view the results, the data were transferred to a spread sheet after each test was concluded, and the combined absolute deflection values, Y, of the gages plotted against moment where Y = ([absolute value of [y.sub.1]] + [absolute value of [y.sub.2]]) and [y.sub.1] and [y.sub.2] refer to the deflections of the top and bottom gages, respectively. A straight line was then fitted to the combined gage data and plotted for viewing as shown in Figure 3. The percentage difference between each combined gage value and the corresponding regression value was determined for each test point and the point noted at which the combined gage value differed from the linear regression value by no more than 5 percent noted. Joint rotations in radians were found as, [phi] = Y / x, where x refers to the spacing between gages, i.e., either 10 or 12 inches. Semirigid connection factors, i.e., Z-values, could then be determined at any moment level as Z = [phi]/M, where + refers to joint rotation in radians and M refers to moment, ft-lb.
Estimated bending moment capacity
Moment capacities of wood dowels (i.e., round tenons), based on Wood Handbook modulus of rupture values, can be computed by restating the terms of the flexure formula for round beams as shown below (Wangaard 1950).
[F.sub.4] = [[pi][D.sup.3]]/[12 x 32] x mor, 
where [F.sub.4] refers to bending moment capacity, ft-lbs; D refers to dowel diameter, in; mor refers to the modulus of rupture of the material, psi; and 12 is a constant used to convert in-lbs to ft-lbs. The MOR of Douglas-fir, eastern white pine, white ash, yellow-poplar, and the average MOR for loblolly (P. taeda), shortleaf (P. echinata), and slash pine (P. elliotti) at current MC levels were used to compute the bending moment capacities of dowels constructed of these species as shown in Table 1.
[FIGURE 2 OMITTED]
[FIGURE 3 OMITTED]
The bending moment capacity of 2-inch, 3-inch, and 4-inch-diameter southern yellow pine tenons without shoulders or cross pins (Fig. 4) averaged 44 percent (set 3), 45 percent (set 17), and 51 percent (set 25), respectively of computed round beam capacity based on Wood Handbook modulus of rupture values. Comparable 2-inch-diameter yellow-poplar tenons averaged 65 percent (set 8) of computed values. All of the pine specimens contained juvenile wood, whereas the yellow-poplar specimens were cut from areas immediately adjacent to but not including pith wood. Likewise, the moment capacity of 2- and 4-inch-diameter yellow-poplar tenons with notched shoulders (Fig. 4) averaged 85 percent (set 14) and 76 percent (set 31), respectively, of computed values, which are higher than the value of 65 percent obtained for the 2-inch yellow-poplar round beam (set 8). These higher values likely result from partial shoulder support of the tenon, but nonetheless, are indicative of the reductions that must be expected when tenons include juvenile wood.
To aid interpretation of the results, a multiple regression expression of the form
M = (([a.sub.1][mor.sub.1] + [a.sub.2][mor.sub.2] + [a.sub.3][mor.sub.3] + [a.sub.4][mor.sub.4]) x [pi][D.sup.3]/(12 x 32)) x (([(D - d)/D).sup.a5]) x (sh + [a.sub.6] x (2 x w)/D) 
was used to evaluate the data where M refers to ultimate moment, ft-lb; [mor.sub.1] refers to the MOR value of Douglas-fir, [mor.sub.2] to eastern white pine, [mor.sub.3] to southern yellow pine, and [mor.sub.4] to yellow-poplar, psi; D refers to tenon diameter, inch; d refers to pin diameter, inch; sh indicates whether there is a shoulder on the tenon, 1 or 0; and w refers to the distance from the longitudinal axis of the tenon to the bottom edge of the rail, inch; and [a.sub.1] to [a.sub.6] re regression coefficients. Analyses of the data gave the following result:
M = (0.83[mor.sub.1] + 0.91[mor.sub.2] + 0.52[mor.sub.3] + 0.73[mor.sub.4]) X ([pi][D.sup.3]/(12 x 32)) x ([((D -d)/D).sup.0.64] x (sh + 0.96 x (2 x w)/D) 
with a coefficient of multiple determination, [R.sup.2], of 97.0 percent.
