Load Duration Behavior of Steel-Doweled Wood Connections

Transcription

1 Load Duration Behavior of Steel-Doweled Wood Connections William M. Bulleit 1, Zeno A. Martin 2, and Robert A. Marlor 3 ABSTRACT Load-duration behavior of steel doweled wood connections, such as bolted and nailed connections, has been studied to only a limited extent. The assumption in design is that the load-duration behavior of connections is identical to the loadduration behavior of wood members in flexure. Load-duration tests on small specimens are underway to examine the adequacy of existing time effect factors. A total of 160 specimens are being tested under long term load. The data available to date was fitted to the exponential damage rate model and a preliminary time effect factor of 0.73 was determined for occupancy live load. This value is somewhat lower than the existing value of 0.8. Judgements about the implications of this difference must be saved until more data is available. INTRODUCTION Load-duration behavior of steel doweled wood connections, such as bolted and nailed connections, has been studied to only a limited extent. The assumption in design is that the load-duration behavior of connections is identical to the loadduration behavior of wood members in flexure ("National" 1997, "Standard 1995). Whether or not this is a valid assumption is not known, although the authors know of no evidence indicating that the assumption is not valid. The research on load-duration of wood in flexure is quite broad and will be briefly discussed below. This information is important because any study of load-duration in connections should be done in the light of past research on wood members in order to examine the adequacy of present design procedures as well as streamline the process of getting any new findings accepted for design code use. The objective of this work was to develop load-duration factors, referred to as a time-effect factors in the new load and resistance factor design (LRFD) code ("Standard" 1995), for use with steel doweled connections. This was done through the testing of steel doweled connections to determine time to failure information, examination of a cumulative damage (CD) model for the connections, and then combination of the CD model with random load histories to determine timeeffect factors suitable for use in an LRFD specification. Only one cumulative damage model will be examined in this paper. LOAD-DURATION BEHAVIOR IN WOOD The effect of prolonged stress on wood bending strength has been recognized since at least 1840 (Haupt 1867). By the 1920's, a 9/16 reduction of the allowable stress was being used without any specific time limitation. Wood (1951), working with small, clear Douglas fir specimens in flexure, developed a time strength curve that was incorporated into the wood design procedure in This curve, often referred to as the "Madison curve," is still in use in present ASD procedures ("National" 1997), although it has been replaced in the new LRFD code ("Standard" 1995) by discrete timeeffect factors. The new time-effect factors were developed using CD models in combination with random load process models ("Standard" 1995, Ellingwood and Rosowsky 1991). In the U.S., the CD model that was used is the so-called exponential damage rate model (EDRM) (Gerhards and Link 1983). It is of the form: 1 Professor, Dept. of Civil and Environ. Engrg., Michigan Tech, 1400 Townsend Dr., Houghton., MI, Former Graduate Research Assistant, Dept. of Civil and Environ. Engrg., Michigan Tech. 3 Assistant Professor, Dept. of Industrial Technologies, Northern Michigan University, Marquette, MI.

