The purpose of truss analysis to determine
the forces experienced by each member.
Remember, since a truss is entirely made of
two-force members, each member is either in
tension, or, in compression.
We will use this information later to identify
the appropriate material and the cross section
of the truss members.
There are two methods used in truss analysis.
One, Method of joints and two, method of sections.
We will discuss Method of Joints in this session.
Consider the simple truss shown here.
The task is to determine the support reactions
and member forces.
You can easily recognize this as a simple
truss.
Let us go through a step-by-step process to
solve this problem.
Step number 1:
Let’s first check the relationship to verify
if we have enough number of equations to solve
for the number of unknowns in this problem.
If you look closely, there are five members
and four joints in this truss.
There are also three support reactions.
So the equation is, 5 = 2 * 4 – 3, which
gives us 5, meaning we can solve this problem.
So we are in good shape, and we can proceed.
Step number 2:
Let’s draw the Free Body Diagram of the
entire structure by removing it from the support.
Take a look at the Free Body Diagram.
We have three unknowns, and they are all support
reactions.
And we also have three equations.
We can now solve this problem for three support
reactions using the three equations of static
equilibrium.
Step number 3:
In method of joints, we take the truss apart,
drawing free body diagram of each joint and
applying equations of equilibrium to each
joint.
Since this is a joint, where all the members
connect, or all the members intersect, this
is actually a particle equilibrium problem.
This means we will have only two equations
and of course, we can solve for two unknowns.
Let’s consider joint D and draw the Free
Body Diagram of this joint.
Notice member AD and CD are connected by joint
D. The FBD shows these two member forces.
Since we do not know if the member is in tension
or in compression, we will assume that the
members are always in tension.
So, each member force is shown as coming out
of the joint indicating that each member is
being pulled.
Also notice the applied load.
Don’t forget that.
Now, you can write the two equations, summing
the forces along x-axis and summing up the
forces along y-axis.
Now we can solve this problem using these
two equations for the two unknown member forces.
We can now proceed to other joints one at
a time and do the same things.
Once completed you need to provide the answer
for each member clearly showing if the member
is in tension or in compression.
The next video I will show how to solve this
problem step-step.