[FIGURE 4 OMITTED]
This expression indicates that the Douglas-fir and eastern white pine tenons machined on rails cut from material that did not include tree centers--although likely cut from adjacent material--developed 83 percent (i.e., 0.83[mor.sub.1] and 91 percent (0.91 [mor.sub.2]), respectively, of computed bending moment capacity based on Wood Handbook MOR values. The southern yellow pine specimens, on the other hand, which essentially always contained tree centers and thereby juvenile wood, developed 52 percent (0.52[mor.sub.3]) of computed capacity. And finally, the yellow-poplar specimens which often included tree centers, or material cut adjacent to tree centers, developed 73 percent (0.73[mor.sub.4]) of computed moment capacity. These results provide useful indications of the reductions in moment capacity that should be expected when dealing with timber cut from small diameter trees or with timbers that include the heart of the tree.
Effect of cross pins
The effect of cross pins on bending moment capacity estimated by expression , i.e., [((D - d) / D).sup.0.64], is illustrated graphically in Figure 4. As expected, and as has previously been shown (Eckelman and Haviarova 2006), use of cross pins can substantially reduce moment capacity. For static tests, the above expression estimates that pinned tenons with cross pins half the diameter of the tenon have only [(0.5).sup.0.64], or 64 percent of the capacity of an unpinned tenon.
[FIGURE 5 OMITTED]
Overall, these, as well as the other cross pinned joints included in the study failed owing to longitudinal shear failures within the tenon. In some cases, a single longitudinal failure extended from the topmost edge of the cross pin to the tip of the tenon, Figure 5. This was often followed by what then appeared as a double shear failure, Figure 6. In a few cases, the end of the tenon split in tension perpendicular to the grain as shown in Figure 6.
Shoulder effect on bending moment capacity
Previous work (Eckelman, Erdil, and Haviarova 2006) with 1-inch rails and tenons that ranged from 0.5 to 1 inch in diameter indicated that the moment capacity of tenon joints with shoulders could be expressed as a function of joints without shoulders by means of the regression expression, [M.sub.s] = 1.08 x ((2 x w)/D) x [M.sub.NS], where Ms refers to the moment capacity of a tenon joint with shoulders, [M.sub.NS] refers to the capacity of a comparable joint without shoulders, D refers to the diameter of the tenon, and w refers to the distance from the diametric center of the tenon to the extreme edge of the shoulder loaded in compression. For the joints in this study, the factor, 0.96 x ((2 x w)/D), Eq. , was found to apply, which differs little from the above factor for smaller diameter tenons.
Yielding and 5 percent bending moment capacity
One objective of the semirigid joint tests was to determine at what moment level the onset of "yielding" occurs as the joints are loaded to failure. In order to investigate this phenomenon, a straight line was fitted to the linear portion of each moment-rotation curve, and the deviation of the curve from the straight line examined--as shown in Figure 3. The moment level at which a 5 percent deviation from this straight line occurred was arbitrarily defined as the point at which the onset of yielding occurred. The 5 percent yield point for the 2-inch tenons averaged 67.4 percent as great as the ultimate moment capacity, whereas the comparable values for the 3-inch and 4-inch tenons averaged 57.9 percent and 52.2 percent, respectively. The overall average for all specimens was 58.3 percent.
If the regression expression
[M.sub.5%] = a x (0.83 X [mor.sub.1] + 0.91 x [mor.sub.2] + 0.52 x [mor.sub.3] + 0.73 x [mor.sub.4]) x ([pi][D.sup.3]/(12 x 32)) x [((D - d)/D).sup.0.64]) x (sh + 0.96 X (2 x w)/D) 
is fitted to the moments at the 5 percent deviation levels, a value of a = 0.55 is obtained with [R.sup.2] = 86 percent. This result indicates that bending moment capacity at the 5 percent yield level amounts to 55 percent of the ultimate moment capacity and that a reasonably regular relationship exists between the 5 percent yield point and ultimate moment, which tends to indicate that a rational basis for estimating the usable strength of such joints can be developed.
