Withdrawal, shear, and bending moment capacities of round mortise and tenon timber framing joints

Transcription

1 Withdrawal, shear, and bending moment capacities of round mortise and tenon timber framing joints Huseyin Akcay C. Eckelman E. Haviarova Abstract An exploratory study was conducted to determine the withdrawal, lateral shear, and bending moment capacities of round mortise and tenon timber framing joints containing substantial amounts of juvenile wood. Most joints were constructed of southern yellow pine. s were 2, 3, and 4 inches. withdrawal capacities of joints with red oak cross pins were about 3,500, 5,000, and 10,000 pounds for 2-, 3-, and 4-inch tenons, respectively. Joints without shoulders had bending moment capacities of about 400, 1,400, and 3,750 ft.-lb. for 2-, 3-, and 4-inch tenons and capacities of 700, 1,650, and 5,200 ft.-lb. for comparable joints with shoulders. Lateral shear capacities of joints with tenons fully seated were about 3,500, 7,500, and 11,000 pounds for joints with 2-, 3-, and 4-inch tenons, respectively. Values for comparable joints with 3- and 4-inch tenons not fully seated were about 2,300 and 3,500 pounds, respectively. Results of the study suggest that the round mortise and tenon joints had sufficient withdrawal, shear, and bending moment capacity to justify their continued evaluation for use in light timber frames constructed from small- timbers. Many forest stands in this country as well as in numerous underdeveloped countries, are overstocked with small- trees (Wolfe 2000, Wolfe and Moseley 2000). These trees pose both a health hazard and a fire hazard to the forests, and excess stems should be removed, but presently they have too little market value to justify their removal. Before these stems are utilized, value-added products must be developed that take advantage of their unique physical characteristics and availability. Presently, one potential outlet for this material, both as rounds and squares, exists in light-timber frame construction that could be used in applications such as backyard barns in this country or as house, farm, and light industrial building frames in developing countries. These frames require the use of relatively large numbers of members and thereby provide sizable outlets for lowvalue small- stems. Round mortise and tenon joinery provides a simple yet efficient means of constructing such frames from small- stems and squares. From a production viewpoint, round mortise and tenon light-timber frame construction differs significantly from traditional timber framing. Most importantly, high-quality round tenons can be cut rapidly with deep hole saws while round mortises can be bored with Forstner bits. Thus, round mortise and tenon light-timber frame construction largely eliminates the need for highly skilled labor, allows high rates of productivity, and lends itself to mass production. Structurally, the behavior of round mortise and tenon light-timber framing differs in several respects from traditional timber framing. In the light-timber frame construction shown in Figure 1, for example, the tie beam to corner post joint is loaded in shear rather than in tension by roof loads (Sobon 2000). This occurs because the tie beams are connected to wall plate beams by corner post or intermediate wall stud tenons that pass through mortises in both the tie beam and the wall plate (Eckelman 2003). Furthermore, mortise and tenon joints in traditional timber frame construction behave as either pinned or The authors are, respectively, Graduate Student, Professor, and Assistant Professor, Purdue Univ., Wood Research Lab., 175 Marsteller St., West Lafayette, IN This paper was received for publication in February Article No Forest Products Society Member. Forest Products Society Forest Prod. J. 55(6): JUNE 2005

2 Figure 1. A tie beam to corner post connection in round mortise and tenon light timber frame construction. semi-rigid joints (Schmidt et al. 1996, Schmidt and MacKay 1997, Bulleit et al. 1999), and resistance of the frame to lateral forces depends on the strength of the knee braces (Schmidt and Daniels 1999). In contrast, resistance to lateral loading in round mortise and tenon lighttimber frame construction results from the internal bending moment resistance developed in the tenons of the wall studs and corner beams. Thus, lateral frame strength depends on the collective bending resistance of the joints of many frame members rather than the withdrawal resistance of only a few members. Finally, round