To model shrink-fitting in metal components, an analytical model for two long compound cylinders with temperature dependent material properties and interference between them is developed for calculating transient temperatures and stresses. A finite element model is developed for the same geometry which incorporated the temperature dependent material properties. A convergence study is performed on the finite element and analytical model. The finite element model is validated by comparing the approximations of finite element model with the analytical solution. In an assembly procedure of fulcrums for bascule bridges, called AP1, the trunnion is shrink-fitted into a hub, followed by shrink fitting the trunnion-hub assembly into the girder of the bridge. In another assembly procedure called AP2, the hub is shrink-fitted into the girder, followed by shrink-fitting the trunnion in the hub-girder assembly. A formal design of experiments (DOE) study is conducted on both AP1 and AP2 using the finite element model to find the influence of geometrical parameters such as radial thickness of the hub, radial interference, and various shrink-fitting methods on the design parameter of overall minimum critical crack length (OMCCL) - a measure of likelihood of failure by cracking. Using the results of DOE study conducted on both the assembly procedures, AP1 and AP2 are quantitatively compared for the likelihood of fracture during assembly. For single-staged shrink-fitting methods, for high and low hub radial thickness to hub inner diameter ratio, assembly procedure AP1 and AP2 are recommended, respectively. For fulcra with low hub radial thickness to hub inner diameter ratio and where staged shrink-fitting methods are used, for AP2, cooling the trunnion in dry-ice/alcohol and heating the girder, and for AP1, cooling the trunnion-hub assembly in dry-ice/alcohol followed by immersion in liquid nitrogen is recommended. For fulcra with high hub radial thickness to hub inner diameter ratio and where staged shrink-fitting methods are used, cooling the components in dry-ice/alcohol and heating the girder is recommended for both AP1 and AP2. Due to the limitations of AP2, assembly procedures by heating the girder with heating coils instead of dipping an already stressed trunnion-hub assembly in liquid nitrogen are studied for decreasing the likelihood of failure by cracking and yielding. In an assembly procedure called AP3-A, only the girder is heated to shrink-fit the trunnion-hub assembly in the girder. This assembly procedure AP3-A is found to be infeasible because the girder fails by yielding if heating is expected to be completed in a reasonable amount of time. An alternative assembly procedure called AP3-B is suggested for shrink-fitting where the heating of the girder is combined with cooling the trunnion-hub assembly in dry-ice/alcohol mixture. This assembly procedure AP3-B is found to be feasible. A complete DOE study is conducted on AP3-B to find the influence of parameters like hub radial thickness and radial interference at trunnion-hub interface on the design parameter of overall minimum critical crack length. The design parameter, OMCCL values during the assembly procedure AP3-B are quantitatively compared with the widely used assembly procedures (AP1 single-stage shrink-fitting and AP1 multi-staged shrink fitting). The results of this work suggest that increasing the hub radial thickness decreases the likelihood of fracture significantly. For hubs with large radial thickness, heating the girder combined with cooling the trunnion-hub in dry-ice/alcohol mixture (AP3-B) is recommended but for hubs with low radial thickness, multistage cooling of the trunnion-hub assembly in dry-ice/alcohol mixture followed by dipping in liquid nitrogen (AP1- multistage cooling) is recommended.