同济大学：《木结构 Timber Engineering》课程教学资源（电子教案）06 Design of Wood Members

2013-4-19 Design of Wood Members Prof.He Minjuan Tongji University,Shanghai China Words and Expressions Design of Wood Members 园 Crushing 压碎 Buckling 1.Tension members Cross-bracing 交叉支推 Bridging 剪刀浮 2.Compression members Notch 缺口，四 (A)Sym 3.Bending members Sendermesraio 长细比 4.Bending combined with tension members 5.Bending combined with compression members Shrinkage crack 1.Tension members 1.Tension members →N -tension -net area(within 150mm) 1

2013-4-19 1 Design of Wood Members Prof. He Minjuan Tongji University, Shanghai China Words and Expressions Crushing 压碎 Buckling 屈曲 Cross-bracing 交叉支撑 Bridging 剪刀撑 Notch 缺口,凹槽 (A)Symmetrically (非)对称地 Slenderness ratio 长细比 Benign 良性的 Brittle 脆性的 Shrinkage crack 收缩裂缝 Design of Wood Members 1.Tension members 2.Compression members 3.Bending members 4.Bending combined with tension members 5.Bending combined with compression members 1. Tension members 1. Tension members Ag An N N t n f A N  where —— tension —— net area (within 150mm) —— tension strength N An ft

2013-4-19 2.Compression members 园 2.Compression members 2.Compression members 2.Compression members Pin-ended struts Glulam arches and cross-bracing (交叉支撑) 2.Compression members 园 2.Compression members 园 4444 ●Material failure(crushing.压碎)TT ●Elastic buckling(Euler屈曲) a buckling and material failure) x'El P 2 m 2

2013-4-19 2 2. Compression members 2. Compression members 2. Compression members Pin-ended struts 2. Compression members Glulam arches and cross-bracing （交叉支撑） 2. Compression members Material failure (crushing,压碎) Elastic buckling (Euler屈曲) Inelastic buckling (combination of buckling and material failure) P P Δ Leff 2. Compression members 2 2 eff cr L EI P   Displacement Δ (mm) Axial load P (kN) Pcr Perfectly straight and elastic column Crooked elastic column Crooked column with material failure P P Δ Leff

2013-4-19 2.Compression members 2.Compression members (1)Strength N (2) compression 309 —trength -s f g on meml 4 calculation area of stability dered 2.Compression members 2.Compression members ” .9 8上 2.Compression members 2.Compression members 3

2013-4-19 3 2. Compression members (1) Strength where —— compression —— net area —— compression strength (2) Stability where —— coefficient of stability —— calculation area of stability N An fc  A0 c n f A N  fc A N   0 N L 2. Compression members (1) No notches: A0=A (2) Notches not at the edge: A0=0.9A (3) Notches at the edge symmetrically: A0=An (4) Notches at the edge asymmetrically: Calculation according to eccentrically compression member (5) When calculate stability, bolt holes may not considered as notches. 2. Compression members 2. Compression members 2. Compression members Pin connected Note: water damage 2. Compression members fixed or pin connected?

2013-4-19 3.Bending members 3.Bending members arallel Strand Lumber girder 3.Bending members 3.Bending members Bending failure Lateral torsional buckling Shear failure ●Notch failure ●Bearing failure Excessive deflections 3.Bending members 园 3.Bending members 园 (1)Bending failure in compression (1)Bending failure in tension Most likely failure mode ●Brittle(脆性的) Combnationofshear.atouh 1 tension fracture is the initiating moc 人1 4

2013-4-19 4 3. Bending members 3. Bending members Parallel Strand Lumber girders 3. Bending members 3. Bending members Bending failure Lateral torsional buckling Shear failure Notch failure Bearing failure Excessive deflections 3. Bending members (1) Bending failure in compression Only likely for very high grade material Benign（良性的） failure mode 3. Bending members (1) Bending failure in tension Most likely failure mode Brittle（脆性的） Combination of tension and shear, although tension fracture is the initiating mode

