chapter 13 answers

chapter 13 answers - Problem 13.1 The components of plane...

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Unformatted text preview: Problem 13.1 The components of plane strain at point p are x = 0 . 003 , y = 0, and xy = 0 . If = 45 , what are the strains x , y , and xy at point p ? Solution: From Equation (13-7): x = x + y 2 + x y 2 (cos 2 )+ xy 2 (sin 2 ) = . 003 + 0 2 + . 003 2 (cos 90 )+ 2 (sin 90 ) ANS: x = 0 . 0015 From Equation (13-8): y = x + y 2 x y 2 (cos 2 ) xy 2 (sin 2 ) = . 003 + 0 2 . 003 2 (cos 90 ) 2 (sin 90 ) ANS: y = 0 . 0015 From Equation (13-9): xy 2 = x y 2 (sin 2 )+ xy 2 (cos 2 ) = . 003 2 (sin 90 )+ 2 (cos 90 ) ANS: xy = . 003 Problem 13.2 The components of plane strain at point p are x = 0 , y = 0 , and xy = 0 . 004 . If = 45 , what are the strains x , y , and xy at point p ? Solution: From Equation (13-7): x = x + y 2 + x y 2 (cos 2 )+ xy 2 (sin 2 ) = 0 + 0 2 + 2 (cos 90 )+ . 004 2 (sin 90 ) ANS: x = 0 . 002 From Equation (13-8): y = x + y 2 x y 2 (cos 2 ) xy 2 (sin 2 ) = 0 + 0 2 2 (cos 90 ) . 004 2 (sin 90 ) ANS: y = . 002 From Equation (13-9): xy 2 = x y 2 (sin 2 )+ xy 2 (cos 2 ) = 2 (sin 90 )+ . 004 2 (cos 90 ) ANS: xy = 0 Problem 13.3 The components of plane strain at point p are x = . 0024 , y = 0 . 0012 , and xy = . 0012 , If = 25 , what are the strains x , y , and xy at point p ? Solution: From Equation (13-7): x = x + y 2 + x y 2 (cos 2 )+ xy 2 (sin 2 ) = . 0024 + 0 . 0012 2 + . 0024 . 0012 2 (cos 50 )+ . 0012 2 (sin 50 ) ANS: x = . 00222 From Equation (13-8): y = x + y 2 x y 2 (cos 2 ) xy 2 (sin 2 ) = . 0024 + 0 . 0012 2 . 0024 . 0012 2 (cos 50 ) . 0012 2 (sin 50 ) ANS: y = 0 . 00102 From Equation (13-9): xy 2 = x y 2 (sin 2 )+ xy 2 (cos 2 ) = . 0024 . 0012 2 (sin 50 )+ . 0012 2 (cos 50 ) ANS: xy = 0 . 00099 Problem 13.4 The components of plane strain at point p of a bit during a drilling operation are x = 0 . 00400 , y = . 00300 , and xy = 0 . 00600 , and the com- ponents referred to the x y z coordinate system are x = 0 . 00125 , y = . 00025 , and xy = 0 . 00910 . What is the angle ? Solution: From Equation (13-8): . 00125 = . 004 + ( . 003) 2 + . 004 ( . 003) 2 (cos 2 )+ . 006 2 (sin 2 ) Using a graphing calculator to determine the value of : 2 = 40 ANS: = 20 Problem 13.5 The components of plane strain at point p are x = 0 . 0024 , y = . 0012 , and xy = . 0048 . The extensional strains x = 0 . 00347 , and y = . 00227 . Determine xy and the angle ....
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chapter 13 answers - Problem 13.1 The components of plane...

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