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**Aerospace Structures and Materials: Postscript on Crippling**

Dr. Tom Dragone Orbital Sciences Corporation

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**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?

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**Buckling / Crippling Interaction**

Radius of Gyration r = I/A Long Column Short Column

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**Buckling / Crippling Interaction**

“Johnson-Euler Curves” Increasing Fcc Long Column Short Column

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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: K depends on End Conditions (Hinged vs Clamped vs Free) Geometry (a/b) Load Type (Compression vs Shear) h depends on material plasticity

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**End Effects COLUMN 2 Sides Restrained FLANGE 3 Sides Restrained PANEL**

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**Geometry Effects LOW ASPECT RATIO Single Buckling Wave**

HIGH ASPECT RATIO Multiple Buckling Waves

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**Loading Effects COMPRESSION Symmetric Buckling Waves SHEAR Skewed**

“BENDING” Offset Buckling Waves

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**Flat Panel Compression Buckling**

Pinned Clamped From Fig Free High Aspect Ratio Lower bucking stress Less Restraint Lower buckling stress Clamp->Hinge->Free

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**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

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**Flat Panel Shear Buckling**

From Fig From Fig

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**Curved Panel Compression**

Curvature Helps Resist Buckling From Fig 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 Clamped Free H L bf

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**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)

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**Combined Shear / Compression**

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Skin-Stringer Panels

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Skin-Stringer Panels Flange Web Skin Stringer

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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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**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

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**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

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**ISS Node 3 Isogrid Construction**

RIB SKIN International Space Station Module

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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 Node**

Machined Pocket A 60° typ tsk tf h Nodes are Convenient Hard Points for Attachments Section A-A

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