Question

For the space truss shown below, there is a Ball-and-socket joint at A. At C, only support reaction is in z direction and at B, there are support reactions in y and z directions. A force P=10k kN is applied to joint D. Triangle ABC is in x-y plane at z=0. For this truss,

(a) Determine the sequence of joints with which the entire truss can be solved for the member forces and support reactions using the method of joints.

(b) Solve the first joint only for forces in members connected to the joint.

Note: For part (a), only the correct sequence of joints is needed as an answer (e.g. A,B,C,D). You do not need to solve the entire truss.

N+ D P 8m с A 1m 5m x 7m B 10m

Answer 1

Solution g) Draw FBD of truss and define the sequence to solve using method of joints:- Note:a. using method of joint we can save for maximum three unknowns , using following equilibrium equatione: Efy=o. Efzzo 4 Efx=0). [Efy= Now we can define our sequence using. Z D Az C A cz Ay »y S.No. By NI Unknown forces (3 Nos) D. FDA, FDB and foc ci Cz, FAC, FBC B FAB, By, B2 Ax, Ay, Az fig: FBD. AC5,-1,0), B(5,6,0) C(-5,-1,0), D(0,018) A sequence, b) Solve the first Joint (Joint D). Unit vectors along member DA, PB, DC´are- si - 9 - 8 15) +61)2+68)2 » PAID

Thanks

i BLD i fclo= -så-Ĵ - BR 2 Alp = 0.53ê -0.11) -0.84 sî +69 - 8 118) +6397682 suj -0.72 res)²+(-1)2 +682 = -0.53î - allŷ -0.Buis BID = 0.45 +0.5 AID P=-10Â KN Equilibrium equation at Joint D > Etayo th In DA FER Now - DATE OR + Fotp²=0 PAID FDA + A OLD FB tacia Foc - 10 Å zo → 40.53 -0.019-0-84ť ) FDA + Co.usî +0.549-0.72) FDA +(-0.532-0./19-0-BUÂ) Foc-lonzo 0.53 FDA +0:45 FDB -0.53 FDCE - {Efx=0} -0.11 FDA +0.54 FDB-O'll Foc=0 0.B4 FDA -0.72 FDB-O-84FBc = 30 kn3 Solving this FDA= -4.17 KN For= -2.06 KN Negative sign shows that are forces are compressive. Foc= -5.92KN Any -2 ② {Efy=0} {{fz=o}