Answer to Question #256730 in Mechanical Engineering for weiou

Question #256730

The bent beam ABC is attached to a pin at C and rests against a roller support at B. Neglecting the weight of the beam, find the reactions at B and C caused by the 150- kg load. 


1
Expert's answer
2021-11-01T08:52:09-0400



MC=0:M_C=0:

mg(3m+2m)+RB(432+42)(2m)-mg(3m+2m)+R_B(\dfrac{4}{\sqrt{3^2+4^2}})(2m)

+RB(332+42)(1.5m)=0+R_B(\dfrac{3}{\sqrt{3^2+4^2}})(1.5m)=0

RB=2mgR_B=2mg

RB=2(150kg)(9.81m/s2)=2943NR_B=2(150kg)(9.81m/s^2)=2943N

iFix=0\sum_iF_{ix}=0

CxRB(35)=0C_x-R_B(\dfrac{3}{5})=0

Cx=0.6(2941N)=1765.8NC_x=0.6(2941N)=1765.8N


iFiy=0\sum_iF_{iy}=0

Cy+RB(45)mg=0C_y+R_B(\dfrac{4}{5})-mg=0

Cy=150kg(9.81m/s2)0.8(2941N)=881.3NC_y=150kg(9.81m/s^2)-0.8(2941N)=-881.3N

RB=2943N,Cx=1765.8N,Cy=881.3NR_B=2943N, C_x=1765.8N,C_y=-881.3N


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