## El theory

In all materials (plastics, metals, wood, etc.) elementary mechanical theory demonstrates that some shapes resist deformation from external loads. This phenomenon stems from the basic physical fact that deformation in beam or sheet sections depends upon the mathematical product of the modulus of elasticity (E) and the moment of inertia (I), commonly expressed as EI (Chapter 3, Stress-strain behavior). It is applied to all types of constructions such as solids, foams, and sandwich structures. In many applications plastics can lend themselves in the form of a sophisticated lightweight stiff structure and the requirements are such that the structure must be of plastics. In other instances, the economics of fabrication and erection of a plastics lightweight structure and the intrinsic appearance and other desirable properties make it preferable to other materials.

This theory has been applied to many different constructions including many plastic products. In each case displacing material from the neutral plane makes the improvement in flexural stiffness. Use of this engineering principle that has been used for many centuries relates to the basic

Figure 4.1 Examples of shapes to increase stiffness

Figure 4.1 Examples of shapes to increase stiffness

physical fact that deformation in beams or sheets depends upon the mathematical product of E and /, more commonly expressed as EI.

The EI principle applies to the basic beam structures as well as hollow channel, I-shape, T-shape, etc. where it imparts increased stiffness in one direction much more than in the other. Result is more efficient strength-to-weight products and so forth. While this construction may not be as efficient as the sandwich panel, it does have the advantage that it can be easily fabricated (molded, extruded, etc.) directly in the required configuration at a low cost and the relative proportions be designed to meet the load requirements.

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