Meriam, Kraige & Bolton — Statics of Particles: Problem 2_133

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/133 The thin rectangular plate is subjected to the four forces shown. Determine the equivalent force–couple system at O. Is R perpendicular to MO? Problem 2/133 1. Analysis of the Force System Based on the provided diagram for Problem 2/133, we identify the coordinates of the application points and the vector expressions for the four forces. The plate lies in the - plane with dimensions along the -axis and along the -axis. Let the origin be at . Points of application: Corner Corner Corner Corner Force vectors (by visual inspection of arrows): 1. Force acting at point . (Note: Interpreted from the arrow pointing upwards at the back corner). 2. Force acting at point . (Arrow pointing in the negative direction). 3. Force acting at point . (Arrow pointing downwards). 4. Force acting at point . This force is in the -plane at an angle of with the extension of the -axis, pointing towards the interior. Its components are: xy 2bxbyO (0,0,0) O:(0,0,0) A:(2b,0,0) B:(0,b,0) C:(2b,b,0) F = 1 FkO(0,0,0) F = 2 −FiB(0,b,0)x F = 3 −FkC(2b,b,0) F 4 A(2b,0,0)xy 30 ∘ x F = 4 F(−cos30i+ ∘ sin30j)= ∘ F− i+ j( 2 3 2 1 ) 2. Determination of the Resultant Force ● Calculation Process 1. Final Formula: 2. Substitute Values: 3. Partial Operations: 4. Final Calculation: 3. Determination of the Resultant Moment ● Calculation Process 1. Final Formula: 2. Substitute Values: 3. Partial Operations: 4. Final Calculation: R R=F =∑ i F + 1 F + 2 F + 3 F 4 R=(Fk)+(−