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

2024
Views:

328

Pages:

2
Author:

Kundulu8mbj

COSMOS: Complete Online Solutions Manual Organization System Chapter 9, Solution 99. I xy = 567 in 4 From the solution to Problem 9.76 Now I x = ( I x )1 − ( I x )2 − ( I x )3 , where = π 4 ( I x ) 2 = ( I x )3 1 12 (15 in.)4 − 2  ( 9 in.)( 6 in.)3  = ( 39761 − 324 ) in 4  = 39, 437 in 4 ( )1 − ( I y )2 − ( I y )3 , Iy = Iy and = π 4 where ( I y )2 = ( I y )3 1  36 1 2 (15 in.)4 − 2  ( 6 in.)( 9 in.)3 + ( 9 in.)( 6 in.)( 6 in.)2   = ( 39, 761 − 243 − 1944 ) in 4 = 37,574 in 4 The Mohr’s circle is defined by the point (X, Y) where X: I ave = Now ( I x , I xy ) R= ( I y , −I xy ) 1 1 I x + I y = ( 39, 437 + 37,574 ) in 4 = 38,506 in 4 2 2 ( ) 2 and Y:  Ix − I y  2   + I xy = 2   2 1  2 4  2 ( 39, 437 − 37,574 )  + 567 = 1090.5 in   continued COSMOS: Complete Online Solutions Manual Organization System tan 2θ m = − I xy Ix − I y 2 = −567 = −0.6087 1 ( 39, 437 − 37,574 ) 2 or θ m = −15.66° clockwise Then I max, min = I ave ± R = ( 38,506 ± 1090.50 ) in 4 or I max = 39.6 × 103 in 4 and I min = 37.4 × 103 in 4 Note: From the Mohr’s circle it is seen that the a axis corresponds to the I max and the b axis corresponds to I min .

COSMOS Chapter 9 Solution 99

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