1a. Fundamental Concepts  (SSES Ch. 1.0-1.5)
Introduction  Size  Shape  Material
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Why "Strength and Stiffness"?
The textbook - Strength and Stiffness of Engineering Systems (Leckie and Dal Bello) - covers the topic traditionally known as Strength of Materials. Strength of Materials is the study of how physical systems respond to mechanical loads - how they support the loads internally, and how those loads cause the system to change shape, i.e., to deform or deflect.

The text covers the standard Strength of Materials topics, with additional chapters on advanced concepts such as plasticity, fracture mechanics, composites and MEMS (micro-electromechanical systems).

In developing and analyzing engineering systems, engineers must ask:

  1. Is the system strong enough? i.e., can each element support its load without breaking?
  2. How does the system deflect under load? Is it stiff enough? i.e., even if the system can support the load, does it deflect too much?

Strength of Materials allows engineers to understand structural systems of a wide range of sizes. It is important to have a good understanding of a component's dimensions - it's cross-sectional area and length - and how they compare with those of other components. The rules learned in this text apply to systems at the micrometer scale on up (click below to see examples):

Cross-sectional shape - how a cross-section's area is distributed - is important in determine a component's strength and stiffness. I-beam cross-sections are used in steel construction as their shape is more weigh-efficient in supporting bending loads than a rectangle, which is the traditional cross-sectional shape of wooden beams.

Round cross-sections are more efficient (and much easier to analyze) than square cross-sections in supporting torsion loads in rotating shafts.

A bridge is primarily made of steel and concrete; a bicycle is made of aluminum or a composite; the AFM is made of silicon nitride. Different materials have different properties. For us, the important properties are:
  • density - mass per unit volume; weight density: weight per unit volume;
  • strength - the force per unit area a material can support;
  • stiffness - a measure of a material's resistance to deformation.

Steel is 3 times as dense and 3 times as stiff as aluminum. For two systems - one of steel, one of aluminum - built with the same dimensions, the steel system is about 3 times as heavy, but under load the aluminum system deforms 3 times as much.

Strength, stiffness (deflection) and weight are all factors to consider in design. Other factors - such as corrosion resistance and ease of manufacture - also influence the choice of one material over another. The bottom line:

The choice of material depends on the requirements of the application.

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Updated: 05/16/09 DJD