mortise and tenon light-timber frame construction lends itself to component standardization. Standardization ensures that parts and components fit together when brought to a building site regardless of their origin. Furthermore, simplification and standardization of parts can be accomplished without unduly limiting design possibilities or dictating the nature of the buildings that can be constructed from them. Thus, a wide variety of frame systems can be fabricated from a relatively few standardized components. The feasibility of round mortise and tenon light-timber frame construction has already been demonstrated (Eckelman et al. 2002). Additional information is needed, however, concerning joint strength characteristics. A limited study was undertaken, accordingly, to obtain first estimates of joint withdrawal, lateral shear, and bending moment capacities. Results of the tests are presented in the report that follows. Figure 2. Nominal configurations of the cross-pinned withdrawal specimens. Specimen description All of the specimens were constructed with nominal 2-, 3-, or 4-inch tenons. Most of the specimens were constructed of southern yellow pine (Pinus spp.), but a small number of yellow-poplar (Liriodendron tulipifera) specimens were included. Typical configurations of the crosspinned withdrawal specimens are shown in Figure 2. Specific dimensional data are given in Table 1. All of the specimens contained boxed heart but did not have significant end splits. Six specimens with 2-inch tenons, six with 3-inch tenons, and six with 4-inch tenons were constructed of No. 2 southern yellow pine (SYP) at about 12 percent moisture content (MC). Specimens with 2-inch tenons were constructed with 1-inch wood cross-pins; half of the specimens with 3-inch tenons were constructed with 1.25-inch and half with 1.5-inch cross-pins; and finally, half of the specimens with 4-inch tenons were constructed with 1.5-inch and half with 2-inch cross-pins. In addition, three specimens with 2-inch tenons and 1-inch wood cross-pins were constructed of yellow-poplar at about 6 percent MC. All of the wood cross-pins were constructed of red oak (Quercus rubra) with a nominal 6 percent MC. Finally, nine specimens were constructed of SYP with black metal pipe cross-pins, instead of red oak. Three of these specimens were constructed with 2-inch tenons and inch (3/4-in., schedule 80) pipe cross-pins. The cross section of the mortise member for these joints was increased to 5.4 by 5.4 inches in order to provide greater bearing area beneath the cross-pin. In addition, three specimens were constructed with 3-inch tenons and inch (1-in.) pipe crosspins and three specimens with 4-inch tenons and 1.90-inch (1-1/2-in.) pipe crosspins. FOREST PRODUCTS JOURNAL Vol. 55, No. 6 61

3 Table 1. Withdrawal capacities of cross-pinned southern yellow pine and yellow-poplar tenons. Nominal cross-pin Cross-pin axis to tenon end distance member cross section Mortise member cross section Ultimate withdrawal capacity Wood species No. of specimens Cross-pin material MC length SD a (%) (in.) (lb.) SYP 6 Wood by by , SYP 3 Wood by by 5.4 5, SYP 3 Wood by by 5.4 5, SYP 3 Wood by by , SYP 3 Wood by by ,933 1,909 SYP 3 Pipe by by , SYP 3 Pipe by by ,716 3,713 SYP 3 Pipe by by , Wood by by , a SD = standard deviation. Table 2. Bending moment capacities of round mortise and tenon joints, with and without shoulders, with and without cross-pins. Mort. drill member cross section Mortise member cross section Bending moment capacity Bending moment capacity at 12% Wood species MC No. of specimens length shoulder Cross-pin SD a (%) (in.) (ft.-lb.) SYP None None SYP None None , ,419 SYP None None , ,750 SYP None SYP None , ,661 SYP None , ,208 SYP None SYP None SYP None , ,814 SYP SYP , ,084 SYP , , None None None None a SD = standard deviation. Typical nominal configurations of the bending moment specimens with 2-inch tenons are shown in Figure 3. Dimensional data for all specimens are given in Table 2. Half of the specimens were constructed with and half without crosspins. Half of the specimens in each of these two sets, in turn, were constructed with shoulders (Fig. 2) and half without. Fifty-seven specimens were constructed of SYP at about 12 percent MC; 12 specimens were constructed of yellowpoplar at about 6.5 percent MC. Typical configurations of the shear specimens with 2-inch tenons are shown in Figure 4. Dimensional data for all specimens are given in Table 3. Fifteen specimens were constructed of SYP at about 