BIZOMAT MAKEOS · Mechanics
Resultant of Concurrent Forces
What single force is equivalent to these forces acting at one point?
Resolve up to four coplanar forces acting through one point into X and Y components, the resultant and the equilibrant.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Force 1 | ||
| Magnitude | N | Magnitude of force 1 from your load analysis. |
| Direction from +X (anticlockwise) | ° | Direction of force 1, anticlockwise from the +X axis. |
| Force 2 | ||
| Magnitude | N | Magnitude of force 2. |
| Direction from +X (anticlockwise) | ° | Direction of force 2. |
| Force 3 | ||
| Magnitude | N | Magnitude of force 3 (0 if not used). |
| Direction from +X (anticlockwise) | ° | Direction of force 3. |
| Force 4 | ||
| Magnitude | N | Magnitude of force 4 (0 if not used). |
| Direction from +X (anticlockwise) | ° | Direction of force 4. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
Force 1
What this means: Magnitude
- What it is
- The size of this force acting through the common point, from your load analysis, without its direction.
- Units and format
- Enter a number in N: newtons. The form accepts 0 N or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1000 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Give the magnitude as a positive number and set its direction with the angle; a force of 0 is skipped.
What this means: Direction from +X (anticlockwise)
- What it is
- The direction this force acts in, measured anticlockwise from the positive X axis in the plane of the forces.
- Units and format
- Enter a number in °: degrees of angle. The form accepts -360° to 360°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use one X axis for all forces. A clockwise direction can be entered as a negative angle.
Force 2
What this means: Magnitude
- What it is
- The size of this force acting through the common point, from your load analysis, without its direction.
- Units and format
- Enter a number in N: newtons. The form accepts 0 N or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 800 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Give the magnitude as a positive number and set its direction with the angle; a force of 0 is skipped.
What this means: Direction from +X (anticlockwise)
- What it is
- The direction this force acts in, measured anticlockwise from the positive X axis in the plane of the forces.
- Units and format
- Enter a number in °: degrees of angle. The form accepts -360° to 360°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 60° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use one X axis for all forces. A clockwise direction can be entered as a negative angle.
Force 3
What this means: Magnitude
- What it is
- The size of this force acting through the common point, from your load analysis, without its direction.
- Units and format
- Enter a number in N: newtons. The form accepts 0 N or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Leave it at 0 when there is no third force; its angle is then ignored.
What this means: Direction from +X (anticlockwise)
- What it is
- The direction this force acts in, measured anticlockwise from the positive X axis in the plane of the forces.
- Units and format
- Enter a number in °: degrees of angle. The form accepts -360° to 360°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Ignored when the matching magnitude is 0.
Force 4
What this means: Magnitude
- What it is
- The size of this force acting through the common point, from your load analysis, without its direction.
- Units and format
- Enter a number in N: newtons. The form accepts 0 N or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Leave it at 0 when there is no fourth force; its angle is then ignored.
What this means: Direction from +X (anticlockwise)
- What it is
- The direction this force acts in, measured anticlockwise from the positive X axis in the plane of the forces.
- Units and format
- Enter a number in °: degrees of angle. The form accepts -360° to 360°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Ignored when the matching magnitude is 0.
Method and formulas
- Rx = Σ F cos θ; Ry = Σ F sin θ.
- R = √(Rx² + Ry²); direction = atan2(Ry, Rx). The equilibrant has the same size, opposite direction.
- Example: 1000 N at 0° and 800 N at 60° give a resultant of 1,562 N at 26.33°.
Limitations
- All forces must act through the same point in one plane; moments from offset forces are not included.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Combine cable, sling or bracket loads
- Find the reaction a support must provide
- Check a free-body diagram quickly
Who it is for
- Design engineers
- Maintenance engineers
- Technicians
What you get
- X and Y components
- Resultant magnitude and direction
- Equilibrant
Interpreting the result
- Design the support or anchor for the equilibrant, with your code’s load factors.
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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