Inclined glue laminated timber beams with an end notch at the tension side

Transcription

1 Inclined glue laminated timber beams with an end notch at the tension side Summary ANDI ASIZ Research Associate University of New Brunswick Fredericton, Canada ( IAN SMITH Professor University of New Brunswick Fredericton, Canada ( Notching glue laminated (glulam) timber beams at the tension side is a crucial decision that arguably should be avoided by design engineers because of the high stress concentrations that develop around such notches. However, it is done in practice to facilitate construction and to reduce the total necessary depth of floors and roofs. Timber design provisions permit designers to account for presence of notches, normally through modification terms that are part of assessing the shear capacity of members. Traditional practices in this respect are empirical and of uncertain origin. Strictly the problem requires a rational fracture mechanics analysis and that is done in a few related instances. For example, the notch design equation in Canada for sawn timber members is based on a simple fracture mechanics theory. However the same practices are not adopted in design of notched glulam members, because of concern that a simple fracture theory might be inaccurate when notches remove only a small proportion of a member s depth. The objective of this study is to investigate the effects of small bird-mouth end-notches on failure behaviour and associated strength of inclined glulam members subjected to short-term static load. Two sets of glulam members with 80 x 532 and 175 x 646 mm cross-sections were tested under a statically determinate four-point bending arrangement. Members were tested in inclined positions to replicate common configurations for roof girders in which a tension face notch is made around the upper support. Results suggest that failures are not dominated by fracturing from the notch if the notch does not exceed about 8% of the member depth. In such instances there was limited local fracture damage near the notch, but it did not propagate into a systemic failure. However, at notch depth of about 10% of the member depth it is quite likely that fracturing from the notches will propagate into unstable systemic failures. It is concluded that stress concentrating effects of notches that remove not more than 8% of member depth are negligible. If deeper notches are present designers need to account for them based on application of fracture mechanics. Keywords: bending, design, fracture mechanics, glulam, notching, shear, testing, wood. 1. Introduction Glue laminated timber (glulam) members are commonly used in structural applications causing high stresses and therefore it is important that these members should not be notched in an unfettered manner. Notching glulam members, particularly on the tension face of bending members, can lead to critical stress concentrations at notch corners inducing high tension perpendicular to grain and high shear parallel to grain stresses. Nevertheless, most current design code provisions permit design of notches at the tension side providing that they are located close to the ends of members and at a simple structural support point [1, 2]. Simple design rules for end-notching glulam members include:

2 d limiting notching height by 10% of the member depth or 3 inches (76mm), whichever is the smaller [3]; providing gradual tapered notch configuration or rounding notch corners, instead of a sharpsquare notches [2]; strengthening notch areas by inserting perpendicular-to-grain screws that extend to above the neutral axis of the member [3]. For a sharp-notched member such as shown in Figure d n 1, shear (reaction) force V f (N) is commonly limited b V f accounting for the notch geometry via the expression: Figure 1: Notched member 2bf v ( d d n ) d d n V f = (1) 3 d where f v = shear parallel to grain (MPa), b = width of the member (mm), d = depth of the member (mm), and d n = depth of the notch (mm) [2]. Origins of this formula are unclear. Contemporary notch design provisions in codes were developed mostly from empirical observations of how flat notched solid lumber beam behave. It is questionable that results apply to notching of large glulam members, particularly those with inclined configurations. Strictly, the problem stress concentrations created by corners of notches requires rational fracture mechanics analysis, and that has been done [4]. For example, the notch design equation in Canada for sawn timber members is based on a simple fracture mechanics theory. However the same practices are not adopted in design of notched glulam members, because of concern that a simple fracture theory might be inaccurate when notches remove only a small proportion of a member s depth. The objective of this study is to investigate the effects of small bird-mouth end-notches on failure behaviour and associated strength of inclined glulam members subjected to short-term static load. 2. Test method Two sets of glulam members with 80 x 532 and 175 x 646 mm cross-sections were tested under a four-point bending arrangement as shown in Figures 2 and 3. The system had frictionless horizontal roller bearings placed under the two interior point loads and at the lower bearing support. The bird-mouth notch cut in the glulam wrapped around the upper bearing support with the member resting on a steel support shoe that could not rotate. This provided horizontal frictional restraint to the member against effects of any horizontal forces resulting from imperfections in the arrangement or large deformation of the member. Only vertical external forces were applied and the system was symmetrical with respect to lines of action of external forces, and each vertical reaction force (i.e. outer external forces) was one half of the total applied force. Transverse support was provided to members near each end and at three interior span locations to prevent lateral instability, Figure 3. Teflon coated plates inserted between the member and transverse supports prevented friction and allowed free vertical deformation of the member. Based on expectations about what failure mechanisms might occur, six Linear Variable Displacement Transformers (LVDTs) were attached to specimens to record movements at locations shown in Figure 2. Those LVDTs measured bending deflections, crushing at the upper and lower supports, and crack opening 2

