Advanced Load Inputs
Formula Used
The calculator applies static equilibrium for a fixed cantilever support.
ΣFy = 0, so Rv = Σ vertical loads.
ΣFx = 0, so Rh = Σ horizontal loads.
Mfix = Σ(Wi × xi) + Σ applied moments.
R = √(Rv² + Rh²).
For a uniform load, W = w(b) and the centroid is at the middle of the loaded length.
For a triangular load, W = qmax(b)/2. The centroid is one third from the heavier end.
How to Use This Calculator
- Select the force and length units for all entries.
- Enter the total cantilever beam length.
- Add any point load, load position, and load angle.
- Enter partial or full distributed load ranges.
- Add triangular load data if the load varies linearly.
- Include self weight and applied couple moment if needed.
- Press the calculate button and read the result above the form.
- Use CSV or PDF buttons to save the current calculation.
Example Data Table
| Case | Beam length | Point load | UDL | Expected main effect |
|---|---|---|---|---|
| End bracket | 2 m | 5 kN at 2 m | 0 kN/m | High fixed-end moment |
| Shelf load | 1.5 m | 1 kN at 1.2 m | 0.8 kN/m full span | Combined shear and moment |
| Sign arm | 3 m | 2 kN at 3 m | 0.2 kN/m full span | Support force plus rotation demand |
Understanding Cantilever Support Force
A cantilever beam is held at one end. The fixed end supplies all balance actions. It gives a vertical reaction. It can also give horizontal reaction. It resists rotation with a fixed-end moment. These values are essential for brackets, balconies, machine arms, signs, and shelves. The free end may look simple. The support still carries every external load.
Load Cases Used in Practice
Real beams often carry more than one load. A point load may act from a suspended item. A uniform load may come from decking, slab weight, or stored material. A triangular load may represent pressure that changes along the span. A couple moment may come from a motor, joint, or attached frame. This calculator lets these actions work together. That makes the result closer to real engineering checks.
How Reactions Are Formed
The fixed support must keep the beam in static equilibrium. The sum of vertical forces must be zero. The sum of horizontal forces must be zero. The sum of moments about the fixed end must be zero. Downward loads create upward support reaction. Horizontal loads create opposite horizontal reaction. Loads away from the support create fixed-end moment. Longer arms create larger moments, even with the same force.
Why Position Matters
A force near the free end produces more turning effect than the same force near the wall. This happens because moment equals force times distance. Distributed loads are first replaced by a single resultant. The resultant acts at the centroid of the loaded length. For a full uniform load, the centroid is at midspan. For a triangular load, the centroid shifts toward the heavier side.
Using Consistent Units
The calculator converts common force and length units internally. You can enter newtons, kilonewtons, or pounds-force. You can enter meters, millimeters, feet, or inches. Distributed loads should match the selected force and length unit. For example, kN with meters means kN per meter. The output reports several useful units for comparison.
Reading the Result
The vertical reaction shows shear demand at the support. The horizontal reaction shows axial restraint demand. The resultant support force combines both components. The fixed-end moment shows rotational demand at the support. A high moment may govern anchor selection, weld size, wall plate design, or beam section choice.
Practical Safety Notes
This tool supports learning and early design checks. It does not replace local code design. Real beams also need deflection, bending stress, shear stress, buckling, vibration, connection strength, and material checks. Load factors should follow your project rules. Always confirm assumptions before construction or fabrication.
Comparing Load Cases
Better early decisions come from comparing cases. Increase the point load distance and watch the moment rise. Extend a uniform load and watch both reaction and moment grow. Change the triangular peak side to see the centroid move. Small input changes can expose sensitive supports. Use this before drawing final connection details safely.
FAQs
What is support force in a cantilever beam?
It is the reaction force supplied by the fixed end. It balances applied vertical and horizontal loads. The fixed end also supplies a resisting moment, which stops rotation.
Why does a cantilever need a fixed-end moment?
A cantilever has no second support. The fixed end must stop both translation and rotation. Loads acting away from the support create turning effect, so a moment reaction is required.
Can I calculate partial uniform loads?
Yes. Enter the load intensity, start position, and end position. The calculator converts that load into one resultant force acting at the middle of the loaded length.
How is a point load position measured?
Measure the position from the fixed support toward the free end. A load farther from the fixed support creates a larger fixed-end moment.
What does point load angle mean?
It is measured from the vertical direction. Zero degrees is a fully vertical load. Larger angles add horizontal load, which increases horizontal support reaction.
How should I enter distributed load units?
Use the selected force unit per selected length unit. If you choose kN and meters, enter kN/m. If you choose lbf and feet, enter lbf/ft.
What is the resultant support force?
It is the combined magnitude of vertical and horizontal reactions. The calculator uses the square root of vertical reaction squared plus horizontal reaction squared.
Does this calculator include beam self weight?
Yes. Enter self weight as force per length. The calculator treats it as a uniform load acting across the full cantilever span.
Can this replace structural design?
No. It is a physics and preliminary checking tool. Final design should also check stress, deflection, stability, connections, load combinations, and local code rules.
Why is my fixed-end moment very high?
Moment increases with load size and distance from the fixed support. Long cantilevers can create large support moments even when the applied force seems moderate.
What happens if a load position exceeds beam length?
The calculator limits the position to the beam span for stability. Still, you should correct the input so the model matches your actual beam geometry.