1 Basic and Special Design Concepts of CLT Elements loaded out-of-plane G. Schickhofer *, A. Thiel **, J. Dröscher * * Institute of Timber Engineering and Wood Technology, Graz University of Technology ** Centre of Competence holz.bau forschungs gmbh, Graz proholz.at+universities.at.si.hr_masterclass Graz April 1, 2016 u www.tugraz.at
CONTENT 2 INTRODUCTION ULS DESIGN OUT-OF-PLANE SLS DESIGN OUT-OF-PLANE SPECIAL DESIGN PROPOSALS SOFTWARE TOOLS SUMMARY AND CONCLUSIONS
CONTENT 3 INTRODUCTION ULS DESIGN OUT-OF-PLANE SLS DESIGN OUT-OF-PLANE SPECIAL DESIGN PROPOSALS SOFTWARE TOOLS SUMMARY AND CONCLUSIONS
INTRODUCTION 4 Graz University of Technology 7 faculties 12,800 students 2,400 staff (2014/15) budget: 207 Mil. (31,5 % 3 rd party budget) Faculty of Civil Engineering Sciences 15 institutes about 1,500 students (2014/15) Institute of Timber Engineering and Wood Technology 1991: Chair for Timber Engineering 10 2004: Institute of Timber Engineering and Wood Technology Scientific staff: 8 FTE 3 rd party budget: 470,000 (2015) Competence Centre holz.bau forschungs gmbh 12 2002 Competence Centre holz.bau forschungs gmbh 01 2013 3 rd acceptance of a 4-year funded programme: COMET-Project focus_sts [till the end of 2016] Scientific staff: 11 FTE budget: 625,000 (2015)
LAB MECH STOCH INTRODUCTION 5 R&D topics regarding Timber Engineering and Wood Technology at TU Graz Shell and Spatial Timber Constructions (SSTC) Innovative and Intelligent Connection Systems (IICS) Lightweight and Hybrid Hardwood Applications (LHHA) Evaluation and Maintenance of Historic Structures (EMHS)
CONTENT 6 INTRODUCTION ULS DESIGN OUT-OF-PLANE SLS DESIGN OUT-OF-PLANE SPECIAL DESIGN PROPOSALS SOFTWARE TOOLS SUMMARY AND CONCLUSIONS
ULS DESIGN OUT-OF-PLANE 7 Methods of Calculation Stresses Well-known procedures: Timoshenko beam theory transversal shear flexible beam (TIMO) shear analogy method (SAV) γ-method (GAMMA) finite element method (FE) 2 x 1.5 t CLT detail 4.8 m 4.8 m
normal stress [N/mm²] shear stress [N/mm²] rolling shear stress [N/mm²] ULS DESIGN OUT-OF-PLANE 8 Methods of Calculation Stresses Well-known procedures: Timoshenko beam theory transversal shear flexible beam (TIMO) shear analogy method (SAV) γ-method (GAMMA) finite element method (FE) 2 x 1.5 t CLT 2 x 1.5 t CLT 2 x 1.5 t CLT 0.3 0.3 6.0 5.0 4.0 3.0 2.0 1.0 0.0-1.0-2.0 4.0 4.8 5.6 x [m] 0.2 0.1 0.0-0.1-0.2-0.3 4.0 4.8 5.6 x [m] 0.2 0.1 0.0-0.1-0.2-0.3 4.0 4.8 5.6 x [m]
ULS DESIGN OUT-OF-PLANE 9 2D Effects are relevant and have to be considered for... 2 5 4 3 1 point-supported CLT plates 1 partial area supported CLT plate cantilever 3 butt joints (construction) 4 point loads etc. 5 2 Deutscher Pavillon of Ludwig Mies van der Rohe build:1929 World Exhibition Barcelona Research activities in progress!
