ders, or riveted iron or steel plate girders used as lintels or as girders. carrying a wall or floor or both, shall be so proportioned that the loads which may come upon them shall not produce strains in tension or compression upon the flanges of more than 12,000 lbs. for iron, nor more than 15,000 lbs. for steel per square inch of the gross section of each of such flanges, nor a shearing strain upon the web-plate of more than 6000 lbs. per square inch of section of such web-plate, if of iron, nor more than 7000 pounds if of steel; but no web-plate shall be less than 4 inch in thickness. Rivets in plate girders shall not be less than 5% inch in diameter, and shall not be spaced more than 6 inches apart in any case. They shall be so spaced that their shearing strains shall not exceed 9000 lbs. per square inch, on their diameter, multiplied by the thickness of the plates through which they pass. The riveted plate girders shall be proportioned upon the supposition that the bending or chord strains are resisted entirely by the upper and lower flanges, and that the shearing strains are resisted entirely by the web-plate. No part of the web shall be estimated as flange area, nor more than one half of that portion of the angle-iron which lies against the web. The distance between the centres of gravity of the flange areas will be considered as the effective depth of the girder. The building laws of the City of New York contain a great amount of detail in addition to the extracts above, and penalties are provided for violation. See An Act creating a Department of Buildings, etc., Chapter 275, Laws of 1892. Pamphlet copy published by Baker, Voorhies & Co., New York. MAXIMUM LOAD ON FLOORS. (Eng'g, Nov. 18, 1892. p. 644.)-Maximum load per square foot of floor surface due to the weight of a dense crowd. Considerable variation is apparent in the figures given by many authorities, as the following table shows: Authorities. French practice, quoted by Trautwine and Stoney Waddell's general specifications... Weight of Crowd, lbs. per sq. ft. ........ 41 70 84 100 120 126 ..... .... 143.1 147.4 Mr. Nash, architect of Buckingham Palace................... Experiments by Mr. B. B. Stoney ("On Stresses," p. 617).... STRENGTH OF FLOORS. (From circular of the Boston Manufacturers' Mutual Insurance Co.) The following tables were prepared by C. J. H. Woodbury, for determining safe loads on floors. Care should be observed to select the figure giving the greatest possible amount and concentration of load as the one which may be put upon any beam or set of floor-beams; and in no case should beams be subjected to greater loads than those specified, unless a lower factor of safety is warranted under the advice of a competent engineer. Whenever and wherever solid beams or heavy timbers are made use of in the construction of a factory or warehouse, they should not be painted, varnished or oiled, filled or encased in impervious concrete, air-proof plastering, or metal for at least three years, lest fermentation should destroy them by what is called "dry rot." It is, on the whole, safer to make floor-beams in two parts, with a small open space between, so that proper ventilation may be secured, even if the outside should be inadvertently painted or filled. These tables apply to distributed loads, but the first can be used in respect to floors which may carry concentrated loads by using half the figure given in the table, since a beam will bear twice as much load when evenly distributed over its length as it would if the load was concentrated in the centre of the span. The weight of the floor should be deducted from the figure given in the table, in order to ascertain the net load which may be placed upon any floor. The weight of spruce may be taken at 36 lbs. per cubic foot, and that of Southern pine at 48 lbs. per cubic foot. Table I was computed upon a working modulus of rupture of Southern pine at 2160 lbs., using a factor of safety of six. It can also be applied to ascertaining the strength of spruce beams if the figures given in the table are multiplied by 0.78; or in designing a floor to be sustained by spruce beams, multiply the required load by 1.28, and use the dimensions as given by the table. Theses tables are computed for beams one inch in width, because the strength of beams increases directly as the width when the beams are broad enough not to cripple. EXAMPLE.