LECTURE+20+COE-3001-A

Secwons or composite areas y0 problem

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Unformatted text preview: the moment of inerWa of the composite secWon. 12.  Use the the individual moments of inerWa, areas, and distances di which you just finished determining. 2/22/13 M. Mello/Georgia Tech Aerospace 17 EXAMPLE 12- 5 ²་  SEE GERE AND GOODNO FOR STEP- BY- STEP SOLUTION FOR THE MOMENT OF INERTIA OF THIS BEAM CROSS SECTION. ²་  ESSENTIALY IDENTICAL TO THE STRATEGY OUTLINED IN THE PREVIOUS CHANNEL SECTION EXAMPLE. ²་  THIS EXAMPLE INTRODUCES YOU TO TABULATED VALUES OF THE MOMENT OF INERTIA FOR SPECIFIC STANDARDIZED BEAM SECTIONS SUCH AS THE WIDE- FLANGE SECTION (HE 450A) AND THE CHANNEL SECTION (UPN 320) ²་  CONSULT PROPETTIES OF STRUCTURAL- STEEL SHAPES TABLES IN GERE AND GOODNO (APPENDIX E) ²་  TABLES ARE PROVIDED IN THE CURRENT ASSIGNMENT ²་  APPLY THE PARALLEL- AXIS THEOREM TO COMPUTE MOMENT OF INERTIA OF BEAM CROSS SECTION 2/22/13 M. Mello/Georgia Tech Aerospace 18 Maximum Stresses at a Cross SecWon ²་  Maximum tensile and compressive bending stresses acWng at any given cross secWon occur along the top and bo=om edges of the beam along points furthest from the neutral axis (c1,c2 in the figure below) M c1 M M c2 M ²་  Maximum normal stress from flexure formula: 1 = = = = (5- 14) 2 I c1 ²་  where: S1 = and S2 = I S1 I S2 I are called secIon moduli. Units of secIon moduli: [Length]3 c2 ²་  Convenient quanIty used in beam design lumps beams cross secIonal properIes into a single term ²་  SecIon moduli listed in tables and handbooks as a property of the beam. 2/22/13 M. Mello/Georgia Tech Aerospace 19 Doubly Symmetric Beams ²་  Doubly symmetric cross secWonal profiles: Cross secWon symmetric with respect to z axis as well as y axis I Mc M S = = = = ²་  c1 = c2 = c 1 2 c I S ²་  Rectangular cross secWon: circular cross secWon: 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 inerWa with respect to x and y axes (different than polar moment of inerWa) 2/22/13 M. Mello/Georgia Tech Aerospace 20 TABLE E-1 PROPERTIES OF EUROPEAN WIDE FLANGE BEAMS Designation 1 HE HE HE HE HE S2 4 cm 3 cm r2 cm 16280 15820 14440 13980 13530 1085 1054 962.7 932.3 902 6.38 6.53 6.87 6.99 7.08 13080 11270 11720 10820 10140 9465 871.8 751.4 781.4 721.3 676.1 631 7.17 7.05 7.33 7.15 7.49 7.29...
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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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