Trusses are amazing structures you’ve probably seen many times without even realizing it. They’re in bridges, roofs, and even bicycle frames! At its core, a truss is a structure made of straight members connected at their ends to form a series of triangles. This triangular shape is what gives trusses their incredible strength and rigidity.

The Basics of a Truss

Think of a truss as a team of individual beams working together. Each of these beams, or members, is connected at a joint (also called a node). The main idea is that forces are only applied at these joints, not in the middle of a member. This means each member is either being pulled apart (in tension) or pushed together (in compression).

The top and bottom members of a truss are called the top chord and bottom chord, respectively. The members connecting the top and bottom chords are known as the webbing.

There are several types of trusses, each with its own unique design and advantages. Some of the most common include:

• Pratt Truss: Characterized by diagonal members that are in tension and vertical members that are in compression.
• Howe Truss: The opposite of a Pratt truss, with diagonal members in compression and vertical members in tension.
• Warren Truss: Composed of equilateral triangles, with members alternating between tension and compression.
  

The Secret to Their Strength: Statistics

The reason trusses are so strong is due to a principle called statics. This simply means the truss is in a state of equilibrium—it’s not moving. All the forces acting on the truss are in perfect balance. To analyze a truss, we use the fundamental idea that at any point in the structure, the sum of all forces is zero.

Before diving into the analysis, there are two crucial first steps:

1. Find the Support Reactions: Trusses are typically supported at certain points. We need to calculate the forces these supports exert on the truss to keep it in place.
2. Identify Zero-Force Members: Sometimes, certain members in a truss don’t carry any load under a specific loading condition. Identifying these “zero-force members” early on can simplify the analysis.

How to Analyze a Truss: Two Main Methods

Once you’ve determined the support reactions, you can figure out the force in each member using one of two primary methods: the Method of Joints or the Method of Sections.

Method of Joints

This method is ideal when you need to determine the force in every member of the truss. As the name suggests, it involves looking at each joint one by one.

Here’s the process:

1. Isolate a Joint: Start at a joint where there are at most two unknown member forces.
2. Draw a Free-Body Diagram: Sketch the joint and all the forces acting on it. This includes external loads and the forces from the members connected to that joint. A good tip is to assume all unknown member forces are in tension (pulling away from the joint).
3. Apply Equilibrium Equations: Since the joint is in equilibrium, the sum of the vertical forces must be zero (∑Fy​=0), and the sum of the horizontal forces must be zero (∑Fx​=0).
4. Solve for the Unknowns: Use these two equations to solve for the unknown member forces. If you get a positive answer, your initial assumption of tension was correct. If you get a negative answer, it means the member is in compression.
5. Move to the Next Joint: Once you’ve found the forces at one joint, you can use that information as you move to adjacent joints, and repeat the process until you’ve solved for all the member forces.

Method of Sections

What if you only need to find the force in a few specific members in the middle of a large truss? The Method of Sections is your go-to for a quicker solution.

Here’s how it works:

1. Make an Imaginary Cut: Pass an imaginary “cut” through the members you are interested in. This cut divides the truss into two separate sections. The cut should generally not pass through more than three members.
2. Draw a Free-Body Diagram: Choose one of the two sections and draw its free-body diagram. This diagram will include the external forces acting on that section and the internal forces of the members you “cut.”
3. Apply Equilibrium Equations: Now, you have three equilibrium equations you can use for your section: the sum of horizontal forces is zero (∑Fx​=0), the sum of vertical forces is zero (∑Fy​=0), and the sum of moments about a point is zero ($\sum M=0$).
4. Solve for the Desired Forces: By strategically choosing the point to sum the moments about, you can often solve directly for the force in a specific member.

By understanding these fundamental principles and methods, you can analyze the forces within these impressive and efficient structures.

This video provides a helpful visual explanation of how to analyze a truss using the Method of Joints.

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