-Required the safe load per square foot of floor, which may be safely sustained by a floor on Southern pine 10 x 14 inch beams, 8 feet on centres, and 20 feet span. In Table I a 1 X 14 inch beam, 20 feet span, will sustain 118 lbs. per foot of span; and for a beam 10 inches wide the load would be 1180 lbs. per foot of span, or 147 lbs. per square foot of floor for Southern-pine beams. From this should be deducted the weight of the floor, which would amount to 17% lbs. per square foot, leaving 130 lbs. per square foot as a safe load to be carried upon such a floor. If the beams are of spruce, the result of 1471⁄2 lbs. would be multiplied by 0.78, reducing the load to 115 lbs. The weight of the floor, in this instance amounting to 16 lbs., would leave the safe net load as 90 lbs. per square foot for spruce beams. Table II applies to the design of floors whose strength must be in excess of that necessary to sustain the weight, in order to meet the conditions of delicate or rapidly moving machinery, to the end that the vibration or distortion of the floor may be reduced to the least practicable limit. In the table the limit is that of load which would cause a bending of the beams to a curve of which the average radius would be 1250 feet. This table is based upon a modulus of elasticity obtained from observations upon the deflection of loaded storehouse floors, and is taken at 2,000,000 Ibs. for Southern pine; the same table can be applied to spruce, whose modulus of elasticity is taken as 1,200,000 lbs., if six tenths of the load for Southern pine is taken as the proper load for spruce; or, in the matter of designing, the load should be increased one and two thirds times, and the dimension of timbers for this increased load as found in the table should be used for spruce. It can also be applied to beams and floor-timbers which are supported at each end and in the middle, remembering that the deflection of a beam supported in that manner is only four tenths that of a beam of equal span which rests at each end; that is to say, the floor-planks are two and one half times as stiff, cut two bays in length, as they would be if cut only one bay in length. When a floor-plank two bays in length is evenly loaded, three sixteenths of the load on the plank is sustained by the beam at each end of the plank, and ten sixteenths by the beam under the middle of the plank; so that for a completed floor three eighths of the load would be sustained by the beams under the joints of the plank, and five eighths of the load by the beams under the middle of the plank: this is the reason of the importance of breaking joints in a floor-plank every three feet in order that each beam shall receive an identical load. If it were not so, three eighths of the whole load upon the floor would be sustained by every other beam, and five eighths of the load by the corresponding alternate beams. Repeating the former example for the load on a mill floor on Southernpine beams 10 X 14 inches, and 20 feet span, laid 8 feet on centres: In Table II a 1 x 14 inch beam should receive 61 lbs. per foot of span, or 75 lbs. per sq. ft. of floor, for Southern-pine beams. Deducting the weight of the floor, 171⁄2 lbs. per sq. ft., leaves 57 lbs. per sq. ft. as the advisable load. If the beams are of spruce, the result of 75 lbs. should be multiplied by 0.6, reducing the load to 45 lbs. The weight of the floor, in this instance amounting to 16 lbs., would leave the net load as 29 lbs. for spruce beams. If the beams were two spans in length, they could, under these conditions, support two and a half times as much load with an equal amount of defiection, unless such load should exceed the limit of safe load as found by Table I, as would be the case under the conditions of this problem. Mill Columns.-Timber posts offer more resistance to fire than iron pillars, and have generally displaced them in millwork. Experiments made on the testing-machine at the U. S. Arsenal at Watertown, Mass., show that sound timber posts of the proportions customarily used in millwork yield by direct crushing, the strength being directly as the area at the smallest part. The columns yielded at about 4500 lbs. per square inch, confirming the general practice of allowing 600 lbs. per square inch, as a safe load. Square columns are one fourth stronger than round ones of the same diameter. 4 Span, feet. I. Safe Distributed Loads upon Southern-pine Beams One Inch in Width. (C. J. H. Woodbury.) (If the load is concentrated at the centre of the span, the beams will sus tain half the amount as given in the table.) II. Distributed Loads upon Southern-pine Beams sufficient to produce Standard Limit of Deflection. : 62 15 16 17 18 19 20 21 :::::::::: 24 25 45 11 18 38 16 33 14 ELECTRICAL ENGINEERING. STANDARDS OF MEASUREMENT. 66 C.G.S. (Centimetre, Gramme, Second) or Absolute" System of Physical Measurements: = 1 centimetre, cm.; = 1 gramme, gm.; Unit of velocity space + time = 1 centimetre in 1 second; Unit of acceleration = Acceleration due to gravity, at Paris, 1 = Unit of force = 1 dyne == gramme = A dyne is that force which, acting on a mass of one gramme during one second, will give it a velocity of one centimetre per second. The weight of one gramme in latitude 40° to 45° is about 980 dynes, at the equator 973 dynes, and at the poles nearly 984 dynes. Taking the value of g, the acceleration due to gravity, in British measures at 32.185 feet per second at Paris, and the metre 39.37 inches, we have C.G.S. Unit of magnetism 1 dyne-centimetre = .00000007373 foot-pound; 7373 1 = of 1 horse-power 550 746 = .00134 H.P. the quantity which attracts or repels ar equal quantity at