Pratt truss bridge: why diagonals take tension and what fails first

In 1844 Thomas and Caleb Pratt patented the truss behind every Pratt truss bridge, a layout that looks, at a glance, like a Howe truss in a mirror. The arrangement of members is almost the same. What changed is which way the diagonals lean, and that one decision swaps tension and compression across the whole bridge. In the Pratt, the diagonals pull.

Six panels, five loads and one diagonal per interior panel

The Pratt preset spans 12 m, stands 3 m high and has six panels, each 2 m wide. Top and bottom chords run parallel. Verticals join the two chords at every interior joint, and one diagonal crosses each of the interior panels, sloping down toward the centre. Two inclined end posts rise from the supports to the first top joints. That gives 21 members and 12 joints, and the truss is statically determinate: 21 + 3 = 24 = 2 × 12.

The load is 20 kN in total, applied as five equal loads of 4 kN on the interior bottom joints. Each support takes 10 kN.

Why the diagonals of a Pratt truss bridge pull

Imagine a vertical cut through the left half. The support pushes up with 10 kN, and the loads already passed take some of that away, so the shear in each panel falls from 10 kN at the support to 6 kN, 2 kN and then reverses. A diagonal sloping down toward the centre has to resist that shear by pulling, since pulling is how a diagonal in that direction transfers an upward force to the next joint. A diagonal sloping the other way would have to push.

This is the point of the layout. A steel member in tension fails by yielding, and nothing about its length makes it weaker. The long members, here the diagonals at 3.606 m, are put in tension, and the verticals, 3.0 m, take compression. Short members are the ones to leave in compression, since buckling gets worse quickly as length grows, as the tension and compression page shows.

Hangers, struts and a 3.6 m end post

Start with the diagonals. The two outer diagonals, H to C and L to E, pull with 7.2 kN; the inner ones, I to D and K to D, pull with 2.4 kN. None passes 5.4 percent of its yield capacity, because the 60 mm by 3 mm tube yields at 134.3 kN.

The verticals are not uniform. C to I and E to K push with 2.0 kN. The middle vertical, D to J, carries 0.0 kN under a symmetric load, and a moving load would wake it up. The two verticals nearest the supports, B to H and F to L, are in tension at 4.0 kN, the exception to the rule that Pratt verticals push. They hang the loaded joint below them: no diagonal lands on that joint from above, so the vertical holds it up.

Chords follow the bending. The top chord pushes with up to 12.0 kN in the middle, and the bottom chord pulls with up to 10.7 kN.

The governing member is the end post: 3.606 m long, pushing with 12.0 kN. The Euler load of that tube is 33.2 kN, so it is used 36.2 percent at the applied load. The failure load factor is 2.764, so the bridge fails at 55.3 kN. Every other member sits under 12 percent, which tells you where the steel is wasted. Upgrade only the two end posts to a 90 mm by 4 mm tube and the same bridge fails at 179.9 kN, at the top chord next, for 270 kg instead of 239 kg.

Steel, timber and the end-post experiment

The Pratt truss bridge suits steel, and above all a steel structure whose long members matter. The same arithmetic that makes the Pratt good with iron makes the Howe truss bridge good with timber, and the full comparison of truss bridge designs puts the two next to each other: with every member the same tube they fail at the same 55.3 kN, but give each the stronger end posts and the Pratt reaches 180 kN against 92 kN for the Howe.

For a first bridge the Warren truss bridge is simpler. The Pratt is the clearest example of why pulled members are the cheap members, since a tube in tension cannot buckle.

The Pratt preset in the truss bridge designer shows it: once the end posts are stronger, the member that fails at 179.9 kN is the top chord segment J to K, 2 m long and carrying 12.0 kN.