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Truss Method of Joints Axial Force Calculator

The Method of Joints evaluates equilibrium (ΣFx = 0, ΣFy = 0) at individual pin-connected joints to determine axial tension and compression across truss frameworks.

Total horizontal distance between end pin and roller supports in meters.

Vertical height from bottom tie chord to roof apex ridge.

Total vertical roof downward load applied at the ridge joint in kN.

Calculated Result
49.62 kN (C)

Rafter Axial Force (Compression)

Rafter Force (Diagonals)

49.62 kN (COMPRESSION)

Bottom Chord Force (Tie)

42.86 kN (TENSION)

Support Reactions (Ra = Rb)

25 kN each

Truss Slope Angle (θ)

30.26°

Diagonal Member Length

6.946 m

Structural Recommendation

Standard member sizing applicable

Calculation Breakdown

  1. 1. Geometry & Support EquilibriumSpan L = 12 m, Half-span = 6 m, Height h = 3.5 m. Angle θ = arctan(3.5 / 6) = 30.26°. Support Reactions R_A = R_B = 50 kN / 2 = 25 kN
  2. 2. Joint A Equilibrium (Method of Joints)ΣFy = 0: R_A - F_rafter · sin(30.26°) = 0 ⇒ F_rafter = 25 / sin(30.26°) = 49.62 kN (Compression)
  3. 3. Bottom Chord Horizontal Tie ForceΣFx = 0: F_tie = F_rafter · cos(30.26°) = 49.62 · cos(30.26°) = 42.86 kN (Tension)

Member Internal Forces (kN)

Interactive visualization based on your current inputs

Force (kN)
0.012253750Support Reaction (Ra)Left Rafter (Compression)Right Rafter (Compression)Bottom Tie (Tension)Truss MemberForce (kN)

What Is the Truss Method of Joints Axial Force Calculator?

The Method of Joints is a fundamental method of static analysis used to determine internal axial forces in all members of an idealized pin-connected truss.

How Does the Truss Method of Joints Axial Force Calculator Work?

Treating each joint as a concurrent force system in static equilibrium, equations ΣFx = 0 and ΣFy = 0 are solved sequentially.

Truss Method of Joints Axial Force Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

\theta = \arctan\left(\frac{h}{L/2}\right), \quad R_A = R_B = \frac{P}{2}, \quad F_{rafter} = \frac{R_A}{\sin\theta} \text{ (C)}, \quad F_{tie} = \frac{R_A}{\tan\theta} \text{ (T)}

Slope angle theta is arctangent of height over half-span. Support reactions are half total load. Equilibrium at supports resolves rafter compression and bottom chord tension.

How to Use the Truss Method of Joints Axial Force Calculator

  1. Enter the overall truss span in meters.
  2. Specify the center apex ridge height.
  3. Supply the design downward vertical point load in kN.

Step-by-Step Example Calculation

12m Roof Truss with 50 kN Ridge Load

Input Values:

spanMeters:12.0
heightMeters:3.5
pointLoadApexKN:50.0
Worked Steps: With 30.26° roof pitch, each 25 kN support reaction creates 49.61 kN compression in rafters and 42.86 kN tension in the bottom tie.

Understanding Your Result

Rafter Axial Force: Compressive force carried by top diagonal members (C).

Bottom Chord Force: Tensile tie force holding the base together (T).

Support Reactions: Vertical reaction force at each end pedestal.

Slope Angle (θ): Roof slope pitch angle in degrees.

Factors That Affect the Result

  • Increasing truss height steepens angle θ, significantly reducing member forces and horizontal thrust.

When Should You Use This Calculator?

  • Timber and steel roof truss sizing, pedestrian bridge analysis, crane booms, and structural engineering education.

Assumptions & Limitations

  • Assumes idealized frictionless frictionless pin connections with loads applied exclusively at joints.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Exact static equilibrium solution for 2D statically determinate triad trusses.

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