As introduced in the previous video the forces exerted by the pin to the truss members are 
actions and reactions with the forces exerted by the truss members onto the pin.
Therefore in order to determine the forces inside the truss members we can solve the forces on 
the pin instead by applying particle equilibrium method. And this is called the method of joints.
If the force developed in the truss member is a tensile force, then on the pin, this force pulls away from the pin. If on the other hand 
the force in the truss member is a compressive force, then on the pin this force pushes towards the pin. 
And don’t forget, for one 2-D particle free body diagram, we can write two force equilibrium equations,
and solve for two unknowns at one time. 
Now let’s look at this example. We need to find the forces in all truss members, 
and we need to specify if each member is in tension or compression. 
And we are going to apply the method of joints. 
The first step, we will inspect the structure and remove any zero-force member. 
Remember, for any joint that is connected to only two truss members that are not collinear, 
and if the joint is not subjected to any external force, 
then these two truss members are both zero force members. 
Or, if a joint is connected to three truss members, and again, the joint is not subjected to any other external force,
and two of these three members are collinear, then, the third member must be a zero-force member as well.
So by inspection, we can tell members BE and DE are both zero-force members.
And they can be removed from the structure. 
Step two, we need to decide if it is necessary to solve for the support reactions, in this case, the support forces at point A and C. Since 
for this problem, we are not asked to find the support reactions, therefore, if we can get away with not solving them, it will save us some time. 
So to determine that, the key will be, for each joint you can write a maximum of two equations and solve for two unknowns. 
Therefore I would like you to pause for now and ask yourself: first of all if you need to solve for the support reactions or not; and secondly if not, 
which of these joints you should start with for your analysis. 
[PAUSE PLEASE]
So hopefully you have come to the conclusion that you don’t need to solve for the support reactions, 
and also you should start with joint F for your analysis.
The reason is at joint F, you have two unknowns, the forces in members DF and EF, 
that can be solved by the two particle equilibrium equations. 
If you wonder why we shouldn’t start with joint B or joint D, since it looks like they only have two unknowns as well, 
for joint B and D, the two unknown forces at each joint are actually collinear, so you can only write one equation for each joint.
And therefore you won’t be able to solve for the forces. Please keep in mind that in some cases you won’t have an easy start, and therefore  
must first treat the entire structure as one rigid body and solve for the unknown reactions first by 
applying rigid body equilibrium.
Now step three, we can start solving for the forces one by one. Before we do that, we still need to figure out some dimensions and angles. 
Since this is
an isosceles right triangle,
this one must also be
an isosceles triangle, and therefore the angles can be determined. 
Now we draw the free body diagram of joint F, noting all the forces, known and unknown, at the joint.
I suggest that you always draw the unknown force in the member as if they're in tension.
This is because, as you will learn later, tension is considered as the positive internal normal force. Therefore, after your calculation, if the 
calculated force is positive then naturally it means it's a tension force.
On the other hand, if your calculated result is negative, then this force is a compression force.
Now we put the free body diagram in an appropriate coordinate system,
and write our two force equilibrium equations, one along the x direction and one along the y direction.
And from these two equations we can solve for the two unknown forces.
As you can see
force F_EF is positive, indicating tension force, therefore noted by a letter T, and force F_DF is negative, indicating a compression force, 
therefore noted by a letter C. And now we know all the forces acting at joint F.
We can make a note on the original graph of the forces that have been solved. And because at point D, members AD and DF are collinear,
therefore from a simple equilibrium analysis we know force in AD must be equal to the force in DF, so it is known now too. 
Now from inspection, we see that at joint E 
we only have two unknowns, so we solve for joint E next. 
Again we draw the free body diagram of joint E, and notice that we already know force EF is 216 pounds.
When we set up the rectangular coordinate system, keep in mind that we can set it up whichever way we want, 
therefore we can set it up this way
for convenience, since the two forces F_AE and F_CE are perpendicular to each other. 
And again, we write the two equations, 
and solve for the unknowns.
And now we know the forces acting at joint E.
And we make another note
for the truss members that have already been solved. Now the question is which comes next?
Joint A or joint C? and I want you to again pause and give it some thought. 
[PAUSE PLEASE]
Again, it is a question about how many unknowns you have associated with each joint, and if you have enough equations to solve them. 
At point C, since you have a pin support, which exerts two support forces, so overall you have three unknowns. 
And you only have two equations, so you can’t solve for them.
So the choice here should be joint A.
Since this is a roller and only exerts one support force, which is perpendicular to the contacting surface,
we can now have overall only two unknowns at joint A and be able to solve for joint A.
And we follow the same procedure and calculate the unknown forces at point A.
And now we’ve solved the force in member AB,
and because member AB and member BC are collinear, again they have the same force.
And now we have calculated the forces in all truss members, and specified if they are in tension or compression as well. 
Hopefully from this example you have learned how to solve simple truss structure by applying the method of joints.
