I I\ K- 1X3 AD STRESSES 



8 L = slope of line AC = tangent <>t nn^lc- which AC 



with the huri/oiital. 



C - - (*L *R) = length of ordinal < unit distance 



from A. 



Slopes are counted numerically positive when upward 

 in the loft. The sign of C (called the coefficient at salient 

 point A) is, accordingly, negative when AC diverges below 

 DA produced to the left of A. The value of C a may be 



determined graphically as -- or it may be figured algebra- 

 ically as (S L 8 R ). 



Proof of Theorem I, or that Z = C a M a . 



Con-i<U'r the load w n distant x n from the salient point </. 

 By the similar triangles AEF and AGH, 



Therefore, 



C a W n X n (A) 



Summing up all of the ordinate-load product-, 



Z = 2w n z n = C a Xw n x n = C a M a (5) 



Proof of Theorem //, or that ^j = C a W a . 



From equation (A) above, the increase in the ordinal <- 

 load product w n z n for an advance dx n of the load is 



w n dz n = C a -w n >dx n . 



Summing up the increases of all the ordinate-load products 

 and noting that dx is the same for all loads, 



dZ = Zw n dz n = C a dx.2w n = C a -W a -dx. 

 Dividing by dx, % = C.W. = *^> = C '<>. . 



