Buckling on Stiffened Panel

AIRFRAME STATIC ANALYSIS

– BUCKLING ON STIFFENED

PANELS

Objectives for this session:

Understand critical cases for an aircraft structure

Able to perform static analysis in order to check margin

of safety of stiffened panels under critical load cases

Assumption

Majority of modern aircraft structure is highly

indeterminate structure due to its complex configuration

Accurate solution requires Finite Element Approach

For quick analysis, there are simpler approaches using

empirical data to support the theory

This empirical approach is very beneficial for analysis or

preliminary sizing at design stage; or as a quick check

toward the computer result from Finite Element calculation

or result from Experimental Test

Critical Loads

Critical Loads

Type of Stiffened Panels

Compression Panels Efficiency

Buckling

Failure Modes of Stiffened Panels

Initial Buckling Inter-Rivet Buckling Flexural Buckling

Failure Modes of Stiffened Panels

Flexural and Torsional Instability Skin WrinklingTorsional Instability

Column Buckling

Plate Buckling

2

62.3

b

tEfcr

22

22

)1(12 L

tkEfcr

2

b

tKEfcror

2

9.0

L

tEfcr

2

6.3

L

tEfcr

if,

All edges: Simply supported

Buckling Coefficients for Different Support

Conditions

Effective Width, be

st

ce

f

EKtb

Where:

fst = Stringer Compression buckling stress

Kc = Skin compression buckling coeff.

E = Young’s Modules (use Et in inelastic

range)

Effective Width: Compression Buckling

Constant, Kc

For large panel with thin skin,

(e.g wing panel near tip) as

shown in fig (a) the torsional

stiffness of a stringer is large in

Comparison to the force tending

to twist it.

This effect produces a fixed edge

condition for the panel and the

compression buckling constant,

Kc = 6.32

A narrow panel with heavy skin

(e.g. wing panels near wing root),

as shown in fig (b) produces buckling

forces so great that the stringer will

twist locally.

This panel will act as if it had

hinged edges and the buckling

constant, Kc = 3.62

Effective Width: Compression Buckling

Constant, Kc

Kc = 3.62 for b/t < 40

Kc = 6.32 for b/t >110

Between the above two

values, Kc is plotted in

the left figure:

Effective Width: an Example

"24.225000

105.108.405.0

6

1

st

ce

F

EKtb

"58.225000

105.1032.605.0

6

1

st

ce

F

EKtb

"41.22

24.258.2

2

)( 21

ee bb

Assume the allowable crippling

stress of the stringers,

Fst = 25000 psi

Determine the skin effective

width Stringer no.2.

For:

(b/t)

= 160 Kc = 6.32

(b/t)

= 60 Kc = 4.8

The effective width is

The total effective width of the no.2 stringer is:

ESDU METHODS

Engineering Science Data Unit (ESDU) for

Buckling Checks on Stiffened Panels

Local Buckling

Panels with un-flanged Integral Stiffeners

Ref: ESDU 7003

Panels with Flanged Stringers

Ref: ESDU 71014

Inter Rivet Buckling

Ref: ESDU 02.01.09

Crippling of Stringer

Ref: ESDU 78020

Local Buckling of Compression Panels with un-

Flanged Integral Stiffeners

Average elastic compressive

stress in panel at which local

buckling first occurs, fb

fb = h (fb)e

Where:

(fb)e = KE (t/b)2

Ref: ESDU 70003

Notation

Ref: ESDU 70003

Example

Ref: ESDU 70003

Ref: ESDU 70003

Local Buckling of Compression Panels with

Flanged Stringers

Average elastic compressive

stress in panel at which local

buckling first occurs, fb

fb = h (fb)e

Where:

(fb)e = KE (t/b)2

Ref: ESDU 71014

Notation

Ref: ESDU 71014

Example

Ref: ESDU 71014

Ref: ESDU 71014

Ref: ESDU 71014

Ref: ESDU 71014

Ref: ESDU 71014

Ref: ESDU 71014

Exercise

Find local buckling stress for build-up ‘Z’ stringer-

skin panel. Use the same data as in previous

example.

Inter Rivet Buckling

22

22

)1(12 s

tKEfir

Type of attachment Fixity

coefficient at

rivets, K

Universal/Flathead

rivets

4

Spotwelds 3½

Roundhead/Mushro

om or snaphead

rivets

3

Countersunk or

dimpled rivets

1 or 1½

Note that: The effective width is important in the interest of structural efficiency

and weight economy. However, If the skin buckles between rivets, it can not

carry the compression load and the calculated effective width will be erroneous

and the structure is much less efficient.

Inter Rivet Buckling

Normally the skin-stringer

construction will be designed

so that rivet spacing is derived

from the crippling stress of the stringer.

However when the inter rivet

buckling stress of the skin is reached

before the crippling stress of the stringer,

the skin exhibit the ability to maintain

the inter rivet buckling stress while

the stringer continues to take load.

Inter Rivet Buckling

Inter Rivet Buckling: - an Example

Question:

Obtain the rivet.spacing for countersunk head rivets from the following given data:

Stringer crippling stress, Fcc = 32 ksi

Skin thickness, t = 0.05”; material is 7075-T6 bare (non-clad material).

Answer:

Using Fig. 14.3.2 with Fir = Fcc = 32 ksi, go across horizontally to curve (8) for 7075-T6 material.

Go down vertically to read the rivet spacing ratio s/t = 33.5 (for universal head rivets, c = 4.0).

s = 33.5 x 0.05 = 1.68”

For countersunk head rivets, c = 1.0.

The rivet spacing of countersunk head rivet is:

s= 1.68(1.0/4.0) = 0.84”

Crippling of Stringer

fc = (c2 fb)1/2

Where:

fb = h fbe

fbe = KE (th/h)2

Ref: ESDU 78020

Notation

Ref: ESDU 78020

Example

Ref: ESDU 78020

Ref: ESDU 78020

Ref: ESDU 78020

Exercise

Calculate the crippling stress for z section. Use the

same material and the associated dimensions

Flexural Buckling

tNE

LfF

The Farrar’s efficiency

factor (F) accounts for

A pure flexural instability

(assume flexural-torsional

Coupling is small):

Where:

f – failure stress of skin stringer panel

N – end load per inch width of skin stringer panel

Et – tangent modulus

L – Length of the panel (rib or frame spacing

Flexural (Euler) Buckling