Truss Calculations
A truss is a structure that is composed of slender members and is joined together by gusset plates or welds. Almost every truss you’ll ever see will just be made of triangles because triangles are the simplest shape and they split the force acting upon the top of it. Today I will show you how to solve trusses.
Here’s an example:
Here’s an example:
Solve for all of it’s angles, reactant forces, and members. The given dimensions are below:
If the angles weren't given, we would use sine and cosine to find them. We don't need to in this because the two smaller sides are both 2ft, therefore the angle is 45 degrees. We know that a roller is one reactant force, and a pin is two reactant forces. When solving a truss, we always solve for the reactant forces first. So:
Now that we have Rcy, we could solve for all of the external forces in the x/y-direction.
RAX is 0lb because there are simply no other forces.
To solve this entire truss, we will use something called method of joints, this is where we solve for all of the members by solving each node for all of it's unknowns. We have found the reaction forces, now we have to solve for the members. First, we have to pick an individual node to start with and to draw the free body diagram for it. To solve for the members, we have to find the sum of the forces in the x/y-direction for each node (or until you found all of the member forces). The sum of these forces will have to be equal to zero because this truss is in static equilibrium.
To solve this entire truss, we will use something called method of joints, this is where we solve for all of the members by solving each node for all of it's unknowns. We have found the reaction forces, now we have to solve for the members. First, we have to pick an individual node to start with and to draw the free body diagram for it. To solve for the members, we have to find the sum of the forces in the x/y-direction for each node (or until you found all of the member forces). The sum of these forces will have to be equal to zero because this truss is in static equilibrium.
We know that FADX will also be 250lb because angle A is 45O. Just like force vectors, we can assume that:
FADX will be positive however, because when we use Pythagoreans Theorem, we find that FADXwill be positive because FAD is negative and so is
FADY.
Now that we have found all of the member forces for node A, we now have enough information to find the member forces for node B. Before you would do any more calculations, you would update the entire free body diagram just to keep your calculations organized.
So now we can solve for node B:
FADY.
Now that we have found all of the member forces for node A, we now have enough information to find the member forces for node B. Before you would do any more calculations, you would update the entire free body diagram just to keep your calculations organized.
So now we can solve for node B:
Simple enough.
Now let's try to solve for node C:
Now let's try to solve for node C:
Let's solve node D:
Since no forces are acting on node D in the x-direction, FDE is equal to 0lb.
We don’t have enough information again, so what we have to do is solve for another node, let’s do node E:
We don’t have enough information again, so what we have to do is solve for another node, let’s do node E:
Now we solved for node E, we can now finally solve for node C. We learned that hypotenuse of an isosceles with the side of 250lb would be 353.55lb (when we were solving for FAD). So FCD is -353.55lb because the -500lb is splitting its force between FAD and FCD, FCD has a two sides of 250lb, therefore FCD has to be -353.55lb and in compression (negative).
Today I showed you an example for solving a truss, hopefully this helped.
Today I showed you an example for solving a truss, hopefully this helped.