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

2021
Views:

240

Pages:

2
Author:

palangresq3v

COSMOS: Complete Online Solutions Manual Organization System Chapter 9, Solution 107. I x = 7.20 × 106 mm 4 , From Figure 9.13B: ( )1 + ( I xy )2 , I xy = I xy Have x1 = Now where 102 − 25.3 = 25.7 mm, 2 I y = 2.64 × 106 mm 4 I xy = I x′y′ + x yA y1 = 50.3 − and I x′y′ = 0 12.7 = 43.95 mm 2 A1 = 102 × 12.7 = 1295.4 mm 2 x2 = −25.3 + 12.7 = −18.95 mm 2 1  y2 = −  (152 − 12.7 ) − ( 50.3 − 12.7 )  = − 32.05 mm 2  A2 = (12.7 )(152 − 12.7 ) = 1769.11 mm 2 Then { ( ) ( )} I xy = ( 25.7 mm )( 43.95 mm ) 1295.4 mm 2  + ( −18.95 mm )( −32.05 mm ) 1769.11 mm 2  × 106     = (1.46317 + 1.07446 ) × 106 mm 4 = 2.5376 × 106 mm 4 The Mohr’s circle is defined by points X and Y, where ( ) ( X I x , I xy , Y I y , − I Now I ave = ) 1 1 I x + I y = ( 7.20 + 2.64 ) × 106 mm 4 = 4.92 × 106 mm 4 2 2 ( ) continued COSMOS: Complete Online Solutions Manual Organization System and R= 2 2    Ix − I y  1  2 2 6 4   + I xy =   ( 7.20 − 2.64 )  + 2.5376  × 10 mm   2 2       = 3.4114 × 106 mm 4 tan θ m = − 2I xy Ix − I y =− 2 ( 2.5376 ) = −1.11298, ( 7.20 − 2.64 ) 2θ = −48.0607° θ = −24.0° clockwise or Now or and I max, min = I ave ± R = ( 4.92 ± 3.4114 ) × 106 mm 4 I max = 8.33 × 106 mm 4 I min = 1.509 × 106 mm 4 Note: From the Mohr’s circle it is seen that the a axis corresponds to I max and the b axis corresponds to I min .