12 percent MC with the tenon seated. In addition, 9 specimens were constructed with the tenon withdrawn 2 inches. These specimens were included in order to investigate the performance of the connection should a tenon not be fully seated or be partially withdrawn in service. Finally, six specimens with 2- inch tenons were constructed of yellow-poplar at about 6 percent MC with the tenon seated; however, one specimen was eliminated because of a defect. Method of test The jig used to hold the specimens in the withdrawal tests is shown in Figure 5. This jig prevents cleavage (Schmidt and Daniels 1999) of the mortise member but does not prevent crushing beneath the cross-pin. All tests were carried out in a universal testing machine. Crosshead movement was 0.15 inch per minute. The test set-up used to evaluate the bending moment capacity of the joints is 62 JUNE 2005

4 Figure 3. Nominal configurations of the bending moment specimens. Figure 4. Nominal configurations of the shear specimens. Figure 5. Test jig used to evaluate withdrawal capacity of cross-pinned specimens. shown in Figure 6. A moment arm of 12 inches was used in all tests. Rate of loading was 0.25 inch per minute. The test set-ups used to evaluate the lateral shear capacities of the joints are shown in Figure 7. Figure 7a shows a joint with tenon fully inserted, whereas Figure 7b shows a joint with tenon withdrawn 2 inches. Rate of loading was 0.25 inch per minute. In all of the above cases, failure was defined as that point at which a rapid fall-off in load occurred. Results and discussion Results of the withdrawal tests are given in Table 1. All but two of the withdrawal specimens with wood cross-pins failed because of crushing/bending of the cross-pins in a manner similar to that reported by Schmidt and Daniels (1999). In the two exceptions to this type of failure, which occurred in SYP specimens with 3-inch tenons and 1.5-inch cross-pins, the walls of the tenon failed adjacent to the cross-pin. These failures were attributed to severe cross grain in this area. The third replicate of this set failed because of bending/crushing of the cross-pin, i.e., in a manner similar to the other joints in the study. All of the 2-inch tenons with pipe cross-pins failed in tension parallel to the grain. In the specimens with 3- and 4-inch tenons, however, the tenons first split lengthwise (Fig. 8), because of failure in tension perpendicular to the grain, with an accompanying substantial loss in testing machine load because of inter- FOREST PRODUCTS JOURNAL Vol. 55, No. 6 63

5 Table 3. Lateral shear capacities of southern yellow pine and yellow-poplar round mortise and tenon joints. member cross section Mortise member cross section Lateral shear capacity diam. Wood species No. of specimens MC diam. length Mort. drill shoulder seated? SD a (in.) (%) (in.) (lb.) SYP yes 3, SYP yes 7,543 1,240 4 SYP yes 11,209 1,833 2 SYP no 2, SYP no 3,509 1, yes 3, a SD = standard deviation. Figure 6. Test set-up used to evaluate bending moment capacity of joints. nal joint deformation. As testing continued, initial load levels were regained, and the joints continued resisting load until longitudinal shear failures of the tenons occurred, which were marked by the emergence of a plug of wood (relish) at the tip of the tenon. At this point, a joint had essentially suffered complete failure. Thus, a two-step failure normally occurred, i.e., a tension perpendicular to the grain failure visible at the tip of the tenon followed by a shear failure of the wood along the remaining wall of the plug supporting the crosspin. Ordinarily, therefore, the initial partial failure gave warning of impending total failure, which occurred at a higher load level. This behavior would be expected, however, only in joints with a close tenon/mortise fit. Finally, as a word of caution, it should be noted that in practical constructions, cleavage failures in the mortise members also would be expected to affect (or, perhaps, limit) the withdrawal capacities of the joints. Presumably, results of the tests with red oak cross-pins provide reasonable estimates of the ultimate withdrawal forces that can be obtained with highstrength wood pins. These results are particularly important, in that, with wood cross-pins of the sizes used, cross-pin crushing/bending failures occurred rather than tenon shear or tension failures. Thus, this type of failure would be expected to give warning of overloading and potential impending failure in contrast to sudden tenon shear