CHAPTER XIV STRENGTH OF MATERIALS STRESS AND STRAIN Extracts from Kent's Engineers' Pocket Book "Stresses are the forces which are applied to bodies to bring into action their elastic and cohesive properties. These forces cause alterations of the forms of the bodies upon which they act. Strain is a name given to the kind of alteration produced by the stresses. The distinction between stress and strain is not always observed, one being used for the other. (Wood.) "Stresses are of different kinds, viz.: tensile, compressive, transverse, torsional, and shearing stresses. "A tensile stress, or pull, is a force tending to elongate a piece. A compressive stress, or push, is a force tending to shorten it. A transverse stress tends to bend it. A torsional stress tends to twist it. A shearing stress tends to force one part of it to slide over the adjacent part. "Tensile, compressive, and shearing stresses are called simple stresses. Transverse stress is compounded of tensile and compressive stresses, and torsional of tensile and shearing stresses. TENSILE STRENGTH * "The following data are usually obtained in testing by tension in a testing-machine a sample of a material of construction: The load and the amount of extension at the elastic limit. The maximum load applied before rupture. "The elongation of the piece, measured between gaugemarks placed a stated distance apart before the test; and the reduction of area at the point of fracture. "The load at the elastic limit and the maximum load are recorded in pounds per square inch of the original area. The elongation is recorded as a percentage of the stated length between the gauge-marks, and the reduction of area as a percentage of the original area. The coefficient of elasticity is calculated from the ratio the extension within the elastic limit per inch of length bears to the load per square inch producing that extension. "Elastic Limit.-The elastic limit is defined as that load at which the deformations cease to be proportional to the stresses, or at which the rate of stretch (or other deformation) begins to increase. It is also defined as the load at which a permanent set first becomes visible. "Yield-point is defined as that point at which the rate of stretch suddenly increases rapidly with no increase of the load." SAFETY FACTORS AND SAFE-WORKING FIBER STRESSES (From National Tube Co. Book of Standards) "Each member of a mechanical structure should be capable of resisting the greatest straining action to which it can Author's Note.-Tests for tensile strength are expressed in pounds per square inch, i.e., from the plane, or surface, of the tested material a measurement of one inch at a right angle. Example: A piece of steel one inch square shows tensile strength of 80,000 pounds, which would be the tensile strength per square inch of the material and also the strength of that size piece. The strength of a piece of steel one inch wide and one-quarter inch thick would be one-fourth of 80,000, or 20,000 pounds. ordinarily be subjected when in use. The designer should, therefore, consider under what conditions the straining actions are greatest. When these actions are of variable character, it is of the utmost importance to take into consideration the effects of this variation upon the endurance of the material. For example, a member may fail under a straining action that causes stresses which fluctuate, or which alternate repeatedly from tension to compression, when the same straining action would be successfully resisted under the conditions of steady loading. "Margin of Security.-It is apparent that the working load on a member of mechanical structure should be less than the calculated breaking load for the member, in order to allow for inaccuracies, deterioration, and probable contingencies, and thus provide a margin of security. It is customary, therefore, to design a member so that either (1) the statical breaking load, or (2) the load that causes the most strained fiber of the material to just reach its elastic limit, shall be a number of times the working load. This number is called the safety factor. Thus, in the first case, if the statical breaking strength were 12,000 pounds and the working load upon it 2,000 pounds, then the safety factor would be 12,000 divided. by 2,000, or 6. In the second case, if the statical load that causes the most strained fiber of the member to just reach the elastic limit of the material were 6,000 pounds and the working load upon it 2,000 pounds, then the safety factor on this basis would be 3. "The elastic and ultimate strengths of the materials, under static loading can be easily obtained. The strength, therefore, under an assumed steady loading, of any member of a mechanical structure can ordinarily be calculated with sufficient accuracy. But the proper safety factor to use under a given set of actual working conditions, involving actions of a more or less variable or uncertain character, can be arrived at in most cases only as the result of long experience, or by tedious. experiment.” TABLE OF FACTORS OF SAFETY (From Kent's Engineers' Pocket Book) Class of Service or Materials. Boilers ..... Piston and connecting rod for single-acting engines.... Steel work in buildings. Steel work in bridges.. Factor 42-6 9-12 634-9 24 4 5 Note: The following data on steel derricks are used through the courtesy of the Carnegie Steel Co. For more information regarding details of construction, etc., refer to Carnegie Steel Co. Catalogue, 1918. "Methods of Design.-The loads which come on derricks and drilling rigs are problematical and cannot be exactly ascertained. The tables indicate what the safe loads should be, figured on the factor of safety of four which is usual in the fabrication of steel for buildings. The yield point of structural steel is rather more than twice as high as the working unit stresses. "Consequently, the derricks will sustain safely infrequent stresses of higher amount than is set down in the tables. Care should, however, be taken not to load drilling structures beyond the tabular safe loads. "No guy lines or other extraneous means of support are necessary. All stresses have been taken care of within the structures. Wind stresses have been figured at 30 pounds per square foot of exposed surface, which is equivalent to the pressure developed by a storm of about 70 miles per hour velocity. "Drilling Loads.-The load over the crown pulley in a Standard or California derrick is made up of the load on the pulley, plus the equivalent downward pull on the drilling cable, and in consequence the load which a derrick will sustain figured on the basis of the pull on the drilling cable is to be taken as one-half of the tabular safe load. "In pulling casing, however, the load is distributed to the crown block beams by the two or four-casing pulleys in a California derrick or by the parting of lines in a Standard derrick. While the derricks will sustain the full theoretical safe loads given, they will do so only when the loads are distributed by the crown block evenly to the four legs. It is obvious that if the entire pull in drawing casing comes on two legs, the derrick cannot be expected to stand its full theoretical load. SAFE WORKING LOADS ON STEEL DERRICKS "The following table shows the theoretical safe loads which various grades of derricks will sustain, computed on the factor of safety of four. It also gives the size and thickness of angles used in the top section to which other panels are proportional. |