Thin-walled structures. Normal stresses Lecture #5 Thin-walled structures. Normal stresses

FOREWORD 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. 2

TYPES OF SHELL 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 case Hard to realize in practice, but typical for thin shells 3

Vertical displacement plot TYPES OF SHELL Vertical displacement plot Not stiffened shell Stiffened shell 4

TYPES OF SHELL Bending stress plot Not stiffened shell Stiffened shell 5

TRUSS STIFFENING OF THE SKIN Junkers F.13, Germany, 1920 6

GEODESIC STIFFENING OF THE SKIN AT FUSELAGE Vickers Wellington, Great Britain, 1938 7

THIN-WALLED STRUCTURES (modern design) 8

THIN-WALLED STRUCTURES (modern design) 9

STRUCTURAL MEMBERS Longitudinal Lateral Wing Spar caps, stringers and skin (panel) Ribs Fuselage Stringers and skin (panel), beams Frames 10

HISTORICAL PROGRESS OF AIRCRAFT STRUCTURES 1903-1920. Truss structures, unstressed skin The skin is not much stressed 11

HISTORICAL PROGRESS OF AIRCRAFT STRUCTURES 1920-1930. Monoplanes and corrugated skin introduced The skin carries only shear stresses Tupolev TB-3, Soviet Union, 1932 Take-off mass 19 500 kg, wingspan 39.5 m 12

HISTORICAL PROGRESS OF AIRCRAFT STRUCTURES 1930-1940. Aluminium extensively used, stressed skin. The skin carries both normal and shear stresses Messerschmitt Bf.109, Germany, 1935 Take-off mass 3 375 kg, max. speed 720 km/h 13

NORMAL STRESSES IN THIN-WALLED BEAMS The distribution of normal stresses obeys the hypothesis of planar cross sections: For the case of uniform linear material, it comes to be: 14

CROSS SECTION DISCRETIZATION 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. 15

CROSS SECTION DISCRETIZATION The problem is to find the moment of inertia. Dimensions: a = 60 mm; h = 22 mm; d1 = 4 mm; d2 = 6 mm; H = 120 mm. 16

CROSS SECTION DISCRETIZATION 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). 17

CROSS SECTION DISCRETIZATION Another option is to use concentrated areas instead of stiffeners and webs. Result: 997 cm4 (exact value: 975 cm4; 2.5% error). 18

… Internet is boundless … WHERE TO FIND MORE INFORMATION? Megson. An Introduction to Aircraft Structural Analysis. 2010 Chapter 15 … Internet is boundless … 19

Method of reduction coefficients TOPIC OF THE NEXT LECTURE Normal stresses. Method of reduction coefficients All materials of our course are available at department website k102.khai.edu 1. Go to the page “Библиотека” 2. Press “Structural Mechanics (lecturer Vakulenko S.V.)” 20