Lecture #5Thin-walled structures.Normal stresses

FOREWORD

2

Modern aircraft structures are usually thin-walled beams (shell beams).

“Thin-walled” means that one of dimensions (thickness) is much smaller than others. Thus, the middle surface could be specified.

Shells could be stiffened and not stiffened.

Stiffeners are used to:a) support the skin from buckling;b) optimize the stress state.

General shell Membrane shell

The stress state is formed by membrane and bending

stresses

Stresses are uniformly distributed along the

thickness (only membrane stresses)

Less effective Most effective

General caseHard to realize in practice, but typical for thin shells

3

TYPES OF SHELL

TYPES OF SHELL

Vertical displacement plot

4

Stiffened shell

Not stiffened shell

TYPES OF SHELL

Bending stress plot

5

Stiffened shell

Not stiffened shell

TRUSS STIFFENING OF THE SKIN

6

Junkers F.13,Germany, 1920

GEODESIC STIFFENING OF THE SKIN AT FUSELAGE

7

Vickers Wellington, Great Britain, 1938

THIN-WALLED STRUCTURES (modern design)

8

THIN-WALLED STRUCTURES (modern design)

9

Longitudinal Lateral

WingSpar caps, stringers

and skin (panel)Ribs

FuselageStringers and skin

(panel), beamsFrames

10

STRUCTURAL MEMBERS

HISTORICAL PROGRESS OF AIRCRAFT STRUCTURES

1903-1920. Truss structures, unstressed skin

11

The skin is not much stressed

HISTORICAL PROGRESS OF AIRCRAFT STRUCTURES

1920-1930. Monoplanes and corrugated skin introduced

Tupolev TB-3, Soviet Union, 1932Take-off mass 19 500 kg, wingspan 39.5 m

12

The skin carries only shear stresses

HISTORICAL PROGRESS OF AIRCRAFT STRUCTURES

1930-1940. Aluminium extensively used, stressed skin.

Messerschmitt Bf.109, Germany, 1935Take-off mass 3 375 kg,max. speed 720 km/h

13

The skin carries both normal and shear stresses

NORMAL STRESSES IN THIN-WALLED BEAMS

14

The distribution of normal stresses obeys the hypothesis of planar cross sections:

,w x y a b x c y

For the case of uniform linear material, it comes to be:

, yz xz

y x

MN Mx y x y

A I I

CROSS SECTION DISCRETIZATION

15

The discretization of real cross section is usually used to possess the calculations of moments of inertia and other geometrical properties:

- small but complex elements like stringers are substituted by point areas;

- skins are substituted by center lines;

- complex center line is substituted by polygonal curve.

CROSS SECTION DISCRETIZATION

16

The problem is to find the moment of inertia.Dimensions:a = 60 mm; h = 22 mm; 1 = 4 mm; 2 = 6 mm;H = 120 mm.

CROSS SECTION DISCRETIZATION

17

One option is to substitute the real cross section by center lines with appropriate thicknesses.

Result:1000 cm4

(exact value:975 cm4;2.5% error).

CROSS SECTION DISCRETIZATION

18

Another option is to use concentrated areas instead of stiffeners and webs.

Result:997 cm4

(exact value:975 cm4;2.5% error).

WHERE TO FIND MORE INFORMATION?

19

Megson. An Introduction to Aircraft Structural Analysis. 2010Chapter 15

… Internet is boundless …

TOPIC OF THE NEXT LECTURE

20

Normal stresses.Method of reduction coefficients

All materials of our course are availableat department website k102.khai.edu

1. Go to the page “Библиотека”2. Press “Structural Mechanics (lecturer Vakulenko S.V.)”