(German, Festigkeit; French, Resistance des materiaux.)

All solid bodies or materials are made up of an infinite number of atoms, fibres or molecules. These adhere to each other and resist separation with more or less tenacity, varying in different materials. This tenacity or tendency of the fibres to resume their former relation to each other after the strain is removed is called the elasticity of the material. It is when this elasticity is overcome that the fibres separate, and the material breaks and gives way.

There are to be considered in calculating strengths of materials two kinds of forces, viz., the external (or applied) forces and the internal (or resisting) forces. The external forces are any kind of forces applied to a material and tending to disrupt or force the fibres apart. Thus a load lying apparently perfectly tranquil on a beam is really a very active force; for the earth is constantly attracting the load, which tends to force its way downwards by gravitation and push aside the fibres of the beam under it. These latter, however, resist separation from each other, and the amount of the elasticity of all these fibres being greater than the attraction of the earth, the load is unable to force its way downwards and remains apparently at rest. Strain. The amount of this tendency to disrupt the fibres (produced by the external forces) at any point is called the "strain" at that point.

Stress. The amount of the resistance against disruption of the fibres at such point is called the "stress" at that point.

External (or applied) forces, then, produce strains. Internal (or resisting) forces produce stresses.

This difference must be well understood and constantly borne in mind, as strains and stresses are the opposing forces in the battle of all materials against their destruction.

When the strain at every point of the material just equals the stress, the material remains in equilibrium. The greatest stress, at any point of a material that it is capable of exerting is the ultimate stress (that is, the ultimate strength of resistance) at that point. Were the strain to exactly equal that ultimate stress, the material, though on the point of breaking, would still be safe theoretically. But it is impossible for us to calculate so closely. Besides we can never determine accurately the actual ultimate stress, for different pieces of the same material vary in practice very greatly, as has been often proved by experiment. Therefore the actual ultimate stress might be very much less than that calculated.

Again, it is impossible to calculate the exact strain that will always take place at a certain point; the applied forces or some other conditions might vary. Therefore, to provide for all possible emergencies, we must make our material strong enough to be surely safe; that is, we must calculate (allow) for a considerably greater ultimate stress at every point than there is ever likely to be strain at that point.

The amount of extra allowance of stress varies greatly, according to circumstances and material. The number of times that we calculate the ultimate stress to be greater than the strain is called the factor-of-safety (that is, the ratio between stress and strain).

If the elasticity of different pieces of a given material is practically uniform, and if we can calculate the strain very closely in a given case, and further, if this strain is not apt to ever vary greatly, or the material to decay or deteriorate, we can of course take a low or small factor-of-safety; that is, the ultimate stress need not exceed many times the probable greatest strain.

On the other hand, if the elasticity of different pieces of a given material is very apt to vary greatly, or if we cannot calculate the strain very closely, or if the strain is apt to vary greatly at times, or the material is apt to decay or to deteriorate, we must take a very high or large factor-of-safety, that is, the ultimate stress must exceed many times the probable greatest strain.

Factors-of-safety are entirely a matter of practice, experience, and circumstances. In general, we might use for stationary loads:

Factor-ofSafety.

For moving-loads, such as people dancing, machinery vibrating, dumping of heavy loads, etc., the factor-of-safety should be one-half larger, or if the shocks are often repeated and severe, at least double of the above amounts. Where the constants to be used in formulæ are of doubtful authority (as is the case with most of them for woods and stones), the factor-of-safety chosen should be the highest one.

In building-materials we meet with four kind of strains, and, of course, with the four corresponding stresses resisting them, viz.: Strains.

Compression, or crushing strains. Tension, or pulling strains. Shearing, or sliding strains, and Transverse, or cross-breaking strains.