Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_90

⚡ Mecademy AIENG정역학 · ch5  Problem Statement Determine the reactions at A for the cantilever beam subjected to the distributed and concentrated loads. Problem 5/90 (a) Vertical Force Reaction 1. Formula: The vertical equilibrium for the beam is given by: 2. Substitution: The equivalent concentrated force for the triangular distributed load is: The given concentrated load is: Substituting these into the equilibrium equation: 3. Calculation: 4. Result: (acting upward) ● Final Conclusion: The vertical support reaction at point is directed upwards. (b) Bending Moment Reaction 1. Formula: Summing moments about the fixed support (taking counter-clockwise as positive): A y F = ∑ y 0⇒A − y R − dist F = conc 0 R = dist ⋅ 2 1 base⋅height= ⋅ 2 1 3 m⋅4 kN/m=6 kN F = conc 2 kN A − y 6 kN−2 kN=0 A = y 6 kN+2 kN=8 kN A = y 8 kN A8 kN M A A M = ∑ A 0⇒M − A (R ⋅ dist )−xˉ dist (F ⋅ conc x )= conc 0 2. Substitution: The centroid of the triangular load is located at of its base from the vertex at : The distance to the concentrated load from is: Substituting values: 3. Calculation: 4. Result: (Counter-clockwise) ● Final Conclusion: The reactive bending moment at the fixed support is in the counter-clockwise direction. (c) Horizontal Force Reaction 1. Formula: Summing horizontal forces: 2. Substitution: There are no external horizontal forces acting on the beam. 3. Calculation: 4. Result: ● Final Conclusion: Since there are no horizontal applied loads, the horizontal reaction at support is zero.