'CHAP, vn.] SIMPLE GIRDERS. 97 



upon which we lay so much stress is fully given by Stoney 

 [" Theory of Strains," vol. i.], and the examples there given will 

 be found of service. 



Finally, then, the strains in upper and lower chords are great- 

 est for full load over whole span. We have, therefore, only to 

 erect upon the given span a parabola whose centre ordinate is 



o 5 where p is the load per unit of length for dead, and 



ra for live load [Art. 44]. The ordinates to this parabola at 

 any point give at once the maximum moment at that point. 

 The depth of truss at this point, if a framed structure, or the 

 moment of inertia of the cross-section at this point, if it is a 

 solid beam [Art. 52], being known, the strain in the flanges or 

 outer fibres may be easily determined. The strain in the web is 

 given by the maximum shear. For dead load alone this is 

 given by the ordinates to a straight line passing through the 



centre of span, whose extreme ordinates are-^ [Art. 77]. The 



2i 



maximum shear due to live load alone (m I) will be given by 

 the ordinates to two semi-parabolas, convex to the span, having 



their vertices at each end, and the extreme ordinates - - [Art. 



a 



78]. At any point, the greatest of the two ordinates to these para- 

 bolas is to be taken. For live and dead loads together, Art. 79 

 may also be useful. The shear being known, the strain in any 

 diagonal is equal to the shear multiplied by the secant of the 

 angle made by the diagonal with the vertical [Art. 10 of Ap- 

 pendix] for parallel flanges. For flanges not parallel, we must 

 find the resultant shear as given in Art. 16 (4) of Appendix, 

 or, better still, the flanges once known, the diagonals can be 

 diagrammed according to the principles of Chap. I. 



For the investigation of load systems, the principles of 

 Arts. 70-75 will be found sufficient, and the application of 

 these principles we have already sufficiently illustrated in Arts. 

 49-51. 



7 



