EXAMPLE 7.0.1. EQUILIBRIUM OF CONCURRENT COPLANAR FORCES

Determine the force exerted by each supporting cable if the crate weighs 50kN.

With coplanar, concurrent forces, there would only be two equilibrium equations used - the equilibrium of forces. Why is the Equilibrium of Moments not applicable in this kind of problem? It is because, there is only one point in consideration - the point of concurrence of the forces. (The perpendicular distance d is equal to zero making .

Both cables AB and AC will be pulling the crate in place, thus the FBD would look like:

By the FBD, we can easily identify that both forces will act with tensile reaction (pulling away from the crate). 

As it is easy to analyze the system now, we can make it even easier by simplifying the inclined unknown forces into their vertical and horizontal components.

The components of the forces are computed in methods depending on the given circumstances. In this problem, one force is inclined with a given angle and the other is inclined with a given slope.

For Force AB:

        

        


For Force AC:

       

      

Using the Equilibrium Equations:

Since the only applied load is the weight of the crate (50kN) applied downwards, the horizontal forces developed from the system should result to zero. There should not be any horizontal movement of the system. Take the sign convention +x moves to the right.
                                 
                                                

                             

We can arrange the equation as follows:

                                                 

                                          
                                           
                                                    
Now, take the summation of vertical forces. Using the sign convention that +y goes upwards, it is important to note the both y-components would be positive.

                                                

                

                  

And by substituting the first derived equation,



                                      

                                                  

And again using the first equation:

                                                 

                                                 



RELATED TOPICS:

7.0 EQUILIBRIUM OF FORCE SYSTEMS