or tension failures, which would be associated with catastrophic structural failures (Schmidt and Scholl 2000, Burnett et al. 2003). The lower average values obtained with the 1.25-inch wood cross-pins in 3-inch- tenons (as opposed to 1.5-in. pins) and with 1.5-inch cross-pins in 4-inch- tenons (as opposed to 2-in. pins) tends to argue for the use of the largest possible cross-pins that do not cause tenon shear or tension failures. It is particularly noteworthy that only two tenon failures occurred with wood cross-pins (with oak cross-pins that were half the of the tenon). It is also noteworthy that no shear plane failures occurred in the tenons considering the small shear plane areas of the relish. Although major differences exist, it is useful to compare the results obtained with round mortise and tenon joints with those obtained by other researchers for rectangular mortise and tenon joints. Schmidt and Daniels (1999), for example, obtained an average withdrawal force of 4,960 pounds in dense select SYP joints constructed with two 1- inch- white oak pegs (or, 2,480 lb./pin). Burnett et al. (2003) obtained average withdrawal forces of 3,274 and 3,590 pounds for 1-inch northern red oak pegs in by 7.5-inch rectangular tenons in eastern white pine and Douglas-fir, respectively, with a 7-inch end distance. Likewise, they obtained an average withdrawal force of 3,607 pounds for a 5-inch end spacing in red oak tenons. As can be seen, comparable withdrawal capacities were obtained with 2-inch round mortise and tenon joints, in wood containing boxed heart. These results tend to imply that round mortise and tenon joints should have sufficient withdrawal capacities to be usable in timber frame construction. Results of the bending moment tests are given in Table 2; those for SYP are shown graphically in Figure 9. Three factors are of particular concern with respect to these results: 1) what are the magnitudes of the test values, i.e., the bending moment capacities of the joints; 2) what are the ratios of the test values relative to estimated bending moment capacities of the joints based on Wood Handbook (USDA 1999) wood strength values; and what is the effect of crosspinning on the bending moment capacities of the joints. The bending moment capacities of the tenons based on Wood Handbook strength values can be estimated by means of the flexure formula as presented below (Wangaard 1950): where: F 4 3 k πd = s F 4 = bending moment capacity (ft.-lb.) D = tenon (in.) s 4 = modulus of rupture (MOR) of the material (psi) 4 64 JUNE 2005

6 Figure 7. Test set-ups used to evaluate the lateral shear capacity of joints. Figure 8. Diagram showing initial tenon failure arising from tension perpendicular to grain. Figure 9. Graph of the results of the bending moment capacity tests for southern yellow pine. k = a form factor for round beams, namely, = a constant used to convert in.-lb. to ft.-lb. Use of the form factor for round beams, 1.18, is questionable in estimating the bending moment capacity of round tenons in these joint tests, however, because of the crushing (perpendicular to the grain) that occurred on the underside of the tenons during testing. Because of this uncertainty, k was set equal to 1 in the following calculations. If, for purposes of discussion, the MOR of the pine included in the tests is estimated as the average of the Wood Handbook MOR values for loblolly (P. taeda), shortleaf (P. echinata), and slash pine (P. elliotti), namely, 14,067 psi, the above expression estimates bending moment capacities of 921, 3,107, and 7,365 ft.-lb. for 2-, 3-, and 4-inch round beams, respectively. The corresponding test values obtained for round tenons, adjusted to 12 percent MC, amounted to 43.5, 45.7, and 50.9 percent of these estimated values. Thus, the bending moment capacities of the test specimens, which contained juvenile wood, were only about half as strong as the estimates based on Wood Handbook strength values. The slight increase in the ratio noted for the larger tenons may result from the inclusion of greater amounts of non-juvenile wood. On average, the yellow-poplar joints had 93 percent of the bending moment capacity of the comparable SYP joints. This result is higher than expected (based on the Wood Handbook MOR value of 10,100 psi for yellow-poplar vs. 14,067 psi for the pines) and may reflect a difference in juvenile wood properties of the hardwood and softwood species. As seen in Figure 9, shoulders on the tenons substantially increased the bending moment capacities of the joints. In this study, the capacities of 2-, 3-, and 4-inch tenons with shoulders (adjusted to 12% MC) were 78.8, 17.1, and 38.9 percent greater, respectively, than those of tenons without shoulders. The contribution of the shoulder to the bending moment capacity of the joint, for the joints tested, may be estimated by multiplying the moment capacity value obtained for tenons without shoulders by the corresponding ratio of rail-width/ tenon- (Eckelman et al. in progress). Multiplying the values (adjusted to 12% MC) obtained for tenons without shoulders by these ratios gives /2, or 702 ft.