2 dα/dt = exp(-a+bσ(t)) (1) where t is the time, α is the damage parameter varying from 0 (no damage) to 1 (failure), σ(t) is the ratio of the applied stress to the failure stress under short-term ramp loading, referred to as the stress ratio, and A and B are constants to be determined from test data. Three other models have been developed in Canada (Foschi and Barrett 1982, Foschi et al. 1989). All three are of a form similar to that shown above except that the change in damage is a function of both stress and past damage dα/dt = F(σ(t),α) (2) where the function F( ) has a number of constants that must be determined from test data, and (t) is either the applied stress or the stress ratio depending on which of the models is being considered. A CD model can be used in combination with load process models to more realistically evaluate the load-duration behavior of the elements. This has been done previously (Bulleit and Schoch 1986, Ellingwood and Rosowsky 1991, Bulleit and Liu 1995) and is how the time effect factors were developed for the LRFD code ("Standard" 1995). LOAD-DURATION BEHAVIOR IN DOWELED CONNECTIONS The only major study of the load-duration behavior of steel doweled wood connections known to the author is one performed in the Netherlands beginning in 1960 (Leijten 1988, van de Kuilen and Blass 1996). The connectors considered were split rings, shear plates, nail-plates, and nails. This study has shown that duration effects are present at load levels at and below 50 percent of short term ultimate capacity. Some of the connections failed at these low load levels, but the unfailed specimens showed no loss of strength when tested to failure after being subjected to the long term load. It appears that gross defects in the joint initiated the failures. The research indicates that studies to examine the load-duration effect in doweled connections are appropriate in order to examine present practice and to gather further information about time effects in wood connections. A study by Bodig and Farquhar (1988) examined load duration over times to failure ranging from 5 seconds to 20 minutes. The study showed that a number of properties, including the load at the proportional limit and the ultimate load, were linearly related to the logarithm of the time to failure. DOWELED CONNECTION BEHAVIOR The types of connections that were examined in this research will be referred to as doweled connections. These could include bolted, nailed, drift pinned, lag screwed, and any other connection where a metal dowel connector joins the pieces of wood together. The preferred method of analyzing these kind of joints is the European yield model (EYM) ("National" 1997, "Standard" 1995, "Mechanical" 1996). The EYM was introduced into U.S. design in the 1991 NDS ("National 1991). It separates the near ultimate behavior of the connection into failure modes. These failure modes are related to yielding of the steel dowel and wood crushing. A capacity equation is used for each possible failure mode and the mode with the lowest capacity controls the design. The existence of different failure modes presents a challenge because they each may exhibit different load-duration behavior. This study was designed to deal with this issue, although from a practical standpoint, the final result should be a single load-duration (time-effect) factor that is independent of failure mode. A second challenge in a study such as this is to use specimens that are reasonably realistic yet can be tested using a relatively small amount of load over a reasonably short period of time. To help deal with these issues, a single-shear connection of relatively small dimensions was used with steel rods as the connectors. The actual member thicknesses and dowel yield stress were varied in order to force each of the four possible failure modes to occur. In general, single shear connections have six possible failure modes, but only four of them need to be tested when side and main members are of the same species and both are loaded parallel to the grain ("National" 1997, "Standard" 1995, "Mechanical" 1996). The study described here met those limitations. The limit state equations and descriptions of these failure modes can be found in the three previous references.

3 TESTING PROGRAM Necessarily, the specimen geometry was different for each of the four possible yield modes. The basic specimen geometry is shown in Figure 1. Each geometry was determined using the mode I through IV equations described in the three references mentioned above with the yield load limited to about 100 lbs. (445 N) or less. This limitation was simply to make loading the specimens easier. The specimen dimensions, material properties, and predicted yield loads are shown in Table 1. The connectors used in this study were steel rods that were allowed to protrude from each side of the specimen as shown in Figure 1. This means that pure dowel action will be transferring forces in the connection. Steel rods were chosen to give a wide range of small diameters which makes forcing a particular yield mode more practical while still maintaining a predicted yield load of about 100 lbs. (445 N) or less During fabrication of the connection, the rods were placed in predrilled holes. End and edge distances were large enough to minimize the possibility of splitting failures. In Figure 1, the end blocks on the specimens were made by gluing a piece of wood to each end of the specimen. This block helps keep the force lined up with the shear plane, although that alignment is not perfect. Eastern white pine was chosen as the wood species because of its availability and its relatively low specific gravity. The wood was dried to indoor ambient conditions prior to fabrication of the specimens. The testing was done under indoor lab conditions in Houghton, Michigan where the measured relative humidity (RH) ranged from about 80 percent to about 10 percent with a mean of about 29. The temperature ranged from about 60 degrees to about 90 degrees with a mean of 74. Although this uncontrolled temperature and humidity will introduce some uncertainties into the data, it seems that at this stage in the study of load-duration of connections allowing the data to implicitly include moisture effects is reasonable from a practical standpoint. Short Term Tests Tests to determine the dowel-on-wood bearing capacity of the chosen species and the chosen rod diameter were performed. The mean dowel bearing strength was 5093 psi (35.1 MPa) with a coefficient of variation of 0.12 from tests on 9 specimens with a in. (3.2 mm) diameter dowel on a wood member in (3.2 mm) thick and 9 specimens with a in. (3.2 mm) diameter dowel on a wood member 1.5 in (38 mm) thick. A t-test showed that the mean dowel strength values from these two tests could be assumed equal, so the two sets of 9 data points were combined into one set of 18 data points.

