This section is from the book "The Building Trades Pocketbook", by International Correspondence Schools. Also available from Amazon: Building Trades Pocketbook: a Handy Manual of reference on Building Construction.
This is the cohesive force by which the particles of a body resist the external load that tends to produce an alteration in the form of the body. Stress is always equal to the effective external force acting upon the body; thus, a bar subjected to a direct pulling force of 1,000 lb. endures a stress of 1,000 lb. Unit stress is the stress or load per square inch of section. For instance, if the bar mentioned above is 1 in. X 2 in. in section, the unit stress of the bar would be 1,000 lb. divided by 2 sq. in. (sectional area) = 500 lb.
Tensile stress is produced when the external forces tend to stretch a body, or pull the particles away from one another.
A rope by which a weight is suspended is an example of a body subjected to tensile stress. Compressive stress is produced when the forces tend to compress the body, or push the particles closer together. A post or column of a building is subjected to compressive stress. Shearing stress is produced when the forces tend to cause the particles in one section of a body to slide over those of the adjacent section. A steel plate acted on by the knives of a shear, or a beam carrying a load, are subjected to shearing stress. Transverse or bending stress is produced by loads acting on a beam tending to bend it, and is a combination of tensile, compressive, and shearing stresses.
The ultimate strength of any material is that unit stress which is just sufficient to break it. The ultimate elongation is the total elongation produced in a unit of length of the material of a unit area, by a stress equal to the ultimate strength of the material.
The amount of alteration in form of a body produced by a stress is called strain. If a steel wire is subjected to a pulling stress, and is elongated 1/10 of an in., this alteration is the strain. Unit strain is the strain per unit of length or of area. It is usually taken per unit of length, and is called the elongation per unit of length. If an iron bar 6 ft. long is subjected to a pulling or tensile force which elongates it 1 in., the unit strain will be 1 in./ 72 (length of the bar in inches) = .0139 in.
The modulus or coefficient of elasticity is the ratio between the stresses and corresponding strains for a given material, which may have a somewhat different modulus of elasticity for tension, compression, and shear. If l be the strain or increase per unit length of a material subjected to tensile stress, and p the unit stress producing this elongation, the modulus of elasticity E = p / l For example, a wrought-iron bar, 80 in. long, subjected to a unit tensile stress p of 10,000 lb., stretched .029 in. The unit strain l. or stretch per inch of length, is .029 in./ 80 in. = .0003625 in.
Then, E = 10,000 / .0003625 = 27,586,200
The relation E = p / l is true only when equal additions of stress cause equal increases of strain. Previous to rupture, this condition ceases to exist, and the material is said to be strained beyond the elastic limit, which, therefore, is that degree of stress within which the modulus of elasticity is nearly constant and equal to stress divided by strain.
The fibers in a beam subjected to transverse stresses are either in compression or tension, but the strength of the extreme fibers agrees neither with their compressive nor tensile strength; hence, in beams of uniform cross-section above and below the neutral axis, a constant determined by actual tests is used. This la called the modulus of rupture, and is generally expressed in pounds per square inch.
This is the ratio of the breaking strength of the material to the load imposed upon it, under usual conditions. For instance, if the ultimate strength of an iron tension bar is 50,000 lb., and the load it sustains is 10,000 lb., the factor of safety is 50,000 lb. / 10,000 lb. = 5.