Abstract
Mechanics, as a scientific discipline, is the study of the behavior of bodies subject to forces and displacements (and, to some extent, heating and cooling). Solid mechanics is the branch of mechanics dealing specifically with solid bodies.
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- 1.
While a very precise and general definition of a solid body is challenging, we will consider here a body to be solid if all of its material points that are close to each other remain so for a long time even when the body is subject to external loads. Another common characteristic of most solid bodies is that they retain their overall shape even when not confined in a container.
- 2.
A rigid motion is sometimes also referred to as ”rigid-body” motion, although it is clear that rigid motions may be experienced by either rigid or deformable bodies.
- 3.
Galileo Galilei (1564–1642) was an Italian physicist and mathematician.
- 4.
Sir Isaac Newton (1643–1727) was an English physicist and mathematician.
- 5.
Johannes Kepler (1571–1630) was a German mathematician and astronomer.
- 6.
Abbreviations of units are written in roman font and without a period.
- 7.
It is spelled metre in most English-speaking countries, including Canada.
- 8.
The previously defined atomic-clock-based second is known as the SI second.
- 9.
In the United Kingdom and Canada a system of volume units (known as imperial units), using the same nomenclature but different definitions, is used semi-officially.
- 10.
Note the distinction between g, gram (roman), and g, acceleration due to gravity (italic).
- 11.
Like other units of measurement named for persons, newton is written in lowercase letters but its abbreviation N is capitalized.
- 12.
A notorious example of the lack of such communication occurred in 1998, when NASA’s Mars Climate Orbiter was destroyed because the operations team entered force data in pounds into a navigation program coded in SI units.
- 13.
An old unit of power that is still used occasionally is the horsepower (hp), variously defined as either 745.7 W (in English-speaking countries, taken to be the default definition here) or 735.5 W (on the European continent).
- 14.
When Fahrenheit-size degrees are used to denote absolute temperature they are called degrees Rankine (\({}^{\circ}\)R); thus, the numerical value of the absolute temperature in \({}^{\circ}\)R is 1.8 times that in \({}^{\circ}\)K.
- 15.
The literal meaning of the Latin word vector is “carrier,” and the position vector, which can be envisioned as “carrying” the particle from one configuration to another, is the prototypical vector.
- 16.
Pierre Varignon (1654–1722) was a French mathematician.
- 17.
It is sometimes also called a torque, but in solid mechanics torque has a more specific meaning that will be defined in the next chapter.
- 18.
What in North America is called a wrench is generally known as a spanner in the British Isles.
- 19.
The same procedure would, of course, apply to any other set of forces that are parallel but not necessarily coplanar.
- 20.
The center may be defined as the intersection of any two lines of symmetry (or antisymmetry, as, for example, in a rhomboid) in two-dimensional figures, or of any three planes of symmetry (or antisymmetry) in three-dimensional figures.
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Lubliner, J., Papadopoulos, P. (2014). Forces and Moments. In: Introduction to Solid Mechanics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6768-7_1
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DOI: https://doi.org/10.1007/978-1-4614-6768-7_1
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