4 Tests were also performed to determine the rod yield strength. Twelve (12) steel rods with a in (3.2 mm) diameter and a nominal 42 ksi (290 MPa) yield stress were tested on a simple span with a single concentrated load at mid span. The results from these tests are shown in Table 1. A few 100 ksi (690 MPa) nominal yield stress rods were tested to confirm that their yield stress was greater than 100 ksi (690 MPa). For modes I and II, this dowel yield stress is large enough that it forces a wood bearing failure mode to control so the exact yield stress values are not necessary. The modes I to IV limit equations were used to design four test specimens which have different geometries and, thus, different failure modes. The objective was to find specimens that are different enough that the each failure mode is so distinct from the others that it controls for that given set of test specimens. Then, for each of the four failure modes, 20 specimens were fabricated and tested under ramp loading with a time to failure of about five minutes. These tests were used to confirm the failure modes of each specimen and to get information on the magnitude and variation of the short term strength. The predicted value and the mean and coefficient of variation of the short term, 5% offset yield loads are given in Table 1. The normal distribution was used as the distribution of short term strength for all four modes even though the lognormal or Weibull distribution had a slightly better fit in some cases. The short term tests confirmed that the four modes had been isolated. Table 1. Short Term Test Specimen Properties and Results Mode t m (in) t s (in) D (in) F y (ksi) Z pred (lbs) Z m (lbs) (V z ) I > (0.17) II > (0.20) III (0.08) IV (0.06) Note: 1 in = 25.4 mm, 1 ksi = MPa, 1 lb = N Long Term Tests In the long term testing portion of this study, there were four sets of specimens corresponding to each of the four failure modes. Each set consisted of two groups of 20 specimens each corresponding to two load levels. This produces a total of 160 specimens tested under long term load. The data from the short term ramp load tests were used to determine the load levels for the long term loading. The short term test data was normalized to 20-minute failure times using the Madison curve ("National" 1997) and a 5 percent exclusion value of this 20-minute to failure time was determined from the normalized data. The two load levels were then 95 percent and 85 percent of the 20-minute, 5 percent exclusion value. This was expected to force the vast majority of the specimens to fail during the project duration and still produce useful duration of load data. This has proven to be correct. It should be emphasized that the high-load-level failure durations seem to be the most important in wood. Simulations under random load histories have shown that for lumber the damage tends to accumulate over a single or at most a few load pulses (Bulleit and Schoch 1986, Bulleit and Liu 1995, Rosowsky and Fridley 1995). Thus, developing CD models for doweled connectors at fairly high load levels seems reasonable. One difficulty in this project was the definition and consequent recording of failure. The two existing failure definitions are 1) 5 percent of connector diameter deformation and 2) rupture. Another important issue is that neither of these are necessarily representative of the yield predicted by the EYM. The EYM seems to predict values between these two definitions (Zahn 1992, Bulleit and Decator 1996). In order to deal with this problem, multiple deformation readings were taken on the long term specimens to characterize the range of behavior. This allowed examination of a few definitions of failure. This paper will discuss the 5-percent connector diameter deformation limit state. At the present time, there is rupture data only for mode I, and we may not get significant rupture data for the other modes based on the condition and deformation behavior of those specimens.

