LECTURE+36+COE-3001-A

2 2 3x 0 x a p x a 2 2ei a x l m

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Unformatted text preview: di=onal examples that I have not covered in the chapter of your text book =tled “Deflec=ons of Beams” (in my text they are examples 8- 2 and 8- 5) •  and redo them yourself (in detail) •  Credit will only be given if it is absolutely clear that you made the effort to decipher and understand every detail of the solu=on. •  You must fill in the appropriate blanks. •  Simply transcribing the solu=on from the book with no effort to understand is unacceptable 4/9/13 M. Mello/Georgia Tech Aerospace 17 Method of SuperposiBon •  Prac=cal and commonly used technique for obtaining deflec=ons and angles of rota=ons of beams •  “here’s the gist” ☞ Equa%ons for slopes and deflec%on of a beam produced by several different loads ac%ng simultaneously is found by superposing the deflec%ons produced by the same loads ac%ng separately. •  Method is only useful when formulas for deflec%ons and slopes are available in tabulated form… (as in appendix G of your text book) •  •  When does this technique work? ☞ whenever the quan%ty to be determined is a linear func%on of the applied loads. This happens to be the case when: ☞ materials obey Hooke’s law ☞ deflec%ons and rota%ons are small ☞ presence of the deflec%ons does not alter ac%ons of the applied loads ☞ this all translates into the differen%al equa%ons being linear… 4/9/13 M. Mello/Georgia Tech Aerospace 18 EXAMPLE 8- 6 Problem: Can=lever beam supports a uniform load intensity q ac=ng over a part of the span and a concentrated load P ac=ng at the free end. The beam has length L and constant flexural rigidity EI. Determine: 1.  Deflec=on δB at the free end of the beam 2.  angle of rota=on ΘB at the free end of the beam SOLUTION: Apply superposi=on principle by combining the solu=ons of the loads ac=ng separately. 1.  Analyze displacement due to uniform load ac=ng alone 2.  consult Appendix G- 1 case 2 for load intensity (q) contribu=on at the free end 3.  consult Appendix G- 1 case 5 for point load (P) contribu=on at the free end 4/9/13 M. Mello/Georgia Tech Aerospace 19 Appendix G- 1: case 2 “q’s contribu=on to deflec=on and ( angle of rota=on at end B” 4/9/13 qa3 (4L B )1 = 24EI a) M...
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