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The depicted in the figure below has a length of 0.635m and a diameter of 50mm. The bar is made of a copper alloy with an elastic modulus E = 110 GPa and a linear thermal expansion coefficient a = 17.5 x 10-6/°C. The bar is initially positioned at room temperature with a gap of 0.2mm between end A and the rigid wall. The bar's right end at B is supported by an elastic spring of negligible thermal expansion coef- ficient and a spring constant of k = 210 × 10 N/m. A small gap maintained between the copper bar and the smooth surrounding sleeve facilitates frictionless motion as the bar thermally expands. Questions: (a) Compute the temperature increase ATer required to close the 0.2 mm gap. (b) Compute the axial force R developed in the copper bar due to a temperature increase of AT = 27°C. State the compatibility condition and solve it for R. (c) Compute the compressive (engineering) stress o developed within the copper bar due to the axial force R. Express your answer in MPa. (d) Compute the total axial strain of the copper bar that develops after it makes contact with the rigid wall. Express your answer in microstrains. (e) Compute the length change of the copper bar after it makes contact with the rigid wall. (f) Compute the length change of the spring.

The depicted in the figure below has a length of 0.635m and a diameter of 50mm. The bar is made of a copper alloy with an elastic modulus E = 110 GPa and a linear thermal expansion coefficient a = 17.5 x 10-6/°C. The bar is initially positioned at room temperature with a gap of 0.2mm between end A and the rigid wall. The bar's right end at B is supported by an elastic spring of negligible thermal expansion coef- ficient and a spring constant of k = 210 × 10 N/m. A small gap maintained between the copper bar and the smooth surrounding sleeve facilitates frictionless motion as the bar thermally expands. Questions: (a) Compute the temperature increase ATer required to close the 0.2 mm gap. (b) Compute the axial force R developed in the copper bar due to a temperature increase of AT = 27°C. State the compatibility condition and solve it for R. (c) Compute the compressive (engineering) stress o developed within the copper bar due to the axial force R. Express your answer in MPa. (d) Compute the total axial strain of the copper bar that develops after it makes contact with the rigid wall. Express your answer in microstrains. (e) Compute the length change of the copper bar after it makes contact with the rigid wall. (f) Compute the length change of the spring.

Mechanics of Materials (MindTap Course List)
Mechanics of Materials (MindTap Course List)
9th Edition
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Barry J. Goodno, James M. Gere
Chapter2: Axially Loaded Members
Section: Chapter Questions
Problem 2.5.17P: A copper bar AB with a length 25 in. and diameter 2 in. is placed in position at room temperature...
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The depicted in the figure below has a length of 0.635m and a diameter of 50mm. The bar is made of a copper alloy with an elastic modulus E = 110 GPa and a linear thermal expansion coefficient a = 17.5 × 10-6/°C. The bar is initially positioned at room temperature with a gap of 0.2mm between end A and the rigid wall. The bar's right end at B is supported by an elastic spring of negligible thermal expansion coef- ficient and a spring constant of k = 210 × 10°N/m. A small gap maintained between the copper bar and the smooth surrounding sleeve facilitates frictionless motion as the bar thermally expands. Questions: (a) Compute the temperature increase ATer required to close the 0.2 mm gap. (b) Compute the axial force R developed in the copper bar due to a temperature increase of AT = 27°C. State the compatibility condition and solve it for R. (c) Compute the compressive (engineering) stress o developed within the copper bar due to the axial force R. Express your answer in MPa. (d) Compute the total axial strain of the copper bar that develops after it makes contact with the rigid wall. Express your answer in microstrains. (e) Compute the length change of the copper bar after it makes contact with the rigid wall. (f) Compute the length change of the spring. 8 = 0.2mm rigid wall L₁= 0.635m AT ww k=200x106 N/m rigid wall
Transcribed Image Text:The depicted in the figure below has a length of 0.635m and a diameter of 50mm. The bar is made of a copper alloy with an elastic modulus E = 110 GPa and a linear thermal expansion coefficient a = 17.5 × 10-6/°C. The bar is initially positioned at room temperature with a gap of 0.2mm between end A and the rigid wall. The bar's right end at B is supported by an elastic spring of negligible thermal expansion coef- ficient and a spring constant of k = 210 × 10°N/m. A small gap maintained between the copper bar and the smooth surrounding sleeve facilitates frictionless motion as the bar thermally expands. Questions: (a) Compute the temperature increase ATer required to close the 0.2 mm gap. (b) Compute the axial force R developed in the copper bar due to a temperature increase of AT = 27°C. State the compatibility condition and solve it for R. (c) Compute the compressive (engineering) stress o developed within the copper bar due to the axial force R. Express your answer in MPa. (d) Compute the total axial strain of the copper bar that develops after it makes contact with the rigid wall. Express your answer in microstrains. (e) Compute the length change of the copper bar after it makes contact with the rigid wall. (f) Compute the length change of the spring. 8 = 0.2mm rigid wall L₁= 0.635m AT ww k=200x106 N/m rigid wall
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