When you first learn about how structures hold up loads, one of the best places to start is the simply supported beam. It's a basic but very important structural element that helps us understand how loads travel through a structure.

What Is a Simply Supported Beam?

A simply supported beam is a straight beam that rests on two supports:

  • One support is pinned, meaning it can stop the beam from moving vertically and sideways, but it can still rotate.
  • The other support is a roller, which only stops vertical movement. It can roll sideways to let the beam expand or contract as needed (like when it gets hotter or colder).

Together, these supports keep the beam balanced while still allowing some flexibility. This type of setup is used all the time in real-life bridges and buildings.

What Happens When We Add Loads?

When we put loads (forces) on a beam, it pushes down, and the supports push back up to keep everything in balance. The beam bends, and internal forces develop to resist the loads. There are three main internal forces you’ll learn about:

  1. Shear Force (V) - the force that tries to cut the beam across.
  2. Bending Moment (M) - the force that tries to bend the beam.
  3. Axial Force (N) - force along the beam (often zero in basic problems with only vertical loads).

Common Types of Loads

Let’s look at a few types of loads you might see:

  • Point Load: A single force at one spot.
    Example: Someone standing in the middle of a wooden plank.
    This creates sharp changes in the internal forces.

  • Uniformly Distributed Load (UDL): A load spread evenly over part or all of the beam.
    Example: Books evenly stacked across a shelf.
    This causes the beam to bend smoothly.

  • Varying Load: A load that starts small and increases across the beam.
    Example: Snow piled up more on one end of a roof.
    This creates a more complex bending shape.

How Do We Analyze the Beam?

In statics, we use the rules of equilibrium to figure out what’s going on inside the beam:

  • The total vertical forces must add up to zero.
  • The total moments (rotations) must also add up to zero.

These rules help us calculate:

  • The reaction forces at the supports
  • The internal forces and bending moments inside the beam
  • The deflection, or how much the beam bends

We also assume a few things to keep the math simple:

  • The material of the beam is the same all the way through (uniform).
  • The beam behaves elastically (bounces back, not permanent bending).
  • The deflections (bending) are small.
  • The cross-section (like a rectangle or circle) stays the same along the beam.

These assumptions let us use something called Euler-Bernoulli Beam Theory, which is the classic way to analyze beams in statics.

Sign Convention (How We Label Forces)

To keep things organized, engineers use a standard way to label the direction of forces:

  • Shear Force (V) is positive when it causes clockwise rotation of the cut part.
  • Bending Moment (M) is positive when the beam sags (bottom in tension).
  • Axial Force (N) is positive when the beam is being pulled apart (tension).

You’ll see diagrams with arrows showing these directions, and they help us solve problems correctly.

Common Symbols You’ll See

  • E - Young’s Modulus (how stiff the material is)
  • I- Moment of inertia (how strong the shape is)
  • L - Beam length (span)
  • R - Reaction force at a support
  • M - Bending moment
  • V - Shear force
  • δ (delta) - Deflection (how much the beam bends)
  • θ (theta) - Slope (angle of the beam as it bends)

Final Thoughts

Learning how loads work on a simple beam is a big step in structural engineering. Once you understand this, you can start figuring out how real structures stay standing, from bridges to buildings.

Just remember:

  • Start with the supports.
  • Add the loads.
  • Apply equilibrium rules.
  • Find internal forces and deflection.

And most importantly, practice a lot of examples - this is the best way to build your intuition as an engineer.

Try It Yourself!

Want to see how different loads affect a beam in real time? Check out my Beam Analysis App!
It's a simple, intuitive tool where you can add point loads, distributed loads, and supports—then instantly see shear force and bending moment diagrams. Perfect for students learning statics or anyone brushing up on the basics.

Try the app here and start experimenting with your own beam scenarios!