Explanation The Rosette’s 1 and 3 are separated by 90 ° . Find the average normal strain ( ε ave ) using the relation. ε ave = ε 1 + ε 3 2 Refer to the given Mohr’s circle diagram. Consider a = ε 1 − ε ave and b = ε 2 − ε ave . a = ε 1 − ε ave = ε 1 − ( ε 1 + ε 3 2 ) = 2 ε 1 2 − ε 1 2 − ε 3 2 = ε 1 − ε 3 2 b = ε 2 − ε ave = ε 2 − ( ε 1 + ε 3 2 ) Find the radius of Mohr’s circle ( R ) as follows. R 2 = a 2 + b 2 Substitute ( ε 1 − ε 3 2 ) for a and ε 2 − ( ε 1 + ε 3 2 ) for b . R 2 = ( ε 1 − ε 3 2 ) 2 + ( ε 2 − ( ε 1 + ε 3 2 ) ) 2 = ε 1 2 − 2 ε 1 ε 2 + ε 3 2 4 + ε 2 2 − ε 2 ( ε 1 + ε 3 ) + ( ε 1 + ε 3 2 ) 2 = ε 1 2 4 − ε 1 ε 2 2 + ε 3 2 4 + ε 2 2 − ε 1 ε 2 − ε 2 ε 3 + ε 1 2 + 2 ε 1 ε 2 + ε 3 2 4 =

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Chapter 7.9, Problem 147P

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Show the principal strains are εmax,min=12(ε1+ε3)±12[(ε1−ε2)2+(ε2−ε3)2]12 using Mohr’s circle.

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Chapter 7.9, Problem 146P

Chapter 7.9, Problem 148P

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Show the principal strains are ε max , min = 1 2 ( ε 1 + ε 3 ) ± 1 2 [ ( ε 1 − ε 2 ) 2 + ( ε 2 − ε 3 ) 2 ] 1 2 using Mohr’s circle.

Solution Summary: The author illustrates the principal strains using Mohr’s circle diagram. The Rosette's 1 and 3 are separated by 90°

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Show the principal strains are εmax,min=12(ε1+ε3)±12[(ε1−ε2)2+(ε2−ε3)2]12 using Mohr’s circle.

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Chapter 7 Solutions