1. Aerospace Structures and Materials: Postscript on Crippling
Dr. Tom Dragone
Orbital Sciences Corporation

2. Buckling / Crippling Interaction
Long Column
Length Critical
Euler Buckling Applies
Short Column
Cross Section Critical
Crippling Applies
What if the column
is somewhere
in between?

3. Buckling / Crippling Interaction
Radius of Gyration
r = I/A
Long Column
Short Column

4. Buckling / Crippling Interaction
“Johnson-Euler Curves”
Increasing
Fcc
Long Column
Short Column

5. Aerospace Structures and Materials: Compression Panel Design
Dr. Tom Dragone
Orbital Sciences Corporation

6. Compression Panel Design
Stability Equation is Analogous to Euler Buckling:
K depends on
End Conditions (Hinged vs Clamped vs Free)
Geometry (a/b)
Load Type (Compression vs Shear)
h depends on material plasticity

7. End Effects COLUMN 2 Sides Restrained FLANGE 3 Sides Restrained PANEL

8. Geometry Effects LOW ASPECT RATIO Single Buckling Wave
HIGH ASPECT RATIO
Multiple Buckling Waves

9. Loading Effects COMPRESSION Symmetric Buckling Waves SHEAR Skewed
“BENDING”
Offset
Buckling Waves

10. Flat Panel Compression Buckling
Pinned
Clamped
From Fig
Free
High Aspect Ratio
Lower bucking stress
Less Restraint
Lower buckling stress
Clamp->Hinge->Free

11. Elastic Buckling Stress
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 h
h is Different for Comp vs Shear
h is Depends on Material
Plastic
Buckling Stress
Elastic Buckling Stress
From Equation

12. Flat Panel Shear Buckling
From Fig
From Fig

13. Curved Panel Compression
Curvature Helps Resist Buckling
From Fig
Flat Plate
Highly Curved Panel

14. 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
Clamped
Free H L bf

15. Combined Loading Implication: What if: Will structure fail? Define
Stress Ratios: Rs Rc
1.0
Actual: Rc2 + Rs = 1
Linear: Rc + Rs = 1
Absolute: Rc=1 Rs=1
Implication:
Cannot use typical margin calculation
Must use graphical method (or numerical)

16. Combined Shear / Compression

17. Skin-Stringer Panels

18. Skin-Stringer Panels
Flange
Web
Skin
Stringer

19. 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

20. Combined Panel Failure Modes

21. Skin-Stringer Panel Design
Proper Design of Skin-Stringer Panels Can Increase Buckling Strength
Actual
Buckling Stress
Mode Change
Skin Buckling
with Clamped Ends
Hinged Panel
Buckling Stress
Lateral / Torsional Instability
Stiff Stringer / Thin Skin
No Stringers

22. IsoGrid Panels Skin-Stringer Panels Sandwich 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

23. ISS Node 3 Isogrid Construction
RIB
SKIN
International Space Station Module

24. Isogrid Panel Examples
Rib
Flange
Skin
Section Through Panel Grid

25. IsoGrid Geometry Nodes are Convenient Hard Points for Attachments Node
Machined
Pocket A
60° typ
tsk tf h
Nodes are Convenient Hard Points for Attachments
Section A-A