MEM202 Engineering Mechanics - Statics MEM

Transcription

1 E Engineering echanics - Statics E hapter 6 Equilibrium of Rigid odies k j i k j i R z z r r r r r r r r z z

2 E Engineering echanics - Statics Equilibrium of Rigid odies E Pin Support N w N/m 5 N m 6 m 5 m m Roller Support ied Support N w N/m 5 N m ree end 6 m 5 m m Simpl-Supported antilever N R,5 N,75 N - m R,5 N c. m N c. m 99 N, N,5 N ree-od Diagram Supports and onnections

3 E E Engineering echanics - Statics 6. ree-od Diagrams Idealized Supports and onnections in -D (Table 6-, pp. 5-5) Transmit a tensile force in the direction of the cable. Transmit a force (tensile or compressive) in the direction of the ais of the link. Transmit a compressive force perpendicular to the surface supporting the ball. Transmit a compressive force perpendicular to the surface at the point of contact.

4 E Engineering echanics - Statics 6. ree-od Diagrams Idealized Supports and onnections in -D (Table 6-, pp. 5-5) E Transmit a force, usuall epressed in terms of its components R and R. Transmit a force, usuall epressed in terms of its components: a compressive normal force R n and a tangential frictional force R t. The angle θ is related to the coefficient of frictional, µ, i.e., µ tanθ R r /R n

5 E E Engineering echanics - Statics 6. ree-od Diagrams Idealized Supports and onnections in -D (Table 6-, pp. 5-5) Transmit a force (tensile or compressive) perpendicular to the surface of the guide. Transmit a force (tensile or compressive) perpendicular to the ais of the shaft. Transmit a force (tensile or compressive) perpendicular to the ais of the shaft, and a moment. Transmit a force, usuall epressed in terms of its components R and R, and a moment. smooth collar with a fied connection. 5

6 E Engineering echanics - Statics 6. ree-od Diagrams Idealized Supports and onnections in -D (Table 6-, pp. 5-5) E Transmit a force (tensile or compressive) along the ais of the spring. Transmit and change the direction of a tensile force. or a frictionless pulle, T T. ore about pulles X Y R R T R R T R R p( θ ) T p( θ ) T 6

7 E Engineering echanics - Statics 6. ree-od Diagrams Idealized Supports and onnections in -D E leible cable able ied support α Rigid link all, roller, or rocker Linear elastic spring Smooth pin or hinge Y X X i i X Link Link Link θ Link Y i tanθ () Y Link () () Roller () () () Y Pin Spring X Pin Pin 7

8 8 E Engineering echanics - Statics E 6. Equilibrium in Two Dimensions ( ) or : D z : z z D Three equations, thus, can onl solve for three unknowns lternativel or or where,, and are three points on the - plane which cannot be chosen arbitraril

9 9 E Engineering echanics - Statics E 6. Equilibrium in Two Dimensions b h b h b h O r r r r h b D O b h b h O Eample b h h b ( ) h b h b or Solution : b h b h b h b h D O ad hoice b h h b

10 E Engineering echanics - Statics 6. Equilibrium in Two Dimensions The Two-orce od (Two-orce embers) E // α L // L L // // // α // The two forces acting on a two-force member must be equal, opposite, and collinear. The weight of the member must be neglected. The connections to the member must not support a moment about the connection (i.e., it must be a pin connection). Eamples of two-force members:

11 E Engineering echanics - Statics 6. Equilibrium in Two Dimensions The Three-orce od (Three-orce embers) (or, ultiple-orce embers) E oncurrent force sstems Parallel force sstems a L r r r r r oncurrent L c a

12 E Engineering echanics - Statics E 6. Equilibrium in Two Dimensions Staticall Determinate, Staticall Indeterminate, Partial onstraints n u : number of unknowns, n e : number of equations In general: n u n e : Staticall determinate n u > n e : Staticall indeterminate n u < n e : Partial onstraints In -D, n e (i.e., Σ, Σ, Σ ), therefore n u : Staticall determinate n u > : Staticall indeterminate n u < : Partial onstraints

13 E Engineering echanics - Statics E 6. Equilibrium in Two Dimensions Staticall Determinate, Staticall Indeterminate, Partial onstraints Staticall Determinate Staticall Indeterminate Partial onstraints n u, n e n u, n e n u, n e n u, n e n u, n e n u, n e

14 E Engineering echanics - Statics E 6. Equilibrium in Two Dimensions Staticall Determinate, Staticall Indeterminate, Partial onstraints Some Special ases Rigid link Pin Rigid link n u, n e Yet, it is unstable! (Σ ) n u, n e Yet, it is unstable! (No horizontal support)

15 E Engineering echanics - Statics 6. Equilibrium in Two Dimensions Eample 6- E Pin o ( ) 6.87 φ tan Tension in cable ( ) T ( ) T 75 lb 75 (Tension in a cable remains constant) NOTE: s a rule of thumb, ou should alwas assume unknown forces in positive directions. 75cosφ 75 75sinφ 6 lb 6 lb lb lb 5

16 E Engineering echanics - Statics 6. Equilibrium in Two Dimensions Eample 6- Equal and opposite to forces acting on pulle E T 75 lb 6 lb lb Pin ( ) 6( 8) 6 6 lb 6 lb lb lb 8 lb 8 lb Roller 6

17 E Engineering echanics - Statics 6. Equilibrium in Two Dimensions Eample 6- R E T 858. N T T W mg ( 75)( 9.8) 76.8 N T W T W 858. N T T NOTE : Overall Equilibrium R T T T W T T 9. N R T 858. N

18 E Engineering echanics - Statics E 6. Equilibrium in Two Dimensions Eample 6-6 Overall..D. unknowns, equations! 8

19 E Engineering echanics - Statics 6. Equilibrium in Two Dimensions Eample 6-6 E is a two-force member! o ( ).7 θ tan o (.6) sin.7 (.6) 6(.) cos.7 sin.7 6 [ or, (.6) (.) 6(.) ] o o 9

20 E Engineering echanics - Statics 6. Equilibrium in Two Dimensions Problem 6-5 T E W 75 kg kg T R R W If the bo is standing on a scale, what would the reading on the scale be?

21 E Engineering echanics - Statics 6. Equilibrium in Two Dimensions Problem 6-55, 6-56 E P P 9P W