Three-fourths of the diameter of the bore, taken at the hinder part, will give the diameter of the cock at the mouth. Of the Weight of Lead, per superficial foot. 1 From one-sixteenth of an inch to one inch thick. Thickness. Weight. Thickns. Weight. Thickns. Weight. Thickness. Weight. When the inside diameter is of an inch, 3 ounces; of an inch, 5 ounces; of an inch, 6 ounces; of an inch, 8 ounces; and of an inch, 10 ounces per foot. : STRENGTH OF MATERIALS. Materials of construction are liable to four different kinds of strain, viz., stretching, crushing, transverse action, and torsion or twisting the first of which depends upon the body's tenacity alone; the second, on its resistance to compression; the third on its tenacity and .compression combined; and the fourth, on that property by which it opposes any acting force tending to change from a straight line, to that of a spiral direction, the fibres of which the body is composed. In bodies, the power of tenacity and resistance to compression, in the direction of their length is as the cross-section of their area multiplied by the results of experiments on similar bodies, as exhibited in the following table; TABLE Showing the Tenacities, Resistances to Compression, and other Properties of the common Materials of Construction. mon Of the Comparative Strength and Weight of Ropes and Chains. Note. It must be understood, and also borne in mind, that in estimating the amount of tensile strain to which a body is subjected, the weight of the body itself must also be taken into account; for according to its position so may it approximate to its whole weight, in tending to produce extension within itself; as in the almost constant application of ropes and chains to great depths, considerable heights, &c. Resistance to Lateral Pressure, or Transverse Action. TABLE Of Data, containing the Results of Experiments on the Elasticity and Strength of various Species of Timber. 137 The strength of a square or rectangular beam to resist lateral pressure, acting in a perpendicular direction to its length, is as the breadth and square of the depth, and inversely as the length. Thus, a beam twice the breadth of another, all other circumstances being alike, equals twice the strength of the other; or twice the depth, equal four times the strength, and twice the length, equal only half the strength, &c., according to the rule. To find the dimensions of a beam capable of maintaining a given weight, with a given degree of deflection, when supported at both ends. RULE. Multiply the weight to be supported in lbs. by the cube of the length in feet; divide the product by 32 times the tabular value of E, multiplied into the given deflection in inches; and the quotient is the breadth multiplied by the cube of the depth in inches. Note 1.-When the beam is intended to be square, then the fourth root of the quotient is the breadth and depth required." Note 2.-If the beam is to be cylindrical, multiply the quotient by 17, and the fourth root of the product is the diameter. EXAMPLE. The distance between the supports of a beam of Riga fir is 16 feet, and the weight it must be capable of sustaining in the middle of its length is 8000 lbs., with a deflection of not more than of an inch what must be the depth of the beam, supposing the breadth 8 inches? 16 × 8000 90 x 32 x 75 15175÷8= 1897 12.35 in., the depth. To determine the absolute strength of a rectangular beam of timber, when supported at both ends, and loaded in the middle of its length, as beams in general ought to be calculated to, so that they may be rendered capable pable of withstanding all accidental cases of emergency. RULE. Multiply the tubular value the beam in inches, and by the area of the cross section in inches; by times the depth of divide the product by the distance between the supports in inches, and the quotient will be the absolute strength of the beam in lbs. Note 1.-If the beam be not laid horizontally, the distance between the supports, for calculation, must be the horizontal distance. Note 2.-One fourth of the weight obtained by the rule is the greatest weight that ought to be applied in practice as permanent load. Note 3-If the load is to be applied at any other point than the middle, then the strength will be as the product of the two distances is to the square of half the length of the beam between the supports; or, twice the distance from one end. multiplied by twice from the other, and divided by the whole length, equal the effective length of the beam. EXAMPLE. In a building 18 feet in width, an engine boiler of 54 tons is to be fixed, the centre of which is to be 7 feet from the wall; and having two pieces of red pine, 10 inches by 6, which I can lay across the two walls for the purpose of slinging it at each end, ma Iwith sufficient confidence apply them, so as to effect this object And 18 feet d to wal adà vd anciano!? atel ledord griet ob beddego 902 95 1 711, double each, or 14 and 22, then al tana 14 x 22. 5 gør noitone dugom inte la od uð neyi dogu 13 the absolute strength of each piece of timber at that point, "To determine the dimensions of a rectangular beam capable of sup porting a required weight, with a given degree of deflection, when fixed | at one end. RULE. Divide the weight to be supported. in lbs., by the tabular value of E, multiplied by the breadth and deflection, both in inches; and the cube root of the quotient, multiplied by the length in feet, equal the depth required in inches. EXAMPLE. A beam of ash is intended to bear a load of 700 lbs. at its extremity, its length being 5 feet, its breadth 4 inches, and the deflection not to exceed of an inch. Tabular value of E 119 x 4 x 5 238 the divisor; = To find the absolute strength of a rectangular beam, when fixed at one end and loaded at the other RULE. Multiply the value of S by the depth of the beam, and by the area of its section, both in inches: divide the product by the leverage in inches, and the quotient equal the absolute strength of the beam in lbs. EXAMPLE. A beam of Riga fir, 12 inches by 41, and projecting 6 feet from the wall; what is the greatest weight it will support at the extremity of its length? When fracture of a beam is produced by vertical pressure, the fibres of the lower section of fracture are separated by extension, whilst at the same time those of the upper portion are destroyed by compression; hence exists a point in section where neither the one nor the other takes place, and which is distinguished as the point |