Calculator
Example Data Table
| Input Type | Example Entry | Meaning |
|---|---|---|
| Joint | A,0,0 | Joint A is placed at x 0 and y 0. |
| Joint | C,6,8 | Joint C is the top joint of the triangle. |
| Member | AC,A,C | Member AC connects joint A to joint C. |
| Load | C,0,-100 | A 100 unit downward load is placed at C. |
Formula Used
This calculator uses the method of joints. Each joint must satisfy two static balance equations.
Sum of horizontal forces: ΣFx = 0
Sum of vertical forces: ΣFy = 0
For each member, direction cosines are found from joint coordinates:
L = √((x2 - x1)² + (y2 - y1)²)
ux = (x2 - x1) / L
uy = (y2 - y1) / L
A positive solved member force is tension. A negative solved member force is compression.
How To Use This Calculator
- Enter each truss joint as name, x, and y.
- Enter each member using its two end joints.
- Enter loads using Fx and Fy values.
- Use negative Fy for downward loads.
- Select the pin support and roller support.
- Press the calculate button.
- Review member signs for tension or compression.
- Export the result as CSV or PDF.
Understanding Truss Force Results
A truss carries load through straight members. Each member is usually treated as a two force part. That means force acts along its own centerline. This calculator follows that classroom idea. It builds joint balance equations from the geometry you enter. Then it solves all member forces at one time.
Why Joint Balance Matters
Every joint must be in static equilibrium. Horizontal forces must add to zero. Vertical forces must also add to zero. Supports create reaction forces. Loads create external forces. Member forces resist those loads. A positive member value means tension. A negative value means compression. A value near zero means the member carries little axial force.
Using Coordinates Carefully
Good coordinates are important. Use the same length unit for every joint. Place each joint name only once. Connect members between existing joints. Enter loads in the force direction you want. Downward loads should be negative in the Fy column. Side loads can be positive or negative in the Fx column. The solver uses these signs directly.
Support Setup
Most PLTW truss problems use one pin and one roller. The pin resists horizontal and vertical motion. The roller resists only one direction. A vertical roller is common. It gives one upward or downward reaction. A horizontal roller can be used for special classroom cases. The truss should be determinate. In simple terms, the number of unknown forces should match the available joint equations.
Reading The Output
The result table lists every member. It shows signed force, absolute force, and condition. Tension pulls away from the joint. Compression pushes toward the joint. Reaction values show how the supports hold the structure. The residual check helps confirm balance. Small residuals mean the equations closed well.
Study Use
This tool is best for checking hand work. First draw a free body diagram. Then calculate reactions by hand. Next solve joint forces using sine, cosine, and equilibrium. Finally compare your values with the table. Differences usually come from sign choices, wrong coordinates, or mixed units. Use the CSV file for spreadsheets. Use the PDF file for a quick report.
Keep a copy of each setup. It makes repeat practice easier. It also supports teacher review during later sessions.
FAQs
1. What does this truss calculator solve?
It solves support reactions and axial member forces for a statically determinate planar truss. It uses joint equilibrium equations and member direction cosines from your entered coordinates.
2. What does a positive member force mean?
A positive member force means tension. The member is pulling away from the joint in the assumed direction. This is the standard sign convention used by the calculator.
3. What does a negative member force mean?
A negative member force means compression. The member pushes toward the joint. Use the absolute value for magnitude and the condition label for interpretation.
4. Why must downward loads be negative?
The calculator uses a normal x and y coordinate system. Upward force is positive y. Downward force is negative y. A 100 unit downward load should be entered as Fy = -100.
5. Why do I get a determinate error?
The number of unknown member forces and reactions must match the number of joint equations. For a pin and roller truss, this usually means M + 3 = 2J.
6. Can I use metric units?
Yes. You may choose metric or customary labels. Keep all coordinates in the same length unit. Keep all loads in the same force unit.
7. Does the calculator check bending?
No. It treats each truss member as a two force axial member. It does not calculate bending stress, buckling strength, connection stress, or deflection.
8. Why is the residual value shown?
The residual shows equation balance error after solving. A very small value means the solved forces satisfy the joint equilibrium equations well.