A DETAILED description of the physical properties of materials, and of the loads and stresses to which they are subjected, would be beyond the province of this volume, especially as the subject will be entered upon in Part IV. The following short explanations of some of the terms employed in describing those properties and stresses may however, be useful.
The combination of external forces acting upon any structure is called the load.
Dead load is that which is very gradually applied, and which remains steady.
Live load is that which is applied suddenly, or is accompanied by shocks or vibration.
Without going into the theory of the subject, it is sufficient to state that practically a live load produces in most cases very nearly twice the stress and strain which a dead load of the same weight would produce.
Therefore to find the dead load which would produce the same effect as a given live load, the latter must be multiplied by 2.
This is called converting the live load into an equivalent dead load.
Abridge may weigh one ton per foot of area (i.e. dead load), and carry a live load of two tons per foot of area; the equivalent dead load would be. (1 + 2x2)= 5 tons per foot of area.
The breaking load for any structure or piece of material is that dead load which will just produce fracture in the structure or material.
The Factor of Safety is the ratio in which the breaking load exceeds the working load (i.e. the load which can be safely applied in practice). This ratio varies with the nature of the load and the nature of the material, and is found by experience.
For the reasons stated above, the factor of safety for a live load is generally taken at double that for a dead load.
Factors of Safety.
For perfect materials and workmanship...
For good ordinary ma- terials and work- manship
Metals . .
4 to 5
8 to 10
When a load is mixed, i.e. partly live and partly dead, the live portion may be converted into an equivalent amount of dead load, and the factors of safety for dead load then applied to the whole; or ...
A compound factor of safety may be deduced by applying the following rule: -
1 Rankine's Useful Rules and Tables.
Multiply the factor of safety for dead load by the fraction that the dead load is of the whole load, and multiply the factor of safety for live load by the fraction that the live load is of the whole load. The sum of the results thus obtained will give the compound factor of safety.
For example : - In a certain iron bridge the dead load is 5 tons per bay, the live load 9 tons per bay; the total load is therefore 14 tons per bay.
The dead load is 5/14 of the whole. „ live „ 9/14 ,,
The factor of safety for dead load is 3, and for live load is 6.
The compound factor of safety will be equal to (5/14 x 3) + (9/14 x 6) = 69/14 = 413/14 = say 5.
The working load is the greatest dead load the material can with safety bear in practice. It is found by dividing the breaking load by that factor of safety which is found to be suitable to the particular case.
The proof load is the greatest load that can be applied to a piece of material to prove or test it by straining it to the utmost extent without producing permanent deformation or injury, i.e. not beyond the elastic limit (see p. 329).
The breaking load or working load may be either live or dead, or a combination of both, but for convenience it is usual to reduce it all to an equivalent dead load, by doubling the live load and adding it to the dead load.
Stress and Strain are words often used indifferently, either to mean the alterations of figure produced in a body by any forces, or to mean the forces producing those alterations.
Of late years, however, the word strain has been taken to mean only the alterations of form caused by the forces, and stress to mean the forces producing these alterations.
Materials are subject to the under-mentioned stresses, which produce strains, and (when carried far enough) fracture as stated.
Mode of Fracture.
Stretching . . . Elongation
Compressive or Thrusting ...
Shortening . . . Squeezing . . .
Transverse or Bending
. Bending ....
Shearing. . . . .
Torsional or Twisting ...
Twisting or wrenching asunder.
The ultimate stress, or breaking stress, on any piece of material is the stress produced by the breaking load.
The proof stress is the stress produced by the proof load.
The working stress is that produced by the working load. It is always much smaller than the proof stress, in order to leave a margin of safety to cover defects in material, etc.
A bar of 1 square inch sectional area might have a breaking strength of twenty tons, but the working stress to which it was subjected might be only live tons. The factor of safety in that case would be four. Its proof strength might be ten tons, this being the weight the bar could bear without exceeding the elastic limit.
Tenacity or tensile strength is the resistance offered by material to tension, that is to a stress tending to tear it asunder, as, for example, in the case of a vertical rod having a weight suspended from it, or in the tie rod of a roof, or the tension flange of a girder.
Strength to resist crushing is the resistance offered by material to a compressive stress, thrust, or pressure. Such a stress tends to make it shorten, and eventually to crush it. Examples of this stress occur in the case of a short column supporting a weight, or in a strut which keeps two tottering walls from falling toward each other, or in the compression flange of a girder.