For member AB:
Length, LAB=√42+42=5.66ft
Weight, WAB=5.66(200)=1132lb
ΣMA=0
4RBH+4RBV=2WAB
4RBH+4RBV=2(1132)
RBH+RBV=566 → Equation (1)
For member BC:
Length, LBC=√32+62=6.71ft
Weight, WBC=6.71(200)=WBC=1342lb
ΣMC=0
6RBH=1.5WBC+3RBV
6RBH−3RBV=1.5(1342)
2RBH−RBV=671 → Equation (2)
Add equations (1) and (2)
RBH+RBV=566 → Equation (1)
2RBH−RBV=671 → Equation (2)
3RBH=1237
RBH=412.33lb
From equation (1):
412.33+RBV=566
RBV=153.67lb
From the FBD of member AB
ΣFH=0
RAH=RBH=412.33lb
ΣFV=0
RAV+RBV=WAB
RAV+153.67=1132
RAV=978.33lb
RA=√R2AH+R2AV
RA=√412.332+978.332
RA=1061.67lb → shear force of pin at A
V=τA
1061.67=5000(14πd2)
d=0.520in answer