Bombardier Strength Manual
Bombardier Inc. B3907002 Buckling of Beam Webs
CAGE CODE 3AB48
1.0
BUCKLING OF BEAM WEBS - INTRODUCTION This section deals with beam webs which are designed to be non-buckling. Collapsing strength of Beam webs is considered in Section B3907003. B3907003.
2.0
GENERAL NOTATION
t D
h
h
w
Formed
Built up
Figure 1 Geometry of Shear beam a
larger beam dimension, in above sketch beam width w .
b
minimum beam dimension, in above sketch, beam height h.
D
hole diameter
E
modulus of elasticity
E c
modulus of elasticity in compression
f s
applied shear stress
h
height of beam, full height for a formed f ormed beam, between rivet lines for built up beam.
K s
shear buckling coefficient, ref. Section B3908001, B3908001, Figure 8. 8.
w
width of beam
q
shear flow
t
web thickness
η
plasticity reduction factor, ref. Section B3908001
η cl υ
3 .0
e
cladding reduction factor, need only be used if using bare material mechanical properties on clad material, ref. Section B3908001. B3908001. poisson's elastic ratio.
BUCKLING STRESS OF A PLAIN WEB. Web buckling Stress is given by,
2 2 t π F = η ⋅ η ⋅ ⋅ K ⋅ E ⋅ sb cl s b 2 12 ⋅ 1 − υ e B3907002
ISSUE: A
DATE: 28 AUGUST 1996
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Bombardier Strength Manual
Bombardier Inc.
CAGE CODE 3AB48
4.0
Applied shear stress
Margin of Safety
q f = s t
F M . S . = sb − 1 f s
BEAM WEBS WITH UNREINFORCED CIRCULAR HOLE. Buckling Stress for beams that are approximately square, i.e. a ≤ 1. 2b , is given by:
2 2 π t ⋅ K ⋅ E ⋅ ⋅ φ F = η ⋅ η ⋅ sb cl s b 1 12 ⋅ 1 − υ 2 o e or,
= F ⋅ φ F 1 sb sb o where:
F sb o
buckling stress of a panel with unreinforced hole.
F sb
buckling stress of panel without hole, ref. Paragraph 3.0.
φ 1
hole influence factor, from Figure 2. Valid for square or nearly square panels with a ≤ 1. 2b . 1 0.9 0.8 0.7 0.6
φ
0.5
1
0.4 0.3 0.2 0.1 0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
D/b
Figure 2 Hole influence factor, φ , for beam with unreinforced circular hole.
1
B3907002
ISSUE: A
DATE: 28 AUGUST 1996
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Bombardier Strength Manual
Bombardier Inc.
CAGE CODE 3AB48
4.1
Applied gross shear stress
Margin of Safety
q f = s t
F sb o −1 M . S . = f s
Maximum Stress level around hole edges This method applies to beams that are approximately square, so that a ≤ 1. 2b
T
C
q T, marks the position of maximum tensile stress
q
C
T
C, marks the position of maximum compressive stress
Figure 3 Maximum local stress levels, tension of compression, at hole edges may be obtained from :
f
max
= f ⋅ C Sa h
Where:
C h
stress concentration factor, ref. Figure 4. Valid for square or nearly square panels with
a ≤ 1. 2b .
f maximum direct stress acting at hole boundary max f Sa
B3907002
average shear stress applied to plate edges, gross area
ISSUE: A
DATE: 28 AUGUST 1996
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Bombardier Strength Manual
Bombardier Inc.
CAGE CODE 3AB48
20 18 16 14 12
C
h
10 8 6 4 2 0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Figure 4 D / b Stress concentration factor around circular hole.
5.0
BEAM WEBS WITH REINFORCED CIRCULAR HOLE This method applies to beams that are approximately square, so that a ≤ 1. 25 ⋅ b . The hole reinforcement may take the form of a web thickness increase or forming around the hole edge, as shown in Figure 5. In the case of flanged lightening holes the dimension 'D ' is equivalent to hole outside diameter. Whilst 'D ' is the inside diameter for a web with a thickness increase around the hole. The design standards for Flanged lightening holes are contained in SB0604005.
b
r=t
r
D
hr
effective height of hole reinforcement
r
effective width of hole reinforcement
r=t
r=t
D
D
h r D
Figure 5 Geometry of beam with reinforced circular hole. Buckling stress of a panel with a reinforced hole.
B3907002
ISSUE: A
DATE: 28 AUGUST 1996
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Bombardier Strength Manual
Bombardier Inc.
