Meriam, Kraige & Bolton — Statics of Particles: Problem 2_58

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/58 The cantilevered W530 × 150 beam shown is subjected to an 8-kN force F applied by means of a welded plate at A. Determine the equivalent force–couple system at the centroid of the beam cross section at the cantilever O. Problem 2/58 1. Analysis of the Force Vector To find the equivalent force at point , we first resolve the applied force at point into its rectangular components. Based on the diagram, the force has a magnitude of and acts at an angle of with respect to the vertical. ● Calculation Process 1. Identify Components: Let the positive -axis be directed to the right along the beam and the positive -axis be directed upwards. The force vector points down and to the right. 2. Substitute Values: 3. Final Force Calculation: 2. Calculation of the Equivalent Couple (Moment) at O The equivalent couple is the moment of the force about point . We use the position vector from the origin to the point of application . ● Calculation Process OFA F8 kN 30 ∘ x y F F = x Fsin(30)= ∘ 8⋅sin(30) ∘ F = y −Fcos(30)= ∘ −8⋅cos(30) ∘ F = x 8⋅0.5=4 kN F = y −8⋅0.8660=−6.928 kN R=F=(4i−6.93j) kN M O FO r OA OA 1. Identify Position Vector: Point is located to the right of and below the centroidal axis. 2. Moment Formula: The moment about is given by the cross product , or using scalar components: 3. Substitute Values: 4. Final Moment Calculation: A negative sign in 2D moment calculations indicates a clockwise direction. Final Conclusion The equiv