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Truss Analysis Calculator

Analyze common roof trusses (Howe, Pratt, Warren, Fink, Scissors) using simplified method of joints. Get member forces, reactions, and deflection estimate.

Structural Analysis Structural engineers, steel fabricators, students Commercial Intent: HIGH

Engineering Formulas

Support Reactions

R = Wtotal / 2
Wtotal = (npanels — 1) × P + selfweight

R: Reaction at each support (kN)

W_total: Total vertical load (kN)

P: Load per joint (kN)

Chord Member Forces (Approx.)

Ftop ≈ Mmax / h (compression)
Fbottom ≈ Mmax / h (tension)
Mmax ≈ Wtotal × L / 4 (simply supported)

F_top: Max top chord force (kN)

M_max: Maximum bending moment (kNm)

h: Truss height (m)

Web Member Forces

Howe: Verticals in tension, diagonals in compression
Pratt: Verticals in compression, diagonals in tension
Warren: Alternating tension/compression in diagonals
Fink: Sub-divided panels with complex web pattern

V: Shear force at panel (kN)

θ: Diagonal angle from horizontal

Deflection Estimate

δ = (5 × w × L⁴) / (384 × E × I)
E = 200 GPa (steel)
I ≈ 0.0001 × L² × h (approximate)

δ: Maximum deflection (m)

w: Uniformly distributed load (kN/m)

E: Modulus of elasticity

I: Moment of inertia (m⁴)

Worked Example

Howe Truss — 12m Span, 2.5m Height

trussType: howetrussSpan: 12trussHeight: 2.5panelCount: 6loadPerJoint: 10includeSelfWeight: 1

Total Load

W = (6–1) × 10 + 0.5 × 12 = 50 + 6 = 56 kN

Reactions

Ra = Rb = 56 / 2 = 28 kN

Max Moment

M_max = 56 × 12 / 4 = 168 kNm

Chord Forces

F = 168 / 2.5 = 67.2 kN (compression top, tension bottom)

Web Forces

Howe: max web compression ≈ 56/6 × 1.2 = 11.2 kN, tension ≈ 56/6 = 9.3 kN

Members

3 × 6 + 1 = 19 members

Result: Top chord: 67.2 kN compression, Bottom chord: 67.2 kN tension, Reactions: 28 kN each, ~19 members

Engineering Notes

Top chord members are in compression and prone to buckling — check slenderness ratio.

Bottom chord members are in tension — use net section for bolted connections.

Longspan trusses (≥30m) may need camber to offset deflection.

For seismic areas, consider truss bracing for out-of-plane stability.

Joint eccentricity can cause secondary bending moments — minimize at design stage.

Assumptions

• All joints are pin-connected (no moment transfer)

• Loads are applied only at top chord panel points

• Self-weight is uniformly distributed and added to joint loads

• Truss is simply supported at both ends

• All members are axially loaded (no bending)

• Linear elastic behavior

Common Mistakes

✕ Assuming web members all have the same force (they vary by position)

✕ Not accounting for self-weight in total load

✕ Ignoring the difference between chord forces at midspan vs supports

✕ Using point load formulas instead of treating load distribution correctly

✕ Not checking slenderness of compression members

Frequently Asked Questions

What is the difference between Howe and Pratt trusses?

In a Howe truss, the diagonal web members slope toward the center and are in compression, while verticals are in tension. In a Pratt truss, diagonals are in tension and verticals are in compression.

Which truss type is most efficient?

Warren trusses (without verticals) are most efficient for uniform loads. Pratt trusses are efficient for combined loads. Fink trusses are common for residential roofs with long spans.

What is a typical span/height ratio for trusses?

Roof trusses: L/h = 4 to 6 (recommended minimum h = L/10). Bridge trusses: L/h = 8 to 12. Higher ratios mean shallower trusses with larger member forces.

How accurate is this simplified analysis?

This provides preliminary member force estimates. For detailed design, use frame analysis software considering member stiffness, joint rigidity (or pin assumptions), and load combinations per applicable codes.

What are the common design standards for trusses?

AISC 360 (USA), IS 800 (India), BS 5950 (UK), and Eurocode 3 (EN 1993) provide design provisions for steel trusses. Wood trusses follow NDS or Eurocode 5.

How is truss deflection calculated?

Exact deflection requires virtual work or matrix analysis. The simplified formula δ = 5wL⁴/(384EI) treats the truss as a beam with equivalent moment of inertia.