Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_102

⚡ Mecademy AIENG정역학 · ch5  Problem Statement Determine the reactions at and on the beam subjected to the point and distributed loads. The beam is supported by a pin at and a roller at . A distributed load acts on the beam from to , where and the load intensity at the right end () is . A concentrated point load of acts vertically downward at a distance of from . Support is located from . Problem 5/102 (a) Reaction at Support 1. Formula: First, determine the constant and the equivalent resultant force and moment of the distributed load. Then apply the moment equilibrium equation about point : 2. Substitution: Determine : At , . Calculate for : Calculate : AB ABw=w − 0 kx 3/2 x=0x=10 mw = 0 2.5 kN/m x=10 m1.5 kN/m7 kN 5 mAB7 mA B kR w M w A w(x)=w − 0 kx 3/2 R = w w (x)dx, M = ∫ 0 L w/A x w (x)dx ∫ 0 L M = ∑ A 0⇒B ⋅ y x − B P⋅x − P M = w/A 0 kx=10 mw=1.5 kN/m 1.5=2.5−k (10)⇒ 3/2 k(10)= 1.5 1.0⇒k=10≈ −1.5 0.03162 kN R w L=10 m R = w (2.5− ∫ 0 10 kx)dx= 1.5 2.5x− = [ 2.5 kx 2.5 ] 0 10 2.5(10)− 2.5 10⋅ −1.5 M w/A M = w/A x(2.5− ∫ 0 10 kx)dx= 1.5 (2.5x− ∫ 0 10 kx)dx= 2.5 −[ 2 2.5x 2 M = w/A 1.25(100)− = 3.5 10⋅10 −1.53.5 125− ≈ 3.5 100 96.43 kN⋅m Apply equilibrium (, , ): 3. Calculation: 4. Result: ● Final Conclusion: The vertical reaction at support is acting upwards. (b) Vertical Reaction at Support 1. Formula: Apply the vertical force equilibrium equation: 2. Substitution: 3. Calculation: 4. Result: ● Final Conclusion: The vertical reaction at support is acting upwards. (c) Hori