Page:Encyclopædia Britannica, Ninth Edition, v. 4.djvu/366

Rh 322 BRIDGES [FRAMES. value for any given materials and any constant ratio of Z to v. Table XIV. gives the values of B for a series of these ratios, and Table XV. gives the values of n for the most usual cross sections. TABLE XIV. Value o/B (Us. and square inches), Strength of Struts and Pillars. I d Bfor Cast Iron. Bfor Wrought Iron. I? for Strong Dry Timber. 10 187 0-033 25 15 42 075 9 20 75 133 1-6 25 1-16 208 2-5 30 1-69 3 3 6 35 2 3 408 4-9 40 3- 533 6-4 50 4-68 833 10- Square of side d, or rectangle with smallest side d..,. TABLE XV. Values of n, Strength of Struts and Pillars. 1 I Hollow rectangle, thin sides Circle, diameter d Thin ring, external diameter d f Angle iron, smallest side d 2 Cruciform, smallest breadth = d id; It is of great importance that the connections between the several struts and ties forming a frame should be so designed that the stresses produced may be axial. If this is not done the maximum intensity of stress on the strut or tie may greatly exceed those com puted on the principles explained in the present paragraph (vide 8). Mr Unwin in his lectures gives the following empirical rules for th e strength of wrought iron struts : for fixed ends, 6. cA, 2 ^-Z - ch* for round ends, where different values are given to /and c according to the different cross sections of the struts. Rectangular bars c = 2500 f= 17 tons. Cylindrical bars c = 3500 /=17 5,, Angle, T, cross, and charcoal iron c 900 /=19 ,, The following are Mr Hodgkinson s formula for the strength of cast-iron cylindrical pillars, the length of which is not less than thirty times the diameter : Let P be the load which will produce failure, d the external diameter in inches, L the length in feet, and A a constant multiplier ; then for solid pillars with either round or Hat ends 8 The value of A for rounded ends is 14 9 tons, and for flat ends 44 - 16 tons. Similarly for hollow pillars of internal diameter d, we have 9 where for rounded ends A is taken as 13 tons, and for flat ends 44-3 tons. When the length is less than thirty times the diameter, let P be the ultimate load calculated by equations 8 and 9, and let P, be the load which would crush a short block of the same sectional area S ; i.e., let P,=49S; let P,, be the actual ultimate strength, thoa, according to Professor Hodgkinson s experiments, 10. For rectangular struts of oak and pine, the smallest side beir.g denoted as before by d t, Hodgkinson gives the formula d 2 11 P A ; a S , where A = 3, 000, 000 Ibs. The same unit must be employed for d and Z, and S must be expressed in square inches. This formula can only give a rough approximation to the truth. In short beams the formula in 5 woiild give a smaller strength than equation 11. This smaller value is, then, the true measure of the strength. VI. COMPOUND STRUCTURES. 58. Many bridges have been built with superstructures such that the stresses on the several parts or members cannot be computed by the rules hitherto given. These superstructures are generally constructed by superposing two or more types so as to form a compound structure capable of acting at once say as an arch and as a girder. These bridges may be called compound bridges. The designs are usually unworthy of imitation. Mr Eobert Stevenson s original design for the Britannia Bridge, in which the great girder would have been partly supported by chains, is an example of this type of structure in which the two parts are clearly visible. Many wooden American bridges are trusses which almost defy analysis, the designs being, however, obviously suggested by an attempt to com bine at least two of the three main types of bridges. No advantage whatever is gained by a combination of this kind ; on the contrary great disadvantage is almost sure to follow its adoption, namely, that it will be impossible that each part of the structure should, under all circumstances, carry that portion of the load which the designer entrusted to it. For suppose a bridge constructed partly as a girder and partly as a suspension bridge, the girder being very stiff and deep and the chain perfectly flexible with considerable clip. Let the chain and girder be each fit to carry half the passing load. It is perfectly conceivable that the deflections of the two should be so different that the girder would, under the actual load, break before the chain was sensibly strained, or the difference in the relative dip of the chain and depth of the girder might be such as to cause the former to give way first. Even if the two were so designed that at a given temperature each should take the designed share of the load, a change of temperature would entirely alter the pro portion borne by the two parts of the structure. A few- forms are free from this defect, and these will now be described. 7 Fig. 85. 59. Fink Truss. This truss (fig. 85) has been much employed in America. The upright struts, numbered 1 to 7, divide the span into eight equal parts. If a weight w rests on the top of each strut the whole truss may be looked upon as made up of seven distinct and independent trusses superposed on one another; strut 4 is used seven times, and is compressed with a total force of 4w. Struts 2 and G are used three times, and each compressed with a total force of 2w. Struts 1, 3, 5, and 7 are used once, and each compressed with a force w. The stresses on the inclined ties are at once got from the compression of the strut by the resolution of forces ; and the stress on the upper member or boom is the sum of all the pulls on the ties resolved horizontally ;