3 displacement if a fracture plane developed from the corner of the notch towards the interior of the span and parallel to the laminations, Figure 3a. P P L s LVDT1 LVDT6 Neutral axis d d LVDT4 LVDT5 V f =P H d LVDT3 slope LVDT4 d n L b V f =P L A L C L A L (a) Test configuration and LVDT locations (b) Notch detail Figure2: Test arrangement and geometric notation L n (a) loading frame (b) upper support (c) lower support Figure 3: Test apparatus Test materials were Canadian manufactured Spruce-Pine glulam of 20f-E grade. Crosssections of such material have an unbalanced arrangement of laminate quality relative to the mid-depth layer. Specified bending strengths are 25.6 MPa and 19.2 MPa depending on which outer surface is loaded in tension [1]. Two cross-section sizes (80 x 532 and 175 x 646 mm) were used to reflect the possibility that there may be size of member effects on mechanisms controlling how specimens failed. Also, for one set of specimens (80 x 532) the notch removed about 8% of the cross-section, while for the other (175 x 646) the notch removed 10% of the cross-section. Details of selected geometric variables for each cross-section size are given in Table 1. Loads were applied by monotonically advancing the loading actuators (interior loading points), at about 4mm per minute, until complete specimen failure. Complete failure occurring in about 15 to 30 minutes after the commencement of loading. Thus, observed behaviour is what is commonly referred to as the static loading response. There were six specimens in each set.

4 3. Results Table 1: Geometric variables for tests (based on notation in Figure 2) Variable Cross-section size 80 x 532 mm 175 x 646 mm L (mm) H (mm) L s (mm) Slope (degree) L A (mm) L C (mm) d (mm) d n (mm) d n / d (%) Span/depth=L/d L b (mm) L n (mm) (a) bending failure (b) shear failure (c) stable notch crack Figure 4: Typical failure mechanisms observed for 80 x 532 members (a) bending failure (b) shear failure (c) unstable notch crack Figure 5: Typical failure mechanisms observed for 175 x 646 members Figures 4 and 5 show images of typical failures observed during the two sets of glulam tests. Before the photographs were taken loading had been continued beyond the point of peak load resistance, under displacement control, until damage propagation was extensive, because that helped clarify the nature of the controlling mechanisms. Bending failures produced highly visible damage that typically was widespread in the tension zone of the cross-section at locations between the interior loading points (Figures 4a and 5a). As illustrated in Figure 4a, damage due to excessive bending moment did not always initiate in the outer lamination. Shear failures were located at about mid-depth of the cross-section at locations between a loading point and an end of a member. Associated fractures exited at an end(s) of members

5 (Figures 4b and 5b). Localised cracking always occurred emanating from the stress concentration at the corner of the bird-mouth notch before the peak load point. However, such cracking did not always propagate into a catastrophic systemic failure. For 80 x 532 members, none of the specimens exhibited signs of incipient unstable fracturing at the notch prior to global instability (Figure 4c). For 175 x 646 members three of six specimens failed catastrophically due to propagation of cracking at the notch. Crack opening deformations recorded by LVDT-4 never exceeded 5 mm, before abrupt unstable crack extension occurred. Tables 2 and 3 summarise the test results for each specimen. Specimen No. Specimen No. Time to failure (minute) Table 3: Test result for (175 x 646) Deformation at failure (mm) * Total load at failure P u ** Ultimate failure mechanism shear bending notch fracture bending notch fracture notch fracture Average (CoV) Time to failure (minute) 24.9 (0.23) Table 2: Test result (80 x 532) Deformation at failure (mm) * 58.2 (0.21) Total load at failure (0.16) P u ** (0.16) Ultimate failure mechanism bending bending bending bending bending shear Average (CoV) (0.35) (0.19) (0.14) (0.14) * measured by LVDT-1 (mid-span); ** = ultimate reaction force at the upper support Figure 6 shows plots of total load versus mid-span displacement for both sets of specimens. As is usual for timber members loaded in bending, the load-deformation curves exhibit initial linear elastic behaviour, followed by limited softening of the response prior to quite brittle systemic failure. There was always rapid reduction in resistive capability after the peak load was reached irrespective of the nature of the controlling mechanism.

