168 GRAPHIC AND ANALYTIC [CIJAP. XH. 



CHAPTEK XII. 



tX>NTINUOT78 GIEDEE (CONTINUED) COMBINATION OF GRAPHICAL 



AND ANALYTICAL METHODS. 



1 1O. In the present chapter we shall develop a method for 

 the solution of continuous girders not purely graphical, but 

 based upon the method of resolution of forces illustrated in 

 Arts. 8-13, together with well-known analytical results, which 

 method for accuracy, simplicity, and ease of application will, 

 we think, be found superior to any hitherto proposed. The 

 method is, of course, applicable only to framed structures, but 

 for such cases is the most satisfactory of any with which we are 

 acquainted. 



111. The Inflection Points being known, the Shearing 

 Forces and moments at the Supports can, by a simple 

 construction, be easily determined. ls. Loaded Span 

 Fig. 77, PI. 21. Thus in the span B C = I, let the distance of 

 the weight P from the left support be #, and let i and i' be the 

 distances of the inflection points from B and C respectively. 

 Then if through any point P of the weight we draw lines, as 

 P D, P E, through i and i', intersecting the verticals at B and C 

 in the points D and E, the vertical ordinates between these lines 

 and B C will be proportional to the moments. For, as we see 

 from the force polygon, the equilibrium polygon must consist 

 of two lines as D P, P E, parallel to O and O 1, and because 

 of the moments at the ends, the closing line D E is shifted to 

 B C (Art. 23). Since the moments at the points of inflection 

 are zero, the ordinates to P D and P E to pole distance H will 

 give the moments. Now the points of inflection being known, 

 and P D and P E drawn, we can easily find the pole distance 

 H and the shearing forces L and 1 L by laying off P verti- 

 cally, and drawing from its extremities lines parallel to P D 

 and P E intersecting in O. A perpendicular through O upon 

 1 gives H and the reactions L and 1 L. In other words, 

 we have simply to decompose P along P D and P E. 



