1

Aerospace Structures and Materials:

Postscript on Crippling

Dr. Tom Dragone

Orbital Sciences Corporation

2

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?

3

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

4

Buckling / Crippling Interaction

cL

cF

Long ColumnShort Column

E

cLF

FFcc

ccc 2

2

2

4

ccF

IncreasingFcc

“Johnson-Euler Curves”

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:

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

7

End Effects

COLUMN2 Sides Restrained

FLANGE3 Sides Restrained

PANEL4 Sides Restrained

8

Geometry Effects

LOW ASPECT RATIOSingle Buckling Wave

HIGH ASPECT RATIOMultiple Buckling Waves

9

Loading Effects

COMPRESSIONSymmetricBuckling Waves

SHEARSkewedBuckling Waves

“BENDING”OffsetBuckling Waves

10

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

11

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

12

Flat Panel Shear Buckling

2

2,

b

tEK

Fs

s

crs

From Fig 11.3.5

From Fig 11.2.5

13

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

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

Lbf

Clamped

Free

H H

15

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

16

Combined Shear / Compression

17

Skin-Stringer Panels

18

Skin-Stringer Panels

Skin Stringer

Flange

Web

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

o

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

22

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

23

ISS Node 3 Isogrid Construction

International Space Station Module

NODE

RIB

SKIN

24

Isogrid Panel Examples

Rib

Flange

Skin

Section Through Panel Grid

25

IsoGrid Geometry

• Nodes are Convenient Hard Points for Attachments

60° typ

Node

MachinedPocket

A

A

tsk tfh

Section A-A