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

2024
Views:

334

Pages:

2
Author:

Arielle Armstrong

COSMOS: Complete Online Solutions Manual Organization System Chapter 9, Solution 53. Locate centroid: x1 = 15.3 mm y1 = 127 mm A1 = 3780 mm 2 x2 = − 21.4 mm y2 = 76 mm − 21.4 mm A2 = 932 mm 2 = 54.6 mm x3 = − 21.4 mm y3 = 76 mm + 21.4 mm A3 = 932 mm 2 = 97.4 mm Then x= = Σxi Ai ΣΑi (15.3 mm ) ( 3780 mm 2 ) + 2 ( − 21.4 mm ) ( 932 mm 2 ) ( 3780 mm 2 + 2 932 mm 2 ) = 3.1794 mm And y= = Σyi Ai ΣΑi (127 mm ) ( 3780 mm 2 ) + ( 76 mm ) ( 2 × 932 mm 2 ) ( 3780 mm 2 + 2 932 mm 2 ) = 110.157 mm Now I x = ( I x )1 + ( I x )2 + ( I x )3 ( ) 2 = 32.6 × 106 mm 4 + 3780 mm 2 (127 mm − 110.157 mm )    ( ) + ( 932 mm ) (110.157 mm − 97.4 mm )   2 + 0.517 × 106 mm 4 + 932 mm 2 (110.157 mm − 54.6 mm )    + 0.517 × 106 mm 4  2 2 continued COSMOS: Complete Online Solutions Manual Organization System ( ) ( + 0.151675 × 10 )  mm  =  32.6 × 106 + 1.07234 × 106 + 0.517 × 106 + 2.8767 × 106  ( + 0.517 × 106 6 ) 4 I x = 37.7 × 106 mm 4 And ( )1 + ( I y )2 + ( I y )3 Iy = Iy ( ) 2 = 1.14 × 106 mm 4 + 3780 mm 2 (15.3 mm − 3.1794 mm )    ( ) 2 + 2 0.517 × 106 mm 4 + 932 mm 4 ( 3.1794 mm + 21.4 mm )    ( ) ( ) =  1.14 × 106 + 0.55532 × 106 + 2 0.517 × 106 + 0.56306 × 106  mm 4   I y = 3.86 × 106 mm 4