Abstract:

【Objective】 SPF dimension lumber is a principal material for light-frame timber structures. In this paper, modulus of elasticity (MOE) of SPF dimension lumbers was accurately measured by frequency method. The feasibility of the measured data was studied by Weibull distribution. Then, the data was fitted linearly and verified by K-S method. Meanwhile, a series of possible Weibull parameters was obtained by linear fitting of MOE data in Weibull coordinate. 【Method】 We randomly extract SPF dimension lumbers with capacity of 300 from Nanjing Cogent Home Manufactory Ltd. We realize free beam of test samples by supporting structure hung vertically and freely with elastic rope. The accuracy of free beam realization is proved by the result of modal test. Under transient excitation, the elastic modulus value of the samples is obtained by testing their first transverse bending frequency. The correctness of the test results of frequency method is proved by stress wave method. To exactly evaluate the quality of SPF dimensional lumbers, the testing data was deeply studied by using methods such as Weibull distribution, K-S method in normal distribution, calculation of probability data of MOE value under given values and probability distribution method. 【Result】 A good correlation was found between elastic modulus tested with frequency method and that tested with wave-speed method. As can be seen from the K-S testing results of Weibull distribution and normal distribution, the elastic modulus of SPF dimension lumbers is not subjected to two-parameter Weibull distribution (E_u=0), but it is subjected to three-parameter Weibull distribution, in which location parameter E_u is larger than half of the minimum test value. By analyzing the probability data of MOE value under given values for the total SPF dimension lumbers, the calculated probability values are stable and similar when using 3 500, 4 000 and 4 500 MPa as the given value of E_u. In this case, the given values of E_u are 63%, 72% and 81% of the minimum value of elastic modulus (5 526 MPa), respectively. Therefore, it is recommended to use the value that is 60%-80% of the minimum actual data as the given value of location parameter E_u in three-parameter Weibull distribution. Probabilities for elastic modulus of SPF dimension lumbers calculated with given value in three-parameter Weibull distribution and normal distribution are equal. According to the probability distribution curve and density curve, probability density in Weibull is slightly asymmetric to its mean value (9 997 MPa), which is different from probability density curve in normal distribution; Probability curve in normal distribution is a little higher than that in Weibull distribution when elastic modulus is less than 7 000 MPa. However, the results would opposite when the elastic modulus is more than 7 000 MPa. 【Conclusion】 Modal test verifies testing unit in the work and realizes the supporting conditions for free hanging of test lumbers. Test schemes of frequency method are put forward to ensure the testing precision of natural frequency of the first bending mode and reliably calculate elastic modulus of SPF dimension lumbers; Testing elastic modulus of SPF dimension lumbers by instantaneous aroused frequency method has virtues of convenience, fast, repeatability and accurate; A good correlation was found between elastic modulus tested with frequency method and that tested with wave-speed method. Such a correlation verifies correctness of elastic modulus tested with frequency method. Results tested by the K-S test method showed that general elastic modulus of SPF dimension lumbers obeyed three-parameter Weibull distribution and normal distribution, but not obeyed two-parameter Weibull distribution. Probability of elastic modulus calculated in normal distribution, which is less than 7 000 MPa, is higher than that calculated in Weibull distribution. In other scope, however, probabilities calculated in these two distribution ways are identical; Probability density curve for overall elastic modulus of SPF dimension lumbers in three-parameter Weibull distribution is slightly asymmetric; It is recommended to use 60%-80% of the minimum test data as location parameter E_u when the parameters of Weibull distribution is determined. The overall average and standard deviation of MOE values of total SPF dimension lumbers were calculated. The probabilities of MOE values under given values were also calculated. As a result, the calculated probabilities were same, except the fact that probabilities calculated by normal distribution were higher than those calculated by Weibull distribution when the MOE values were within the scope of low end. To evaluate the quality of these SPF dimension lumbers, the methods of three-parameters Weibull distribution and normal distribution were particularly used to calculate the probability that general MOE value was less than 8 000 MPa (the minimum standard value for Canadian No.2 lumbers), and the probability values were 13.8% and 13.6% respectively.

Key words: spruce, pine and fir, modulus of elasticity, frequency, stress wave, Weibull distribution, normal distribution