Question

Question 1 (20 points) Determine the components of reaction at the ball-and-socket joint A and the tension in each cable necessary for equilibrium of the rod. .4m 150 N/m D B E 400 W

Answer 1

ACMA, 4A, 2A) =A (0,0,0);B(XB, , 78)=B (12,0,0) clke, yc, Zw=200,-4,6); 0620,40,20)=P(0,4,5) (HE, YE, Z) = E(6,0,0) ;G (ha, Ya, Ra)=(4,0,0) let w be equivalent point load for triangular loading W=1/(x150 x R =goon cacting at 12 = 4m fromA) AB let it be a W-goon А a akam w Step I Coordinates of various points step II displecent vectors & unit vectors "Unit vector BC, û pe = (het) î+ (y Ys) + (2226) R ſexe-23)²+(y-Yo)²+(222632 û Be=-12î -4} +6 übc=-6 1 -2 + 3 1 14 Unit vector BD ,üco = (466-80) it (yo-Yolj +(20-2008 V rots? Hyo-Y²+(20-25 û Bo = -12ê +4jt6 û Bo=-6 -bat2 g + 2 vector AB, RAB = (%6-X) + Cyo Ya) j + (262) " ARAB = 12 i toj torm 14

vector AE, ELA 6î toj top vector AG LAG = 4i tojtor Step II forces in vector form forces Pec- TBC (-62-2 7 leto, Tac, Too , FE be magnitudes of various force at a, ū=-WÂ =-900kn .force at E, F:-400 ỂN • Tension in BC, Psc = TBC. UBC = Toc (- 6 1 - 2 - 2 + 3 ) +3 F) N Tension in BD, Too = TBP (-6itzğ +3%) N Reaction at A, Ra= Axit Apf + AzE Stebit Equilibrium conditions I) Net moment of all forces about A, EMA- Moment n = R X EMA = 0 = 2 x Tec TFART ToothAEXPE+ RAKO 7 di f î a, î K ܙܠܘ + o 6 + Too TBC 12 0 O 7 12 -6 2 3 0 0-400 7 -6 -2 3 k î ܙ ܥܠܘ + =oitoj tor O & o 0-900

t 7 0 0 Toc +36 -Top = 6000 7 7 TBC=1750N 3 → TBC (07-36f - 248) + Too 6î - 367 +245) + (02 +2400g toff) +60+360oģtor) -oi toj toid comparing x, y,2, components of inserts x y -36 TBC -36 TBD + 6000=0 -036 TB Z= 24 oct 24 TB =0 Toc - Too=0 solving eq 080 1990 Top=1750N II) Net force on AB, EFAs = 0 > Pect Post Peto + Razo > 1750 (-61-2/ +34) + 1750 (-6it2j +3%) – 400 F -goof taxat Ax jt AzR=0 Comparing X, Y, 2 of uns frus x 1750x+6) +1750 66) + Ax = 0 Ax=1000N y lz 50 (-2) +1250(2) +Ay = 0 Ay=0 2 1750 (3) +1750 (3) — 1300 + Az=0 A₂=800N 7x3 743 21 21 25 21 Tension in BC, TBC= 1790 N=583.333N Tension in BD, Top-17 Şon = 583.333 N Reaction at A; Ax= 1000N , Ay-ON; A2=800N Answer