Steel Truss Internal Forces Calculator

Analyze planar steel trusses, support reactions, member tension, compression, stress, buckling, utilization, and safety factors using editable joints, members, and loads.

Results

Positive axial force means tension. Negative axial force means compression.
Determinacy—
Maximum tension—
Maximum compression—
Critical utilization—
Load a preset or edit the tables, then select Calculate.

Support reactions

JointRxRy
No results yet.

Member forces and checks

MemberLengthAxial forceTypeStress Euler PcrStress FOSUtilizationStatus
No results yet.

Truss setup

Supports restrain horizontal and/or vertical joint translation. A planar pin-jointed truss has no rotational joint degree of freedom.

Joints and supports

Coordinates use the selected length unit.
IDXYRestrain XRestrain Y

Members

Area uses mm². Inertia uses mm⁴ for optional Euler buckling checks.
NameStartEndArea mm²E GPaFy MPaI mm⁴K

Joint loads

Enter horizontal and vertical loads using the selected force unit.
JointFxFy

Formula used

The calculator assembles the two-dimensional truss stiffness matrix. Each member contributes axial stiffness EA/L. Joint equilibrium is solved from K·u = F.

Joint equilibrium
ΣFx = 0
ΣFy = 0
Member stress
σ = F / A
Determinacy guide
m + r = 2j
Euler buckling
Pcr = π²EI / (KL)²
Stress safety factor
FOS = Fy / |σ|
Utilization
|σ| / Fy, with buckling also checked for compression.

How to use this calculator

  1. Choose a preset or enter custom joint coordinates.
  2. Define supports by restraining joint X or Y movement.
  3. Connect joints with steel truss members.
  4. Enter area, modulus, yield strength, inertia, and K factor.
  5. Add joint loads with the required directions.
  6. Select Calculate truss and review reactions and member forces.
  7. Export results using CSV or PDF when needed.

Steel Truss Internal Forces

A steel truss carries loads mainly through axial member forces. Ideal truss analysis assumes straight members, pin-connected joints, and loads applied at joints. Under these assumptions, each member develops either tension, compression, or nearly zero axial force. This calculator uses the direct stiffness method, making it useful for small and medium planar trusses with custom geometry.

Understanding the calculated forces

Positive member force is reported as tension. Negative force is reported as compression. Tension stretches a member, while compression shortens it. The stress check divides axial force by cross-sectional area. The resulting stress is compared with the entered steel yield strength. This produces a simple stress safety factor and utilization ratio. These values are screening tools, not complete code checks.

Compression and buckling

Compression members can fail by buckling before yielding. When a moment of inertia is supplied, the calculator estimates Euler critical load. Effective length is controlled by the entered K factor. Euler theory is most appropriate for slender, idealized columns. Real truss design may require code-specific buckling curves, connection checks, local slenderness limits, and resistance factors.

Reactions and stability

Support reactions are recovered after joint displacements are solved. A pinned support usually restrains both translations. A roller usually restrains one translation. The common condition m + r = 2j is displayed as a determinacy guide. It does not guarantee geometric stability. A poorly arranged truss can still form a mechanism even when the count appears correct.

Using results responsibly

Use the diagram to locate heavily loaded members quickly. Then inspect stress, buckling capacity, utilization, and safety factor. Final structural design should also consider load combinations, connection behavior, member slenderness, fabrication tolerances, corrosion, fatigue, and governing building standards. Engineering review remains essential for safety-critical structures.

Example steel truss data

MemberArea mm²Typical force kNClassificationExample stress MPa
B11200+42Tension35.0
T11000-36Compression36.0
D1900+18Tension20.0
V1850-12Compression14.1
Z17500.2Near zero0.3

Frequently asked questions

What does a positive member force mean?

A positive force means the member is in tension under the calculator's sign convention.

What does a negative member force mean?

A negative force means the member is in compression.

Can the calculator identify zero-force members?

Yes. Very small axial forces are classified as near zero using a numerical tolerance.

Does it check buckling?

Yes. Compression members receive an Euler buckling estimate when inertia and effective-length factor values are available.

Does m + r = 2j prove that a truss is stable?

No. It is only a counting test. Geometry can still create an unstable mechanism.

Can I model a roller support?

Yes. Restrain only the translation normal to the roller surface.

Why might the solver report a singular matrix?

The truss may be unstable, disconnected, under-supported, or contain duplicate or zero-length members.

Is this a complete steel design code check?

No. It provides structural analysis and screening calculations, not full jurisdiction-specific member and connection design.

Structural calculations can affect safety. Verify important designs with applicable standards and a qualified structural professional.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.