A copper tube 12 in. long and having a cross-sectional area of 3 in² is placed between two very rigid caps made of Invar^* as shown in the figure. Four SAE Grade-5 ¾-in. steel bolts are symmetrically arranged parallel to the axis of the tube and are lightly tightened for a bolt preload, F_i ~ 0.0 lbf. Find the stress in the tube and the bolts if the temperature of the assembly is raised from 60 °F to 200 °F. The assembly is installed at a stress-free temperature, T_Ref = 60 °F. The materials have the following properties: ESteel = 30 x 10⁶ psi, ECopper = 17 x 10⁶ psi, ?Steel = 6.5 x 10^-6 in/in-°F, ?Copper = 9.1 x 10^-6 in/in-°F.

 

a. Write the system of equations for each element in the form, [k]{u}={f}.

b. Using the Direct Stiffness Partitioned Matrix Method, assemble the global equations, [K]{U}={F}.

c. Apply the boundary conditions and applied loads to the assembled system of equations.

d. Compute the unknown displacements and reaction forces at each node.

e. Compute the force, strain and stress in each element using Strain-Displacement, Stress-Strain Method, SSM.

f. Solve the Problem by hand/MATLAB.

*Note: Invar is a steel alloy which at ordinary temperatures has a coefficient of thermal expansion, ?_Invar » 0.0 in/in-°F. For this reason Invar is used in the best grades of components that require dimensional stability, such as precision scales/equipment.

Transcribed Image Text:

Final position Elastic deformations Thermal deformations S C Cu (a) (b) Final position Elastic deformations Thermal deformations S C Cu (a) (b)

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yWivent length of copper fubeyl a 12 in Area of cross sechon A 3 ... View the full answer