To reduce the vertical displacement of the roadway floor system of the arch (shown in P6.32, part b) produced by the 48-kip load at joint 18, diagonal cables of 2 in. in diameter are added as shown in Figure P6.34. For this configuration, determine the vertical displacement of all the floor system joints. Compare the results of this analysis with part b of P6.32 by plotting to scale the vertical deflections of all joints along the roadway from joints 1 to 11. Properties of the diagonal cables are the same as those of the vertical cables.
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.
Uniformly distributed dead load + 48-kip live load
Reactions (kips),
Deflections (in),
and Deflected Shape
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