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







Related Discussions:- Problems on cantilever truss, Assignment Help, Ask Question on Problems on cantilever truss, Get Answer, Expert's Help, Problems on cantilever truss Discussions

Write discussion on Problems on cantilever truss
Your posts are moderated
Related Questions
Consider radar with a PRF of 5 kHz. What is the maximum unambiguous range R ua of this radar, in km?  If a target is located at a range of 50 miles, how many pulses will the r

Dead Centre The position of the working piston and the moving parts which are mechanically connected to it, at the moment when the direction of the piston motion is reserved

SHIELDED METAL ARC WELDING (SMAW) It also known as Manual Metal Arc Welding (MMAW). The heat required for welding is generated by the electric arc formed between metallic elect

instant center of direct contact slider

Condition for Carnot theorem - thermodynamics: 1 .   If T 1  = T 2 ; No work, = 0 2 .   Higher the temperature difference, greater the efficiency. 3.   For the same

Condenser ( Capacitor ) : A capacitor is used to store the electrical energy. The maximum value of stored energy depends on its capacity. It helps to achieve required high voltag

Q. Describe Elastic and plastic deformation? When a sufficient load is applied to a metal or other structural material, it will cause the material to change shape. This chang

EQUIPMENT FOR RESISTANCE WELDING-Stored energy equipments   Energy can be stored and further utilised for welding. One method of storing energy is in capacitors electrostat

Centrifugal Filter and Screen Filter Cleaning :   Oil may contain impurities. Since the oil passes through all the engine parts, the impurities may harm the parts and cause imprope

Compute minimum value of the horizontal force: Block A of weight 520N rest on horizontal top of block B having weight of 700N as shown in the figure given below. Block A