[FIGURE 6 OMITTED]
Results of the tests are given in Table 1. Overall, the semirigid rotation factors for the 2-inch tenons ranged from a low of 3.1 x [10.sup.-5] rad/ft-lb (set 16) to a high of 11 x [10.sup.-5] rad/ft-lb (set 2) with an average of 7 x [10.sup.-5] rad/ft-lb. Likewise, factors for the 3-inch tenons ranged from 1.5 x [10.sup.-5] rad/ft-lb (set 23) to 2.6 x [10.sup.-5] rad/ft-lb (set 21) with an average value of 2 x [10.sup.-5] rad/ft-lb. Finally, factors for the 4-inch tenons ranged from 1 x [10.sup.-5] to 1.3 x [10.sup.-5] rad/ft-lb (sets 29 to 31) with an average of 1.2 x [10.sup.-5] rad/ft-lb. The overall relationship of joint rigidity to tenon diameter is given by the regression expression Z = 39/[D.sup.2.55] (with an [R.sup.2] value of 0.80), as shown in Figure 7.
To further assist in interpreting results, an expression of the form
Z = 1/([a.sub.0] x (([a.sub.1][moe.sub.1] + [a.sub.2][moe.sub.2] + [a.sub.3][moe.sub.3] + [a.sub.4][moe.sub.4]) x ([pi][D.sup.a5]/(12 x 64)) x (1 + [a.sub.6]d) x [([a.sub.7] x H x (2 X w)/D).sup.a8])) 
was fitted to the data where Z refers to the semirigid rotation factor, radians/ft-lb; [moe.sub.i] refers to moment of elasticity, psi; D refers to tenon diameter, in; d refers to cross pin diameter, in; H refers to side hardness, lbf; the term, (1 + [a.sub.6]d), accounts for cross pin effect, and [a.sub.i] refers to the regression coefficients. The side effect term, H, was included in the above expression to account for the stiffening that results as the bottom edge of the shoulder of the rail presses against the side wall of the post. This effect proved to be reasonably well-correlated with the side hardness values presented in the Wood Handbook (1999), which are the average of radial and tangential penetrations. Solving this expression gives
Z = 1/(0.0064 x ((0.72[moe.sub.1] + 0.72[moe.sub.2] + 0.51[moe.sub.3] + 1.20[moe.sub.4]) x ([pi][D.sup.2.56]/(12 x 64)) x (1 + 0.18 x d) x [(1.26 x H x (2 + w)/D).sup.0.56])) 
with an [R.sup.2] value of 98.5 percent. The greatest difference with this expression occurs with cross pinned white ash specimens where the difference between the measured and predicted values amounts to -38%; the next greatest difference is 22.8 percent with the notched 4-inch- diameter yellow-poplar specimens, Table 1.
[FIGURE 7 OMITTED]
The coefficients of the modulus of elasticity values are relative since they are responsive to the coefficient, [a.sub.0]. Presumably, however, they reflect the effect of juvenile wood on tenon stiffness. In this respect, the coefficient for southern yellow pine is noteworthy because all of the tenons contained juvenile wood. The expression is also particularly sensitive to the coefficient of tenon diameter; use of a value of 4.0 instead of 2.56, for example, results in serious under-prediction of values for the larger tenons.
The small cross pin effect is somewhat surprising. Intuitively, it seems that as the joints are loaded, the tenons would withdraw from the mortise. Cross pins would be expected to hinder this action and thereby increase joint stiffness compared to unpinned joints. Removal of the cross pin term, 0.18 x d, however, causes the [R.sup.2] value to decrease only slightly to 97.7 percent. In contrast, removal of the hardness/ shoulder term causes the [R.sup.2] value to decrease to 68.8 percent, which does indicate a strong shoulder effect.
