Unbonded post-tensioned timber gravity frames for multi-storey buildings

Transcription

1 Unbonded post-tensioned timber gravity frames for multi-storey buildings W. van Beerschoten*, A. Palermo*, D. Carradine* and P. Law** * Department of Civil and Natural Resources Engineering, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand ( w.a.vanbeerschoten@pg.canterbury.ac.nz; alessandro.palermo@canterbury.ac.nz; david.carradine@canterbury.ac.nz) ** Wesbeam, 190 Pederick Road, Neerabup, WA 6031, Australia ( peter.law@wesbeam.com) ABSTRACT This paper describes the use of post-tensioning for long span timber gravity frames. These frames can be used for multi-storey commercial and office buildings. Two different configurations are described, one with prefabricated post-tensioned timber beams and one with post-tensioning through the full length of the frame. In the latter, beam-column connections are created by the clamping force due to the post-tensioning. It is shown that post-tensioning of timber beams can create a precamber which helps to satisfy deflection criteria. This makes it possible to create long span timber beams while limiting the section height. Key design issues including deflections, tendon profile, deviators and tendon anchorage are addressed. The behaviour of these connections is presented and the three deformation components of the connection are explained. A design example of a post-tensioned timber frame is also included. KEYWORDS Beams; Frames; LVL; Post-Tensioning; Timber. INTRODUCTION Recent developments in New Zealand and Australia, facilitated by the Structural Timber Innovation Company (STIC), have resulted in the development of unbonded post-tensioned timber frames for use in multi-storey and long-span structures (Buchanan et al., 2011). Initially the system was developed as moment-resisting frames to resist earthquake loading (Palermo et al., 2005), following developments in precast concrete seismic design (Priestley et al., 1999). Unbonded post-tensioned concrete frames have further evolved to non-seismic frames, called the Brooklyn system (Pampanin et al., 2004). The same design principles are now being applied to timber with recent research focusing on gravity design of post-tensioned frames for multi-storey timber buildings. In the past, multi-storey timber buildings have typically been used as residential and hotel buildings (FWPA, 2009). These types of buildings have numerous walls placed within the building resulting in short span floors and beams. For office and commercial buildings this is often not desired and large open floor plans are required. Timber-concrete composite flooring systems can span 8 to 10 m (FWPA, 2010), though supporting beams become highly loaded and need large section sizes to withstand floor loads. Post-tensioned timber beams and frames can reduce the depth of these beams opening up the way for multi-storey timber office and commercial buildings. Frames designed for gravity loading can be used anywhere in a building, as long as lateral forces are resisted by other structural elements, such as diagonal bracing, shear walls or moment-resisting frames.

2 The objective of this paper is to give an overview of the technology and preliminary design methods for post-tensioned timber gravity frames. Two different configurations are described, one using prefabricated post-tensioned timber box beams and one with post-tensioning throughout the full length of the frame. This paper limits the investigation to laminated veneer lumber (LVL), but glue laminated (glulam) timber can also be used (Smith et al., 2011). Only hollow core box sections are considered, as they form an efficient cross-section and allow for easy application of internal posttensioning. Key design issues are addressed and the behaviour of post-tensioned beam column connections is presented. A design example of a two bay timber frame is also included. POST-TENSIONED BEAMS Design of long span timber beams is often governed by deflection criteria, resulting in an underutilization of the strength of timber. This can be partly resolved by adding a precamber which can be achieved during fabrication of glulam beams, but is difficult for LVL beams. Similar to concrete applications, the use of post-tensioning induces a precamber to hollow core box beams resulting in decreased deflections. Either straight tendons, anchored at the bottom of the beam, or draped tendons, anchored centrically can be used (Figures 1 and 2). Post-tensioned timber box beams can create long spans necessary for large open spaces. Beams can be manufactured and stressed off-site, similar to precast concrete beams. On the building site beams can be placed between columns onto corbels. (a) Figure 1. Longitudinal section of timber box beams with (a) straight post-tensioning and draped post-tensioning tendons. (a) (c) Figure 2. Experimental testing of 9m post-tensioned timber box beam, (a) side view, deviator and (c) end view (Lago et al., 2009). Application of unbonded post-tensioning also improves the load-carrying capacity since the compressive strength of LVL is considerably higher than the tensile strength. Though despite the precamber, the design of post-tensioned timber beams is still governed by long term deflections (Table 1). When assessing deflections, not only bending deflection but also shear deflection needs to be taken into account, which can increase deflections by 5 to 20%. If draped tendons are used, shear deformation is reduced as upward forces decrease shear stresses. Comparisons have been made among four beams in order to illustrate the benefits of posttensioning; a simply supported box beam, a box beam with fixed ends, a simply supported posttensioned box beam and a post-tensioned box beam with moment resisting connections (as part of a

