Fixed-Fixed Beam Calculator — Uniform and Point Loads

If you bolt a beam solidly at both ends—no rotation, no slip—you’re dealing with a very different situation than just resting it on supports. This fixed-fixed setup changes how loads are distributed and deflection is controlled. The calculator below lets you work out max deflection, moments at the ends, and center moments, once you know your beam geometry, material, and the loads you’re fighting. These beams show up anywhere you can’t tolerate much bending: heavy machine frames, actuator mounts, bridges. If you need to keep deflection down, it’s often the way to go—as long as you properly handle those high reactions at the supports.

What is a Fixed-Fixed Beam?

A fixed-fixed beam can’t move or rotate at either support—both ends are clamped solid. This gives you much less deflection under load than a beam that’s just resting or pinned, at the cost of bigger reactions and moments at the ends.

Simple Explanation

Picture a board anchored tight at both ends—not just sitting on supports but actually bolted so neither end can even try to turn. When you load it, it barely sags, even with a big weight, because both ends work together to resist bending. You do end up with large bending moments at the supports, so you need to design those joints carefully to avoid trouble.

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Fixed-Fixed Beam Diagram

How to Use This Calculator

1. Select your load type — Point Load at Center or Uniform Distributed Load.
2. Enter your beam length (L), load value (P or w), modulus of elasticity (E), and moment of inertia (I) in consistent units.
3. Double-check your units — deflection output units match whatever length units you entered.
4. Click Calculate to see your result.

Fixed Beam Calculator

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Mathematical Equations

Here are the working equations for fixed-fixed beams with common loading cases.

The fixed beam calculator picks the right set depending on how your loads are applied:

Point Load at Center:

• Maximum Deflection: δ = PL³/(192EI)
• End Moments: M_end = PL/8
• Center Moment: M_center = -PL/8

Uniform Distributed Load:

• Maximum Deflection: δ = wL⁴/(384EI)
• End Moments: M_end = wL²/12
• Center Moment: M_center = -wL²/24

Where:

• P = Point load (force)
• w = Distributed load per unit length
• L = Beam length
• E = Modulus of elasticity
• I = Second moment of area (moment of inertia)
• δ = Maximum deflection
• M = Bending moment

Simple Example

Point load at center, steel beam:

• L = 4 m, P = 10,000 N, E = 200 × 10⁹ Pa, I = 8.33 × 10⁻⁶ m⁴
• Maximum Deflection: δ = (10,000 × 4³) / (192 × 200×10⁹ × 8.33×10⁻⁶) = 0.20 mm
• End Moments: M_end = (10,000 × 4) / 8 = 5,000 N·m
• Center Moment: M_center = −5,000 N·m

Engineering Theory and Principles

Fixed-fixed beams (sometimes called built-in beams) are everywhere in structural and machine design. If both ends are clamped, the beam can’t lift, slide, or twist at the supports. All this constraint makes the math more involved—you have to solve for reactions and moments that aren’t obvious up front. For the same size and load, a fixed-fixed beam will flex a lot less than a simply supported type. That’s why you’ll see them used where you just can’t have bending messing up alignment.

When you load a fixed beam, the connections at both ends create reaction moments. These moments push back against your applied loads and help flatten out the bending at midspan, at the expense of introducing high negative moments right at the supports.

The theory comes down to standard beam equations, but for fixed ends, you need boundary conditions that nail down both the position and slope at the supports. That makes it a statically indeterminate problem, which requires a bit more work or the use of tabulated solutions.

The upshot: a fixed-fixed beam loaded at the center will deflect only 1/4 as much as a simply supported one, all else being equal. For applications where tight tolerances matter and flexibility is a problem, this can be a big help—if you’re willing to deal with the higher support reactions.

Practical Applications

You’ll spot fixed-fixed beams in plenty of structures. Multi-span floors and bridge decks often act this way over interior supports. The same goes for roof beams that pass over several walls or columns. You’re trying to keep material use down and spans long—rigid supports help get more with less.

On the mechanical side, machine frames, and especially actuator mounts, often function as fixed-fixed when they’re bolted down both ends. With actuators and automation gear, the less the structure flexes, the better your positioning works. That’s why reducing beam deflection matters for precision assemblies.

Manufacturing gear, conveyors, and CNC bases use fixed-fixed beams to keep things straight and maintain repeatability. It isn’t just about supporting weight—the goal is to ensure tolerances stay tight no matter how much the load varies.

Aircraft wing spars, some car chassis parts, and even some large robotic arms are essentially fixed-fixed beams in practice, because the ends are so tightly clamped relative to the member’s stiffness. Where weight and strength are at a premium, this approach is common.

Worked Example

Let’s run some numbers for a steel beam:

• Length (L) = 4.0 meters
• Point load (P) = 10,000 N at the center
• Modulus of elasticity (E) = 200 × 10⁹ Pa (steel)
• Moment of inertia (I) = 8.33 × 10⁻⁶ m⁴ (W150×24 section)

Step 1: Calculate Maximum Deflection

δ = PL³/(192EI)

δ = (10,000 × 4³)/(192 × 200×10⁹ × 8.33×10⁻⁶)

δ = 640,000/(3.199×10⁹) = 2.00 × 10⁻⁴ meters = 0.20 mm

Step 2: Calculate End Moments

M_end = PL/8

M_end = (10,000 × 4)/8 = 5,000 N⋅m

Step 3: Calculate Center Moment

M_center = -PL/8

M_center = -5,000 N⋅m

You can see from these numbers that the max deflection is just 0.20 mm under a 10 kN center load, which is much stiffer than a simply supported beam. The high end moments and negative center moment tell you what must be handled in the connection and beam sizing.

Design Considerations and Best Practices

In theory, fixed ends are perfectly rigid. In reality, bolts stretch, welds deflect, and anchorages give a little. Even small end flexibility bumps up your actual deflection, so never count on textbook values unless your connections are truly rock-solid. Expect real-world deflections to be noticeably higher, especially with bolted joints.

Since support moments are much bigger on a fixed beam than a simply supported one, your connection has to resist both the vertical load and this large bending action. This often governs your fastener size, weld throat, or embedment detail.

For best performance, use materials with a high modulus—steel and aluminum are common. If you’re mounting an actuator or need precision, beefing up both the beam and the anchor points improves repeatability and positioning. Poor support stiffness can quickly undo the benefits of a fixed-fixed setup.

If you’re supporting shaking loads or dynamic machinery, note that fixed beams have higher natural frequencies than simply supported ones—sometimes good, sometimes a vibration problem. You’ll need to check your application’s sensitivity to transmitted vibrations or resonance.

Frequently Asked Questions

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