A beam of the cross section shown is made of a steel that is assumed to be elastoplastic with E= 200 GPa. The be axis. A couple of moment equal to the full plastic moment Mp is applied and then removed. Using a yield strength determine the residual stress at y = 45 mm. C 30 mm 30 imm 30 inm

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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**Problem Description:**

A beam of the cross-section shown is made of a steel that is assumed to be elastoplastic with \( E = 200 \, \text{GPa} \). The bending is about the z-axis. A couple of moment equal to the full plastic moment \( M_p \) is applied and then removed. Using a yield strength of 236 MPa, determine the residual stress at \( y = 45 \, \text{mm} \).

**Diagram Explanation:**

The diagram displays a cross-section of the beam with dimensions indicated:

- The overall height of the beam is 90 mm, divided into three segments of 30 mm each.
- The width is 15 mm on either side and 30 mm in the central segment.

The cross-section is symmetrical about the y-axis, and the bending occurs around the z-axis that is perpendicular to the length of the rectangle. 

**Calculation:**

(Fill in calculation details here, which can be derived based on the information provided and using principles of elastoplastic behavior and bending stress distribution.)

**Answer:**

The residual stress is \( \boxed{} \) MPa.

(Note: Insert the numerical value obtained from the detailed calculation in the box, if performed.)
Transcribed Image Text:**Problem Description:** A beam of the cross-section shown is made of a steel that is assumed to be elastoplastic with \( E = 200 \, \text{GPa} \). The bending is about the z-axis. A couple of moment equal to the full plastic moment \( M_p \) is applied and then removed. Using a yield strength of 236 MPa, determine the residual stress at \( y = 45 \, \text{mm} \). **Diagram Explanation:** The diagram displays a cross-section of the beam with dimensions indicated: - The overall height of the beam is 90 mm, divided into three segments of 30 mm each. - The width is 15 mm on either side and 30 mm in the central segment. The cross-section is symmetrical about the y-axis, and the bending occurs around the z-axis that is perpendicular to the length of the rectangle. **Calculation:** (Fill in calculation details here, which can be derived based on the information provided and using principles of elastoplastic behavior and bending stress distribution.) **Answer:** The residual stress is \( \boxed{} \) MPa. (Note: Insert the numerical value obtained from the detailed calculation in the box, if performed.)
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