KEVOS® MAKEOS · Mechanics
Force Group Support Check (Resultant, Line of Action, Support Reactions, Uplift)
For several forces acting on a frame, base or beam resting on two supports, what is their resultant, where does it act, and what does each support carry?
Check of a rigid member or base on a pinned support A and a roller support B: the resultant of up to four forces in any direction, its moment about the origin and where its line of action crosses the support line (as the force system tool), then the reactions at A (both directions) and B (perpendicular to the support line), any uplift at either support, and the reactions against the support capacities.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Force 1 | ||
| Magnitude | N | Size of force 1 (0 if unused). |
| Direction from +X | ° | Direction of force 1, anticlockwise from +X (−90 is straight down). |
| X of a point on its line | mm | X of any point on the line of force 1. |
| Y of that point | mm | Y of that point. |
| Force 2 | ||
| Magnitude | N | Size of force 2. |
| Direction from +X | ° | Direction of force 2. |
| X of a point on its line | mm | X of a point on force 2. |
| Y of that point | mm | Y of that point. |
| Force 3 | ||
| Magnitude | N | Size of force 3. |
| Direction from +X | ° | Direction of force 3. |
| X of a point on its line | mm | X of a point on force 3. |
| Y of that point | mm | Y of that point. |
| Force 4 | ||
| Magnitude | N | Size of force 4. |
| Direction from +X | ° | Direction of force 4. |
| X of a point on its line | mm | X of a point on force 4. |
| Y of that point | mm | Y of that point. |
| Supports (on the X axis) | ||
| Pinned support A at X | mm | Position of the pinned support (takes both X and Y loads). |
| Roller support B at X | mm | Position of the roller support (takes Y load only). |
| Capacity of support A | N | Load support A can carry. |
| Capacity of support B | N | Load support B can carry. |
Method and formulas
- R_x = Σ F cos θ; R_y = Σ F sin θ; moment about the origin M = Σ (x F_y − y F_x); line of action crosses the X axis at M ÷ R_y (as the force system tool).
- Roller B: R_By = −(M − x_A R_y) ÷ (x_B − x_A); pin A: R_Ay = −R_y − R_By, R_Ax = −R_x.
- A negative (downward) reaction means uplift: that support must be held down.
- Example: resultant 3,000 N acting at X 366.67 mm; A carries 1,900 N and B 1,100 N.
Limitations
- Rigid member, forces in one plane, supports on the X axis.
- Static loads; dynamic and impact loads need factors.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Find the support loads under a machine with several forces
- Check a base for uplift at one support
- Check bracket or beam supports for inclined loads
Who it is for
- Design engineers
- Structural detailers
- Engineering students
What you get
- Resultant, moment and line of action
- Reactions at A and B
- Uplift and capacity checks
Interpreting the result
- When the line of action of the resultant falls outside the supports, the far support lifts off unless it is held down.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 153–163. Topic reference; no source tables or recommended settings are reproduced.
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Open the Force Group Support Check (Resultant, Line of Action, Support Reactions, Uplift) calculator
