Problems on cantilever truss, Mechanical Engineering

Problems on Cantilever Truss:

In the case of cantilever trusses, it is not required to determine the support reactions. The forces in members of cantilever truss are obtained by begning the calculations from free end of cantilever.

Q Determine forces in all the member of cantilever truss shown in the figure given below 

 

1370_Problems on Cantilever Truss.png

Sol.: From ?ACE, we have

tan θ = AE/AC = 4/6 = 0.66                                                                             ...(i)

Also,                                      1027_Problems on Cantilever Truss1.png

cos θ = AC/EC = 6/7.21 = 0.8321     ... (iii)

sin θ = AE/CE = 4/7.21 = 0.5548 

 

543_Problems on Cantilever Truss2.png

Joint C:

Consider free body diagram of joint C as shown in the given figure;

 

1746_Problems on Cantilever Truss3.png

As the three forces are acting, so apply lami's theorem at the joint C.

TBC/sin(90 - θ) = TCD/sin270 = 2000/sin θ

TBC/cos θ = TCD/sin 270 = 2000/sin θ

TBC = 2000/tan θ = 2000/0.66 = 3000.3N         ...(v)

Joint B:

 

2358_Problems on Cantilever Truss4.png

TBC = 3000.3N (Tensile)                                          .......ANS

TCD = - 2000/sin θ = 2000/0.55 = 3604.9N      ...(vi)

TCD = 3604.9N (Compressive)                              .......ANS

Consider free body diagram of joint B as shown in the given figure

As,                           TBC = 3000.3N

Let,                          TAB = Force in the member AB

TDB  = Force in member DB

As the four forces are acting at the joint B, So apply resolution of forces at joint B

RH = TAB  - TBC  = 0, TAB  = TBC = 3000.03 = TAB

TAB = 3000.03                                                            ...(vii)

TAB = 3000.03N (Tensile)                                       .......ANS

RV = - TDB  - 2000 = 0

TDB = -2000N                                                             ...(viii)

TDB = 2000N (compressive)                                   .......ANS

Joint D:

Consider free body diagram of joint D as shown in figure given below

 

1248_Problems on Cantilever Truss5.png

As,                           TDB = - 2000N

TCD = 3604.9N

Let, TA = Force in member AD

TDE  = Force in member DE

As the four forces are acting at the joint D, So apply resolution of forces at

217_Problems on Cantilever Truss6.png

 

By solving equation (ix) and (x),

2402_Problems on Cantilever Truss7.png

 

Member

AB

BC

CD

DE

DB

AD

Force in N

3000.03

3000.03

3604.9

5542.31

2000

1818.18

Nature

C = Compression

T = Tension

 

T

 

T

 

C

 

T

 

C

 

C

Posted Date: 10/29/2012 1:06:51 AM | Location : United States







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