ENGI 1313 Mechanics I

Transcription

1 ENGI 1313 echnics I Lecte 18: oment of oce Abot Specified Ais Shwn Kenn, Ph.D., P.Eng. Assistnt Pofesso clt of Engineeing nd Applied Science emoil Univesit of Newfondlnd spkenn@eng.mn.c

2 id-tem o This Clss Dte: Octobe 18 Time: 830m-945m Loction: to be detemined teil: Up to nd inclding poblem set #4 Altente Em Onl if thee is compelling eson to miss Octobe 18 th nd I mst be infomed b Octobe 15 th with eson povided Dte: Octobe 22 Time: 700pm-815pm Loction: EN 2007 teil: Up to nd inclding poblem set # S. Kenn, Ph.D., P.Eng. ENGI 1313 Sttics I Lecte 18

3 id-tem (cont.) Genel Comments All stdents will be eqied to tke the emintion Resoces Ttoil poblem sets Qi poblems Stdent societies S. Kenn, Ph.D., P.Eng. ENGI 1313 Sttics I Lecte 18

4 Lecte 18 Objective to povide scl nd vecto methods fo detemining the moment of foce bot specified is S. Kenn, Ph.D., P.Eng. ENGI 1313 Sttics I Lecte 18

5 oment Abot Specified Ais The is of the moment (o) bot point O is pependicl to foce () nd position vecto () plne Wht is the component moment bot the -, - o -es? Wh is this infomtion impotnt? S. Kenn, Ph.D., P.Eng. ENGI 1313 Sttics I Lecte 18

6 oment Abot Specified Ais (cont.) Wht is the oment Abot Point O? o d ( 20N)( 0.5m) 10N m S. Kenn, Ph.D., P.Eng. ENGI 1313 Sttics I Lecte 18

7 oment Abot Specified Ais (cont.) Wht is the oment Abot the X-Ais? Tending to bend the pipe bot O (4 / d 5 )o N m ( 20N)( 0.4m) 8N m 8N m S. Kenn, Ph.D., P.Eng. ENGI 1313 Sttics I Lecte 18

8 oment Abot Specified Ais (cont.) Wht is the oment Abot the Y-Ais? Tending to nscew the pipe bot O (3 / d 5 )o N m ( 20N)( 0.3m) 6N m 6N m S. Kenn, Ph.D., P.Eng. ENGI 1313 Sttics I Lecte 18

9 oment Abot Specified Ais (cont.) L d cosθ L cosθ Z A d ' S. Kenn, Ph.D., P.Eng. ENGI 1313 Sttics I Lecte 18

10 oment Abot Specified Ais (cont.) oment Vecto Abot Point O Use coss podct O A { A 0.3î ĵ + 0kˆ }m û 20N 0î + 0 ĵ 1kˆ { 20kˆ }N { } S. Kenn, Ph.D., P.Eng. ENGI 1313 Sttics I Lecte 18

11 oment Abot Specified Ais (cont.) oment Vecto Abot Point O O i j k 0 20 O A { A 0.3î ĵ + 0kˆ }m { 20kˆ }N O O {( 0.4)( 20) ( 0)( 0) } î {( 0.3)( 20) ( 0)( 0) } {( 0.3)( 0) ( 0.4)( 0) } + { 8î + 6 ĵ} N m ĵ N kˆ m S. Kenn, Ph.D., P.Eng. ENGI 1313 Sttics I Lecte 18

12 oment Abot Specified Ais (cont.) oment Component Pojected on Y-is Recll dot podct A û O û { 8î + 6 ĵ}{ 1 ĵ} N m { 8î + 6 ĵ}{ 1 ĵ} N m 6 N m o ( 1)( 1) cos0 1 o ( 1)( 1) cos90 0 î î ĵ ĵ kˆ kˆ î ĵ î kˆ ĵ kˆ S. Kenn, Ph.D., P.Eng. ENGI 1313 Sttics I Lecte 18

13 Tiple Scl Podct Genelied Sttement Detemine the component moment mgnitde ( ) on specified is de to the moment ( o ) O O cos θ ( ) û û ( ) O û S. Kenn, Ph.D., P.Eng. ENGI 1313 Sttics I Lecte 18

14 Tiple Scl Podct (cont.) Detemine the component moment mgnitde ( ) on specified is de to the moment ( o ) û ( ) S. Kenn, Ph.D., P.Eng. ENGI 1313 Sttics I Lecte 18

15 15 ENGI 1313 Sttics I Lecte S. Kenn, Ph.D., P.Eng. Tiple Scl Podct (cont.) ( )( ) ( )( ) [ ] ( )( ) ( )( ) [ ] ( )( ) ( )( ) [ ] + ( ) û

16 16 ENGI 1313 Sttics I Lecte S. Kenn, Ph.D., P.Eng. Tiple Scl Podct (cont.) ( )( ) ( )( ) [ ] ( )( ) ( )( ) [ ] ( )( ) ( )( ) [ ] + ( ) û

17 17 ENGI 1313 Sttics I Lecte S. Kenn, Ph.D., P.Eng. Tiple Scl Podct (cont.) ( )( ) ( )( ) [ ] ( )( ) ( )( ) [ ] ( )( ) ( )( ) [ ] + ( ) û

18 18 ENGI 1313 Sttics I Lecte S. Kenn, Ph.D., P.Eng. Tiple Scl Podct (cont.) ( )( ) ( )( ) [ ] ( )( ) ( )( ) [ ] ( )( ) ( )( ) [ ] + ( ) û

19 oment Vecto on Specified Ais Detemine the moment vecto ( ) on specified is de to the moment ( o ) û [ ( )] û û S. Kenn, Ph.D., P.Eng. ENGI 1313 Sttics I Lecte 18

20 Compehension Qi The foce is cting long DC. Using the tiple podct to detemine the moment of bot the b BA, o cold se n of the following position vectos ecept. A) BC oce Line of Action A) AD C) AC D) DB A) BD Answe: D oment Ais S. Kenn, Ph.D., P.Eng. ENGI 1313 Sttics I Lecte 18

21 Compehension Qi o finding the moment of the foce bot the -is, the position vecto () in the tiple scl podct shold be. A) AC A) BA C) AB D) BC Answe: C S. Kenn, Ph.D., P.Eng. ENGI 1313 Sttics I Lecte 18

22 Refeences Hibbele (2007) mech_ S. Kenn, Ph.D., P.Eng. ENGI 1313 Sttics I Lecte 18