Other rigidity factors that we have

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Unformatted text preview: axis I Mc M S = = = = ²་  c1 = c2 = c 1 2 c I S ²་  Rectangular cross sec\on: circular cross sec\on: d h c1 = c2 = c = c1 = c2 = c = 2 2 bh3 I= 12 ⇡ d4 I= 64 bh2 S= 6 (5- 16) ⇡ d3 S= 32 Note: moment of iner\a with respect to x and y axes (different than polar moment of iner\a) 2/22/13 M. Mello/Georgia Tech Aerospace 30 Limita\ons of the theory presented so far… •  Only strictly applies only to pure bending of prisma\c beams composed of homogeneous, linear elas\c materials •  •  Nonuniform bending implies that shear forces are present. If shear forces present then warping will result (out of plane distor\on) and Ini\ally plane cross sec\ons will not remain plane aGer bending. This complicates things! •  The good news is … the flexure formula s\ll works pre=y well! Normal stress calculated from the flexure formula is s\ll fairly accurate even in the presence of shear forces and associated warping. •  The flexure formula can therefore be applied to beams subjected to nonuniform bending •  Must s\ll avoid loca\ons where the beam abruptly changes shape or where there may be sharp discon\nui\es in loading such as near the supports or close to a concentrated load. 2/22/13 M. Mello/Georgia Tech Aerospace 31...
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This note was uploaded on 09/19/2013 for the course CEE 3001 taught by Professor Zhu during the Spring '09 term at Georgia Tech.

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