ULS DESIGN OUT-OF-PLANE 10 Stiffness Values Bending Stiffness Major direction K (E I ) (E A e ) 2 CLT i i i i i I i moment of inertia of layer i E i modulus of elasticity of layer i (E 0,i or E 90,i ) A i cross-sectional area of layer i e i distance between gravity centers S i and S Minor direction for example: 5s (30-20-30-20-30 mm) K 1.818 10 Nmm CLT,0 CLT,90 12 2 K 0.305 10 Nmm 12 2 factor 6
ULS DESIGN OUT-OF-PLANE 11 Bending Normal Stress Distribution S M y,d σ max,d My (z) z E(z) K f max,d m,clt,d CLT 1.0 σ max,d S M y,d σ max,d f m,clt,d maximum design bending stress bending strength design value
ULS DESIGN OUT-OF-PLANE 12 Bending Shear Stress Distribution S V z,d τ r,max,d τ max,d (z ) 0 V z E(z) z da A 0 K b(z ) CLT 0 shear: rolling shear: f max,d v,clt,d 1.0 f r,max,d r,clt,d 1.0 S V z,d τ r,max,d τ max,d τ max,d τ r,max,d f v,clt,d f r,clt,d maximum shear stress maximum rolling shear stress shear strength design value rolling shear strength design value
CONTENT 13 INTRODUCTION ULS DESIGN OUT-OF-PLANE SLS DESIGN OUT-OF-PLANE SPECIAL DESIGN PROPOSALS SOFTWARE TOOLS SUMMARY AND CONCLUSIONS
SLS DESIGN OUT-OF-PLANE 14 Stiffness Values Shear Stiffness SCLT S tot (Gi A i) κ ~ 0.25 for ratio G 0 /G r = 10 nearly const. G i κ S(z) G(z) b(z) S 2 1 S (z,e(z)) tot 2 K CLT G(z) b(z) t CLT 1 dz shear modulus of layer i (G 0,i or G r,i ) shear correction coefficient first moment of area shear modulus width of cross section not considered: different board widths and gaps Δκ = 10 % to 15 %
SLS DESIGN OUT-OF-PLANE 15 Deflections Calculation including Shear Deformations CLT 1 1 w M M dx V V dx K S CLT single-span beam under uniform load: w(l / 2) 5 ql ql 384 K 8 S 4 2 CLT CLT w w(l/2) deflection out-of-plane deflection at midspan
SLS DESIGN OUT-OF-PLANE 16 Deflections Long-term Effects (Creep) Cross layers (rolling shear) lead to higher values than for ST or GLT SC 1: SC 2: k 0.85 def k 1.10 def Combinations acc. to EN 1990 and EN 1995-1-1 combination limit instantaneous t = 0 w inst w inst,g + w inst,q l/300 final t = w fin w inst + w creep l/150 net final t = w net,fin w fin - w c l/250
SLS DESIGN OUT-OF-PLANE 17 Vibrations Design Methods For l > 4 m: vibration governs design! Common procedures for CLT: verification according to EN 1995-1-1 verification according to ON B 1995-1-1:2015 verification according to Hamm/Richter Canadian approach of Hu (CLT Handbook from FPInnovations) Parameters: natural frequency, stiffness criterion, vibration acceleration
SLS DESIGN OUT-OF-PLANE 18 Vibrations Design Concept according to ON B 1995-1-1:2015 specification of performance limits for f, w and a 1 st natural frequency: f 1 f crit YES YES stiffness: w(1kn) w crit YES verification fulfilled NO NO 1 st natural frequency: f 1 f min YES vibration acceleration: a a crit verification not fulfilled NO NO
SLS DESIGN OUT-OF-PLANE 19 Vibrations Fundamental Natural Frequency Basics beams: km EI f 1,beam Hz 2 l 2 m plates: support conditions mass effective long. bending stiffness effective trans. bending stiffness effective twisting stiffness span resp. ratio span to width support condition k m hinged at both ends π 2 = 9.87 fixed at both ends 22.4 fixed / free (cantilever) 3.52
SLS DESIGN OUT-OF-PLANE 20 Vibrations Fundamental Natural Frequency Basics beams: km EI f 1,beam Hz 2 l 2 m plates: a higher mass decreases the fundamental natural frequency considering the shear flexibility (e.g. with apparent bending stiffness) reduces the fundamental natural frequencies (high influence of ratio l/t CLT ) considering continuous beam effect leads to a factor 1.0 to 1.5 depending on span ratio min to max
SLS DESIGN OUT-OF-PLANE 21 Vibrations Fundamental Natural Frequency Requirements critical frequency f crit applied method high requirements normal requirements ON B 1995-1-1:2015 8 Hz 6 Hz Minimum frequency: f min = 4.5 Hz