Although a formal study of juvenile wood was not conducted, tenons cut from material located near the center of the tree stem would be expected to have reduced bending moment capacity compared to estimated capacities based on Wood Handbook MOR values. Specimens cut from southern yellow pine, for example, had only 52 percent of computed capacity. Use of cross pins can substantially reduce the bending moment capacity of a joint. Loss of capacity is proportional to pin diameter. Cross pins equal to one half the diameter of the tenon, for example, can reduce moment capacity by 36 percent. Thus, the smallest appropriate diameter pins should be used. Shoulders on the tenons substantially increase moment capacity. For symmetrical tenon/shoulder constructions, the increase in capacity is nearly directly proportional to the width of the rail divided by the diameter of the tenon. Results indicate that a reasonably regular relationship exists between the moment resistance of the joints and a defined "5% yield point." Overall, moment resistance of the joints at the 5 percent "yield point" averaged about 55 percent as great as the ultimate capacities of the joints.
Semirigid connection factors averaged from Z = 7 x [10.sup.-5] rad/ft-lb for 2-inch tenons to Z = 2.0 x [10.sup.-5] rad/ft-lb for 3-inch tenons, and Z = 1.2 x [10.sup.-5] rad/ft-lb for 4-inch tenons. Overall, stiffness of the joints appears to be affected by juvenile wood in the tenon. Contrary to expectations, joints stiffness was not greatly influenced by the use of cross pins. Stiffness was affected by tenon shoulders. Finally, for tenons with shoulders, joint stiffness was found to be related to the side hardness of the mortised member.
Akcay, H. 2006. Use of round mortise and tenon joints in light timber frame construction. Ph.D. thesis, Purdue Univ., West Lafayette, Indiana. 105 pp.
Bulleit, W.M., L.B. Sandberg, M.W. Drewek, and T.T. O'Bryant. 1999. Behavior and modeling of wood-pegged timber frames. J. Struct. Eng. 125(1):3-9.
Eckelman, C.A. 1968. Furniture frame analysis and design. Ph.D. thesis, Purdue Univ., West Lafayette, Indiana. 231 pp.
Eckelman, C., Y. Erdil, and E. Haviarova. 2006. Effect of shoulders on the bending moment capacity of round mortise and tenon joints. Forest Prod. J. 56(1):82-86.
Eckelman, C.A., H. Akcay, and E. Haviarova. 2006c. Performance tests of small barn frame constructed with round mortise and tenon joints. Forest Prod. J. 56(4):41-47.
-- and E. Haviarova. 2006. Performance tests of school chairs constructed with round mortise and tenon joints. Forest Prod. J. 56(3): 51-57.
Lothers, J.E. 1960. Advanced Design in Structural Steel. Prentice-Hall, Inc. Englewood Cliffs, New Jersey. 583 pp.
USDA Forest Serv. 1999. Wood Handbook: Wood as an Engineering Material. Forest Products Soc., Madison, Wisconsin. 466 pp.
Wangaard, F.F. 1950. The Mechanical Properties of Wood. John Wiley and Sons, New York. 377 pp.
Carl Eckelman *
Eva Haviarova *
The authors are, respectively, Professor, Assistant Professor, and Graduate Student, Purdue Univ., West Lafayette, Indiana (email@example.com, firstname.lastname@example.org, email@example.com). This paper was received for publication in October 2007. Article No. 10413.
* Forest Products Society Member.