5 CUMULATIVE DAMAGE MODEL The time-to-failure data was used to determine the appropriate parameters for the EDRM (Gerhards and Link 1983). The procedure was similar to the technique used by Foschi et al (1989). In this procedure, the constants A and B in equation 1 are assumed to be lognormally distributed random variables and (t) =, i.e., a constant stress ratio. Simulations are performed using the damage model and the load level appropriate to each data set with many possible values for the mean and standard deviation of the constants until the function shown below is minimized. λ = [ log( T ) log( )] 2 d Ts (3) N where, N is the total number of time-to-failure values from the test data, T d is one value from the test data, and T s is the value from simulation that corresponds to T d in an ordered sense. In this paper, the data used in the fitting was the available data for modes I, III, and IV. Data from mode II was not included since mode II does not occur in double shear connections. Future work will examine the effects of including mode II data. The results shown below will be based on 17 failures out of 20 specimens for mode I at the low load level and 20 out of 20 for the high load level, 14 out of 20 for mode III at the high load level, and 9 out of 20 for mode IV at the high load level. For each of the four sets of data, 1049 simulations were performed. This number allows every 50th simulation to be related to a time to failure from the tests. For example, for mode I at the low load level, the 17 times to failure are ordered from smallest to largest. Then the 1049 simulations are performed and these are ordered from smallest to largest. The lowest value in the set of 17 ordered data points is paired with the 50th value in the set of 1049 ordered simulations. The second lowest is paired with the 100th simulation and so on. This procedure was performed four times, one for each of the data sets. was then calculated from the paired times to failure. This procedure was developed by assuming that the cumulative probability of failure for the i'th test value is i/(n+1) and for the j'th simulation value is j/(ns+1) where n is the total number of specimens at a given load level and ns is the number of simulations. This procedure allows the inclusion of censored data since the simulated data includes the equivalent of 20 test data points but 20 or less are used in the pairings. This procedure gave a mean value for A of 9.6 (ln days) and a mean value for B of 9.9 for the EDRM constants. These values were used in the calculation of a time effect factor for occupancy live load. TIME-EFFECT FACTORS The first approximation for a time effect factor for occupancy live load can be determined by assuming that failure occurs during a single live load pulse. This assumption is valid if the vast majority of the damage accumulates over a single pulse. There has been some work that shows that this assumption may be appropriate (Bulleit and Schoch 1986, Rosowsky and Fridley 1995). Solving eq. 1 for the time to failure gives T f = exp(a-bσ) (4) where T f is the time to failure in days. Substitute the constants into the equation, let the time to failure be 7 days and solve for σ. This is the stress ratio at which failure would occur in 7 days. This procedure gives a value of 0.77 for the stress ratio, which is analogous to the time effect factor. This value is essentially equal to 0.80, the time effect factor for live load given in the LRFD specification (Standard 1995). But, the use of the single pulse assumption means that this value may be a bit unconservative. To further examine the adequacy of this value, the CD model was combined with a pulse model for occupancy live load to determine the time effect factor. The 50-year maximum live load was Gumbel distributed with a mean/nominal of 1.0 and a coefficient of variation of 0.25 (Ellingwood and Rosowsky 1991). A pulse model was used to simulate the live load (Turkstra and Madsen 1980) with an average intensity of one pulse per year and a pulse duration of one week (Ellingwood and Rosowsky 1991). The reliability from these simulations was compared to the reliability determined using a first-order reliability analysis incorporating the constant stress ratio of The reliability from the first-order analysis was slightly higher than that from simulation. This result implies that the single pulse assumption is unconservative. A constant stress ratio of 0.73 in the first-order analysis produced a reliability equal to that from

