290 Improvement in the Construction of Bridges, Sfc. 



Here follow some formulce, for the invesligation of models, in 

 accordance with the best writers on the subject : 



From an experiment, made to ascertain the firmness of the 

 model of a bridge, or of an edifice, certain precautions are neces- 

 sary, before we can infer the firmness of the structure itself. 



1. If the side of a model be to the corresponding side of the 

 structure, as 1 to n, the stress which tends to draw asunder, or to 

 break transversely the parts, increases from the smaller to the 

 greater scale, as 1 to w^; while the resistance of those ruptures 

 increases only as 1 to n^. The structure, therefore, will have so 

 much less firmness than the model, as 7i is greater. If w be the 

 greatest weight which one of the beams of the model can bear, 

 and w the weight or stress which it actually sustains, then the 



limit of n will be ?i= — . 



ID 



2. The side of the model being to the corresponding side of 

 the structure as 1 to n, the stress which tends to crush the parts 

 by compression, increases from the smaller to the greater scale, as 

 1 to n^, while the resistance increases only in the ratio of 1 to n. 

 Hence, if w were the greatest load which a modular wall or col- 

 umn could carry, and iv the weight with which it is actually 

 loaded ; then the greatest limit of increased dimensions would be 



w 

 found from the expression w= \/—. If, retaining the length or 



height n h, and the breadth n b, we wished to give to the solid 

 such a thickness xt, as that it should not break in consequence of 



• • '^ 



Its increased dimensions, we should have x=n^ V~- In the case 

 ' ^ w 



of a pilaster with a square base, or of a cylindrical column, if the 



dimension of the model were d, and of the largest pillar, which 



should not crush with its own weight when 7i times as high, x d, 



3 /jj^ 2 ^ 



we should have x = n v/ . These theorems will often find 



^ w 



their application in the profession of an architect or an engineer. 



3. Suppose, for an example, it were required to ascertain the 

 strength of a bridge on this improvement, from experiments made 

 with a model. In this construction, the truss-work is carried 

 across from pier to pier, so that the road-way entirely across, shall 

 be in a horizontal plane, and all the parts shall retain their own 

 respective magnitudes throughout the structure. Now, let / rep- 



