Allowable bending strength enhancement of 2 by 4 lumber by tension and compression proofloading

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Virginia Polytechnic Institute and State University


Research has established that correlations exist between bending and tension, and bending and compression strength of lumber. Because of this correlation, improvement in bending strength may be realized from proofloading in tension or compression.

The data utilized in a reliability analysis was from Galligan et al. (1986) that characterized the properties of 2-inch softwood dimension lumber with regressions and probability distributions. Randomly selected groups of 2 by 4 1650f-1.5E Hem-fir and No.2 KD Southern Pine were evaluated for bending strength. One group from each species was selected as a control and tested in bending. The other groups were proofloaded in tension and compression at two stress levels and the survivors were tested in bending to failure.

Based on the concept of equal reliability and utilizing the load distributions from Thurmond (1986), the tensile and compressive proofloaded strength distributions were compared to the control. The probability of failure for the control group is found, then with an iterative approach, the bending strength values of the proofloaded sample distribution are artificially altered by a factor K until the probabilities of failure for the proofloaded and control groups are similar. The K is a shift factor relating the amount the proofloaded strength distribution must be shifted on the x-axis to give the same reliability as the control.

Simple 5th percentile comparisons, the advanced first order second moment (AFOSM) and numerical integration analysis methods were used to evaluate increases in allowable bending strength from proofloading in tension and compression. Proofloading in tension or in compression both produced significant increases in allowable bending strength for the Hem-fir grade. Proofloading in tension to a target 15 percent breakage level, or 2,838. psi, yielded for the survivors an increase of 72 percent in allowable bending strength. The allowable bending strength increased 60 percent due to a compressive proofloading to a target 15 percent breakage level.

The allowable bending strength increased as the proofloading level increased for both tension and compression proofloading with the Hem-fir grade. The southern pine visual stress grade did not show a consistent trend between proofloading level and improvement in allowable bending strength. The lack of a trend between proofloading level and allowable bending strength was attributed to possible sampling error.

The fifth percentile analysis method, the AFOSM method and numerical integration method were compared. For lumber strength comparisons, a simple fifth percentile analysis was not the preferred method. The AFOSM method and the numerical integration method provided identical results in terms of their application in adjusting allowable bending stresses. It was not possible to show that the approximate AFOSM method can be used exclusively in lieu of the numerical integration method for reliability calculations.