同济大学木结构第六章 木结构力学性能
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w —— calculating deflection based on
standard load effects
3
Notch
Bearing failure
The “soft” property of wood
Not only compression perpendicular to grain but also tension of the fibres along edges
f m —— bending resistance strength
Lateral torsional buckling of deep I-joists
Lateral torsional buckling
Elastic buckling: Mcr = π / Le (G J E Iy )0.5
Torsional stiffness
Lateral bending stiffness
Le
y x
y
y
Δx
Δy x
θ
x
y
Lateral torsional
buckling
M ϕlW
≤
fm
where M —— bending moment W —— section modulus
f m —— bending resistance strength ϕl —— lateral stability factor of member in
Combination of tension and shear, although tension fracture is the initiating mode
Bending failure
M Wn
≤
fm
where
M —— bending moment Wn —— net elastic section modulus
N + M ≤1 An f t Wn f m
where
N —— tension M —— bending moment An —— net area Wn —— net elastic section modulus ft —— tension strength fm —— bending strength
but,
Direct compression transfer of loads in the end zones reduces the total shear force to be carried.
This part of the load transferred in direct compression
Notch failure
3V 2bhn
⎜⎜⎝⎛
h hn
⎟⎟⎠⎞ ≤
fv
where h —— depth
hn —— net depth of the section not including the notch depth
Excessive deflections
w ≤ [w]
[ ] where w —— deflection limit of a bending member
ϕL —— lateral stability factor for bending
Reading Materials
《木结构设计》（Timber Engineering）
（中国建筑工业出版社） 《木结构设计规范》（GB 50005-2003）
5
decking or joists
< 610 mm
top edge < 8d plus bridging
<9
both edges
Bridging for floor joists
Shear failures
One of the very weak properties of wood，and
Shrinkage cracks often occur at the ends of beams in the zone of maximum shear stress.
3.4 Bending Members
Bending Test
Parallel Strand Lumber girders
Bending Test
Bending Test
What can go wrong ?
Bending failure Lateral torsional buckling Shear failure Notch failure Bearing failure Excessive deflections
ϕl = 1.0
when lateral support is provided as shown
h/b h
b
<4
Lateral support at spacing:
no support
<5 < 6.5 < 7.5
purlins or tie rods
< 610 mm compression e来自百度文库ge held by
flexure, determined based on
the ratio of the height to width of section,
lateral brace and timber strength grade etc.
2
Prevention of lateral torsional
buckling
1
Bending failure in compression
Only likely for very high grade material Bending failure mode
Bending failure in tension
Most likely failure mode
Brittle
4
Bending combined with compression member
③ Stability out the bending plane
N ϕ y A0
fc
+
⎜⎜⎝⎛
ϕ
M LWf
m
⎟⎟⎠⎞ 2
≤1
where ϕ y —— stability factor for compression out the bending plane
3.6 Bending combined with compression member
① strength
N + M ≤1 An f c Wn f m
② Stability in the bending plane
N ϕϕm A0
≤
fc
where ϕ ——stability factor for compression ϕm —— load combination factor
45o
critical section
Shear failure
VS Ib
≤
fv
where V —— shear force, without consideration within h S —— area modulus I —— moment of inertia b —— width f v —— shear resistance strength parallel to grain
tension of fibres along the edges
compression perpendicular to grain
notch bearing plate
glulam beams
bearing plate on steel column
I joists
3.5 Bending combined with tension member
standard load effects
3
Notch
Bearing failure
The “soft” property of wood
Not only compression perpendicular to grain but also tension of the fibres along edges
f m —— bending resistance strength
Lateral torsional buckling of deep I-joists
Lateral torsional buckling
Elastic buckling: Mcr = π / Le (G J E Iy )0.5
Torsional stiffness
Lateral bending stiffness
Le
y x
y
y
Δx
Δy x
θ
x
y
Lateral torsional
buckling
M ϕlW
≤
fm
where M —— bending moment W —— section modulus
f m —— bending resistance strength ϕl —— lateral stability factor of member in
Combination of tension and shear, although tension fracture is the initiating mode
Bending failure
M Wn
≤
fm
where
M —— bending moment Wn —— net elastic section modulus
N + M ≤1 An f t Wn f m
where
N —— tension M —— bending moment An —— net area Wn —— net elastic section modulus ft —— tension strength fm —— bending strength
but,
Direct compression transfer of loads in the end zones reduces the total shear force to be carried.
This part of the load transferred in direct compression
Notch failure
3V 2bhn
⎜⎜⎝⎛
h hn
⎟⎟⎠⎞ ≤
fv
where h —— depth
hn —— net depth of the section not including the notch depth
Excessive deflections
w ≤ [w]
[ ] where w —— deflection limit of a bending member
ϕL —— lateral stability factor for bending
Reading Materials
《木结构设计》（Timber Engineering）
（中国建筑工业出版社） 《木结构设计规范》（GB 50005-2003）
5
decking or joists
< 610 mm
top edge < 8d plus bridging
<9
both edges
Bridging for floor joists
Shear failures
One of the very weak properties of wood，and
Shrinkage cracks often occur at the ends of beams in the zone of maximum shear stress.
3.4 Bending Members
Bending Test
Parallel Strand Lumber girders
Bending Test
Bending Test
What can go wrong ?
Bending failure Lateral torsional buckling Shear failure Notch failure Bearing failure Excessive deflections
ϕl = 1.0
when lateral support is provided as shown
h/b h
b
<4
Lateral support at spacing:
no support
<5 < 6.5 < 7.5
purlins or tie rods
< 610 mm compression e来自百度文库ge held by
flexure, determined based on
the ratio of the height to width of section,
lateral brace and timber strength grade etc.
2
Prevention of lateral torsional
buckling
1
Bending failure in compression
Only likely for very high grade material Bending failure mode
Bending failure in tension
Most likely failure mode
Brittle
4
Bending combined with compression member
③ Stability out the bending plane
N ϕ y A0
fc
+
⎜⎜⎝⎛
ϕ
M LWf
m
⎟⎟⎠⎞ 2
≤1
where ϕ y —— stability factor for compression out the bending plane
3.6 Bending combined with compression member
① strength
N + M ≤1 An f c Wn f m
② Stability in the bending plane
N ϕϕm A0
≤
fc
where ϕ ——stability factor for compression ϕm —— load combination factor
45o
critical section
Shear failure
VS Ib
≤
fv
where V —— shear force, without consideration within h S —— area modulus I —— moment of inertia b —— width f v —— shear resistance strength parallel to grain
tension of fibres along the edges
compression perpendicular to grain
notch bearing plate
glulam beams
bearing plate on steel column
I joists
3.5 Bending combined with tension member