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
Joint
Rx
Ry
No results yet.
Member forces and checks
Member
Length
Axial force
Type
Stress
Euler Pcr
Stress FOS
Utilization
Status
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.
ID
X
Y
Restrain X
Restrain Y
Members
Area uses mm². Inertia uses mm⁴ for optional Euler buckling checks.
Name
Start
End
Area mm²
E GPa
Fy MPa
I mm⁴
K
Joint loads
Enter horizontal and vertical loads using the selected force unit.
Joint
Fx
Fy
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
Choose a preset or enter custom joint coordinates.
Define supports by restraining joint X or Y movement.
Connect joints with steel truss members.
Enter area, modulus, yield strength, inertia, and K factor.
Add joint loads with the required directions.
Select Calculate truss and review reactions and member forces.
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
Member
Area mm²
Typical force kN
Classification
Example stress MPa
B1
1200
+42
Tension
35.0
T1
1000
-36
Compression
36.0
D1
900
+18
Tension
20.0
V1
850
-12
Compression
14.1
Z1
750
0.2
Near zero
0.3
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.
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.