2013-4-19 3.Bending members 3.Bending members (1)Bending failure 6 Cuw here hendine moment net elastic section modulus f. -bending resistance strength 3.Bending members 3.Bending members 触 (2)Lateral torsional buckling (2)Lateral torsional buckling Elastic buckling:Mr=√E,Gg % wher -lateral stability factor of member in flexure.determined based on the ioof the height to width of section. ateral brace and timber strength grade ete. 3.Bending members eral suppo 3.Bending members t spacing Bridging(剪刀)for Prevention of lateral 4 torsional buckling 5 <6.5 9-1.0 <7.5TK- 5

2013-4-19 5 3. Bending members (1) Bending failure —— net elastic section modulus —— bending resistance strength m n f W M  where M —— bending moment Wn fm 3. Bending members Lateral torsional buckling of deep I-joists 3. Bending members (2) Lateral torsional buckling x x x y y y y Δx Δy θ Le 3. Bending members (2) Lateral torsional buckling m l f W M   where —— bending moment —— section modulus —— bending resistance strength —— lateral stability factor of member in flexure, determined based on the ratio of the height to width of section, lateral brace and timber strength grade etc. M fm W l 3. Bending members Prevention of lateral torsional buckling φl = 1.0 when lateral support is provided as shown h/b Lateral support at spacing: < 4 no support < 5 purlins or tie rods < 6.5 compression edge held by decking or joists < 7.5 top edge plus bridging < 9 both edges h b < 610 mm < 610 mm < 8h 3. Bending members Bridging（剪刀撑） for floor joists

2013-4-19 3.Bending members 3.Bending members (3)Shear failure (3)Shear failure 。One of the ven operties of wood （收缩裂缝)oc cur at the whereshear force,without consideration within h 5- ulus transfer of loads in the -mo ent of inertia e oe b e strength parallel to grain critical section 3.Bending members 3.Bending members (④)Notch failure 11111111111111111 盖) where—dept -net depth of the section not including the notch depth 3.Bending members 园 3.Bending members (⑤)Bearing failure notch The"soft"property of wood Ofen govems tension of the fibersa 6

2013-4-19 6 3. Bending members (3) Shear failure One of the very weak properties of wood Shrinkage cracks （收缩裂缝） often occur at the ends of beams in the zone of maximum shear stress Direct compression transfer of loads in the end zones reduces the total shear force to be carried. 45o critical section This part of the load transferred in direct compression 3. Bending members (3) Shear failure where —— shear force, without consideration within h —— area modulus —— moment of inertia —— width —— shear resistance strength parallel to grain f v Ib VS  V S I b fv 3. Bending members (4) Notch failure where —— depth —— net depth of the section not including the notch depth v n n f h h bh V          2 3 h hn 3. Bending members 3. Bending members (5) Bearing failure The “soft” property of wood Often governs Not only compression perpendicular to grain but also tension of the fibers along edges compression perpendicular to grain tension of fibres along the edges 3. Bending members bearing plate notch

2013-4-19 3.Bending members 3.Bending members (6)Excessive deflections glulam beam vhere bending membe culating detlection based on 4.Bending combined wth tension members Bk时nmm圆 (1)Strength 家玩 (2)Stability in the bending plane lastic section modulus where 5.Bending combined with compression members (3)Stability out the bending plane 谢谢/ 何装绑hca叫回tongji..edu.n out the h 7

2013-4-19 7 3. Bending members bearing plate on steel column glulam beams I joists 3. Bending members (6) Excessive deflections w  w  where —— deflection limit of a bending member —— calculating deflection based on standard load effects w  w 4. Bending combined with tension members   1 n t W nfm M A f N —— tension —— bending moment —— net area —— net elastic section modulus —— tension strength —— bending strength N M An W n ft fm where 5. Bending combined with compression members (1) Strength (2) Stability in the bending plane where ——stability factor for compression —— load combination factor   1 n c W nfm M A f N c m f A N   0  m 5. Bending combined with compression members (3) Stability out the bending plane where —— stability factor for compression out the bending plane —— lateral stability factor for bending 1 2 0           y c LWfm M A f N   y L 谢 谢！ 何敏娟 hemj@tongji.edu.cn