Formula Used
The calculator assumes a pin at A and a roller at B. The roller surface is inclined by θ from the horizontal.
Roller components: Bx = -RB sinθ, By = RB cosθ
Moment of any force about A: M = xFy - yFx
Roller moment about A: MB = RB(xB cosθ + yB sinθ)
Roller reaction: RB = -ΣMloads / (xB cosθ + yB sinθ)
Pin reactions: Ax = -(ΣFxloads + Bx), Ay = -(ΣFyloads + By)
Positive moments are counterclockwise. Negative vertical loads can also be entered by using a load angle of -90 degrees.
How To Use This Calculator
- Enter the unit labels for force and length.
- Enter the incline angle of the roller surface.
- Enter the roller coordinates from the pin support.
- Add point loads with magnitude, direction angle, and location.
- Add uniform or linearly varying loads when needed.
- Add applied couple moments with positive counterclockwise signs.
- Press Calculate and review the reaction table.
- Use CSV or PDF download for saving the results.
Example Data Table
| Input | Example Value | Meaning |
|---|---|---|
| Incline angle | 25 deg | Roller plane angle from horizontal |
| Roller xB | 6 m | Horizontal distance from pin |
| Roller yB | 0 m | Vertical offset from pin |
| Point load P1 | 12 kN at -90 deg | Downward point load |
| P1 location | x = 3 m, y = 0 m | Load position from pin |
| Uniform load | 2 kN/m from 1 m to 5 m | Downward distributed load |
| Applied moment | 4 kN-m | Positive counterclockwise couple |
Article
About This Calculator
An inclined roller support creates a reaction not vertical. Its reaction acts normal to the contact plane. That detail changes the equilibrium model. This helps build that model without manual component errors. It supports point loads, uniform loads, linearly varying loads, and applied couples. You can place each load by coordinates. You can also place the roller above or below the pin line. This is useful for brackets, frames, ramps, and beam problems with sloped seats.
Why The Incline Matters
On a flat roller, the reaction is often vertical. On a sloped roller, the reaction turns with the normal line. The horizontal part matters. It may increase the pin force. It may reverse the expected direction. The calculator first resolves every load into x and y parts. Then it takes moments about the pin support. That step removes the pin reactions from the moment equation. The remaining equation finds the roller reaction.
Formula Used
The tool uses planar static equilibrium. The load moment is found by x times vertical force minus y times horizontal force. The roller component is based on the incline angle. Its horizontal component equals negative reaction times sine theta. Its vertical component equals reaction times cosine theta. The moment arm term becomes roller x times cosine theta plus roller y times sine theta. The pin reactions are then found from force balance.
How To Use This Calculator
Enter the roller angle from the horizontal plane. Add the roller coordinates from the pin support. Enter point loads with their angle and position. Use negative ninety degrees for a downward vertical load. Enter uniform load intensity between start and end positions. Use trapezoid loads for ramps, soil, water, or variable pressure. Add any applied moments with a positive value for counterclockwise action. Press Calculate to see reactions and checks.
Result Review
A positive roller reaction means the support pushes along the chosen normal direction. A negative value means the assumed contact direction is reversed. In real rollers, that can mean lift off. Review the equilibrium checks before using the result. Rounding errors are normal. Large checks usually mean wrong signs, wrong angles, or missing loads. The CSV and PDF buttons save the result for reports.
FAQs
What is a roller on incline reaction?
It is the support force from a roller resting on a sloped surface. The force acts normal to the slope, not straight upward.
Why is the roller reaction not vertical?
A roller can only push perpendicular to its contact plane. When that plane is inclined, the reaction has both horizontal and vertical components.
What angle should I enter?
Enter the angle of the roller surface from the horizontal. The calculator automatically uses the normal direction for the reaction force.
How do I enter a downward point load?
Enter a positive magnitude and use -90 degrees as the load angle. That creates a vertical downward force in the calculation.
Can this handle distributed loads?
Yes. It supports uniform distributed loads and linearly varying loads. Each is converted into an equivalent resultant force and centroid location.
What does a negative roller reaction mean?
It means the assumed normal direction is reversed. For a free roller, this may indicate uplift or loss of contact.
Are moments clockwise or counterclockwise?
Counterclockwise moments are positive. Clockwise moments should be entered as negative values.
Why are the check values not exactly zero?
Small differences come from rounding. Large differences usually mean an incorrect sign, angle, position, or missing load.