900 Nm 400 Nm 04 m 06 m Solution Fx 0 HA 0 MA 0 U1left 04

900 N/m 400 N/m 0.4 m 0.6 m

Solution

Fx = 0: HA = 0 MA = 0: (U1left *0.46153846153846/2) * (0.86153846153846 - (2/3)*0.46153846153846) - (U1right *1.0384615384615/2) * (1.9 - (1/3)*1.0384615384615) + RB*2.5 = 0 MB = 0: - RA*2.5 - (U1left *0.46153846153846/2) * (2.50 - 0.86153846153846 + (2/3)*0.46153846153846) + (U1right *1.0384615384615/2) * (2.50 - 1.9 + (1/3)*1.0384615384615) = 0 Solve this system of equations: HA = 0 (N) Calculate reaction of roller support about point B: RB = ( - (U1left *0.46153846153846/2) * (0.86153846153846 - (2/3)*0.46153846153846) + (U1right *1.0384615384615/2) * (1.9 - (1/3)*1.0384615384615)) / 2.5 = ( - 92.307692307692 * 0.55 + 467.30769230769 * 1.55) / 2.5 = 270.00 (N) Calculate reaction of pin support about point A: RA = ( - (U1left *0.46153846153846/2) * (2.50 - 0.86153846153846 + (2/3)*0.46153846153846) + (U1right *1.0384615384615/2) * (2.50 - 1.9 + (1/3)*1.0384615384615)) / 2.5 = ( - 92.307692307692 * 1.95 + 467.30769230769 * 0.95) / 2.5 = 105.00 (N) The sum of the forces is zero: Fy = 0: RA - (U1right *1.0384615384615)/2 + RB = 105.00 + (400*0.46153846153846)/2 - (900*1.0384615384615)/2 + 270.00 = 0