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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,...
εxx = 0.001, εyy = 0.002
rxy = 0.003
Length of the diagonal (PR)
rxy = 0.003
Length of the diagonal (PR)
To find the diagonal (PR) strain, the direction of the plane angle from the +ve x-axis will from `R` towards `P`
εθ= ?
εθ= ?
Where θ = 180 + tan -1 (3 / 4) 216.87°
Most Upvoted Answer
A rectangular region in a solid is in a state of plane strain. The (x,...
Εx and εy, in the x and y directions respectively. To find the deformed coordinates of the rectangle, we can use the equation:
x' = x + εx * x
y' = y + εy * y
Let's calculate the deformed coordinates of each corner:
For point P (0,0):
x' = 0 + εx * 0 = 0
y' = 0 + εy * 0 = 0
So the deformed coordinate of P is (0,0).
For point Q (4,0):
x' = 4 + εx * 4 = 4εx
y' = 0 + εy * 0 = 0
So the deformed coordinate of Q is (4εx,0).
For point S (0,3):
x' = 0 + εx * 0 = 0
y' = 3 + εy * 3 = 3εy
So the deformed coordinate of S is (0,3εy).
Therefore, the deformed rectangle has corners P'(0,0), Q'(4εx,0), and S'(0,3εy).
x' = x + εx * x
y' = y + εy * y
Let's calculate the deformed coordinates of each corner:
For point P (0,0):
x' = 0 + εx * 0 = 0
y' = 0 + εy * 0 = 0
So the deformed coordinate of P is (0,0).
For point Q (4,0):
x' = 4 + εx * 4 = 4εx
y' = 0 + εy * 0 = 0
So the deformed coordinate of Q is (4εx,0).
For point S (0,3):
x' = 0 + εx * 0 = 0
y' = 3 + εy * 3 = 3εy
So the deformed coordinate of S is (0,3εy).
Therefore, the deformed rectangle has corners P'(0,0), Q'(4εx,0), and S'(0,3εy).
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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 GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE 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 GATE 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?.
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 GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE 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 GATE 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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