Question

Question 1 The rigid frame ABCEFGH is supported by ball-and-socket supports at A and E. The support at A has been modified to allow free movement along the z-axis. A cable is also attached between C and D. Point C is at the mid-point of AB. Determine the force in the cable and the reaction force components at E. Answers: 4-w TCD= 144.0 kN (Tension) Ex 89.5 kN Ey 66.4 kN E, = 119.0 kN WL 50kW B 75KN

Answer 1

Soln 50KN 3m 2 KN H SOKN Fn this problem there are Ax, Ay, Tco , Ex,Ey, E t we have 6 Conditions for egusli briam SFr50) EFy =0 EMy =0 3 +. Honce the problem is determinate. Connicbr onigin is at E Then Coordinates af- cis a midgointaf AB Ĉ = A+B 2. H: (6,2,0) = Ĥ = +2 %3D %3D F:(0,9,0)

:- 1-rsi+e9-sR) = Ten (-159 +6 - ) = Tcp (Hi5î +6ŷ-k) Tep 6.5 The fore at B,75 KN, adts alorg BH Fol = 75 KN - 75(3i+2) J13 75 (37 +ý) V3422 %31 so KN (4) = -50î %3D Reaction ad A Efy=0 Efz=0 Roaction at E +. V13 fx î+&yj+ Ez& =o 6.5

Equating thex, y,z compe nonts to zevo Ef =0 Tco(-1"5) + 75(3)+ Ax +Ex 0- 5.2 VTB {fy 0 + 75 (2) + Ay + Ey =0 VIB +Az + E, =0 6.5 Eginen in] ro blem EMy =0 Taking moment about E +. ALSD as ne know E is arigin. bacaese 6.5 + si x as) + (di-jix(-0î) + (67+}vx so?-o VT3 +(4(Ax) 3 + y(Ay ) (-) + 35 B)2) Ŕ + (-2X-50X-R) +(2) (sO)(-R) TCP 6.5 100 k - lo0 k

Equating the y y, 2 COmponends to zoro ie E Mx=0 -Tep(12)- uAy 6.5 EMy: Tcp (9) +450 -200 =0 6.5 TeAs) 200-450 VT3 %3D TCD (75-192) x 6'5 54.30 KN - Tcn f12) - UAy=0 6'5 -4Ay = Tcp(2) 6.5 (s4.30)2) 6:5 x4 Ay = - Ay =-8-354 kN asing eg , - + 15x (3) - M+Ex= TTo (5) 6.5 V13 TCD= 543o kN Ex = TCD (15)-75 (3) 6.5 E= -ug-87KN Ex acts along -x din" |Ex=49.97 KN

wsing eqt@ ? Ed)+25(2) ot Ay + Ey =0 Ay=-8:354 putting valuecof TcD = 5430 54-3 (6 ) +_150 -8.354 +Ey =0 6.5 Ey = -34.64 KN %3D =) Ey acts alorg -y disn Ey = 34.64 KN Ubing eq ☺ ? - TCD(2) +Ez=0 6-5 f2=Tco+2 6.5 Ez = 16.70 KN Ans wers Althugh these are not matching with the an swers given in problom, = 54.30 KN TCp = Ex=4g.87 KN Ey = 3u.64 KN Ez = 16.70 KN F agsure you thet the methodolagy adoptod to Solve the problem is abrolutely arrected. And dirn af %3D This do viation is may be deo to 7SKN force a pplied at B. ambiquouo