Tip:
Highlight text to annotate it
X
Here's a basic truss. The problem is to solve for the forces in each member and determine if the members are in tension or compression.
First thing to always do is solve for external forces.
There is no horizontal load so there can't be a horizontal reaction at C.
Finding these external forces usually requires summing moments about a point. Let's sum moments about point A
The 100 pound force has a lever arm of 9 feet in the negative moment direction...
and CY has a lever arm of 21 feet in the positive moment direction.
The reaction at C will equal 42.85 pounds.
Next is summing forces in the y direction to find the reaction at A.
Now that all the reactions have been found, we can begin Method of Joints.
Beginning at any joint will suffice, so why not start at A?
AB and AC have been drawn assuming they pull on joint A . They will fix themselves later if we are careful with the signs.
Draw in the components.
Sum the forces in the y-direction first because this will utilize the known force.
Next is using ratios to substitute the y- component
Simple Pythagorean Theorem being used here.
Notice how these units in the dimensions cancel out, this is a signal that ratios was done correctly.
The answer came out as a negative, what does that mean?
The force was drawn in the wrong direction!
The signs of our answers only tell us direction, nothing more.
Doesn't the Free Body Diagram make more sense now?
Next, sum forces in the x direction.
We have all the forces at this joint, so let's move some around.
When transferring forces from the joint to the member, the force is applied equal and opposite.
Now to keep that member in equilibrium, the exact same forces must be placed on its other side as well.
This is a visual aid to see members in compression,
and members in tension.
When transferring forces from the member back to the next joint, the force is applied equal and opposite again.
Now we can analyze joint B or C by drawing a new Free Body Diagram. Let's do B
Since we transferred a force, we transfer it's components as well.
Draw in BC's components as well.
Then apply the laws of equilibrium.
So now that both of BC's components have been found, we can use those to find its magnitude.
Let's transfer this force to C now
I'll walk through how to do this one more time.
Apply equal and opposite force
then the member
and, lastly, mirror the 2 forces.
So, to sum it up...
One force
Member
Two forces.
Try to remember that when transferring forces on a truss.
Moving on.
We can see here that BC is also in compression
Now that all the forces have been found, it's always nice to check the work.
If the answers are correct, joint C's Free Body Diagram will show it in complete equilibrium.
To solve for these components, we can use ratios.
The 16.97 is a length for BC acquired using Pythagorean Theorem.
We already know the value for BC so that can be used here.
Our answer is slightly off, but that is because some numbers were rounded during the calculations. Be careful.
We can see that BC's components balance this joint to keep it in equilibrium.
Now, we can be positive the answers are correct.
Here is the complete result of the truss.