98 SUPPLEMENT TO CHAP. VU. [CHAP. L 



SUPPLEMENT TO CHAPTER VII. 



CHAPTER \'. 



METHODS OP CALCULATION. 



1. In Chapter I. of the text we have already obtained a method of dia- 

 gram which will be found both simple and general, and by which we can 

 readily determine the strains for any given loading in any framed struc- 

 ture, no matter how irregular in its shape or dimensions, provided only that 

 all the outer forces are known. 



In Chap. VII. we have also been put in possession of another method of 

 diagram, by which we may for any structure of the above class, framed or 

 not, determine the moment at any point, and can then properly proportion 

 the cross-section. 



Thus far, indeed, we are unable to apply these methods to the continuous 

 girder or braced arch, as in these cases there are not only upward reactions 

 but also end moments, and in the latter case a thrust also, which must first 

 be determined. The determination of these requires that the elasticity of 

 the material and cross-section of the structure be taken into account. But 

 with these exceptions, and they are of rare occurrence in practice, we can 

 already solve any case which may present itself. 



In the Appendix, if he has attended to our numerous references to it, 

 the reader will have already become familiar with two corresponding meth- 

 ods of calculation, viz., that by resolution of forces and that by moments. 



It is, however, in many cases desirable to know not only the strains in 

 every piece of a structure, but also the deflection of the structure, and this 

 also requires a knowledge of the theory of flexure or of elasticity. For the 

 sake of completeness, therefore, aiming as we do to put the reader in pos- 

 session of methods of calculation as well as of graphic determination, we 

 shall devote a few pages here to a brief notice of these two above-men- 

 tioned methods of calculation, and then pass on to the theory of elasticity 

 itself. . This latter has been too generally considered by those unacquainted 

 with the methods of the calculus as difficult and abstruse. It is true that 

 the calculus must be called into requisition ; but so simple are the processes 

 for bea'ms of single span and it is with these only we have at present to 

 do that we indulge the hope that by going back to first principles we may 

 enable even those at present unacquainted with the calculus to follow our 