SLS DESIGN OUT-OF-PLANE 22 Vibrations Stiffness Criterion Deflection of a single-span girder with a single force F at midspan w(f,b ) F 3 F l F l 48 EI b 4 GA b l,ef F ef F with b F l EI 4 1.1 EI b,ef l,ef limit values w crit,1kn applied method high requirements normal requirements ON B 1995-1-1:2015 0.25 mm 0.5 mm
CONTENT 23 INTRODUCTION ULS DESIGN OUT-OF-PLANE SLS DESIGN OUT-OF-PLANE SPECIAL DESIGN PROPOSALS SOFTWARE TOOLS SUMMARY AND CONCLUSIONS
SPECIAL DESIGN PROPOSALS 24 Ribbed Plates of CLT and GLT Effective Width b ef Non-uniformly distributed normal stresses in the flange due to shear deformations reduced (virtual) flange width b ef with constant normal stress and plane strain resultant of real stress over total flange width b = resultant of idealised stress over effective width b ef
SPECIAL DESIGN PROPOSALS 25 Ribbed Plates of CLT and GLT Effective Width b ef Influences type of loading (distributed concentrated) type of static model (single-span continuous beam) stiffness values of CLT c x, c xy, b x shear flexibility of CLT type of verification (ULS SLS) ratio L / b 0.72 0.44 ULS distributed load SLS distributed load ULS concentrated load SLS concentrated load for example: L / b = 10 / 1.65 = 6.1 b ef,q = 0.72 b b ef,f = 0.44 b 6.1
SPECIAL DESIGN PROPOSALS 26 Ribbed Plates of CLT and GLT Effective Width b ef Influences Continuous beams under distributed loads shows also reduced areas in the effective width distribution at their supports. Proposal of Petersen (1988) Use of single-span solution field areas: distributed load span L F support area: concentrated load span L S bending moment course
SPECIAL DESIGN PROPOSALS 27 Ribbed Plates of CLT and GLT Effective Width b ef Stresses normal stress field area shear stress support area or concentrated loads effective width for shear stress calculation
SPECIAL DESIGN PROPOSALS 28 Local Load Introduction in Floors Compression perpendicular to Grain Adaption of strength and stiffness of a CLT cube to real structures and load situations factor k c,90,clt Model of Brandner and Schickhofer (2014) based on load distribution model of van der Put (1988): long. 45 ; cross 15 consideration of edge bonding or cracks in the top layers possible restricted to load applications where resultant forces acting in the same line Case load introduction (continuous supported) load application k c,90,clt = A dis A = w l dis dis w l continuous support w c,ef = l c,ef = w dis w w = l dis l l = w dis w l dis l
SPECIAL DESIGN PROPOSALS 29 Local Load Introduction in Floors Compression perpendicular to Grain General case (different size of load introduction areas) related values k c,90,clt = A c,ef A c,sec A c,ef = max émin( ëê w 1,dis (z) w 1 ; w 2,dis (z) w 2 ) min l 1,dis (z) l 1 ; l 2,dis (z) l 2 A c,sec = min(w 1 ;w 2 ) min(l 1 ;l 2 ) ( ) ù ûú
SPECIAL DESIGN PROPOSALS 30 Local Load Introduction in Floors Compression perpendicular to Grain Central load transmission example 5s 160 mm (40 20 40 20 40) edge bonded top layers load introduction area 20 x 20 cm² k c,90,clt = 1,50
SPECIAL DESIGN PROPOSALS 31 Local Load Introduction in Floors Compression perpendicular to Grain Central load introduction example 5s 160 mm (40 20 40 20 40) edge bonded top layers load introduction area 20 x 20 cm² k c,90,clt = 1,99
SPECIAL DESIGN PROPOSALS 32 Local Load Introduction in Floors Compression perpendicular to Grain Wall on column (wall parallel to top layers) example 5s 160 mm (40 20 40 20 40) edge bonded top layers load introduction area 20 x 20 cm² k c,90,clt = 1,56
SPECIAL DESIGN PROPOSALS 33 Local Load Introduction in Floors Compression perpendicular to Grain Load transmission at edges top layers parallel to edge example 5s 160 mm (40 20 40 20 40) edge bonded top layers load introduction area 20 x 20 cm² k c,90,clt = 1,39
SPECIAL DESIGN PROPOSALS 34 Local Load Introduction in Floors Compression perpendicular to Grain Load transmission at edges top layers transversal to edge example 5s 160 mm (40 20 40 20 40) edge bonded top layers load introduction area 20 x 20 cm² k c,90,clt = 1,33
