Tuesday 12 March 2019

EXAMPLE 8.0.2. METHOD OF JOINTS

Determine the forces of all the member of the truss.



Even without solving for the reaction, we can start the analysis by considering point D. However, to have a complete analysis, reactions are usually solved first.



                     
                 
                         upwards



                             
                               

                         downwards

        

                     

                       to the right


Consider Point D:




Before solving the magnitude of forces in the members, you should be able to make the most probable assumption of the vector directions.

The applied load is horizontal, which means, we can solve the member with a horizontal force first. That will be Fdb. We can assume that Fdb is compression because its x-comp should be in equilibrium with the applied load.

Knowing that Fdb is a compression member, it is automatic that its y-comp goes up. Thus, Fde can be assumed to go down to be in equilibrium. So we can conclude that Fde is a tension member.



                      
                 
                                   (Compression) 




                   

                                       
               
                                    (Tension)

After joint D, the next joints comprise of more than two members which would make it impossible for us to solve the next member forces. However, joints A and F have two members. So continue the analysis by considering either joint A or joint F.


Consider Joint A. Assume directions of force members in joint A. The applied load is vertical, so we can assume the direction of the force with a vertical component first. Fab turns to be in compression to resist the reaction. This compressive assumption directs the x-component of Fab to go to the left. Thus Fac should go to the right.



The procedure on how you assumed the vector directions should be the same procedure in solving the force member magnitudes.




                     

                                      (Compression)




                   
                     

                     

                                                 (Tension)

Consider Joint F. Notice that this joint contain 2 reactions and also 2 perpendicular members. Being perpendicular, these members will not affect each other. So,



                                          (Tension)



                                          (Compression)

Now that most of the members are determined, we can continue solving for the other member forces.



Consider Joint E. With forces surrounding the joint. Assuming the vector direction of the unknown member forces is a little more complicated where sometimes, pure simple assumption will be used. A simple analysis is check the result of the vertical loads. This gives us the idea that Fce should be in compression. Although that hypothesis maybe is certain, Fbe will be purely an assumption. So if the result turns to be positive, the assumption is correct, if not then it is the other direction.


                 

                   
               
                                           (Compression)



                 

               

                                                     (Compression) 

Lastly, consider joint B. Although the known loads are inclined, it is easy to detect that the load going downward is less than that going up. So Fbc can be assumed as going down, making the force in tension.


                   
                  

                                             (Tension)


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