750_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

750_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 9/27/08 744 1:33 PM Page 744 CHAPTER 9 Deflections of Beams dC 5qL4 384EI qb2 L2 a b 2 8EI qL2 (5L2 384EI 24b2) (downward is positive) (1) Rearrange and simplify the equation: 48b4 96b3L 24b2L2 16bL3 5L4 or b3 b2 b4 48 a b + 96 a b + 24 a b L L L BEAM AB: 0 (a) RATIO b 16 a b L 5 0 b L Solve the preceding equation numerically: b L Table G-1, Case 1: dA qb4 8EI uBb qb4 8EI qb (3b3 + 6b2L 24EI qL 2 (L 24EI 6b2)b dC 3 L) DEFLECTION dC EQUALS DEFLECTION dA 24b2) qb (3b3 + 6b2L 24EI b L Say, 0.4030 ; (b) DEFLECTION dC (EQ. 1) (downward is positive) qL2 (5L2 384EI 0.40301 L3) qL2 (5L2 24b2) 384EI qL2 24 (0.40301 L)2] [5L2 384EI qL4 0.002870 EI ; (downward deflection) Problem 9.5-24 A frame ABC is loaded at point C by a force P acting at an angle a to the horizontal (see figure). Both members of the frame have the same length and the same flexural rigidity. Determine the angle a so that the deflection of point C is in the same direction as the load. (Disregard the effects of axial deformations and consider only the effects of bending due to the load P.) Note: A direction of loading such that the resulting deflection is in the same direction as the load is called a principal direction. For a given load on a planar structure, there are two principal directions, perpendicular to each other. P L a B C L A Solution 9.5-24 Principal directions for a frame P1 and P2 are the components of the load P P1 P cos a P2 P sin a If P1 ACTS ALONE ¿ dH P1L3 3EI ¿ dv uBL (to the right) a P1L2 bL 2EI P1L3 2EI (downward) ...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online