3 frame). The design has been performed according to the Australian/New Zealand Timber Structures Standard AS/NZS 3603:1993 (Standards New Zealand, 1993). Dead load of 3kPa of a timberconcrete-composite floor and live load of 3kPa for an office building have been used. A duration of load factor (k 2 ) of 2.0 has been applied in the calculation of the long-term deflections. The required beam height and governing design criteria are shown in Table 1, including unity checks for bending strength, shear strength, short term deflections and long term deflections. The unity check is the design value divided by the allowable value and thus must be smaller than one. A simply supported beam would need a section height of 780mm to satisfy the long term deflection criteria. A 300mm reduction in section height is possible if a fully fixed connection (No. 2) were created, but this is almost impossible (or too expensive) to achieve in timber. A 200mm reduction in beam height can be reached when applying post-tensioning (No. 3). The beam height can be even further reduced when a moment resisting connection in a post-tensioned frame is introduced (No. 4). Table 1. Required beam height and governing design criteria for different beam designs with a 7.6m span loaded by a 6.1m timber-concrete-composite floor. Unity checks* No. Schematics Beam height 1 780mm L/h mm 2 L/h mm 3 L/h mm 4 L/h 18 * Unity check is the design value divided by the allowable value Bending Shear Short defl. Long defl An essential part of the post-tensioning system is the anchorage, which requires careful design. Extra sheets of LVL can be glued inside the box beam to create sufficient bearing area, as shown in Figure 1. The permanent duration of the loading means that bearing strength needs to be significantly reduced and a reduction factor of 0.6 needs to be included according to AS/NZS3603 (Standards New Zealand, 1993). Deviators can be manufactured from LVL sheets with grain running vertically, as deviators need high strength in that direction due to the tendon forces. Several sheets can be glued together to create the required geometry (Figure 2). No steel reinforcement within deviators is needed as the compression strength of LVL is sufficient to resist the upward force from tendons. Post-tensioning tendons require a minimum curvature of 2.0m (BBR VT International Ltd, 2006), which can be achieved by providing curvature to the bottom of deviators. As in every post-tensioned construction, the post-tensioning losses need to be analyzed in order to determine the long term behaviour. Post-tensioned timber beams are loaded parallel to grain only and experimental testing has shown that long-term losses are in the order of 10% in this direction (Davies et al., 2007). An analytical study (Giorgini, 2010) confirmed that long term losses parallel to grain vary between 6.5% and 14.0%, depending on the amount of post-tensioning applied.

