Pratt Truss Footbridge — Method of Sections Worked Example

By Michael Flynn, PE · water resources & dam safety engineer · Last updated Oct 21, 2026

A 60 ft steel Pratt truss carrying a walkway deck on its bottom chord, solved two ways. The method of sections finds the governing chord and diagonal forces in a few lines, and the stiffness solution confirms them and finds the member that actually governs: the end post, not the chord.

The structure

Truss	Pratt, 60 ft span, 6 panels at 10 ft, 8 ft deep; two trusses carry a 10 ft wide deck, so each takes a 5 ft tributary width
Loads (on the bottom chord)	Deck dead load 15 psf (assumed); pedestrian live load 90 psf (AASHTO Guide Specifications for the Design of Pedestrian Bridges)
Combination	1.2D + 1.6L (ASCE 7, what the calculator runs). See the AASHTO note in step 5.
Trial sections, F_y = 50 ksi	Chords A = 3.5 in², r = 1.2 in · Webs A = 2.0 in², r = 0.8 in

Template "Pratt": span 60, depth 8, 6 panels, spacing 5. Set TCDL 0, TCLL 0, BCDL 15, BCLL 90, and "TCLL is" to floor live. Member check: steel, LRFD, chords A 3.5 / r 1.2, webs A 2.0 / r 0.8.

Open the truss calculator →

Step 1 · Factored panel loads and reactions

Deck load on the bottom chord

w_u = (1.2 × 15 + 1.6 × 90) psf × 5 ft = 810 plf
Interior bottom joints: P_u = 810 × 10 = 8,100 lb; end joints 4,050 lb
R_u = 810 × 60 / 2 = 24,300 lb each end

Step 2 · Method of sections

End diagonal and midspan chord

Cut panel 1: V = R_u − 4,050 = 20,250 lb. The diagonal is 12.806 ft long; sinθ = 8 / 12.806 = 0.6247
End diagonal T = 20,250 / 0.6247 = 32,416 lb tension
Cut at midspan: M = 24,300 × 30 − 4,050 × 30 − 8,100 × (20 + 10) = 364,500 lb-ft
Top chord C = bottom chord T = M / d = 364,500 / 8 = 45,563 lb

That is the Pratt pattern: diagonals in tension, verticals in compression, and chord forces that grow toward midspan like the moment diagram.

Step 3 · Zero-force members

Spot them before you size them

Bottom chord end panels (1–2 and 6–7). At the support joint, only the bottom chord can resist horizontal force, and nothing pushes on it horizontally. Its force is zero.
Center vertical. At the top-center joint, two collinear top chords meet the vertical and no load is applied, so the vertical carries nothing.

They still matter: they brace the bottom chord and the top joint, and they carry force under unsymmetric live load.

Step 4 · AISC checks: the end post governs

Compression vertical at the support, 20,250 lb

KL/r = 96 / 0.8 = 120 → F_e = π²(29,000)/120² = 19.88 ksi; F_y/F_e = 2.52 > 2.25 → F_cr = 0.877F_e = 17.43 ksi
φP_n = 0.9 × 17.43 × 2.0 = 31.38 kip → 20.25 / 31.38 = 0.645
Top chord at midspan: KL/r = 100, F_cr = 24.07 ksi, φP_n = 75.81 kip → 45.56 / 75.81 = 0.601
End diagonal: φP_n = 0.9 × 50 × 2.0 = 90 kip → 32.42 / 90 = 0.360

The top-chord check assumes lateral bracing at every panel point. That's true for a through truss with overhead bracing, or a deck truss. In a pony (half-through) truss, the top chord has no top lateral bracing. Its out-of-plane buckling is restrained only by the U-frames formed by the verticals and floor beams, and the effective length is much longer than one panel. That needs a separate U-frame stability analysis.

Step 5 · If this is designed to AASHTO

Scale the ratios, don't reuse them

AASHTO Strength I for a pedestrian bridge: 1.25 DC + 1.75 PL = 1.25 × 15 + 1.75 × 90 = 176.25 psf
ASCE 7 used above: 1.2 × 15 + 1.6 × 90 = 162 psf → ratio 1.088
End post under AASHTO ≈ 0.645 × 1.088 = 0.70

AASHTO also uses different resistance factors for steel members (φ_c = 0.95 for compression). A trail bridge also needs the guide specification's vibration check and the AASHTO deflection limit. Use the ASCE 7 result as a sizing pass, not as the bridge design.

Step 6 · Deflection

Service loads, all members elastic

D + L: 0.534 in = L/1,348 · L only: 0.458 in = L/1,573

Truss deflection comes from the axial strain of every member (Δ = Σ F f L / AE). The light webs contribute more than their size suggests, so increasing the web areas is often the cheapest way to cut deflection.

Tools used in this example

Truss calculator (Pratt template, steel LRFD check), AISC LRFD design strength to cross-check one member, Euler buckling for the end post, and the truss coefficient card for a quick check of other depths.

Frequently asked questions

Which members of a Pratt truss are in tension?

Under gravity load, the diagonals of a Pratt truss slope down toward midspan and carry tension, the verticals carry compression, the top chord is in compression and the bottom chord in tension. A Howe truss reverses the diagonals, so its diagonals are in compression and its verticals in tension.

How do you find a truss chord force quickly?

Use the method of sections: cut through the panel, take moments about the joint where the other two cut members meet, and divide the bending moment by the truss depth. For a simply supported truss with uniform panel loads, the maximum chord force is roughly the beam moment wL²/8 divided by the depth.

What live load is used for pedestrian bridges?

The AASHTO Guide Specifications for the Design of Pedestrian Bridges use a pedestrian live load of 90 psf, combined with dead load in the AASHTO LRFD Strength I combination (1.25 DC + 1.75 PL), plus a maintenance-vehicle check where vehicles can get onto the bridge.