Example Data Table
| Input Area |
Example Row |
Meaning |
| Nodes |
A,0,0 |
Node A is at x 0 and y 0. |
| Members |
AC,A,C,0.0025 |
Member AC joins A to C with area 0.0025. |
| Loads |
C,0,-12000 |
Node C carries a 12000 N downward load. |
| Supports |
A,1,1 |
Node A is fixed in x and y translation. |
| Supports |
B,0,1 |
Node B is fixed only in y translation. |
Formula Used
Member length: L = sqrt((x2 - x1)^2 + (y2 - y1)^2).
Direction cosines: c = (x2 - x1) / L and s = (y2 - y1) / L.
Member stiffness: k = AE / L multiplied by the 2D truss direction matrix.
Joint equation: K u = F, after restrained degrees of freedom are removed.
Axial deformation: d = c(ujx - uix) + s(ujy - uiy).
Axial force: N = AE d / L. Stress: sigma = N / A.
Strain: epsilon = d / L. Utilization = absolute stress / allowable stress.
Reaction force: R = K u - F at restrained directions.
How to Use This Calculator
- Enter each node with an id, x coordinate, and y coordinate.
- Enter each member with its start node, end node, and area.
- Add optional member elastic modulus when a member differs from default.
- Enter joint loads with Fx and Fy values.
- Enter supports with 1 for fixed and 0 for free.
- Set elastic modulus, allowable stress, and load factor.
- Press Submit to view results above the form.
- Use CSV or PDF buttons to save the report.
Understanding Member Forces
A truss carries load through straight members and pinned joints. Each member mainly resists axial force. That force may pull the member in tension. It may also push the member in compression. Good estimates help builders compare member sizes before drawings become final. This calculator uses joint coordinates, restraints, areas, loads, and material stiffness. It then forms a global stiffness model. The model solves joint displacement first. Member force and stress follow from those displacements.
Why Stress Matters
Force alone does not show member safety. A small bar can carry less force than a wide bar. Stress divides axial force by area. This makes different members easier to compare. Tensile stress may cause yielding. Compressive stress may also require buckling review. Use the utilization result as an early screening value. A value below one means the entered allowable stress is not exceeded. Final design still needs code checks.
Practical Construction Checks
Truss input should match the real support layout. One support often restrains horizontal and vertical movement. Another support may restrain only vertical movement. This avoids a locked model and reflects a roller condition. Loads should be placed at joints. Distributed roof or floor loads should be converted into joint loads. Use consistent units through the whole form. If coordinates use meters, use square meters for area and newtons for loads.
Reading The Results
Positive force means tension. Negative force means compression. The reaction table shows support forces that balance the applied loads. The displacement table helps identify flexible joints. Large movement can signal weak geometry or small areas. Stress results show which member controls the design. The CSV and report downloads help save the run for checking, pricing, or review. Treat the output as analysis support, not an approval stamp.
Common Input Mistakes
Many errors come from mixed units. Another common issue is an unstable support set. The solver needs enough restraints to stop rigid body motion. Duplicate node names can also break the model. Member areas should be positive. Joint loads need correct signs. Downward loads are usually negative. Review every warning before using the result. Small input changes can move force from one member to another quickly. Save checked examples for future comparisons too.
FAQs
What does positive member force mean?
Positive member force means the member is in tension. The member is being pulled along its axis. Negative force means compression. The member is being pushed along its axis.
Can this calculator check buckling?
It reports compression force and stress. It does not perform a full buckling code check. Use the compression result with member length, section properties, and your local design standard.
What units should I use?
Use one consistent unit system. The sample uses meters, square meters, newtons, and pascals. If you use inches and pounds, keep all related values consistent.
Why does the solver show a singular matrix?
A singular matrix usually means the truss is unstable. Check missing members, duplicate nodes, incorrect supports, or geometry that allows rigid body movement.
Can I enter different material stiffness per member?
Yes. Add an optional fifth value in the member row. Use the format id,start,end,area,elastic modulus. Blank values use the default modulus.
Where should loads be applied?
Loads should be applied at joints for this truss model. Convert distributed roof, floor, or wind loads into equivalent joint forces before entering them.
Does utilization below one mean final approval?
No. It only compares axial stress with your entered allowable stress. Final design may need buckling, connection, deflection, load combination, and code reviews.
Why are support reactions important?
Support reactions show how loads return to bearings, walls, or foundations. They help check load paths and confirm that applied loads are balanced.