This preview shows page 1. Sign up to view the full content.
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...
View Full
Document
 Spring '09
 ZHU

Click to edit the document details