Example Data Table
| Input Area |
Example Lines |
Meaning |
| Joints |
A,0,0
B,3,0
C,6,0
D,3,2.5 |
Four joint coordinates in meters. |
| Members |
AB,A,B,900,200
AD,A,D,900,200 |
Member name, start joint, end joint, area, modulus. |
| Supports |
A,1,1
C,0,1 |
A is a pin. C is a vertical roller. |
| Loads |
B,0,-12
D,0,-18 |
Downward joint loads in kilonewtons. |
Formula Used
The calculator uses the two dimensional truss stiffness method. Each member stiffness is assembled into the global stiffness matrix.
Member length: L = √((x₂ - x₁)² + (y₂ - y₁)²)
Direction cosines: c = (x₂ - x₁) / L and s = (y₂ - y₁) / L
Axial stiffness: k = AE / L
Global equation: [K]{u} = {F}
Axial deformation: δ = [-c -s c s]{uₑ}
Member force: P = AEδ / L
Stress and strain: σ = P / A and ε = σ / E
Positive member force is reported as tension. Negative member force is reported as compression.
How to Use This Calculator
Enter each joint on a new line. Use the format joint, x, y. Coordinates should use meters.
Enter each member on a new line. Use member, start joint, end joint, area, and modulus.
Enter support restraints as one or zero. Use one for restrained movement. Use zero for free movement.
Enter loads in kilonewtons. Positive Fx acts right. Positive Fy acts upward.
Set allowable stress, displacement limit, and load factor. Press the submit button. Results appear above the form and below the header.
Understanding Activity 2.17 Truss Force Analysis
A truss carries loads through straight members. Each member connects at pin joints. The ideal member carries axial force only. It is either in tension, compression, or nearly zero force. Activity 2.17 usually asks students to connect geometry, equilibrium, and member behavior. This calculator extends that activity with a matrix based method. It can handle joints, bars, mixed supports, and loads.
Why Geometry Matters
Joint coordinates define every member angle. The angle controls how a bar splits force into horizontal and vertical parts. A shallow member may create large axial force. A steep member may carry more vertical action. Input geometry gives reliable force signs. Use the length unit for all coordinates. This tool assumes meters for coordinates.
How The Solver Works
The calculator assembles a two dimensional truss stiffness matrix. Every joint receives two degrees of freedom. One degree is horizontal. The other degree is vertical. Supports remove selected degrees of freedom. Loads are placed on joint directions. After solving displacements, the page calculates reactions and member forces. Positive force means tension. Negative force means compression.
Reading The Results
Start with the reaction table. It should balance the applied loads. Then check the displacement table. Large movement may show weak support, missing members, or a flexible design. Finally review each member force. Tension members stretch. Compression members shorten. A near zero result suggests the member has little axial demand for that load case. Stress and utilization help compare members against an allowable value.
Good Modeling Practice
Keep member names simple. Avoid duplicate joint names. Add at least enough restraints to stop rigid body motion. A pin support may restrain x and y movement. A roller usually restrains one direction only. Check that every member connects two valid joints. Use realistic area and modulus values. A steel member might use 200 GPa. Area is entered in square millimeters. Loads are entered in kilonewtons.
Limits Of This Tool
The model uses linear elastic behavior. It does not check buckling, welds, bolts, yielding after overload, or joint eccentricity. It also assumes small deflection. Use it for study, quick comparison, and preliminary classroom checks. Final structural work needs codes, load combinations, and safe professional review.
FAQs
1. What does positive member force mean?
Positive member force means tension. The member is stretching between its end joints. Negative force means compression. The member is shortening along its own axis.
2. What units should I use?
Use meters for joint coordinates, kilonewtons for loads, square millimeters for area, and gigapascals for modulus. The output gives force in kN and stress in MPa.
3. Can this solve indeterminate trusses?
Yes. The stiffness method can solve determinate and many indeterminate trusses if the model is stable. A singular warning means supports or connectivity need correction.
4. Why did I get a singular matrix error?
The structure may move as a rigid body. It may also contain disconnected joints, missing supports, duplicate coordinates, or an unstable member layout.
5. How do I model a pin support?
Use one for both x and y restraint. For example, A,1,1 fixes horizontal and vertical movement at joint A.
6. How do I model a roller support?
Restrain only the supported direction. A vertical roller can be entered as C,0,1. That keeps vertical movement fixed and horizontal movement free.
7. Does this calculator check buckling?
No. It reports axial compression and stress. Slender compression members need separate buckling checks before final design decisions.
8. Can I export my results?
Yes. After calculation, use the CSV button for spreadsheet data. Use the PDF button for a printable report of the visible result tables.