

APPLIED MECHANICS. 



[TRAKSVRBSB STRAIX. 



i . '. 



cubical piece. 



. 1 inch . 



the number of experiments made, scarcely warrant* their 

 establishment as practical data, 



TABLE V. liaiating Pmeer of Material* to Cruihing 

 Force. 



Name of SUUtUL 



Elm . 



American pine . 

 White d.-al . 

 English oak 



\- . ..: . .:.. 



Chalk . 

 Soft brick . 

 Redbrick . 



1. burnt brick 



'.rick ...;;.. 



(irindstone grit ..,,.. 8000 



.ue 10300 



York paving 12800 



White marble 13600 



Cornish granite . . . . 14300 



1 ' in !i 



Crushing pi 



1300 Ibs. 



1 til HI 



1900 

 B800 



6000 

 1100 

 1200 

 1800 



Compact limestone 

 Peterhead granite (red) 

 Purbeck granite (red) . 

 1 1. -in I freestone . 

 AVhite Italian marble . 

 Aberdeen granite (blue) 

 Cast lead 

 Cast tin 



Wrought copper . . 

 Cast copper 



17300 

 18600 

 90600 

 21200 

 21800 

 21500 

 480 

 960 

 6400 

 7300 

 Wrought iron . . ' . . 8000 



inch 



Bn - 

 Cast iron 



10000 

 10000 



3. TRANSVERSE STRAIN. The effect of a load 

 on the end of a beam projecting from a wall, or on the 

 middle of a beam supported at both ends, is to throw a 

 transverse strain on the beam ; and if the load be exces- 

 sive, to break the beam transversely, or across its fibres. 

 Of all questions respecting the strength of materials, this 

 is certainly the most important. In architectural struc- 

 tures, the stability of roofs, floors, and walls supported 

 on beams or girders ; in civil engineering, the safety of 

 girder-bridges and rails ; in mechanical engineering, the 

 strength of beams, levers, framing, and the like all 

 depend mainly upon the correct solution of questions re- 

 lating to transverse strain. It is to this branch of the 

 subject, therefore, that the consideration of engineers 

 has been chiefly directed ; and a vast number of experi- 

 ments have been made with a view to ascertain practical 

 data, from which the transverse strength of all useful 

 materials may be calculated. 



The theoretical investigation of transverse strain is by 

 no means a difficult one ; but the application of data in 

 computation involves some very complicated questions, 

 which the practical mechanic generally solves more by 

 the eye, as he sees proportions in his drawing or model, 

 than by any very accurate calculation. Such a mode of 

 meeting the difficulty implies experience and observation; 

 and without these, wo fear no amount of theoretical 

 knowledge, and no expertness in calculation, will serve 

 for determining the strength of any structure. In 

 machinery, especially, the strains to which parts may be 

 subjected are so various in magnitude, owing to their 

 respective movements, and the local qualities of mate- 

 rials differ so greatly, that the mere calculated strain and 

 strength offer very little aid in guiding to the most suit- 

 able proportions. When the architect determines on the 

 diniuiiMons of an iron girder destined to carry a heavy 

 wall, he can calculate, with tolerable precision, the weight 

 to bo supported, and the strength of girder required to 

 carry it without danger. The girder is placed, the wall 

 is built, and twenty yean after, the load is the same, and 

 the strength of the junior but little diminished. 



But when the mechanic makes a pattern of a beam for 

 a steam-engine, although ho may readily calculate the 

 train which the pressure of steam on the piston throws 

 the beam while the engine works steadily, he has 



little notion of the sudden though transient strain which 

 may be thrown upon it by the sudden stoppage of some 

 part of the machinery, or the occurrence of some alight 

 obstacle to the movement It not unfrequently occurs 

 that a little water in the cylinder of a steam-engine, 

 causes the fracture of some of the strongest parts. The 

 machinery being all in motion, the piston descends upon 

 a film of water which has no ready means of escape, and 

 which being almost totally incompressible, offers as deter- 

 mined an obstacle as solid iron would do. In such a case, 

 the momentum of all the moving parts must be suddenly 

 destroyed ; some of the beams, rods, or levers, through 

 which the piston is connected with the rest of the engine, 

 must give way ; or the cylinder itself, which holds the 

 water, must yield to the strain, and break under it. 

 That we may form some idea of what damage such a 

 strain as we have described may effect, we have only to 

 reckon that in a Urge steam-engine there are 15 or 20 

 tons of iron, moving probably at an average velocity of 

 100 feet per minute, to be suddenly arrested. In de- 

 stroying the momentum, as much force is expended as 

 would be measured by the blow of a 68 Ib. cannon-ball 

 striking its mark at a very near range. Nor do these 

 sudden and unexpected strains constitute the only diffi- 

 culty under which the mechanic labours when he com- 

 putes the strength of his work. He cannot always de- 

 pend upon the internal soundness of the material with 

 which he deals. Cast-iron is especially treacherous in 

 this respect ; and it often happens that a casting, exter- 

 nally sound, has some sponginess or air-bubbles under 

 the skin, which are discovered only in the event of frac- 

 ture. It is, therefore, his business not only to contrive 

 devices for regulating the movements of his machinery, 

 and for affording relief in cases of undue pressure, and to 

 use every precaution against unsounduess in his mate- 

 rials ; but also to provide such strength as shall meet 

 the contingencies which a slight derangement may fre- 

 quently bring about. It may be asked then, why, if the 

 mechanic have to apply such excess of strength to meet 

 contingencies, he should take any trouble in calculating 

 or ascertaining practical data from which he may com- 

 pute ? The answer is plain. While he makes every part 

 strong to excess, yet ho has to maintain a proportionate 

 strength in all. To make one part of a beam strong 

 enough to sustain ten times its usual strain might be 

 very proper ; but to make another part of it capable of 

 sustaining twenty times its load would be absurd, for 

 then either the weaker part is only half as strong as it 

 should be, or the stronger is twice as strong as required. 

 The mechanic, then, must have a clear conception of 

 how strains affect materials of different forms, and how 

 far the change of one dimension or another may affect 

 the strength, before he can venture to design or execute 

 a machine justly proportioned in all its parts, and suffi- 

 ciently strong throughout to meet the contingencies of 

 its action, without undue waste of material and labour 

 in its construction. 



The most simple case of transverse strain is that to 

 which a beam projecting from a wall is subjected, when a 

 weight is suspended from its outer end. It is clear that 

 the longer the beam, the greater the strain ; and that if 

 the beam give way anywhere, presuming it to be of 

 uniform strength throughout, it will be at a point close to 

 the wall where it is fixed, because at that point the 

 weight acts with the greatest leverage. On tracing the 

 breaking effect of the weight, wo see that in bringing the 

 end of the beam down to the position marked by the 

 dotted lines, some action must take place among the 

 fibres of the material at A B, where the weight acts with 

 greatest power. This action must bo that of tension 

 among the upper fibres, and of compression among the 

 lower ones ; and there must bo some point C in the beam 

 where the extension and the compression of the fibres 

 meet, and where there is neither of these actions. Such 

 a point marks the position of what is called the neutral 

 axis : that is, a line extending along the beam horizon- 

 tally, and separating that part of the material which is 

 extended or torn asunder, from that part which is com- 

 pressed or squeezed together. It is manifest that, when 



