Post on 31-Mar-2015
transcript
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Aerospace Structures and Materials:
Postscript on Crippling
Dr. Tom Dragone
Orbital Sciences Corporation
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Buckling / Crippling Interaction
2
2
cL
EIcPE
Long Column• Length Critical• Euler Buckling Applies
Short Column• Cross Section Critical• Crippling Applies
ii
icciicc tb
FtbF ,
What if the column
is somewherein between?
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Buckling / Crippling Interaction
2
2
2
2
2
2
cL
Ec
Ac
L
EIcF
cL
EIcP
c
E
Radius of Gyration = I/A
Long ColumnShort Column
cL
cF
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Buckling / Crippling Interaction
cL
cF
Long ColumnShort Column
E
cLF
FFcc
ccc 2
2
2
4
ccF
IncreasingFcc
“Johnson-Euler Curves”
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Aerospace Structures and Materials:
Compression Panel Design
Dr. Tom Dragone
Orbital Sciences Corporation
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Compression Panel Design
• Stability Equation is Analogous to Euler Buckling:
2
22
2
32
2
2
1212 L
Etc
btL
Ebtc
AL
EIcFcr
2
2
b
tKEFcr
K depends on • End Conditions (Hinged vs Clamped vs Free)• Geometry (a/b)• Load Type (Compression vs Shear)
depends on material plasticity
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End Effects
COLUMN2 Sides Restrained
FLANGE3 Sides Restrained
PANEL4 Sides Restrained
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Geometry Effects
LOW ASPECT RATIOSingle Buckling Wave
HIGH ASPECT RATIOMultiple Buckling Waves
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Loading Effects
COMPRESSIONSymmetricBuckling Waves
SHEARSkewedBuckling Waves
“BENDING”OffsetBuckling Waves
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Flat Panel Compression Buckling
2
2,
b
tEK
Fc
c
crc
• High Aspect Ratio– Lower bucking stress
From Fig 11.3.1
Clamped
Pinned
Free• Less Restraint
– Lower buckling stress
– Clamp->Hinge->Free
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Plasticity Effects
• Buckling Resisted by Bending Stress
• Yielding Limits Bending Stress and Reduces Buckling Resistance
• Peak Panel Stress is Much Higher than Average Stress
• Local Yielding Occurs Even if Average Stress < Yield Stress
• True Buckling Stress < Elastic Buckling Stress
• Accounted for by • is Different for Comp vs Shear
• is Depends on Material
Plastic Buckling Stress
Elastic Buckling StressFrom Equation
2
2
b
tEKc
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Flat Panel Shear Buckling
2
2,
b
tEK
Fs
s
crs
From Fig 11.3.5
From Fig 11.2.5
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Curved Panel Compression
• Curvature Helps Resist Buckling
2
2
2
2,
112 b
tE
kF c
c
crc
From Fig 11.4.1
22
1 Rt
bZ
Flat Plate Highly Curved Panel
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Local Buckling
• Instability of the Free Segments of Stringers, Frames, Longerons, Beams, Columns
• Can Be Predicted by Treating the Segment as a Long Panel (a/b>>1) with a Single Free Edge
Lbf
Clamped
Free
H H
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Combined Loading
• Implication:– Cannot use typical margin calculation
– Must use graphical method (or numerical)
What if: %50%65,,
crscrc
x
Ftq
Ft
NWill structure fail?
Rs
Rc
1.0
1.0
DefineStress Ratios:
crc
cc FR
,
crss FR
,
Absolute: Rc=1 Rs=1
Linear: Rc + Rs = 1
Actual: Rc2 + Rs = 1
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Combined Shear / Compression
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Skin-Stringer Panels
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Skin-Stringer Panels
Skin Stringer
Flange
Web
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Skin-Stringer Panels
So far, we have treated skin-stringer panels as independent elements
• Skin Buckling Between Stringers => Panel with Hinged Ends• Stringer Column Buckling => Euler Buckling• Stringer Flange Buckling => Local Long Panel Buckling• Stringer Crippling => Crippling Failure
There are other failure modes to consider
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Combined Panel Failure Modes
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i
f
f
sk
stA
A
sk
w
t
t
Skin-Stringer Panel Design
• Proper Design of Skin-Stringer Panels Can Increase Buckling Strength
No Stringers
ActualBuckling Stress
Hinged PanelBuckling Stress
Lateral / Torsional InstabilityStiff Stringer / Thin Skin
Skin Bucklingwith Clamped Ends
Mode Change
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IsoGrid Panels
• Skin-Stringer Panels – Very Weight Efficient
– Resist Loads in One Direction Only
– Weak in Transverse Direction
• Sandwich Panels– Bidirectional Strength/Stiffness
– Interior Cannot Be Inspected
• Isogrid Construction– Isotropic In-Plane Strength and Stiffness
– Can Be Easily Inspected
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ISS Node 3 Isogrid Construction
International Space Station Module
NODE
RIB
SKIN
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Isogrid Panel Examples
Rib
Flange
Skin
Section Through Panel Grid
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IsoGrid Geometry
• Nodes are Convenient Hard Points for Attachments
60° typ
Node
MachinedPocket
A
A
tsk tfh
Section A-A