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Week 8: moment about center

by: Eleanor Notetaker

Week 8: moment about center coe 3001 I

Eleanor Notetaker
Georgia Tech
Deformable Bodies
Dr. Kennedy

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About this Document

It begins with deflections on beams. It then moves on to talk about how to find the moments about the center of an object (and how to find the center). We also go over the parallel axis theorem.
Deformable Bodies
Dr. Kennedy
Class Notes
25 ?




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This 9 page Class Notes was uploaded by Eleanor Notetaker on Sunday October 11, 2015. The Class Notes belongs to coe 3001 I at Georgia Institute of Technology taught by Dr. Kennedy in Summer 2015. Since its upload, it has received 53 views. For similar materials see Deformable Bodies in Engineering and Tech at Georgia Institute of Technology.

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Date Created: 10/11/15
COE 3001 Mechanics of Deformable Bodies Week 8 LE ds p aB gtp ds ds z dX for small de ections e dl39 dx x dx dl p yde 3p cB dede yde d9 exz yE yk yk Stresses in beams 0 linear elastic materials Ox 2 E ex yEK 0 Find relationship between O39X and MX COE 3001 Mechanics of Deformable Bodies Week 8 In general El El Mx EyZKdAZEKIyZdA A A El IZZI ysz A MxEIzK Mx EIZ O yEK x Flexure Formula yM x x I Z 039 Max stresses occur at max absolute distance from centerline Axial force a a Nxf OxydA nyKdA A A u L EK I ydA 0 for pure bending A El ydAzo A 0 quotbalance pointquot COE 3001 Mechanics of Deformable Bodies Week 8 2nd moments of area Example COE 3001 Mechanics of Deformable Bodies Week 8 b h 2 2 2 2 2210 22 2 Circular crosssection H 4 I d x 64 H 4 I d y 64 Parallel axis theorem 0 Given 2nd moments of area in initial frame determine moments of area in final frame El ycdydAf yf2ycdydy2dA Ac I ysz2 x gtD gt5 CI CI CI tfyfdA2yfychdy2fdA Ac Ac AC z Ixcdy2A COE 3001 Mechanics of Deformable Bodies Week 8 x z LCLL22xCdxdx2dAIy 61sz z 2 1y I x dA f r A A Method of com osite Areas 0 Area decomposed into simple areas 0 Area with known crosssectional properties fy ycdA0 CI ydA ycAzo Centroid ID 1 CI CI CI ycz fydAz mm ydAfydA A A A A1 A2 A3 CI yclAFf ydA A1 C 1 C C C y 2 Y1A1y 2A2y 3A3l c 1 c c c Apply parallel axis theorem IyZchllxcl 2A11y02x622A2Iy03x632 A3 COE 3001 Mechanics of Deformable Bodies Week 8 xcl is different from xc found before new frame IxZIxclIycl2A1Ixc2y622A2Ixc3yc32A3 If we have it is symmetric so we immediately know yaxis from balance point so we only need to find x axis Example 1 Hollow circular section 0 By symmetry centroid is at center Ixc6 4d04 51263444 Ix6 4d04 d4 zy6 4ltdotdfgt 0 What is stress 0 1st need to define point yd02 results in max stress Example 2 Calculate IX a Ixzf yszzlxl Ixz Ix3 COE 3001 Mechanics of Deformable Bodies Week 8 h Zt3b t I 2 1 x2 12 x3 Note PAT Ix2dy2 A h3bh 2t3b t quot 12 12 I Example 3 Select reference oint vim mm c c b t c x1 x3 c Iv Mm x 2tbth t 2nd moment of inertia c X Alztb A2th t A3tb A22mMh 1 C C C x1A1x 2A2x 3A3 COE 3001 Mechanics of Deformable Bodies Week 8 h t3t 12 2 Z I 7 gtU g Q amp Dgt II N1 5 1 g He 1 9 N1 3 L x we 1 Dgt J N1 8 L x we 1 Dgt m 22 12 b 2 2 7 Example 4 0 Find max absolute stress in bar COE 3001 Mechanics of Deformable Bodies Week 8 RAZqL L MAqL E x 1 5 RAx qL20 A13pr exture formula yMx O39x Iz CI IZZIyZdA A 3 b t b 2t 2 I 2 w 1 Z 12 2 12 Iz277x103i4 ymax48 Om18psi


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