6 simulation. This is a preliminary result and cannot be confirmed until more data becomes available from the long term tests. DISCUSSION The preliminary results from this study suggest that the time-effect factor for occupancy live load in the LRFD wood design specification ("Standard" 1995) may be a bit high for connections, 0.73 in this study versus 0.80 in the specification. This result may change when more data becomes available. No data is available from the low load level for modes III and IV and more failure data will become available for the high load level for modes III and IV. But, there may be another reason that this study will show time effect factors that are lower than those presently in use. It is apparent that the specimens used in the study are small with, in some cases, relatively thin members. Thin members exhibit a steep moisture gradient during relative humidity changes and a steep moisture gradient causes increased creep rate in wood. Increased creep in thin members would likely affect the bearing behavior of the connections which would in turn affect the load-duration behavior. Observations of the response of the specimens to large relative humidity changes supports this hypothesis. When large increases in relative humidity occurred in the summers, specimens had a strong tendency to exhibit significant deformations and in some cases failed completely, particularly Mode I specimens. It will not be possible to remove this from the data, so this study will likely give time effect factors that are lower than would be required for connections fabricated with larger members. FUTURE WORK As more time-to-failure data becomes available, it will be incorporated in the fitting of constants. Each mode will be considered separately, all four will be combined, and modes I, III, and IV will be combined since those are more representative of double shear connection behavior. The EDRM will continue to be examined, but three others will also be considered: Madison curve (Hendrickson et. al. 1987), Barrett and Foschi Model II (Foschi and Barrett 1982) and Foschi/Yao (Foschi et al 1989). These models will be combined with pulse load models to develop time effect factors. A set of 20 specimens consisting of 0.5 in (12.7 mm) diameter bolts and nominal four-inch lumber members will be tested to failure under a step-load history. The specimen will be a double shear connection with side members and main members loaded parallel to the grain and sized to produce the possibility of more than one failure mode. The step-load history will be designed to make the expected time to failure in the range of one to two days. The lumber species will be eastern white pine. This set of tests will be used to further examine the adequacy of the above CD models. REFERENCES Bodig, J. and Farquhar, B. J. M "Behavior of Mechanical Joints of Wood at Accelerated Strain Rates," Proceedings of the 1988 International Conference on Timber Engineering, Vol. 2, FPRS, Madison, WI, Bulleit, W. M. and Decator, D. B "Reliability Analysis of Bolted Wood Connections," Probabilistic Mechanics and Structural Reliability, ASCE, New York, NY, Bulleit, W. M. and Liu, W.-F "First-Order Reliability Analysis of Wood Structural Systems," Journal of Structural Engineering, ASCE, 121(3), Bulleit, W. M. and Schoch, C. G. III "Simulation of Load-Duration Effects in Wood," Wood Science and Technology, 20, Ellingwood, B. R. and Rosowsky, D. V "Duration of Load Effects in LRFD for Wood Construction," Journal of Structural Engineering, ASCE, 117(2), Foschi, R. O. and Barrett, J. D "Load-Duration Effects in Western Hemlock Lumber," Journal of the Structural Division, ASCE, 108(ST7), Foschi, R. O., Folz, B. R., and Yao, F. Z Reliability-Based Design of Wood Structures, Department of Civil Engineering, University of British Columbia, Vancouver, B. C.,

7 Gerhards, C. C. and Link, C. L "Use of a Cumulative Damage Model to Predict Load-Duration Characteristics of Lumber," IUFRO Division 5 Conference, Madison, WI. Haupt, H General Theory of Bridge Construction, Appleton, New York, NY, Hendrickson, E. M., Ellingwood, B. R., and Murphy, J "Limit State Probabilities for Wood Structural Members," Journal of Structural Engineering, ASCE, 113(1), Leijten, A. J. M "Load-Duration Strength of Joints with High Working Load Levels," Proceedings of the 1988 International Conference on Timber Engineering, Vol. 2, FPRS, Madison, WI, Liu, W.-F. and Bulleit, W. M "Approximate Reliability Analysis of Wood Structural Systems," Structural Safety, 17, Mechanical Connections in Wood Structures American Society of Civil Engineers, New York, NY. National Design Specification for Wood Construction National Forest Products Association, Washington, DC. National Design Specification for Wood Construction American Forest and Paper Association, Washington, DC. Rosowsky, D. V. and Fridley, K. J "Directions for Duration-of-Load Research," Forest Products Journal, 45(3), Turkstra, C. J. and Madsen, H. O "Load Combinations in Codified Structural Design," Journal of the Structural Division, ASCE, 106(ST12), Standard for Load and Resistance Design for Engineered Wood Structures American Forest and Paper Association, Washington, D C van de Kuilen, J.-W. G. and Blass, H. J "Does Damage Accumulate in Timber Joints Loaded at Load Levels Below 50% of the Average Short Term Strength?", Proceedings of the International Wood Engineering Conference, Vol. 4, Omnipress, Madison, WI,