User:Eas4200c.f08.aero6.ortega

Leactures 1-4: 8/25/2008 - 9/1/2008 For this class we will be submitting homework through Wikiversity. The homework assignments will include lecture summaries, assigned homework problems, and extra group contributions. The advantage to submitting assignments this way is that the knowledge can be shared.

The following is an outline of material presented in the text, Mechanics of Aircraft Structures by C.T. Sun

Preface Notes Second Edition modifications include material on the following topics: Primary Warping Boundary Constraint Effects Saint-Venant’s Principle Shear Lag Timoshenko Beam Theory Plasticity and Fracture

Preface to First Edition Three main tasks of the text include: 1. FEA modeling of problems and judging correctness of numerical results. Realizing new FEA codes have recently revolutionized the field of structural analysis in all mechanical applications. 2. Fracture mechanics 3. Composite properties in aircraft structures, brief study of laminates and the calculation of Young’s modulus derived from directional displacements as opposed to isotropic alloy mechanics for the purpose of describing torsion and bending problems. In addition, Griffith’s Criterion is introduced for describing the relation between the strain energy release rate and crack extension. Also, buckling and post-buckling of bars and panels utilized in aircraft structures is introduced.

Chapter 1: Characteristics of Aircraft Structures and Materials Introduction Weight is the main consideration in aircraft structure design, unlike the structures of most civil engineering applications. Also, an aircraft’s structural design is modeled after the primary concern of the components, such as lift/drag considerations. Thus, limiting structural design options and resorting to material of the highest strength to weight ratios. Aircraft components typically follow the shell-like monocoque or stiffened shell semimonocoque structure. In the past, aluminum and titanium alloys have been the material of choice in aircraft design due to their high stiffness/weight and strength/weight ratios. Today, fiber-reinforced composites are replacing much of the weight in designs. Basic structural loads of an aircraft include axial, bending or torsional.

Axial Member

Recall $$F = A\sigma = EA\epsilon\!$$

$$E\!$$ and $$\epsilon\!$$ are the Young’s modulus and normal strain in the loading direction and $$F\!$$ is the total axial force. $$EA\!$$ is termed axial stiffness and is independent of the shape of the cross-section, rather determined by modulus and cross-sectional area. Channels are used in place of rods to increase bending stiffness. Buckling strength is enhanced by adding lateral supports such as ribs and frames. -Insert diagram pg 4.

Shear Panel These are thin sheets of material that carries in-plane shear loads. In the following formula: $$V_x = \tau ta = G\gamma ta\!$$

G is shear modulus, $$\gamma$$ is shear strain, $$t$$ is thickness.



Curved plates may have their shear stress loads decomposed into Vx and Vy. Due to the ratio of geometric value in the x/y directions and the corresponding shear stresses, a flat plate is the most efficient in providing shear force per unit of material.

Bending Member These are members that carry a moment (Beams). Beams can also carry axial loads in tension or compression. Bending moments depend of beam deflection. Bending stresses lead to transverse stresses, however bending is still the dominant role. Again, optimizing the cross-sections of beams is the key to increase bending stiffness. To utilize a materials full capacity, the cross-section should move material as far from the neutral axis as possible to take advantage of the linearity of the bending stress distribution over depth in the elastic range. Ex. is the I-beam.

Torsion Torque induced shear stress τ is also linearly distributed along the cross-section just now in the radial direction. $$T=GJ\theta\!$$ where J is torsional constant. GJ is torsional stiffness. Thin walled structures are very efficient torsional members.

Load Transfer Box beams due well to illustrate the beam and torsional members of aircraft substructure design. Loads generally are caused by air-pressure, landing gears, power-plants and seats, etc. Box beams are this sheets (shear panel) and longitudinal stringers (axial members) that distribute loads to major load-carrying members to avoid excessive deflection. Ribs collect all transverse loads from the stringers and transfer them to two wide-flange beams (spars).

Wing and Fuselage Structures Main wing function is to carry air and power-plant loads to the fuselage. The wing itself acts as a beam and torsional member with an outer form designed by aerodynamic considerations. Spars are heavy beams that run span-wise to take transverse shear and bending loads. Wing ribs are planar structures that hold stringers to the desired contour and improve compressive ability of the wing. They are supported by span-wise spars. Subsonic aircraft have relatively thin skins and utilize spars and stringers as the main bending resistance. These wings may be composed of simple spars or a combination of spars and stringers. Supersonic wings on the other hand have thinner airfoils, at the same time requiring thicker skins to withstand high surface air-loads and improve bending resistance of the wing. To improve efficiency, stiffeners may be manufactured as integral parts of the wing. The fuselage must be designed to handle concentrated loads from wings and landing gears primarily. Also, payload and internal pressures must be supported. Again, stringers run along the length of the fuselage and rings maintain the shape of the fuselage and shorten the stringer length, increasing its bending resistance.

Aircraft Materials These materials include metal alloys, such as steel, aluminum and titanium, and fiber-reinforced composites of either polymer, metal or ceramic matrices. Costs and properties of materials dictate their usage in design. Costs include manufacturing, maintaining and of course initial bulk. Properties vital to performance are density, strength, stiffness, durability, damage tolerance and corrosion resistance. Steel alloys are denser and corrosion prone so they are used for highly loaded critical points and must be coated. Aluminum alloys range from higher strength to higher toughness; yet both are light-weight and serve vital tasks at different sections of the aircraft. Titanium is lighter and stronger than steel but much more expensive and therefore used mostly in military aircraft. They also withstand higher temperatures than aluminum (350o F versus 1000o F). Fiber-reinforced composites usually employ unidirectional fibers of high tensile strength in a matrix of polymer, metal or ceramic material. These sections form thin laminae with a stacking pattern of different fiber orientations to produce laminates with excellent material properties and multidirectional load capabilities. Ceramic composites in particular have excellent heat resistance, fatigue life, damage tolerance and corrosion resistance.

]]