MP HW 4 1. ( MA ) R = 0 M4 = 170 Z M3 From M3, 0 (0,0,0) C (2,-2, 1) 0 x M3= M3 MOC My 45" My cos 45 COS 45 My COS 45 45 My COS 45 COS 45 M2 B A MI = M3 21 -2j+k = M3 (?)-3]+/*) From My, MÃ = Macos 45 . cos 45] - My COS 45. COS 45 ? + My sin45 È From M1, M = M. j From M2, M2 = - M27 1 .- ZFx =? M3 - M4 COS45 COS45 - M2 =0 E Fy = 3 + M4COS45 cos45 + MI =0 EF= M3 + M4 sin 45 = 0 MI= - 325 Mz= - 325 M3 =- 361
2 -F Y A 3 F2 B 3 F, C 300 30 7 60° 3 -F 5 4 9 D 36-87. - F3 6 -FI = -i. sinzo sin 60 . i= Ersin30 sinon = 3 COSA= 32+52-42 2X3x5 : Q=53.13 : K= - Ficos53.13 : j= Ficos 36.89 ???+Ficos36.89j-F100553·13? - 531 + 12]" - 9K' TAB = (6,0,0) PcD = (6,0,0) F2 = F2 22 F3 = F3 ] (MR)O = M1 + (TAB × F2) + (PCD XF3) .50 1 0 = -- M 3 00) 1 + 600 5 V3 12-9/ i j k You 0 0 F2 ijk +600) 0 f3 0 =i(3×12)-j(3x-9)+K(3×12)+j(-6F2) + K (6F3) = 361-27j+36k +j(-6F2) + K (6F3) = j (-27-6F2)=0 : F2=4.50 lb = K (36+6F3) =0 -.: F3 = 6 lb
3. C y Fe 4-y 1 FA FB FB FC Ny B Coordinates A (0, 0,0) B (0,4, 0) C (0, 4, 6) FA' = 450 K FB = - 600T Fc = 350} FR = - 600} + 350} + 450} FRE 4500+(-600)2+(350)2 = 828 N UFR = - 600i + 350j + 450 828 Ufr =Umr =- 0.7257+0.4227}+ 0.543K (MR)x' = EMx' => - 0.725 MR = - 350 (6-2) - 450 y - (i) (MR)y' = ['My' - > => 0.4227 MR = 600z - (ii) MR = 1419.43 z (MR)2' = { M2' => 0.543 MR= 600(4-y) -(iii)