User:Eas4200c.f08.radsam/Structures and Materials

=1.1 - Introduction= Weight is the key differing factor between aerospace structures and all other structures. It is also the focus of aerospace material design and development, in that materials with high strength and stiffness and light weight are constantly being sought out.

No excess material is allowed in the design of aircraft, and this point alone is a major driving factor for the direction taken in aircraft design. Further still, more restrictions are in place when designing, say, wing structures, in that the wings are originally formed for maximum aerodynamic performance--not structural integrity. Thus, structural solutions are forced to conform to the original aerodynamic designs, reducing the degree of freedom one has in terms of those solutions.

Traditionally, metals such as aluminum and titanium have been employed to fulfill necessary design requirements. Recently, however, advanced composites have been used more and more and at a weight savings of up to 40% over customary metals, too. As an example, the latest Boeing airliner--the 787--uses up to 50 percent composites in its structural components.

=1.2 - Basic Structural Elements in Aircraft Structure= Aircraft structures are composed of several structural elements, which are designed to withstand various types of loads. It is the combination of these elements that make the entire structure of an aircraft capable of resisting applied loads.

For better comprehension of structural mechanics, we must introduce a few important definitions:


 * Stiffness: It is an extensive material property that determines the resistance of an elastic body to deflection. In Engineering, the modulus on elasticity or Young's Modulus (E) is an extremely important characteristic of materials, which shows how much a given material will be able deflect before a permanent deformation occurs. The Young's Modulus or is the radio of applied stress to strain: E = $$\displaystyle \sigma$$/$$\displaystyle \epsilon$$


 * Strength: The strength of a material is the ability to resist an applied force. In engineering, the Yield strength ($$\displaystyle\sigma$$y) is defined as "the stress at which a material begins to deform plastically." Elastic or elastoplastic materials are able to withstand certain loads and go back to their original shape when the given load is removed. This effect will occur as long as the applied stress is less than the Yield stress (strength). However, if the applied load exceeds the yield stress, the material will deform permanently even when the load is removed. If the strain or deformation keeps increasing, the material may reach its ultimate rupture stress ($$\displaystyle\sigma$$u) point where it will break.


 * Toughness: The difference between toughness and fracture toughness is that the former is the ability of a material to resist fracture, while the latter is the ability of the material to resist fracture when a crack is already present. If a material has a high value of fracture toughness, it will most likely undergo ductile fracture. This means that it will have the ability to bend (passed the yield strength) before it fractures. On the other hand, if a material has a low value of fracture toughness, such as ceramics, it will undergo brittle fracture.

1.2.1 - Axial Member

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! Axial Member

The length of axial members is significantly larger than their cross-sections and are meant to hold compressive and extensional loads applied along its length (axial direction). Deriving from the slope of the stress vs. strain curve, we may obtain a relation for the applied stress: $$\displaystyle\sigma$$ = E$$\displaystyle\epsilon$$

The applied stress $$\displaystyle\sigma$$ is equal to the applied force per the cross-sectional area of the axial member, so substituting in the above equation we obtain: F = EA$$\displaystyle\epsilon$$

EA is the axial stiffness, which is only a function of the Young's Modulus and the cross-sectional area. This tells us that the stiffness of a member does not vary by changing the shape of a cross-section unless the actual total area increases or decreases. For instance, if a member with a circular cross-section has the same area as a member with a square cross-section (or any other shape), the axial stiffness will be the same for both members. Axial members are good for tensile stresses but may cause buckling failure when compressed. Two ways of improving the buckling strength are to increase the bending stiffness or to shorten the buckle mode by adding supporting members at the joints.

In aircraft structures, aside of the longitudinal axial members, supporting members must be added at the wings and the fuselage to be able to withstand stresses. The two most important parts in a wing structure are the spars (2, refer to figure) and ribs (3). Spars extend lengthwise to the wing covering its entire length (from the fuselage to the wing tip). The main purpose of these members is to provide support to the wing and carry all loads back to the fuselage. The ribs on the other hand, give the aerodynamic shape to the wing while providing support to the spars.

Contribution by: radsam.d
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1.2.3 - The Structural Beam

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! Bending Member (Beam)

The beam is an elemental structure used in all walks of life, from civil engineering to aerospace engineering. Beams provide structural support by providing resistance to bending moments. "A beam can also be used as an axial member carrying longitudinal tension and compression."



The bending moment is mathematically described to beam deflection as...

$$M=-EI\frac{d^2w}{dx^2}$$

where... EI= Bending stiffness of the beam I= Moment of Inertia

The Beam in Aerospace Structures
An example of a beam used in the aerospace industry is that in some airplane wings. This type of beam is called a cantilever beam, which is only supported in one end, carries both a bending moment and a transverse shear stress. However for a beam of large span/depth ratio, as in the case in aircraft wings, the bending stress is much greater than the shear stress.

