STRENGTH AND STIFFNESS REDUCTION OF LARGE NOTCHED BEAMS By Joseph F. Murphy 1 ABSTRACT: Four large glulam beams with notches on the tension side were tested for strength and stiffness. Using either bending net section beam theory or shear formula to calculate crack propagation critical load is very unconser- vative. A linear elastic fracture mechanics approach, taking into account the high tension stresses perpendicular to grain and shear stresses at the notch reentrant comer, conservatively predicts the critical load. The data corroborate the substantial analytic effect of size predicted by fracture mechanics for notched beams. Results quantify the observed behavior of bending of beams with notches on the tension side. The strength reduction is so severe for large beams that substituting a beam having the net depth of the notched beam is preferable. Removing material would remove the stress concentrator and would increase the strength up to net section theory prediction at the notch location. Using an effective notch length (actual notch length + notch depth added to each end of the notch) and variable moment of inertia, beam theory accurately predicts the notch beam deflection under load. OBJECTIVE AND BACKGROUND In current practice, notches are cut into wood beams to allow for clear- ance and to adjust the top surfaces to desired levels. Bending stress val- ues calculated at the notch by dividing the applied bending moment by the net section modulus are not accurate in predicting beam strength because the notch reentrant corners cause additional shear stresses and tension stresses perpendicular to the grain. This also applies to using net section shear stress in predicting beam strength. These stresses cause crack propagation at loads lower than the breaking load determined by net section (6). This paper compares fracture mechanics predicted stength, bending net section predicted strength, and a modified shear net section pre- dicted strength to experimental crack initiation/propagation (failure) load for large glued-laminated wood beams. This comparison was used to find the most accurate method to quantify and predict notched beam strength and to check the rational recommended practice ”avoid notches in beams” (12); ”notching on the tension side of single beam in the cen- ter of the span is not recommended” (11); and “notching of bending members should be avoided, especially on the tension side of the lum- ber” (7). A modified net section approach to predict beam stiffness is shown to give good engineering answers. Murphy (6) analyzed crack propagation loads for notched beams (notch on tension side) using linear elastic fracture mechanics theory on small wood beams. However, he used a (conservative) linear combined mode 1 Research Engr., Forest Products Lab., Forest Service, U.S. Dept. of Agricul- ture, Madison, WI 53705. Note.-Discussionopen until February 1, 1987. To extend the closing date one month, a written request must be filed with the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on October 12, 1984. This paper is part of the Journal of Structural Engineering, Vol. 112, No. 9, September, 1986. 1989
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