a centimetre's distance with the force of 1 dyne. C.G.S. Unit of electrical current = the current which, flowing through a length of 1 centimetre of wire, acts with a force of 1 dyne upon a unit of magnetism distant 1 centimetre from every point of the wire. The ampere, the commercial unit of current, is one tenth of the C.G.S. unit. The Practical Units used in Electrical Calculations are: Ampere, the unit of current strength, or rate of flow, represented by I. Volt, the unit of electro-motive force, electrical pressure, or difference of potential, represented by E. Ohm, the unit of resistance, represented by R. Coulomb (or ampere-second), the unit of quantity, Q. Ampere-hour 3600 coulombs, Q'. Watt (ampere-volt, or volt-ampere), the unit of power, P. Joule (volt-coulomb), the unit of energy or work, W. Farad, the unit of capacity, represented by K. Henry, the unit of induction, represented by L. Using letters to represent the units, the relations between them may be expressed by the following formulæ, in which t represents one second and Tone hour: As these relations contain no coefficient other than unity, the letters may represent any quantities given in terms of those units. For example, if E represents the number of volts electro-motive force, and R the number of ohms resistance in a circuit, then their ratio E + R will give the number of amperes current strength in that circuit. The above six formulæ can be combined by substitution or elimination so as to give the relations between any of the quantities. The most impor tant of these are the following: The definitions of these units as aaopted at the International Electrical Congress at Chicago in 1893, and as established by Act of Congress of the United States, July 12, 1894, are as follows: The ohm is substantially equal to 109 (or 1,000,000,000) units of resistance of the C.G.S. system, and is represented by the resistance offered to an unvarying electric current by a column of mercury at 32° F., 14.4521 grammes in mass, of a constant cross-sectional area, and of the length of 106.3 centimetres. The ampere is 1/10 of the unit of current of the C.G.S. system, and is the practical equivalent of the unvarying current which when passed through a solution of nitrate of silver in water in accordance with standard specifications deposits silver at the rate of .001118 gramme per second. The volt is the electro-motive force that, steadily applied to a conductor whose resistance is one ohm, will produce a current of one ampere, and is practically equivalent to 1000/1434 (or .6974) of the electro-motive force between the poles or electrodes of a Clark's cell at a temperature of 15° C., and prepared in the manner described in the standard specifications. The coulomb is the quantity of electricity transferred by a current of one ampere in one second. The farad is the capacity of a condenser charged to a potential of one volt by one coulomb of electricity. The joule is equal to 10,000,000 units of work in the C.G.S. system, and is practically equivalent to the energy expended in one second by an ampere in an ohm. The watt is equal to 10,000,000 units of power in the C.G.S. system, and is practically equivalent to the work done at the rate of one joule per second. The henry is the induction in a circuit when the electro-motive force induced in this circuit is one volt, while the inducing current varies at the rate of one ampere per second. The ohm, volt, etc., as above defined, are called the "international" ohm, volt, etc., to distinguish them from the "legal" ohm, B.A. unit, etc. The value of the ohm, determined by a committee of the British Association in 1863, called the B.A. unit, was the resistance of a certain piece of copper wire. The so-called "legal" ohm, as adopted at the International Congress of Electricians in Paris in 1884, was a correction of the B.A. unit, and was defined as the resistance of a column of mercury 1 square millimetre in section and 106 centimetres long, at a temperature of 32° F. 1 legal ohm 1 international ohm = 1.0136 66 66 66 66 = 1.0112 B.A. units, 1 B.A. unit = 0.9889 legal ohm; 1 megohm = 1 million ohm3; 1 microhm = 1 millionth of an ohm; 1 British thermal unit RELATIONS OF VARIOUS UNITS. 1 kilowatt, or 1000 watts..... 1 kilowatt-hour, 1000 volt-ampere hours, 1 British Board of Trade unit, 1 horse-power. = 1 coulomb per second; 66 = 1 watt 1 volt-coulomb per second; = .0009477 heat-units per second (Fahr.), .7373 foot-pound, = work done by one watt in one second, = .0009477 heat-unit; = 1055.2 joules; = 1000/746 or 1.3405 horse-powers; 3412 heat-units; The ohm, ampere, and volt are defined in terms of one another as follows: Ohm, the resistance of a conductor through which a current of one ampere will pass when the electro-motive force is one volt. Ampere, the quantity of current which will flow through a resistance of one ohm when the electromotive force is one volt. Volt, the electro-motive force required to cause a current of one ampere to flow through a resistance of one ohm. |