Timber Frame Moment Joints with Glued-In Steel Rods - A Designer s Perspective. Mark L Batchelar 1

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2 yields prior to the development of compression failure in the timber. Should limited timber compression failure occur it is however unlikely to lead to sudden brittle collapse. In the application of this method it is assumed that the choice of adhesive for securing the threaded or deformed steel rods into the timber will provide a strong bond with the timber and have a stiffness greater than that of the timber so that adhesive deformation can be ignored. Epoxy resin adhesives have demonstrated good performance in service and are considered appropriate as they exhibit stable properties under short and long term loads in varying humidity and at normal operating temperatures of below 50 o C [7,8]. Figure 1 shows a timber member cross-section of depth D and width b with tension only rod reinforcing a distance e from the bottom edge. The section has an applied moment M resisted by timber compression C and steel rod tension T. b fc kd C D d d-kd jd=d-kd/3 M e fs/n T n.as Figure 1 fc = timber compression stress fs = steel tensile stress modular ratio n = Esteel/Etimber e = rod edge distance C = 0.5 fc b kd T = As fs The neutral axis lies at the centroid of the transformed area. Taking moment of areas about the neutral axis gives a quadratic equation that is solved for kd. b (kd) 2 /2 = n.as (d-kd) Having determined kd, jd is known and the section moment capacity can be determined. T = C = M/jd The following simple numerical example illustrates the approach. Example: Applied Short Duration Ultimate Moment M*= 51.0 knm D = 630 mm b = 115 mm e = 65 mm d = 565 mm Volume 15 ISSUE 2 5 NZ TIMBER DESIGN JOURNAL

3 Timber properties: Characteristic tensile stress ft = 10 MPa compr. // fc = 24 MPa bending fb = 22 MPa Modulus of Elasticity Etimber = 10 GPa Capacity reduction factor Φ = 0.8 Rod properties: 16mm diameter Grade 8.8 Ultimate tensile stress fut = 800MPa Capacity reduction factor Φ = 0.8 Modulus of Elasticity Esteel = 200 GPa Modular ratio n = Esteel/ Etimber = 20 As (mm 2 ) = 156 n.as =3120 kd =150.1 jd = C = T = 99.0 kn fc = 14.4 MPa ( Φ fc =19.2 MPa ) fs = 637 MPa ( Φ fut = 640 MPa ) In frame knee joint design the timber compression bearing surface is often loaded perpendicular to the grain (Figure 2) and therefore an estimate of Etimber perpendicular to the grain (Eperp) is required to obtain an appropriate transformed section property. There is a degree of uncertainty about Eperp but if is expected to be about 1/15 to 1/20 of Eparallel. Securing nut & bearing plate frame rafter grain direction Figure Creep Deformation: An issue confronting designers is the effect that time dependant deformation (creep) in the timber will have on the distribution of forces within the joint. Creep in timber is typically allowed for by factoring up the expected permanent load displacements. This is in effect applying a reduction factor to the elastic modulus for long term loads. Applying this principal to joint design means an effective reduction in Etimber for long duration load which in turn reduces the lever arm jd and causes an adjustment to the calculated rod force. In practise the reduction in Etimber for long term effects is only critical when permanent loads are a significant proportion of the total applied load. Volume 15 ISSUE 2 6 NZ TIMBER DESIGN JOURNAL

4 In the above example if a permanent load duration factor of 0.6 is applied to material characteristic stresses and Etimber is reduced to 5.0 GPa to allow for creep effects, the maximum permanent load moment available is 31.5 knm. The magnitude of this moment is governed by the timber compression stress (0.6*Φ fc = 11.5 MPa). The corresponding rod tensile load is approximately 2/3 of the rod capacity. 4.0 Stress Concentrations: In structural detailing it is recognised that sharp changes in section property and/or forced changes in stress flow paths cause stress concentrations that can lead to premature failure. Experimental bending tests on jointed timber members [2,3,11] have demonstrated timber rupture initiating at the embedded end of the steel rod in the outer zone in the region of maximum timber bending stress. Assuming that full load transfer from an embedded rod into the timber is completed at the embedded end of the rod it is reasonable to assume that maximum stress in the timber cross-section is achieved at that point. Typically N.Z. plantation grown timber the characteristic strength in tension is in the order of 50% of the characteristic bending stress and therefore timber failure in this transition region at stress levels below the characteristic bending stress is highly probable. It is therefore the author s practice to identify a contributing cross-section of timber into which the rod force is transferred and to and limit the tensile stress in that section to the allowable timber tensile stress. For a single tension rod the area of timber in tension is taken as b.2e. For multiple layers of rods the timber tension block for each internal rod is taken as b.s where s is the rod spacing. For the case of more than one tension rod the tension block for the extreme rod would be checked for an area of b.(e+s/2). In the numerical example above the tension stress in the timber block is given by ft = T/(b.2e) = 99.0 x 10 3 /(115*130) = 6.6 MPa (<Φ ft = 8.0 MPa) With multiple tension rods the tension stresses in the timber can be controlled by choice of different rod diameters and rod tensile strength. Staggering rod embedment lengths in joints with multiple rods is considered prudent to avoid accumulation of stress concentrations. Limiting the stress in the timber to the timber characteristic tensile strength defines that the full bending strength capacity of a timber member cannot be developed using glued-in threaded steel rods. Designs using N.Z. plantation grown timber are generally governed by stiffness considerations rather than strength therefore this does not often present a problem. 5.0 Summary: Application of the above elastic transformed section approach for the design of glued-in threaded steel rods in moment joints has been successfully used by the author in projects for over 15 years. The approach illustrated is a very simple moment only example but in practice the method is expanded to include member axial tension and compression forces. The likely effects of timber creep deformation at bearing interfaces has been considered in the joint analysis and also limitations applied to timber stresses to counter the effects of stress concentrations imposed by the steel rods at termination points. The time dependant response of loaded timber bearing surfaces, particularly those surfaces loaded perpendicular to grain are matters that warrant further investigation. 6.0 Update:.01 Following presentation of this paper at the World Conference on Timber Engineering 2006, Portland USA, an experimental research programme on the long-term performance of epoxy-glued glulam connections has been commissioned at Canterbury University School of Engineering under the supervision of Dr. Massimo Volume 15 ISSUE 2 7 NZ TIMBER DESIGN JOURNAL

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