4 POST-TENSIONED FRAMES Developing moment resisting connections in timber is difficult and usually large steel components are necessary (Buchanan et al., 1993), compromising cost-efficiency of the structural system. If tendons pass through supporting columns, a continuous post-tensioned frame is created, as shown in Figure 3. Unbonded tendons are anchored at the exterior columns of the frame and the posttensioning force clamps beams and columns together, thus creating partially moment resisting connections at the ends of each beam. This leads to a more optimal design, as shown by the reduced member height in Table 3 (No. 4). Draped tendons have a larger inclination compared to simply supported beams, thus resulting in an increased vertical force at deviators. Figure 3. Post-tensioned timber gravity frame. One stressing operation can create several beam-column connections at once, making it an efficient construction system. A practical example can be seen in Figure 4, which shows construction of the recent Massey University College of Creative Arts building in Wellington, New Zealand. The building has draped post-tensioning tendons running along the full length of the frame. (a) Figure 4. Massey University timber building with draped post-tensioning tendons (a) overview and bottom view of beams (c/o A. Buchanan). Total frame deformation consists of three components; beam, joint and column deformation (Figure 5(a)). The beam and column deformations can be calculated based on standard mechanical equations. The beam-column joint is held together by the post-tensioning force. Without vertical loading this force creates compression stresses along the full height of the beam. When vertical loading is increased a point is reached when the compressive stress at the top is zero, called the decompression point. When the connection is loaded past the decompression point a gap will open between the beam and column (Figure (5b)) and connection stiffness reduces. Determining this connection stiffness is complex, due to anisotropic timber behaviour and non-uniform contact stresses. Previous research on joint deformation (Van Beerschoten et al., 2011b) has shown that it can be split into three parts; joint panel shear deformation, interface compression deformation and gap opening (Figure 5). The opening of the gap results in a reduced contact area and an increase in tendon length and stress. The behaviour of this jointed connection can be calculated using the Modified Monolithic Beam Analogy, or MMBA (Palermo, 2004).

5 (a) Figure 5. Frame and joint deformation components. The interface of the column is subjected to high localized compression stresses perpendicular to grain. The low modulus of elasticity in this direction results in deformations which need to be taken into account when analyzing the joint stiffness. The compressive stresses spread out into the column, resulting in non-linear stress and strain profiles (Blass et al., 2004). A multi-spring model has been developed to capture this compressive behaviour. The stiffness of the springs is given by integrating the strain profile over the depth of the column. This method is outlined in more detail in van Beerschoten et al. (2011b). Steel reinforcement, such as long fully threaded screws, can be added to reinforce the column against compression perp. to grain and thus increase the interface stiffness. Joint panel shear deformation in the column is caused by the compression force of the anchorage plate at top of the connection and the compression force exerted by the beam at bottom of the connection. A region with high shear stress is created (Figure 5) and the relatively low shear modulus of timber results in significant deformations. These deformations only occur in external connections, whereas internal connections undergo compression at the bottom of the connection on both sides which does not create the area of high shear stresses within columns. The various deformation components make predicting the behaviour of a post-tensioned beamcolumn connection complex, but it is critical for the design of post-tensioned timber frames as it influences deflections and moment distribution in the frame. Several tests have been performed on the seismic behaviour of the connection; firstly on reduced size specimens (Palermo et al., 2005) and later on full scale LVL (Iqbal et al., 2010; Van Beerschoten et al., 2011a) and full scale glulam (Smith et al., 2011) connections. Post-tensioning force in the frame depends on the amount of gap opening at connections and beam deflections, both resulting in tendon elongation. This elongation means an iterative procedure is needed, as outlined in (Palermo et al., 2010). Post-tensioning losses in frames are up to 3 times higher compared to post-tensioned beams due to compression in the columns (Davies et al., 2007). Perpendicular to grain stresses result in relatively large deformations, which cause a reduction in post-tensioning force. Steel reinforcement like fully threaded screws located in high perpendicular to grain stress zones can help to minimize losses, as proposed by Crocetti et al. (2010). DESIGN EXAMPLE A prototype building, based on a reinforced concrete building in New Zealand, has been redesigned with a post-tensioned timber frame (Figure 6(a)). The beams span 7.6m and the floor between the frames span 6.1m. A beam height of 460mm has been taken as a first assumption, further section dimensions are shown in Figure 6. A timber-concrete composite floor results in a dead load of 3kPa and the office building is designed with 3kPa live load. Three load cases are considered; Ultimate Limit State (ULS), short term Serviceability Limit State (SLS) and long term SLS. The corresponding distributed loads are 49.4kN/m, 31.1kN/m and 25.6kN/m, respectively.

