M1=−50(4)(2)=−400 lb⋅ft
Apply three-moment equation between spans (1) and (2)
M1L1+2M2(L1+L2)+M3L2+6A1ˉa1L1+6A2ˉb2L2=0
−400(6)+2M2(6+10)+M3(10)+14(50)(63)+760(60)(103)=0
−2400+32M2+10M3+2700+7000=0
32M2+10M3=−7300 ← equation (1)
Apply three-moment equation between spans (2) and (3)
M2L2+2M3(L2+L3)+M4L3+6A2ˉa2L2+6A3ˉb3L3=0
M2(10)+1M3(10+0)+0+860(60)(103)+0=0
10M2+20M3+8000=0
10M2+20M3=−8000 ← equation (2)
From equations (1) and (2)
M2=−11009 lb⋅ft=−122.22 lb⋅ft answer
M3=−30509 lb⋅ft=−338.89 lb⋅ft answer
Simple beam reactions
V0=4(50)=200 lb
V1=12(6)(50)=150 lb
V2L=13×(10)(60)=100 lb
V2R=23×12(10)(60)=200 lb
End-moment reactions
R0′=0
R1′=(400−11009)/6=125027 lb=46.30 lb
R2′=(30509−11009)/10=653 lb=21.67 lb
Support reactions
R1=200+196.30=396.30 lb answer
R2=103.7+78.33=182.03 lb answer
R3=221.67 lb answer