194 STRENGTH OF MATERIALS 



Solving these three equations simultaneously for J/^ J/ 2 , and r, the 

 linear arch is constructed by laying off M^ and J/ 2 from A and F 

 respectively, and then reducing the ordinates to the equilibrium 

 polygon in the ratio r : 1, and laying them off from the line A'F'. 



The stresses in the rib can then be calculated by the methods 

 previously given (Article 149). 



157. Temperature stresses in continuous arched rib. I'sing the 

 notation of Article 154, the change in the length of the span due to 

 a change in temperature of T degrees is 



/ = 2 cLT. 

 Therefore, for temperature stresses equations (103) become 



/!= /"- /*-- "" 



By hypothesis, the only external forces acting on the rib are tin- 

 reactions and moments at the abutments due to tin* temperature 

 stresses. Consequently, If R denotes the vertical reaction, P k the hori- 

 zontal reaction, and J/ the moment at the left abutment, the moment 

 M at any other point of the rib is 



M = j/, + Kx - P k z. 



If, then, this value of M is inserted in the above integrals and the 

 resulting equations solved simultaneously for M lt R, and P A , the linear 

 arch is thereby determined. 



