Find out force on each member - Truss:

A truss is as shown in the figure given below. Find out force on each member and the nature of it. 

Sol.: First we calculate support reaction, Draw FBD as shown in figure given below

Determine forces in all members of truss loaded and supported as shown in the figure given below.

Sol.: The reaction at the supports is determined by considering equilibrium of entire truss. As both the external loads are vertical, only vertical component of reaction at hinged ends A required to be considered. As the ?AEC is a right angle ?, having angle AEC = 90º. Then,

AE = AC cos 60º = 5 X 0.5     = 2.5m

CE = AC sin60º = 5 X 0.866 = 4.33m

As? ABE is an equilateral triangle and thus,

AB = BC = AE = 2.5m

The distance of line of action of force 10KN from the joint A,

AF = AE cos 60º = 2.5 X 0.5 = 1.25m

Again, ?BDC is a right angle ? having angle BDC = 90º. Also,    BC = AC - AB = 5 - 2.5 = 2.5m

BD = BC cos 60º = 2.5 X 0.5 = 1.25m

The distance of line of action of force 12KN from the joint A,

AG = AB + BG = AB + BD cos 60º = 2.5 + 1.25 X 0.5 = 3.125m

By taking moment about end A,

RC  X 5 = 12 X 3.125 + 10 X 1.25 = 50

RC = 10KN                                                                                                                         ...(i)

∑V = 0, R_C  + R_A  = 10 + 12 = 22KN

R_A = 12KN                                                                                                                       ...(ii)

Joint A:

Consider free body diagram of joint A as shown in figure given below Let, TAE = Force in the member AET_AB = Force in member AB Direction of both the forces (T_AE and T_AB) is taken away from the point A. As the three forces are acting at the joint A. Thus apply lami's theorem at A.TAE/sin 270º = TAB/sin 30º = RA/sin 60º T_AE/

Consider free body diagram of joint C as shown in given figure  Assume,
T_BC  = Force in member T_BC and T_CD  = Force in member CD Direction of both the forces (T_BC  & T_CD) is taken away from point C. As the three forces are acting at joint C. So apply lami's theorem at point C.

                 =

Joint B:

Consider free body of joint B as shown in fig.

As,                           T_AB = 6.92KN

T_BC = 17.32KN

Let, T_BD  = Force in member BD

T_EB  = Force in member EB

Direction of both forces (T_BD  and T_EB) is taken away from point B. As the four forces are acting at joint B. Thus apply resolution of forces at the B.

Joint D:

Consider free body diagram of joint D as shown in the figure.

As,                         T_CD = -20KN

Let,                        T_ED = Force in member ED

Direction of force (T_ED) is taken away from the point D. As the four forces are acting at joint D. Thus apply resolution of forces at the joint D. 

Resolve all the forces along E_DC,

T_ED  + 12cos 60º + T_CD = 0

T_ED  + 6 - 20 = 0

T_ED = 14KN                                                                                                        ...(xi)

T_ED = 14KN (Tension)                                              .......ANS