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What kind of simplified structural system would a Leonardo bridge use?

I've tried approximating the system to a simple statically determined beam (see below) but our calculations did not give any realistic results. I believe it is due to a negligence of the potential strain in each beam. Maybe using a Spring Load Constant combined with nodes would help? A Leonardo bridge is a bridge constructed without any kind of binding, but just using uniform length pieces of Wood. It can be constructed in this manner:

My own approximation is rough but each of the connections cannot be considered nodes because none of the pieces are loose or movable.

P.S. It would greatly simplify my calculations if any answers would consider a statically determined system even if it is a simplification.

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    $\begingroup$ It should only be referred to as a "Leonardo" bridge. Signed, your local art historian. For those who care: "da Vinci," as with (Rembrandt) van Rjin, indicates the birthplace of a person and is not actually a name. $\endgroup$ – Carl Witthoft Jul 28 '16 at 12:11
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We will solve for n members with these assumptions.
members are L ft long by 2H, (H=L/20) thick and assuming the notch depth at H on the center to accommodate next member linkage.

Loads are applied uniformly spread vertically over the exposed top of the bridge at m. ton/ meter.
The structure as we add to members looks more and more like an arch.

The radius of which is deduced from similar triangles H/L = L/R
$R=L^2/h$

From here we apply as an approximation the arch formulas with one caveat the moment will be converted to compression and tension on the joints by this formula
$T=C=M/H$ and also shear converts to vertical joint loads.
There are many ways to solve a pin end support arch but an starter is to assume one support on rollers and solve then superimpose the lateral load needed to bring the roller end back in. I have some hand books if you need, but here is a link.
http://www.civilengineeringx.com/bdac/stresses-in-arches/

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