Find out force on each member - truss, Mechanical Engineering

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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,

1414_Find out force on each member.png

 

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, RC  + RA  = 10 + 12 = 22KN

RA = 12KN                                                                                                                       ...(ii)

Joint A:

Consider free body diagram of joint A as shown in figure given below Let, TAE = Force in the member AETAB = Force in member AB Direction of both the forces (TAE and TAB) 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 TAE/

1086_Find out force on each member5.png                  1975_Find out force on each member1.png

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

2463_Find out force on each member6.png                 1466_Find out force on each member2.png=

Joint B:

Consider free body of joint B as shown in fig.

As,                           TAB = 6.92KN

TBC = 17.32KN

Let, TBD  = Force in member BD

TEB  = Force in member EB

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

1919_Find out force on each member7.png                   1322_Find out force on each member3.png

Joint D:

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

As,                         TCD = -20KN

Let,                        TED = Force in member ED

                                                               2161_Find out force on each member4.png

Direction of force (TED) 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 EDC,

TED  + 12cos 60º + TCD = 0

TED  + 6 - 20 = 0

TED = 14KN                                                                                                        ...(xi)

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

 

Member

AE

AB

BC

CD

BD

BE

DE

Force in KN

13.85

6.92

17.32

20

10.4

10.4

14

Nature

C = Compression

T = Tension

 

C

 

T

 

T

 

C

 

T

 

C

 

T

 


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