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54 and 7.55 Determine the principal planes and the principal stresses for the state of plane stress resulting from the superposition of the two states of stress shown. 14 ksi 12 ksi 45° 8 ksi + + 8 ksi

54 and 7.55 Determine the principal planes and the principal stresses for the state of plane stress resulting from the superposition of the two states of stress shown. 14 ksi 12 ksi 45° 8 ksi + + 8 ksi

Elements Of Electromagnetics
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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7.54 plz
**Problem 7.54 and 7.55: Principal Planes and Principal Stresses in Plane Stress** **Objective:** Determine the principal planes and the principal stresses for the state of plane stress resulting from the superposition of the two states of stress shown. **Diagram Explanation:** 1. **Left Diagram:** - A square stress element is oriented with its sides not parallel to the horizontal and vertical axes. - There are arrows representing shear stresses of 8 ksi acting along the edges of the square. - The element is rotated 45 degrees counterclockwise from the horizontal axis. 2. **Right Diagram:** - A square stress element oriented with its sides parallel to the horizontal and vertical axes. - The element experiences normal stresses of 14 ksi (vertical upward), 12 ksi (horizontal to the right), 8 ksi (horizontal to the left), and a vertical downward force of 8 ksi. **Combined Analysis:** - The problem involves superposing these two states of stress to analyze the resulting principal planes and principal stresses.
Transcribed Image Text:**Problem 7.54 and 7.55: Principal Planes and Principal Stresses in Plane Stress** **Objective:** Determine the principal planes and the principal stresses for the state of plane stress resulting from the superposition of the two states of stress shown. **Diagram Explanation:** 1. **Left Diagram:** - A square stress element is oriented with its sides not parallel to the horizontal and vertical axes. - There are arrows representing shear stresses of 8 ksi acting along the edges of the square. - The element is rotated 45 degrees counterclockwise from the horizontal axis. 2. **Right Diagram:** - A square stress element oriented with its sides parallel to the horizontal and vertical axes. - The element experiences normal stresses of 14 ksi (vertical upward), 12 ksi (horizontal to the right), 8 ksi (horizontal to the left), and a vertical downward force of 8 ksi. **Combined Analysis:** - The problem involves superposing these two states of stress to analyze the resulting principal planes and principal stresses.
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