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)
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...
Related questions
Question
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 7 steps with 1 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning