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Problem 2) As a result of loading, the rectangle with a = 25 mm and b = 18 mm deforms into a paral- lelogram in which sides QA and BC shorten by 0.003 mm and rotate by 550uɛ rad counterclockwise. Sides AB and QC elongate by 0.004 mm and rotate by 1000 µɛ rad clockwise. Find the principal strains and principal axes at point Q. Sketch a body showing the orientation and deformation of each

Problem 2) As a result of loading, the rectangle with a = 25 mm and b = 18 mm deforms into a paral- lelogram in which sides QA and BC shorten by 0.003 mm and rotate by 550uɛ rad counterclockwise. Sides AB and QC elongate by 0.004 mm and rotate by 1000 µɛ rad clockwise. Find the principal strains and principal axes at point Q. Sketch a body showing the orientation and deformation of each

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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**Problem 2**: As a result of loading, the rectangle with \( a = 25 \, \text{mm} \) and \( b = 18 \, \text{mm} \) deforms into a parallelogram in which sides \( QA \) and \( BC \) shorten by \( 0.003 \, \text{mm} \) and rotate by \( 550 \, \mu \varepsilon \, \text{rad} \) counterclockwise. Sides \( AB \) and \( QC \) elongate by \( 0.004 \, \text{mm} \) and rotate by \( 1000 \, \mu \varepsilon \, \text{rad} \) clockwise. Find the principal strains and principal axes at point \( Q \). Sketch a body showing the orientation and deformation of each principal strain.
Transcribed Image Text:**Problem 2**: As a result of loading, the rectangle with \( a = 25 \, \text{mm} \) and \( b = 18 \, \text{mm} \) deforms into a parallelogram in which sides \( QA \) and \( BC \) shorten by \( 0.003 \, \text{mm} \) and rotate by \( 550 \, \mu \varepsilon \, \text{rad} \) counterclockwise. Sides \( AB \) and \( QC \) elongate by \( 0.004 \, \text{mm} \) and rotate by \( 1000 \, \mu \varepsilon \, \text{rad} \) clockwise. Find the principal strains and principal axes at point \( Q \). Sketch a body showing the orientation and deformation of each principal strain.
The image features a rectangle positioned on an XY coordinate plane. - The rectangle has vertices labeled as A, B, C, and Q. - Vertex A is positioned at the top-left corner of the rectangle. - Vertex B is positioned at the top-right corner. - Vertex C is at the bottom-right corner. - Vertex Q is located at the bottom-left corner. The horizontal dimension (length) of the rectangle is labeled "a," while the vertical dimension (width) is labeled "b." The positive x-axis extends to the right, originating from point Q, passing through point C. Similarly, the positive y-axis extends upwards, originating from point Q, passing through point A. This diagram is useful for explaining basic geometric and coordinate plane concepts, illustrating how rectangles can be oriented within a coordinate system.
Transcribed Image Text:The image features a rectangle positioned on an XY coordinate plane. - The rectangle has vertices labeled as A, B, C, and Q. - Vertex A is positioned at the top-left corner of the rectangle. - Vertex B is positioned at the top-right corner. - Vertex C is at the bottom-right corner. - Vertex Q is located at the bottom-left corner. The horizontal dimension (length) of the rectangle is labeled "a," while the vertical dimension (width) is labeled "b." The positive x-axis extends to the right, originating from point Q, passing through point C. Similarly, the positive y-axis extends upwards, originating from point Q, passing through point A. This diagram is useful for explaining basic geometric and coordinate plane concepts, illustrating how rectangles can be oriented within a coordinate system.
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