To assemble the fulcrum of bascule bridges, a trunnion is immersed into liquid nitrogen so that it can be shrunk fit into the hub. This is followed by immersing the resulting trunnion-hub assembly into liquid nitrogen so that it can be then shrunk fit into the girder. On one occasion in Florida, when the trunnion-hub assembly was put into liquid nitrogen, development of cracks on the hub was observed. Experimental and numerical studies conducted since 1998 at University of South Florida show that the cracking took place due to combination of high interference stresses in the trunnion-hub assembly, low fracture toughness of steel at cryogenic temperatures, and steep temperature gradients due to sudden cooling. In this study, we are studying the benefit of staged cooling to avoid cracking in the trunnion-hub assembly when it is cooled down for shrink fitting. We looked at three cooling processes - 1) Direct immersion into liquid nitrogen 2) Immersion into a refrigerated chamber, then liquid nitrogen 3) Immersion into a refrigerated chamber, then a dry-ice/alcohol bath, and finally liquid nitrogen. The geometry of the trunnion-hub assembly was approximated by a composite made of two infinitely long hollows cylinders. The transient problem of temperature distribution and the resulting stresses was solved using finite difference method. Using critical crack lengths and Von-Mises stress as failure criteria, the three cooling processes were compared. The study showed that the minimum critical crack length and stress ratio is increased by as much as 200% when cooling first in refrigerated air followed by liquid nitrogen. However, there is little benefit from adding dry-ice/alcohol as an intermediate step in the cooling process.

Modeling at the structural scale most often requires the use of beam and shell elements. This simplification reduces modeling complexity and computation requirements but sacrifices the accuracy of through-the-thickness information. Several studies have reported various design approaches for analyzing functionally graded material structures. One of these studies proposed a two-node beam element for functionally graded materials (FGMs) based on first order shear deformable (FOSD) theory. The derivation of governing equations included spatial temperature variation. However, only the constant temperature case was carried through in the element formulation. This investigation explore the effects of spatial temperature variation in the axial and through-the-thickness direction of this proposed element and present a new standard three-node beam finite element modified for structure constructed of FGMs. Also, the influence of the temperature dependency of the thermo-elastic material properties on the thermal stresses distribution was studied. In addition, variations in the layer thicknesses within multilayer beam models were studied to determine the effect on stresses and factor of safety. Finally, based on the specific factor of safety, which combines together the strength and mass of the beam, the best layer thicknesses for the beam models were established. The key contributions expected from this research are: 1. development and implementation of a three-node beam element as a finite element code into the commercial computational tool MATLAB® to analyze thermo-mechanical stresses in structures constructed of functionally graded materials; 2. a strategy to simulate different load cases in structures constructed of functionally graded materials; 3. an analysis of the influence of the FGM interlayer thickness on the factor of safety/specific gravity ratio in structures constructed of functionally graded materials under thermo-mechanical loads; 4. and an analysis/comparison of the advantages/benefits of using structures constructed of functionally graded materials with respect to those constructed with homogenous materials.