Truss Analysis Simulator: Member Forces in Tension & Compression

simulator intermediate ~12 min
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Max chord force = 50 kN — 4-panel Pratt truss, 12 m span

A 12 m span Pratt truss with 3 m height and 50 kN center load develops maximum chord forces of 50 kN in tension (bottom) and compression (top) at midspan.

Formula

F_chord = M/H = PL/(4H) at midspan
F_diagonal = V/sin(θ) where θ = atan(H/d)
R_A = R_B = P(n-1)/(2n) for symmetric panel loads

The Power of Triangulation

A truss transforms bending into pure axial forces through geometric triangulation. Where a solid beam must resist bending across its entire cross-section, a truss concentrates material into discrete members that carry only tension or compression. This principle, understood since ancient Roman timber bridges, makes trusses extraordinarily efficient for spanning large distances — from highway bridges to stadium roofs spanning over 100 meters.

Method of Joints

At each pin joint of an ideal truss, the sum of all forces must equal zero. Starting from a support where the reaction is known, you can solve for two unknown member forces at each joint, progressing through the entire structure. This simulation computes all member forces for a Pratt truss and color-codes them: cyan for tension, red for compression. The thickness of each member scales with force magnitude, immediately revealing the load path through the structure.

Chord Forces & Height

The top and bottom chords of a truss act like the flanges of a deep beam — the top chord compresses while the bottom chord stretches in tension. Their forces are inversely proportional to the truss height: F = M/H. This relationship is why doubling truss depth halves the chord forces and roughly halves the required steel tonnage. Practical trusses balance structural efficiency against headroom constraints, typically targeting a height-to-span ratio between 1:8 and 1:12.

Diagonal Members & Buckling

Diagonal members carry shear forces as axial loads. In a Pratt truss, diagonals are oriented so they carry tension under gravity loading — a deliberate choice because tension members never buckle and can be made from slender rods or cables. Compression diagonals and the top chord require stockier sections to resist Euler buckling, making member orientation a critical design decision that affects both weight and cost.

FAQ

How do you analyze forces in a truss?

Truss analysis uses the method of joints or method of sections. At each joint, equilibrium equations (ΣFx=0, ΣFy=0) determine the axial force in each connected member. All members are assumed to carry only axial loads — no bending — because joints are modeled as frictionless pins.

What is the difference between a Pratt and Warren truss?

A Pratt truss has vertical members and diagonals that slope toward the center, placing diagonals in tension under gravity loads. A Warren truss uses only diagonals (no verticals) in an alternating pattern. Pratt trusses are generally preferred for steel because tension members can be lighter than compression members.

Why does truss height matter so much?

Chord forces are inversely proportional to truss height: F = M/H. Doubling the height halves the chord forces, allowing smaller, lighter members. However, taller trusses use more diagonal material and require more headroom. The optimal H/L ratio is typically 0.1 to 0.15.

How does a truss carry load without bending?

A truss converts bending into axial forces through triangulation. Each triangle is geometrically stable, so loads applied at joints are resisted purely by tension and compression in the members. This is far more efficient than solid beams because material is concentrated where forces flow.

Sources

Embed

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