Beam model
Use positive force magnitudes with an angle, or enter signed distributed-load intensities. A downward point force uses −90°.
Beam and load diagram
The sketch updates from the form. Reaction arrows appear after a successful calculation.
Formula used
The solver forms a coefficient matrix for every selected reaction. It solves up to three independent rigid-body unknowns. More unknowns require stiffness, compatibility, or deformation equations.
How to use this calculator
- Enter the beam length and choose consistent display units.
- Add supports, select their types, and set their positions.
- Add point forces, distributed loads, or applied moments.
- Use −90° for a downward point load and 90° for upward.
- Use negative distributed intensities for downward loading.
- Calculate, review the reactions, and confirm equilibrium passes.
Worked example data
A six-meter beam has a pin at the left end. A vertical roller supports the right end. A 12 kN point force acts downward at midspan.
| Item | Type | Position | Value |
|---|---|---|---|
| Support A | Pin | 0 m | Horizontal and vertical reactions |
| Support B | Vertical roller | 6 m | Vertical reaction |
| Load | Point force | 3 m | 12 kN at −90° |
| Expected result | Reactions | A and B | 6 kN upward at each support |
Support reaction analysis guide
Support reactions keep a loaded beam in static equilibrium. A pin usually resists horizontal and vertical movement. A roller normally provides one reaction perpendicular to its surface.
A fixed support also prevents rotation and develops a moment. These reaction assumptions determine the number of unknowns. A planar rigid body supplies only three independent equilibrium equations.
Point forces are resolved into horizontal and vertical components. Their moments depend on force direction and lever arm. A force applied along the beam axis creates no left-end moment.
Distributed loads are replaced by equivalent resultants before solving. Uniform loads act through the middle of their loaded length. Triangular loads act one-third from the larger-intensity end.
Trapezoidal loads are handled through direct integration. This avoids errors when the two intensities differ greatly. Signed intensities also allow upward and downward loading combinations.
A valid reaction solution must satisfy force and moment balance. Small numerical residuals come from floating-point rounding. Large residuals usually indicate instability or an incompatible support model.
Negative reactions are meaningful and should not be deleted. They indicate the actual direction is opposite the assumed positive direction. A negative vertical result can indicate uplift restraint is required.
This calculator focuses on statically determinate rigid-body equilibrium. It does not calculate deflection, shear stress, bending stress, or member stiffness. Indeterminate beams require compatibility and material properties.
Always verify support details against the real connection behavior. Construction joints can differ from ideal pins, rollers, and fixed supports. Qualified engineers should review safety-critical structural decisions.
Frequently asked questions
What does a negative reaction mean?
It means the real reaction acts opposite the direction assumed by the solver. Negative vertical reactions commonly indicate uplift.
Can this solve a simply supported beam?
Yes. Use one pin and one vertical roller. Their three reaction unknowns match the three planar equilibrium equations.
Can it solve a cantilever?
Yes. Use one fixed support. The solver returns horizontal force, vertical force, and fixed-end moment.
Why is my beam marked indeterminate?
More than three independent reaction unknowns cannot be found from rigid-body equilibrium alone. Additional stiffness and compatibility equations are required.
How are distributed loads entered?
Enter their start and end positions plus initial and ending intensities. Use equal values for a uniform load.
Which sign should downward loads use?
Use a positive point-force magnitude with an angle of −90°. Use negative intensity values for downward distributed loads.
Can I enter inclined forces?
Yes. Enter the force magnitude and its angle measured counterclockwise from the positive beam axis.
Does it calculate shear and bending diagrams?
No. The included diagram shows supports, loads, and reactions. It does not generate internal shear or bending-moment distributions.
Is the result suitable for final structural design?
Use it for checking and education. Safety-critical designs require verified loads, connection behavior, code compliance, and professional engineering review.
Engineering disclaimer
This calculator uses idealized two-dimensional static equilibrium. Real structures may include connection flexibility, three-dimensional effects, dynamic loads, settlement, nonlinear behavior, and code requirements. Verify every result before design, fabrication, or construction.