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A rectangular region in a solid is in a state of plane strain. The (x,y) coordinates of the corners of the under deformed rectangle are given by P(0,0), Q (4,0), S (0,3). The rectangle is subjected to uniform strains,εxx =0.001 , εyy =0.002, γxy =0.003. The deformed length of the elongated diagonal, up to three decimal places, is _________ units.
Correct answer is between '5.013,5.015'. Can you explain this answer?
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A rectangular region in a solid is in a state of plane strain. The (x,...
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A rectangular region in a solid is in a state of plane strain. The (x,...
Given Information
We are given the coordinates of the corners of the under deformed rectangle as:
P(0,0), Q(4,0), S(0,3)
The uniform strains applied on the rectangle are:
xx = 0.001
yy = 0.002
xy = 0.003
Calculating the Deformed Length of Elongated Diagonal
To calculate the deformed length of the elongated diagonal, we can use the formula:
L' = √(Δx'^2 + Δy'^2)
Calculating Δx' and Δy'
Δx' represents the change in x-coordinate and Δy' represents the change in y-coordinate after deformation.
For point P(0,0),
Δx' = xx * x + xy * y = 0.001 * 0 + 0.003 * 0 = 0
Δy' = xy * x + yy * y = 0.003 * 0 + 0.002 * 0 = 0
For point Q(4,0),
Δx' = xx * x + xy * y = 0.001 * 4 + 0.003 * 0 = 0.004
Δy' = xy * x + yy * y = 0.003 * 4 + 0.002 * 0 = 0.012
For point S(0,3),
Δx' = xx * x + xy * y = 0.001 * 0 + 0.003 * 3 = 0.009
Δy' = xy * x + yy * y = 0.003 * 0 + 0.002 * 3 = 0.006
Calculating the Length of Elongated Diagonal
Using the coordinates of the deformed rectangle, we can calculate the length of the elongated diagonal:
L' = √(Δx'^2 + Δy'^2)
L' = √(0.004^2 + 0.012^2) = √(0.000016 + 0.000144) ≈ √0.00016 ≈ 0.012649 ≈ 0.013 (up to three decimal places)
Final Answer
The deformed length of the elongated diagonal is approximately 0.013 units.
However, the correct answer is given between 5.013 and 5.015 units. It seems that there might be a mistake in the given information or the calculations. Please recheck the values and calculations to find the correct answer.
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A rectangular region in a solid is in a state of plane strain. The (x,y) coordinates of the corners of the under deformed rectangle are given by P(0,0), Q (4,0), S (0,3). The rectangle is subjected to uniform strains,εxx=0.001 ,εyy=0.002,γxy=0.003.The deformed length of the elongated diagonal, up to three decimal places, is _________ units.Correct answer is between '5.013,5.015'. Can you explain this answer?
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A rectangular region in a solid is in a state of plane strain. The (x,y) coordinates of the corners of the under deformed rectangle are given by P(0,0), Q (4,0), S (0,3). The rectangle is subjected to uniform strains,εxx=0.001 ,εyy=0.002,γxy=0.003.The deformed length of the elongated diagonal, up to three decimal places, is _________ units.Correct answer is between '5.013,5.015'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A rectangular region in a solid is in a state of plane strain. The (x,y) coordinates of the corners of the under deformed rectangle are given by P(0,0), Q (4,0), S (0,3). The rectangle is subjected to uniform strains,εxx=0.001 ,εyy=0.002,γxy=0.003.The deformed length of the elongated diagonal, up to three decimal places, is _________ units.Correct answer is between '5.013,5.015'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rectangular region in a solid is in a state of plane strain. The (x,y) coordinates of the corners of the under deformed rectangle are given by P(0,0), Q (4,0), S (0,3). The rectangle is subjected to uniform strains,εxx=0.001 ,εyy=0.002,γxy=0.003.The deformed length of the elongated diagonal, up to three decimal places, is _________ units.Correct answer is between '5.013,5.015'. Can you explain this answer?.
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