I accidentally submitted the wrong question initially. This is the correct one. I do not know how to progress past finding the force at yielding. The two-segment statically indeterminate bar in Fig. has a constant cross-sectional area $ A = 0.8 \, \text{in}^2 $.It is made entirely of material that has an elastic, perfectly-plastic stress-strain behavior illustrated, with $ \sigma_Y = 36 \, \text{ksi} $ and $ E = 30 \times 10^3 \, \text{ksi} $.(a) Determine the load $ P_Y $ at which first yielding occurs, and determine the corresponding displacement $ u_Y $ of section B where the load $ P $ is applied.(b) Determine the load $ P_U $ at which yielding occurs in the remaining segment of the bar, and determine the corresponding displacement $ u_U $ of section B.(c) Sketch a load-displacement diagram, that is, sketch a diagram of $ P $ versus $ u $ up to $ P_U $.### Explanation of Graphs/Diagrams:**(a) A two-segment bar:**The diagram shows a vertical bar with two segments: - Segment AB is 20 inches long.- Segment BC is 40 inches long.The load is applied at point B. Cross section of the entire bar is constant. **(b) A stress-strain diagram for an elastic, perfectly-plastic material:**- The $ y $-axis represents stress ($ \sigma $), and the $ x $-axis represents strain ($ \varepsilon $).- The graph shows a linear region where stress is proportional to strain (Hooke's Law) up to the yield stress $ \sigma_Y $.- Beyond the yield point, the material exhibits perfectly plastic behavior where the stress remains constant as strain increases.

(a) To find: The load Py and corresponding displacement uy. Given: The cross-sectional area is A=0.8…

The two-segment statically indeterminate bar in Fig. has a constant cross-sectional area A -0.8 in². It is made entirely of material that has an elastic, per- fectly-plastic stress-strain behavior illustrated , with oy - 36 ksi and E-30 x 10 ksi. (a) Determine the load Py at which first yielding occurs, and determine the corresponding displacement uy of section B where the load P is applied. (b) Determine the load P at which yielding occurs in the remaining segment of the bar, and determine the corresponding displacement u, of section B. (c) Sketch a load-displacement diagram, that is, sketch a diagram of P versus & up to P 20 in (a) A two-segment bar. (b) A stress-strain diagram for an elastic, perfectly-plastic material.

The two-segment statically indeterminate bar in Fig. has a constant cross-sectional area A -0.8 in². It is made entirely of material that has an elastic, per- fectly-plastic stress-strain behavior illustrated , with oy - 36 ksi and E-30 x 10 ksi. (a) Determine the load Py at which first yielding occurs, and determine the corresponding displacement uy of section B where the load P is applied. (b) Determine the load P at which yielding occurs in the remaining segment of the bar, and determine the corresponding displacement u, of section B. (c) Sketch a load-displacement diagram, that is, sketch a diagram of P versus & up to P 20 in (a) A two-segment bar. (b) A stress-strain diagram for an elastic, perfectly-plastic material.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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I accidentally submitted the wrong question initially. This is the correct one. I do not know how to progress past finding the force at yielding.

The two-segment statically indeterminate bar in Fig. has a constant cross-sectional area $ A = 0.8 \, \text{in}^2 $.

It is made entirely of material that has an elastic, perfectly-plastic stress-strain behavior illustrated, with $ \sigma_Y = 36 \, \text{ksi} $ and $ E = 30 \times 10^3 \, \text{ksi} $.

(a) Determine the load $ P_Y $ at which first yielding occurs, and determine the corresponding displacement $ u_Y $ of section B where the load $ P $ is applied.

(b) Determine the load $ P_U $ at which yielding occurs in the remaining segment of the bar, and determine the corresponding displacement $ u_U $ of section B.

(c) Sketch a load-displacement diagram, that is, sketch a diagram of $ P $ versus $ u $ up to $ P_U $.

### Explanation of Graphs/Diagrams:

**(a) A two-segment bar:**

The diagram shows a vertical bar with two segments:
- Segment AB is 20 inches long.
- Segment BC is 40 inches long.

The load is applied at point B. Cross section of the entire bar is constant.

**(b) A stress-strain diagram for an elastic, perfectly-plastic material:**

- The $ y $-axis represents stress ($ \sigma $), and the $ x $-axis represents strain ($ \varepsilon $).
- The graph shows a linear region where stress is proportional to strain (Hooke's Law) up to the yield stress $ \sigma_Y $.
- Beyond the yield point, the material exhibits perfectly plastic behavior where the stress remains constant as strain increases.

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