EMPA, Swiss Federal Laboratories for Materials Science and Technology

Transcription

1 Notched Beams Robert Widmann Image: Robert Butler EMPA, Swiss Federal Laboratories for Materials Science and Technology With strong contributions from: Robert Jockwer ETHZ, Swiss Federal Institute of Technology, Zurich EMPA, Swiss Federal Laboratories for Materials Science and Technology COST FP1101 Training School University of Mons B December 2013

2 Outline Introduction Principals Types of notches Design of notches Shear design Reinforcement perpendicular to grain SIA 265 and EN :2004 (German Version) Example Research Inclined reinforcements Conclusions COST FP1101 Training School University of Mons B December

3 Introduction Notches at the support of beams Reduced depth of the beams at the support Connection of members Jockwer 2012 COST FP1101 Training School University of Mons B December

4 Introduction - Principals Notches at the support of beams Reduced depth of the beams Connection of members High stresses perpendicular to the grain Stress concentrations at notch edge V d Notches should be avoided or strengthened! Tension perpendicular to the grain: high low Scholten, American Lumberman, 1935 COST FP1101 Training School University of Mons B December

5 Introduction - Types of Notches Rectangular Rounded / Tapered Drawings from: COST FP1101 Training School University of Mons B December

6 Introduction - Types of Reinforcements Bonded Straps Fully threaded screws Glued-in profiled rods Drawings from: COST FP1101 Training School University of Mons B December

7 Outline Introduction Principals Types of notches Design of notches Shear design Reinforcement perpendicular to grain SIA 265 and EN :2004 (German Version) Example Research Inclined reinforcements Conclusions COST FP1101 Training School University of Mons B December

8 Design of Notches (SIA 265:2012) Calculation of shear stresses V Ed d 1.5 b hef k red f v, d h ef Δ h ef b i 1 c V Ed h A) A) A) B) Reduction of shear strength General conditions: (c 0.4 h und h ef 0.5 h ) Δh 0 25mm for solid timber from softwood 45mm for glulam from softwood B) For rounded / inclined notches with inclinations 1:10 the influence of stress concentrations can be neglected (k red = 1,0). COST FP1101 Training School University of Mons B December

9 Abminderungsfaktor k red [-] Design of Notches (SIA 265:2012) 1.2 Calculation of shear stresses Reduction factor k red V Ed d 1.5 1b hef 0.8 A) 0.6 A) 0.4 B) k red f v, d Reduction of shear strength 0.2 General conditions: (c 0.4 h und h ef 0.5 h ) SIA 265:2012 EN :2004 h ef DIN 1052:1988 Δ h ef b Scholten Δh 25mm for solid timber from softwood 0 45mm for glulam from softwood For rounded / Ausklinkungsverhältnis inclined notches Notch with ratio inclinations h ef / h h ef / 1:10 h [-] the influence of stress concentrations can be neglected (k red = 1,0). A) B) i 1 c V Ed h COST FP1101 Training School University of Mons B December

10 Flowchart for notch design - DIN EN :2010 Notched bending member Notch in tension zone Notch in compression zone Inclination i < 10 Inclination i 10 Notch same side as support Notch opposite side to support x h ef x < h ef for LVL for solid timber for glulam 10

11 Shear Capacity [%] Shear Capacity [%] Shear Capacity [%] Notch design - DIN EN :2010 for LVL for structural timber for glulam Shear capacity as function of inclination i, a= 0.8, h = 600mm, x = 100mm k v as function of notch ratio Shear a, capacity i = 0, h = 600mm, x = 100mm as function of distance x, i = 0, a= 0.8, h = 600mm Glulam Solid LVL 1 Glulam Solid LVL notch ratio a = h ef /h Distance x Reduction Factor k v Shear capacity as function of notch ratio a, i = 0, h = 600mm, x = 100mm 100 Glulam Solid LVL 100 Glulam Solid LVL Inclination i Notch ratio a = h ef /h 11

12 Shear Capacity [%] Flowchart for notch design - DIN EN :2010 k v as function of notch ratio a, i = 0, h = 600mm, x = 100mm 2.5 Reduction Factor k v Notch ratio a = h ef /h Shear capacity as function of notch ratio a, i = 0, h = 600mm, x = 100mm Notch ratio a = h ef /h 12

13 Force [N] Variation of strength values h c F Nordtest method to determine mode 1 fracture energy on 3-point bending SENB-specimens Parameters that influence fracture energy G f,i Knots Angle of grain Annual ring structure Cracks W G f,i W mgu h b u Displacement [mm] c 0 Nordtest Method, NT Build 422, Wood: Fracture energy in tension perpendicular to the grain,

14 Probability Density [-] Probability Density [-] Variation of strength values High variation of fracture energy G f,i Fracture energy Gf,I [N/m] Test results Lognormal Test results Normal Lognormal 2p-Weibull Notch Strength A' [Nmm -3/2 ] Consequence: high variation in notch strength Gustafsson, P.J., A study of strength of notched beams, 1988 Larsen, H.J. and P.J. Gustafsson, The fracture energy of wood in tension perpendicular to the grain, 1990 Riberholt, H., et al., Timber beams notched at the support,

15 Reinforcement of Notches Unreinforced Notches: Low strength Big variations of strength values Notches have to be reinforced! Types of reinforcements Embedded reinforcements Glued-in rods Fully threaded screws External reinforcements Bonded wood based panels GFRP and / or CFRP Nail Plates 15

16 F t,90,d / V Ed [-] Design of Notches F 1.2 F t,90,d F Notch ratio a = h ef /h [-] αh F t,90,d τ h V Ed 2 a 2, 90, d Ed F t 1 a V Δh ef V Ed 16

17 Introduction - Types of Reinforcements Bonded Straps Fully threaded screws Glued-in profiled rods Drawings from: COST FP1101 Training School University of Mons B December

18 Design of reinforced notch 1 Fully threaded screws 2 Bonded wood based panels Glued-in rods with d r Bond line Bond line for glued-in rods Wood based panel 18

19 Outline Introduction Principals Types of notches Design of notches Shear design Reinforcement perpendicular to grain SIA 265 and EN :2004 (German Version) Example Research Inclined reinforcements Conclusions COST FP1101 Training School University of Mons B December

20 Example for design of reinforced notch V d = 78kN, f v,g,k = 3.5MPa, k mod = 0.9, g M = 1.3 h = 600mm, h ef = 450mm, b = 140mm, c = x = 100mm V Ed h h ef Δ h ef b i 1 c 20

21 Example for design of reinforced notch V d = 78kN, f v,g,k = 3.5MPa, r,k = 385kg/m 3, k mod = 0.9, g M = 1.3 h = 600mm, h ef = 450mm, b = 140mm, c = x = 100mm GL24h V Ed h h ef i 1 Reinforcement with fully threaded screws Δ h ef b c Pull-out strength R 1,k [kn] Pull-out strength R 1,k [kn] 21

22 Example for design of screw reinforced notch 22

23 Example for design of reinforced notch V d = 78kN, f v,g,k = 3.5MPa, r,k = 385kg/m 3, k mod = 0.9, g M = 1.3 GL24h h = 600mm, h ef = 450mm, b = 140mm, c = x = 100mm V Ed h h ef i 1 Reinforcement with wood based panel Δ h ef b c τ ef,d 0.52 MPa = 0.75 MPa = f k2,k k mod γ M l r F t,90,d 2 h- h ef 0.52 l r = 101mm 38mm l r 75mm 38mm 101mm 75mm Requirement not fulfilled, notch can t be strengthened with wood based panels 23

24 Outline Introduction Principals Types of notches Design of notches Shear design Reinforcement perpendicular to grain SIA 265 and EN :2004 (German Version) Example Research Inclined reinforcements Conclusions COST FP1101 Training School University of Mons B December

25 Reinforcement of Notches Shear deformations of reinforcement F Jockwer, R

26 Reinforcement of Notches Image correlation measurements ARAMIS V Unreinforced notch Strain perpendicular to grain Shear strain y x y x Jockwer, R

27 Reinforcement of Notches Image correlation measurements ARAMIS V Reinforced notch: Fully threaded screw 90 Strain perpendicular to grain Shear strain y x y x Jockwer, R

28 Reinforcement of Notches Image correlation measurements ARAMIS V Reinforced notch: Fully threaded screw 45 Strain perpendicular to grain Shear strain y x y x Jockwer, R

29 Shear Stress at failure Residual Cross Section [N/mm2] Tests on reinforced notches Aim: Determination of influence of inclined reinforcement Glulam Gl28h, 10 beams b/h 90/315 mm Reinforcement: Fully threaded screws: SFS WRT-13 d= 13mm l= 400mm 45 and 90 CFRP sheets: SikaWrap t= 1mm b= 50mm 45 and Unreinforced unverstärkt Schraube Screw Schraube Screw 45 CFRP 90 CFRP Jockwer, R

30 Outline Introduction Principals Types of notches Design of notches Shear design Reinforcement perpendicular to grain SIA 265 and EN :2004 (German Version) Example Research Inclined reinforcements Conclusions COST FP1101 Training School University of Mons B December

31 Conclusions Notched members to decrease depth at supports Shear capacity significantly decreases Tension stresses perpendicular to grain are present From mechanical point of view notches should be avoided Rounded / inclined notches have a better performance Notches need to be strengthened / reinforced Most used techniques: bonded wood based panels, fully threaded screws, nail plates and glued-in rods Research shows that strengthening should also be applied for shear Thank you for your attention! COST FP1101 Training School University of Mons B December