1 F4 = 195 lb a = 60° B = 60° Y= 135. F4 = F4 COS45COS30 1 - F4 COS 45 Sin30j + F4 sin45 k F1 = F1 (cosa [+ cosBj +cosy k) Z FRx = F, cosa + F4COS45. COS30 - 225 E. FRy = F, COS B - F4 COS 45· sin30 - F3 E FRZ = F4 sin 45 + FICOSY + F2 unknowns: F1, F2, F3 we know, EFRX + EFRY + SFR= = O FicoSa + F4 COS 45 . COS30 = 225 - (i) FICOSB - F4 COS45. sin30 - F3 = 0 -(ii) Fusing5 + Ficosy +F2 =0 -(iii) .: F1 = 211.17 F2 = 11. 4 : F3 = 36.6
2. 2 C - Fc COS 30 . COS60 7 60 60 $ FOCOS30. COS60 60° D Fc COS 30 FOCOS 30 Fc cos 30 . sin 30 Focos 30 . sin30 FB sin 45 B 45° 30. 30 FD COS 30 . COS 30 Fc COS30 . COS30 4 300 A 45° FBCOS 45 y > FR From FB, Fy = FB COS 45 Fz = FB Sin 45 From Fc, Fx = - Fc COS30. COS60 Fy = - Fc cos30 - COS30 Fz = Fc cos 30- sin 30 EFx =- FccOs30.COS60 + FD COS 30. COS60 = 0 & Fy = FB COS 45 - Fc COS 30. COS30 - FD COS 30 COS30 = 0 E F2= FB sin 45 + Fc cos 30. Sin30 + FD COS30.sin30 - 333.54 = 0 From Fo, Fx = FD COS30- COS 60 Fy = - FD COS 30 COS 30 F2= FD COS30· Sin 30 From FA, F2 = - (34 ×9.81) = - 333.54
3 . 2 F A B D 45 3 0 C Isin45 x 45 100345 & B Y D Coordinates: A (0, 0, 2.4) B (0, -1, 0) PAC = (1, 0, -2.4) V C (1, 0, 0) PAD = (-sin 45, cos45, -2.4)V D (-sin45 , cos 45, 0) PAB = (0, -1, - 2.4) V FR = F (cosa + COS B +cosy) FAB = FAB FAB = PAB X = (0 , - 1 , - 2.4) x PAB FAC = FAC PAC = PAC Y = ( 1 , 0 , - 2.4) Y PAC FRO = FAD PAD = PAOZ = (-sin45, COS45, -2.4) Z PAD EFRx = Y - sin 45 Z = Fcosa & FRY = - X + cos 45 Z = F Cos B E FRZ = - 2.4 X - 2.4Y - 2.4Z = F COSY X= 4983.50 Y =- 1026.90 Z =- 1452.26 FAB = 2.6 x = 12957-10828 FAC = 2.6 Y = - 2669.95 FAD = 2.6 Z = - 3775.88