ten feet long, securely fastened at one end, and to the other end we apply a pulling-force of 40,000 pounds. This force causes the bar to stretch, and by careful measurement we find the elongation to be 0.0414 of an inch. Now, as the bar is ten feet, or 120 inches, long, if we divide 0.0414 by 120, we shall have the elongation of the bar per unit of length. inch. Performing this operation, we have as the result 0.00034 of an As the bar is two inches square, the area of cross-section is four square inches, and hence the pulling-force per square inch is 10,000 pounds. Then, dividing 10,000 by 0.00034, we have as the modulus of elasticity of the bar 29,400,000 pounds. This is the method generally employed to determine the modulus of elasticity of iron ties; but it can also be obtained from the deflection of beams, and it is in that way that the values of the modulus for most woods have been found. Another definition of the modulus of elasticity, and which is a natural consequence of the one just given, is the number of pounds that would be required to stretch or shorten a bar one inch square by an amount equal to its length, provided that the law of perfect elasticity would hold good for so great a range. The modulus of elasticity is generally denoted by E, and is used in the determination of the stiffness of beams. Moment. If we take any solid body, and pivot it at any point, and apply a force to the body, acting in any direction except in a line with the pivot, we shall produce rotation of the body, provided the force is sufficiently strong. This rotation is produced by what is called the moment of the force; and the moment of a force about any given point or pivot is the product of the force into the perpendicular distance from the pivot to the line of action of the force, or, in common phrase, the product of the force into the arm with which it acts. The Centre of Gravity of a body is the point through which the resultant of the weight of the body always acts, no matter in what position the body be. If a body be suspended at its centre of gravity, and revolved in any direction, it will always be in equilibrium. (For centre of gravity of surfaces, lines, and solids, see Chap. IV.) CLASSIFICATION OF STRAINS WHICH MAY BE PRODUCED IN A SOLID BODY. The different strains to which building-materials may be exposed are: I. Tension, as in the case of a weight suspended from one end of a rod, rope, tie-bar, etc., the other end being fixed, tending to stretch or lengthen the fibres. II. Shearing Strain, as in the case of treenails, pins in bridges, etc., where equal forces are applied on opposite sides in such a manner as to tend to force one part over the adjacent one. III. Compression, as in the case of a weight resting on top of a column or post, tending to compress the fibres. IV. Transverse or Cross Strain, as in the case of a load on a beam, tending to bend it. V. Torsion, a twisting strain, which seldom occurs in building-construction, though quite frequently in machinery. CHAPTER II. FOUNDATIONS. THE following chapter on Foundations is intended to furnish the reader with only a general knowledge of the subject, and to enable him to be sure that he is within the limits of safety if he follows what is here given. For foundations of large works, or buildings upon soil of questionable firmness, the compressibility of the soil should be determined by experiments. The term "foundation" is used to designate all that portion of any structure which serves only as a basis on which to erect the superstructure. This term is sometimes applied to that portion of the solid material of the earth upon which the structure rests, and also to the artificial arrangements which may be made to support the base. In the following pages these will be designated by the term "foundation-bed." Object of Foundations.-The object to be obtained in the construction of any foundation is to form such a solid base for the superstructure that no movement shall take place after its erection. But all structures built of coarse masonry, whether of stone, or brick, will settle to a certain extent; and, with a few exceptions, all soils will become compressed under the weight of almost any building. Our main object, therefore, is not to prevent settlement entirely, but to insure that it shall be uniform; so that, after the structure is finished, it will have no cracks or flaws, however irregularly it may be disposed over the area of its site. Foundations Classed.-Foundations may be divided into two classes: CLASS I. Foundations constructed in situations where the natural soil is sufficiently firm to bear the weight of the intended structure. CLASS II. Foundations in situations where an artificial bearing-stratum must be formed, in consequence of the softness or looseness of the soil. Each of these two great classes may be subdivided into two divisions: a. Foundations in situations where water offers no impediment to the execution of the work. b. Foundations under water. It is seldom that architects design buildings whose foundations are under water; and, as this division of the subject enters rather deeply into the science of engineering, we shall not discuss it here. Boring. Before we can decide what kind of foundation it will be necessary to build, we must know the nature of the subsoil. If not already known, this is determined, ordinarily, by digging a trench, or making a pit, close to the site of the proposed works, to a depth sufficient to allow the different strata to be seen. For important structures, the nature of the subsoil is often determined by boring with the tools usually employed for this purpose. When this method is employed, the different kinds and thickness of the strata are determined by examining the specimens brought up by the auger used in boring. Foundations of the First Class.-The foundations included under this class may be divided into two cases, according to the different kinds of soil on which the foundation is to be built:CASE I. Foundations on soil composed of materials whose stability is not affected by saturation with water, and which are firm enough to support the weight of the structure. Under this case belong, — Foundations on Rock. — To prepare a rock foundation for being built upon, all that is generally required is to cut away the loose and decayed portions of the rock, and to dress the rock to a plane surface as nearly perpendicular to the direction of the pressure as is practicable; or, if the rock forms an inclined plane, to cut a series of plane surfaces, like those of steps, for the wall to rest on. If there are any fissures in the rock, they should be filled with conerete or rubble masonry. Concrete is better for this purpose, as, when once set, it is nearly incompressible under any thing short of a crushing-force; so that it forms a base almost as solid as the rock itself, while the compression of the mortar joints of the masonry is certain to cause some irregular settlement. If it is unavoidably necessary that some parts of the foundation shall start from a lower level than others, care should be taken to keep the mortar joints as close as possible, or to execute the lower portions of the work in cement, or some hard-setting mortar: otherwise the foundations will settle unequally, and thus cause much injury to the superstructure. The load placed on the rock should at no time exceed one-eighth of that necessary to crush it. Pro fessor Rankine gives the following examples of the actual intensity of the pressure per square foot on some existing rock foundations: Average of ordinary cases, the rock being at least as strong as the strongest red bricks. Pressures at the base of St. Rollox chimney (450 feet below 20000 the summit) On a layer of strong concrete or beton, 6 feet deep 6670 4000 The last example shows the pressure which is safely borne in practice by one of the weakest substances to which the name of rock can be applied. M. Jules Gaudard, C.E., states, that, on a rocky ground, the Roquefavour aqueduct exerts a pressure of 26,800 pounds to the square foot. A bed of solid rock is unyielding, and appears at first sight to offer all the advantages of a secure foundation. It is generally found in practice, however, that, in large buildings, part of the foundations will not rest on the rock, but on the adjacent soil; and as the soil, of whatever material it may be composed, is sure to be compressed somewhat, irregular settlement will almost invariably take place, and give much trouble. The only remedy in such a case is to make the bed for the foundation resting on the soil as firm as possible, and lay the wall, to the level of the rock, in cement or hard-setting mortar. Foundation on Compact Stony Earths, such as Gravel or Sand. Strong gravel may be considered as one of the best soils to build upon; as it is almost incompressible, is not affected by exposure to the atmosphere, and is easily levelled. Sand is also almost incompressible, and forms an excellent foundation as long as it can be kept from escaping; but as it has no cohesion, and acts like a fluid when exposed to running water, it should be treated with great caution. The foundation bed in soils of this kind is prepared by digging a trench from four to six feet deep, so that the foundation may be started below the reach of the disintegrating effects of frost. The bottom of the trench is levelled; and, if parts of it are required to be at different levels, it is broken into steps. Care should be taken to keep the surface-water from running into the trench; and, if necessary, drains should be made at the bottom to carry away the water. The weight resting on the bottom of the trench should be proportional to the resistance of the material forming the bed. |