Truss Force Analysis Calculator (Method of Sections)
Find the top chord, bottom chord, and diagonal member forces in a parallel-chord truss using the method of sections.
🌉 What is the Method of Sections?
The method of sections is a technique for finding the internal force in specific members of a truss by slicing the truss with an imaginary vertical (or otherwise convenient) cut through no more than three members whose forces are unknown, then treating one resulting half as a free body and applying the three equations of static equilibrium (sum of horizontal forces, sum of vertical forces, and sum of moments about a point) to solve directly for those forces. This calculator applies the method to one specific, common textbook scenario: a parallel-chord truss of constant height h, cut through a single diagonal panel, with no applied load anywhere between the near support and the cut.
Engineers reach for the method of sections whenever they only need one or two member forces rather than the force in every member of the truss. It is the standard way to spot-check a bridge truss's top and bottom chord forces at midspan, to size a specific diagonal in a roof truss, or to verify a computer model's output for a single critical member without re-solving the entire structure by hand. Because it isolates exactly the members you cut through, it is almost always faster than working joint by joint from one end of the truss to the member you care about.
A common misconception is that the method of sections works for any arbitrary cut. It only works cleanly when the cut passes through three or fewer unknown members (or when extra equilibrium equations are available), because a standard free body only supplies three independent equations. It is also easy to forget that any applied load sitting between the support and the cut changes the shear carried across the section, which is why this calculator is explicit about assuming no such load exists in that region.
This calculator computes the diagonal angle and the top chord, bottom chord, and diagonal member forces directly from the support reaction, the cut location, the panel width, and the truss height, along with a labeled diagram of the cut panel so you can see exactly which members and dimensions the formulas refer to.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Standard Bridge Truss Panel
R = 100 kN, x = 4 m, d = 4 m, h = 3 m
Example 2 — Taller, Wider Panel
R = 150 kN, x = 6 m, d = 5 m, h = 4 m
Example 3 — Shorter Panel Near a Support
R = 80 kN, x = 3 m, d = 3 m, h = 2.5 m
❓ Frequently Asked Questions
🔗 Related Calculators
What is the method of sections in truss analysis?
The method of sections finds forces in specific truss members by cutting the truss with an imaginary section through no more than three unknown members, then applying the three equilibrium equations (sum Fx = 0, sum Fy = 0, sum M = 0) to the resulting free body to solve for those member forces directly, without analyzing every joint.
What is the formula for the top chord force in this calculator?
F_top = R times x divided by h, found by taking moments about the bottom-chord joint where the diagonal and bottom chord meet, which eliminates both of those unknowns and leaves only the top chord force, R is the support reaction, x is the distance from the support to that joint, and h is the truss height.
What is the formula for the bottom chord force in this calculator?
F_bottom = R times (x+d) divided by h, found by taking moments about the top-chord joint where the diagonal and top chord meet, which eliminates both of those unknowns and leaves only the bottom chord force, d is the horizontal panel width between the two cut joints.
How is the diagonal member force calculated?
F_diagonal = R divided by sin(theta), found from vertical force equilibrium of the cut section, since the diagonal is the only cut member with a vertical component able to balance the vertical reaction R. Theta is the diagonal's angle from horizontal, atan(h/d).
Does this calculator tell me if the diagonal is in tension or compression?
No. The diagonal force magnitude is always R/sin(theta), but whether that force is tension or compression depends on which way the diagonal leans relative to the support, information this simplified single-section tool does not track. Sketch the free body and check the diagonal's line of action against the reaction direction to determine the sign by hand.
What does this calculator assume about loading between the support and the cut?
It assumes no applied load acts anywhere between the near support and the section cut, so the vertical shear carried across that whole region equals the support reaction R unchanged. If a load falls in that span, R must be replaced with the actual local shear force before using these formulas.
Why does the diagonal force not depend on the cut position x?
Because with no load between the support and the cut, the shear force is constant (equal to R) in every panel of that region, and the diagonal force depends only on that shear and the panel geometry (through theta = atan(h/d)), not on how far the cut is from the support.
What is a parallel-chord truss?
A parallel-chord truss has its top and bottom chords running horizontally at a constant separation (height h) along the full span, such as a Warren or Pratt truss used in bridges and roof trusses, as opposed to trusses with sloped chords like a triangular roof truss.
Can this calculator be used for any truss shape?
No. It is scoped specifically to a parallel-chord truss (constant height h) cut through a single diagonal panel, with no load between the near support and the cut, the classic textbook method of sections case. Trusses with sloped chords, multiple loaded panels before the cut, or more than three unknown cut members need a different or more general analysis.
How do I find the panel width d and truss height h for my truss?
Panel width d is the horizontal spacing between adjacent joints along the top or bottom chord (usually constant for a repeating truss). Truss height h is the vertical distance between the top and bottom chords, also usually constant for a parallel-chord truss. Both are normally given directly in the truss geometry or drawing.