DESIGN OF TWO-HINGED ARCH 141 



For the arch in Fig. 73 



720" 



A ' = =*= -200CT = - 36 inches 



<}/- 



This will be equivalent to a change in H of -Wj x 20000 = 



12540 Ibs. The stresses due to temperature in the two-hinged arch 

 will be equal to the stresses in column 4, Table VIII, multiplied by 

 .627. The maximum stresses due to external loads and temperature 

 will be found by adding algebraically the temperature stresses to the 

 stresses due to the external loads. If the arch is not erected at a mean 

 temperature this fact must be taken into account in setting the pedestals. 



Design of Two-Hinged Arch. In designing a two-hinged roof 

 arch proceed as follows : ( I ) With one end free to move, calculate 

 the stresses in the arch as a simple truss ; (2) with an assumed horizon- 

 tal reaction, H 1 , of, say, 20000 Ibs., calculate the stresses in the arch as 

 a simple truss ; (3) calculate the stresses in the arch for some assumed 

 value of H, this value of H may be guessed at or often may be estimated 

 with considerable accuracy; (4) design the members for approximate 

 stresses in the arch; (5) calculate the deformation of the arch as a truss 

 for the approximate sections and stresses ; (6) calculate the deforma- 

 tion of the arch as a truss for an assumed horizontal reaction of 20000 

 Ibs. ; (7) determine a more accurate value of H from the deformations 

 as previously described; (8) recalculate the stresses in the arch, re- 

 design the members, recalculate the deformations, recalculate a new 

 value of H, etc., until satisfactory sections are obtained. The second 

 approximation is usually sufficient. Corrections for horizontal tie and 

 temperature should be applied in making the approximations. The 

 gross area of the sections of all members should be used in determining 

 the deformation of the members. If riveted tension members are much 

 weakened, a somewhat smaller value of H, say, 26,000,000, may be 

 used than the 29,000,000 commonly used for the compression members. 



The method just described is much more expeditious than the 

 usual method of designing the members for the stresses found by con- 



