Oral

Some Preliminaries for Structural Sizing



Before we can start designing the fuselage, it is beneficial to know how it is likely to fail. The likely mode of failure is buckling as can be seen in the figures below and on the following page.

Shown in the figures below is an idealization of the frame and skin-stringer combination. The frames act as springs to resist the displacement of theskin-stringer combination.

In the case were the frames or ribs are themselves not stiff enough, the structure buckles in a global sense much like a long rod. If the frames or ribs are stiff enough, a node is enforced and a local type of buckling occurs. Theoretically, the minimum weight is achieved when both modes are likely to occur simultaneously. In practice, structures are designed sothat the local buckling occurs first. The general type of failure is considered to be unacceptable for aerospace structures.
























Our job as structural designers is to prevent the skin-stringer combination from buckling and to make the frames stiff enough to prevent the global type of failure. It should be noted that there is nothing to gain by makingthe structure any more stiff than it needs to be.


Frames

The primary purpose of frames is to provide end restraints for the skin panels and to resist out of plane deflections when the skins “try” to buckle. The primary factor in buckling and resisting deflections in general is the stiffness, EI. The goal of frame or rib design is to select a stiffness, that is a material and crosssectional area, and spacing to make the local buckling of the skins as likely as the global buckling of the entire structure (large spacing and low stiffness).

Shanley has shown that a proper model for this type of behavior is

(Insert Figure here)

When the panel buckles, it does so as if were hinged at the buckling point. The required spring constant to prevent buckling is

[pic]

Anapplied bending moment causes the highest stresses at the top and bottom of the structure and zero stress at the neutral axis. Therefore only a small portion of the structure supports the bending load. So if we assume that the load is applied over the top and bottom fraction of the structure, the fraction represented by c2, we can find an equivalent load by using the definition of torque or moment.[pic]

Now that we know what spring stiffness is required, we can compare it to the spring stiffness of a circular frame under diametrically applied loads.

[pic]

Equating spring constants

[pic][pic]

and substituting for the load P

[pic]

Solving for the required stiffness

[pic]

where [pic]is just the collection of the three constants.

If experiments can be conductedwith frames of known stiffness, a value of [pic]can be calculated when the other parameters are selected in a way that causes local and global buckling to occur simultaneously. According to Shanley, this value is

[pic]

Gerard in doing a similar calculation showed [pic]. The higher the value of this parameter, the more likely local buckling is to occur.

Recall which cross sectional area isused in the definition of the moment of inertia I of the frame. Because I contains geometric information, we can use it to determine an area. This area swept around the circumference gives a volume.

If it is assumed that the frame cross section is rectangular (remember in conceptual design we aren’t too concerned with the actual shape), then

[pic] [pic]

By definition,

[pic]where ( is the radius of gyration. If a typical value is known, then it is easy to find the frame area.

However, Shanley has shown that another parameter better captures the efficiency of the frame in bending.

[pic]

For a rectangular cross section,

[pic]

The height-to-width ratio can be thought of as an aspect ratio. For one of Shanley’s examples, the value of k was about 5. This...