SPECIAL DESIGN PROPOSALS 35 Local Load Introduction in Floors Compression perpendicular to Grain Load transmission at corners example 5s 160 mm (40 20 40 20 40) edge bonded top layers load introduction area 20 x 20 cm² k c,90,clt = 1,24
Mestek (2011) SPECIAL DESIGN PROPOSALS 36 Shear and Bending Failure of pointsupported CLT plates loaded out-of-plane concentrated load introduction locally high shear forces shear failure around the concentrated load ( punching ) 2D consideration shear flexible Reissner-Mindlin plate theory critical perimeter rolling shear stresses acc. to Mestek (2011) locally applicable rolling shear strength acc. to Mestek higher than base value, confirmed by Bogensperger (2015) critical perimeter
SPECIAL DESIGN PROPOSALS 37 Shear and Bending Failure of pointsupported CLT plates loaded out-of-plane Rolling shear failure of CLT elements with practically common spans possible? Tests on 5- and 7-ply CLT elements with 2.5 x 4.0 m² generally bending failure within longitudinal or cross layers
SPECIAL DESIGN PROPOSALS 38 Shear and Bending Failure of pointsupported CLT plates loaded out-of-plane Conclusion from tests type of failure (shear or bending) strongly dependent on geometrical dimensions and layup of the CLT plate verification of both types necessary reliable and practical design concept still missing and further investigations required (currently in progress)
CONTENT 39 INTRODUCTION ULS DESIGN OUT-OF-PLANE SLS DESIGN OUT-OF-PLANE SPECIAL DESIGN PROPOSALS SOFTWARE TOOLS SUMMARY AND CONCLUSIONS
SOFTWARE TOOLS 40 CLTdesigner The software tool for designing cross laminated timber elements (CLT) based on design concepts of EC 5 and numerous research works developed and provided by the Centre of Competence holz.bau forschungs gmbh and the Institute of Timber Engineering and Wood Technology of Graz University of Technology available in DE, EN, FR, IT and ES at www.cltdesigner.at
SOFTWARE TOOLS 41 CLTdesigner The software tool for designing cross laminated timber elements (CLT) www.cltdesigner.at
SOFTWARE TOOLS 42 CLTcalculator first CLT App for iphone and ipad available on the App Store
CONTENT 43 INTRODUCTION ULS DESIGN OUT-OF-PLANE SLS DESIGN OUT-OF-PLANE SPECIAL DESIGN PROPOSALS SOFTWARE TOOLS SUMMARY AND CONCLUSIONS
SUMMARY AND CONCLUSIONS 44 Summary and Conclusions CLT loaded out-of-plane Different methods of calculation approximations, but applicable, locally stress deviations at supports and point loads, consistency between design method and that used for derivation of strength and stiffness properties For floor and roof elements the SLS design is very important Due to shear-flexible cross layers, it is essential to include deformations caused by shear when calculating deflections and checking vibration behaviour Shown methods are limited to homogeneous CLT elements load bearing and design models for combined CLT are missing Interaction equations for stresses of combined actions are required
SUMMARY AND CONCLUSIONS 45 Summary and Conclusions Special Design Proposals Ribbed floor elements Proposal how to calculate T-beams according to beam theory higher shear stresses in the CLT element above the rib Compression perpendicular to grain model to determine the factor k c,90,clt restricted to load applications where resultant forces acting in the same line (no bending) include bending proposal of A.J.M. Leijten (2012) for structural timber elements Shear and bending failure of point-supported plates type of failure highly depends on geometrical dimensions reliable and practical design concept still missing, further investigations required
46 Basic and Special Design Concepts of CLT Elements loaded out-of-plane Contact: Univ.-Prof. DI Dr.techn. Gerhard Schickhofer Institute of Timber Engineering and Wood Technology, Graz University of Technology Inffeldgasse 24/I A-8010 Graz gerhard.schickhofer@tugraz.at Tel.: +43 316 873 4600 u www.tugraz.at