751_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

751_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 09Ch09.qxd 9/27/08 1:33 PM Page 745 745 SECTION 9.6 Moment-Area Method If P2 ACTS ALONE ¿¿ dH P2L3 3EI P2L3 3EI ¿¿ dv uBL P2L3 2EI a (to the left) P2L2 bL EI P2L3 2EI L3 (2P1 6EI 3Pcosa + 8Psina 2Pcosa 3Psina dv 4P2L3 3EI L3 ( 6EI 3 + 8 tana 3 tana The deflection of point C is in the same direction as the load P. 3P2) ‹ tan a (to the right) P1L3 2EI 2 PRINCIPAL DIRECTIONS DEFLECTIONS DUE TO THE LOAD P P1L3 3EI 3P1 8P2 2P1 3P2 4P2L3 3EI (upward) dH dv dH 3P1 + 8P2) P2 P1 d dH 1 ; 12 Rearrange and simplity: tan2a (quadratic equation) Solving, tan a (upward) 3 + 8 tan a 2 3 tan a or tan a a ° 22.5 , ° 112.5 , 67.5°, 2 tan a 157.5° 1 0 ; Moment-Area Method q The problems for Section 9.6 are to be solved by the moment-area method. All beams have constant flexural rigidity EI. Problem 9.6-1 A cantilever beam AB is subjected to a uniform load of intensity q B A acting throughout its length (see figure). Determine the angle of rotation uB and the deflection dB at the free end. L Solution 9.6-1 Cantilever beam (uniform load) M EI DIAGRAM: uB/A uA uB 0 uA uB A1 qL3 6EI qL3 6EI (clockwise) ; DEFLECTION Q1 Q1 ANGLE OF ROTATION Use absolute values of areas. Appendix D, Case 18: A1 x 3L 4 qL2 1 (L) a b 3 2EI qL3 6EI dB First moment of area A1 with respect to B qL4 qL3 3L ba b A1x a 6EI 4 8EI 4 qL Q1 (Downward) ; 8EI (These results agree with Case 1, Table G-1.) ...
View Full Document

This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.

Ask a homework question - tutors are online