-lb. (vs. 717 ft.-lb. for a difference of 2.1%), 1, /3, or, 1,660 ft.-lb. (vs. 1,661 ft.-lb. for a negligible difference), and 3, /4, or 5,109 ft.-lb. (vs. 5,208 ft.-lb. for a difference of -1.9%) for 2-, 3-, and 4-inch tenons, respectively. Bending moment specimens with cross-pins failed because of the development of longitudinal shear failures that extended from the outer edge of the cross-pin to the tip of the tenon (Fig. 10). As is shown in Figure 9, the bending moment capacities of the joints with cross-pins were substantially less than the capacities of the joints without. Overall, the SYP joints with cross-pins and shoulders averaged 60.0 percent of the capacity of the comparable SYP joints without pins but with shoulders. Similarly, the average for the SYP joints with pins but without shoulders was 75.0 percent as great as for the comparable SYP joints without pins or shoulders. As can be seen, cross-pins of the size used in this study substantially lowered the bending moment capacities of the joints. Thus, these results indicate that the effects of cross-pinning should be considered in the design of connections subjected to bending moment. Use of smaller pins might result in lower reductions in capacity; but a functional relationship between cross-pin and reduction in bending moment capacity remains to be established. Comparative information was not readily available concerning the bending FOREST PRODUCTS JOURNAL Vol. 55, No. 6 65

7 Figure 10. Use of cross-pins caused shear plane failures to develop in the tenons subjected to bending moments, F 4. Figure 11. Diagram illustrating lateral shear load failures. moment capacity of pegged rectangular mortise and tenon joints, presumably because the bending moment capacity of these joints is not taken into consideration in frame design. Bulleit et al. (1999) reported that rectangular mortise and tenon joints transmitted very little moment and function essentially as hinges. They indicated that these joints should be assumed to carry no moment when analyzing traditionally connected timber frames. The lateral shear capacities of the joints are given in Table 3; the modes of failure are shown in Figures 11a and 11b. In those joints in which the tenons were fully seated, failures occurred in the shoulder of the tenon because of fracture of the wood in tension perpendicular to the grain (Fig. 11a). In contrast, failures in those joints in which the tenon was not seated arose from fracture of the tenon in bending (Fig. 11b). The tests of beams constructed with 2- and 3-inch tenons in which the tenons were not fully inserted (Fig. 7b) were carried out in order to determine the shear capacities of the tenons when the tenons are partially withdrawn as might occur in service. As can be seen, the shear capacity of the joints constructed with 2-inch tenons with a 2-inch shoulder separation was 2,280/3,657, or 62 percent as great as the joints with tenons fully seated, whereas the shear capacity of the joints with 3-inch tenons was only 3,509/7,543, or 47 percent as great as comparable seated joints. The results of these tests clearly indicate the importance of fully seating the tenons in the joints. But, it also should be noted that the tenons had substantial lateral shear capacity even when they were not fully seated. Schmidt et al. (1996) indicated that a pegged joint in a timber frame is analogous to a semi-rigid connection in a steel frame. When a floor joist frames into a member such as a post, the semi-rigid nature of the connection with respect to moment transfer thus allows some discretion in designing for end moments; specifically, the tenon can be sized to minimize the difference between center and end moments acting on a joist. Semi-rigid connection factors, or Z-values (Lothers 1960), must be known before the distribution of forces can be determined, but the ability to modify the distribution of forces in