LECTURE+19+COE-3001-A

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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