Computer study of arch with a continuous floor girder. Repeat part (b) in problem P6.32 if a continuous girder with A = 102.5 in 2 and I = 40,087 in. 4 , as shown in Figure P6.33, is provided to support the floor system. For both the girder and the arch, determine all forces acting on the arch joints as well as the joint displacements. Discuss the results of your study of P6.32 and P6.33 with particular emphasis on the magnitude of the forces and displacements produced by the 48-kip load.

Question

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.

Answer 1

The structure is composed of a deep, stiff, continuous girder, which is supported by pin

supports at each end as well as by vertical cables that transmit roadway loads to the

supporting arch. Loads applied to the roadway have two paths to the end supports. They can

be transmitted directly by the continuous girder to the supports or they can be carried upward

to the arch by the cables and then transmitted through the arch to the end supports. Since all

vertical cables carry a portion of the live load applied to the stiff continuous girder, the

distribution of forces to the arch is more uniform, which in turn creates a more uniform stress

distribution on the arch’s cross section. As a result, the arch undergoes less deformation and

deflections of the floor system are significantly reduced.

Details of the Barracks Bridge over the Mississippi River–a 909 ft-long, 280 ft high arch-

continuous beam system uses a l2?-5? deep continuous I-shaped plate girder supported by 17

hangers.