Problem 1-7 - R 0.5 D . R 1.5 in = Area A D 2 . 8 A 3.534...

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MACHINE DESIGN - An 1-7-1 PROBLEM 1-7 Statement: Prepare a Mathcad template from which the cross-sectional properties for the shapes shown in Appendix A can be calculated. Solution: See Appendix A and Mathcad file P0107. 1. Rectangle, let: b 3 in . h 4 in . Area Ab h . A 12.000 in 2 = Moment about x -axis I x bh 3 . 12 I x 16.000 in 4 = Moment about y -axis I y hb 3 . 12 I y 9.000 in 4 = Radius of gyration about x -axis k x I x A k x 1.155 in = Radius of gyration about y -axis k y I y A k y 0.866 in = Polar moment of inertia J z I x I y J z 25.000 in 4 = 2. Solid circle, let: D 3 in . Area A π D 2 . 4 A 7.069 in 2 = Moment about x -axis I x D 4 . 64 I x 3.976 in 4 = Moment about y -axis I y D 4 . 64 I y 3.976 in 4 = Radius of gyration about x -axis k x I x A k x 0.750 in = Radius of gyration about y -axis k y I y A k y 0.750 in = Polar moment of inertia J z D 4 . 32 J z 7.952 in 4 = 3. Hollow circle, let: D 3 in . d 1 in . Area A 4 D 2 d 2 . A 6.283 in 2 = Moment about x -axis I x 64 D 4 d 4 . I x 3.927 in 4 = P 0107.mcd
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MACHINE DESIGN - An 1-7-2 Moment about y -axis I y π 64 D 4 d 4 . I y 3.927 in 4 = Radius of gyration about x -axis k x I x A k x 0.791 in = Radius of gyration about y -axis k y I y A k y 0.791 in = Polar moment of inertia J z 32 D 4 d 4 . J z 7.854 in 4 = 4. Solid semicircle, let: D 3 in .
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Unformatted text preview: R 0.5 D . R 1.5 in = Area A D 2 . 8 A 3.534 in 2 = Moment about x-axis I x 0.1098 R 4 . I x 0.556 in 4 = Moment about y-axis I y R 4 . 8 I y 1.988 in 4 = Radius of gyration about x-axis k x I x A k x 0.397 in = Radius of gyration about y-axis k y I y A k y 0.750 in = Polar moment of inertia J z I x I y J z 2.544 in 4 = Distances to centroid a 0.4244 R . a 0.637 in = b 0.5756 R . b 0.863 in = 5. Right triangle, let: b 2 in . h 1 in . Area A b h . 2 A 1.000 in 2 = Moment about x-axis I x b h 3 . 36 I x 0.056 in 4 = Moment about y-axis I y h b 3 . 36 I y 0.222 in 4 = Radius of gyration about x-axis k x I x A k x 0.236 in = P 0107.mcd MACHINE DESIGN - An 1-7-3 Radius of gyration about y-axis k y I y A k y 0.471 in = Polar moment of inertia J z I x I y J z 0.278 in 4 = P 0107.mcd...
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This note was uploaded on 04/26/2010 for the course MAE 3242 taught by Professor N/a during the Fall '10 term at University of Texas-Tyler.

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Problem 1-7 - R 0.5 D . R 1.5 in = Area A D 2 . 8 A 3.534...

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