Problem

Computer study of a two-hinged arch. The objective is to establish the difference in respo...

Computer study of a two-hinged arch. The objective is to establish the difference in response of a parabolic arch to (1) uniformly distributed loads and (2) a single concentrated load.

(a) The arch in Figure P6.32 supports a roadway consisting of simply supported beams connected to the arch by high-strength cables with area A = 2 in.² and E = 26,000 ksi. (Each cable transmits a dead load from the beams of 36 kips to the arch.) Determine the reactions, the axial force, shear, and moment at each joint of the arch, and the joint displacements. Plot the deflected shape. Represent the arch by a series of straight segments between joints. The arch has a constant cross section with A = 24 in.², I = 2654 in.⁴, and E = 29,000 ksi.
(b) Repeat the analysis of the arch if a single 48-kip vertical load acts downward at joint 18. Again, determine all the forces acting at each joint of the arch, the joint displacements, etc., and compare results with those in (a). Briefly describe the difference in behavior.