Table 1.--Bending moment capacity of joints. Akcay (2006) data shown in bold type. Three specimens each unless otherwise noted. Set Wood Cross no. species MC (1) Sh. (2) pin dia. (3) (percent) (inches) 1 D-fir (9) 10.4 yes 0.68-S (14) 2 EP (10) 12.0 yes 0.68-S 3# (8) SYP (11)# 12# none# none# 4# (8) SYP# 12# none# 1-W# (15) 5# (8) SYP# 12# yes# none# 6 SYP 12 yes 0.68-S (14) 7# (8) SYP# 12# yes# 1-W# 8# Y-pop (12)# 6.9# none# none# 9# Y-pop# 5.8# none# 1-W# 10# Y-pop# 6.2# yes# none# 11# Y-pop# 7.3# yes# 1-W# 12 Y-pop 11 yes none 13 Y-pop 11 yes 0.68-S 14 Y-pop 11 notch none 15 Y-pop 9 yes none 16 Y-pop 9 yes 0.68-S 17# SYP# 12.3# none# none# 18# SYP# 11.8# yes# none# 19# SYP# 10.8# none# 1.5-W# 20# SYP 10.3 yes 1.5-W# 21 Y-pop 9.8 yes none 22 Y-pop 9.8 yes none 23 W-ash (13) 18 yes none 24 W-ash 18 yes 0.68-S 25# SYP# 13.1# none# none# 26# SYP# 13# yes# none# 27# SYP# 11.6# none# 2-W# 28# SYP# 11# yes# 2-W# 29 Y-pop 9.8 yes none 30 Y-pop 9.8 yes 1-S 31 Y-pop 9.8 notch none Tenon & Set Wood Tenon Rail mortise no. species dia. depth length (inches) 1 D-fir (9) 2 3.4 3.4 2 EP (10) 2 3.5 3.4 3# (8) SYP (11)# 2# 3.5# 3.47# 4# (8) SYP# 2# 3.48# 3.45# 5# (8) SYP# 2# 3.5# 3.47# 6 SYP 2 3.5 3.4 7# (8) SYP# 2# 3.48# 3.45# 8# Y-pop (12)# 2# 3.85# 3.89# 9# Y-pop# 2# 3.86# 3.82# 10# Y-pop# 2# 3.88# 3.88# 11# Y-pop# 2# 3.79# 3.74# 12 Y-pop 2 3.8 4 13 Y-pop 2 3.8 4 14 Y-pop 2 3.8 4 15 Y-pop 2 5.9 5.90 16 Y-pop 2 5.9 5.90 17# SYP# 3# 3.5# 5.47# 18# SYP# 3# 3.51# 5.47# 19# SYP# 3# 3.48# 5.41# 20# SYP 3# 3.5# 5.38# 21 Y-pop 3 3.8 5.5 22 Y-pop 3 5.6 5.5 23 W-ash (13) 3 5.8 5.9 24 W-ash 3 5.8 5.9 25# SYP# 4# 5.46# 7.3# 26# SYP# 4# 5.45# 7.3# 27# SYP# 4# 5.37# 7.3# 28# SYP# 4# 5.39# 7.3# 29 Y-pop 4 5.9 7.4 30 Y-pop 4 5.9 7.4 31 Y-pop 4 5.9 7.4 Ultimate W Handbk (6) moment computed Set Wood dowel no. species Avg. (4) SD (5) capacity (ft-lb) 1 D-fir (9) 890 150 860 2 EP (10) 540 215 610 3# (8) SYP (11)# 400# 105# 915 4# (8) SYP# 370# 35# 915 5# (8) SYP# 720# 175# 915 6 SYP 570 165 915 7# (8) SYP# 460# 75# 915 8# Y-pop (12)# 520# 95# 800 9# Y-pop# 445# 35# 800 10# Y-pop# 855# 70# 800 11# Y-pop# 485# 45# 800 12 Y-pop 770 140 690 13 Y-pop 650 65 690 14 Y-pop 585 40 690 15 Y-pop 1,000 60 740 16 Y-pop 1,185 255 740 17# SYP# 1,420# 95# 3,125 18# SYP# 1,660# 120# 3,113 19# SYP# 825# 60# 3,236 20# SYP 1,085# 110# 3,298 21 Y-pop 2,735 265 2,430 22 Y-pop 3,650 145 2,430 23 W-ash (13) 4,110 580 2,520 24 W-ash 3,730 340 2,520 25# SYP# 3,590# 236# 6,995 26# SYP# 5,010# 340# 6,995 27# SYP# 2,860# 661# 7,200 