ch3_eq-3D - FBD 3D Force Reaction 1 FBD 3D Force Reaction 1...

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1 FBD: 3D Force Reaction
2 FBD : 3D Force Reaction 1 unknown 3 unknown 2 unknown No moment suppo
3 3 unknown 6 unknown 6. smooth pin 5 unknow
4 For some problem , the couples in both case should be treated as zero to provide statical determinacy thrust-bearing support journal-bearing support 7. bearing 5 unknown 4 unknown
6 If thrust barring If glue or friction exist
7 3D Equilibrium Supports #2
8 3D Equilibrium Supports #3
9 3D Equilibrium Supports #4
10 3D Equilibrium Supports #5 Comparison with 2D supports
12 Equilibrium in 3D 0 R F r r r 0 M M r r r F x = 0 F y = 0 F z = 0 M x = 0 M y = 0 M z = 0 Body (bodies) in Equilibrium or or any but only one point OR any but only three independent (perpendicular) axis any but only three independent axis x y z 0 O M r x y z 0 R r Direction of moment axis has a affect on solving problem. position (where the axis pass) also matters. The 3 axises need not interesect at one point
13 Equilibrium in 3D 0 R F r r r 0 M M r r r F x = 0 F y = 0 F z = 0 M x = 0 M y = 0 M z = 0 Body (bodies) in Equilibrium or or any but only one point OR any but only three independent (perpendicular) axis any but only three independent axis at most 6 unknowns may be found. vector approach may be easier - Each of the equation may be applied independently ; e.g., an accelerating car on a flat surface may be treated as in equilibrium in the vertical direction. Same for the moment equations. - Not in this class, but be careful about the moment equations, things get very complicated if the body is not spinning in a single plane! 0 x a 0 z
15 A r d F M X Y Z ˆ n r , ˆˆ { ( ) } F M r F n n r r r r position vector: from any point on line to any point on tline of action of the force. ? M r 5 i=1 ˆˆ { {( ) } } i r F n n r r 1 F r 2 F r 5 F r ˆ n 3 F r 4 F r 4 ˆˆ { ( ) } r F n n r r Forces which interest or parallel with axis, do not cause the moment in that axis
17 Example 3/5 The uniform 7m steel shaft has a mass of 200kg and is supported by a ball-and-socket joint at A in the horizontal floor. The ball end B rests against the smooth vertical walls . Find the force exerted by the walls and the floor on the ends of the shaft. this is not FBD.
18 FBD: frequent mistake No system isolation (surrounding still exists) Don’t forget axis Write force name Caution: In some slides using in this class, FBD may be drawn wrongly according to the rule introduced, DO NOT IMITATE this style in your homework or examination. Correct FBD Use (at least) 3 different colors No axis System Isolation
19 200(9.81) 1962 N W mg 2 2 2 7 (6 2 ) 3 h A= (2,6,0) B=(0,0,3) G=(1,3,1.5) 0 x F 0 y F 0 z F 0 x M 0 y M 0 z M any point but only one point 1 ˆ ˆ ˆ 3 1.5 2 AG AB r r i j k    r r ( ) 0 A B x x A G r B B r W r r r r r r 0 A M r r ˆˆ ˆˆˆˆ 2 6 3 1 3 1.5 0 0 0 0 1962 x y i j k i j k B B   r 654 N 1962 N x y B B ˆ ˆ ˆ 2 6 3 AB r i j k   r ˆ ˆˆ (6 5 4 ) (1 9 6 2 ) ( 1 9 6 2 ) 0 x y z A i A j A k r 0 F r r 2 2 2 | | 654 1962 1962 2850 N A r 654 N A 1962 N A 1962 N x y y A Ans Ans Independent Eq. = 2 Vector Cross Product is useful in 3D Problem

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