The maximum bending stress at the root... $$\sigma_{max}=\frac{M_{max}(\frac{h}{2})}{I}$$

The maximum transverse shear stress distribution at the neutral plane... $$\tau_{max}=\frac{3}{2}\frac{V}{bh}$$

If we take the ratio of both the maximum bending stress and maximum shear stress... $$\frac{\sigma_{max}}{\tau_{max}}=\frac{4L}{h}$$

From this it is clear that the bending stress is the ruling factor in aircraft wings. So in order to address this issue aircraft engineers focus in the improvement of airfoils depending on the type of aircraft. For instance high performance military jet-aircraft, that undergo high-loading forces would definitely need stronger wings (cantilever beams) than say a cargo aircraft. In order to make an aircraft more "resistant" to these high bending forces, engineers design these type of aircraft with a low aspect ratio ...

$$AR = {b^2 \over S}$$                    where... b = wingspan S = planform area

Contribution by: radsam.Z
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1.2.4 - Torsion Member

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! Torsion

Torque is very important when it comes to aircraft structures. Torsion is the twisting of an object due to an applied torque. In structural members of circular sections, the resultant shear stress acts in the plane of the cross-section. For solid or hollow cylinder of uniform circular cross-section and constant wall thickness, the torque is related to the twist angle $$\displaystyle\theta_{}$$ per unit length:


 * $$\displaystyle T = {G J \phi_{}} $$

Torsion of Circular Cylinders

where $$\displaystyle J $$ is the torsional constant.

The torsion constant is a geometrical property of a beam's cross-section which determines the relationship between angle of twist and applied torque.

Circle
$$ J = \frac{\pi b^4}{2} $$ b is the radius This is identical to the polar moment of inertia and is exact.

Hollow concentric circular tube
$$ J = \frac{\pi}{2} \left ( b^4 - a^4 \right ) $$ $$b$$ is the outer radius $$a$$ is the inner radius This is identical to the polar moment of inertia and is exact.

If the wall thickness $$\displaystyle t = b - a $$ is small enough compared to the inner radius, then the approximate expression of $$\displaystyle J $$ is given by:

$$\displaystyle J = {2 t \pi_{}r^3} $$

where $$\displaystyle r= \frac{(a+b)}{2} $$is the average value of the outer and inner radii.

Contribution by: radsam.r
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=1.3 - Wing and Fuselage= A wing is a shaped surface used to produce lift for flight through the air. The wing shape is usually an airfoil. Wings are contoured to take maximun advantage of lift, and may be attached at the top, middle, or lower portion of the fuselage. These designs are referred to as high-, mid-, and low-wing respectively. Attached to the rear, or trailing edge, of the wings are two types of control surfaces referred to as ailerons and flaps. Ailerons extend from about the midpoint of each wing outward to the tip and move opposite to each other to achieve rotation movement about the airplane's longitudinal axis. Flaps extend outward from the fuselage to the midpoint of each wing. The flaps move donward so as to generate more lift at lower airspeeds.

The fuselage is an aircraft's main body section that holds the payload. The fuselage also serves to position the wings, powerplant and empennage. The empennage consists of the vertical stabilizer and the horizontal stabilizer. These two surfaces act like the feathers on an arrow to steady the airplane and mantain a straight path through the air.

The wing and the fuselage are the two major airframe components of an airplane, also the horizontal and vertical stabilizers have a very close resemblance to the wing.

1.3.1 - Load Transfer

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! Load In structural design, loads such as lift and weight cause stresses, deformations and displacements on of aircraft's main structure. Study of their effects is carried out by the methods of structural analysis such as bending, torsion and tension. Excess load or overloading may cause structural failure, such as wings clapping, empennage braking apart from the fuselage or severe structural damage and therefore such possibility should be either considered in the design or strictly controlled.

Contribution by: radsam.r
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1.3.2 - Wing Structure

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! Wing Structure The wing produces lift acting as a beam and torsion member while transferring the force of lift to the fuselage. It takes the shape of an airfoil to generate the necessary lift for the aircraft. As such, the wing is subjected to tremendous forces throughout flight. In order to handle these forces the wing is built of spars, ribs, and the skin.

Contribution by: radsam.m
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1.3.3 - Fuselage

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! Fuselage

The fuselage is subjected to concentrated forces from payloads and wing and landing gear reactions. The fuselage takes a circular cross-section due to the internal pressure. Shear stresses on the fuselage are carried by the skin along with hoop stresses. Stringers are added to the fuselage to reinforce the skin and carry axial forces. A circular frame is used to prevent buckling and reinforce the shape of the fuselage, along with shortening the length of the stringers.

Contribution by: radsam.m


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=1.4 - Aircraft Materials=

Material selection has always been a driving force throughout the history of aeronautics. The technology involved with developing new materials has pushed next generation aircraft to be lighter, stronger, and more resistant to nature's elements. From the wood and canvas structures of early aircraft to modern-day titanium alloys and composites, aircraft have come a long way with the help of advances in material.

Currently, the common materials used in aircraft structures are aluminum, titanium, and steel alloys. The advantages and disadvantages of each are listed below:


 * Aluminum is relatively light weight, and has good fatigue life. It is not as strong as other materials and cannot stand high temperatures.
 * Steel Alloys are most used for their high strength. They are heavy and strongly affected by corrosion.
 * Titanium can withstand very high temperatures, and has good resistance to corrosion. It is, however, difficult to machine which makes its manufacturing cost higher.

Another material being used more frequently is fiber-reinforced composites. These composites are manufactured in a careful manner in order to provide maximum strength without being too brittle. Different types of composites exist, such as glass-fiber and carbon-fiber. The mechanical properties for some of these materials yield great strength to weight ratios, which make them an attractive option for aerospace applications.

Look at how far aircraft structures have come due to material influences in the span of a few decades:


 * An early Wright Brothers' airplane made of wood and canvas:
 * [[Image:flyght1.gif|200px|center|Wright's Brother First Flight]]
 * A modern-day airplane constructed mostly of composite materials:
 * [[Image:carbonf.jpg|200px|center|Composite Fuselage and Wings]]
 * [[Image:carbonf.jpg|200px|center|Composite Fuselage and Wings]]

=References=