a timber frame simply by changing the of the tenons on the ends of selected members may open interesting design possibilities. Conclusions The round mortise and tenon joints evaluated during the study, which contained substantial amounts of juvenile wood, had sufficient withdrawal, shear, and bending moment capacity to justify continued study of their use in light timber frames constructed from small timbers. Additional studies are needed, however, to develop design values for these joints. Studies also are needed to determine the joint capacities that would be required in various constructions in order to find the applications for which these joints are best suited. withdrawal capacities of about 3,500, 5,000, and 10,000 pounds were developed with 1-, 1.5-, and 2-inch- red oak cross-pins in 2-, 3-, and 4-inch- tenons, respectively. Most failures result from crushing/ bending of the cross-pins. Substantially higher capacities are obtained when pipe cross-pins are substituted for wood cross-pins. Failures of these joints result from shear or tension fracture of the tenons. Thus, metal cross-pipes may be expected to produce stronger joints than wood cross-pins, but the differences in the mode of failure of the joints must be considered since the crushing/bending mode of failure of the wood cross-pins would give warning of overloading and potential impending failure. Round mortise and tenon joints also can develop high bending moment capacities relative to the size of the member containing the tenon. In bending tests, 2-, 3-, and 4-inch tenons without shoulders developed average bending moment capacities of 401, 1,419, and 3,750 ft.-lb., respectively, whereas 2-, 3-, and 4-inch tenons with shoulders developed comparable average bending moment capacities of 717, 1,661, and 5,208 ft.-lb., respectively. Collectively, these joints provide substantial resistance to lateral and racking forces acting on a frame. Cross-pinning the joints substantially reduces bending moment capacity, however. The shear capacities of fully seated 2-, 3-, and 4-inch tenons amounted to 3,657, 7,543, and 11,209 pounds, respectively. Comparable values for 2- and 3-inch tenons with a 2-inch shoulder separation were 2,280 and 3,509 pounds, respectively. These values indicate that the shoulder separation between tenon and mortise members should be minimized in shear connections. Literature cited Bulleit, W.M., L.B. Sandberg, M.W. Drewek, and T.L. O Bryant Behavior and modeling of wood-pegged timber frames. J. of Structural Engineering 125(1):3-9. Burnett, D.T., P. Clouston, D. Damery, and P. Fisette Structural properties of pegged timber connections as affected by end distance. Forest Prod. J. 53(2): Eckelman, C.A Exploratory study of high-strength low-cost through-bolt with cross pipe and nut construction for roundwood and squared timber frame construction. Forest Prod. J. 54(12):29-37., Y. Erdil, and E. Haviarova. 200_. Effect of shoulders on bending moment capacity of round mortise and tenon joints. Forest Prod. J. (in progress)., H. Akcay, R. Leavitt, and E. Haviarova Demonstration building constructed with round mortise and tenon joints and salvage material from small- tree stems. Forest Prod. J. 52(11/12): Lothers, J.E Advanced Design in Structural Steel. Prentice-Hall, Inc., Englewood Cliffs, NJ. 583 pp. Schmidt, R.J. and C.E. Daniels Design considerations for mortise and tenon joints. Interim Rept. April. Dept. of Civil and Architectural Eng., Univ. of Wyoming, Laramie, WY. 66 JUNE 2005

8 and R.B. MacKay Timber frame tension joinery. Dept. of Civil and Architectural Eng., Univ. of Wyoming, Laramie, WY. and G.F. Scholl Load duration and seasoning effects on mortise and tenon joints. Dept. of Civil and Architectural Eng., Univ. of Wyoming, Laramie, WY., R.B. MacKay, and B.L. Leu Design of joints in traditional timber frame buildings. In: Proc. Inter. Wood Engineering Conf., New Orleans, LA. Vol. 4. Omnipress, Madison, WI. Sobon, J.A Historic American timber joinery - A graphic guide. Timber Framing 55:4, 56:8, 57:6, 58:6, 59:6, 60:6. USDA Forest Service, Forest Products Laboratory (USDA) Wood Handbook: Wood as an Engineering Material. Forest Prod. Soc., Madison, WI. Wangaard, F.F The Mechanical Properties of Wood. John Wiley and Sons, New York. 377 pp. Wolfe, R Research challenges for structural use of small- round timber. Forest Prod. J. 50(2): and C. Moseley Small- log evaluation for value-added structural applications. Forest Prod. J. 50(10): FOREST PRODUCTS JOURNAL Vol. 55, No. 6 67