5_48 - 5.48 The assembly shown in Fig. P5.48 consists of a...

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5.48 The assembly shown in Fig. P5.48 consists of a brass shell (1) fully bonded to a solid ceramic core (2). The brass shell [ E = 115 GPa, α = 18.7 × 10 6 /°C] has an outside diameter of 50 mm and an inside diameter of 35 mm. The ceramic core [ E = 290 GPa, = 3.1 × 10 6 /°C] has a diameter of 35 mm. At a temperature of 15°C, the assembly is unstressed. Determine the largest temperature increase that is acceptable for the assembly if the normal stress in the longitudinal direction of the brass shell must not exceed 80 MPa. Fig. P5.48 Solution Section properties: The cross-sectional areas of brass shell (1) and ceramic core (2) are: 22 2 2 2 1 2 (50 mm) (35 mm) 1,001.3827 mm (35 mm) 962.1128 mm 44 AA ππ ⎡⎤ =− = = = ⎣⎦ Equilibrium Consider a FBD cut through the assembly. Sum forces in the horizontal direction to obtain: 12 2 1 0 x FF F Σ= −− = ∴= (a) Geometry of Deformations Relationship For this configuration, the deformations of both members will be equal; therefore, δ = (b) Force-Temperature-Deformation Relationships
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5_48 - 5.48 The assembly shown in Fig. P5.48 consists of a...

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