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

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?

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

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

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

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

End Effects COLUMN 2 Sides Restrained FLANGE 3 Sides Restrained PANEL

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

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

Flat Panel Compression Buckling Pinned Clamped From Fig 11.3.1 Free High Aspect Ratio Lower bucking stress Less Restraint Lower buckling stress Clamp->Hinge->Free

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

Flat Panel Shear Buckling From Fig 11.3.5 From Fig 11.2.5

Curved Panel Compression Curvature Helps Resist Buckling From Fig 11.4.1 Flat Plate Highly Curved Panel

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

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)

Combined Shear / Compression

Skin-Stringer Panels

Skin-Stringer Panels Flange Web Skin Stringer

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

Combined Panel Failure Modes

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

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

ISS Node 3 Isogrid Construction RIB SKIN International Space Station Module

Isogrid Panel Examples Rib Flange Skin Section Through Panel Grid

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