6 (a) (c) (d) (e) Figure 6. Modeling of post-tensioned timber frame with non-linear rotational springs; (a) prototype building, cross-section of beam, (c) longitudinal section of frame, (d) schematization of beam, (e) non-linear spring stiffness. In gravity design, post-tensioning tendons can be represented by equivalent forces (Figure 6(d)). Initial post-tensioning force is assumed at 520kN, which results from four tendons (Ø12.7mm) stressed to 130kN (70% of ultimate strength). The geometry of the beam gives an uplift force at the deviator of 41kN. At ULS with 15% tendon elongation (Palermo et al., 2010) the post-tensioning force will reach 600kN, resulting in a uplift of 47kN. Long term post-tensioning losses of 15% have been estimated, resulting in a post-tensioning force of 442kN and an uplift of 35kN. The external connection has four deformation components; column, joint panel, interface compression and gap opening. Mechanical equations and experimental testing results suggested a column stiffness of approximately 140kNm/mrad for a 500 x 326mm column. Experimental testing showed that the joint panel stiffness for this dimension of column is approximately 40kNm/mrad, and the interface compression deformation results in a stiffness of 50kNm/mrad. Therefore the initial stiffness of the external connection is 19kNm/mrad, as is shown by Equation 1. The internal connection does not have any column rotation or joint panel deformation; therefore only interface deformation needs to be taken into account, as is shown in Equation k external = + + = + + = 19 knm/mrad k k k internal column jointpanel interface k =k = 50 knm/mrad interface -1 Eq. 1 Eq. 2 Gap opening happens when the bending stress (f b ) at the connection equals the compressive stress due to the post-tensioning (f pt ). This decompression point (M dec ) is calculated using Equation 3. The

7 reduced stiffness after this point follows from MMBA calculation, which is not further elaborated upon in this paper. The resulting non-linear moment-rotation curves are shown in Figure 6(e). F M = f Z f Z = b Z = = 55kNm Eq. 3 3 pt 6 dec y pt y y At A non-linear framework analysis program can be used to calculate compressive force, bending moments, shear forces and deflections under ULS, short term SLS and long term SLS loading. Table 3(a) shows the compressive force in the beam, which equals the post-tensioning force. Bending moment diagram under ULS loading is shown in Table 3. It can be seen that field and end moment are of almost equal value, which makes for an optimal design. The section capacity in compression is 2283kN and in bending 261kNm. Table 3. Compressive force, bending moment, shear force and deflections of post-tensioned beam Section capacity / Type Schematics deflection limit (a) Compressive force under ULS load [kn] 2238kN Bending moment under ULS load [kn] 261kNm (c) Shear force under ULS load [kn] 186kN (d) Short term deflections [mm] 25mm (e) Long term deflections 1 [mm] 25mm 1 needs to be multiplied by a factor of 2 according to New Zealand Standard (Standards New Zealand, 1993) The maximum shear force (Table 3(c)) is reduced to 143kN due to uplift force at the deviators. The capacity of the section is 186kN. Short and long term deflections (Table 3(d) and (e) respectively) are well within the deflection limits of span over 300, which is 25mm. CONCLUSIONS Longitudinally post-tensioning of timber beams can enhance structural performance. Post-tensioned tendons can induce a precamber in LVL box beams and thus limit deflections. In this way section height can be reduced and the high strength of LVL can be better exploited. Design issues such as shear deflection, tendon profile, deviators and post-tensioning anchorage have been highlighted. It has been shown that although long term deflections still govern the design, there are significant benefits to post-tensioning of timber beams. Post-tensioned timber frames have a high potential for use in multi-storey timber buildings. The construction system is efficient and fully utilizes the capabilities of engineered timber products. Though the connection behaviour of a post-tensioned frame is complex and use of non-linear framework analysis program is required, as is shown by a design example. Care needs to be taken with compression perpendicular to grain stresses in columns, where steel reinforcement can be needed to increase strength and reduce deformations.