28# SYP# 3,215# 778# 7,610 29 Y-pop 4,440 605 6,130 30 Y-pop 4,500 630 6,130 31 Y-pop 4,630 565 6,130 Ratio 5% moment ultimate/ capacity Set Wood computed no. species capacity Avg. SD (percent) (ft-lb) 1 D-fir (9) 103 600 105 2 EP (10) 89 435 85 3# (8) SYP (11)# 44 4# (8) SYP# 40 5# (8) SYP# 79 6 SYP 62 435 75 7# (8) SYP# 50 8# Y-pop (12)# 65 9# Y-pop# 56 10# Y-pop# 107 11# Y-pop# 60 12 Y-pop 112 375 200 13 Y-pop 94 620 80 14 Y-pop 85 365 115 15 Y-pop 135 580 120 16 Y-pop 160 600 95 17# SYP# 45 18# SYP# 53 19# SYP# 25 20# SYP 33 21 Y-pop 113 1,310 495 22 Y-pop 150 2,810 675 23 W-ash (13) 163 2,190 660 24 W-ash 148 2,000 215 25# SYP# 51 26# SYP# 72 27# SYP# 40 28# SYP# 42 29 Y-pop 72 2,700 550 30 Y-pop 73 1,910 160 31 Y-pop 76 2,475 450 Ratio 5% moment/ Z-connection factors Set Wood ultimate no. species moment Avg SD rad/ft-lb rad/ft-lb [10.sup.-5] [10.sup.-5] 1 D-fir (9) 67.4 7.9 2.2 2 EP (10) 80.6 11.0 1.6 3# (8) SYP (11)# 4# (8) SYP# 5# (8) SYP# 6 SYP 76.3 9.5 0.6 7# (8) SYP# 8# Y-pop (12)# 9# Y-pop# 10# Y-pop# 11# Y-pop# 12 Y-pop 48.7 6.3 1.9 13 Y-pop 95.4 5.0 1.3 14 Y-pop 62.4 8.1 2.0 15 Y-pop 58.0 5.1 0.9 16 Y-pop 50.6 3.1 1.3 17# SYP# 18# SYP# 19# SYP# 20# SYP 21 Y-pop 47.9 2.6 0.5 22 Y-pop 77.0 2.0 0.1 23 W-ash (13) 53.3 1.5 0.3 24 W-ash 53.6 1.9 0.5 25# SYP# 26# SYP# 27# SYP# 28# SYP# 29 Y-pop 60.8 1.0 0.2 30 Y-pop 42.4 1.3 0.2 31 Y-pop 53.5 1.3 0.1 Z-connection factors Set Wood no. species Avg. Est. (9) rad/in-lb rad/ft-lb [10.sup.-6] [10.sup.-5] 1 D-fir (9) 6.6 7.9 2 EP (10) 9.2 10.8 3# (8) SYP (11)# 4# (8) SYP# 5# (8) SYP# 6 SYP 7.9 9.4 7# (8) SYP# 8# Y-pop (12)# 9# Y-pop# 10# Y-pop# 11# Y-pop# 12 Y-pop 6.0 13 Y-pop 4.2 5.0 14 Y-pop 6.8 8.5 15 Y-pop 4.3 4.4 16 Y-pop 2.6 3.7 17# SYP# 18# SYP# 19# SYP# 20# SYP 21 Y-pop 2.4 2.2 22 Y-pop 1.8 1.7 23 W-ash (13) 1.2 2.4 24 W-ash 1.6 2.0 25# SYP# 26# SYP# 27# SYP# 28# SYP# 29 Y-pop 0.9 1.2 30 Y-pop 1.3 1.0 31 Y-pop 1.1 1.5 (1) MC, (2) Shoulder, (3) Diameter, (4) Average, (5) Standard deviation, (6) Wood Handbook, (7) Estimated connection factors, Eq. , (8) Six samples each, (9) Douglas-fir, (10) White pine, (11) Southern yellow pine, (12) Yellow poplar, (13) White ash, (14) Steel pin; (15) Red oak pin. Note: Akcay (2006) data shown in bold type indicated with #.
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|Title Annotation:||Technical Note|
|Author:||Eckelman, Carl; Haviarova, Eva; Akcay, Huseyin|
|Publication:||Forest Products Journal|
|Date:||Jul 1, 2008|
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