i28 STRESSES IN TWO-HINGED ARCH 



of the members can be calculated, the stresses which depend upon the 

 deformations must be known. Any method for the calculation of the 

 stresses in a two-hinged arch is, therefore, necessarily a method of 

 successive approximations. With a skilled computer, however, it is 

 rarely necessary to make more than two or three trials before obtain- 

 ing satisfactory results in designing roof arches. Two-hinged bridge 

 arches require somewhat more work to design than roof arches on 

 account of the greater number of conditions for maximum stresses in 

 the members. 



Having determined the correct value of the horizontal thrust, H f 

 the stresses in a two-hinged arch may be calculated by the ordinary 

 algebraic or graphic methods used in the solution of the stresses in 

 simple trusses. 



Calculation of the Reactions. In Fig. 70 the vertical reactions, 

 V and V 2 , are the same as for a simple truss. The horizontal reactions, 

 H, will be equal and will be the forces which would prevent change in 

 length of span if the ends of the arch were free to move. The horizon- 

 tal thrust, H, will therefore be the force which, applied at the roller end 

 of a simple truss, will prevent deformation and make the truss a two- 

 hinged arch. 



An expression for H may be determined as follows: In Fig. 70 

 assume that all members are rigid except the member i-y, which is 

 increased in length 8, under the action of the external load, W. The 



FIG. 70. 



