140 STRESSES IN TWO-HINGED ARCH 



Assume that the joints L and L ' in (a) Fig. 73 are connected by 

 a tie having 3 sq. in. cross-section. A force of 1000 Ibs. will stretch 

 the tie 



A , 1000 X 720" 



= 3X29,000,000 = -0083 inches. 



The movement for 1000 Ibs. applied as H is equal to ^ - = .0287 



inches. The value of H therefore which will produce equilibrium for 

 the arch with vertical loads will be 



+ .0083 H + .0287 H = .956 x 1000 Ibs. 



The stresses in the arch for this case may be found from the stresses 

 in Table VII and Table VIII as previously described. 



Temperature Stresses. Where a horizontal tie is used and all 

 parts of the structure are exposed to the same conditions and range of 

 temperature, the entire arch will contract and expand freely and tem- 

 perature stresses will not enter into the calculations. Where the tie is 

 protected and where rigid abutments are used the temperature stresses 

 must receive careful attention. 



The deformation A' due to a uniform change of temperature of t 

 degrees Fahr. when the arch is assumed to be a truss supported on 

 frictionless rollers, will be etL, where e is the coefficient of expansion 

 of steel per degree Fahr. = . 00000665 ; t equals change in temperature 

 in degrees Fahr.; and L equals the length of the span. 



For a change of 75 degrees Fahr. from the mean, the deformation 

 will be 



A' = .00000665 X 75 L 



- *L 

 2000 



