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Load capacity is difficult to quantify because it involves the geometry, type of use, point load, concentrated load, distributed load, shock load, lateral stability, deck plank thickness, arch spacing and footings. All these specification can be adjusted to suit.|
An example is choice of decking. Selecting 5/4 decking with an extra arch (for a shorter deck plank span), would be more efficient and likely use less total lumber than using 2x decking with one less arch. Dead load would be decreased and strength & stability would be increased. The deck usually weighs more than the entire supporting structure.
Generally I consider the load as being garden machinery on 4 tires, moving at lawn mower speeds.
These arch bridges are not "vehicular bridges" designed to be rammed by a loaded pickup, late for work, at 50mph. At lawnmower speed however, these bridges can carry surprising loads safely.
An 18" span model
A 3' span model
A brave Bride
The arch assembly is a very shallow, curved truss, permitting flexibility, without damage, under severe overload.
Load test 40'
2 40' arches, temporarily assembled. Asymetrical load, wheels over each arch, 2,500 lbs, 90% of safe load capacity.
Load test 20'
Overloaded 20' arches from 1x4s. 1,000 lbs per wheel. Note the distortion from the asymetrical load.
Overloaded arches from 1 1/2" dowels. The stainless steel cable fixing the arch feet is starting to stretch so I couldn't put a 5th or 6th body on without better "footings".
I consider a safe load any load that doesn't bend the deck more than 1/400 span. I've bent arches more than 1/40 span with no structural damage whatsoever, so there is a very large safety factor. Except under severe overload, all components are stressed in compression parallel to the wood grain. The few fasteners (bolts) suffer no stress and act merely as clamps to keep components in line. With a reasonable fit of parts, all stress is evenly distributed over the entire structure with no one critical point prone to failure.
Measuring deck deflection, and thereby safe load capacity for a particular bridge, is relatively easy - but only after everything is built.
If the wood makes a lot of creaking and loud cracking sounds, the deck bends noticably or tips sideways, reconsider your crossing. Wood gives a lot of warning.
Sudden failure should not be possible under any foreseeable circumstances.
Keep in mind that horizontal stress on the footings will be several times the vertical weight, especially under shock load.
For an approximate indication, physical tests show that a 2x4x30' arch or shorter, can safely support 1,000 lbs on 2 tires, per arch. A 2x6x40' arch can safely support 1,500 lbs on 2 tires, per arch, if all other requirements have been met.
This design is an arch that depends on the post strength of the components, not the beam strength. Beam strength of the components resists deformation of the arch under concentrated or point load. Distributed load would be almost totally dependent on the post strength of the components.
The actual load capacity also depends on the shape of the arch. An arch with a H/L of 1/6 could carry close to the full post strength of the components. A lower arch of 1/10 would suffer more horizontal stress from the vertical load but have more lateral stability, with all other things being equal.
If you have solid footings and a fair fit of parts, with a well-fastened deck (for lateral stability), a ton on 4 tires might be a safe max load on a 2-arch 2x4x30' bridge. To fit a 1 ton load on the bridge you'd want a deck width of at least 5~6 feet which would require another arch or two for a reasonable deck plank span, increasing your load capacity or safety factor even further.