COSMOS Chapter 9 Solution 101 | Answer Key - Edubirdie

University:
Michigan State University
Course:
ERG 160 | Success in Science, Technology, Engineering, and Mathematics
Academic year:

2019
Views:

139

Pages:

1
Author:

marthamanayay9qr12

COSMOS: Complete Online Solutions Manual Organization System Chapter 9, Solution 101. From Problems 9.74 and 9.83 I x = 0.166 × 106 mm 4 , I y = 0.453 × 106 mm 4 , X ( 0.166, −0.1596 ) × 106 mm 4 Define points I ave = Now and I xy = −0.1596 × 106 mm 4 Y ( 0.453, 0.1596 ) × 106 mm 4 1 1 I x + I y = ( 0.166 + 0.453) × 106 mm 4 2 2 ( ) = 0.3095 × 106 mm 4 2 and R=  Ix − I y  2   + I xy = 2   2  ( 0.166 − 0.453) × 106  6   + −0.1596 × 10 2   ( ) 2 = 0.21463 × 106 mm 4 Also  −2I xy 2θ m = tan −1   Ix − I y    −2 ( −0.1596 )   = tan −1   = −48.04°   0.166 − 0.453   θ m = −24.02° or θ = −24.0° clockwise Then I max, min = I ave ± R = ( 0.3095 ± 0.21463) × 106 mm 4 or I max = 0.524 × 106 mm 4 and I min = 0.0949 × 106 mm 4 Note: From the Mohr’s circle it is seen that the a axis corresponds to I min and the b axis corresponds to I max .

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