6 (b) 80 x 532 (b) 175 x 64 Figure 6: Total load versus mid-span deflection 4. Discussion For 80 x 532 members, it can be concluded that cutting a quite shallow (42mm deep) notch that removes 7.9% of the member depth at an end support did not lead to a critical notch fracturing situation for an inclined member with a span to depth ratio (L/d) of about 11. However, for 175 x 646 members, a deeper (65 mm) notch removing 10% of the member depth did lead to a critical notch fracturing situation in 50 percent of tests for a span-to-depth ratio of about 10. This finding supports the idea that effects of end notches on tension faces of simply supported members are negligible if the ratio d n / d is less than a certain value. However, the results also indicate that the recommendation of the APA-The Engineered Wood Association [3] that stress concentrating effects of notches that do not exceed either 10% of the cross-section depth or 76mm (3 inches) is too liberal for inclined softwood glulam members with bird-mouth notches. Existing design procedures for strength of notched glulam members involve checking three possible failure mechanisms, i.e. bending, shear at the notch, and support bearing capacity. Using specified strengths applicable in Canada [1] for Spruce-Pine glulam of 20f-E grade, and applying equation (1) to the calculation of the shear capacity at the notch, the expected characteristic reaction resistances for tested members are as summarised in Table 4. NOTE: the Canadian timber design code currently does not utilise equation (1) but does specify shear strength. The values in the table are expected 5-percentile values applicable to what is termed Standard Term loading. Figure 7 compares 5-percentile test and expected code reaction resistances for various modes. For consistency what are termed test values were estimated from the data (assuming a normal distribution) multiplied by a factor of 0.8, which converts from test loading duration to Standard Term duration. Comparing the predicted reaction forces and the test results (Figure 7), it can be seen that the design prediction is that shear at the notch (including the effects of stress concentration) should govern for both test situations. The predicted reaction capacity is fairly accurate for the smaller members (80 x 532), but non-conservative for the larger members (175 x 64). Overall, it would seem that the principle of the APA design recommendation [3] is correct, but for inclined glulam members it is appropriate to limit those notches for which effects of stress concentrations can be ignored to ones that do not exceed 8% of member depth. Also, it would appear that equation (1) does not correctly reflect how end notches affect shear capacities of inclined members.

7 Failure mechanism Table 4: Predicted 5-percentile reaction forces based on the current Canadian code Related strength property (Mpa) Predicted reaction force Predicted reaction force equation 80 x x 646 Bending f b-d=646 =25.6 Shear at notch Support bearing f v =1.75 f c-18.4 =6.28 f c-19.5 =6.34 f b bd 6L A bf v ( d d n ) d d n d f c Lbb Notes: - f v = longitudinal shear strength, f b = bending strength on the bottom side of the member, f cα = compression strength with reaction load oriented with angle (90 0 -α) to the grain. - Geometrical parameters are given in Table 1. 5-percentile reaction x x646 Code-bending Codeshear@notch Code-support bearing Test Cross-section size (mm) Figure 7: 5-percentile reaction forces, comparison of code expected and test values for standard term load conditions 5. Conclusions and future study The following conclusions are drawn in respect of end notches on tension faces of inclined glulam members: Stress concentrating effects of notches that remove not more than 8% of member depth are negligible. Stress concentrating effects of notches that remove more than 8% of member depth should not be ignored in structural design. Simple empirical expressions, such as have traditionally been used to adjust shear capacities of members, fail to capture the intricacies of how relatively shallow notches affect the strengths of members. Future study of this subject should focus on practical application of fracture mechanics to notched member design.

8 Continuing work by the authors is placing emphasis on creating numerical models that properly explain test findings, reinforcing members with screws in the area of end notches, and creation of more appropriate design rules. 6. Acknowledgements The authors gratefully acknowledged the contribution of glulam material by Canadian manufacturers. Thanks are also extended to Mr. Gary Williams, President of Timber Systems Limited, Markham, Ontario for technical advice and provision of metal loading and support hardware. 7. References [1] Canadian Standard Association (CSA) Engineering Design in Wood, CAN/CSA Standard (consolidated edition), CSA, Toronto, ON, Canada. [2] American Institute of Timber Construction (AITC) Timber Construction Manual, 5 th edition, John Wiley & Sons, Hoboken, NJ, USA. [3] APA-The Engineered Wood Association Field Notching and Drilling of Glued Laminated Timber Beams, Technical Notes, No. EWS S560E, APA, Tacoma, WA, USA. [4] Smith, I., Chui, Y.H., Hu, L.J Reliability Analysis for Critical Reaction Forces of Lumber Members With an End Notch, Canadian Journal of Civil Engineering, 23(1):