DISPOSAL OF MATERIAL.] 



APPLIED MECHANICS. 



809 



Fig. 82. 



avoiding air-bubbles and flaws, which are apt to occur in 

 thick castings ; and which, if they do occur in thin cast- 

 ings, do not take so much from the strength, or, at all 

 events, are more likely to be visible, and can be allowed 

 for. In malleable iron bars, when they are required for 

 strength and stiffness, the T form is usually employed. 

 In plates, corrugating or wrinkling adds greatly to the 

 stiffness, because it provides depth of material trans- 

 versely. 



The question of how to dispose material in order to 

 secure the greatest strength with the least weight and 

 cost, is indeed the main subject of mechanical contrivance 

 as to form. We have already instanced the contrivance 

 of the Britannia Tubular Bridge, as an example of skill 

 in device going hand-in-hand with experiment. Were 

 the material employed in one of the great tubes of this 

 bridge all compressed into one solid bar, having a section 

 of dimensions proportional to those of the tube, we 

 question if it could support its own weight without 

 breaking, even if the span were reduced to half that of 

 the tube ; while with one-fourth of 

 the span, the deflection, from its 

 own weight, would be enormous. 

 In this tube, the material is dis- 

 posed in such a manner as to attain 

 the greatest strength with the least 

 weight, and the most suitable form 

 for the purposes of the traffic. The 

 additional material required in the 

 upper part of the section (as in the 

 case of other wrought-iron girders), 

 is arranged in the sides of cells or 

 subsidiary tubes (Fig. 82) ; and due 

 regard has been paid to the securing 

 of lateral stiffness, to resist the pressure of strong winds 

 against its immense side-surface, as well as to the attain- 

 ment of vertical stiffness to resist the strain and shake 

 of a heavy passing load. The annexed plate represents 

 an elevation and plan of this great work, as much 

 admired for its grandeur and simplicity as for its 

 strength and durability. 



In some other cases, where malleable iron is used in 

 the construction of bridges, a girder has been formed of 

 plates, disposed in a manner somewhat different. The 

 upper part is a tube bent over to an arch-form (Fig. 83), 

 and the lower portion forms a flange or ledge, as well for 

 strength as for receiving the ends of the beams that 

 carry the roadway. The upper and lower portions are 



Kg. 83. 



form of the transverse section so as to secure strength 

 with economy of material, but the longitudinal section 

 and a plan of a beam are also susceptible of modifica- 

 tions. 



In the case of a beam projecting from a wall (Fig. 84), 

 with a weight suspended at its extreme end, the strain is 

 greatest at A, close to the support, and diminishes to- 

 wards the end, because the leverage with which the 

 weight acts to fracture the beam, diminishes. Thus, at 

 C, midway, the strain is only half that at A ; at B it is 

 yths ; and at D it is ^th. If, then, the breadth of the 

 beam be uniform throughout its length, its depth may 

 be with safety diminished towards the extremity. As 

 the strength is proportioned to the square of the depth, 

 the depths at B C D may be made such that their squares 

 are respectively J, J, J of the square of A. This may be 

 done by removing material from the upper or lower side 

 of the beam, so as to give it a curved outline above or 

 below ; and still the strength of the beam is maintained. 

 The curve for such a beam is what is called a parabola, 

 the peculiar property of which is, that a square of the 



Kg. 85. 



ELEVATION. 



PLAN. 



Section. 



connected by a longitudinal fin, with several transverse ribs for stiffen- 

 ing, and more firmly connecting the whole together. This ingenious 

 arrangement of parts is due, we believe, to Mr. Brunei, the engineer. 



Fig. M. 



length of each of the vertical lines or ordinates, A, B, C, 

 D, is proportional to its distance from the apex or ex- 

 tremity E. Let us take, as an example, a beam of cast- 

 iron projecting 12 feet, and 12 inches deep at A by 3 



inches broad. The 

 weight of such a 

 beam of uniform 

 depth throughout 

 would be about 12 

 cwt. But by taper- 

 ing it off, as we have 

 indicated, its weight 

 would be reduced to 

 8 cwt., jrds of what 

 it was. Thus, not 

 only is a saving effect- 

 ed in the cost of the 

 beam, but as its own 

 weight is an impor- 

 tant part of the strain 

 element of strain is 



1 





Not only, however, is there scope for modification of | 

 VOL. i. 



at A, this 



considerably diminished, and the 

 weight hanging from the end may be pro- 

 portionately increased. The depths at the 

 different points would be as follow : 

 At A, close to the support, 12 inches. 

 ,, B, Jths of the length from A, about 

 10J, because 10 squared is about 

 Jths of 12 squared. 10 X 10 = 

 110J, and 12 X 12 = 144, j ths of 

 which is 108. 

 C, ^ the length, or 6 feet from A, 



about 8 inches. 

 D, |th the length, or 9 feet from A, 



6 inches. 



If the depth of the beam cannot conveniently be varied, 

 6 L 



