Elements Of Electromagnetics
7th Edition
ISBN: 9780190698614
Author: Sadiku, Matthew N. O.
Publisher: Oxford University Press
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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.
Transcribed Image Text: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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