8 ACKNOWLEDGEMENT The funding for several of the experimental testing campaigns was by the Structural Timber Innovation Company (STIC) Ltd. The LVL was supplied by Carter Holt Harvey and Nelson Pine Industries Ltd. Post-tensioning material was supplied by BBR Contech. REFERENCES BBR VT International Ltd [2006]. "BBR VT Cona CMM - Unbonded Post-tensioning System". European Organisation for Technical Approvals, Osterreichisches Institut fur Bautechnik, Wien, Austria, 32p. Blass, H. J., and Görlacher, R. [2004]. "Compression perpendicular to the grain". World Conference on Timber Engineering, Lahti, Finland. Buchanan, A., and Fairweather, R. H. [1993]. "Seismic design of glulam structures". Bulletin of the New Zealand National Society for Earthquake Engineering, Vol. 26, 4, p. Buchanan, A., Palermo, A., Carradine, D., and Pampanin, S. [2011]. "Post-Tensioned Timber Frame Buildings". The Structural Engineer, Vol. 89, 17 p. Crocetti, R., and Kliger, R. [2010]. "Anchorage systems to reduce the loss of pre-stress in stress-laminated timber bridges". ICTB 2010, Lillehammer, Norway. Davies, M., and Fragiacomo, M. [2007]. "Long Term Behaviour of Laminated Veneer Lumber Members Prestressed with Unbonded Tendons". NZ Timber Design Journal, Vol. 16, Issue 3, 8 p. FWPA [2009]. "New Applications of Timber in Non-traditional Market Segments: High Rise Residential and Nonresidential (commercial) Buildings". PNA , Forest & Wood Products Australia, Melbourne, Australia. FWPA [2010]. "Innovative engineered timber building systems for non-residential applications, utilising timber concrete composite flooring capable of spanning up to 8 to 10m". PNA , Forest & Wood Products Australia, Melbourne, Australia. Giorgini, S. [2010]. "Service load analysis and design of long span unbonded post-tensioned timber beams". Master Thesis, Facolta di Ingegneria edile - Architettura, Politecnico Di Milano, Milan, Italy. Iqbal, A., Pampanin, S., and Buchanan, A. H. [2010]. "Seismic Performance of Prestressed Timber Beam-Column Sub- Assemblies". New Zealand Society for Eearthquake Engineering Conference, Wellington, New Zealand. Lago, B. A. D., and Dibenedetto, C. [2009]. "Use of longitudinal unbonded post-tensioning in multi-storey timber buildings". Master of Science, Master Thesis, Technical University of Milan, Milan, Italy. Palermo, A. [2004]. "Use of Controlled Rocking in the Seismic Design of Bridges". Doctate Thesis, Technical University of Milan, Technical Institute of Milan, Milan. Palermo, A., Pampanin, S., Buchanan, A. H., and Newcombe, M. P. [2005]. "Seismic design of multi-storey buildings using Laminated Veneer Lumber (LVL)". NZSEE Conference, Wairakei Resort, Taupo, New Zealand. Palermo, A., Pampanin, S., Carradine, D., Buchanan, A., Lago, B., Dibenedetto, C., Giorgini, S., and Ronca, P. [2010]. "Enhanced performance of longitudinally post-tensioned long-span LVL beams". 11th WCTE, Trentino, Italy. Pampanin, S., Pagani, C., and Zambelli, S. [2004]. "Cable-stayed and suspended post-tensioned solutions for precast concrete frames: the Brooklyn system". New Zealand Concrete Society Conference, Queenstown, New Zealand. Priestley, M. J. N., Sritharan, S., Conley, J. R., and Pampanin, S. [1999]. "Preliminary Results and Conclusions from the PRESSS Five-story Precast Concrete Test-Building". PCI journal, Vol. 44, 6, p. Smith, T., Pampanin, S., Carradine, D., Buchanan, A., Ponzo, F., Cesare, A., and Nigro, D. [2011]. "Experimental Investigations into Post-Tensioned Timber Frames with Advanced Damping Systems.". Il XIV Convegno di Ingegneria Sismica, Bari, Italy. Standards New Zealand [1993]. "Timber structures standard". NZS 3603:1993, Standards New Zealand, Wellington, New Zealand. Van Beerschoten, W., Palermo, A., Carradine, D., Sarti, F., and Buchanan, A. [2011a]. "Experimental Investigation on the Stiffness of Beam-Column Connections in Post-Tensioned Timber Frames". Structural Engineering World Conference, Como, Italy. Van Beerschoten, W., Smith, T., Palermo, A., Pampanin, S., and Ponzo, F. [2011b]. "The Stiffness of Beam to Column Connections in Post-Tensioned Timber Frames". CIB-W18/44, Alghero, Italy.