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

2019
Views:

213

Pages:

1
Author:

salcignofi14

COSMOS: Complete Online Solutions Manual Organization System Chapter 9, Solution 41. Determination of centroid: y = 0 by symmetry. Part 1 2 3 Σ x = Area (3( 0.75 ) ) = 2.25 2 6 ( 0.75 ) = 4.50 3 ( 0.75 ) = 2.25 9.00 x ( in.) 1.5 ( ) xA in 3 3.375 0.375 1.6875 1.5 3.375 8.4375 ΣxA 8.4375 in 3 = = 0.9375 in. ΣΑ 9.00 in 2 Determination of I x : Part : I x = 1 ( 3 in.)( 0.75 in.)3 + ( 3 in.)( 0.75 in.)( 3.375 in.)2 = 25.734 in 4 12 1 Part : I x = ( 0.75 in.)( 6 in.)3 = 13.50 in 4 12 Part : (Same as Part ) I x = 25.734 in 4 Entire Section: I x = ( 25.734 + 13.50 + 25.734 ) in 4 = 64.97 in 4 I x = 65.0 in 4 Determination of I y : Part : I y = 2 1 ( 0.75 in.)( 3 in.)3 + ( 0.75 in.)( 3 in.) (1.5 − 0.9375) in. 12 = 2.3994 in 4 Part : I y = 2 1 ( 6 in.)( 0.75 in.)3 + ( 6 in.)( 0.75 in.) ( 0.9375 − 0.375) in. 12 = 1.6348 in 4 Part : (Same as Part ) I y = 2.3994 in 4 Entire Section: I y = ( 2.3994 + 1.6348 + 2.3994 ) in 4 = 6.434 in 4 I y = 6.43 in 4

COSMOS Chapter 9 Solution 41

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