CAGE CODE 3AB48
2 2 t π ⋅ K ⋅ E ⋅ ⋅ φ = η⋅ η ⋅ cl 12 ⋅ 1 − υ e2 s b 2
F sb R
or, F = F sb ⋅ φ 2 sb R
where
F sb
buckling stress of panel without hole, ref. Paragraph 3.0.
F sb R
buckling stress of panel with reinforced hole.
φ
influence factor of reinforcing - ref. Figure 6, Figure 7, Figure 8
2 4
D / r
10
3. 5 20 3 50 2. 5
10 0 20 0
φ
2
2
1. 5 1 0. 5
0 1
2
3
4
5
h r
6
7
ISSUE: A
9
10
t
Figure 6 Influence factor of reinforcing
B3907002
8
D/b =0.25.
DATE: 28 AUGUST 1996
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Bombardier Strength Manual
Bombardier Inc.
CAGE CODE 3AB48
3 D / r
50
2. 5 10 0 20 0
2
φ
2
1. 5
1
0. 5
0 1
2
3
4
5
h r
6
7
8
9
10
t
Figure 7 Influence factor of reinforcing
D/b =0.5.
1. 8 50
D / r
1. 6 10 0 1. 4
20 0
1. 2 1
φ
2
0. 8 0. 6 0. 4 0. 2 0 1
2
3
4
5
h r
6
7
ISSUE: A
9
10
t
Figure 8 Influence factor of reinforcing
B3907002
8
D/b =0.75.
DATE: 28 AUGUST 1996
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Bombardier Strength Manual
Bombardier Inc.
CAGE CODE 3AB48
Applied gross shear stress
F sb R − 1 M . S . = f s
q
f = s t
6.0
Margin of Safety
BEAMS WITH FLANGED LIGHTENING HOLES - NO STIFFENERS The design standards for Flanged lightening holes are contained in SB0604005 Paragraph 5.0.
Bent web attached to skin b
d
D
A
Figure 9 Geometry of beam with Flanged lightening holes.
or,
2 2 π t ⋅ K ⋅ H ⋅ E ⋅ F = η⋅ η ⋅ sb cl s b 2 h 12 ⋅ 1 − υ e = H ⋅ F F sb sb h
B3907002
ISSUE: A
DATE: 28 AUGUST 1996
PAGE 7 OF 9
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Bombardier Strength Manual
Bombardier Inc.
CAGE CODE 3AB48
where :
K s
shear buckling coefficient for panel size 'A' x 'b', ref. Section B3908001, figure 8.
A
hole separation
F sb h
critical Buckling of a panel with flanged lightening holes.
F sb H
buckling stress of panel without hole, assume panel size is 'A' by 'b', ref. Paragraph 3.0. factor to account for presence of holes, see Figure 8.
1.60 1.40
D / A
1.20
0.65 0. 6
1.00 0.55
H
0.80 0.60
0. 8
0.40
0. 7
0.75
0.20 0.00 50
100
150
b
200
250
300
t
Figure 10 H , Buckling correction factor to account for presence of holes.
Applied gross shear stress
q
f = s t
B3907002
ISSUE: A
Margin of Safety
F sb h −1 M . S . = f s
DATE: 28 AUGUST 1996
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Bombardier Strength Manual
Bombardier Inc.
CAGE CODE 3AB48
7.0
BEAMS WITH VERTICAL CORRUGATIONS AND FLANGED LIGHTENING HOLES
h
D
A
A
Corrugations Section 'AA' Figure 11 The method presented here is for a lightly loaded clad 2024 T4 or 7075 T6 panel in pure shear with beaded holes and interpitched corrugations. It will only apply if the corrugations are formed long enough to extend as close to the beam flanges as assembly will allow.
q
The allowable buckling shear flow, b , for the web is read directly from Figure 12. The curves are
b D o ≈ 0. 6 and s ≈ 1. 0 . valid for a beam with bead depth ≈ 0. 25 ins, h h 40 0
h c 35 0 n i r e 30 0 p s b l 25 0 -
0.072
0.064
web thickness, t 0.051 0.04
w o 20 0 l f r a e 15 0 h S g 10 0 n i l k c 50 u B
0.032
0.025
0 2
3
4
5
6
7
8
9
10
11
12
13
14
Height of the web, h - ins
q
Figure 12 Buckling shear flow, b , for a beam with beaded holes and interpitched vertical corrugations. Margin of Safety
q M . S .= b − 1 q
B3907002
ISSUE: A
DATE: 28 AUGUST 1996
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