同济木结构6-Design of members

N fc m A0
where
——stability factor for compression m —— load combination factor
5. Bending combined with compression members
(3) Stability out the bending plane 2 M N 1 y A0fc LWfm where y —— stability factor for compression out the bending plane L —— lateral stability factor for bending
3. Bending members
Prevention of lateral torsional buckling
h/b h
b
<4 <5
Lateral support at spacing:
no support purlins or tie rods
< 6 1 0 mm
3. Bending members
Elastic buckling (Euler屈曲) Inelastic buckling (combination of
Leff
P
Axial load P (kN)
Crooked elastic column
P
Δ
Crooked column with material failure
Leff
Δ
buckling and material failure)
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
Bending failure
Lateral torsional buckling
Shear failure Notch failure
Bearing failure
Excessive deflections
3. Bending members
(1) Bending failure in compression
3. Bending merpendicular to grain
tension of fibres along the edges
bearing plate
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3. Bending members
glulam beams
3. Bending members
(2) Stability in the bending plane
N —— tension
M —— bending moment An —— net area W n —— net elastic section modulus ft —— tension strength fm —— bending strength
3.Bending members
4.Bending combined with tension members 5.Bending combined with compression members
1. Tension members
1. Tension members
N ft An
where
(6) Excessive deflections
w w
w
where
w —— deflection limit of a bending member
—— calculating deflection based on standard load effects
bearing plate on steel column
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
Pcr
EI
2
L2 eff
P
P
Displacement Δ (mm)
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2. Compression members
(1) Strength N fc An where N —— compression An —— net area f —— compression strength (2) Stabilityc
Bridging （剪刀撑） for floor joists
φl = 1.0 when lateral support is provided as shown
< 6.5
< 610 mm
compression edge held by decking or joists
< 8h
< 7.5
<9
top edge plus bridging
3. Bending members
(3) Shear failure VS fv Ib
where V —— shear force, without consideration within h S —— area modulus I —— moment of inertia b —— width f —— shear resistance strength parallel to grain
N
N Ag
An
N An
—— tension —— net area (within 150mm)
ft —— tension strength
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2. Compression members
2. Compression members
2. Compression members
2. Compression members
2013-4-5
Design of Wood Members
Prof. He Minjuan Tongji University, Shanghai China
Words and Expressions
Crushing 压碎
Design of Wood Members
Buckling
Cross-bracing
屈曲
交叉支撑
1.Tension members pression members
Bridging
Notch (A)Symmetrically Slenderness ratio Benign Brittle Shrinkage crack
剪刀撑
缺口,凹槽 (非)对称地 长细比 良性的 脆性的 收缩裂缝
v
3. Bending members
(4) Notch failure
3 V 2bhn
where
3. Bending members
h h n
fv
h —— depth hn —— net depth of the section not
including the notch depth
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3. Bending members
(1) Bending failure
M fm Wn
where
3. Bending members
M —— bending moment
Lateral torsional buckling of deep I-joists
W n —— net elastic section modulus
both edges
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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 This part of the stress load transferred in direct compression Direct compression transfer of loads in the end zones reduces the total shear force to be 45 o carried. critical section
Pin connected
Note: water damage
fixed or pin connected?
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3. Bending members
3. Bending members
Parallel Strand Lumber girders
3. Bending members
3. Bending members
y
M —— bending moment W —— section modulus
y
θ
x
fm —— bending resistance strength l —— lateral stability factor of member in